THE 
COAL  MINERS'  POGKETBOOK 


McGraw-Hill  BookCompany 


Electrical  World         The  Engineering  andMining  Journal 
Engineering  Record  Engineering  News 

Railway  Age  Gazette  American  Machinist 

Signal  Engineer  AraaicanEngneer 

Electric  Railway  Journal  Coal  Age 

Metallurgical  and  Chemical  Engineering  Power 


COAL  MINERS' 
POCKETBOOK 


FOEMEELY  THE 

COAL  AND  METAL  MINERS'  POCKETBOOK 


PRINCIPLES,  RULES, 
FORMULAS  AND  TABLES 


ELEVENTH  EDITION 
REVISED,  ENLARGED,  AND  ENTIRELY  RESET 


McGRAW-HILL  BOOK  COMPANY,  INC, 

239  WEST  39TH  STREET.     NEW  YORK 


LONDON:  HILL  PUBLISHING  CO.,  LTD. 

6  &  8  BOUVERIE  ST.,  E.  C. 

1916 


COPYRIGHT,  1916,  BY  THE 
MCGRAW-HILL  BOOK  COMPANY,  INC. 


COPYRIGHT,  1901,  1905,  BY  THE 
INTERNATIONAL  TEXTBOOK  COMPANY 


COPYRIGHT,  1890,  1893,  1900,  BY  THE 
COLLIERY  ENGINEER  COMPANY 


ENTERED  AT  STATIONERS'  HALL,  LONDON 


All  Rights  Reserved 


PREFACE  TO  ELEVENTH  EDITION 

Perhaps  the  most  important  change  in  the  present  edition 
of  this  book,  is  the  omission  of  matter  pertaining  strictly  to  ore 
mining,  in  order  that  the  space  formerly  occupied  by  it,  and  a 
large  amount  in  addition,  might  be  devoted  to  coal  mining. 
In  consequence  of  this,  the  publishers  have  deemed  it  wise  to 
change  the  title  from  "The  Coal  and  Metal  Miners'  Pocket- 
book,"  to  "  The  Coal  Miners'  Pocketbook."  It  is  believed  that 
the  pocketbook  will  still  prove  of  interest  and  value  to  all  men 
engaged ^  in  mining,  as  well  as  to  many  in  other  branches  of 
engineering,  but  it  seemed  no  longer  possible,  within  the  limits 
of  a  compact  handbook,  to  cover  both  fields  in  full  detail. 

The  present  edition  represents  a  thorough  revision.  Not 
only  have  material  changes  been  made  throughout  the  text,  but 
substantial  additions  to  many  sections,  which  bring  the  work  up 
to  date,  and,  it  is  hoped,  increase  its  usefulness. 

The  subjects  of  Weights  and  Measures  and  Mathematics 
have  been  entirely  rewritten  and  greatly  enlarged.  The  depart- 
ment on  Surveying  has  been  expanded  to  include  Leveling  with 
the  aneroid  barometer,  so  much  of  Railroad  Surveying  as  is 
necessary  at  mines,  and  Determination  of  the  Meridian,  both 
by  solar  and  pole-star  observations;  and  to  it  have  been  added 
some  practical  notes  on  Surveying,  as  ordinarily  practised  in 
flat  seams.  Under  the  heading  of  Mechanics,  Strength  of  Mate- 
rials, etc.,  will  be  found  very  complete  tables  of  specific  gravi- 
ties and  weights  of  various  substances  per  cubic  foot.  The  de- 
partment on  Concrete  Construction  is  entirely  new  and  complete 
and  is  of  timely  interest.  Hydrostatics  and  Hydraulics  have 
been  enlarged  by  the  addition  of  entirely  new  tables.  Pump 
Machinery  now  includes  centrifugal  pumps.  The  department 
on  Fuels  has  been  practically  rewritten  and  now  contains  the 
best  formulas  for  calculating  the  heating  values  of  coals  from 
their  proximate  and  ultimate  analyses,  as  well  as  very  complete 
tables  of  analyses  of  American  and  foreign  coals.  The  notes 
upon  Prospecting  include  the  newer  types  of  drilling  machinery. 
The  matter  on-Mine  Timbering  is  practically  new  and  includes 
notes  on  the  preservation  of  timber,  steel  timbers,  etc.  The 
subject  of  Flushing  Culm  has  been  brought  up  to  date  with 
numerous  examples  drawn  from  recent  practice.  The  sub- 
jects of  Explosives  and  Mining  Machines  have  been  rewritten 
on  the  lines  of  modern  practice.  Under  Hoisting  and  Haulage 
will  be  found  much  entirely  new  matter  on  gasoline  and  storage- 
battery  motors,  and  the  subject  of  Tracklaying  has  been  entirely 
rewritten.  The  subject  of  the  Treatment  of  Injured  Persons  is 
now  up  to  date,  and  the  Glossary  has  been  enlarged. 

Those  who  use  this  book  are  kindly  and  earnestly  requested 
to  advise  us  of  any  errors  or  omissions  they  may  note  and  to 
offer  suggestions  for  the  betterment  of  subsequent  editions. 

394012 


CONTENTS 

(For  detailed  Index,  see  back  of  volume.     See  also  Glossary  of  Mining  Terms 
page  1102.)  

WEIGHTS  AND  MEASURES 
Linear  Measure. — Surveyor's  Linear  Measure,  1;  Decimals  of  an  Inch  and 

Millimeters  for  Each  ^64  In.,  Table,  2;  Decimals  of  a  Foot  for  Each 

fa  In.,  Table,  4,  5. 

Measures  of  Surface. — Square  Measure,  3;  Surveyor's  Square  Measure,  3. 
Measures  of  Weight. — Troy,  4;  Apothecaries',  4;  Avoirdupois,  5. 
Measures   of   Volume. — Masonry,   6;   Brickwork,   6;   Shipping,   7;  Liquid 

(U.  S.),  7;  Dry  (U.  S.),  7;  Relation  Between  Volumes  and  Weights 

of  Water,  U.  S.  Liquid  Measure,  8;  Equivalent  Weights  and  Volumes 

of  Water,  8. 
Angular,  or  Circular,  Measure. — Laying  off  Right  Angles,  9;  Ratio  of  Sides 

of  Right- Angled  Triangle,  Table,  9;  Laying  off  an  Angle  With  a  Tape, 

Measures  of  Time. — Longitude  and  Time,  10. 

The  Metric  System. — Metric  Measures  of  Length,  11;  Of  Surface,  11;  Of 

Weight,  12;  Of  Volume,  12;  Of  Capacity,  12;  Equivalents  of  Volume, 

Weight  of  Water,  and  Capacity,  12. 
Conversion  Factors. — Metric  to  United  States,  13;  United  States  to  Metric, 

14. 

Weights  and  Measures  of  Great  Britain  and  Colonies. — Imperial  Measure, 
Both  Liquid  and  Dry,  15. 

Money. — United  States  Currency,  16;  Standard  United  States  Coins,  16: 
Currency  of  Great  Britain,  16;  Foreign  Monetary  Systems  and 
Equivalents  in  United  States  Gold,  17;  Values  of  Foreign  Coins,  18. 

MATHEMATICS 

Arithmetic. — Mathematical  and  Other  Commonly  Used  Signs  and  Abbrevia- 
tions, 18,  19;  Common  Fractions,  19;  Decimals,  20;  Formulas,  20; 
Proportion,  or  Cause  and  Effect,  21;  Percentage,  22;  Interest,  23; 
Trade  Discount,  23;  Reciprocals,  23;  Arithmetical  Progression,  24; 
Geometrical  Progression,  25;  Involution,  25;  First  Nine  Powers  of 
First  Nine  Numbers,  Table,  26;  Evolution,  26;  To  Find  the  Square 
Root  of  a  Number,  26;  To  Find  the  Cube  Root  of  a  Number,  27: 
Finding  the  Fourth  and  the  Fifth  Root  of  a  Number,  28;  Table  of 
Fifth  Powers,  28.;  Simple  Method  of  Extracting  Roots,  29. 

Logarithms. — Exponents,  29;  Rule  for  Characteristics,  30;  Finding  the  Loga- 
rithm of  a  Number,  30;  To  Find  a  Number  Whose  Logarithm  is 
Given,  31;  Multiplication  by  Logarithms,  32;  Division  by  Logarithms, 
33;  Involution  by  Logarithms,  34;  Evolution  by  Logarithms,  34; 
Solution  of  Equations  by  Logarithms,  36. 

Geometry. — Principles,  36;  Problems  in  Geometrical  Construction,  38-43. 

Mensuration  of  Surfaces. — Triangles,  43;  Parallelograms,  44;  Trapezoids, 
44;  Trapeziums,  45;  Polygons,  45;  Names  and  Relations  of  Regular 
Polygons,  Table,  46;  Circles,  48;  Rings,  49;  Sectors,  49;  Circular 
Segments,  49;  Ellipse,  50. 

Mensuration  of  Solids. — Values  Used  in  Formulas,  50;  Prismoid  and  Pris- 
moidal  Formula,  50;  Regular  Polyhedrons,  50;  Regular  Polyhedrons 
Whose  Edges  are  Unity,  51;  The  Sphere,  51;  Spherical  Segments,  52; 
Spherical  Zones,  52;  Cylindrical  Rings,  52;  Parallelepipeds,  52 
Cylinders,  53;  The  Pyramid,  53;  The  Wedge,  53;  The  Cone,  53. 


viii  CONTENTS 

Plane  Trigonometry. — Definitions,  54;  Fundamental  Relations,  55;  Signs  of 
Trigonometric  Functions,  55;  Functions  of  Angles  Between  90°  and 
180°,  55;  Functions  of  90°+ A,  55;  Functions  of  180° -A  and  of 
180°  +  A,  55;  Functions  of  (A  +  B)  and  of  (A-B),  56;  Func^ns 
of  2A  and  of  \iA.,  56;  Sums  and  Differences  of  Functions,  56;  Solution 
of  Right- Angled  Triangles,  56;  Relations  Between  Angles  and  Sides  of 
Right-Angled  Triangles,  57;  Solution  of  Oblique-Angled  Triangles, 
57;  Practical  Examples,  58. 

SURVEYING 

The  Compass. — General  Description,  60;  Compass  Adjustments,  60;  Using 
the  Compass,  61;  Magnetic  Variation,  61;  Reading  the  Vernier,  62; 
Field  Notes  for  an  Outside  Compass  Survey,  62. 

The  Transit. — General  Description,  62;  Transit  Verniers,  63;  Transit  Tele- 
scope, 64;  Transit  Adjustments,  64. 

Chain,  Steel  Tape,  and  Pins. — 65. 

Transit  Surveying. — Reading  Angles,  67;  Making  a  Survey  With  a  Transit, 
67;  Meridians,  or  Base  Lines,  67;  Monuments,  68;  Outside  Surveys, 
68;  Preliminary  Work,  68;  Angular  Measurements,  69;  Distance 
Measurements,  70;  Locating  Corners,  Etc.,  70;  Keeping  Notes,  71; 
Transit  Notes,  71;  Closing  Surveys,  72. 

Leveling. — Description  of  Instruments,  73;  Level  Adjustments,  73:  Using 
the  Level,  74;  Field  Work,  75;  Level  Notes,  75;  Proof  of  Calculations, 
76;  Trigonometric  Leveling,  76. 

Connecting  Outside  and  Inside  Work  Through  Shafts  and  Slopes. — Survey- 
ing Shafts,  77;  The  T-Square  Method,  81;  Check  Methods,  81;  Sur- 
veying Slopes  or  Inclined  Shafts,  82;  Bent  Plumb-Line  Method,  82; 
Method  by  a  Single  Wire  in  the  Slope,  82. 

Underground,  or  Mine,  Surveying. — Introduction,  83;  Flat  Work,  83; 
Stations,  84;  Sighting,  85;  Centers,  86;  Placing  Stations  on  Line,  86; 
Placing  Sights,  87;  Surveying  and  Note  Keeping,  88;  Level  Notes, 
90;  Pitching  Work,  90;  Stations,  90;  Surveying  Methods,  91;  Locating 
Pillars  for  Surface  Support,  92;  Mine  Corps,  92;  Care  of  Instruments, 
92. 

Traversing  and  Mapping. — Traversing,  93;  Traversed  Survey  Notes,  Table, 
94;  Errors  in  Closure,  94;  Balancing  Surveys,  95;  Locating  Special 
Work,  95;  Mapping,  95;  Laying  Off  a  Map,  95;  Mapping  the  Field 
Notes,  97;  Coloring  a  Map,  98. 

Determination  of  Meridian. — Latitude  and  Longitude,  99;  Celestial  Sphere, 
99;  Reference  Circles,  99;  Time,  100;  Civil  Time  and  Astronomical 
Time,  100;  Longitude  and  Time,  101;  Relation  Between  Time  and 
Longitude,  101;  Standard  Time,  101;  To  Change  Standard  Time  Into 
Local  Time  and  Vice  Versa,  101;  Determination  by  Observing  Polaris 
at  Culmination,  101;  Field  Work,  101;  Local  Mean  Astronomical 
Time  of  Upper  Culmination  of  Polaris,  Table,  102;  Time  of  Culmina- 
tion of  Polaris,  103;  Determination  by  Observing  Polaris  at  Elonga- 
tion, 103;  Making  the  Observation  and  Marking  the  Meridian,  103; 
Azimuths  of  Polaris  at  Elongation,  Table,  104;  Determination  by 
Solar  Observation,  105;  Formula  for  Azimuth  of  the  Sun,  105;  Values 
of  5  and  <f>,  105;  Determination  of  Latitude,  and  Corrections  for  Alti- 
tude, 105;  Approximate  Determination  of  Latitude  from  Polaris,  105; 
Latitude  by  Solar  Observation,  106;  Corrections  for  Altitude,  106; 
Sun's  Parallax  in  Altitude  to  be  Applied  to  All  Measured  Altitudes 
of  the  Sun,  Table,  106;  Corrections  for  Observation  of  the  Sun  for 
Azimuth,  106;  Mean  Refraction  to  be  Applied  to  All  Measured  Alti- 
tudes, Table,  107. 

Railroad  Surveying. — Definitions  of  Circular  Curves,  109;  Geometry  of  Cir- 
cular Curves,  109;  Elements  and  Methods  of  Laying  Out  a  Circular 
Curve,  110;  Relation  Between  Radius  and  Deflection  Angle,  110; 
Tangent  Distance,  110;  Laying  Out  a  Curve  With  a  Transit,  110; 
Table  of  Radii  and  Deflections,  111;  Tangent  and  Chord  Deflec- 
tions, 112;  Special  Values  of  Chord  and  Tangent  Deflection,  113; 
Application  of  Chord  and  Tangent  Deflection,  113;  Middle  Ordinate, 
113;  To  Determine  Degree  of  Curve  from  Middle  Ordinate,  113; 


CONTENTS  ix 

Rules  for  Measuring  the  Radius  of  a  Curve,  114;  Other  Ordinates 
114;  Field  Notes  for  Curves,  115;  Earthwork,  115;  Cuts  and  Fills 
115;  Slope  Ratio,  115;  Width  of  Excavations  and  Embankments,  116- 
Grade  Profile,  116;  Slope  Stakes,  117;  Form  of  Notes  in  Cross-Section 
Work,  118;  Railroad  Location,  119;  Preliminary  Estimate,  119;  Loca- 
tion, 120;  Curvature,  120;  Compensation  for  Curvature,  120;  Final 
Grade  Lines,  121;  Vertical  Curves,  1 22j  Vertical  Curve  at  a  Spur,  122 : 
Vertical  Curve  at  a  Sag,  124;  Curved  Track,  124;  Curving  Rails,  124; 
Middle  Ordinates  for  Curving  Rails,  Table,  125;  Turnouts,  125; 
Switches,  125;  Frogs  and  Guard-Rails,  126;  Frog  Angle  and  Frog 
Number,  126;  Guard-Rails,  127;  Radius  and  Lead  of  a  Turnout  for 
Stub  Switches,  127;  Dimensi9nsof  Stub-Switch  Turnouts,  Table,  127; 
Turnout  Dimensions  for  Point  Switches,  128;  Dimensions  of  Point- 
Switch  Turnouts,  Table,  128;  Turnouts  From  the  Outer  Side  of  a 
Curved  Track,  129;  Turnout  From  the  Inner  Side  of  a  Curved  Track, 
130;  Connecting  Curves,  130;  Cross-Overs,  130;  Cross-Over  Between 
Two  Parallel  Straight  Tracks,  130;  Another  Form,  131;  Laying  Out 
Turnouts,  131;  To  Lay  Out  a  Stub  Switch,  131;  To  Lay  Out  a  Point 
Switch,  132;  Switch  Timbers,  133;  Practical  Method  of  Laying  Out 
Sharp  Curves  in  a  Mine,  133. 

Stadia  Surveying. — Definition,  134;  Reduction  of  Inclined  Sights,  135;  Use 
of  Stadia,  136;  Stadia  Reduction  Tables,  137-139. 

Barometric  Leveling. — General,  140;  Barometric  Formulas,  141;  Barometric 
Elevations,  Table,  142;  Corrections  for  Temperature  and  Humidity, 
Table,  143;  Use  of  Barometer,  143;  Care  of  the  Barometer,  144. 

Practical  Problems  in  Surveying. — 144-148. 

MECHANICS 

Elements  of  Mechanics. — General  Law,  149;  Levers,  149;  Wheel  and  Axle 
150;  Inclined  Plane,  151;  To  Find  Weight  Required  to  Balance  Any 
Weight  on  Any  Inclined  Plane,  151;  Screw,  151;  Wedge,  151;  Pulley, 
152;  Combinations  of  Pulleys,  152;  Differential  Pulley,  152. 

Falling  Bodies. — 153. 

Work.— 153. 

Composition  and  Resolution  of  Forces. — Parallelogram  of  Forces,  154;  Reso- 
lution of  Forces,  154. 

Moments  of  Forces. — 154. 

Center  of  Gravity. — Definitions,  155;  Of  Solids,  156. 

Moment  of  Inertia.— Table,  157;  Principles,  158. 

Radius  of  Gyration. — 158. 

Section  ^odulus  and  Moment  of  Resistance. — 159. 

Friction. — Coefficient  of  Friction,  159;  Angle  of  Friction,  160;  Angle  of 
Repose,  160;  Coefficients  of  Friction  and  Angles  of  Repose  for 
Masonry  Materials,  Table,  160;  Rolling  Friction,  160;  Coefficients 
of  Friction,  Angles  of  Repose,  and  Weights  of  Earth,  Table,  161; 
Coefficients  and  Angles  of  Friction  for  Miscellaneous  Materials, 
Table,  161;  Rolling  Friction  for  Different  Roadway  Surfaces,  Table, 
162;  Coefficients  of  Friction  in  Axles,  Table,  152;  Frictional  Resist- 
ance of  Shafting,  162;  Friction  of  Mine  Cars,  163;  Summary  of 
Friction  Tests  on  Old-Style  Mine-Car  Wheels,  Table,  164}  On 
Self-Oiling  Mine-Car  Wheels,  Table,  165;  Ball  and  Roller  Bearings, 
166;  Lubrication,  166;  Lubricant  Tests,  168;  Best  Lubricants  for 
Different  Purposes  (Thurston),  169. 

STRENGTH  OF  MATERIALS 

Definitions.— 169;  Average  Ultimate  Strengths  of  Metals,  in  Pounds  per 

Square  Inch     Table,    170;  Of   Woods,   in   Pounds  per   Square   Inch, 

Table,  171. 
Simple,    or   Direct    Stress. — Formula    for    Simple    Stress,    172;  Important 

Applications  of  Formulas  for  Direct  Stress,  172;  Shearing  and  Bear- 

,-g  Values  of  Rivets,  in  Pounds,  Table,  173. 


x  .         CONTENTS 

Beams. — Reactions,  175;  External  Shear  and  Bending  Moment,  175;  Design- 
ing of  Beams,  176-  Formulas  for  Maximum  Shear  and  Bending  Mo- 
ments of  Beams,  Table,  177;  Stiffness,  178;  Formulas  for  Deflection 
of  Beams,  Table,  179. 

Columns. — Values  of  Ki  (Rankine's  Formula),  Table,  180;  Constants  for 
the  Straight-Line  and  Euler's  Formulas,  Table,  180;  Safe  Loads  for 
Hollow,  Cylindrical,  Cast-Iron  Columns,  Table,  181;  Euler's  For- 
mula, 182;  Formula  for  Wooden  Columns,  182. 

Combined  Stresses. — Bending  Combined  With  Compression  or  Tension, 
182;  Strength  of  Hemp  and  Manila  Ropes  and  of  Chains,  183;  Ulti- 
mate Resistance  and  Proof  Tests  of  Chain  Cables,  Table,  183. 

Practical  Problems  in  the  Strength  of  Beams  and  Props. — 184;  Table  of 
Constants  for  Seasoned  Timber,  184;  Crushing  Loads  of  Well- 
Seasoned  American  Woods,  Table,  185;  Safe  Loads  Uniformly 
Distributed  for  Standard  and  Special  I-Beams,  Table,  186;  Iron  and 
Steel  Beams,  187. 

CONCRETE 

Cementing  Materials. — Definitions,  187;  Limes,  188;  Cements,  188; 
Properties  of  Cements,  188;  Average  Weights  of  Hydraulic  Cements, 
189;  Sand  and  Its  Mixtures,  189;  Properties  of  Sand,  190;  Prepara- 
tion of  Sand,  191 ;  Lime  and  Cement  Mortars,  191 ;  Materials 
Required  per  Cubic  Yard  of  Mortar,  Table,  192;  Properties  and  Uses 
of  Cement  Mortars,  193;  Tensile  Strength  of  Cement  Mortars, 
Table,  193;  Retempering  of  Mortar,  194;  Laying  Mortar  in  Freezing 
Weather,  194;  Shrinkage  of  Mortars,  194;  Grouting,  194. 

Cement  Testing.— Field  Inspection  and  Sampling,  195;  Sampling,  195; 
Purpose  and  Classification  of  Tests,  195:  Primary  Tests,  196;  Tests 
for  Soundness,  196;  For  Tensile  Strength,  198:  Percentage  of  Water 
for  Standard  Sand  Mortar,  Table,  199;  Sand  for  Mortar  Tests,  199; 
Briquets,  200;  Testing  Machines,  200:  Results  of  Tensile-Strength 
Tests,  201;  Tensile  Strength  of  Cement  Briquets,  201;  Secondary  Tests, 
202;  Tests  for  Time  of  Setting,  202;  For  Fineness,  203;  For  Specific 
Gravity,  203;  Tests  of  Natural  and  Slag  Cements,  204. 

Cement  Specifications. — Specifications  for  Portland  Cement,  204;  Require- 
ments for  High-Grade  Cements,  Table,  205. 

Plain  Concrete.— Definitions  and  Terms,  206;  Aggregates  Other  Than  Sand, 
206;  Size  of  Aggregates,  206;  Selection  of  Aggregates,  207;  Propor- 
tioning of-  Ingredients,  207;  Effect  on  Strength  and  Imperviousness, 
207;  Proportioning  by  Weights,  207;  Compressive  Strength  of  Con- 
'  crete  Made  of  Different-Sized  Stones,  Table,  208;  Usual  Proportions 
of  Materials,  208;  Water  for  Concrete,  209;  Destructive  Agencies,  209; 
Effect  of  Fire  on  Concrete,  210;  Effect  of  Mine  Water,  210;  Expan- 
si9n  and  Contraction,  211;  Effect  of  Thermal  Changes,  211;  Effect  of 
Vibration,  211;  Working  Stresses  and  Strength  Values,  211;  Con- 
crete Mixtures,  211;  Methods  of  Measuring  Ingredients,  211;  Aver- 
age Ultimate  Crushing  Strength  of  Concrete,  Table,  212;  Fuller's 
Rule  for  Quantities,  212;  Working  of  Concrete,  212;  Mixing,  212; 
Retempering,  213;  Concreting  at  High  Temperatures,  213;  In 
Freezing  Weather,  213;  Joining  of  Old  Concrete  With  New,  213. 

Elements  of  Steel  Reinforcement. — Principles  of  Construction,  214;  Parts 
of  Steel  Reinforcement,  214;  Members  to  Resist  Lines  of  Failure,  215; 
Areas  and  Weights  of  Square  and  Round  Bars,  Table,  216;  Rein- 
f9rcing  Materials,  217;  Plain  Bar  Iron,  217;  Bars  of  Special  Construc- 
tion, 217;  Square-Twisted  Bars,  217;  Corrugated  Bar,  217;  Kahn 
Trussed  Bar,  218;  Expanded  Metal,  218;  Woven  Wire,  218;  Floor 
Systems,  218. 

Form  Work. — Construction  and  Finish,  220;  Forms  for  Floor  Systems,  220; 
Common  Types  of  Form  Work,  220;  Forms  Constructed  of  Plank, 
221;  Wall  Forms  With  Wire  Ties,  221 ;  Wall-Form  Construction 
With  Clamp  Bolts,  222;  Clamping  Devices  and  Plank  Holders  for 
Wall  Forms,  223 ;  Braces  for  Wall  Forms,  223. 

Concrete  Mixers.— 223. 


CONTENTS  xi 

Concrete  Structures. — Tank  Tower  of  Reinforced  Concrete,  223;  Rein- 
forced-Concrete  Retaining  Walls,  226;  High  Retaining  Walls,  226; 
Conduits,  226;  Coal  Breakers  in  Reinforced  Concrete,  227;  Con- 
crete Coal  Pockets,  229;  Concrete  Shaft  Lining,  230-233. 

MASONRY 

Materials  of  Construction. — Stone,  234;  Strength  of  Stone,  234;  Crushing 
Strength  and  Modulus  of  Rupture  of  Building  Stone,  234;  Minimum 
Safe-Bearing  Values  of  Masonry  Materials,  234;  Ultimate  Unit 
Crushing  Strength  of  Various  Stones  and  Stone  Masonry  Piers,  Table, 
235;  Of  Brick  Masonry  Piers,  Table,  235;  Absorptive  Power  of 
Stone,  236;  Durability  of  Stone,  236;  Brick,  236;  Size  and  Weight, 
236;  Weight  and  Strength,  236;  Requisites  for  Good  Brick,  236. 

WIRE  ROPES 

General  Description. — Wire- Rope  Materials,  237;  Construction  of  Wire 
Ropes,  238;  Lay  of  Ropes,  238. 

Hoisting  Ropes. — Round  Ropes,  239;  Non-Spinning  Ropes,  240;  Flattened- 
Strand  Ropes,  240;  Scale  Ropes,  240;  Flat  Ropes,  241;  Taper 
Ropes,  241. 

Haulage  Ropes. — 6X7  Ropes,  241;  Flattened-Strand  Ropes,  242;  Scale 
Ropes,  242. 

Ropes  for  Miscellaneous  Purposes. — For  Cableways,  242;  For  Suspension 
Bridges,  213;  Derrick  Ropes,  243;  Hawsers,  243. 

Rope  Drums  and  Fastenings. — Fastening  Rope  to  Drum,  244;  Rope  Sockets, 
244. 

Wire-Rope  Tables. — Sizes  and  Strengths  of  Standard  Hoisting  Ropes,  246; 
Of  Patent,  Flattened-Strand  Hoisting  Ropes,  247;  Of  Flat  Hoisting 
Ropes,  248;  Of  Standard  6X7  Haulage  Ropes,  248;  Galvanized 
Steel  Cables  for  Suspension  Bridges,  248;  Sizes  and  Strengths  of 
Patent,  Flattened-Strand  Haulage  Ropes,  249;  Cast-Steel  Locked- 
Wire  Cable,  249;  Tramway  or  Smooth-Coil  Cable,  249;  Galvanized 
Iron  and  Steel  Running  Rope,  250;  Galvanized  Steel  Hawsers,  250; 
Galvanized  Steel  Mooring  Lines,  250. 

Wire-Rope  Calculations.— Working  Load,  251;  Proper  Working  Load,  253; 
Starting  Stress  on  Rope,  Table,  253;  On  Hoisting  Rope,  254;  Stress 
of  Rope  on  Planes,  254;  On  Inclined  Planes,  254;  Relative  Effect 
of  Various  Sized  Sheaves  or  Drums  on  Life  of  Wire  Ropes,  254; 
Cast-Steel  Ropes  for  Inclines,  Table,  254;  Cast-Steel  Hoisting  Ropes, 
Table,  255;  Iron  Hoisting  Ropes,  Table,  255. 

Care  of  Wire  Ropes.— Ordinary  Method  of  Splicing,  255;  Rapid  Method, 
256;  Wear  of  Wire  Ropes,  257;  Inspection,  257;  Lubrication,  257; 
General  Precautions,  258. 

Cableways  and  Tramways. — Cableways,  258. 

Wire-Rope  Tramways.— Single  Tramways,  260;  Double,  261. 

Glossary  of  Rope  Terms. — 262. 

POWER  TRANSMISSION 

Transmission  by  Wire  Ropes. — General,  264;  Value  of  Coefficients,  Table, 
265;  Minimum  Diameters  of  Sheaves,  Table,  266;  Sheaves,  266; 
Power  Transmitted.  266;  Table  of  Constants  for  Ropes  on  Different 
Materials  267'  Horsepower  That  May  Be  Transmitted  by  a  Steel 
Rope  Making  a  Single  Lap  on  Wood-Filled  Sheaves,  Table,  267. 

Transmission  by  Hemp  Rope.— General,  268;  Horsepower  of  Manila 
Ropes,  Table,  269. 

Line  Shafting.— Constants,  Table,  270;  Maximum  Distance  Between  Bear- 
ings, Table,  270;  Horsepower  Shafting  Will  Transmit,  Table,  271. 

Belt  Pulleys.— Solid  and  Split  Pulleys,  271;  Wooden  Pulleys,  272;  Driving 
and  Driven  Pulleys,  272;  Diameter  and  Speed  of  Driver,  272;  O 
Driven,  272. 


xii  CONTENTS 

Belting.— Sag  of  Belts,  273;  Speed,  273;  Horsepower,  273;  Allowable 
Effective  Pull,  Table,  174;  Lacing,  274;  Care  and  Use,  274;  Flapping, 
275. 

SPECIFIC  GRAVITY,  WEIGHT,  AND  OTHER  PROPERTIES  OF 

MATERIALS 
Definitions. — 275. 

Specific  Gravity  of  Common  Substances. — Of  Minerals  and  Earths,  276; 
Of    Metals,   277;  Of  Liquids,   277;  Of   Gases   and   Vapors,   277;  Of 
"  Dry  Woods,  278;  Of  Miscellaneous  Substances,  278. 

Average  Weight  of  Various  Substances. — Weight  of  1  Cu.  Ft.  of  Various 
Metals,  278;  Of  Various  Woods,  When  Dry,  279;  Of  Philippine 
Woods,  When  Dry,  281;  Of  Australian  Woods,  When  Dry,  281;  Of 
Indian  Woods,  282;  Of  American  Timbers,  283;  Of  1  Sq.  Ft.  of 
Building  Materials,  283;  Of  1  Cu.  Ft.  of  Building  Materials,  284; 
of  Miscellaneous  Materials,  284-285. 

Properties  of  Coal. — Specific  Gravity  of  American  Coals,  286:  Weights  and 
Measurements  of  Coal,  287;  Average  Weight  and  Bulk  of  American 
Coals,  288;  Specific  Gravities  of  Various  Coals,  288;  Weight  of  Sus- 
quehanna  Coal  Co.'s  White  Ash  Anthracite,  288;  Contents  of  Hori- 
zontal Coal  Seams,  289;  Sizes  of  Prepared  Anthracite,  289;  Cubic 
Feet  in  1  T.  of  Anthracite  Broken  in  Trade  Sizes,  290;  Weights  of 
English  and  French  Coals,  290. 

Wire  and  Sheat-Metal  Gauges.— Table,  291;  Standard  Decimal  Gauge,  292. 

Miscellaneous  Tables. — Weight  of  Wrought-Iron  Bolt  Heads,  Nuts,  and 
Washers,  292;  Of  Sheets  and  Plates  of  Steel,  Wrought  Iron,  Copper, 
and  Brass,  293;  Of  Cast-Iron  Pipe  per  Ft., in  Pounds,  294;  Contents 
of  Cylinders  or  Pipes  for  1  Ft.  in  Length,  295:  Standard  Dimensions 
of  Wrought-Iron  Welded  Pipes,  296;  Strength  of  Metals  per  Square 
Inch,  296;  Standard  and  Extra-Gauge  Steel  Boiler  Tubes,  297; 
Standard  Lap-Welded  Charcoal-Iron  Boiler  Tubes,  297;  Weight  of 
Wrought  Iron,  298;  Diameter  and  Number  of  Wood  Screws.  298; 
Spikes  and  Nails,  299;  Weight  of  100  Bolts  With  Square  Heads  and 
Nuts,  299;  Proportions  of  the  United  States  Standard  Screw  Threads, 
Nuts,  and  Bolt  Heads,  300;  Weight  of  1  Lin.  Ft.  of  Flat  Wrought 
Iron,  301. 

Timber  and  Board  Measure. — Timber  Measure,  301;  Table  of  Quarter 
Girths,  302;  Board  Measure,  302;  Table  of  Board  Feet,  302. 

HYDROSTATICS 

General. — Equilibrium  of  Liquids,  303;  Pressure  of  Liquids  on  Surfaces,  303; 
To  Find  Pressure  Exerted  by  Quiet  Water  Against  Side  of  Gangway  or 
Heading,  304;  Pressure  Against  Dams,  Etc.,  304;  Distribution  of 
Pressure,  304;  Transmission  of  Pressure  Through  Water,  305;  To 
Find  Pressure  on  Plane  Surface  at  Any  Given  Depth  of  Water,  305; 
Pressure  at  Different  Vertical  Depths,  Table,  305;  Pressure  of  Water 
in  Pipes,  306;  Thickness  of  Pipe  for  Different  Heads  and  Pressures, 
306;  Wooden  Pipe,  306;  Standard  Sizes  of  Wood  Pipe,  307;  Compres- 
sibility of  Liquids,  307. 

HYDRAULICS 

Definitions. — To  Find  Theoretical  Velocity  of  Jet  of  Water,  307;  To  Find 
Theoretical  Quantity  of  Water  Discharged  in  Given  Time,  308; 
Flow  of  Water  Through  Orifices,  308;  Coefficient  of  Contraction,  of 
Velocity,  of  Discharge,  308;  Suppression  of  Contraction,  308. 

Gauging  Water.— Miners'  Inch,  309;  Duty  of  Miners'  Inch,  Table,  309; 
Duty  or  Work  Performed  by  a  Miners'  Inch  of  Water,  310;  Sluice 
Head,  310;  Gauging  by  V  Notch,  311;  Discharge  of  Water  Through 
a  Right-Angled  V  Notch,  Table,  311;  Gauging  by  Weirs,  312; 
Coefficient  of  Discharge  for  Weirs  with  End  Contractions,  Table,  313; 
Without  End  Contractions,  Table,  313;  Discharge  per  Minute  for 
Each  Inch  in  Length  of  Weir  for  Depths  From  1-8  In.  to  25  In.,  314. 

Conversion  Factors. — 314. 


CONTENTS  xiii 

Flow  of  Water  in  Open  Channels. — Ditches,  315;  Safe  Bottom  Velocity,  315- 
Safe  Bottom  and  Mean  Velocities  of  Streams,  Table,  315;  Resistance* 
of  Soils  to  Erosion  by  Water,  316;  Carrying  Capacity  of  Ditches,  316  ; 
Grade,  316;  Influence  of  Depth  on  Ditch,  316;  Measuring  the  Flow 
of  Water  in  Channels,  317;  Coefficient  of  Roughness  Under  Various 
Conditions,  317;  Flow  in  Brooks  and  Rivers,  317. 

Flumes. — Grade  and  Form,  318;  Connection  With  Ditches,  319;  Trestles 
319;  Curves,  319;  Waste  Gates,  319;  Flow  of  Water  Through 
Flumes,  319. 

Tunnels. — 319. 

Flow  Through  Pipes. — Hydraulic  Gradient,  320;  Flow  in  Pipes,  320; 
Eytelwein's  Formula  for  Delivery  of  Water  in  Pipes,  321;  Hawksley's 
Formula,  321 ;  Neville's  General  Formula,  321 ;  Comparison  of 
Formulas,  321;  Value  of  C  in  Darcy's  Formula,  322;  Loss  of  Head  in 
Pipe  by  Friction,  322;  Friction  of  Knees  and  Bends,  323;  Relative 
Quantities  of  Water  Delivered  in  24  Hours,  in  1  Hour,  and  in  1  Minute, 
Table,  323;  Actual  Amount,  or  80%  of  the  Theoretical  Flow,  in 
Pipes  From  1  In.  to  30  In.  Diameter,  Table,  324;  Loss  of  Head  by 
Friction,  Table,  325-326. 

Reservoirs. — 327. 
Mine  Dams. — 327. 

Outside  Dams. — Wooden  Dams,  328;  Abutments  and  Discharge  Gates, 
328;  Spillways,  or  Waste  Ways,  329;  Stone  Dams,  329;  Earth  Dams, 
329;  Irrigation  Quantity  Tables,  330;  Refuse  Dams,  331;  Wing 
Dams,  331;  Masonry  and  Concrete  Dams,  331. 

Water-Power. — Theoretical  Efficiency,  331;  Horsepower  of  a  Running 
Stream,  331;  Current  Motors,  332;  Utilizing  Power  of  Waterfall, 
332. 

Pump  Machinery. — Classification  of  Pumps,  333;  Cornish,  333;  Simple  and 
Duplex,  333;  Speed  of  Water  Through  Valves,  Pipes,  and  Pump 
Passages,  334;  Ratio  of  Steam  and  Water  Cylinders  in  a  Direct- 
Acting  Pump,  335;  Piston  Speed  of  Pumps,  335;  Strokes  for  Piston 
Speed  of  100  Ft.  per  Min.,  Table,  335;  Boiler  Feed-Pumps,  335; 
Theoretical  Capacity  of  Pumps  and  Horsepower  Required  to  Raise 
Water,  336;  Ratios  of  Areas  to  Diameters  of  Steam  and  Water  Cylin- 
ders, Table,  336-337;  Depth  of  Suction,  338;  Suction  Lift  of  Pumps 
at  Different  Altitudes,  Table,  338;  Theoretical  Horsepower  Required 
to  Raise  Water  to  Different  Heights,  Table,  339;  Amount  of  Water 
Raised  by  a  Single-Acting  Lift  Pump,  340;  Capacity  of  Pumps, 
Table,  340;  Pump  Valves,  341;  Power  Pumps,  341;  Electrically 
Driven,  342;  Theoretical  Consumption  of  Electric  Current  for  Pump- 
ing Water  per  1,000  Gal.,  Table,  342;  Precautions  Necessary  With 
Electrically  Driven  Mine  Pumps,  343;  Centrifugal  Pumps,  343;  Dis- 
charge of  Pumps  at  Various  Piston  Speeds,  Table,  344;  Pumps  for 
Special  Purposes,  346;  Sinking  Pumps,  346;  For  Acid  Waters,  346; 
Pump  Foundations,  346;  Pump  Management,  346;  Miscellaneous 
Forms  of  Water  Elevators,  349;  Jet  Pump,  349;  Vacuum  Pump,  349; 
Air-Lift  Pumps,  349;  Water  Buckets,  350;  Siphons,  351. 

HEAT  AND  FUELS 

Heat. — Thermometers,  352;  Comparison  of  Thermometer  Scales,  353;  Abso- 
lute Zero,  353;  British  Thermal  Unit,  353;  Calorie,  354;  Pound 
Calorie,  354;  Equivalence  of  Heat  Units,  354;  Mechanical  Equiva- 
lent of  Heat,  354;  Expansion  by  Heat,  354;  Equivalent  Temperatures 
by  the  Fahrenheit  and  Centigrade  Thermometers,  Table,  355;  Equiva- 
lent Temperatures  by  the  Centigrade  and  Fahrenheit  Thermometers, 
Table,  357;  Coefficients  of  Linear  Expansion  per  1°  P.,  359;  Conduc- 
tion of  Heat,  359;  Relative  Heat  Conductivities  of  Metals,  359; 
Radiation  of  Heat,  359;  Specific  Heat,  360;  Specific  Heat  of  Water 
at  Various  Temperatures,  360;  Specific  Heats  of  Solids,  360;  Of 
Liquids,  361;  Of  Gases,  361;  Sensible  and  Latent  Heat,  361;  Melting 
Points  and  Latent  Heat  of  Fusion  of  Metals,  Table,  362 ;  Boiling  Point 
of  Water  at  Various  Altitudes,  Table,  363;  Combustion,  363. 


xiv  CONTENTS 

FUELS 

Fuels  in  General. — 365. 

Wood  as  Fuel. — Weights  per  Cord  of  Dry  Wood  Arranged  According  to  Fuel 
Values,  366;  Weight  of  Coal  Equivalent  to  1  Cord  of  Air-Dried  Wood, 
366;  Composition  and  Calorific  Value  per  Pound  of  Wood,  366. 

Peat  as  Fuel.— 367. 

Coal. — Constituents,  368:  Changes  in  Chemical  Composition  from  Wood  to 
Anthracite,  368;  Classification  of  Coals,  370;  Classification  Based  on 
Their  Content  of  Fixed  Carbon  and  Volatile  Matter,  371 ;  Anthracite, 
371;  Semianthracite,  372;  Semibituminous,  372;  Bituminous,  372; 
Subbituminous,  372:  Lignite,  373;  Gas  Coals,  373;  Domestic,  373; 
Blacksmith,  or  Smithing,  374;  Steam  Coals,  374;  Coking,  374; 
Yield  of  Coke,  376;  Pishel's  Test  for  Coking  Qualities  of  Coal,  377; 
Non-Coking  Coals,  378;  Fat  and  Dry,  or  Lean,  378;  Free-Burning 
Coal,  378;  Cannel,  378,  Splint,  378;  Proximate  Analysis  of  Coal,  378; 
Sampling,  378;  Moisture,  379;  Volatile  Combustible  Matter,  379; 
Ash,  379;  Fixed  Carbon,  379;  Sulphur  (Eschka's  Method),  379; 
Forms  of  Reporting  Analyses,  379;  Coal  114  from  Sewell  Seam, 
McDonald,  W.  Va.,  Table,  380;  Analyses  of  Typical  Coals,  381 ; 
Proximate  and  Ultimate  Analyses  and  Heating  Values  of  American 
Coals,  Table,  382-385;  Proximate  Analyses  and  Heating  Values  of 
Pennsylvania  Anthracites,  Table,  386;  Proximate  Analyses  of  Mis- 
cellaneous American  Coals,  Table,  387;  Proximate  Analyses  and 
Heating  Values  of  Canadian  Coals,  Table,  388-389;  Proximate 
Analyses  of  Alaskan  Coals,  Table,  390;  Of  Foreign  Coals,  Table,  391; 
Determination  of  Heating  Value  of  Coal  from  a  Proximate  Analysis, 
392;  Kent's  Method,  392;  Approximate  Heating  Value  of  Coals,  392; 
Method  of  Lord  and  Haas,  392;  Value  of  K  for  Various  Coals,  393; 
Determination  of  Heating  Value  of  Coal  from  an  Ultimate  Analysis, 
394 ;  Dulong's  Formula,  394. 

Petroleum  as  Fuel. — Composition  of  Crude  Petroleum,  395;  Flash  Point 
and  Firing  Point,  395;  Ultimate  Analyses  of  Crude  Petroleum,  Table, 
396;  Calorific  Value  of  Fuel  Oil,  396;  Comparative  Value  of  C9al  and 
Oil  as  Fuel,  Table,  397;  Advantages  and  Disadvantages  of  Oil  Fuel, 
397. 

Gaseous  Fuels. — Kinds  of  Gas,  398;  Analyses  and  Heating  Values  of  Vari- 
ous Gases,  Table,  398;  Blast-Furnace  Gases,  398;  Analyses  of 
Natural,  Producer,  and  Coke-Oven  Gases,  Table,  399;  Heating 
Value  of  Gases  at  32°  F.,  400;  Natural  Gas,  400;  By-Product  Gas, 
401;  Coke-Oven  Gas,  402;  Coal  Gas,  402;  Analyses  of  Gas  Coals, 
Table,  403;  Water  Gas,  403;  Producer  Gas,  404;  Quantity  of  Gas 
Produced  per  Pound  of  Fuel  in  an  Up- Draft  Pressure  Producer, 
Table,  404;  Yield  and  Heat  Value  of  Gas  per  Ton  of  Fuel  as  Fired  in 
an  tip-Draft  Pressure  Producer,  Table,  405-  Gas  Producers,  405; 
Typical  Analyses  by  Volume  of  Producer  Gas,  Table,  405. 

BOILERS 

Steam. — Properties  of  Steam,  406;  Saturated  Steam,  406;  Properties  of 
Saturated  Steam,  Table,  407;  Use  of  Steam  Table,  408;  Superheated 
Steam,  409;  Quality  of  Steam,  410;  Moisture  in  Steam,  410;  Heat  in 
Wet  Steam,  410;  Flow  of  Steam,  410;  Weight  of  Steam  Discharged, 
410;  Weight  Delivered  per  Minute  Through  100  Ft.  of  Pipe  with  1  Lb. 
Drop  of  Pressure,  Table,  411;  Resistance  of  Elbows  and  Valves,  411; 
Steam  Pipes  for  Engines,  412. 

Boiler  Piping. — Principal  Considerations,  412;  Materials  for  Pipes,  412;  Ex- 
pansion Joints,  412;  Expansion  Bends,  413;  Arrangement  of  Piping, 
413. 

Boiler  Fittings. — Safety  Valves,  414;  Weight  of  Ball  for  Lever  Safety  Valve, 
414;  Position  of  Ball,  414;  Roper's  Safety  Valve  Rules,  414;  Area  of 
Safety  Valve,  415;  Location,  415;  Fusible  Plugs,  415;  Location,  415; 
Connection  of  Steam  Gauge,  416;  Blow-Offs,  416;  Blow-Off  Cocks 
and  Valves,  417;  Protection  of  Blow-Off  Pipe,  417. 

Furnace  Fittings.— Bridge  Wall,  417;  Fixed  Grates,  417;  Dead  Plate,  418; 
Objection  to  Stationary  Grate  Bars,  418;  Shaking  Grates,  418; 


CONTENTS  xv 

Classes  of  Mechanical  Stokers,  418;  Overfeed  Stoker,  418;  Underfeed 
Stoker,  419. 

Covering  for  Boilers,  Steam  Pipes,  Etc. — Losses  by  Radiation,  419;  Loss  of 
Heat  from  Steam  Pipes,  Table,  420;  Conducting  Power  of  Various 
Substances,  421;  Relative  Value  of  Non-Conductors,  421, 

Boiler  Feeding  and  Feedwater. — Injectors,  422;  Classification,  422;  Advan- 
tages and  Disadvantages,  422;  Size,  422;  Water  Delivered  by  In- 
jectors, Table,  422;  Water  Required  per  Minute  to  Feed  Boilers, 
Table,  423;  Location  of  Injector,  423;  Steam  Supply  to  Injector,  423; 
Injector  Troubles,  423;  Incrustation  and  Corrosion,  424;  Impurities 
in  Feedwater,  425;  Formation  of  Scale,  425;  Danger  of  Scale,  425; 
Scale  Containing  Lime,  425;  Kerosene  as  Scale  Remover,  425;  Re- 
moval by  Chipping,  426;  Removal  of  Mud,  426;  Internal  Corrosion, 
426;  Pitting  or  Honeycombing,  426;  Grooving,  426;  External  Corro- 
sion, 426;  Lamination,  426;  Overheating,  427;  Prevention  of  Incrusta- 
tion and  Corrosion,  427;  Scale-Forming  Substances  and  Their  Reme- 
dies, 427;  Use  of  Zinc  in  Boilers,  428;  Testing  of  Feedwater,  428; 
Purification  of  Feedwater,  428;  By  Settlement,  428;  By  Filtration, 
428;  By  Chemicals,  428;  Treatment  for  Sulphate  of  Lime,  429;  Quan- 
tity of  Chemicals  to  Use,  429;  Use  of  Carbonate  of  Soda,  429;  Of  Tri- 
sodium  Phosphate,  429;  Neutralization  of  Acids,  429;  Purification  by 
Heat,  429;  Feedwater  Heating,  430;  Types  of  Exhaust-Steam  Feed- 
water  Heaters,  430;  Selection  of  Heater,  430. 

Boiler  Trials. — Purposes,  430;  Observations  During  Trial,  430;  Weighing 
the  Coal,  431;  Measurement  of  Feedwater,  431;  Standard  of  Boiler 
Horsepower,  431;  Equivalent  Evaporation,  431;  Factors  of  Evapora- 
tion, 431;  Table  of  Same,  432;  Boiler  Efficiency,  433;  Standard  Code, 
433. 

Boiler  Management. — Filling  Boilers,  433;  Preparation,  433;  Height  of 
Water,  433;  Escape  of  Air,  433;  Management  of  Fires  When  Starting, 
434;  Precautions,  434;  Starting,  434;  Value  of  Slow  Fires,  434;  Trying 
the  Fittings,  434;  Connecting  Boilers,  434;  Cutting  Boiler  Into  Service, 
434;  Connecting  Boilers  to  Main,  434;  Changing  Over,  434;  Equal- 
izing the  Feed,  435;  Firing  With  Solid  Fuel,  435;  Cleaning  of  Fires, 
435;  Uniform  Steam  Pressure,  436;  Desirability,  436;  Maintenance, 
436;  Keeping  Water  Level  Constant,  436;  Priming  and  Foaming,  436; 
Evidences  of  Priming,  437;  Foaming,  437;  Shutting  Down  and  Start- 
ing Up  437;  Preparations  for  Shutting  Down,  437;  Starting  the  Fires, 
437;  Blowing  Down,  438;  Care  of  Boilers,  438;  Safety  Valves,  438; 
Pressure  Gauge,  438;  Water  Level,  438;  Gauge-Cocks  and  Water 
Gauges,  438;  Feed-Pump  or  Injector,  438;  Low  Water,  438;  Blisters 
and  Cracks,  438;  Fusible  Plugs,  438;  Firing,  438;  Cleaning,  438; 
Hot  Feedwater,  439;  Foaming,  439;  Air  Leaks,  439;  Blowing  Off,  439; 
Leaks,  439;  Filling  Up,  439;  Dampness,  439;  Galvanic  Action,  439; 
Rapid  Firing,  439;  Standing  Unused.  439;  Repair  of  Coverings,  439; 
General  Cleanliness,  439. 

Boiler  Inspection. — Nature  of  Inspection,  439;  External  Inspection,  440; 
Preparation,  440;  Inspection  of  Externally  Fired  Boilers,  440;  In- 
spection of  Internally  Fired  Boilers,  440;  Inspection  of  New  Boilers, 
440;  Internal  Inspection,  440;  Preparation,  440;  Inspection  of  Loco- 
motive-Type Boilers,  441;  Flues  and  Combustion  Chambers.  441;  In- 
spection of  Vertical  Boilers,  441;  Inspection  of  Fittings,  441. 

Selection  of  Boilers.— General  Requirements,  441;  Liability  to  Explosion 
442;  Durability,  443;  Repairs,  443;  Facility  for  Removal  of  Scale  and 
for  Inspection,  443;  Water  and  Steam  Capacity,  443;  Water  Circu- 
lation, 444;  Ratio  of  Heating  Surface  to  Horsepower  and  to  Grate 
Area,  Table,  444;  Heating  Surface,  444;  Probable  Maximum  Work 
of  a  Plain  Cylindrical  Boiler  of  120  Sq.  Ft.  Heating  Surface  and  12 
Sq.  Ft.  Grate  Surface,  Table,  445. 

Chimneys.— Products  of  Combustion,  446;  Weight  of  Air,  Water  Vapor,  and 
Saturated  Mixtures  at  Different  Temperatures,  Table,  447;  Oxygen 
and  Air  Required  for  the  Combustion  of  Carbon,  Hydrogen.  Etc., 
Table,  447;  Temperature  of  Ignition  of  Various  Fuels,  448;  iempera- 
ture  of  Fire  449'  Heat  and  Products  of  Combustion  of  Burning 
Carbon  Table,  449;  Estimation  of  Air  Supply,  451;  Production  and 


xvi  CONTENTS 

Measurement  of  Draft,  451;  Erection  of  Chimneys,  452;  Height  and 
Area  of  Chimneys,  452;  Maximum  Combustion  Rate,  453;  Forced 
Draft,  453;  Size  of  Chimneys  and  Horsepower  of  Boilers,  Table,  454. 

STEAM  ENGINES 

Principles  and  Requirements. — Clearance,  454;  Cut-Off,  455;  Ratio  of  Ex- 
pansion, 455;  Mean  Effective  Pressure,  455;  Constants  Used  in  Calcu- 
lating Mean  Effective  Pressure,  456;  Horsepower,  456;  Finding  the 
Indicated  Horsepower,  456;  Stating  Sizes  of  Engines,  457;  Mechanical 
Efficiency,  458;  Piston  Speed,  458;  Allowance  for  Area  of  Piston  Rod, 
458;  Cylinder  Ratios,  458. 

Condensers. — Surface  Condensers,  459;  Cooling  Water  for  Surface  Con- 
denser, 459;  Injection  Water  for  Jet  Condenser,  460. 

Engine  Management. — Starting  and  Stopping,  460;  Warming  Up,  460;  Oil 
and  Grease  Cups,  461;  Starting  and  Stopping  Non-Condensing  Slide- 
Valve  Engine,  461;  Condensing  Slide-Valve  Engine,  461;  Simple  Cor- 
liss Engine,  461;  Compound  Slide- Valve  Engine,  462;  Compound 
Corliss  Engine,  463. 

Pounding  of  Engines. — Faulty  Bearings,  463;  Pounding  in  Cylinders,  464; 
Improper  Valve  Setting,  464;  Reversal  of  Pressure,  464;  Insufficient 
Lead,  465;  Pounding  at  Crosshead,  465;  In  Air  Pump,  465;  In  Circu- 
lating Pump,  465;  Hot  Bearings,  465;  Dangerous  Heating,  466;  Re- 
fitting Cut  Bearing,  466;  Newly  Fitted  Bearings,  466;  Faulty  Brasses, 
466;  Edges  of  Brasses  Pinching  Journal,  467;  Hot  Bearings  Due  to 
Faulty  Oiling,  467;  Grit  in  Bearings,  468;  Overloading  of  Engine,  468; 
Engine  Out  of  Line,  468;  Effect  of  External  Heat  on  Bearings,  468; 
Springing  of  Bedplate,  468;  Springing  or  Shifting  of  Pillow-Block,  469. 

Steam  Turbines. — Types,  469;  Steam  Consumption,  469;  Comparison  of 
Turbines  and  Engines,  470;  Steam  Consumption  per  Hour  of  Tur- 
bines, 470;  Finding  Horsepower  of  Turbines,  470;  Turbine  Troubles, 
470;  Operation  of  Turbines,  471;  Economy  of  Turbine,  472;  Care  of 
Gears  in  De  Laval  Turbines,  472. 

Rules  for  Stationary  Engineers. — 473. 

COMPRESSED  AIR 

Classification  and  Construction  of  Compressors. — Theory  of  Air  Compres- 
sion, 475;  Construction  of  Compressors,  475;  Rating,  475;  Efficiencies 
at  Different  Altitudes,  Table,  476;  Cooling,  476. 

Transmission  of  Air  in  Pipes. — 476^ 

Losses  in  the  Transmission  of  Compressed  Air. — Cause  of  Loss,  478;  Loss 
of  Pressure,  in  Pounds  per  Square  Inch,  by  Flow  of  Air  in  Pipes  1,000 
Ft.  Long,  Table,  482;  Friction  of  Air  in  Pipes,  482;  Loss  by  Friction  in 
Elbows,  483. 

Design,  Operation,  and  Installation  of  Air  Compressors. — Design  for  avoid- 
ing Explosions,  483;  Installation  of  Compressor,  483;  Operation,  484. 

ELECTRICITY 

Practical  Units. — Strength  of  Current,  484;  Electromotive  Force,  485;  Re- 
sistance, 485;  Ohm's  Law,  485;  Electric  Power,  485;  Electrical  Ex- 
pressions and  Their  Equivalents,  486. 

Circuits. — Series,  486;  Parallel,  487. 

Resistances  in  Series  and  Multiple.— In  Series,  488;  In  Parallel,  488;  Shunt, 
488. 

Electric  Wiring  (Conductors). — Materials,  488;  Properties  of  Annealed  Cop- 
per Wire;  American,  or  Brown  &  Sharpe,  Gauge,  Table,  489;  Wire 
Gauge,  490;  Carrying  Capacity  of  Copper  Cables,  Table,  490;  Com- 
parison of  Properties  of  Aluminum  and  Copper,  490;  Estimation  of 
Resistance,  491;  Breaking  Strength  of  Copper  and  Aluminum  Wires 
and  Cables,  Table,  491. 

Calculation  of  Wires  for  Electric  Transmission. — Direct-Current  Circuits, 
492;  Insulated  Wires,  494;  Weather-Proof  Line  Wire  (Roebling's), 
Table,  494. 


CONTENTS  xvii 

Current  Estimates. — Incandescent  Lamps,  494;  Arc  Lamps,  495;  Motors 
495;  Current  Required  for  Direct- Current  Motors,  Table,  496;  Con- 
ductors  for  Electric- Haulage  Plants,  496. 

Dynamos  and  Motors. — Direct- Current  Dynamos,  497;  Factors  Determin- 
ing Electromotive  Force  Generated,  500;  Field  Excitation  of  Dyna- 
mos, 500;  Direct-Current  Motors,  501;  Principles  of  Operation,  501; 
Speed  Regulation  of  Motors,  503;  Connections  for  Continuous-Cur- 
rent Motors,  504;  Alternating-Current  Dynamos,  506;  Uses  of  Multi- 
phase Alternators,  507;  Alternating-Current  Motors,  508;  Selection 
of  Induction  Motors  for  Mine  Use,  509;  Installation  and  Care  of 
Induction  Motors,  511. 

Transformers. — 513. 

Electric  Signaling. — Batteries,  514;  Elements  of  Primary  Batteries,  Table, 
515;  Bell  Wiring,  516;  Annunciator  System,  517;  Diagrams  for  Wiring 
Systems,  517-523. 

Dynamo  and  Motor  Troubles. — Sparking  at  Brushes,  523;  Brush  Faults,  523; 
Commutator  Faults,  524;  Heating  of  Armature,  Field  Coil,  and  Bear- 
ings, 524;  Noise,  525;  Regulation  of  Speed,  526;  Motor  Stops,  Fails 
to  Start,  or  Runs  Backwards  or  Against  the  Brushes,  526;  Failure  of 
Dynamo  to  Generate,  527;  Reversed  Residual  Magnetism,  527; 
Short  Circuits,  527;  Field  Coils  Opposed  to  One  Another,  527;  Open 
Circuit,  527;  Overloaded  Dynamos,  528;  Miscellaneous  Troubles,  528; 
Weak  Magnetic  Field,  528;  Excessive  Current  in  Armature  Due  to 
an  Overload,  528;  Armature  Faults,  528;  General  Precautions,  528. 

General  Rules  for  Handling  Electricity.— 529-531. 

INTERNAL-COMBUSTION  ENGINES 

Definitions  and  Principles. — Internal- Combustion  Engines,  532;  Single-  and 
Double- Acting  Engines,  532;  Gasoline-Engine  Cycles,  532;  Four- 
Cycle  Engines,  532;  Two-Cycle  Engines,  533;  Application  of  Four- 
Cycle  Principle,  533;  Graphic  Representation  of  Four-Stroke  Cycle, 
533;  Application  of  Two- Cycle  Principle,  534. 

Gas-Engine  Fuels. — Gaseous  Fuels,  536;  Alcohol,  536;  Gasoline,  536; 
Kerosene,  537;  Fuel,  or  Compound,  Oils,  537;  Rating  of  Oil  and 
Gasoline,  537;  Baum6  Hydrometer,  537;  Comparative  Value  of 
Liquid  Fuels:  Specific  Gravities  Corresponding  to  Baum6  Readings 
for  Liquids  Lighter  Than  Water,  Table,  538. 

Types  of  Internal- Combustion  Engines. — Internal- Combustion  Engines  at 
Mines,  538;  Stationary  Gas  Engines,  540;  Haulage- Motor  Gasoline 
Engines,  540. 

Carburetion  and  Ignition. — Carbureters  for  Constant-Speed  Engines,  541; 
For  Variable-Speed  Engines,  541;  Make-and-Break  Ignition,  542; 
Jump-Spark  Ignition,  542;  Requirements  of  Spark  Plugs,  544. 

Operation  of  Internal-Combustion  Engines. — Engine  Starters,  545;  Start- 
ing the  Engine,  545;  Stopping,  545;  Lubrication,  546. 

Engine  Troubles  and  Remedies. — Hot  Bearings,  547;  Misfiring,  547; 
Back  Firing,  547;  Preignition,  548;  Carbureter  Troubles,  548; 
Compression  Troubles,  548. 

PROSPECTING 

Outfit  and  Methods. — Outfit  Necessary,  549;  Plan  of  Operations,  549. 

Coal -Bearing  Formations. — Outcrops,  550;  Formations  Likely  to  Contain 
Coal,  550;  Geological  Chart  for  the  United  States,  551;  Faults,  553. 

Exploration  by  Drilling  or  Bore  Holes. — Earth  Augers,  553;  Percussion 
Drills,  554;  Percussion  Core  Drill,  Cost  of  Well  Drilling,  554;  Core 
Drills,  554;  Selecting  the  Machine,  555;  Size  of  Tools,  555;  Dia- 
mond-Drilling, 555;  Calyx  Drilling,  556;  Prospecting  for  Petroleum, 
Natural  Gas,  and  Bitumen,  557;  Construction  of  Geological  Maps  and 
Cross- Sections,  557;  To  Obtain  Dip  and  Strike  From  Bore-Hole  Rec- 
ords, 558;  Sampling  and  Estimating  the  Amount  of  Mineral  Avail- 
able, 559;  Diagram  for  Reporting  on  Coal  Lands,  560-563. 


xviii  CONTENTS 

MINING 

General  and  Financial  Considerations. — Relation  Between  Investment  and 
Cost  of  Production,  564 ;  Relative  Cost  of  Different  Types  of  Open- 
ing, 564;  Cost  of  Production  as  Affected  by  Type  of  Opening,  564. 

Location  of  Surface  Plant. — Grades,  565;  Length  and  Number  of  Sidings.  565; 
Mining  Plant,  566;  Mining  Village,  566;  Coke  Ovens,  566. 

Location  of  Mine  Opening. — Flat  Seams,  567;  Seams  of  Moderate  Dip,  568; 
Of  High  Dip,  568;  Method  of  Working,  568. 

Drifts.— 568. 

Tunnels. — Through  Loose   Ground,   569;  Forepoling,   569;  Wedging,   570; 

Tunnels    Through    Rock,    571;  Arrangement    of    Drill    Holes,    571; 

American  and   European   Practice,   571;  Conical   Center   Cut,   572; 

The  Billy  White  Cut,  573;  Square-Cut  Drillinp  and  Blasting,  574; 

Side    Cut    in    Heading,    574;  Special    Arrangement    for    Throwing 

Broken  Rock  from  Face,  575. 

Slopes. — Safety  Appliances,  575;  Data  Concerning  Well-Known  Shafts 
Table,  576-577. 

Shafts. — Introduction,  578;  Form  of  Shaft,  578;  Compartments,  578;  Size, 
578;  Width,  578;  Length,  579;  Sinking  Tools  and  Appliances,  580; 
Buckets,  580;  Bucket  Guides,  580;  Dumping  Buckets,  581;  Engines 
and  Boilers,  581;  Sinking  Head  Frame,  581;  Shaft  Coverings,  582; 
Ventilation  and  Lighting,  583;  Sinking  Through  Firm  Ground,  583; 
Preliminary  Operations,  583;  Sinking  Through  Earth  and  Loose 
Rock,  583;  Through  Rock,  584;  Long-Hole,  or  Continuous-Hole, 
Method,  585;  Sinking  in  Swelling  Ground,  586;  Sinking  Through 
Running  Ground,  586;  Draining  the  Ground,  586;  Piling,  586;  Fore- 
poling,  587;  Shoes  for  Shaft  Sinking,  588;  Pneumatic  Process,  590; 
Freezing  Processes,  591;  Cementation  Process,  591;  Other  Methods 
of  Shaft  Sinking,  592;  Enlarging  and  Deepening  Shafts,  593;  Up- 
raising, 594;  Shaft  Drainage  and  Pumping,  596;  Water  Rings,  596; 
Coffer  Dams,  596;  Lodgements,  or  Basins,  596;  Sump,  596. 

Slope  and  Shaft  Bottoms. — Slope  Bottoms,  596;  Vertical  Curves,  599;  Shaft 
Bottoms,  599;  General  Bottom  Details,  601;  Mine  Stables,  601; 
Pump  Room,  602;  Engine  Room,  602;  Lamp  Stations,  602;  Shanties, 
603;  Manway  About  the  Shaft,  603;  Surface  Tracks  for  Slopes  and 
Shafts. 

METHODS  OF  OPEN  WORK 

General. — 604;  Steam-Shovel  Mines,  605. 

METHODS  OF  CLOSED  WORK 

Introductory. — General  Considerations,  606;  General  Systems  of  Mining, 
607. 

Room-and -Pillar  Systems  of  Mining. — Preliminary  Considerations,  607; 
Number  of  Entries,  607;  Size,  609;  Distance  Between  Entries,  610; 
Direction  of  Entries  in  Flat  Seams,  610;  In  Inclined  Seams,  611; 
Alinement  and  Grade  of  Entries,  611 ;  Rooms  in  General,  611 ;  Double 
Rooms,  612;  Rooms  With  Extra  Entry  Pillars,  613;  Inclination  of 
Rooms  to  the  Entry,  613;  Direction  of  Rooms  as  Determined  by 
Cleat,  614;  Distance  from  Center  to  Center  of  Rooms  or  Breasts 
Measured  on  Entry  or  Gangway,  Table,  615;  Direction  of  Rooms  as 
Determined  by  Slips  in  the  Roof,  616;  Working  Flat  Seams,  616; 
Pittsburg  Region,  616;  Clearfield,  616;  Reynoldsville,  617;  West 
Virginia,  617;  George's  Creek  District,  Md.,  617;  Blossburg  Coal 
Region,  Pa.,  618;  Indiana  Coal  Mining,  618;  Iowa  Coal  Mining,  618; 
Steep  Rooms,  619;  Working  Pitching  Seams,  619;  Difficulties,  619; 
Working  Thick  and  Gaseous  Seams  That  Run,  620;  Thick  Non- 
Gaseous  Seams,  621;  Small  Seams  Laying  From  Horizontal  to  10°, 
621;  Laying  at  More  Than  10°,  622;  Buggy  Breasts,  622;  Chutes, 
623;  Single-Chute  Rooms,  624;  Double-Chute  Rooms,  625;  Method 
Suitable  for  Use  in  Inclined  Seams,  626;  Battery  Breasts,  626; 
Working  Contiguous  Seams,  629;  New  Castle,  Col.,  Method,  631; 
Alabama  Methods,  631;  Tesla,  Cal.,  Method,  632. 


CONTENTS  xix 

Pillar -and-Stall  Systems  of  Mining. — General,  634;  Connellsville  Region, 
635;  J.  L.  Williams'  Method,  636. 

Panel  System  of  Mining. — Col.  Brown's  Method,  637. 

Mining  and  Blasting  Coal. — Shooting  Off  the  Solid,  638;  Precautions  in 
Solid  Shooting,  641;  Objections,  642;  Blasting  after  Undercutting, 
642;  Combined  Undercutting  and  Solid  Shooting,  643;  Undercutting 
in  Longwall,  644:  Machine  Mining,  644;  Pick  Machines,  644;  Chain 
Machines,  645;  Capacity  of  Coal- Cutting  Machines,  646;  Longwall 
Machines,  646;  Heading  Machines,  647;  Machine  Mining  in  Anthra- 
cite Mines,  648. 

Drawing  Pillars  -General,  648;  Work  of  Drawing,  650;  Delayed  Pillar 
Drawing,  651;  Precautions,  651. 

Longwall  System  of  Mining. — Systems  of  Longwall,  652;  Considerations 
Affecting  Its  Adoption,  653;  Roof  Pressure,  653;  Nature  of  Coal 
Seam,  653;  Waste,  653;  Surface  Damage,  Water,  Gas,  Etc.,  654: 
Timber  Supply,  654;  Labor  and  Trade  Conditions,  654;  Longwall 
Working  in  Flat  Seams,  655;  Scotch,  or  Illinois,  Plan,  655;  Rectangu- 
lar Longwall,  656;  Longwall  Working  in  Pitching  Seams,  657;  On 
Low  Inclination,  658;  When  Inclination  is  Less  Than  40°,  658;  When 
Inclination  is  From  30°  to  60°,  659;  In  Steeply  Inclined  Seams,  661; 
Special  Forms  of  Longwall  Working,  661;  In  Panels,  661;  In  Thick 
Seams,  663;  In  Inclined  Thick  Seams,  664;  In  Contiguous  Seams, 
664;  Details  of  Longwall  Working,  664;  Starting,  664;  Roadways, 
665,  Control  of  Roof  Pressure,  665;  Building  Pack  Walls  and  Stowing, 
666;  Timbering  a  Longwall  Face,  666. 

EXPLOSIVES  AND  BLASTING 

Classification  of  Explosives. — Low,  667;  High,  667;  Sizes  of  Grains  of 
Black  Blasting  Powder,  Table,  667. 

Explosives  for  Rock  Work. — Straight  Nitroglycerin  Dynamite,  668;  Com- 
positions, Table,  668;  Slow,  or  Low- Freezing,  Dynamites,  668; 
Compositions,  Table,  668;  Ammonia  Dynamites,  668;  Composi- 
tions, Table,  669;  Gelatin  Dynamites,  669:  Compositions,  Table, 
669;  Analyses  or  High  Explosives,  Table,  669;  Comparative 
Analyses,  670;  Products  of  Combustion,  670;  Analyses  of  Mine  Air 
After  Blasting,  Table,  670;  Comparative  Strength  of  Explosives, 
670;  Results  of  Tests  to  Determine  Potential  Energy  and  Disruptive 
and  Propulsive  Effects  of  Explosives,  Table,  671. 

Explosives  for  Coal  Mines. — Classes  of  Permissible  Explosives,  672. 

Care  of  Explosives. — Storing,  673;  Thawing  Dynamite,  673;  Handling 
Explosives,  674;  Precautions  When  Handling,  675. 

Firing  Explosives. — Means  of  Firing  Low  Explosives,  676;  Squibs,  676; 
Fuse,  676;  Electric  Squibs,  677;  Means  of  Firing  High  Explosives, 
677;  Fuse  and  Caps,  677;  Electric  Detonators,  677;  Delay- Action 
Detonators,  678;  Charging  and  Firing  Explosives  With  Squibs  or 
With  Cap  and  Fuse,  678;  Charging  Black  Powder  and  Firing  With 
Squib,  678;  Firing  With  Fuse  and  Cap,  679;  Charging  and  Firing 
Dynamite  With  Cap  and  Fuse,  680;  Precautions  When  Tamping  Ex- 
plosives, 680;  Firing  Explosives  by  Electricity,  681;  Charging  for 
Electric  Firing,  681;  Shot  Firing  With  the  Electric  Blasting  Machine, 
682;  Connecting  Wires,  682;  Connecting  Up  and  Firing  the  Blasts, 
682;  Firing  With  Dry  Batteries,  683;  Precautions  When  Firing  With 
the  Electric  Blasting  Machine,  683;  Firing  From  Dynamo,  684; 
Firing  Single  Shots  From  the  Surface,  685. 

Substitutes  for  Blasting  in  Dry  and  Dusty  Mines.— Wedging  Down  Coal, 
685;  Hydraulic  Cartridge,  686;  Lime  Cartridges,  687;  Water  Car- 
tridge, 687. 

General  Considerations  Affecting  Blasting. — Definitions,  687;  Effect  of  Free 
Faces  in  Mining,  688;  Diameter  of  Shot  Holes,  690;  Amount  and 
Kind  of  Explosive,  690. 

SUPPORTING  EXCAVATIONS 

Introduction. — 692. 

Coal  Pillars.— General  Considerations  Affecting  Size,  692;  Amount  of  Pillar 
Coal,  692;  Practical  Considerations  Determining  Size,  692;  Depth  of 


xx  CONTENTS 

Cover,  693;  Weight  of  Rocks,  694;  Crushing  Strength  of  Anthracite, 
and  Table,  694;  Of  Bituminous  Coal,  695;  Room,  Entry,  and  Slope 
Pillars,  695;  Load  on  Pillars,  695;  Strength  9f  Pillars,  695;  Width  of 
Room  Pillars,  695;  Weight  on  Pillars  at  Various  Depths,  Table,  696; 
Slope  Pillars,  696;  Entry  Pillars.  697;  Shaft  Pillars,  697;  Pillars  in 
Flat  Seams,  697;  Rules,  Merivale's,  Andre's,  Wardle's,  Pamely's,  Min- 
ing Engineering  (London),  Poster's,  697;  Dron's,  Hughes 's,  Central 
Coal  Basin,  698;  Size  of  Shaft  Pillar  Obtained  by  Use  of  Several 
Formulas,  Table,  698;  Pillars  in  Inclined  Seams,  698;  Pillars  for  Mis- 
cellaneous Purposes,  699;  For  Supporting  Buildings,  Etc.,  699;  Re- 
serve Pillars,  699;  Chain  Pillar,  699;  Barrier  Pillars,  699;  Size  of 
Barrier  Pillars  to  be  Left  Between  Adjoining  Properties,  700;  Squeeze 
and  Creep,  701;  Stopping  a  Squeeze,  701;  Reopening  a  District  Closed 
by  Squeeze,  701. 

Flushing  of  Culm.— 702-705. 

Built-Up  Packs  and  Cribs. — Strength,  705;  Supporting  Strength  of  Various 
Forms  of  Dry  Filling,  Table,  706. 

Timbering  With  Wood. — Nature  of  Rock  Pressure,  707;  Choice  of  Timber, 
707;  R9om  Timbering  in  Flat  Seams,  707;  Props,  707;  Systematic 
Timbering,  708;  Bad  Roofs,  709;  Supporting  the  Face  While  Under- 
cutting, 710;  Entry  Timbering  in  Flat  Seams,  710;  Two-Stick  Sets, 
710;  Three-Stick  Sets,  711;  Four-Stick  Sets,  711;  Room  Timbering 
in  Pitching  Seams,  712;  Undersetting  of  Props,  Table,  712;  Entry 
Timbering  in  Pitching  Seams,  713;  Two-Stick  Sets,  713;  Three-Stick 
Sets,  714;  Shaft  Timbering,  715;  General  Principles,  715;  Timbering 
in  Rock,  715;  In  Loose  Dry  Material,  716;  In  Swelling  Ground,  717; 
In  Very  Wet  Ground  or  Quicksand,  717;  Square  Frame  at  Foot  of 
Shaft,  718;  Square-Set  Timbering,  718;  Miscellaneous  Forms  of  Tim- 
bering, 719. 

Framing  Timbers. — Limiting  Angle  of  Resistance,  720;  Placing  Timber  Sets, 
720;  Timber  Joints,  721. 

Care  and  Preservation  of  Timber. — Cutting  and  Storing,  722;  Time  to  Cut. 
722;  Peeling,  722;  Seasoning  and  Storing,  722;  Preservation  of  Mine 
Timber,  723;  Destructive  Agencies,  723;  General  Principles  of  Timber 
Preservation,  723;  Brush  Treatments,  724;  Open-Tank  Treatments, 
724;  Pressure  Treatments,  724;  Comparison  of  Open-Tank  and  Pres- 
sure Treatments,  724;  Cost  of  Open-Tank  Plant,  725;  Cost  of  Pressure 
Plant,  725;  Cost  of  Treatment,  725;  Cost  of  Untreated  and  Treated 
Loblolly  Pme  Gangway  and  Entry  Sets  Placed  by  the  Philadelphia 
&  Reading  Coal  &  Iron  Co.,  in  Cooperation  With  the  Forest  Service, 
Table,  726:  Durability  of  Treated  Timbers,  727;  Economy  in  Use  of 
Treated  Timbers,  728;  Peeled  and  Treated  Loblolly  and  Shortleaf 
Pine  Gangway  Sets  Placed  in  Mines  of  Philadelphia  &  Reading  Coal 
&  Iron  Co.,  Table,  728;  Summary,  729. 

Steel  and  Masonry  Supports.— Iron  and  Steel  Props,  730;  Cylindrical  Cast- 
iron  Props,  730;  Steel  H-Beam  Props,  730;  Cast-Iron  Posts  With 
I-Beam  Caps,  730;  Steel  Entry  Timbers,  730;  Standard  Forms,  730; 
Steel  Gangway  Timbers,  Table,  732;  Relative  Cost  of  Steel  and  Wood 
Timbering,  733;  Advantages  of  Steel  Timbering,  735;  Preservation  of 
Steel  Mine  Timbers,  735;  Masonry  and  Iron  Shaft  Linings,  735; 
Tubbing,  736;  Steel  and  Concrete  Shaft  Linings,  737;  Steel  Sets,  737; 
Steel  Buntons,  738;  Concrete  and  Steel  Shaft  Linings,  738. 

HOISTING 
General.— 739. 

Hand-  and  Horse-power  Hoists.— 739. 

Steam-Power    Hoisting    Engines. — Second-Motion,    or    Geared,     Hoisting 
Engines,  740;  First- Motion,  or  Direct- Acting,  Hoisting  Engines,  741. 
Hoisting  Engines  Using  Other  Power  Than  Steam. — Compressed-Air  Hoist- 
ing Engines,  741;  Gasoline,  741;  Hydraulic,  742;  Electric,  742. 

Conical  Drums, 
ting  System, 

„  _. ,  .        , „ ,  .JO;  Monopol 

System,  751. 


CONTENTS  xxi 

Calculations  for  First-Motion  Hoisting  Engines.— General  Considerations, 
751;  Forces  and  Moments  in  Hoisting,  Table,  755. 

Calculations  for  Second-Motion  Hoisting  Engines. — Standard  Sizes  of 
Second- Motion  Hoisting  Engines,  Table,  757;  Dimensions,  758. 

HAULAGE 

Resistances  to  Haulage. — Total  Resistance,  758;  Due  to  Friction,  758;  Due  to 
Curvature,  759;  Due  to  Grade,  760;  Grade  Equivalents,  Table,  761; 
Resistance  Due  to  Inertia,  762. 

Trackwork.— Choice  of  Grade,  762;  Curvature,  763;  Rule,  763;  Rail  Eleva- 
tion, Table,  764;  Table  of  Rails  and  Accessories,  764-767;  Gauge  of 
Track,  765;  Rails,  766;  Weight  of  Rails,  in  Tons  of  2,240  Lb.,  Required 
to  Lay  1,000  Ft.  Single  Track,  Table,  768;  Ties,  768;  Sizes  and  Quan- 
tities of  Spikes,  Table,  769;  Number  of  Track  Bolts  in  a  Keg  of  200 
Lb.,  Table,  769;  Spaces  Between  Ends  of  Rails,  Table,  769;  Feet, 
Board  Measure,  in  Mine  Ties  of  Various  Lengths,  Table,  770;  Number 
of  Ties  per  1,000  Ft.,  and  per  Mile  of  Track,  Table,  770;  Entry 
Switches,  770;  Frogs,  771;  Room  and  Branch  Switches,  771;  Diamond 
Switch,  773;  Notes  on  Tracklaying,  773. 

Animal  Haulage. — Selection  of  Stock,  775;  Feeding  Mules,  775;  Care,  776; 
Work,  777;  Cost  of  Mule  Haulage,  777;  Safe  Grade,  778. 

Self-Acting  Inclines. — Tracks,  Switches,  Etc.,  779;  Rollers,  779;  Ropes, 
Drums,  Barneys,  Etc.,  779;  Grades  and  Their  Effects,  781;  Condi- 
tions Unfavorable  to  Use  of  Inclines,  781;  Calculations  for  Self-Acting 
Inclines,  781;  Profile  of  Inclines,  783. 

Jig  Planes. — Definition,  783;  Calculations,  784. 

Slopes  and  Engine  Planes. — Slopes  784;  Engine  Planes,  785. 

Endless-Rope  Haulage. — General,  785;  General  Arrangement  of  Systems, 
786;  Engines  and  Drums,  787;  Rope- Tightening  Arrangements,  788; 
Grips  and  Grip  Cars,  788;  Rollers  and  Sheaves,  789;  Side-Entry 
Haulage,  789;  Overhead,  790;  High-Speed,  or  Reversing,  790;  On 
Inclines,  791;  Calculations  for  Low-Speed,  Endless-Rope,  Haulage 
Engines,  791;  For  High-Speed,  791. 

Tail-Rope  Haulage. — General  Arrangement,  792;  Engines,  Drums,  Etc., 
793;  Sheaves,  Rollers,  Etc.,  794;  Comparison  of  Endless-  and  Tail- 
Rope  Haulage,  794;  Calculations,  795. 

Steam-Locomotive  Haulage. — Steam  Mine  Locomotives,  795;  Power  of 
Steam  Locomotives,  795;  Dimensions  of  Four- Wheel  Steam  Loco- 
motives, Table,  796;  Speed,  798;  Horsepower,  798. 

Compressed -Air  Haulage. — General,  798:  Simple,  or  Single-Stage,  Locomo- 
tives, 799;  Reheating  Compressed  Air,  799;  Compound,  or  Two-Stage, 
Locomotives,  799;  Dimensions  of  Single-Stage  Compressed- Air 
Locomotives,  Table,  800;  Dimensions  of  Two-Stage  Compressed- 
Air  Locomotives,  801;  Table,  802;  Tractive  Power,  803;  Locomotive 
Storage  Tanks,  803;  Stationary  Storage,  804:  Standard  Steam  and 
Extra-Strong  Pipe  Used  for  Compressed-Air  Haulage  Plants,  Table, 
805;  Pipe  Lines  and  Charging  Stations,  805;  Air  Compressors  for 
Haulage  Plants,  806;  Horsepower  Necessary  to  Compress  100  Cu.  Ft. 
of  Free  Air,  Table,  807. 

Gasoline -Motor  Haulage. — Construction  of  Gasoline  Locomotives,  807; 
Hauling  Capacity  and  Fuel  Requirements,  808;  Cost,  809;  Compari- 
son of  Gasoline  and  Other  Types  of  Haulage  Motors,  810;  Analyses 
of  Mine  Air  as  Affected  by  Exhaust  of  Gasoline  Locomotives,  Table, 
811;  Volume  of  CO  and  CO2  Discharged  by  Gasoline  Locomotives, 
in  Cubic  Feet  per  Minute,  Table,  812;  Purification  of  the  Exhaust, 
814. 

Electric-Locomotive  Haulage. — General  Considerations,  815;  Advantages 
and  Disadvantages,  815;  Current  and  Voltage,  816;  Electric  Genera- 
tors 816;  Classes  of  Electric  Locomotives,  816;  Wiring  for  Electric 
Haulage,  816;  Arrangement  of  Power  Lines,  816;  Shape  of  Trolley 
Wire,  816;  Location  of  Wires,  817;  Trolley  Frogs,  817;  Resistance  of 
Steel  Rails,  817;  Sizes  of  Locomotives,  Rails,  and  Bonds,  Table,  818; 
Resistance  of  Steel  Rails,  Table,  818;  Bonding,  818;  Cross-Bonding, 


xxii  .  CONTENTS 

819;  Feeders,  819;  Sizes  of  Wires  for  Three-Phase  Transmission  Serv- 
ice, Table,  821;  Voltages  Advisable,  Table,  821;  Direct-Current  Loco- 
motives, 822;  Number  and  Arrangement  of  Motors,  822;  Construction 
of!  Motors,  822;  Controllers,  823;  Frames,  823;  Wheels  and  Jour- 
nals, 823;  Brakes,  824;  Trolleys,  824;  Headlights,  824;  Capacity  of 
Locomotives,  824;  Selection  of  Motors,  825;  Tandem  Locomotives, 
826;  Cable-Reel  Locomotives,  826;  Crab  Locomotives,  827;  Combina- 
tion Cable-Reel  and  Crab  Locomotives,  827;  Rack-Rail  Locomotives, 
827;  Operation  of  Electric  Locomotives,  828;  Troubles  of  Electric 
Locomotives,  828;  Alternating-Current  Locomotives,  830;  Storage- 
Battery  Locomotives,  830. 

VENTILATION  OF  MINES 

Chemical  and  Physical  Properties  of  Gases. — Chemistry,  831;  Matter  and  Its 
Divisions,  831;  Classes  of  Matter,  831;  Forms  of  Matter,  831;  Changes 
in  Matter,  832;  Symbols  and  Formulas,  832;  Atomicity  of  Elements, 
832;  Chemical  Reactions,  832;  Chemical  Equations,  832;  Atomic 
Weight,  833;  Table  of  the  Elements  With  Their  Symbols  and  Atomic 
Weights,  833;  Molecular  Weight,  834;  Formulas  and  Molecular 
Weights  of  Common  Gases,  Table,  834;  Percentage  Composition,  834; 
Weights  of  Substances  Concerned  in  Reactions,  834;  Volumes  of  Gases 
Concerned  in  Reactions,  835;  Volumes  of  Gases  When  Burned  in  Air, 
835;  Weight  and  Volume  of  Gases  in  Reactions,  836;  Physics  of  Gases, 
836;  Avogadro's  Law,  836;  Density  of  Gases,  836;  Density  at  32°  F.  and 
29.92  In.  of  Mercury,  Table,  837:  Specific  Gravity,  Weight,  and  Volume 
of  Gases  at  32°  F.  and  29.92  In.  of  Mercury,  Table,  837;  Atmos- 

gheric  Pressure,  838;  Measurement  of  Atmospheric  Pressure,  838; 
quivalent  Heights  of  Columns  of  Air,  Water,  and  Mercury,  Table, 
838;  Corresponding  Mercury  and  Air  Columns,  and  Pressure  per 
Square  Foot  for  Each  Inch  of  Water  Column,  Table,  838;  Water 
Column,  and  Pressure  per  Square  Foot  for  Each  Inch  of  Mercury 
Column,  Table,  839;  Barometers,  839;  Relation  Between  Volume  and 
Temperature  of  Gases,  840;  Between  Volume  and  Pressure,  840; 
Between  Volume,  Temperature,  and  Pressure,  840;  Between  Weight, 
Temperature,  and  Pressure,  841;  Weight  and  Volume  of  Air  and 
Gases,  841;  Volume  and  Weight  of  Air  at  Sea  Level  at  Different 
Temperatures,  Table,  842;  Diffusion  of  Gases,  842;  Rates  of  Diffusion 
and  Transpiration  of  Gases  Compared  to  Air,  Table,  843;  Occlusion 
and  Transpiration  of  Gases,  843;  Humidity,  843;  Gallons  of  Water 
in  100,000  Cu.  Ft.  of  Saturated  Air  at  Temperatures  From  —  20°  F. 
to  +  100°  F.,  Table,  844;  Psychrometers  or  Hygrometers,  844. 
Mine  Gases. — Atmospheric  and  Mine  Air,  845;  Composition  of  Pure  Air, 
Table,  845;  Mine  Air,  846;  Oxygen,  846;  Properties  and  Sources, 
846;  Effect  on  Life,  846;  On  Combustion,  847;  Composition  of  Resid- 
ual Atmospheres  That  Extinguish  Flame,  Table,  847;  Absorption  of 
Oxygen  by  Coal,  848;  Nitrogen,  848;  Properties  and  Sources,  848; 
Effectjfcn  Life,  848;  On  Combustion,  848;  Carbon  Dioxide,  848; 
Properties  and  Sources,  848;  Effect  on  Life,  849;  On  Combustion, 
850;  Explosive  Range  of  Mixtures  of  Methane  and  Carbon  Dioxide, 
Table,  850;  Blackdamp,  851;  Haldane's  Blackdamp  Indicator,  851; 
Carbon  Monoxide,  852;  Properties  and  Sources,  852;  Effect  on  Life, 
853;  Explosibility,  855;  Detection,  856;  Reaction  of  CO  on  PIClii, 
856;  Effect  on  Mice  and  Canaries,  857;  Per  Cent,  of  CO  in  Air 
Corresponding  to  Various  Percentages  of  Saturation  of  Blood  Solu- 
tion, Table,  858;  Methane,  859;  Properties  and  Sources,  859: 
Pressure  of  Occluded  Gas,  Table,  860;  Formation,  861;  Occurrence 
in  Mines,  861;  Effect  on  Life,  862;  Explosibility,  862;  Limiting 
Explosive  Mixtures  of  Various  Explosive  Gases  With  Air,  Table,  863; 
Firedamp,  864;  Coal  From  Face,  Naomi  Mine  (Gas  Coal,  Pittsburgh, 
Pa.,  District),  Table,  864;  Coal  From  Face,  No.  1  North  Shaft, 
Nanticoke,  Pa.  (Anthracite),  Table,  864;  Gases  Enclosed  in  the  Pores 
of  Coal  and  Evolved  in  a  Vacuum  at  212°  P.,  Table,  865;  Analyses 
of  Firedamp,  Table,  865;  Analyses  of  Firedamp  from  Blowers, 
Table,  866;  From  Feeders,  Table,  866;  Gases  From  An  Enclosed 
Area  in  an  Anthracite  Mine,  Table,  866;  Analyses  of  Firedamp,  Con- 
nellsville  Region,  Table,  867;  Analyses  of  Gas  From  Drill  Holes, 
Table,  867;  Combustion  Products  of  Methane,  867;  Products  of 


CONTENTS  xxiii 

Explosion  of  Methane  in  Air,  Table,  867;  Effect  of  Atmospheric 
Changes  on  Escape  of  Firedamp,  868;  Afterdamp,  869;  Detection  of 
Methane,  870;  The  Rarer  Mine  Gases,  870;  General  Considerations, 
870;  Ethane  and  Other  Paraffin  Gases,  870;  Ethylene  and  Other 
Olefin  Gases,  871;  Hydrogen,  871;  Acetylene,  871;  Hydrogen  Sul- 
phide, 871;  Sulphur  Dioxide,  872;  Nitric  Oxide  and  Nitrogen  Diox- 
ide. 872;  Effect  of  Heat  and  Humidity  on  Mine  Workers,  873. 
Safety  and  Of  her  Lamps. — Principle  and  Origin,  874;  Description,  874- 
Dates  of  Discovery,  874;  Principles,  874;  Early  Classification,  874; 
Approved  Lamps,  874;  Construction,  875;  Specifications,  875; 
Design,  875;  Materials,  875;  Gauzes,  875;  Glasses,  876;  Multiple 
Gauzes,  876;  Bonnets,  876;  Circulation  of  Air,  877;  Wick  Tubes, 
Wicks,  Etc.,  877;  Igniters,  or  Relighters,  for  Safety  Lamps,  878- 
Locks,  878;  Oils,  879;  Illuminating  Power,  S80;  Table,  880;  Testing 
for  Methane,  881;  Desirable  Features  in  Lamps  for  Testing  and  for 
General  Use,  881;  Testing  for  Gas,  882;  Height  of  Gas  Cap,  Table. 
882;  Care  of  Safety  Lamps,  883:  Cleaning,  883;  Assembling,  884- 
Failure,  884;  Relighting  Stations,  Lamp  Houses,  Etc.,  884;  Standard 
Types  of  Safety  Lamps,  884;  Davy,  884;  Stephenson,  886:  Clanny, 
886;  Evan  Thomas,  886;  Deflector,  887;  Bull's  Eye,  or  Mauchline, 
887;  Marsaut,  887;  Mueseler,  887;  Ashworth-Hepplewhite-Gray. 
887;  Wolf,  888;  Protector,  888;  Hailwood,  888;  Special  Types,  889- 
Clowes  Hydrogen,  889;  Stokes  Alcohol,  889;  Pieler,  890;  Chesneau, 
890;  Stuchlick  Acetylene,  891;  Tombelaine  Acetylene,  891;  Gas 


William's     Methanometer,     894;  Aitkin's     Indicator,     894;  Beard- 


Mackie  Sight  Indicator,  894;  Brigg's  Wire  Loop,  894;  Cuninghame- 
Cadbury  Indicator,  894;  Colored  Glass  Indicators,  895;  Forbes,  895; 
Firedamp  Whistle,  895;  Hardy  Indicator,  895;  Shaw  Gas- Testing 
Machine,  895;  Hanger  and  Pescheux  Gas-Signaling  Apparatus,  896; 
Low  Gas-Signaling  Apparatus,  896;  Electric  Safety  Lamps,  896; 
Points  of  PDanger,  896;  Types,  897;  The  Ceag  Lamp,  897;  Special 
Forms,  898;  Cap  Lamps,  898;  Charging  Stations,  899;  Acetylene 
Lamps,  900. 

Explosive  Conditions  in  Mines. — Causes,  900;  Derangement  of  Ventilating 
Current,  901;  Sudden  Increase  9f  Gas,  901;  Effect  of  Coal  Dust  in 
Mine  Workings,  901;  Humidifying  the  Air  Current,  902;  Hygrome- 
ters, 904;  Pressure  as  Affecting  Explosive  Conditions,  905;  Rapid 
Successi9n  of  Shots  in  Close  Workings,  906;  Quantity  of  Air  Required 
for  Ventilation,  906;  Quantity  Required  by  State  Laws,  906;  Quantity 
Required  for  Dilution  of  Mine  Gases,  906;  Quantity  Required  to  Pro- 
duce the  Necessary  Velocity  of  Current  at  the  Face,  907;  Elements  in 
Ventilation,  907;  Horsepower  or  Power  of  the  Current,  907:  Mine 
Resistance,  907;  Velocity  of  the  Air  Current,  907;  Relation  of  Power, 
Pressure,  and  Velocity,  907;  Measurement  of  Ventilating  Currents, 
907;  Of  Velocity,  908:  Water  Gauge,  908:  Calculation  of  Mine 
Resistance,  909;  Table  of  Various  Coefficients  of  Friction  of 
Air  in  Mines,  909;  Calculation  of  Power,  or  Units  of  Work  per 
Minute,  910;  The  Equivalent  Orifice,  910;  P9tential  Factor  of  a  Mine, 
910;  Table  of  Water  Gauges  for  Calculating  the  Amount  of  Air 
Required  for  Mine  Workings,  911;  Formulas,  913;  Variation  of  the 
Elements,  915;  Quantity  Produced  by  Two  or  More  Ventilators,  916. 

Distribution  of  Air  in  Mine  Ventilation. — General,  917;  Requirements  of 
Law  in  Regard  to  Splitting,  918;  Practical  Splitting  of  the  Air  Cur- 
rent, 918;  Natural  Division,  918;  Calculation  of 'Natural  Splitting, 
918;  Proportional  Division  of  the  Air  Current,  919;  Box  Regulator. 
919;  Door  Regulator,  920;  Calculation  of  Pressure  for  Box  Regula- 
tors, 920;  Size  of  Opening,  920;  Size  of  Opening  for  a  Door  Regulator, 
921;  Calculation  of  Horsepower  for  Box  Regulators,  921;  For  Door 
Regulators,  921;  Splitting  Formulas,  922. 

Methods  and  Appliances  in  the  Ventilation  of  Mines. — Ascensional  Ventila- 
tion, 925;  General  Arrangement  of  Mine  Plan,  925;  Natural  Ventila- 
tion, 925;  Ventilation  of  Rise  and  Dip  Workings,  926;  Influence  of 
Seasons,  926;  Furnace  Ventilation,  927;  Construction  of  a  Mine 


xxiv  CONTENTS 

Furnace,  927;  Air  Columns,  927;  Inclined  Air  C9lumns,  928;  Calcula- 
tion of  Ventilating  Pressure  in  Furnace  Ventilation,  928;  Calcula- 
tion of  Motive  Column  or  Air  Column,  928;  Influence  of  Furnace 
Stack,  929;  Mechanical  Ventilators,  929;  Fan  Ventilation,  929;  Disk 
Fans,  929;  Centrifugal  Fans,  930;  Exhaust  Fans,  930;  Force  Fans 
and  Blowers,  930;  Vacuum  System  of  Ventilation,  930:  Plenum 
System,  930;  Comparison  of  Vacuum  and  Plenum,  930;  Types  of 
Centrifugal  Fans,  931;  Nasmyth,  931;  Biram's  Ventilator,  931: 
Waddle,  932;  Schiele,  932;  Guibal,  932;  Murphy,  933;  Capell,  933; 
Sirocco  Fan,  933;  Direct-Connected  Engines,  934;  Other  Drives, 
934;  Method  of  Determining  Fan  Diameter,  934;  To  Ascertain  Fan 
Speed  Required,  934;  Horsepower  Needed,  934;  Size  of  Motor,  934; 
Evase  Stack,  934;  Maximum  Inlet  Velocity,  935;  Loss  at  Inlets,  935; 
Standard  Air,  935:  Inlet  Velocities,  935;  Special  Fans,  935:  Equiva- 
lent Orifice,  935;  Murgue's  Formula,  936;  Sullivan  Reversible  Fans, 
936;  Sullivan  Fans,  Sizes,  Weights,  Dimensions,  Table,  937;  Fan 
Ratings,  Tables,  938-940;  Table  of  Capacities,  941;  Position  of  Any 
Fan,  Etc.,  941;  Manometrical  Efficiency,  942-  Mechanical  Efficiency, 
942;  Fan  Construction,  942;  Size  of  Central  Orifice,  942;  Diameter  of 
Fan,  942;  Curvature  of  Blades,  943;  Tapered  Blades,  943;  Number 
of  Blades,  943;  Spiral  Casing,  944;  Evase  Chimney,  944;  High- 
Speed  and  Low-Speed  Motors,  944;  Fan  Tests,  944;  Conducting  Air 
Currents,  944;  Doors,  944;  Stoppings,  945;  Air  Bridges,  945;  Air 
Brattice,  945;  Curtains,  944. 

MINE  FIRES 

Means  of  Extinguishing. — Isolating  the  Section,  945;  Sealing  Off  Fires,  946; 

Stopping  Materials,  946;  Unsealing  After  the  Fire  Is  Out.  947. 
Spontaneous  Combustion.— Causes,  948;  Coal  Storage,  949. 

THE  PREPARATION  OF  COAL 

Crushing  Machinery.— Object,  949;  Cracking  Rolls,  949;  Corrugated 
Rolls,  950;  Disintegrating  Rolls  and  Pulverizers,  950;  Hammers,  950; 
Miscellaneous  Forms  of  Crushers,  951;  Sizing  and  Classifying 
Apparatus,  951;  Stationary  Screens,  Grizzlies,  Head-Bars,  or  Plat- 
form Bars,  951;  Shaking  Screens,  952;  Size  of  Mesh,  Table,  952; 
Revolving  Screens,  or  Trommels,  952;  Speed,  953;  Duty  of  Anthracite 
Screens,  953;  Revolving  Screen  Mesh  for  Anthracite,  953;  Hydraulic 
Classifiers,  953;  Jeffrey-Robinson  Coal  Washer,  953;  Scaife  Trough 
Washer,  954;  Jigs,  954;  Stationary  Screen  Jigs,  954;  Heberle  Gate, 
955;  Theory  of  Jigging,  955;  Equal  Settling  Particles,  955;  Table  of 
Equal  Settling  Factors  or  Multipliers,  956;  Interstitial  Currents,  or 
Law  of  Settling  Under  Hindered  Settling  Conditions,  956;  Interstitial 
Factors,  957;  Acceleration,  957;  Suction,  957;  Removal  of  Sulphur 
From  Coal,  957;  Preparation  of  Anthracite,  958;  Preparation  of 
Bituminous  Coal,  959:  Sizes,  959;  Method,  960;  Screening  Area,  961; 
Shaker  Screens  for  Small  Sizes,  961;  Screen  Feeders,  962;  Tipple 
Design,  962;  Washing  Bituminous  Coal,  962. 

Handling  of  Material. — Anthracite  Coal,  962:  Weights  and  Capacities  of 
Standard  Steel  Buckets,  Table,  963;  Elevating  Capacities  of  Malle- 
able Iron  Buckets,  Table,  963;  Conveying  Capacities  of  Flights  at  100 
Ft.  per  Min.,  Table,  963;  Horsepower  for  Bucket  Elevators,  Table, 
964;  Pitch  at  Which  Anthracite  Coal  Will  Run,  Table,  964;  Horse- 
powers for  Coal  Conveyors,  Table,  965;  Horizontal  Pressure  Exerted 
by  Bituminous  Coal  Against  Vertical  Retaining  Walls,  Table,  965; 
By  Anthracite,  Table,  966;  Cost  of  Unloading  Coal,  966;  Briqueting, 
967;  Machines,  967;  Briqueting  of  Fuel,  967;  Of  Flue  Dust,  968; 
Cubic  Feet  Occupied  by  2,000  Pounds  of  Various  Coals,  Table,  968. 

SAFETY  AND  FIRST  AID 

Rules  for  First-Aid  Corps.— 969:  Shock,  970;  Burns  and  Scalds,  970;  Heat 
Prostration,  970;  Convulsions,  970;  Artificial  Respiration,  Shafer 
Method,  970;  Sylvester  Method,  971;  Treatment  for  Electrical 
Shock,  972;  Rescue  From  Electrical  Contact,  972;  Fractures,  973; 
Drowning,  973. 

Method  of  Moving  Injured  Persons. — 973. 


CONTENTS  xxv 

MINE  SAFETY 

Safety    First. — Systematic    Timbering,    975;  Adequate    Supervision,    975; 

Premium  System  and  Company  Rules,  976;  Safeguarding  Machinery, 

978;  Protecting  from  Electricity,  980;  Failure  of  Machine  Parts,  980; 

Preventing    Mismanipulation    of    Controlling    Devices,    980;  Safety 

Practices  of  the  H.  C.  Frick  Coke  Co.,  982. 
Mine-Rescue  Work. — Organization,  984;  First  Steps,  984;  Reversing  the 

Air  Current,  985;  Work  of  Recovery,  985. 
Mine-Rescue   Apparatus. — Breathing  Apparatus,   986;  Self   Rescuer,   987; 

Resuscitation  Apparatus,  987. 

NATURAL    SINES,    COSINES,    TANGENTS,    AND    COTANGENTS 
Explanation  of  Tables.— 989. 
Tables  of  Natural  Sines  and  Cosines, — 991-999. 
Tables  of  Natural  Tangents  and  Cotangents.— 1000-1008. 

LOGARITHMIC  TABLES 

Explanation  of  Tables. — 1009;  Common  Logarithms  of   Numbers,   Table, 

1009. 

Tables  of  Logarithms  of  Numbers.— 1010-1027. 
Tables  of  Logarithms  of  Trigonometric  Functions. — 1028-1072. 

TRAVERSE  TABLES 
Directions  for  Use.— 1073. 

Tables  of  Latitudes  and  Departures.— 1074-1080. 
Tables  of  Squares,  Cubes,  Square  and  Cube  Roots,  Circumferences,  and 

Areas.— 1081-1096. 
Tables  of  Circumferences  and  Areas  of  Circles  From  ^4  to  100. — 1097-1101. 

GLOSSARY  OF  MINING  TERMS 
Explanation. — 1101. 
Glossary.— 1102-1149. 
Index.— 1151-1172. 


The  Coal  Miners5  Pocketbook 

WEIGHTS  AND  MEASURES 


LINEAR  MEASURE 

Immediately  following  each  table  of  weights  or  of  measures  is  given  a  table 
of  equivalents  showing  the  relation  existing  between  the  different  denomina- 
tions. All  figures  on  the  same  horizontal  line  are  of  equal  or  equivalent  value. 

The  United  States  unit  of  length,  of  which  unit  all  other  denominations 
are  multiples  or  submultiples,  is  the  yard,  originally  derived  from  the  Imperial 
yard  of  Great  Britain.  Since  1893,  the  United  States  Bureau  of  Standards 
has  been  authorized  to  derive  the  yard  from  the  meter,  using  the  relationship 

established  by  Congress  in  the  act  of  July  28,  1866,  viz.,  1  yard  =  ^r^  meter. 

12  inches  (in.) =1  foot ft. 

3  feet =1  yard yd. 

5.5  yards =1  rod rd. 

40  rods =1  furlong fur. 

8  furlongs =1  mile mi. 

in.  ft.             yd.             rd.            fur.           mi. 

1  -  .083333  =  .027778  =  .005051  =  .000126  =  .000016 

12  =  1  =  .333333  =  .060606  =  .001515  =  .000189 

36=  3=             1  =  . 181818  =  .004545  =  .000568 

198=  16.5=         5.5=             1  =  . 025000  =  .003 125 

7,920=  660=         220=          40=             1  =  . 125000 

63,360=  5,280=      1,760=        320=            8=             1 

The  rod  of  16.5  ft.,  and  variously  known  as  the  perch  or  pole,  is  the  same  as 
in  surveyor's  measure.  The  furlong  is  now  no  longer  used. 

The  land  league  of  3  statute  mi.  is  15,840  ft.;  the  nautical,  or  marine,  league 
of  3  geographical  mi.  is  18,240  ft. 

The  nautical,  marine,  or  geographical  mile  is  the  &  part  of  1°  of  a  great 
circle  of  a  sphere  whose  surface  is  equal  to  the  surface  of  the  earth.  This  is 
commonly  taken  as  6,080  ft.,  but  is  more  accurately  6,080.26  ft.,  and  is 
equivalent  to  1.1516  stat.  mi.  One  statute  mile  equals  .8684  naut.  mi. 

The  fathom  of  6  ft.  is  used  at  sea  in  measuring  depths  of  water,  and  some 
times  (England)  in  giving  depths  of  mine  shafts. 

The  pace  is  commonly  3  ft.     The  U.  S.  military  pace  is  30  in. 

SURVEYOR'S  LINEAR  MEASURE 

The  surveyor's  linear  measure  is  no  longer  in  common  use  but  its  denomi- 
nations are  found  in  descriptions  of  the  boundaries  of  farms  taken  from  old 
deeds.  Lengths  of  land  lines  are  now  measured  and  recorded  in  feet  and 
decimal  parts  thereof. 

7.92  inches  (in.) =  1  link li. 

25  links. . .    =  1  rod  (16.5  ft.) rd. 

4  rods. .' =1  chain  (66  ft.) ch. 

80  chains =1  mile mi. 


2  WEIGHTS:  A.ND  MEASURES 

'in.     '  W.   '   rd.'     ch.     mi. 

1  ~  .126263  -  .005051."  .001263  =  .000016 

7.92=     1^:040000  =  .010000  =.000125 

198=     25=      1  =  . 250000  =  .003125 

792=    100=     4=     1  =  . 012500 

63,360=  8.000=    320=    80=     1 

Surveyors  commonly  use  the  engineer's  chain  of  50  or  100  ft.,  the  feet  being 
divided  into  tenths  and  hundredths. 

The  annexed  scale  shows  on  one  side,  proportionately  reduced,  a  scale  of 
tenths.  On  the  other,  a  scale  of  twelfths,  corresponding  to  inches.  To 
reduce  inches  to  decimal  parts  of  a  foot,  find  the  number  of  inches  and  frac- 
tional parts  thereof  on  the  side  marked  "inches."  Opposite,  on  the  scale  of 


ft"  |  

• 

*    •   *    i    fi 

,,,,£,,,, 

rn.^,....,^. 

V,,,^^/IMI| 

1  r^J  i 

"""i111 

i  '  "  '  i  '  M  ]  M 

^" 

1  "i1  "  'A 

tenths,  will  be  found  the  decimal  part  of  a  foot.  Thus,  if  it  is  wanted  to  find 
the  decimal  part  of  a  foot  represented  by  7^  in.,  find  the  mark  corresponding 
to  7$  in.  on  the  side  marked  "inches."  Opposite  this  mark  may  be  read 
6  tenths,  2  hundredths,  and  5  thousandths;  or,  expressed  decimally,  .625. 
This  scale  may  be  laid  out,  full  size,  upon  stiff  cardboard  and  will  be  found  very 
useful  in  figuring  lengths  in  construction  work. 

DECIMALS  OF  AN  INCH  AND  MILLIMETERS  FOR  EACH  1-64TH  IN. 


64ths  of 
an  Inch 

Decimal 
Parts  of 
lln. 

Millimeters 

64ths  of 
an  Inch 

Decimal 
Parts  of 
1  In. 

Millimeters 

A 

.015625 

.397 

i 

.515625 

13.097 

*"* 

.031250 

.794 

.531250 

13.494 

_s^ 

.046875 

1.191 

A 

.546875 

13.891 

A 

.062500 

1.588 

! 

.562500 

14.288 

JL 

.078125 

1.984 

1 

.578125 

14.684 

A 

.093750 

2.381 

1 

.593750 

15.081 

J_ 

.109375 

2.778 

1 

1 

.609375 

15.478 

.125000 

3.175 

•• 

.625000 

15.875 

.140625 

3.572 

.640625 

16.272 

i 

.156250 

3.969 

. 

.656250 

16.669 

H 

.171875 

4.366 

.671875 

17.066 

JL 

.187500 

4.763 

.687500 

17.463 

if 

.203125 

5.159 

.703125 

17.859 

A 

.218750 

5.556 

• 

.718750 

18.256 

is. 

.234375 

5.953 

j 

i 

.734375 

18.653 

i 

.250000 

6.350 

.750000 

19.050 

H 

.265625 

6.747 

.765625 

19.447 

& 

.281250 

7.144 

.781250 

19.844 

y 

.296875 

7.541 

.796875 

20.241 

/ 

.312500 

7.938 

.812500 

20.638 

.328125 

8.334 

.828125 

21.034 

i 

.343750 

8.731 

.843750 

21.431 

i 

.359375 

9.128 

.859375 

21.828 

i 

.375000 

9.525 

.875000 

22.225 

i 

.390625 

9.922 

1 

.890625 

22.622 

1 

.406250 

10.319 

I 

.906250 

23,019 

& 

.421875 

10.716 

5 

.921875 

23.416 

I 

.437500 

11.113 

.937500 

23.813 

* 

.453125 

11.509 

.953125 

24.209 

& 

.468750 

11.906 

.968750 

24.606 

i 

• 

.484375 

12.303 

.984375 

25.003 

* 

.500000 

12.700 

1.000000 

25.400 

WEIGHTS  AND  MEASURES  3 

MEASURES  OF  SURFACE 

SQUARE  MEASURE 

144  square  inches  (sq.  in.) =1  square  foot sq.  ft. 

9  square  feet =1  square  yard sq.  yd. 

30.25  square  yards -  1  square  rod sq.  rd. 

40  square  rods =1  rood rood. 

4  roods  (160  sq.  rd.) =1  acre A.  or  ac. 

640  acres=  1  section =1  square  mile sq.  mi. 

sq.  in.  sq.ft.  sq.  yd.         sq.  rd.         rood          A.  sq.  mi. 

1=       .006944=     .000772  =  .000026 

144=  1=     .111  111  =  .003673  =  .000092  =  .000023 

1 ,296  =  9  =  1  =  .033058  =  .000826  =  .000207 

39,204=        272.25=         30.25=  1  =  .025000  =  .006250  =  .000009 

1,568,160=         10,890=         1,210=  40=  1  =  . 250000  =  .000391 

6,272,640=         43,560=         4,840=         160=  4=  1  =  . 001563 

4,014,489,600  =  27,878,400  =  3,097,600  =  102,400=     2,560=        640=  1 

The  square  rod  is  also  known  as  the  perch.  The  rood,  equal  to  40  sq.  rd., 
or  1  A.,  is  obsolete.  640  A.  make  one  section;  320  A.,  one  half-section;  160  A., 
a  quarter  section,  etc.  36  sections,  or  23,040  A.,  make  1  township  (twp.). 
The  areas  of  small  tracts  of  land,  such  as  city  lots,  are  usually  given  in  square 
feet  and  decimals  thereof;  of  larger  bodies  of  land,  in  acres  and  decimals  of  an 
acre.  A  square  measuring  208.71  ft.,  or  69.57  yd.,  on  each  side  contains 
1  A. 

Squares  of  100  sq.  ft.  or  of  1  sq.  yd.  are  used  in  estimating  various  kinds  of 
work,  such  as  roofing,  lathing,  plastering,  etc.  It  is  advisable  to  specify  the 
size  of  the  square  in  all  contracts. 

SURVEYOR'S  SQUARE  MEASURE 

The  surveyor's  square  measure  is  practically  obsolete  in  the  United  States, 
although  its  denominations  are  commonly  found  in  old  deeds  in  describing  the 
area  of  lands.  As  lengths  of  land  lines  are  now  generally  measured  in  feet, 
tenths,  and  hundredths,  areas  are  commonly  expressed  in  square  feet  or  in 
acres  and  in  decimal  parts  thereof. 

62.7264  square  inches  (sq.  in.) =1  square  link sq.  li. 

625  square  links =1  square  rod sq.  rd. 

16  square  rods =1  square  chain sq.  ch. 

10  square  chains =1  acre A.  or  ac. 

640  acres  =  1  section =1  square  mile sq.  mi. 

36  square  miles =1  township tp.  or  twp. 

sq.  in.  sq.  li.       sq.  rd.       sq.  ch.           A.          sq.  mi. 

1=  .015942  =  .000026  =  .000002 

62.7264=  1  =  . 001600  =  .000100  =  .000010 

39 ,204  =  625  =     1  =  .062500  =  .006250  =  .000009 

627,264=  10,000=     16=     1  =  . 100000  =  .000156 

6,272,640=  100,000=    160=     10=      1  =  . 001563 

4,014,489,600  =  64,000,000  =  102,400=  6,400=    640=  1 

1  township  =  36  sq.  mi.  =  23,040  A.  =-230,400  sq.  ch.  =  3.686,400  sq.  rd. 
«  2,304 ,000,000  sq.  li.  =  144,521,625,600  sq.  in. 


MEASURES  OF  WEIGHT 

The  United  States  standard  of  weight  is  the  troy  pound  of  Great  Britain 
from  which  the  avoirdupois  pound  is  derived  in  the  ratio  1  pound  avoirdupois 
=  LP^  pound  troy.  Since  1893,  the  United  States  Bureau  of  Standards  has 
been  authorized  to  derive  the  pound  avoirdupois  from  the  kilogram,  using  the 


4  WEIGHTS  AND  MEASURES 

relationship  established  by  Congress  in  the  act  of  July  28,  1866,  viz.,  1  pound 


avoirdupois  = 


kilogram.     The  weight  of  the  grain  in  the  troy,  apothe- 


2.2046 
caries',  and  avoirdupois  pounds,  is  the  same. 

TROY  WEIGHT 

Troy  weight  is  used  in  weighing  gold  and  silver. 

24  grains  (gr.) =  1  pennyweight dwt. 

20  pennyweights =1  ounce oz. 

12  ounces =  1  pound Ib. 

gr.          dwt.  oz.  Ib. 

1  =  .041667  =  .002083  =  .000174 

24=  1  =  .  050000  =.004167 

480=  20=  1  =  . 083333 

5,760=        240=  12=  1 

1  oz.  troy  =  1  oz.  apothecaries'  =  1.09714  oz.  avoirdupois 
1  Ib.  troy  =  1  Ib.  apothecaries'  =    .82286  Ib.  avoirdupois 
1  oz.  avoirdupois  =    .91146  oz.  troy  or  apothecaries' 
1  Ib.  avoirdupois  =  1.21528  Ib.  troy  or  apothecaries' 

APOTHECARIES'  WEIGHT 

20  grains  (gr.) =1  scruple sc. 

3  scruples .\=  1  dram dr. 

8  drams =1  ounce oz. 

12  ounces =  1  pound Ib. 

DECIMALS  OF  A  FOOT  FOR  EACH  1-64TH  IN. 


Inch 

0" 

"l" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

0 

0 

.0833 

.1667 

.2500 

.3333 

.4167 

.5000 

.5833 

.6667 

.7500 

.8333 

.9167 

.0013 

.0846 

.1680 

.2513 

.3346 

.4180 

.5013 

.5846 

.6680 

.7513 

.8346 

.9180 

A 

.0026 

.0859 

.1693 

.2526 

.3359 

.4193 

.5026 

.5859 

.6693 

.7526 

.8359 

.9193 

j_ 

.0039 

.0872 

.1706 

.2539 

.3372 

.4206 

.5039 

.5872 

.6706 

.7539 

.8372 

.9206 

A 

.0052 

.0885 

.1719 

.2552 

.3385 

.4219 

.5052 

.5885 

.6719 

.7552 

.8385 

.9219 

JL 

.0065 

.0898 

.1732 

.2565 

.3398 

.4232 

.5065 

.5898 

.6732 

.7565 

.8398 

.9232 

A 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

.5078 

.5911 

.6745 

.7578 

.8411 

.9245 

J_ 

.0091 

.0924 

.1758 

.2591 

.3424 

.4258 

.5091 

.5924 

.6758 

.7591 

.8424 

.9258 

1 

.0104 

.0937 

.1771 

.2604 

.3437 

.4271 

.5104 

.5937 

.6771 

.7604 

.8437 

.9271 

» 

.0117 

.0951 

.1784 

.2617 

.3451 

.4284 

.5117 

.5951 

.6784 

.7617 

.8451 

.9284 

5 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

.5130 

.5964 

.6797 

.7630 

.8464 

.9297 

|i 

.0143 

.0977 

.1810 

.2643 

.3477 

.4310 

.5143 

.5977 

.6810 

.7643 

.8477 

.9310 

JL 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

.5156 

.5990 

.6823 

.7656 

.8490 

.9323 

|| 

.0169 

.1003 

.1836 

.2669 

.3503 

.4336 

.5169 

.6003 

.6836 

.7669 

.8503 

.9336 

& 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349 

.5182 

.6016 

.6849 

.7682 

.8516 

.9349 

8 

.0195 

.1029 

.1862 

.2695 

.3529 

.4362 

.5195 

.6029 

.6862 

.7695 

.8529 

.9362 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

.5208 

.6042 

.6875 

.7708 

.8542 

.9375 

H 

.0221 

.1055 

.1888 

.2721 

.3555 

.4388 

.5221 

.6055 

.6888 

.7721 

.8555 

.9388 

J» 

.0234 

.1068 

.1901 

.2734 

.3568 

.4401 

.5234 

.6068 

.6901 

.7734 

.8568 

.9401 

if 

.0247 

.1081 

.1914 

.2747 

.3581 

.4414 

.5247 

.6081 

.6914 

.7747 

.8581 

.9414 

JL 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

.5260 

.6094 

.6927 

.7760 

.8594 

.9427 

fi 

.0273 

.1107 

.1940 

.2773 

.3607 

.4440 

.5273 

.6107 

.6940 

.7773 

.8607 

.9440 

ii 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

.5286 

.6120 

.6953 

.7786 

.8620 

.9453 

H 

.0299 

.1133 

.1966 

.2799 

.3633 

.4466 

.5299 

.6133 

.6966 

.7799 

.8633 

.9466 

I 

.0312 

.1146 

.1979 

.2812 

.3646 

.4479 

.5312 

.6146 

.6979 

.7812 

.8646 

.9479 

II 

.0326 

.1159 

.1992 

.2826 

.3659 

.4492 

.5326 

.6159 

.6992 

.7826 

.8659 

.9492 

33 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

.5339 

.6172 

.7005 

.7839 

.8672 

.9505 

H 

.0352 

.1185 

.2018 

.2852 

.3685 

.4518 

.5352 

.6185 

.7018 

.7852 

.8685 

.9518 

~lS 

.0365 

.1198 

.2031 

.2865 

.3698 

.4531 

.5365 

.61-98 

.7031 

.7865 

.8698 

.9531 

II 

.0378 

.1211 

.2044 

.2878 

.3711 

.4544 

.5378 

.6211 

.7044 

.7878 

.8711 

.9544 

M 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

.5391 

.6224 

.7057 

.7891 

.8724 

.9557 

U 

.0404 

.1237 

.2070 

.2904 

.3737 

.4570 

.5404 

.6237 

.7070 

.7904 

.8737 

.9570 

1 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

WEIGHTS  AND  MEASURES  5 

gr.   sc.    dr.      oz.     lb. 

1  =  .050  =  .016667  =>  .002083  =  .000174 

20=   1  =  . 333333  =  .041667  =  .003472 

60=   3=     1  =  .  125000  =  .010417 

480=  24=     8=     1  =  . 083333 

5,760=  288=    96=     12=     1 

For  equivalents  in  troy  and  apothecaries'  weights,  see  under  the  former. 

AVOIRDUPOIS  WEIGHT 

SHORT  TON 

27.34375  grains  (gr.) =1  dram dr. 

16  drams =1  ounce oz. 

16  ounces =1  pound lb. 

100  pounds =1  hundredweight cwt. 

20  hundredweight  \                t  + 
2,000  pounds  / =  lton... 

gr.  dr.  oz.  lb.  cwt. 

1  =  .036571  =  .002286  =  .000143  =  .000001 
27.34375  =  1  =  .062500  =  .003906  =  .000039  =  .000002 

437.5  =  16  =  1  =  .062500  =  .000625  =  .00003 1 

7,000=         256=  16=  1  =  . 010000  =  .000500 

700,000=   25,600=      1,600=         100=  1  =  . 050000 

14,000,000  =  512,000=   32,000=     2,000=          20=  1 

The  ton  of  2,000  lb.  is  the  trade  standard  of  the  United  States,  except  in 
transactions  involving  anthracite  (in  Pennsylvania)  and  certain  iron  and  steel 
products  in  bulk.  A  hundredweight  is  sometimes  known  as  a  quintal  and  is 
not  uncommonly  used  among  fishermen.  The  dram  is  practically  obsolete. 

DECIMALS  OF  A  FOOT  FOR  EACH  1-64TH  IN. 


..T. 
T. 


Inch 

0" 

1" 

2" 

3" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

11" 

i 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

.5417 

.6250 

.7083 

.7917 

.8750 

.9583 

|i 

.0430 

.1263 

.2096 

.2930 

.3763 

.4596 

.5430 

.6263 

.7096 

.7930 

.8763 

.9596 

Jr 

.0443 

.1276 

.2109 

.2943 

.3776 

.4609 

.5443 

.6276 

.7109 

.7943 

.8776 

.9609 

M 

.0456 

.1289 

.2122 

.2956 

.3789 

.4622 

.5456 

.6289 

.7122 

.7956 

.8789 

.9622 

TS 

.0469 

.1302 

.2135 

.2969 

.3802 

.4635 

.5469 

.6302 

.7135 

.7969 

.8802 

.9635 

fl 

.0482 

.1315 

.2148 

.2982 

.3815 

.4648 

.5482 

.6315 

.7148 

.7982 

.8815 

.9648 

M 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

.5495 

.6328 

.7161 

.7995 

.8828 

.9661 

i» 

.0508 

.1341 

.2174 

.3008 

.3841 

.4674 

.5508 

.6341 

.7174 

.8008 

.8841 

.9674 

1 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.5521 

.6354 

.7188 

.8021 

.8854 

.9688 

: 

x 

.0534 

.1367 

.2201 

.3034 

.3867 

.4701 

.5534 

.6367 

.7201 

.8034 

.8867 

.9701 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.5547 

.6380 

.7214 

.8047 

.8880 

.9714 

.0560 

.1393 

.2227 

.3060 

.3893 

.4727 

.5560 

.6393 

.7227 

.8060 

.8893 

.9727 

.0573 

.1406 

.2240 

.3073 

.3906 

.4740 

.5573 

.6406 

.7240 

.80-73 

.8906 

.9740 

i 

.0586 

.1419 

.2253 

.3086 

.3919 

.4753 

.5586 

.6419 

.7253 

.8086 

.8919 

.9753 

i 

.0599 

.1432 

.2266 

.3099 

.3932 

.4766 

.5599 

.6432 

.7266 

.8099 

.8932 

.9766 

h 

.0612 

.1445 

.2279 

.3112 

.3945 

.4779 

.5612 

.6445 

.7279 

.8112 

.8945 

.9779 

i 

.0625 

.1458 

.2292 

.3125 

.3958 

.4792 

.5625 

.6458 

.7292 

.8125 

.8958 

.9792 

% 

.0638 

.1471 

.2305 

.3138 

.3971 

.4805 

.5638 

.6471 

.7305 

.8138 

.8971 

.9805 

•i 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.5651 

.6484 

.7318 

.8151 

.8984 

.9818 

i 

.0664 

.1497 

.2331 

.3164 

.3997 

.4831 

.5664 

.6497 

.7331 

.8164 

.8997 

.9831 

i 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

.5677 

.6510 

.7344 

.8177 

.9010 

.9844 

1 

.0690 

.1523 

.2357 

.3190 

.4023 

.4857 

.5690 

.6523 

.7357 

.8190 

.9023 

.9857 

i 

• 

.0703 

.1536 

.2370 

.3203 

.4036 

.4870 

.5703 

.6536 

.7370 

.8203 

.9036 

.9870 

M 

.0716 

.1549 

.2383 

.3216 

.4049 

.4883 

.5716 

.6549 

.7383 

.8216 

.9049 

.9883 

1 

.0729 

.1562 

.2396 

.3229 

.4062 

.4896 

.5729 

.6562 

.7396 

.8229 

.9062 

.9896 

1 

.0742 

.1576 

.2409 

.3242 

.4076 

.4909 

.5742 

.6576 

.7409 

.8242 

.9076 

.9909 

j 

I 

.0755 

.1589 

.2422 

.3255 

.4089 

.4922 

.5755 

.6589 

.7422 

.8255 

.9089 

.9922 

1 

.0768 

.1602 

.2435 

.3268 

.4102 

.4935 

.5768 

.6602 

.7435 

.8268 

.9102 

.9935 

I 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.5781 

.6615 

.7448 

.8281 

.9115 

.9948 

| 

.0794 

.1628 

.2461 

.3294 

.4128 

.4961 

.5794 

.6628 

.7461 

.8294 

.9128 

.9961 

\ 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.5807 

.6641 

.7474 

.8307 

.9141 

.9974 

J 

i 

.0820 

.1654 

.2487 

.3320 

.4154 

.4987 

.5820 

.6654 

.7487 

.8320 

.9154 

.9987 

l 

1.0000 

6  WEIGHTS  AND  MEASURES 

LONG  TON 
The  grains,  drams,  ounces,  and  pounds  are  the  same  as  in  the  short  ton. 

16  ounces =1  pound Ib. 

14  pounds =1  stone st. 

2  stones. =1  quarter qr. 

4  quarters =1  hundredweight cwt. 

20  hundredweight =  1  ton  (2,240  Ib.) T. 

oz.  Ib.  st.  qr.  cwt.  T. 

1  =  .062500  =  .004464  =  .002232  =  .000558  =  .000028 

16=      1  =  .071429  =  .035714  =  .008929  =  .000446 

224  =     14  =      1  =  .500000  = .  125000  =  .006250 

448=     28=     2=      1  =  . 250000  =  .012500 

1,792=    112=     8=     4=     1  =  .050000 

35,840=  2,240=    160=    80=    20=     1 

Short  tons  multiplied  by  1.12  equal  long  tons.  Long  tons  multiplied  by 
.892857  equal  short  tons.  The  long  ton  is  the  standard  in  Great  Britain  and 
colonies,  except  Canada,  but  its  use  in  the  United  States  is  limited.  The 
long  ton  is  used  in  estimating  custom  duties. 


MEASURES  OF  VOLUME 

1,728  cubic  inches  (cu.  in.) =1  cubic  foot cu.  ft. 

27  cubic  feet =1  cubic  yard. . ...  .cu.  yd. 

cu.  in.       cu.  ft.       cu.  yd. 
1  =  . 000579  =  .000021 
1,728=  1  =  . 037037    ' 

46,656=          27=  1 

A  cord  of  wood  is  128  cu.  ft.,  or  a  pile  8  ft.  long  and  4  ft.  high  when  cut  in 
4-ft.  lengths.  It  is  used  in  estimating  amounts  of  fire  and  pulp  wood,  tan- 
bark,  etc. 

A  ton  (2,240  Ib.)  of  Pennsylvania  anthracite,  when  broken  for  domestic 
use,  occupies  about  42  cu.  ft.  of  space;  bituminous  coal  about  46  cu.  ft.;  and 
coke,  about  88  cu.  ft. 

A  bushel  of  coal  is  80  Ib.  in  Kentucky,  Illinois,  and  Missouri;  76  Ib.  in  Penn- 
sylvania and  Montana;  and  70  Ib.  in  Indiana. 

Masonry. — A  perch  of  masonry  is  24.75  cu.  ft.,  or  is  a  section  of  wall  16.5  ft. 
(1  rd.  or  perch)  long,  1.5  ft.  thick,  and  1  ft.  high.  It  is  very  frequently  taken 
as  25  cu.  ft.  Methods  and  customs  of  estimating  masonry  vary  locally  and  it 
is  highly  advisable,  when  preparing  contract  specifications,  to  insert  in  the 
agreement,  upon  what  basis  the  measurements  are  to  be  made;  that  is,  if  by 
the  perch,  the  number  of  cubic  feet  therein.  Owing  to  the  confusion  in  the 
dimensions  of  the  perch,  the  term  is  falling  into  disuse,  and  contracts  specify 
measurements  either  in  cubic  feet  or  cubic  yards. 

Masonry  is  measured  solid,  no  deductions  being  made  for  corners,  which 
are  counted  twice,  or  for  openings  under  3  ft.  in  width.  This  is  the  custom 
of  the  trade  and  holds  in  law  unless  the  contract  specifies  differently.  Thus, 
a  foundation  wall  1  ft.  thick,  8  ft.  high,  and  with  outside  dimensions  of  10  ft. 
by  12  ft.,  and  with  one  door  opening  2  ft.  wide  and  8  ft.  high,  actually  contains 
[(12X2)  +  (10-1-1)X2]X8-(2X8)  =  304  cu.  ft.  On  the  trade  basis,  the 
door  opening  is  neglected  arid  the  four  side  walls  are  counted  at  their  total 
length  (2  of  12  ft.,  and  2  of  10  ft.),  and  the  wall  contains  [(12X2) +  (10X2)1 
X8  =  352  cu.  ft. 

Brickwork. — Brickwork  is  generally  estimated  by  the  thousand  bricks 
laid  in  the  wall,  but  measurements  by  the  cubic  foot  and  the  perch  are  also 
used.  When  making  calculations  of  the  volume  of  walls,  etc.,  to  allow  for 
mortar,  it  is  customary  to  add  J  in.  to  the  length  and  thickness  of  each  brick. 
The  following  data  will  be  useful  in  calculating  the  number  of  bricks  in  a  wall. 
For  each  superficial  foot  of  wall  4  in.  in  thickness  (the  width  of  one  brick), 
allow  7 5  bricks;  for  a  9-in.  wall  (the  width  of  two  bricks),  allow  15  bricks;  and 
so  on,  estimating  7£  bricks  for  each  additional  4  in.  in  thickness  of  wall.  If 
brickwork  is  estimated  by  the  cubic  yard,  allow  500  bricks  to  1  cu.  yd.  This 
figure  is  based  on  the  use  of  a  8J  in.  by  4  in.  by  2j  in.  brick,  with  mortar  joints 
not  over  f  in.  thick.  If  the  joints  are  i  in.  thick,  as  in  face  brickwork,  1  cu.  yd. 
will  require  about  575  bricks.  An  allowance  of  5%  should  be  made  for  waste 
in  breakage,  etc. 


WEIGHTS  AND  MEASURES  7 

Shipping.— The  gross  tonnage  of  a  ship  is  its  entire  internal  capacity,  cal- 
culated according  to  certain  rather  complicated  rules  laid  down  in  the  Revised 
Statutes  of  the  United  States.  The  net  tonnage  of  a  ship  is  obtained  by  deduct- 
ing from  the  gross  tonnage  the  space  given  over  to  engines,  coal,  quarters  for 
the  crew,  etc.;  that  is,  it  is  the  net  space  available  for  cargo  or  paying  load. 
Registered  tonnage  is  the  entire  internal  cubic  contents  of  the  vessel  divided  by 
100,  or  100  cu.  ft.  equals  1  registered  ton.  The  term  gives  no  idea  of  the  dimen- 
sions of  the  vessel,  and  is  merely  an  arbitrary  way  of  forming  some  conception 
of  its  relative  size. 

Displacement  is  the  weight  of  the  volume  of  water  displaced  by  the  hull  of 
a  vessel  and  is  often  confused  with  some  one  of  the  meanings  of  tonnage  just 
given.  The  displacement  of  a  ship  naturally  varies,  depending  on  the  weight 
of  cargo,  stores,  fuel,  etc.,  aboard.  Thus,  the  displacement  of  a  transatlantic 
liner  will  be  markedly  less  on  arriving  at  New  York  than  when  leaving 
England.  Displacement  is  frequently  calculated  at  a  normal,  or  standard, 
depth  of  water,  to  which  draft  the  ship  is  usually  loaded,  or  for  which  it  was 
designed;  from  this  is  derived  the  expression,  say,  "displacement  18,500  T.  on 
23  ft.  draft." 

For  the  purpose  of  calculating  vessel  freights,  estimating  stowage  capacity, 
etc.,  1  U.  S.  shipping  ton  equals  40  cu.  ft.  and  is  equivalent  to  32.143  U.  S.  bu., 
or  31.16  imp.  bu.  of  England.  The  British  shipping  ton  is  42  cu.  ft.  and  is 
equal  to  32.719  imp.  bu.,  or  33.75  U.  S.  bu. 

For  weights  of  various  materials  see  under  the  heading  Specific  Gravity. 

LIQUID  MEASURE 

By  act  of  Congress  the  standard  of  liquid  measure  is  the  gallon  of  231  cu.  in. 

1  gill gi 7.21875  cu.  in. 

4  gills =  1  pint pt 28.875  cu.  in. 

2  pints =1  quart qt 57.750  cu.  in. 

4  quarts =1  gallon  gal 231.000  cu.  in. 

31.5  gallons =1  barrel bbl 4.211  cu.  ft. 

2  barrels =1  hogshead  .  .hhd 8.422  cu.  ft. 

gi.  pt.        qt.         gal.           bbl.           hhd. 

1  =  .250  =  .125  =  .03125  =  .000992  =  .000496 

4=  1  =  . 500  =.12500  =  .003968  =  .001984 

8=  2=   1  =  . 25000  =  .007936  =  .003968 

32  =  8-=   4=     1  =  . 031746  =  .015873 

1,008=  252=  126=   31.5=      1  =  . 500000 

2,016=  504=  252=    63=     2=     1 

The  U.  S.  liquid  pint,  quart,  and  gallon  are  equal,  respectively,  to  .85937 
U.  S.  dry  pint,  quart,  and  gallon.  The  U.  S.  dry  pint,  quart,  and  gallon  are 
equal,  respectively,  to  1.16365  U.  S.  liquid  pint,  quart,  and  gallon. 

A  box  19 f  in.  long  on  each  edge  contains  1  bbl. 

In  approximate  calculations,  1  cu.  ft.  of  water  may  be  considered  equal  to 
7j  gal.,  and  1  gal.  as  weighing  8|  Ib. 

The  capacity  of  a  cylinder  in  U.  S.  liquid  gallons  =  square  of  the  diameter, 
in  inches X  height,  in  inches  X. 0034  (accurate  within  1  part  in  100,000). 

The  following  cylinders  contain  the  given  measures  very  closely: 


Diam.     Height 
Inches    Inches 


Gill If 

Pint 3* 

Quart 3£ 


Diam.  Height 

Inches  Inches 

Gallon 7  6 

8gal 14  12 

10  gal 14  15 


DRY  MEASURE 


By  act  of  Congress  the  standard  of  dry  measure  is  the  bushel  defined  as  a 
cylinder  18£  in.  in  diameter,  8  in.  deep,  and  containing  2,150.42  cu.  in. 


1  pint 

2  pints 

4  quarts 

2  gallons 

4  pecks  


pt 33.6003125  cu.  n 

1  quart. .  .qt. 67.200625  cu.  n 

268.8025  cu.  n 

537.605  cu.  n 

2,150.42  cu.  n 


1  gallon  .  .gal 

=1  peck. . .  .pk 

=1  bushel .  .bu 


8 


WEIGHTS  AND  MEASURES 


pt.      qt.      gal.       pk.          bu. 

1  =  .500  =  .125  =  .0625  =  .015625 

2=       1  =  . 250  =.1250  =  .031250 

8=      4  =       1  =  . 5000  =  .125000 

16=      8=       2=         1  =  .250000 

64=     32=      8=        4=  1 

The  standard  bushel  is  a  struck,  or  level  full,  bushel.  The  heaped  bushel 
is  approximately  equal  to  1J  struck  bu.,  the  cone,  or  heap,  being  not  less  than 
6  in.  in  height. 

The  standard  bushel  is  equal  to  1.24445,  or  approximately  lj,  cu.  ft. 
1  cu.  ft.  is  equal  to  .80356,  or  approximately  f ,  bu. 

A  cube  3.227  in.  on  an  edge  contains  1  pt.;  one  4.066  in.  on  an  edge,  1  qt.; 
one  6.454  in.  on  an  edge,  1  gal.;  one  8.131  in.  on  an  edge,  1  pk.;  and  one  12.908 
in.  on  an  edge,  1  bu. 

The  capacity  of  a  cylinder  in  U.  S.  bushels  =  square  of  diameter  in  inches 
X  height  in  inches  X. 0003652. 

There  appears  to  be  no  standard  barrel,  dry  measure,  although  one  of 
3  struck  bu.  is  frequently  recognized. 

The  relation  between  the  dimensions  of  the  units  of  dry  and  liquid  measure 
will  be  found  under  the  former. 

RELATION  BETWEEN  VOLUMES  AND  WEIGHTS  OF  WATER,  U.  S. 
LIQUID  MEASURE 

The  mass  of  a  given  volume  of  water,  such  as  1  cu.  ft.  or  1  gal.,  depends 
on  the  conditions  under  which  it  is  weighed,  being  less  if  weighed  in  air  than  in 
a  vacuum,  at  the  equator  than  at  the  poles,  at  sea  level  than  at  any  elevation 
above,  and  at  higher  than  at  lower  readings  of  either  the  thermometer  or  bar- 
ometer. Reduced  from  the  French  measurements  made  to  determine  the 
relations  existing  between  the  units  of  the  metric  system,  the  weight  in  vacuuo 
of  1  cu.  ft.  of  pure  distilled  water,  free  from  air,  at  the  temperature  of  its  maxi- 
mum density  (4°  C.,  or  39.3°  F.)  and  under  a  barometric  pressure  of  760  milli- 
meters (29.92  in.)  of  mercury,  at  sea  level  and  at  the  latitude  of  Paris 
(48°  50'  N),  is  62.42664  Ib.  This  is  the  weight  commonly  used  in  pocketbooks 
and  is  often  given  as  62.427  Ib.,  62.43  Ib.,  and  even  as  62.5  Ib.,  depending  on 
the  degree  ol  accuracy  required.  From  this,  the  weight  of  1  cu.  in.  of  water 
under  the  given  conditions  may  be  taken  as  .036126  Ib.,  .036  Ib.,  or  even  .04  Ib. 
At  other  temperatures  commonly  used  in  calculations  the  weight  of  1  cu.  ft. 
of  water  is:  at  32°  F.,  62.418  Ib.;  at  62°  P.,  62.355  Ib.;  and  at  212°  F.,  59.846  Ib. 

The  following  table  gives  the  weight  in  air  of  1  gal.  and  of  1  cu.  ft.  of  dis- 
tilled water.  These  weights  are  reduced  from  the  French  : 


are  referred  to  sea  level  at  the  latitude  of  Paris. 
or  ordinary  manner  of  weighing. 


measurements  and 
They  represent  the  customary 


Temperature  Pressure 

4°  C.  (39.3°  F.) .  .  760  mm.  (29.92  in.) . 
62°  F.  (16.7°  C.) .  .760  mm.  (29.92  in.) . 
62°  F.  (16.7°  C.) . .   30  in.  (762.0  mm.) . 
The  following  table  of  equivalents  is  based  upon  the  weight  of  1  cu.  ft.  of 
water  weighed  in  air  at  39.3°  P.,  and  29.92  in.  of  mercury,  viz.:  62.356562  Ib. 
avoirdupois. 


Weight  of 

1  Gal. 

Pounds 

..8.33586... 

..8.32675... 

..8.32673.. 


Weight  of 
Cu.  Ft. 
Pounds 
.62.35656 

.62.28844 
.  62.28827 


EQUIVALENT  WEIGHTS  AND  VOLUMES  OF  WATER 


Gills 

Pints 

Quarts 

Gallons 

Cubic 
Inches 

Cubic 
Foot 

Weight 
of  Water 

Pounds 

1 

.250000 

.125000 

.031250 

7.218750 

.004178 

.260496 

4 

1 

.500000 

.125000 

28.875000 

.016710 

1.041983 

8 

2 

1 

.250000 

57.750000 

.033420 

2.083965 

32 

8 

4 

1 

231 

.133681 

8.335860 

.138528 

.034632 

.017316 

.004329 

1 

.000579 

.036086 

239.376624 

59.844156 

29.922078 

7.480520 

1,728 

1 

62.356562 

3.838836 

.959709 

.479855 

.119964 

27.711598 

.016037 

1 

WEIGHTS  AND  MEASURES 


ANGULAR,  OR  CIRCULAR,  MEASURE 

60  seconds  (sec.  or  ") =1  minute min.  or  ' 

60  minutes =1  degree deg.  or  ° 

360  degrees =1  circumference  . . .  .cir. 

sec.  min.         deg.  cir. 

1  =  .016667  =  .000278  =  .000008 

60=     1  =  . 016667  =  .000463 

3,600=    60=     1  =  . 002778 

1,296,000=  21,600=    360=     1 

For  tables  of  grades,  grade  angles,  etc.,  see  under  the  head  of  Tracklaying. 
Laying  Off  Right  Angles. — Right  angles  may  conveniently 
be  laid  off  in  the  field  by  using  the  relation  existing  between 
the  hypotenuse  and  sides  of  a  right-angled  triangle,  viz.:  The 
square  of  the  hypotenuse  is  equal  to  the  sum  of  the  squares 
of  the  sides.  The  commonly  used  ratio  is  3  for  the  horizontal 
side,  4  for  the  vertical  side,  and  5  for  the  hypotenuse,  or  slope. 
There  are  many  other  ratios,  such  as  8,  15,  17,  and  the  like,  a 
number  of  which  are  given  in  the  following  table.  Likewise, 
any  multiple  or  submultiple  of  these  ratios  may  be  used.  Thus, 
instead  of  3,  4,  and  5,  f,  1%,  or  2  times  the  proportion  may  be 
used,  as  1.5,  2,  2.5,  or  4.5,  6,  7.5,  or  6,  8,  and  10,  respectively. 


RATIO  OF  SIDES  OF  RIGHT-ANGLED  TRIANGLE 


Hori- 
zontal 

Verti- 
cal 

Slope 

Hori- 
zontal 

Verti- 
cal 

Slope 

Hori- 
zontal 

Verti- 
cal 

Slope 

3 

4 

5 

12 

16 

20 

18 

24 

30 

4 

3 

5 

12 

9 

15 

20 

15 

25 

6 

8 

10 

14 

48 

50 

20 

48 

52 

7 

24 

25 

15 

8 

17 

24 

32 

40 

8 

6 

10 

15 

20 

25 

24 

18 

30 

8 

15 

17 

15 

36 

39 

24 

45 

51 

9 

12 

15 

16 

12 

20 

24 

7 

25 

10 

24 

26 

16 

30 

40 

25 

60 

65 

Laying  Off  an  Angle  With  a  Tape. — It  is  frequently  necessary  to  lay  off 
other  than  right  angles  as,  for  example,  when  a  cut  or  two  must  be  taken  from 


„ _- 

tion  from  which 

Angle  Is  fumed 

the  rib  of  an  entry  at  a  point  where  a  branch  entry  is  to  be  started,  in  order  that 
there  may  be  room  to  place  the  sights.     Suppose  it  is  desired  to  turn  an  angle 


10  WEIGHTS  AND  MEASURES 

of  50°  to  the  left.  Fasten  the  0  end  of  an  ordinary  tape  at  A ,  then  stretch  the 
tape  to  B  a  distance  of  10  ft.,  and  fasten  the  10-ft.  mark  at  B.  If  the  angle  is 
to  be  turned  from  an  entry,  the  points  A  and  B  can  be  lined  in  from  the  entry 
sights.  Then  fasten  the  30-ft.  mark  of  the  tape  at  A.  This  will  leave  20  ft. 
of  slack  tape  between  A  and  B.  Find  the  19-ft.  mark  on  the"  tape,  and  draw 
the  tape  tight  from  both  A  and  B.  The  tape  line  from  A  to  the  19-ft.  mark 
will  make  an  angle  of  50°  at  A  with  the  line  A  B.  If  the  angle  is  to  the  right, 


tape 
mark;  for  30°,  hold  it  at  the  16'  9|"  mark,  and  similarly  for  other  angles. 


MEASURE  OF  TIME 

60  seconds  (s.) =1  minute min.  or  m 

60  minutes =1  hour hr.  or  h 

24  hours =  1  day da.   or  d 

sec.         min.  hr.  da. 

1  =  .016667  =  .000278  =  .000012 

60=  .    1  =  . 016667  =  .000694 

3,600=     60=     1  =  .  041667 

86,400=   1,440=    24=     1 

Solar,  astronomical,  civil,  and  standard  time  are  discussed  in  the  chapter 
on  Surveying  under  the  heading  Determination  of  the  Meridian. 

LONGITUDE  AND  TIME 

As  the  earth  makes  a  complete  revolution  of  360°  upon  its  axis  in  24  hr., 
degrees,  minutes,  and  seconds  of  arc,  or  longitude,  may  be  expressed  in  hours, 
minutes,  and  seconds  of  time. 

Arc  =  Time  Arc  =  Time 

360  degrees  =  24  hours  1  minute  =  4  seconds 

15  degrees  =    1  hour  15  seconds  =  1  second 

1  degree    =   4  minutes  1  second  =  .0666  +  second 

15  minutes  =    1  minute 


THE  METRIC  SYSTEM 

The  fundamental  unit  of  the  metric  system  is  the  meter,  which  is  the  unit 
of  length  and  which  was  intended  to  be  equal  in  length  to  TTnn&rnrff  part  of  the 
quadrant  of  the  earth,  or  the  distance  from  the  equator  to  the  pole,  measured 
on  the  meridian  of  Paris,  France.  Owing  to  imperfection  in  instruments,  etc., 
the  length  of  the  arc  of  10°  that  was  used  in  determining  the  length  of  the 
quadrant  was  not  measured  with  absolute  accuracy,  so  that  the  meter,  as  well  as 
the  units  derived  from  it,  is  not  of  exactly  the  dimensions  it  was  intended  to  be. 
Since  its  adoption  by  France  in  the  law  of  June  22,  1799,  the  use  of  the  system 
has  become  world  wide,  until  the  only  countries  of  commercial  importance 
where  it  is  not  now  in  general  use  are  China,  Great  Britain,  Japan,  Russia, 
and  the  United  States. 

While  Congress  has  authority,  under  Article  I  of  the  Constitution,  to  compel 
the  use  of  the  metric  system,  it  has  never  done  so,  contenting  itself,  under  the 
act  of  July  28,  1866,  with  legalizing  its  use  and  establishing  the  relations 
between  the  units  of  the  ordinary  and  the  metric  systems.  By  Executive 
Order  of  April  5,  1893,  the  yard  and  the  avoirdupois  pound  may  now  be  derived 
from  the  meter  and  the  kilogram.  The  ratios  established  by  Congress  are 
1  meter  =  39.37  in.,  and  1  kilogram  =  2. 2046  Ib.  avoirdupois.  As  these  values 
are  less  than  the  true  ones,  the  yard  and  the  pound  thus  derived  are  longer 
and  heavier,  respectively,  than  the  true  yard  and  the  true  pound. 

The  names  applied  to  the  various  denominations  of  the  system  are  not 
always  those  used  in  France,  but  are  frequently  adapted  from  the  names  of 


WEIGHTS  AND  MEASURES  11 

the  measures  that  the  metric  system  has  displaced.  In  almost  all  of  these 
countries  the  old  and  replaced  systems  are  still  in  use,  the  extent  of  this  usage 
being,  apparently,  in  inverse  ratio  to  the  commercial  importance  of  the  country 
and  to  the  length  of  time  during  which  the  metric  system  has  been  in  force. 

The  original  standards  of  the  metric  system  were  a  meter  and  a  kilogram 
of  platinum  deposited  in  the  Palais  des  Archives,  Paris,  at  the  time  of  the 
formal  adoption  of  this  system  in  France.  At  the  second  meeting  of  what  is 
now  the  International  Bureau  of  Weights  and  Measures,  held  in  Paris,  Sept.  24, 
1872,  the  representatives  of  thirty  nations  present  decided  that  the  standards 
of  the  system  should  be  made  of  an  alloy  of  90%  platinum  and  10%  iridium, 
because  of  its  hardness,  fine  grain,  and  ability  to  withstand  the  action  of  acids. 
A  number  of  meters  and  kilograms  were  made  and  the  ones  corresponding  to 
the  original  platinum  standards  are  deposited  in  the  permanent  headquarters 
of  the  bureau,  near  Paris.  Each  nation  subscribing  to  the  expenses  of  the 
bureau  received  two  copies  each  of  the  meter  and  the  kilogram,  which  are 
known,  respectively,  as  the  national  prototype  meter  and  kilogram.  These  are 
of  the  same  materials  and  accuracy  as  the  originals.  The  United  States 
prototypes  were  received  by  the  President  on  Jan.  2,  1890,  and  one  of  each  was 
selected  as  a  reference  standard,  while  the  other  is  used  for  working  purposes. 

The  unit  of  weight  of  the  metric  system  is  the  kilogram,  originally  intended 
to  be  the  weight,  in  vacuuo,  of  1  cubic  decimeter  of  pure,  distilled  water  at  the 
temperature  of  its  maximum  density,  4°  C.  (39.3°  P.),  with  the  barometer  at 
760  millimeters  (29.92  in.)  of  mercury.  As  with  the  meter,  this  relation  is 
not  exact,  owing  to  errors  in  the  original  standard. 

The  unit  of  capacity  is  the  liter,  which  was  designed  to  be  the  volume  of 
1  kilogram  of  pure  water  under  the  conditions  just  named. 

The  unit  of  area  for  land  measure  is  the  are,  a  square  10  meters  on  the  side. 
Among  engineers,  superficial  dimensions  are  usually  expressed  in  square  centi- 
meters, square  meters,  and  square  kilometers. 

Cubic  dimensions  are  expressed  in  cubic  centimeters,  cubic  meters,  etc. 

Multiples  of  the  various  units  of  the  metric  system  are  obtained  by  prefixing 
to  the  names  of  the  units  (meter,  gram,  and  liter)  the  Greek  words,  deka  or 
deca  (10),  hekto  or  heclo  (100),  kilo  (1,000),  and  myria  (10,000).  The  sub- 
multiples  or  divisions  are  obtained  by  prefixing  to  the  names  of  the  units,  the 
Latin  words  deci  tfs),  centi  (Tfo),  and  milli  ddro). 

METRIC  MEASURES  OF  LENGTH 

1  millimeter mm .001 

10  millimeters =1  centimeter. .  .cm .01 

10  centimeters. =1  decimeter dm .1 

10  decimeters =  1  meter m 

10  meters =1  dekameter.  .  .  Dm 10 

10  dekameters =1  hektometer  .  .Hm 100 

10  hektometers =1  kilometer Km l.OCK 

10  kilometers =1  myriameter .  .  Mm 10,001 

Of  these  denominations  the  ones  commonly  employed  are  the  millimeter, 
centimeter,  meter,  and  kilometer.  The  United  States  Coast  and  Geodetic 
Survey,  since  1884,  has  used  the  value  1  m.=  39.370432  in.;  the  legal  equiva- 
ent  by  Act  of  Congress  is  1  m.  =39.37  in. 

METRIC  MEASURES  OF  SURFACE 

1  sq.  millimeter sq.  mm.,  or  mm.*  .000001 

100  sq.  millimeters.  =  1  sq.  centimeter .  .sq.  cm.,  or  cm.2 
100  sq.  centimeters.  =  1  sq.  decimeter. .  .sq.  dm.,  or  dm.2 

100  sq.  decimeters  .  =  1  sq.  meter sq.  m.,  or  m.2 

100  sq.  meters =  1  sq.  dekameter  .  .sq.  Dm.,  or  Dm.2 

100  sq.  dekameters.  =  1  sq.  hektometer. . sq.  Hm.,  or  Hm.2  10,000 

100  sq.  hektometers  =  1  sq.  kilometer.  .  .  sq.  Km.,  or  Km.2        l-OOO.OOl 
100  sq.  kilometers. .  =  1  sq.  myriameter  .sq.  Mm.,  or  Mm.2  100,000,001 

The  square  meter  is  sometimes  known  as  the  centare;  the  square  dekameter 
as  the  are;  and  the  square  hektometer  as  the  hectare.  Farm  measurements 
are  generally  given  in  hectares.  Engineers  use  the  square  millimeter,  square 
centimeter,  square  meter,  and  square  kilometer.  The  other  denominations 
are  but  little  used.  The  square  meter,  or  centare,  is  a  little  larger  than 
1  sq.  yd.;  the  hektometer,  or  hectare,  is  about  2*  A. 


12  WEIGHTS  AND  MEASURES 

METRIC  MEASURES  OF  WEIGHT 

1  milligram mg .001 

10  milligrams =1  centigram ...  eg .01 

10  centigrams =1  decigram . . .  .  dg .1 

10  decigrams =1  gram g 1 

10  grams =1  dekagram . .  .  Dg 10 

10  dekagrams =1  hektogram  .  .Hg 100 

10  hektograms =1  kilogram.  .  .  .Kg 1,000 

10  kilograms =1  myriagram.  .  Mg 10,000 

10  myriagrams =1  quintal Q 100.000 

10  quintals =1  tonne T 1,000,000 

The  denominations  in  common  use  are  the  milligram,  centigram,  gram, 

kilogram  (commonly  called  kilo),  and  tonne.     Commercially,  the  kilogram  is 

divided  into  halves,  quarters,  etc.     As  near  as  may  be  determined,   1  Kg. 

=  2.2046223  Ib.  avoirdupois.     The  ratio  legalized  by  Congress  is  1  Kg.  =  2.20-46 

Ib.  avoirdupois. 

METRIC  MEASURES  OF  VOLUME 

1  cubic  millimeter cu.  mm.,  or  mm.8  . .   .000000001 

1,000  cubic  millimeters   =1  cubic  centimeter. c.c.,  cc.3,  or  cu.  cm..    .000001 

1,000  cubic  centimeters  =  1  cubic  decimeter,  .cu.  dm.,  or  dm.3 001 

1,000  cubic  decimeters    =  1  cubic  meter cu.  m.,  or  m.3    1 

The  cubic  millimeter  and  cubic  decimeter  are  rarely  used.  The  cubic 
centimeter  is  a  common  unit  with  chemists,  and  engineers  use  the  cubic  meter 
in  the  same  way  as  the  cubic  yard. 

METRIC  MEASURES  OF  CAPACITY 

1  milliliter ' ml /I7"1;       .001 

10  milliliters =1  centiliter cl .01 

10  centiliters =1  deciliter dl .\   '         .1 

10  deciliters. . .  f =1  liter 1 v"  *  *      1 

10  liters .  =  1  dekaliter,  or Dl 10 

1  centistere cs. 

10  dekaliters =1  hektoliter,  or HI 100 

1  decistere ds. 

10  hektoliters =1  kiloliter,  or Kl 1,000 

1  stere s. 

10  kiloliters =1  myrialiter,  or Ml 10,000 

1  dekastere Ds. 

The  liter  and  the  milliliter  (but  in  its  equivalent  form  the  cubic  centimeter) 
are  in  use  among  chemists.  Engineers  use  the  liter  and  kiloliter,  the  latter 
being  called  by  its  equivalent  name,  cubic  meter.  Groceries  and  the  like  are 
purchased  by  the  liter,  half  liter,  and  quarter  liter,  instead  of  by  the  decimal 
parts  of  a  liter.  Grain  is  measured  by  the  stere  and  by  the  decistere,  the 
latter  being  called  hektoliter. 

Congress  has  not  established  a  ratio  between  the  units  of  the  measures  of 
capacity  of  the  metric  and  ordinary  systems. 

EQUIVALENTS  OF  VOLUME,  WEIGHT  OF  WATER,  AND   CAPACITY 

Distilled  water  at  4°  C.  (39.3°  F.)  and  760  mm.  (29.92  in.)  pressure. 

Volume  Weight  Capacity  Ratio 

1  cubic  centimeter =1  gram =1  milliliter 1 

10  cubic  centimeters =1  decagram =1  centiliter 10 

100  cubic  centimeters =1  hektogram =1  deciliter 

1  cubic  decimeter =1  kilogram =1  liter 1.000 

10  cubic  decimeters =1  myriagram =1  dekaliter 10,000 

100  cubic  decimeters =1  quintal =1  hektoliter 100,000 

1  cubic  meter/ =1  tonne =1  stere 1,000,000 


WEIGHTS  AND  MEASURES 


13 


LIQUID  MEASURE 
ml.  X.  008454  =  gi. 
L  XI. 066717 -qt. 
I.X.  264 179  =  gal. 
HI.  X  26.417916  =  gal. 
HI.  X.  838664  =  bbl. 
s.X  264.179164  =  gal. 
s.X  8.386640  =  bbl. 

MEASURES  OF  LENGTH 
mm.  X. 039370  =  in. 
cm.  »X. 393704  =  in. 
cm.  X. 032809  =  ft. 
m.     X  39. 370432  =  in. 
m.     X  3.280869  =  ft. 
m.     XI. 093623  =  yd. 
m.     X. 000621  =  mi. 
Km.  X  3,280.869300  =  ft. 
Km.  X  1,093.623100  =  yd. 
Km.  X. 621375  =  mi. 

MEASURES  OF  WEIGHT 
mg.X. 015432  =  gr. 
eg.  X.  154324  =  gr. 
eg.  X. 000353  =  oz. 
g.     XI  5.432356  =  gr. 
g.     X. 035274  =  oz. 
g.     X. 002205  =  lb. 
Kg.  X  35.273957  =  oz. 
Kg.  X  2.204622  =  lb. 
Kg. X. 001 102  =  short  T. 
tonnes  X  1.102311  =  short  T. 
tonnes X. 984206  =  long  T. 
RELATION  OF  WEIGHT  AND  VOLUME 

OF  WATER 

cu.  cm.  X  15.432356  =  gr. 
l.X  2.204622  =  lb.  (avoir.) 
cu.m.X  2,204.622341  =  lb. 
cu.  m.X  264. 179164  =  gal. 
cu.m.X  8.386640  =  bbl. 
cu.  m.X  1.102311  =  short  T. 
cu.  m.  X  .984206  =  long  T. 
Kg.  X  1.056717  =  qt. 


CONVERSION  FACTORS 

METRIC  TO  UNITED  STATES 

RELATION  OF  WEIGHT  AND  VOLUME  OF 

WATER— Continued 
Kg.  X. 264179  =  gal. 
Kg.  X  61.025387  =  cu.  in. 
Kg. X. 035316  =  cu.  ft. 

DRY  MEASURE 
I.X.  908107  =  qt. 
I.X.  028378  =  bu. 
HI.  X  22.702686  =  gal. 
HI.  X  2.837836  =  bu. 
s.X  227.026857  =  gal. 
s.X  28.378357  =  bu. 

MEASURES  OF  VOLUME 
ml.  X. 061025  =  cu.  in. 
cl.X. 610254  =  cu.  in. 
dl.X  6. 1025^9  =  cu.  in. 
l.X 61. 025387  =  cu.  in. 
l.X.035316  =  cu.  ft. 

^'  }  X  3.531562  =  cu.  ft. 
?-L)x  35.315617  =  cu.  ft. 

S.        J 

JP' }  XI. 307986 -cu.  yd. 

SQUARE  MEASURE 
sq.  mm. X. 001550  =  sq.  in. 
sq.  cm. X.I 55003  =  sq.  in. 
sq.  m.X  10.764104  =  sq.  ft. 
sq.  m.  XI. 196012  =  sq.  yd. 
sq.  m.X. 000247  =  A. 
hectares  X  2.471098  =  A. 
hectares  X  .003861  =  sq.  mi. 
sq.  Km.  X  247. 109816  =  A. 
sq.  Km. X. 386109  =  sq.  mi. 
CUBIC  MEASURE 
cu.  cm. X. 061025  =  cu.  in. 
cu.  dm.  X  61.025387  =  cu.  in. 
cu.  dm. X. 035316  =  cu.  ft. 
cu.  m.   X  35.315617  =  cu.  ft. 
cu.  m.  X 1. 307986  =  cu.  yd. 


MISCELLANEOUS  CONVERSION  FACTORS 


cm.  per  sec.  X  1.968522  =  ft.  per  min. 
cu.  cm.  per  sec. X. 015851  =  gal.  per 

min. 

cm.  per  m.X. 12  =  in.  per  ft. 
m.  per  Km. X.  10  =  ft.  per  100  ft. 
m.  per  Km.  X  5.28  =  ft.  per  mi. 
m.  (depth)  per  hectare XI. 327697 

=  A.-ft. 

Kg.  per  m.X.671963  =  lb.  per  ft. 
Kg.  per  sq.  cm.  X  14.223084  =  Ib.  per 

sq.  in. 

Kg.    per    sq.    cm.  X  .967557  =  atmos- 
pheres (14.7  Ib.)  per  sq.  in. 
Kg.  per  sq.  m.X. 204812  =  lb.  per  sq. 

ft. 
g.  per  cu.  cm. X. 036126  =  lb.  per  cu. 

in. 
Kg.    per   l.X 8.345217  =  lb.    per    gal. 

(liquid) 
Kg.  per  cu.  m.  X  .062426  =  Ib.  per  cu. 

ft. 


Kg.    per    cu.    m.  X  .008345  =  Ib.    per 

gal.  (liquid) 
francs  (fr.)  per  m.X.  176386  =  dollars 

(dol.)  per  yd. 

fr.  per  Km. X. 310441  =  dol.  per  mi. 
fr.  per  hectare X. 078063  =  dol.  per  A. 
fr.  per  Kg.  X  .087498  =  dol.  per  Ib. 
fr.  per  tonne X.  174996  =  dol.  per  T. 

(short) 
fr.  per  l.X.  182547  =  dol.  per  qt. 

(liquid) 
fr.  per  l.X. 730187  ='dol.  per  gal. 

(liquid) 
fr.  per  1.  X  .212419  =  dol.  per  qt. 

(dry) 

fr.  per  HI. X. 067974  =  dol.  per  bu. 
fr.  per  cu.  m.X.  147478  =  dol.  per  cu. 

mik's   (mk.)   per  m.X. 217717  =  dol. 

per  yd. 
mk.  per  Km. X. 383182  =  dol.  per  mi. 


14 


WEIGHTS  AND  MEASURES 
MISCELLANEOUS  CONVERSION  FACTORS — Continued 


mk.  per  hectare  X  .096354  =  dol.  per  A. 
mk.  per  Kg.  X.  108000  =  dol.  per  Ib. 
mk.  per  tonne X. 2 16001  =  dol.  per  T. 

(short) 
mk.    per    l.X. 225321  =  dol.    per    qt. 

(liquid) 
mk.    per    l.X. 901282  =  dol.    per   gal. 

(liquid) 
mk.    per    l.X. 262194  =  dol.    per    qt. 

(dry) 
mk.  per  HI.  X  .083902  =  dol.  per  bu. 


mk.   per  cu.   m. X.I 82036  =  dol.   per 

cu.  yd. 

m.-Kg.  X  7.233077  =  ft.-lb. 
m.-Kg.X. 009297  =  B.  T.  U. 
joules  X  .737308  =  ft.-lb. 
Kw.X  1.341113  =  H.  P. 
cheval-vapeurX. 986329  =  H.  P. 
PonceletX  1.315105  =  H.  P. 
cal.X  3.968320  =  6.  T.  U. 
cal.  X  3,087.3531 12  =  ft.-lb. 
Gravity  (Paris)  =  980.90  cm.  per  sec. 


LIQUID  MEASURE 
gi.  XI  18.290925  =  ml. 
qt.X. 946327  =  1. 
gal.  X  3.785310  =  1. 
gal.  X. 037853  =  HI. 
gal.  X. 003785  =  s. 
bbl.X  1.192373  =  HI. 
bbLX. 119237  =  s. 
RELATION  OF  WEIGHT  AND  VOLUME 

OF  WATER 

gr.X. 064799  =  cu.  cm. 
Ib.  (avoir.)  X  .453592  =  1. 
Ib.X. 000454  =  cu.  m. 
gal. X. 003785  =  cu.  m. 
bbl.X.  119237  =  cu.  m. 
short  T.X.907185  =  cu.  m. 
long  T.X  1.016047  =  cu.  m. 
qt.X. 946327  =  Kg. 
gal.X3.785310  =  Kg. 
cu.  in. X. 01 6387  =  Kg. 
cu.  ft.X  28.3 16094  =  Kg. 

MEASURES  OF  LENGTH 
in.  X  25.399780  =  mm. 
in.  X 2.539978  =  cm. 
in.  X. 025400  =  m. 
ft.  X  30.4797260  =  cm. 
ft.  X. 304797  =  m. 
ft.  X. 000305  =  Km. 
yd.  X. 914391 792  =  m. 
yd.  X. 00091 4  =  Km. 
mi.  X. 001609  =  m. 
mi.  X  1.609330  =  Km. 

MEASURES  OF  WEIGHT 
gr.X  64.798918  =  mg. 
gr.X  6.479892  =  eg. 
gr.X.  064800  =  g. 
oz.  X  2,834.952670  =  eg. 
oz.X  28.349527  =  g. 
oz.X. 028350  =  Kg. 
Ib.X  453.592428  =  g. 


UNITED  STATES  TO  METRIC 


MEASURES  OF  WEIGHT — Continued 
Ib.X. 453592  =  Kg. 
short  T.X 907. 184856  =  Kg. 
short  T.X. 907 185  =  tonnes 
long  T.  X  1.016047  =  tonnes 
DRY  MEASURE 
qt.Xl. 101191  =  1. 
gal.  X. 044048  =  HI. 
gal.  X. 004405  =  s. 
bu.X35.238122  =  l. 
bu.X. 352381  =  HI. 
bu.X. 035238  =  s. 

MEASURES  OF  VOLUME 
cu.  in.  X  16.386623  =  ml. 
cu.  in. XI. 638662  =  cl. 
cu.  in. X.I 63866  =  dl. 
cu.  in. X. 016387  =  1. 
cu.  ft.X 28.316094  =  1. 

cu.  ft.X. 283161  ={ gj' 
cu.  ft.X. 028316 ^{f1' 

cu.  yd.  X. 764535  ={f"1' 

SQUARE  MEASURE 
pq.  in.X645.148422  =  sq.  mm. 
sq.  in.  X  6.451484  =  sq.  cm. 
sq.  ft.X. 092901  =sq.  m. 
sq.  yd.X.836112  =  sq.  m. 
A.  X  4,046.787846  =  sq.  m. 
A.  X  .404679  =  hectares 
sq.  mi.  X  258.994161  =  hectares 
A. X. 004047  =  sq.  Km. 
sq.  mi. X 2.589942  =  sq.  Km. 

CUBIC  MEASURE 
cu.  in.  X  16.386623  =  cu.  cm. 
cu.  in.  X. 016387  =  cu.  dm. 
cu.  ft.  X  28.316094  =  cu.  dm. 
cu.  ft.  X.028316  =  cu.  m. 
cu.  yd. X. 764534  =  cu.  m. 


MISCELLANEOUS  CONVERSION  FACTORS 


ft.  per  min.X. 507996  =  cm.  per  sec. 

gal.  per  min.  X  63. 088498  =  cu.  cm. 
per  sec. 

in.  per  ft.X 8.333333  =  cm.  per  m. 

ft.  per  100  ft.X  10.00  =  m.  per  Km. 

ft.  per  mi. X. 189394  =  m.  per  Km. 

A.-ft.X.753183  =  m.  (depth)  per  hec- 
tare 

Ib.  per  ft.X  1.488177  =  Kg.  per  m. 

Ib.  per  sq.  in. X. 070309  =  Kg.  per  sq. 
cm. 


atmospheres    (14.7    Ib.)  X  1.033539 

=  Kg.  per  sq.  cm. 
Ib.    per    sq.  ft.X 4.882535  =  Kg.  per 

sq.  m. 
ib.  per  cu.  in.  X  27.680653  =  g.  per  cu. 

cm. 
Ib.    per   gal.    (liquid) X.I  19829  =  Kg. 

per  1. 
Ib.  per  cu.  ft.X  16.018897  =  Kg.  per 

cu.  m. 


WEIGHTS  AND  MEASURES 


15 


Ib. 


=  Kg.  per  cu.  m. 

dol.  per  yd.  X  5.669377  =  fr.  per  m. 
dol.  per  mi.  X  3.221224  =  fr.  per  Km. 
dol.  per  A.  X  12.810239  =  fr.per  hectare 
dol.  per  Ib.X  11.428835  =  fr.  per  Kg. 
dol.  per  T.X  5.714417  =  fr.  per  tonne 
dol.    per   qt.    (liquid)  X  5.478052  =  fr. 


MISCELLANEOUS  CONVERSION  FACTORS — Continued 
gal.      (liquid)  XI  19.829666        dol.  per  Ib.X  9.259228  =  mk.  per  Kg. 
dol.  per  TX4.629614«=mk.  per  tonne 
dol.  per  qt.  (liquid)  X  4.4381 13  =  mk. 

perl, 
dol.  per  gal.  (liquid)  XI.  109530  =  mk. 

per  1. 
dol.    per    qt.    (dry)  X  3.813588  =  mk. 

per  1. 
dol.  per  bu.  X  11.918671  =  mk.  per 

HI. 
dol.  per  cu.  yd.  X  5.4934 13  =  mk.  per 

cu.  m. 

ft.-lb.X. 138254  =  m.-Kg. 
ft.-lb.  X  1.356284  =  joules 
ft.-lb.X.  000324  =  cal. 
H.  P. X. 745649  =  Kw. 
H.  P.X1.013861  =  cheval-vapeur 
H.  P.  X. 760396  =  Poncelet. 
B.  T.  U.X  107.561415  =  m.-Kg. 
B.  T.U.X. 251995  =  cal. 


dol.  per  gal.   (liquid)  X  1.369513  =  fr. 

dol.     per     qt.     (dry)  X  4. 707659  =  fr. 
per  1. 

dol.  per  bu.X  14.71 1434  =  fr.  per  HI. 

dol.   per  cu.   yd.  X  6.780771  =  fr.   per 
cu.  m. 

dol.  per  yd.X4.593124  =  mk.  per  m. 

dol.  per  mi.X2.609677  =  mk.  per  Km. 

dol.  per  A.  X  10.378394  =  mk.  per  hec- 
tare 
One  dm.  =  3.937043  in.;   1    Dk.  =  32.808693    ft.  or   10.936231  yd.;   1  Hm. 

=  109.362310  yd.;    1  Mm.  =  6.213750  mi.      The  U.  S.  5c.  piece,  or  nickel,  is 

slightly  over  2  cm.  across. 

One  sq.  dm.  =  15.500309  sq.  in.;  1  sq.  Dm.  =  119.601151  sq.  yd.;  1  sq.  Mm. 

=  38.610909  sq.  mi.,  or  a  little  more  than  1  township. 

One  Q.  =  220.462230  Ib.;  1  Mg.  =  22.046223  Ib.;  1  Hg.  =  . 220462  Ib.;  the 

Dg.  =  .35273957  oz. 

The  United  States  50c.  silver  coin  weighs   12.5  g.;  the  25c.  coin,  6.25  g.; 

and  the  lOc.  coin,  2.5  g.     These  weights  have  been  assigned  by  congressional 

enactment. 


WEIGHTS  AND   MEASURES   OF   GREAT  BRITAIN  AND 
COLONIES 

The  measures  of  length,  of  surface,  of  weight,  and  of  volume,  while  not 
absolutely  identical,  are,  for  all  practical  purposes,  the  same  as  those  of  the 
United  States.  It  should  be  noted,  however,  that  the  United  States  long  ton 
of  2,240  Ib.  is  used  in  Great  Britain  and  all  of  her  colonies,  except  Canada, 
where  the  ton  has  been  fixed  by  statute  at  2,000  Ib.  The  quarter  of  28  Ib.  and 
the  stone  of  14  Ib.  are  used  to  some  extent. 

The  chief  difference  between  the  measures  of  Great  Britain  and  the  United 
States  is  to  be  found  in  the  sizes  of  the  units  of  dry  and  liquid  measure.  The 
United  States  liquid  gallon  is,  by  Act  of  Congress,  equal  to  231  cu.  in.,  and  the 
United  States  bushel  is,  by  similar  enactment,  equal  to  2,150.42  cu.  in.,  no 
reference  being  made  to  the  weight  of  water  contained  in  either  of  the  measures. 
They  were  founded  upon  the  former  British  wine  gallon  and  the  Winchester 
struck  (level  full)  bushel,  respectively,  which  have  not  been  current  in  Great 
Britain  since  1825,  when  they  were  replaced  by  the  imperial  gallon  and  bushel. 
By  Act  of  Parliament,  the  imperial  gallon  is  the  volume  of  10  Ib.  of  pure  water 
at  62°  F.,  weighed  against  brass  weights  in  air  at  the  same  temperature  and  at 
a  barometric  pressure  of  30  in.  of  mercury.  The  imperial  bushel  is  the  volume 
of  80  Ib.  of  pure  water  under  the  preceding  conditions.  From  this,  it  is  apparent 
that  the  imperial  gill,  pint,  quart,  and  gallon,  are  the  same  in  both  the  liquid 
and  dry  measure. 

Using  the  value  for  the  weight  of  1  cu,  ft.  of  water,  62.28827  Ib.,  the  volume 
of  the  imperial  gallon  is  found  to  be  277.4203  cu.  in.,  and  of  the  imperial  btfshel, 
2,219.3613  cu.  in. 

IMPERIAL  MEASURE,  BOTH  LIQUID  AND  DRY 

Volume  Weight  of  Water 

Cubic  Inches  Pounds 

8.6694 =      .3125 

=   34.6775 =  1.2500 

=   69.3551 =  2.5000 

=  277.4203 =  10.0000 

=  554.8403 =  20.0000 

...=2,219.3613 =80.0000 


*  &*• 

4gi.-  
2pt  
4  qt 

= 

pt  

qt.  

gal  

.    .  .  . 

2  gal. 
4pk  

.....= 

e, 
pk  
bu  

16 


WEIGHTS  AND  MEASURES 


One  imp.  gal.  equals  1.20085  U.  S.  liquid  gal.,  and  1  imp.  bu.  equals  1.03206 
U.  S.  bu,  Likewise,  1  U.  S.  liquid  gal.  equals  .83267  imp.  gal.,  and  1  U.  S. 
bu.  equals  .96894  imp.  bu. 


MONEY 

UNITED  STATES  CURRENCY 


Denominations 
10  mills     =  1  cent 
10  cents    =  1  dime 
10  dimes  =  1  dollar 
10  dollars  =1  eagle 


Mill        Cent        Dime        Dol.       Eagle 

1=  .1=        .01=      .001=    .0001 

10=         1     =        .1  =      .010=   .0010 

100=       10    =      1.0   =      .100=    .0100 

1,000=     100    =    10.0   =    1.000=   .1000 

10,000=1,000    =100.0   =10.000=1.0000 


STANDARD  UNITED  STATES  COINS 


Gold 


Silver 


Denomination 

Value 

Weight 
Grains 

Denomination 

Value 

Weight 
Grains 

*Dollar 

$1  00 

258 

*Trade  dollar 

$1  00 

420  0 

Quarter-eagle  
Three-dollar  piece  .  . 
Half-eagle  

Eagle 

2.50 
3.00 
5.00 
1000 

64.5 

77.4 
129.0 
2580 

Standard  silver  dol- 
lar   
Half-dollar  

1.00 
.50 
25 

412.5 
192.9 
96  45 

Double  eagle  

20.00 

516.0 

Dime 

10 

38  58 

Fineness  expresses  the  proportion  of  pure  metal  in  1,000  parts;  thus, 
"900  fine"  means  that  900  of  every  1,000  parts  are  pure  metal.  Fineness  of 
U.  S.  coins  =  900  pure  metal,  100  alloy;  alloy  of  gold  coin  is  copper  or  copper 
and  silver,  but  in  no  case  shall  silver  exceed  one-tenth  of  total  alloy.  Alloy 
of  silver  coin  is  copper. 

Weight 
Piece  Grains  Contents 

5-cent  (nickel) 77.16 75%  copper,  25%  nickel 

*3-cent 30      75%  copper,  25%  nickel 

*2-cent 66      95%  copper,    5%  tin  and  zinc 

1-cent  (copper) 48      95%  copper,    5%  tin  and  zinc 

CURRENCY  OF  GREAT  BRITAIN 

Denominations  far.        d.  s.  £ 

4  farthings  (far.) =1  penny d 1  =       .25=     .0208  =   .0010 

12  pence =1  shilling s 4=5      1.00=      .0833=    .0042 

20  shillings =1  pound £ 48jfc    12.00=    1.0000=    .0500 

21  shillings =1  guinea 960  =  240.00  =  20.0000  =  1.0000 

The  unit  is  the  pound  sterling,  valued  at  $4.8665.  English  silver  is  .925  fine; 
gold,  .916|.  The  larger  silver  coins  are  the  shilling,  the  florin  or  2s.,  the 
crown  or  5s.,  and  the  half-crown  or  2s.  6d.  The  gold  coins  are  the  sovereign 
or  pound,  and  the  half-pound,  or  10s. 


Great  Britain  United  States 

1  pound =  $4.8665 

1  shilling =     .243325 

1  penny =      .0202771 

*No  longer  coined. 


United  States  Great  Britain 

1  cent =  .49312  pence 

1  dollar.  .  . =4  sh.  1.312  pence 

1  dollar =4.109333  shillings 

1  dollar =  .205466  pound 


WEIGHTS  AND  MEASURES  17 

FOREIGN    MONETARY   SYSTEMS   AND   EQUIVALENTS   IN    UNITED 
STATES  GOLD 


Argentine 100  centavos  =  1  peso 

Austria 100  heller  =  1  krone 

Belgium 100  centimes  =  1  franc 

Bolivia 100  centavos  =  1  boliviano . . 


Bosnia . . 

Brazili 

Bulgaria 

Canada 

Chilei 

China2.  . 

Colombia 

Costa  Rica 

Cuba' 

Denmark ........ 

Ecuador 

Egypt* 

France 

Germany 

Great  Britain 

Greece 

Guatemala1 

Holland. 


100  heller  =  1  krone 

1,000  reis  =  l  milreis 

.  100  stotmki  =  1  leva 

.100  cents  =  1  dollar 

.  100  centavos  =  1  peso 

.100parts=l  yuan 

.  100  centavos  =  1  peso 

.  100  centavos  =  1  colon 

.  100  centavos=  1  peso 

.  100  ore  =  1  krona 

.  100  centavos  =  1  sucre 

.  40  paras  =  1  piastre 

.  100  centimes  =  1  franc 

.  100  pfennige  =  1  mark , 

.   20  shillings  =  1  pound 

.  100  lepta  =  1  drachma 

.  100  centavos  =  1  peso 

100  cents  =1  gulden... 


Honduras1 100  centavos  =  1  peso 

India5 16  annas  =  1  rupee. .  . 


100  centesimi  =  1  lira 

100  sen  =  1  yen 

100  centavos  =  1  peso 

100  heller  =1  krone 

100  cents  =  1  gulden 

100  centavos  =  1  peso 

100  ore  =  l  krona 

100  centavos  =  1  balboa 

100  centavos  =  1  peso 

20  chahi  =  1  kran 

Isol 

1  peso. 


Uruguay7 

Venezuela 


Italy 

Japan 

Mexico 

Montenegro 

Netherlands 

Nicaragua 

Norway 

Panama 

Paraguay 

Persia8 

Peru 100  centavos 

Philippine  Islands 100  centavos 

Porto  Rico 100  cents  =  1  dollar. . . . 

Portugal1 1,000  reis  =  1  milreis 

Roumania 100  bani  =  1  leu 

Russia 100  kopecs  =  1  rouble 

Salvador1 100  centavos  =  1  peso 

Servia 100  paras  =  1  dinar 

Spain6 100  centavos  =  1  peseta 

Sweden 100  ore  =  1  krona 

Switzerland 100  centimes  =  1  franc 

Turkey 40  paras=  1  piastre 

.  100  centesimos  =  1  peso 

.  100  centimes  =  1  bolivar 


$  .9647 
.2026 
.1929 
.3893 
.2026 
.5463 
.1929 
1.0000 
.3649 
.4772 
1.0000 
1.0000 
1.0000 
.2679 
.4866 
.0494 
.1929 
.2381 
4.8665 
.1929 
.3998 
.4020 
.3998 
.3244 
.1929 
.4984 
.4984 
.2026 
.4020 
.3998 
.2679 
1.0000 
.9646 
.1704 
.4866 
.5000 
1.0000 
1.0804 
.1929 
.5145 
.3998 
.1929 
.1929 
.2679 
.1929 
.0439 
.9647 


.1929 

1  The  actual  currency  is  either  depreciated  or  inconvertible  paper  of  fluctu- 
ating value.     The  values  given  are  for  the  standard  gold  coin. 

2  This  is  the  new  coinage.     The  former  tael  is  still  largely  used.     Its  value 
differs  from  town  to  town  and  ranges  between  $.599  at  Shanghai  to  $.660  at 
Takau.     The  Haikwan,/or  tael  in  which  customs  are  payable,  is  valued  at 
$.667.     The  Hong  Kong  and  British  dollar,  valued  at  $.431,  and  the  Mexican 
dollar,  valued  at  $.434,  circulate  widely. 

3  Cuba  has  no  national  currency,  gold,  silver,  or  paper,  relying  upon  the 
money  of  the  United  States,  Great  Britain,  and  Spain  for  its  needs. 

4  The  actual  standard  is  the  pound  sterling  of  Great  Britain. 
6  Fifteen  rupees  equal  1  pound  sterling. 

6  The  values  given  are  for  the  gold  kran  and  peseta  respectively.     The 
actual  currency  is  silver  circulating  above  its  metallic  value. 

7  The  value  given  is  for  the  silver  peso.     While  under  the  gold  standard, 
Uruguay  has  never  coined  this  metal.     The  standard  value  of  the  gold  peso 
is  $1.0342. 


18 


MATHEMATICS 
VALUES  OF  FOREIGN  COINS 


Alexander,  Bulgaria  

$  3.8589 
4  8236 

Groschen,  Prussian  Poland. 
Gulden   Baden 

$  .0240 
.4000 

Boliviano,  Bolivia  
Condor  Chile 

.9700 
7  2995 

Imperial,  Russia  
Jirmilik   Turkey 

7.7183 
.8000 

Condor,       Colombia       and 
Ecuador  

9.6470 

Kreutzer,  Bavaria  
Libra,  Colombia  

.0067 
4.8665 

2  3819 

Libra  Ecuador 

4.9429 

10  8043 

Libra,  Peru  

4.8665 

Crown,  Sicily  
Crown,  Spain 

.9600 
1.9500 

Lira,  Turkey  
Maria  Theresa  Dollar,  Ab- 

4.3960 

Dos,  Spain  

3.7084 

yssinia  

.4139 

14  5000 

3  3000 

Doubloon  Chile 

3.6497 

Menelik  Dollar,  Abyssinia.  . 

.4139 

Doubloon,  New  Grenada.  .  . 
Doubloon  Spain  Mexico 

15.3400 
15.6500 

Mohur,  India  
Napoleon,  France  

7.1050 
3.8400 

Ducat,    Austria,    Bohemia, 
Hamburg,  Hanover  
Ducat   Holland                  .    . 

2.2800 
2.2826 

Peseta,  Peru  
Peso  fuerte,  Peru.  :  
Pistole,  Rome  

.0973 
.4866 
3.3700 

1.1100 

Pistole   Spain 

3  9000 

Ducat,  Sweden  

2.2000 

Pound,  Egypt  

4.9429 

Escudo,  Chile  
Florin,  Austria-Hungary   .  . 
Florin,  Hanover  (gold)  .  . 
Florin,  Hanover  (silver)  .    .  . 
Florin,  Holland  
Florin  Prussia 

1.8248 
1.9290 
1.6600 
.5600 
.4019 
.5500 

Real,  Peru  
Rial  (Azizi),  Morocco  
Rial  (Hassani),  Morocco  .  . 
Rupee,  Persian  
Sou,  France  .•  
Sovereign   England 

.0486 
.4000 
.4663 
.3750 
.0100 
4  8665 

Florin,  Silesia  
Fuange,  Siam  .  . 

.4800 
.0600 

Toman,  Persia  

1.7046 

MATHEMATICS 


MATHEMATICAL  AND  OTHER  COMMONLY  USED  SIGNS 
AND  ABBREVIATIONS 


=  plus,  or  addition 

=  minus,  or  subtraction 

=  plus  or  minus 

=  multiplication 

=  division 

=  ratio 

f  proportion  2  :  3  : :  4  :  6 
=  <  or  2:3  =  4:6  shows 

I  that  2  is  to  3  as  4  is  to  6 
=  equality 


V 

= 

square  root            , 

* 

= 

cube  root,,  etc. 

,  V3     ' 

= 

square  root  of  3 

•^ 

= 

cube  root  of  5 

.  72 

== 

7  squared 

83 

= 

8  cubed 

a 
ft 

- 

a/b  or  c-T-6 

_ 

therefore,  or  hence 

8>7 

= 

8  is  greater  than  7 

3<5 

n= 

3  is  less  than  5 

D 

= 

square 

D' 

=  square  feet 

D" 

= 

square  inches 

=  round 

signs  of  aggregation  and 
denote  that  the  numbers 

=  enclosed  are  to  be  taken 
together ;  as  (a + b)  X  c 
=  4+3X5  =  35 

=  degrees,  arc  or  thermom- 
eter 

=  minutes  or  feet 

'  =  seconds  or  inches,  30°  40' 
4"  is  30  degrees  40  min- 
utes 4  seconds;  4'  6"  is 
4  feet  6  inches 

=  accents  to  distinguish  let- 
ters as  a',  a",  a"'  and 
read  a  prime,  a  second,  a 
third 

are  read  a  sub  1,  a  sub  £,  and 
a-subb 

=  a  to  the  two-thirds  power, 
or  the  Cube  root  of  a 
squared 

=a  to  the  three  halves 
power,  or  square  root  of  a 
cubed 


MATHEMATICS 


19 


MATHEMATICAL  SIGNS  AND 

Z  =  angle 

L        .       =  right  angle 

_L  =  perpendicular  to 

log  =  logarithm 

log  sin    (  =  logarithmic     sine,     loga- 

log  cos    l          rithmic  cosine 

sin  =  sine 

cos  =  cosine 

tan  = tangent 

cotan         =  cotangent 

sec  =  secant 

cosec          =  cosecant 

versin        =  versed  sine 

coversin     =coversed  sine 

TT  =pi,  or  ratio  of  circum- 

ference of  circle  to  diam- 
eter, 3.14159265 

g  =  acceleration  due  to  grav- 

ity =32.16  ft.  per  sec. 

h,  m,  s  =  hours,  minutes,  seconds, 
6h  5m  4s  is  6  hours,  5  min- 
utes, 4  seconds 

R,  or  r       =  radius 

W,  or  w    ==  weight 


ABBREVIATIONS— Continued 


H.  P. 
G.  C.  D. 
B.  M. 
c.  o.  d. 

oo 

2 

I.  H.  P. 
B.  H.  P. 

A.  W.  G. 

B.W.'G. 

r.   p.  m. 
c.  p. 

B.  T.  U. 
cal 

kw.  or  \ 
K.  W.  / 
f.  o.  b. 
c.  i.  f. 

D.  C. 

A.  C. 


:  horsepowei 

=  greatest  common  divisor 

=  board  measure 

=  cash  on  delivery 

=  infinity 

=  summation ,  or  the  sum 
of  a  series  of  terms 

=  indicated  horsepower 

=  brake  horsepower 

=  American  wire  gauge,  or 
Brown  &  Sharpe 

=  Birmingham  wire  gauge 

=  revolutions  per  minute 

=  candlepower,  or  chem- 
ically pure 

=  British  thermal  units 

=  calories 

=  kilowatts 

=  free  on  board 

=  cost,    insurance,    freight; 

i.  e.,  included  in  cost 
=  direct  current 
=  alternating  current 


ARITHMETIC 

COMMON  FRACTIONS 

To  Add  Fractions.  —  If  the  fractions  are  of  the  same  denominator,  add 
together  the  numerators  only.  Thus,  |  +  f  +  |  =  §=ls- 

If  they  have  different  denominators,  change  them  to  fractions  with  common 
denominators,  and  proceed  as  before.  Thus,  $  +  i+f  =  %%+*$+$$  =  %%• 

To  Subtract  Fractions.  —  If  the  fractions  are  of  the  same  denominator, 
subtract  the  lesser  numerator  from  the  greater.  Thus,  jg  —  fg  =  i*8  =  i- 

If  they  have  different  denominators,  change  them  to  fractions  with  common 
denominators,  and  proceed  as  before.  Thus,  I  —  f  =  f  i  —  ii  =  A- 

To  Multiply  Fractions.  —  Multiply  the  numerators  together  for  the  numer- 
ator, and  the  denominators  for  the  denominator.  Thus,  $  X  fe  XI  =  T?B  =  T&- 

To  Divide  Fractions.  —  Invert  the  divisor  and  multiply.  Thus,  to  divide 
&  by  f  the  §  is  inverted,  and  ^i  =  &Xf  =  T¥s- 

To  Reduce  Compound  Fractions  to  Simple  Fractions.  —  Multiply  the  integer 
by  the  denominator  of  the  fraction,  add  the  numerator  for  the  new  numerator, 
and  place  it  over  the  denominator. 

EXAMPLE.  —  Reduce  5f  to  a  simple  fraction. 

SOLUTION.  —     (5  X  3)  +2  =  17,  the  numerator,  the  fraction  is  therefore  ty. 

To  Reduce  Simple  Fractions  to  Compound  Fractions.  —  Divide  the  numera- 
tor by  the  denominator,  and  use  the  remainder  as  the  numerator  of  the  remain- 
ing fraction. 

EXAMPLE.  —  Reduce  *&  to  a  compound  fraction. 

SOLUTION.  —          9)64(7 

6  3        Compound  fraction  is  7J 

To  Reduce  Common  Fractions  to  Decimal  Fractions.  —  Annex  ciphers  to  the 
numerator,  and  divide  by  the  denominator,  and  point  off  as  many  decimal 
places  in  the  quotient  as  there  are  ciphers  annexed. 
EXAMPLE.  —  Reduce  A  to  a  decimal  fraction. 
SOLUTION.—  1  6  )  9.0  0  0  0  (.5  6  2  5 

80. 
100 
9_6 
40 


80 
80 


20  MATHEMATICS 

NOTE.  —  Ciphers  annexed  to  a  decimal  do  not  increase  its  value.  1.13 
is  the  same  as  1.1300.  Every  cipher  placed  between  the  first  figure  of  a 
decimal  and  the  point  divides  the  decimal  by  10.  Thus,  .13-7-  10  =  .013. 

DECIMALS 

Decimals  are  fractions  that  have  for  their  denominators  10  or  a  power 
of  10,  but  the  denominator  is  usually  omitted.  Thus,  .1  =  ^;  .01  =  TJ0;  .001 

=  ^'etc'  .0075 

•   To  Add  Decimals.  —  Place  whole  numbers  under  whole  .6  3 

numbers,  tenths  under  tenths,  hundredths  under  hund-  1.0  6 

redths,  etc.,  and  add,  placing  the  decimal  point  in  the  sum  1  7.9  3  4  2 

directly  under  the  points  above.     Thus,  1  9.6  3  1  7 

To  Subtract  Decimals.  —  Arrange  the  figures  as  in  addi-         5.9  6  9  7  8 
tion,  and  proceed  as  in  simple  subtraction.     Thus,  o.2  8694 

2.6  8  2  8  4 

To  Multiply  Decimals.  —  Proceed  as  in  4.6  7  5  3  1     (5  decimal  places) 

simple   multiplication,    pointing    off    as  .053     (3  decimal  places) 

many  decimal  places  in  the  result  as  there          1402593 
are  decimal  places  in  both  multiplicand       2337655 
and  multiplier.     Thus,  .24779143     (8  decimal  places) 

To  Divide  Decimals.  —  Proceed  as  in  simple  division,  and  point  off  as  many 
decimal  places  in  the  quotient  as  the  number  of  decimal  places  in  the  dividend 
exceeds  those  in  the  divisor. 

EXAMPLE  1.—  Divide  4.756  by  3.3. 

SOLUTION.—  3.3  )  4.7  5  6  0  0  (  1.4  4  1  2 

33 


EXAMPLE  2.—  Divide  .006  by  20. 
SOLUTION.—  2  0  ).0  0  6  0  (.0  0  0  3 

.60 

To  Reduce  Decimals  to  Common  Fractions.  —  Omit  the  decimal  point  and 
use  the  figures  thus  obtained  for  the  numerator.  The  denominator  will  be  1 
with  as  many  ciphers  attached  as  there  are  places  after  the  decimal  point  and 
will  always  be  10  or  some  multiple  thereof.  Reduce  the  fraction  thus  obtained 
to  its  lowest  terms.  Thus,  in  the  form  of  a  common  fraction,  the  decimal  .025 

-m-«.-*  FORMD1AS 

The  term  formula,  as  used  in  mathematics  and  in  technical  books,  may  be 
defined  as  a  rule  in  which  symbols  are  used  instead  of  words;  in  fact,  a  formula 
-may  be  regarded  as  a  shorthand  method  of  expressing  a  rule. 

The  well-known  rule  for  finding  the  indicated  horsepower  of  a  steam  engine 
may  be  stated  as  follows: 

Divide  the  continued  product  of  the  mean  effective  pressure,  in  pounds  per 
square  inch,  the  length  of  the  stroke,  in  feet,  the  area  of  the  piston,  in  square  inches, 
and  the  number  of  strokes  per  minute  by  83,000;  the  result  will  be  the  horsepower. 

An  examination  of  the  rule  will  show  that  four  quantities  (viz.,  the  mean 
effective  pressure,  the  length  of  the  stroke,  the  area  of  the  piston,  and  the 
number  of  strokes)  are  multiplied  together,  and  the  result  is  divided  by  33,000. 
Hence,  the  rule  might  be  expressed  as  follows: 

mean  effective  pressure     ^,  stroke 
{n  ^^  pgr  squ&re  inch)  X  (in  feet)       ^ 

area  of  piston     v  number  of  strokes     .  oo  nnn 
(in  square  inches)  X        (per  minute)          '  ddlUUU 


MA  THEM  A  TICS  21 

This  expression  may  be  shortened  by  representing  each  quantity  by  a 
single  letter,  thus:  representing  horsepower  by  the  letter  H,  the  mean  effective 
pressure  m  pounds  per  square  inch  by  P,  the  length  of  the  stroke  in  feet  by  L 
the  area  of  the  piston  in  square  inches  by  A,  the  number  of  strokes  per  minute 
by  2V,  and  substituting  these  letters  for  the  quantities  that  they  represent 
the  foregoing  expression  will  reduce  to 

H_PXLXAXN 

33,000       ' 

a  much  simpler  and  shorter  expression.  This  last  expression  is  called  a  formula 
It  is  customary,  however,  to  omit  the  sign  of  multiplication  between  two 
or  more  quantities  when  they  are  to  be  multiplied  together,  or  between  a 
number  and  a  letter  representing  a  quantity,  it  being  always  understood  that 
when  two  letters  are  adjacent  with  no  sign  between  them,  the  quantities 
represented  by  these  letters  are  to  be  multiplied.  Bearing  this  fact  in  mind 
the  formula  just  given  can  be  further  simplified  to 

PL  A  N 

33,000 

PROPORTION,  OR  CAUSE  AND  EFFECT 

Ratio  is  the  relation  of  one  number  to  another  as  obtained  by  dividing  one 
by  the  other.  The  ratio  of  8  to  4  is  8  -4-  4  =  2. 

Simple  proportion  is  the  expression  of  equality  between  equal  ratios;  thus, 
the  ratio  of  10  to  5  is  2  and  the  ratio  of  4  to  2  is,  also,  2.  The  relations  between 
these  are  expressed  thus,  10  :  5  : :  4  :  2,  or  as  10  :  5  =  4  :  2.  The  equality  sign  ( = ) 
being  easier  to  write  than  the  double  colon  (  : :  )  is  the  form  commonly  used. 

Proportions  may  also  be  expressed  as   fractions.     The  preceding  ratio, 

10  :  5  =  4  :  2,  may  be  written  i?  =  |- 

There  are  four  terms  in  every  proportion.  The  first  and  last  terms  are  the 
extremes,  and  the  second  and  third  terms  the  means. 

In  the  ratio  10  :  5  the  first  term,  10,  is  the  antecedent,  and  the  second  term,  5, 
is  the  consequent.  In  the  question  "  If  10  men  earn  $20,  how  much  will  30  men 
earn?"  which  may  be  expressed  in  the  form  10  :  20  =  30  :  y  (y  representing 
the  unknown  amount  the  30  men  will  earn),  the  number  of  men,  10  and  30, 
are  the  antecedents,  or  causes,  and  the  sums  earned,  $20  and  y  dollars,  are  the 
consequents  or  effects. 

Quantities  are  in  proportion  by  alternation  when  antecedent  is  compared 
with  antecedent  and  consequent  with  consequent.  Thus,  if  10  :  5  =  4  :  2, 
then  10  :  4  =  5  :  2. 

Quantities  are  in  proportion  by  inversion  when  the  antecedents  are  made 
consequents  and  the  consequents  antecedents.  Thus,  if  10  :  5  =  4  :  2,  then 
5  :  10  =  2  :4. 

In  any  proportion,  the  product  of  the  means  will  equal  the  product  of  the 
extremes.  Thus,  if  10  :  5  =  4  :  2,  then  5X4  =  10X2. 

A  mean  proportional  between  two  quantities  equals  the  square  root  of  their 
product.  Thus,  a  mean  proportional  between  12  and  3  =  the  square  root  of 
12X3,  or  6,  and  the  proportion  is  expressed  thus,  12  :  6  =  6  :  3. 

If  the  two  means  and  one  extreme  of  a  proportion  are  given,  the  other 
extreme  may  be  found  by  dividing  the  product  of  the  means  by  the  given 
extreme.  Thus,  10  :  5  =  4  :  (),  then  (4X5) -=-10  =  2,  and  the  proportion 
is  10  :  5  =  4  :  2.  This  may  also  be  expressed  algebraically.  If  y  =  the  unknown 
quantity,  the  proportion  is  written  10  :  5  =  4  :  y.  Then  10Xy  =  5X4,  or  Wy 
=  20  and  y  =  20-MO  =  2,  as  before. 

If  the  two  extremes  and  one  mean  are  given,  the  other  mean  may  be  found 
by  dividing  the  product  of  the  extremes  by  the  given  mean.  Thus,  10  :  ( ) 
=  4:2,  then  (10X2)  -^4  =  5,  and  the  proportion  is  10  :  5  =  4  :  2.  This  may  be 
expressed  algebraically.  Thus,  10  :  y  =  4  :  2,  or  10X2  =  yX4,  or  4y  =  20, 
and  y  =  20  -f-  4  =  5,  as  before. 

EXAMPLE. — If  6  men  load  30  cars  in  1  da.,  how  many  cars  will  10  men  load? 

SOLUTION. — The  antecedents,  or  causes  are  the  number  of  men  and  the 
consequents,  or  effects,  the  number  of  cars  loaded  by  them.  If  y  represents 
the  unknown  number  of  cars  loaded  by  the  30  men,  the  proportion  may  be 

cause  effect  cause  effect 

expressed  6  (men)  :  30  (cars)  =  10  (men)  :  y  (cars).     Prom  this,  6Xy  =  30X  10, 
or  6?  =  300,  and  y  =  300  -5-  6  =  50,  the  number  of  cars  loaded  by  10  men. 

A  compound  proportion  is  one  in  which  one  or  both  of  the  ratios  contains 
more  than  one  term.  The  governing  principles  are  as  follows: 


22  MA  THEM  A  TICS 

1.  The  product  of  the  simple  ratios  of  the  first  couplet  equals  the  product 
of  the   simple  ratios  of   the   second   couplet.      Thus,    (7:}5)  =  («:}2) 

-i  Z-=AVI 

~12X14~10X18' 

2.  The  product  of  all  the  terms  in  the  extremes  equals  the  product  of  all 
the  terms  in  the  means.     Thus,  in   {7  !  }|}  =  {Q  !  Jg},  4X7X10X18  =  12 

3.  Any  term  in  either  extreme  equals  the  product  of  the  means  divided 
by  the  product  of  the  other  terms  in  the  extremes.     Thus,  in  the  same  pro- 

5X6X12X14 
portion,  4- 


4.     Any  term  in  either  mean  equals  the  product  of  the  extremes  divided 

by  the  product  of  the  other  terms  in  the  means.  Thus,  in  {2  j  |?  \  =  {  5  j  J9  V, 
5-  (4X7X10X18)-*-  (6X12X14). 

EXAMPLE  1.  —  If  4  men  in  7  da.  earn  $24,  how  much  can  14  men  earn 
in  12  da.? 

SOLUTION.  —  Here  the  antecedents,  or  causes,  are  the  men  and  the  number 
of  days  they  worked  and  the  consequents,  or  effects,  are  the  sums  of  money 
they  earned.  If  y  is  considered  equal  to  the  second  effect,  that  is,  the  unknown 
number  of  dollars  earned  by  14  men  in  12  da.,  the  proportion  is  7  V^) 

:  24  (dollars  =  J^da?  :  y  (dollars>  •  From  this'  y  X  4  X  7  =  24  X  14  X  12,  or  28? 
=  4,032,  or  y  =  $144. 

EXAMPLE  2.  —  If  12  men  in  35  da.  build  a  wall  140  rd.  long,  6  ft.  high,  how 
many  men  can,  in  40  da.,  build  a  wall  of  the  same  thickness  144  rd.  long, 
5  ft.  high? 

SOLUTION.  —  Here,  the  causes  are  the  men  and  the  number  of  days  worked 
and  the  effects  are  the  length  and  height  of  wall  built  by  them.  It  is  to  be 
noted  that  the  thickness  of  the  wall  is  not  considered  as  it  is  the  same  for  each 

set  of  men.     If  y  is  made  equal  to  the  unknown  number  of  men,  35  ^a) 

:  6%  I"*0  =  40  Oil?  :  54(1  tOi*'*  '  From  this>  I2  X  35  X  144  X  5  =  140  X  6  X  y 
X40,  or  33,600^  =  302,400,  or  y  =  9. 

PERCENTAGE 

Percentage  is  a  process  of  computation  in  which  the  basis  of  comparison 
is  a  hundred. 

Per  cent,  means  by,  or  on,  the  hundred.  6  per  cent,  (also  written  6%,  or  .06) 
of  a  quantity  means  6  of  every  hundred  in  the  quantity. 

The  base  is  the  amount  upon  which  the  percentage  is  computed.  In  the 
case  of  money  at  interest,  the  base  is  known  as  the  principal. 

The  rate,  or  rate  per  cent.,  is  the  number  of  hundredths  of  the  base  that  are 
to  be  taken.  In  monetary  transactions,  the  rate  is  commonly  called  interest. 

The  percentage  is  the  sum  obtained  by  multiplying  the  base  (or  principal) 
by  the  rate.  In  finance,  the  percentage  is  always  known  as  the  interest. 

The  amount  is  the  sum  of  the  base  and  percentage  or,  what  is  the  same  thing, 
the  sum  of  the  principal  and  interest. 

To  Find  the  Percentage,  Having  the  Rate  and  the  Base.  —  Multiply  the  base 
by  the  rate  expressed  in  hundredths.  Thus  6%  of  1,930  is  found  as  follows: 
1.  930  X.  06  =115.80. 

To  Find  the  Amount,  Having  the  Base  and  the  Rate.  —  Multiply  the  base 
by  1  plus  the  rate.  Thus,  the  amount  of  $1,930  for  1  yr.  at  6%  is  $  1,  930  X  1.06 
=  $2,045.80. 

To  Find  the  Base,  Having  the  Rate  and  the  Percentage.  —  Divide  the  per- 
centage by  the  rate.  Thus,  if  the  rate  is  6%  and  the  percentage  is  115.80,  the 
base  =  1  15.80  -r-  .06  =  1,930. 

To  Find  the  Rate,  Having  the  Percentage  and  the  Base.  —  Divide  the  per- 
centage by  the  base.  Thus,  if  the  percentage  is  115.80  and  the  base  1,930,  the 
rate  equals  115.80  -5-1,930  =  .06,  or  6%. 

To  Find  the  Rate,.  Having  the  Amount  and  Base.  —  Subtract  the  base  from 
the  amount  ;  this  will  give  the  percentage.  Divide  the  percentage  by  the  base 
to  find  the  rate.  Thus,  if  the  amount  is  $2,045.80  and  the  base  is  $1,930,  the 


MA  THEM  A  TICS  23 

percentage  (or  interest)  is  $2,045.80 -$1,930  =  $115.80.  The  rate  is  then 
115.80 -M.930  =  .06,  or  6%. 

Interest. — Interest  is  money  paid  for  the  use  of  money,  and  may  be  likened 
to  rent  paid  for  the  use  of  a  house  by  a  tenant  to  his  landlord.  Interest  is 
figured  as  a  certain  per  cent,  of  the  money  lent;  6%  is  the  prevailing  rate  in 
the  United  States. 

In  banks  interest  is  generally  figured  on  the  basis  of  there  being  360  da., 
or  12  mo.  9f  30  da.  each,  in  the  year.  The  following  are  short  rules  for  calcu- 
lating 6%  interest  when  360  da.  are  taken  as  l^r.: 

Rule  I. — Multiply  the  principal  by  the  number  of  days  and  divide  by  6,000. 

Rule  II. — Multiply  the  principal  by  the  number  of  months  and  divide  by  200. 

At  6%  a  year,  the  interest  on  $1  for  1  mo.  is  3%. 

A  note  is  a  written  promise  to  pay  a  certain  sum  of  money  at  a  certain 
time  and  at  a  certain  rate  of  interest  and,  usually,  at  a  certain  place.  The 
amount  of  money  to  be  paid  is  the  principal  and  is  often  called  the  face  of  the 
note.  The  discount  is  the  interest  on  the  money  for  the  given  time  and  at  the 
given  rate,  and  is  so  called  because  it  is  deducted  (or  discounted)  in  advance. 
The  proceeds  is  the  net  amount  received;  that  is,  it  is  the  face  of  the  note  less  the 
discount  (or  interest)  paid  in  advance. 

Banks  charge  interest,  as  already  explained,  on  the  basis  of  there  being  360 
da.  in  the  year,  and  for  the  exact  number  of  days  elapsed.  N9tes  are  com- 
monly made  for  1,  2,  or  3  mo.,  or  for  30,  60,  or  90  da.  Thus,  if  on  June  15 
three  sums  are  borrowed  at  1,  2,  and  3  mo.  time,  the  notes  will  be  due  on  the 
15th  day  of  July,  August,  and  September,  respectively.  But  interest  will  not 
be  charged  for  TV  B,  and  \  yr.  in  the  individual  cases,  but  for  30,  61,  and  92  da., 
and  these  days  are  ^g,  3%,  and  $&  yr.,  respectively.  On  the  other  hand,  should 
three  other  sums  of  money  be  borrowed  on  the  same  day  for  30,  60,  and  90  da., 
the  notes  will  fall  due  on  July  15,  August  14,  and  September  13,  and  interest 
would  be  charged  for  the  30,  60,  and  90  da. 

EXAMPLE  1. — What  is  the 'date  of  payment,  discount,  and  proceeds  of  a 
90-da.  note,  for  $150,  dated  July  27? 

SOLUTION. — The  date  of  payment  will  be  90  da.  from  July  27,.  or  on  October 
25,  as  there  are  31  da.  each  in  the  months  of  July  and  August.  The  discount 
will  be  the  interest  for  90  da.  at  6% ,  which  by  rule  I  is  (150X  90)  -r  6,000  =  $2.25. 
The  proceeds  will  be  $150 -$2.25  =  $147.75. 

EXAMPLE  2. — What  is  the  date  of  payment,  discount,  and  proceeds  of  a 
3-mo.  note  for  $150,  dated  July  27? 

SOLUTION. — The  date  of  payment  is  3  mo.  from  July  27,  or  October  27.  As 
the  number  of  days  between  these  dates  is  92,  by  rule  I  the  discount  will  be  (150 
X  92)  -=-6,000  =  $2.30.  The  proceeds  will  be  $150  -$2.30  =  $147.70. 

Trade  Discount. — A  discount  is  an  abatement  from  the  price  of  an  article 
for  some  consideration,  frequently  the  payment  of  cash  upon  the  receipt  of  the 
goods  or  material  purchased.  Discounts  are  generally  expressed  as  a  certain 
per  cent,  of  the  purchase  price;  therefore,  the  net,  or  real,  cost  of  an  article  is 
found  by  multiplying  the  first  cost  by  1.00  minus  the  discount.  Thus,  if  a  car- 
load of  corn  is  billed  at  $438,  with  a  discount  of  5%  for  cash,  the  price  for 
immediate  payment  will  be  438X  (1.00-.05)  =438X.95  =  $416.10. 

Discounts  are  frequently  compound  or  continuous;  that  is,  there  are  two 
or  more  discounts  upon  the  price  of  an  article.  Thus,  a  discount  may  be 
quoted  as  "ten,  ten,  and  fiye."  This  does  not  mean  that  the  total  discount 
is  the  sum  of  the  three  single  discounts,  or  25%;  each  discount  and  the 
resultant  net  price  are  figured  separately.  In  the  case  in  queston,  if  the  first 
cost  of  the  article  was  $100,  the  first  net  cost  will  be  100  X  (1.00-  .10  =  .90)  =  $90; 
the  second  net  cost  will  be  90 X  (1.00 -.10  =  .90)  =  $81;  and  the  third  net,  or 
final  cost  will  be  81 X  (1.00-  .05  =  .95)  =  $76.95.  The  total  discount  is,  there- 
fore, $100.00 -$76.95  =  $23.05,  or  23.05%  and.not  25%. 

RECIPROCALS 

The  reciprocal  of  a  number  is  unity,  or  1,  divided  by  the  number.  Thus, 
the  reciprocal  of  5  is  l-f-5  =  .2.  Reciprocals  are  always  expressed  decimally. 
The  reciprocal  of  a  whole  number  is  entirely  decimal,  while  the  reciprocal  of 
a  number  less  than  unity  is  either  a  whole  number  or  a  whole  number  followed 
by  a  decimal.  Thus,  the  reciprocal  of  .5  is  1  -T-  .5  =  2,  and  the  reciprocal  of  .6  is 
1-7- .6  =  1.6666+.  Reciprocals  are  used  to  avoid  the  labor  of  division.  Thus, 
the  operation  represented  by  100  -f-  621  may  be  performed  in  the  ordinary  way 
by  long  division,  or  100  may  be  multiplied  by  the  reciprocal  of  621.  Reciprocals 
of  numbers  from  1  to  1,000  are  given  in  connection  with  the  table  of  powers, 


24  MATHEMATICS 

etc.,  near  the  end  of  this  volume.  From  this  table,  the  reciprocal  of  621  is 
found  to  be  .001610306,  and  100  -v-  621  =  100  X. 001610306  =  .1610306. 

Reciprocals  of  numbers  that  are  multiples  or  submultiples  of  those  in  the 
table  may  be  obtained  directly  therefrom  by  shifting  the  decimal  point.  Thus, 
the  reciprocal  of  62,100  is  rfo  of  the  reciprocal  of  621,  or  .00001610306.  The 
reciprocal  of  6.21  is  100  times  the  reciprocal  of  621,  or  .1613036,  and  the  reci- 
procal of  .0621  is  10,000  times  that  of  621,  or  16.10306. 

Reciprocals  of  numbers  intermediate  between  those  in  the  table  may  be 
found  therefrom  by  interpolation.  Thus,  the  reciprocal  of  621.25  is  .0016096579, 
and  by  shifting  the  decimal  point  the  reciprocal  of  6.2125  is  .16096579. 

ARITHMETICAL  PROGRESSION 

Quantities  are  said  to  be  in  arithmetical  progression  when  they  increase  or 
decrease  by  a  common  difference.  The  following  is  an  increasing  series  in  arith- 
metical progression:  1,  3,  5,  7,  9,  11,  13;  if  the  figures  are  read  backwards, 
13,  11,  9,  etc.,  it  becomes  a  decreasing  series.  In  the  first  series,  the  first  term 
is  1;  the  last  term  13;  the  number  of  terms  7;  the  common  difference  2;  and  the 
sum  of  the  terms  49.  In  any  arithmetical  progression, 
Let  /=  first  term; 

I  =  last,  or  »th  term; 
d  =  common  difference; 
«  =  number  of  terms; 
5  =  their  sum. 


(1) 

(2)  .  za 

n  =  2l+d^(2l+W-8ds 

(3)  ,_,          2d 

<-i±T  (") 

«=?fe^  (u> 

(5)          ^^ffSr  d5) 

(6>  :     - (16) 

(17) 
s  =  ?(2f+(n-l)d]  (18) 

n  =  ^+l  (9)  ,.W+«i^=/>  (19) 

d  2  ^         2d 

n=^Tl  (10>  s  =  ^[2l-(n-l)d]  (20) 

EXAMPLE  1. — During  the  last  month  of  the  year,  the  mules  at  a  certain  mine 
used  40  bales  of  hay.  The  consumption  was  2  bales  less  than  this  during 
November,  and  similarly  less  for  each  month  until  the  first  of  the  year.  What 
was  the  consumption  of  hay  during  January,  and  how  many  bales  were  used 
during  the  year? 

SOLUTION. — Here  w  =  12  (mo.),  d  =  2  (bales),  and  /  =  40  (bales  during 
December).  It  is  required  to  find  / and  s.  To  find  /,  substituting  the  various 
values  in  formula  6  gives  /=  40  —  (12  —  1)  X  2  =  40  —  22  =  18  =  number  of  bales 
used  in  January.  To  find's,  substituting  in  formula  20  gives  5  =  ^X[2X40 
-(12-1)X2]  =  6X(80-22)=6X58  =  348  bales  during  the  year.  It  will  be 
noted  that  /  has  been  found  in  the  first  part  of  the  solution  and  it  may  be  used 
to  find  5  in  formula  17  which  is  more  simple  than  formula  20. 

EXAMPLE  2. — A  contractor  agrees  to  put  down  a  bore  hole  for  $1  a  ft.  for 
the  first  100  ft.;  $3  a  ft.  for  the  second  100  ft.;  and  $2  a  ft.  additional  for  each 
successive  100  ft.  Upon  completion  of  the  work  he  was  paid  $6,400.  How 
deep  was  the  hole  and  what  was  the  cost  per  foot  of  the  last  100  ft.? 

SOLUTION.— Here /=  100  (dollars),  s  =  $6,400,  and  d  =  200  (dollars  increase 
in  cost  per  100  ft.).  Using  formula  11, 


MATHEMATICS  25 

=  200-  (2X  100)  +  V[(2X  100)  -200p+  (8X200X6.  400) 
_  2X200  ~~ 

__  200  -  200  +  V(200  -  200)2+  10,240,000     0+  Vp2+  10,240,000 

400  400 

=  A/10,240,000     3,200 
400  400 

That  is,  there  are  8  sections  each  100  ft.  deep,  or  the  total  depth  of  the  hole  is 
8X100  =  800  ft.  By  using  the  value  of  n,  just  found,  the  last  term  may  be 
determined  by  means  of  the  simple  formula  1.  By  substitution,  the  last  term 
=  100+(8-l)X200  =  100  +  1,400=  1,500.  That  is,  the  last  100  ft.  cost 
$1,500.  or  $15  a  ft. 

GEOMETRICAL  PROGRESSION 

A  series  of  quantities,  in  which  each  is  derived  from  that  which  precedes 
it,  by  multiplicaton  by  a  constant  quantity,  is  called  a  geometrical  progression. 
If  the  multiplier  is  a  whole  number,  the  progression  is  styled  increasing;  if 
it  is  a  fraction,  the  progression  is  styled  decreasing.  The  series  1,  2,  4,  8,  16,  32 
has  2  for  a  multiplier,  and  is  an  increasing  progression.  The  series  32,16,  8,  4,  2, 
1,  \,  i.  I.  A.  T*  has  \  for  a  multiplier,  and  is  a  decreasing  progression. 

The  common  multiplier  in  a  geometrical  progression  is  called  the  common 
ratio;  or,  briefly,  the  ratio. 
Let  /=  first  term; 

J  =  last  term,  whose  number  from  /  is  n; 
n  =  number  of  terms; 
r  =  ratio; 
5  =  sum  of  terms. 


(2)  log, 

log 


f=s-r(s-l)  (4)  r=J=l 

log'  "^T"  <9) 

n»-|fl  (5)  ,-£/  (10) 

EXAMPLE  1.—  How  much  will  it  cost  to  sink  a  shaft  1,500ft.  deep  at  the 
rate  of  &c.  for  the  first  50  ft.;  {c.  for  the  second  50  ft.;  £c.  for  the  third  50  ft.; 
and  so  on  at  the  same  rate? 

SOLUTION.  —  In  this  case,/=  ^;  n  =  30;  and  r  =  2.  Substituting  in  formula  1, 
I  =  AX  (2»)=  33,554,432,  and  from  formula  10 


EXAMPLE  2.  —  At  the  end  of  a  certain  period  a  mine  had  produced  126,000 
T.  of  coal.  The  production  for  the  first  6  mo.  was  2,000  T.,  which  was  doubled 
each  6  mo.  How  long  had  the  mine  been  in  operation? 

SOLUTION.—  In  this  case,  5  =  126,000;  /=  2,000;  and  r  =  2.  Using  formula  6 
log  rl26.000X(2-l)  i 


• 

mine  had  been  in  operation  for  six  periods  of  6  mo.  each,  or  for  3  yr. 

INVOLUTION 

Involution  is  the  process  of  finding  any  power  of  a  number.  The  power 
of  a  number  is  the  product  arising  from  multiplying  the  number  by  itself  as 
many  times  as  is  indicated  by  another  number  known  as  the  exponent.  Thus, 
42  is  read  four  squared,  or  four  to  the  second  power,  and  is  equal  to  4X4  =  16. 
Similarly  53  is  read  five  cubed,  or  five  to  the  third  power,  and  is  equal  to  5X5X5 
=  125.  Likewise,  25  is  read  two  to  the  fifth  power,  or  the  fifth  power  of  two,  and 
is  equal  to  2X2X2X2X2  =  32.  The  figures  2,  3,  and  5,  written  to  the  right 
and  above  the  numbers  are  the  exponents, 


MATHEMATICS 
FIRST  NINE  POWERS  OF  FIRST  NINE  NUMBERS 


1 

j) 

8 

Jl  u, 

•E  S 

3$ 

3% 

J3  t-. 

£  w 

3  v 

3 
a 
£ 

I 

3 
O 

II 

Kjfi 

II 

0)    ^ 

is 

."§0 

W^ 

Is 

1 

1 

1 

1 

i 

i 

1 

1 

1 

2 

4 

8. 

16 

32 

64 

128 

256 

512 

3 

9 

27 

81 

243 

729 

2,187 

6,561 

19,683 

4 

16 

64 

256 

1,024 

4,096 

16,384 

65,536 

262,144 

5 

25 

125 

625 

3,125 

15.625 

78,125 

390,625 

1,953,125 

6 

30 

216 

1,296 

7,776 

46,656 

279,936 

1,679,616 

10,077,696 

7 

49 

343 

2,401 

16,807 

117,649 

823,543 

5,764,801 

40,353,607 

8 

64 

512 

4,096 

32,768 

262,144 

2,097,152 

16,777,216 

134,217,728 

9 

81 

729 

6,561 

59,049 

531,441 

4,782,969 

43,046,721 

387,420,489 

The  power  of  a  number  may  be  obtained  by  multiplying  together  any  two 
or  more  lower  powers,  the  sum  of  whose  exponents  is  equal  to  the  exponent  of 
the  required  power.  Thus,  if  n  =  any  number,  «9  =  n4X«8  =  wXn2Xw6  =  »2Xw3 
X«4,  etc.  Similarly,  w7  =  w2Xn2Xw3  =  n2X«5,  etc. 

A  table  of  squares  and  cubes  is  given  at  the  end  of  this  volume.  The 
powers  of  numbers  not  in  the  table  may  be  found  by  interpolation  with  suffi- 
cient accuracy  for  most  purposes.  Logarithms  afford  a  rapid  method  of 
determining  powers. 

EVOLUTION 

'  The  root  of  a  number  is  one  of  the  equal  factors  of  a  number.  The  number 
of  equal  factors  in  any  number  is  indicated  by  a  number  known  as  the  index 
of  the  root.  This  index,  which  is  written  to  the  left  and  a  little  above  the 
sign  \,  shows  how  many  factors  compose  the  number,  or  how  many  times  the 
root  must  be  multiplied  by  itself  to  produce  the  number. 

To  Find  the  Square  Root  of  a  Number: 

Rule. — I.  Separate  the  given  number  into  periods  of  two  figures  each,  begin- 
ning at  the  units  place. 

n.  Find  the  greatest  number  whose  square  is  contained  in  the  period  on  the 
left;  this  will  be  the  first  figure  in  the  root.  Subtract  the  square  of  this  figure  from 
the  period  on  the  left,  and  to  the  remainder  annex  the  next  period  to  form  a  dividend. 

HI.  Divide  this  dividend,  omitting  the  figure  on  the  right,  by  double  the  part  of 
the  root  already  found,  and  annex  the  quotient  to  that  part,  and  also  to  the  divisor; 
then,  multiply  the  divisor  thus  completed,  by  the  figure  of  the  root  last  obtained, 
and  subtract  the  product  from  the  dividend. 

IV.  Add  the  root  last  found  to  the  last  trial  divisor  to  form  a  new  trial  divisor. 
Divide  the  dividend  by  this  new  trial  divisor  and  the  quotient  will  be  the  next  figure 
of  the  root,  which  quotient  is  to  be  annexed  to  the  trial  divisor  to  form  a  new  complete 
divisor.     Multiply  this  last  complete  divisor  by  the  figure  of  the  root  last  obtained 
and  subtract  from  the  dividend. 

V.  Bring  down  the  next  period  to  form  a  new  dividend  and  continue  'as  before 
until  all  the  periods  have  been  used. 

VI.  //  it  is  desired  to  carry  the  root  farther,  annex  periods  of  two  ciphers  each, 
and  proceed  as  before. 

EXAMPLE.— Find  the  square  root:  (a)  of  874.225;  (b)  of  .00874225. 
SOLUTION. — 


(a) 


874.2  2'50  (29.56  7  + 

4 

474 

441 

3322 

2925 


59127 


183 

3 

1865 


.0  0'8  7'4  2'2  5  (.0  9  3  5 
0 

~87 
8J 
642 
549 
9325 
9325 


MA  THEM  A  TICS  27 

To  Find  the  Cube  Root  of  a  Number: 

Rule. — I.  Separate  the  given  number  into  periods  of  three  figures,  each  begin- 
ning at  the  units  place. 

II.  Find  the  greatest  number  whose  cube  is  contained  in  the  period  on  the  left; 
this  will  be  the  first  figure  in  the  root.  Subtract  the  cube  of  this  figure  from  the 
period  on  the  left,  and  to  the  remainder  annex  the  next  period  to  form  a  dividend. 

HI.  Divide  this  dividend  by  the  partial  divisor,  which  is  three  times  the  square 
of  the  root  already  found  considered  as  tens;  the  quotient  is  the  second  figure  of  the 
root. 

IV.  To  the  partial  divisor  add  3  times  the  product  of  the  second  figure  of  the 
root  by  the  first,  considered  as  tens,  also  the  square  of  the  second  figure;  the  result 
will  be  the  complete  divisor. 

V.  Multiply  the  complete  divisor  by  the  second  figure  of  the  root,  and  subtract 
the  product  from  the  dividend. 

VI.  //  there  are  more  periods  to  be  brought  down,  proceed  as  before,  using  the 
part  of  the  root  already  found,  the  same  as  the  first  figure  in  the  previous  process. 

VII.  //  it  is  desired  to  carry  the  root  farther,  annex  periods  of  three  ciphers 
each,  and  proceed  as  above. 

EXAMPLE. — Find  the  cube  root  of  12,813,904. 

SOLUTION. —  1  2'8  1  3'9  0  4  (  2  3  4 

First  partial  divisor,  3X20'       =        1200          4813 
3X20X3=  180 

32=  9 

First  complete  divisor  =        1389 

Second  partial  divisor,  3X2302=  1  5  8700 

3X230X4  =        2760 

42  = 16^ 

Second  complete  divisor  =  161476  645904 

A  table  of  squares  and  cubes  is  given  at  the  end  of  this  volume  by  means 
of  which  square  roots  and  cube  roots  may  be  readily  extracted.  The  roots 
of  numbers  whose  powers  are  within  the  limits  of  the  table,  1,000,000  for 
squares  and  1,000,000,000  for  cubes,  may  be  obtained  directly,  by  finding  in 
the  proper  column,  the  number  whose  root  is  to  be  extracted  and  in  the  column 
headed  Number  the  root  will  be  found.  Thus,  if  it  is  desired  to  extract  the 
cube  root  of  825,293,672,  the  number  will  be  found  in  the  column  headed  Cube, 
and  on  the  same  line  in  the  column  headed  Number  are  the  figures  938,  which 
is  the  cube  root  of  the  required  number. 

Often,  by  shifting  and  replacing  the  decimal  point,  the  roots  of  numbers 
not  in  the  table  may  conveniently  be  found.  The  decimal  point  must  be  shifted 
the  number  of  figures  there  are  in  a  period,  two  in  the  case  of  squares  and 
three  in  that  of  cubes.  Thus,  if  it  is  desired  to  extract  the  cube  root  of 
14.706125,  the  decimal  point  may  be  shifted  either  three  or  six  figures  (one  or 
two  periods)  to  the  right  and  the  cube  root  of  14,706.125  or  of  14,706,125 
extracted.  After  the  root  is  extracted,  the  decimal  point  must  be  restored. 
In  the  case  just  given,  by  shifting  the  decimal  point  six  places,  or  two  periods, 
the  cube  root  of  14,706,125  is  found  to  be  245.  As  there  is  but  one  period 
before  the  decimal  point  in  the  number,  there  can  be  but  one  figure  before  the 
decimal  point  in  the  root;  hence,  the  root  is  2.45.  Similarly,  in  extracting 
the  cube  root  of  .000000100544625  the  decimal  point  and  the  six  ciphers  (two 
periods)  may  be  dropped  and  the  cube  root  of  100,544,625  extracted.  This 
root  is  found  to  be  465.  As  there  are  two  periods  (of  three  ciphers  each)  after 
the  decimal  point  in  the  number,  there  must  be  two  ciphers  (one  for  each  period) 
after  the  decimal  point  in  the  root.  Hence,  the  cube  root  of  .000000100544625 
is  .00465. 

The  square  or  cube  roots  of  numbers  not  in  the  table  may  be  found,  approx- 
imately, by  interpolation.  When  finding  the  square  root  of  874.225,  the 
decimal  point  may  be  shifted  one  period,  or  two  figures,  to  the  right,  and  the 
square  root  of  87'422.50  extracted.  This  is  found  to  be  between  the  squares 
of  295  and  296.  The  interpolation  is  made  as  follows: 

Number    Root  Number  Root 

87,616  =  2962  87,422.50  =  ? 

87,025  =  2952     -  87,025.00  =  2952 

591  =  first  difference  397.50  =  second  difference 


28 


MATHEMATICS 


Then,  second  difference-?- first  difference  =  397.50 -5- 591  =  .656.  This  is  to 
be  added  to  295  and  the  square  root  of  87,422.50  is  found  to  be  295.656.  As 
the  decimal  point  has  been  shifted  one  period  to  the  right  it  must  now  be 
shifted  one  figure  to  the  left,  and  the  square  root  of  874.225  is  29.5656.  As 
the  true  root,  29.5673,  is  within  .0017  of  the  root  found  by  interpolating  in 
the  table,  this  method  is  accurate  enough  for  all  practical  purposes. 

Finding  the  Fourth  and  the  Fifth  Root  of  a  Number. — Fourth  roots  may  be 
found  by  taking  the  square  root  of  the  square  root,  that  is,  by  extracting  the 
square  root  twice. 

Fifth  roots  are  rarely  required,  and  when  needed,  occur  in  formulas  involving 
coefficients  of  friction  (k,  in  problems  relating  to  ventilation,  etc.)  whose 
values  are  uncertain  within  50%  or  more.  Under  such  circumstances,  it  is 
apparent  that  even  a  very  large  percentage  of  error  in  the  fifth  root  is  allow- 
able. In  the  vast  majority  of  cases,  no  error  of  importance  will  be  introduced 
by  using  for  the  true  root  the  nearest  value  thereto,  taken  directly  from  the 
table. 

TABLE  OF  FIFTH  POWERS 


No. 

Power 

No. 

Power 

No. 

Power 

No. 

Power 

1.0 

1.00000 

3.3 

391.35393 

5.6 

5,507.31776 

7.9 

30,770.56399 

1.1 

1.61051 

3.4 

454.35424 

5.7 

6,016.92057 

8.0 

32,768.00000 

1.2 

2.48832 

3.5 

525.21875 

5.8 

6,563.56768 

8.1 

34,867.84401 

1.3 

3.71293 

3.6 

604.66176 

5.9 

7,149.24299 

8.2 

37,073.98432 

1.4 

5.37824 

3.7 

693.43957 

6.0 

7,776.00000 

8.3 

39,390.40643 

1.5 

7.59375 

3.8 

792.35168 

6.1 

8,445.96301 

8.4 

41,821.19424 

1.6 

10.48576 

3.9 

902.24199 

6.2 

9,161.32832 

8.5 

44,370.53125 

1.7 

14.19857 

4.0 

1,024.00000 

6.3 

9,924.36543 

8.6 

47,042.70176 

1.8 

18.89568 

4.1 

1,158.56201 

6.4 

10,737.41824 

8.7 

49,842.09207 

1.9 

24.76099 

4.2 

1,306.91232 

6.5 

11,602.90625 

8.8 

52,773.19168 

2.0 

32.00000 

4.3 

1,470.08443 

6.6 

12,523.32576 

8.9 

55,840.59449 

2.1 

40.84101 

4.4 

1,649.16224 

6.7 

13,501.25107 

9.0 

59,049.00000 

2.2 

51.53632 

4.5 

1,845.28125 

6.8 

14,539.33568 

9.1 

62,403.21451 

2.3 

64.36343 

4.6 

2,059.62976 

6.9 

15,640.31349 

9.2 

65,908.15232 

2.4 

79.62624 

4.7 

2,293.45007 

7.0 

16,807.00000 

9.3 

69,568.83693 

2.5 

97.65625 

4.8 

2,548.03968 

7.1 

18,042.29351 

9.4 

73,390.40224 

2.6 

118.81376 

4.9 

2,824.75249 

7.2 

19,349.17632 

9.5 

77,378.09375 

2.7 

143.48907 

5.0 

3,125.00000 

7.3 

20,730.71593 

9.6 

81,537.26976 

2.8 

172.10368 

5.1 

3,450.25251 

7.4 

22,190.06624 

9.7 

85,873.40257 

2.9 

205.11149 

5.2 

3,802.04032 

7.5 

23,730.46875 

9.8 

90,392.07968 

3.0 

243.00000 

5.3 

4,181.95493 

7.6 

25,355.25376 

9.9 

95,099.00499 

3.1 

286.29151 

5.4 

4,591.65024 

7.7 

27,067.84157 

10.0 

100,000.00000 

3.2 

335.54432 

5.5 

5,032.84375 

7.8 

28,871.74368 

This  table  may  be  used  in  the  same  way  as  the  table  of  squares  and  cubes,  to 
find  the  fifth  roots  of  intermediate  values.  It  must  be  remembered  that  the 
periods  are  composed  of  five  figures  and  that  there  must  be  one  figure  in  the 
root  for  each  such  period  in  the  number. 

EXAMPLE.— Find  the  fifth  root  of  3,827,963,000. 

SOLUTION. — By  pointing  off  and  inserting  a  decimal  point,  the  fifth  root 
of  38,279.63  is  to  be  extracted.  This  is  seen  to  lie  between  8.2  and  8.3  and 
an  interpolation,  which  may  be  made  mentally,  shows  it  to  be  about  midway 
between  these  or  is  8.25.  By  restoring  the  decimal  point,  the  fifth  root  of  the 
given  number  is  found  to  be  82.5.  As  the  root,  by  seven-place  logarithms,  is 
found  to  be  82.5265,  this  simple  approximation  is  accurate  enough  for  use  in 
those  formulas  in  which  fifth  roots  occur.  Should  greater  accuracy  be 
demanded  it  is  possible  to  interpolate  as  follows: 

Number      Root  Number        Root 

39,390.40463  =  8.35  38,279.63000=      ? 

37,073.98432  =  8.25  37,073.98432  =  8.25 

2,316.42031  =  first  difference  1,205.64568  =  second  difference 

Second  difference -5- first  difference  =  1,205.64568-^2,316.42031  =  .5205,  which 
is  to  be  annexed  to  8.2,  making  the  root  8.25205.  By  restoring  the  decimal 
point  the  fifth  root  of  3,827,963,000  is  82.5205. 


MATHEMATICS  29 

Simple  Method  of  Extracting  Roots.— A  simple  method  of  extracting  roots 
where  tables  are  not  available  and  the  rules  have  been  forgotten,  is  based  upon 
Sir  Isaac  Newton's  Method  of  Approximating  the  Roots  of  Higher  Equations. 
The  method  is  based  on  the  fact  that  any  number  is  composed  of  as  many 
equal  factors  as  are  indicated  by  the  index  of  the  root.  Thus,  the  fifth  root  is 
one  of  the  five  equal  factors  of  the  number  and  the  cube  root  is  one  of  the  three 
equal  factors,  and  similarly. 

If  the  number  whose  root  is  required  is  placed  equal  to  n  in  the  case  of  the 
cube  root,  it  may  be  considered  that  aXbXc  =  n.  When  these  factors  are 
equal,  that  is,  when  a  =  b  =  c,  the  cube  root  is  found.  From  the  given  equation, 

aXbXc  =  n,  c=       ..     If  a  is  made  equal  to  b,  and  a  value  is  assumed  for  them 

as  near  the  cube  root  as  possible,  the  average  of  the  values  of  a,  b,  and  c,  will 
be  nearer  the  true  root  than  either  a  or  b.  This  value  of  c  is  known  as  the 
first  approximation,  and  may  be  placed  equal  to  a  and  b  to  find  a  new  value 
for  c,  the  average  of  the  three  values  being  the  second  approximation.  These 
approximations  may  be  carried  indefinitely,  but  with  a  little  practice  it  will 
be  found  that  the  first  approximation  answers  all  practical  purposes. 

EXAMPLE  1.— Find  the  cube  root  of  987,654,321. 

SOLUTION. — Pointing  off  and  inserting  a  decimal  point,  it  is  necessary  to 
extract  the  cube  root  of  987.654321.  If  a  table  of  cubes  is  not  available,  one 
should  be  prepared.  The  number  will  be  found  between  729  =  93  and  1,000 
=  103;  that  is,  the  cube  root  of  the  number  is  between  9  and  10.  In  this  case  a 
XbXc  =  987.654321,  and  when  a  =  b  =  c,  the  root  is  found.  An  interpolation 
between  the  cube  roots  of  729  and  1 ,000  shows  that  the  cube  root  of  the  number 
is  about  9.92.  Making  a  =  &  =  9.92  and  substituting  gives  9.92X9.92Xc 
=  987.654321,  from  which  c=  10.036.  The  mean  of  these  values  is  (9.92 
+9.92  +  10. 036)  -5- 3  =  9.95867.  This  is  the  first  approximate  root,  which  may 
be  placed  equal  to  a  and  b  to  find  a  second  approximate  root.  In  the  case  of  the 
first  root,  by  restoring  the  decimal  point,  the  cube  root  of  987,654,321  is  found 
to  be  995.867,  which  is  identical  with  that  extracted  by  means  of  seven-place 
logarithms.  Such  coincidence  is  unusual,  but  indicates  that  by  carefully 
selecting  the  trial  factors,  a  first  approximation  answers  for  all  but  abstract 
problems. 

EXAMPLE  2.— Find  the  fifth  root  of  3,827,963,000. 

SOLUTION. — Pointing  off  and  placing  a  decimal  point  between  the  periods 
gives  a XbXcXdXe  =  38,279.63.  From  a  table  of  powers,  the  fifth  root  of 
this  number  is  found  to  lie  between  8  and  9,  and  an  interpolation  shows  it  to 
be  about  8.21.  Then  8.21X8.21X8.21X8.21X«  =  38,279.63.  From  this  e 
=  8  425  and  the  mean  of  the  five  factors  is  8.253.  Restoring  the  decimal  point 
shows  that  the  first  approximate  fifth  root  of  3,827,963,000  is  82.53.  This  may 
be  used  for  a  second  approximation,  giving  82.5261,  but  the  first  should  answer 
any  purpose.  This  method  may  be  compared  with  that  based  on  the  use  of 
tables.  

LOGARITHMS 

EXPONENTS 

By  the  use  of  logarithms,  the  processes  of  multiplication,  division,  involu- 
tion, and  evolution  are  greatly  shortened,  and  some  operations  may  be  per- 
formed that  would  be  impossible  without  them.  Ordinary  logarithms  cannot 
be  applied  to  addition  and  subtraction.  A  logarithm  is  the  exponent  of  the 
power  to  which  a  fixed  number,  called  the  base,  must  be  raised  to  produce  a 
given  number. 

Although  any  positive  number  except  1  can  be  used  as  a  base  and  a  table 
of  logarithms  calculated,  but  two  numbers  have  ever  been  employed.  For  all 
arithmetical  operations  (except  addition  and  subtraction)  the  logarithms  used 
are  called  the  Briggs,  or  common,  logarithms,  and  the  base  used  is  10.  In 
abstract  mathematical  analysis,  the  logarithms  used  are  variously  called 
hyperbolic,  Napierian,  or  natural  logarithms,  and  the  base  is  2.718281828+ . 
the  common  logarithm  of  any  number  may  be  converted  into  a  Napierian 
logarithm  by  multiplying  the  common  logarithm  by  2.30258509 +  ,  which  is 
usually  expressed  as  2.3026,  and  sometimes  as  2.3.  Only  the  common  system 
of  logarithms  will  be  considered  here. 

As  in  the  common  system  the  base  is  10,  all  numbers  are  to  be  regarded 
as  powers  of  10;  therefore,  as  !Qi  =  10.  10*=  100,  10»  =  1,000,  etc.,  the  logarithms 
(exponents)  of  10,  100,  1,000,  etc.,  are  1,  2,  3,  etc.,  respectively.  Similarly, 


30  M  A  THEM  A  TICS 

as  10-1  =  ^5  =  .!,  10-2  =  Tfo  =  .01,  10-3  =  ^3  =.001,  etc.,  the  logarithms  (expo- 
nent?) of  .1,  .01,  .001,  etc.,  are  -1,  -2,  -3,  etc.,  respectively. 

From  the  foregoing,  it  is  seen  that  while  the  logarithms  of  exact  powers 
of  10  and  of  decimals  like,  .1,  .01,  .001,  etc.,  are  whole  numbers,  the  logarithms 
of  all  other  numbers  are  wholly  or  in  part  fractional,  the  fractional  part  being 
expressed  decimally.  Thus,  to  produce  20,  10  must  have  an  exponent  of 
approximately  1.30103,  or  101'30103  =  20,  very  nearly,  the  degree  of  exactness 
depending  on  the  number  of  decimal  places  used.  Hence,  log  20=1.30103. 
A  logarithm,  therefore,  usually  consists  of  two  parts;  a  whole  number,  called 
the  characteristic,  and  a  fraction,  called  the  mantissa.  While  mantissas  are 
always  to  be  regarded  as  positive,  characteristics  may  be  either  positive  or 
negative.  From  the  foregoing,  it  is  apparent  that  the  characteristics  of  the 
logarithms  of  all  numbers  less  than  unity  are  negative,  while  for  numbers 
greater  than  unity,  they  are  positive.  Negative  characteristics  are  expressed 
by  the  sign,  — ,  placed  above  the  figures;  thus,  log  .20  =  1.30103. 

Rule  for  Characteristics. — The  characteristic  of  the  logarithm  of  a  number 
equal  to  or  greater  than  unity  is  1  less  than  the  number  of  digits  in  the  number. 
In  the  case  of  numbers  less  than  unity,  the  characteristic  is  determined  by  the 
position,  with  respect  to  the  decimal  point,  of  the  first  digit  in  the  number.  If  the 
first  digit  is  found  in  the  tenths  column,  the  characteristic  is  1;  if  in  the  hundredths 
column,  it  is  2;  and  similarly;  or  the  characteristic  is  1  more  than  the  number  of 
ciphers  following  the  decimal  point. 

Log  .0005  =  2.69897  Log  5  =    .69897 

Log  .005   =3.69897  Log  50         =1.69897      ' 

Log  .05     =2.69897  Log  500       =2.69897 

Log  .5       =1.69897  Log  5,000   =3.69897 

Log  50,000  =  4.69897 

FINDING  THE  LOGARITHM  OF  A  NUMBER 

A  table  of  logarithms,  containing  the  mantissas  of  the  logarithms  from  1 
to  9,999  to  five  places  of  decimals,  is  given  at  the  end  of  this  volume.  The 
mantissas  of  logarithms  of  larger  numbers  can  be  found  by  interpolation. 
This  table  depends  on  the  principle  that  all  numbers  having  the  same  figures 
in  the  same  order  have  the  same  mantissa,  without  regard  to  the  position  of 
the  decimal  point,  which  affects  the  characteristic  only.  This  is  apparent  from 
an  inspection  of  the  table  giving  the  logarithm  of  5  and  its  multiples  and 
submultiples  by  10. 

The  logarithm  of  a  number  having  not  more  than  four  figures  may  be  found 
by  the  following  rule: 

Rule. — Find  the  first  three  significant  figures  of  the  number  whose  logarithm 
is  desired,  in  the  left-hand  column;  find  the  fourth  figure  in  the  column  at  the  top 
(or  bottom)  of  the  page;  and  in  the  column  under  (or  above)  this  figure,  and  opposite 
the  first  three  figures  previously  found,  will  be  the  mantissa  or  decimal  part  of  the 
logarithm.  The  characteristic  being  found,  as  previously  described,  write  it  at  the 
left  of  the  mantissa,  and  the  resulting  expression  will  be  the  logarithm  of  the  required 
number. 

EXAMPLE.— Find  the  logarithm:  (a)  of  6;  (6)  of  48;  (c)  of  300;  (d)  of  3,717; 
(e)  of  .006195. 

SOLUTION. — (c)  The  mantissa  of  the  logarithm  of  6  is  the  same  as  the 
mantissa  of  the  logarithm  of  600.  The  mantissa  is  found  in  the  column 
headed  L.  0  and  opposite  600  in  the  column  headed  N.  (number).  The  first 
two  figures  in  the  mantissa  are  not  repeated  for  each  number,  but  are  found 
(in  this  instance)  opposite  the  number  589,  and  are  77.  The  last  three  numbers 
are  found  opposite  the  figures  600.  The  complete  mantissa  is  77815.  The 
characteristic  is  positive  and  since  the  number  (6)  consists  of  but  one  digit, 
the  characteristic  is  1  —  1  =  0,  therefore,  log  6  =  .77815. 

(b)  The  mantissa  of  the  logarithm  of  48  is  the  same  as  the  mantissa  of 
the  logarithm  of  480.  As  before,  this  is  found  in  the  column  headed  L.  0 
and  opposite  480  in  the  column  headed  N.  The  mantissa  is  68124.  As  the 
number  is  composed  of  two  figures,  the  characteristic  is  2  —  1  =  1,  therefore, 
log  48  =1.68124. 

-  (c)  The  mantissa  of  300  may  be  taken  directly  from  the  table,  being  found 
in  the  column  headed  L.  0  opposite  300  in  the  column  headed  N.  The  man- 
tissa is  47712.  The  characteristic,  as  the  number  is  composed  of  three  figures, 
is  3  - 1  =  2,  therefore,  log  300  =  2.47712. 

(d)  First  find  371  in  the  column  headed  N.  On  the  same  horizontal  line 
and  in  the  column  headed  7,  the  last  three  figures  of  the  mantissa  are  found 


MATHEMATICS  31 

to  be  *019.  This  star  means  that  the  first  two  figures  of  the  mantissa  are  to 
be  found  below  the  horizontal  line  in  which  019  is  found  and  not  above,  and 
are  57  and  not  56.  The  entire  mantissa  becpmes  57019.  As  the  number  is 
composed  of  four  figures,  the  characteristic  is  4  —  1  =  3;  therefore,  log  3,717 
=  3.57019. 

(e)  The  mantissa  of  6,195  is  found  opposite  619.  The  first  two  figures, 
79,  are  found  in  the  column  headed  L.  0,  and  the  last  three,  204,  in  the  column 
headed  5.  The  entire  mantissa  is  79204.  As  the  first  digit  in  the  number  is 
found  in  the  third  decimal  place,  the  characteristic  is  5,  therefore,  log  .006195 
=  3.79204. 

The  logarithm  of  a  number  consisting  of  five  or  more  figures  may  be  found 
by  the  following  rule: 

Rule. — I.  //  the  number  consists  of  more  than  five  figures  and  the  sixth  figure 
is  5  or  greater,  increase  the  fifth  figure  by  1  and  ivrite  ciphers  in  place  of  the  sixth 
and  remaining  figures. 

II.  Find  the  mantissa  corresponding  to  the  logarithm  of  the  first  four  figures, 
and  subtract  this  mantissa  from  the  next  greater  mantissa  in  the  table;  the  remainder 
is  the  difference. 

III.  Find  in  the  secondary  table,  headed  P.  P.,  a  column  headed  by  the  same 
number  as  that  just  found  for  the  difference,  and  in  this  column,  opposite  the  num- 
ber corresponding  to  the  fifth  figure  (or  fifth  figure  increased  by  1)  of  the  given 
number  (this  figure  is  always  situated  at  the  left  of  the  dividing  line  of  the  column), 
will  be  found  the  P.  P.  (proportional  part)  for  that  number.     The  P.  P.  thus 
found  is  to  be  added  to  the  mantissa  found  in  II,  as  in  the  preceding  examples, 
and  the  result  is  the  mantissa  of  the  logarithm  of  the  given  number,  as  nearly  as 
may  be  found  with  five-place  tables. 

To  take  out  the  logarithm  of  a  number  consisting  of  more  than  four  figures, 
it  is  inexpedient  to  use  more  than  five  figures  of  the  number  when  using  five- 
place  logarithms  (the  logarithms  given  at  the  end  of  this  volume  are  five-place) . 
Hence,  if  the  number  consists  of  more  than  five  figures  and  the  sixth  figure  is 
less  than  5,  replace  all  figures  after  the  fifth  with  ciphers;  if  the  sixth  figure 
is  5  or  greater,  increase  the  fifth  figure  by  1  and  replace  the  remaining  figures 
with  ciphers.  Thus,  if  the  number  is  31,415,926,  find  the  logarithm  of 
31,416,000;  if  31,415,426,  find  the  logarithm  of  31,415,000. 

EXAMPLE.— Find  log  31,416. 

SOLUTION. — Find  the  'mantissa  of  the  logarithm  of  the  first  four  figures,  as 
already  explained.  This  is,  in  the  present  case,  .49707.  Now,  subtract  the 
number  in  the  column  headed  1,  opposite  314  (the  first  three  figures  of  the  given 
number),  from  the  next  greater  consecutive  number,  in  this  case  721,  in  the 
column  headed  2.  721  —  707  =  14;  this  number  is  called  the  difference.  At 
the  extreme  right  of  the  page  will  be  found  a  sec9ndary  table  headed  P.  P.,  and 
at  the  top  of  one  of  these  columns,  in  this  table,  in  bold-face  type,  will  be  found 
the  difference.  It  will  be  noticed  that  each  column  is  divided  into  two  parts 
by  a  vertical  line,  and  that  the  figures  on  the  left  of  this  line  run  in  sequence 
from  1  to  9.  Considering  the  difference  column  headed  14,  opposite  the 
number  6  (6  is  the  last  or  fifth  figure  of  the  number  whose  logarithm  we  are 
taking  out)  is  the  number  8.4,  which,  added  to  the  mantissa  just  found,  dis- 
regarding the  decimal  point  in  the  mantissa,  gives  49,707  +  8.4  =  49,715.4. 
Now  as  4  is  less  than  5,  it  is  rejected,  giving  for  the  complete  mantissa  .49715. 
As  the  characteristic  of  the  logarithm  of  31,416  is  5- 1  =  4,  log  31,416  =  4.49715. 

TO  FIND  A  NUMBER  WHOSE  LOGARITHM  IS  GIVEN 
Rule.— I.     Consider  the  mantissa  first.     Glance  along  the  different  columns 
of  the  table  that  are  headed  0,  until  the  first  two  figures  of  the  mantissa  are  found. 
Then,  glance  down  the  same  column  until  the  third  figure  is  found  (or  1  less  than 
the  third  figure).     Having  found  the  first  three  figures,  glance  to  the  right  along  the 
row  in  which  they  are  situated  until  the  last  three  figures  of  the  mantissa  are  found. 
Then,  the  number  that  heads  the  column  in  which  the  last  three  figures  of  the  man- 
tissa are  found  is  the  fourth  figure  of  the  required  number,  and  the  first  three  figures 
lie  in  the  column  headed  N,  and  in  the  same  row  in  which  lie  the  last  three  figures 
of  the  mantissa.  ..         ..    .    . 

H.  //  the  mantissa  cannot  be  found  in  the  table,  find  the  mantissa  that  is 
nearest  to,  but  less  than,  the  given  mantissa,  and  which  call  the  next  less  mantissa. 
Subtract  the  next  less  mantissa  from  the  next  greater  mantissa  in  the  table  to  obtain 
the  difference.  Also,  subtract  the  next  less  mantissa  from  the  mantissa  of  the 
given  logarithm,  and  call  the  remainder  the  P.  P.  Looking  in  the  secondary  table 
headed  P  P.  for  the  column  headed  by  the  difference  just  found,  find  the  number 
opposite  the  P.  P.  just  found  (or  the  P.  P.  corresponding  most  nearly  to  that  just 


32  MATHEMATICS 

found);  this  number  is  the  fifth  figure  of  the  required  number;  the  fourth  figure 
will  be  found  at  the  top  of  the  column  containing  the  next  less  mantissa,  and  the 
first  three  figures  in  the  column  headed  N  and  in  the  same  row  that  contains  the 
next  less  mantissa. 

HI.  Having  found  the  figures  of  the  number  as  directed,  locate  the  decimal 
point  by  the  rules  for  the  characteristic,  annexing  ciphers  to  bring  the  number  up 
to  the  required  number  of  figures  if  the  characteristic  is  greater  than  1. 

EXAMPLE. — Find  the  number  corresponding:  (a)  to  the  logarithm  3.56867; 
(fc)  to  the  logarithm  2.05753. 

SOLUTION. — (a)  The  first  two  figures  of  the  mantissa  are  56;  glancing 
down  the  column,  the  third  figure,  8  (in  connection  with  820  )is  found  opposite 
370  in  the  N  column.  Glancing  to  the  right  along  the  row  containing  820, 
the  last  three  figures  of  the  mantissa,  867,  are  fpund  in  the  column  headed  4; 
hence,  the  fourth  figure  of  the  required  number  is  4,  and  the  first  three  figures 
are  370,  making  the  figures  of  the  required  number  3,704.  As  the  characteristic 
is  3,  there  must  be  3+1  =  4  figures  to  the  left  of  the  decimal  point.  Hence, 
the  number  is  3,704. 

(ft)  The  mantissa  05753  is  not  found  in  the  table.  The  next  less  mantissa 
is  found  in  the  column  headed  1,  opposite  the  figures  114  in  the  column 
headed  N;  hence,  the  first  four  figures  are  1,141.  The  mantissa  of  log  1141 
=  05729,  and  of  log  1142  =  05767.  The  difference  is  38.  The  P.  P.  (propor- 
tional part)  is  the  given  logarithm— the  lesser  tabular  logarithm,  or  05753 
-05729  =  24.  Under  the  head  of  38  in  the  P.  P.  section,  24  is  found  between 
22.8  (opposite  6)  and  26.6  (opposite  7).  As  24  is  nearer  the  smaller  number, 
the  fifth  figure  of  the  number  is  6,  and  the  entire  number  is  11,416.  As  the 
characteristic  is  2,  the  number  is  a  decimal  and  there  is  2  —  1  =  1  cipher  after 
the  decimal  point;  hence,  the  number  is  .011416. 

MULTIPLICATION  BY  LOGARITHMS 

The  principle  on  which  the  process  of  multiplication  by  means  of  logarithms 
is  based  is  that  log  06  =  log  o+log  b.  To  multiply  two  or  more  numbers  by 
using  logarithms  apply  the  following  rule: 

Rule. — Add  the  logarithms  of  the  several  numbers,  and  the  sum  will  be  the 
logarithm  of  the  product.  Find  the  number  corresponding  to  this  logarithm,  and 
the  result  will  be  the  number  sought. 

EXAMPLE  1.— Multiply  4.38,  5.217,  and  83  together. 

SOLUTION.—  Log    4.38=  .64147 

Log  5.217=   .71742 

Log       83  =  1.91908 
Adding,  3.27797  =  log  (4.38X5.217X83) 

Number  corresponding  to  3.27797  is  1,896.6.  Hence,  4.38X5.217X83 
=  1,896. 6,nearly.  By  actual  multiplication,  the  product  is  1,896.58818,  show- 
ing that  the  result  obtained  by  using  logarithms  was  correct  to  five 


When  adding  logarithms,  the  algebraic  sum  is  always  to  be  found.  Hence, 
if  some  of  the  numbers  multiplied  together  are  wholly  decimal,  the  algebraic 
sum  of  the  characteristics  will  be  be  the  characteristic  of  the  product.  It  must 
be  remembered  that  the  mantissas  are  always  positive. 

EXAMPLE  2.— Multiply  49.82,  .00243,  17,  and  .97  together. 

SOLUTION. — 

Log  49.82  =  1.69740 
Log  .00243  =  3.38561 
Log  17  =  1.23045 
Log  .97  =  1.98677 
Adding,  0.30023  =  log  (49.82  X  .00243  X 17  X  .97) 

Number  corresponding  to  .30023  is  1.9963.  Hence,  49. 82 X. 00243X17 
X. 97  =  1.9963. 

In  this  case  the  sum  of  the  mantissas  was  2.30023.  The  integral  2  added 
to  the  positive  characteristics  makes  their  sum  =  2+ 1  +  1  =  4;  sum  of  negative 
characteristics  =  3+1  =  3,  whence  4+(  — 4)=0.  If,  instead  of  17,  the  number 
had  been  .17  in  this  example,  the  logarithm  of  .17  would  have  been  1.23045, 
and  the  sum  of  the  logarithm  would  have  been  2.30023;  the  product  would 
then  have  been  .019963. 


MATHEMATICS  33 

DIVISION  BY  LOGARITHMS 

The  principle  upon  which  the  process  of  division  by  means  of  logarithms 
is  based  is  that  log  r  =  log  a  —  log  b. 

Rule  I. — Subtract  the  logarithm  of  the  divisor  from  the  logarithm  of  the  dividend, 
and  the  result  will  be  the  logarithm  of  the  quotient. 
EXAMPLE  1.— Divide  6,784.2  by  27.42. 
SOLUTION.—  Log  6,784.2  =  3.83150 
Log     27.42  =  1.43807 

difference  =  2.39343  =  log  (6,784.2  -4-  27.42) 

Number  corresponding  to  2.39343  is  247.42.  Hence,  6,784.2 -=-27.42 
=  247.42. 

When  subtracting  logarithms,  their  algebraic  difference  is  to  be  found; 
The  operation  may  sometimes  be  confusing,  because  the  mantissa  is  always 
positive,  and  the  characteristic  may  be  either  positive  or  negative. 

Rule  II. — When  the  logarithm  to  be  subtracted   is  greater   than  the  logarithm 
from  which  it  is  to  be  taken,  or  when  negative  characteristics  appear,  subtract  the 
mantissa  first,  and  then  the  characteristic,  by  changing  its  sign  and  adding. 
EXAMPLE  2.— Divide  274.2  by  6,784.2. 
SOLUTION.—  Log     274.2  =  2.43807 

Log  6,784.2  =  3.83150 
2\60657 

First  subtracting  the  mantissa  .83150  gives  .60657  for  the  mantissa  of  the 
quotient.  In  subtracting,  1  had  to  be  taken  from  the  characteristic  of  the 
minuend,  leaving  a  characteristic  of  1.  Subtract  the  characteristic  3  from  this, 
by  changing  its  sign  and  adding_  1  —  3  =  2,  the  characteristic  of  the  quotient. 
The  number  corresponding  to  2.60657  is  .040417.  Hence,  274.2 -i- 6,784.2 
=  .040417. 

EXAMPLE  3.— Divide  .067842  by  .002742. 
SOLUTION.—  Log  .067842  =  2.83 150 

Log  .002742  =  3.43807 
difference  =  1.39343 

As  .83150  — .43807  =  .39343  and  —2  +  3  =  1,  number  corresponding  to  1.39343 
is  24.742.  Hence,  .067842  +  .002742  =  24.742. 

The  only  case  that  is  likely  to  cause  trouble  in  subtracting  is  that  in  which 
the  logarithm  of  the  minuend  has  a  negative  characteristic,  or  none  at  all,  and 
a  mantissa  less  than  the  mantissa  of  the  subtrahend.     For  example,  let  it  be 
required  to  subtract  the  logarithm  3.74036  from  the  logarithm  3.55145.     The 
logarithm  3.55145  is  equivalent  to  —3 +  .55 145.     Now,  if  both_+l  and  —  1  are 
added  to  this  logarithm,  it  will  not  change  its  value.     Hence,  3.55145=  —3  —  1 
+  1  +  . 55145  =  3  + 1.55145.     Therefore,  3.55145-3.74036  = 
5+1.55145 
3+   .74036 

difference  =  1+  .81109  =  7.81109 

Had  the  characteristic  of  the  logarithm  been  0_instead  of  3,  the  process 
would  have  been  exactly  the  same.     Thus,  .55145  =  1  +  1.55145;  hence, 
1+1.55145 
3+   .74036 

difference  =  l+  .81109  =  2.81109 
EXAMPLE  4.— Divide  .02742  by  67.842. 
SOLUTION.—  Log  .02742  =  2.43807  =  3+1.43807 
Log  67.842  =  1.83150  =  1+  .83150 

difference  =  3+   .60657  =  2.60657 

Number  corresponding  to  2.60657  is  .00040417.  Hence,  .02742 -=- 67.842 
=  .00040417. 

EXAMPLE  5. — What  is  the  reciprocal  of  3.1416? 

SOLUTION.— Reciprocal   of   3.1416  =  ^J^Q>   and   Io8   O4i6  =  log    1~log 

3.1416  =  0 -.49715.     Since  0=  - 1  +  1, 

I +1.00000 
.49715 

difference  =  1+  .50285  =  1.50285 
Number  whose  logarithm  is  1.50285  is  .31831. 


34  MATHEMATICS 

INVOLUTION  BY  LOGARITHMS 

The  process  of  involution  by  means  of  logarithms  is  based  on  the  principle 
that  log  an  =  «  log  a. 

Rule  I.  —  Multiply  the  logarithm  of  the  number  by  the  exponent  that  denotes 
the  power  to  which  the  number  is  to  be  raised;  the  result  will  be  the  logarithm  of  the 
required  power. 

EXAMPLE  1.—  What  is:  (a)  the  square  of  7.92?  (6)  the  cube  of  94.7?  (c)  the 
1.6  power  of  512.  that  is,  the  value  of  512i:«? 

SOLUTION.—  (a)  Log  7.92  =  .89873;  exponent  of  power  =  2.  Hence,  .89873 
X  2  =  1.79746  =  log  7.922.  Number  corresponding  to  1.79746  is  62.727.  Hence, 
7.922  =  62.727,  nearly. 

(b)  Log  94.7  =  1.97635;  1.97635X3  =  5.92905  =  log  94.7".     Number  corre- 
sponding to  5.92905  is  849,280,  nearly.     Hence,  94.73  =  849,280,  nearly. 

(c)  Log  512i-  e=  1.6  X  log  512  =  1.6X2.70927  =  4.334832,  or  4.33483  (when 
using  five-place  logarithms)  =  log  21,619.     Hence,  5121-6  =  21,619,  nearly. 

Rule  II.  —  //  the  number  is  wholly  decimal,  so  that  the  characteristic  is  negative, 
multiply  the  two  parts  of  the  logarithm  separately  by  the  exponent  of  the  number. 
If,  after  multiplying  the  mantissa,  the  product  has  a  characteristic,  add  it,  alge- 
braically, to  the  negative  characteristic  multiplied  by  the  exponent,  and  the  result 
will  be  the  negative  characteristic  of  the  required  power. 

EXAMPLE  1.  —  'Raise  .0751  to  the  fourth  power. 

SOLUTION.—  Log;  .0751*  =  4Xlog  .0751=4X2.87564.  Multiplying  the  parts 
separately,  4X2  =  8  and  4  X.  87564  =  3.50256.  Adding  the  3  and  8,  3 
+  (-8)=  -5;  therefore,  log  .0751*  =  3.50256.  Number  corresponding  to  this 
is  .00003181.  Hence,  .0751*  =  .00003181. 

A  decimal  may  be  raised  to  a  power  whose  exponent  contains  a  decimal 
as  follows: 

EXAMPLE  2.  —  Raise  .8  to  the  1.21  power. 

SOLUTION.—  Log  .8f;21  =  1.21X1.90309.  There  are  several  ways  of  per- 
forming the  multiplication. 

First  Method.  —  Adding  the  characteristic  and  mantissa  algebraically,  the 
result  is  -.09691.  Multiplying  this  by  1.21  gives  -.1172611,  or  -.11726, 
when  using  five-place  logarithms.  To  obtain  a  positive  mantissa,  add  +1 
and  -1;  whence,  log  .8»-»  =  -  1  +  1  -.11726  =  1.88274. 

Second  Method.  —  Multiplying  the  characteristic  and  mantissa  separately 
gives  —  1.21  +  1.09274.  Adding  characteristic  and  mantissa  algebraically,  gives 
-.11726;  then,  adding  +1  and  -1,  log  .81-«1  =  1.88274. 

Third  Method.  —  Multiplying  the  characteristic  and  mantissa  separately 
gives  —1.21  +  1.09274.  Adding  the  decimal  part  of  the  characteristic  to  the 
mantissa  gives  —  1  +  (  —  .21  +  1.09274)  =  1.88274  =  log  .81'21.  The  number  corre- 
sponding to  the  logarithm  1.88274  =  .76338. 

Any  one  of  these  methods  may  be  used,  but  the  first  or  the  third  is  recom- 
mended. The  third  saves  figures  but  requires  the  exercise  of  more  caution 
than  does  the  first  method.  Below  will  be  found  the  entire  work  of  multipli- 
cation for  both  .81'21  and  .8<21. 

1.90309  1.90309 

1.21  _  .21 

90309  90309 

180618  180618 

90309  +1.1896489 

-1-.21 

1.9796489,  or  1.97965 
i     1.8827389,  or  1.88274 

In  the  second  case,  the  negative  decimal  obtained  by  multiplying  —  1  and  .21 
was  greater  than  the  positive  decimal  obtained  by  multiplying  .90309  and  .21; 
hence,  +  1  and  —1  were  added,  as  shown. 

EVOLUTION  BY  LOGARITHMS 

The  process  of  evolution  by  logarithms  is  based  on  the  principle  that 


Rule.  —  Divide  the  logarithm  of  the  number  by  the  index  of  the  root;  the  result 
will  be  the  logarithm  of  the  root. 

EXAMPLE.—  Extract:  (a)  the  square  root  of  77,851;  (b)  the  cube  root  of 
698,970;  (c)  the  2.4  root  of  8,964,300. 


MA  THEM  A  TICS 


35 


SOLUTION.  —  (a)  Log  77,851  =4.89127;  index  of  root  is  2;  hence,  log  V77.851 
=  4.89  127  -=-2  =  2.44564;  number  corresponding  to  this  is  279.02.  Hence, 
V77.851  =  279.02,  nearly. 

(6)  Log  %98,970  =  5.84446  -i-3  =  1.94815  =  log  88.746;  or,  ^698,970 
=  88.746. 

(c)  Log  2'^8,946,300  =  6.95251  -^  2.4  =  2.89688  =  log  788.64;  or,  2->/8,964,300 
=  788.64,  nearly. 

If  it  is  required  to  extract  a  root  of  a  number  wholly  decimal,  and  the 
negative  characteristic  will  not  exactly  contain  the  index  of  the  root,  without 
a  remainder,  the  following  rule  may  be  used: 

Rule.  —  Separate  the  two  parts  of  the  logarithm;  add  as  many  units  (or  parts 
of  a  unit)  to  the  negative  characteristic  as  will  make  it  exactly  contain  the  index 
of  the  root.  Add  the  same  number  to  the  mantissa,  and  divide  both  parts  by  the 
index  The  result  will  be  the  characteristic  and  mantissa  of  the  root. 

EXAMPLE  1.—  Extract  the  cube  root  of  .0003181. 

*-7vSi^n  i      log  .0003181     4.50256 
SOLUTION.—  Log  \.0003181  =—  —  ^  --  =  —  ^  —  . 

(1+2  =  6)  +  (2  +  .50256  =  2.50256) 

(6  -5-  3  =  2)  +J2.50256  -5-  3  =  .834  19) 

or,  log  -^0003181  =  2.834  19  =  log  .068263 

Hence,  ^.0003181  =  .068263 

EXAMPLE  2.—  Find  the  value  of  1-*>l.0003181. 

T        1-4Vnnrwi5T     log-  0003181     3.50256 
SOLUTION.—  Log      \.0003181  =  -  ^  -  =    1  41    . 

If  —.23  is  added  to  the  characteristic,  it  will  contain  1.41  exactly  three 

aCe>  [-4+  (-.23)  =  -4.23]  +  (.23  +  .  50256  =  .73256) 

(-4.23  -s-1.41  =  3)  +  (.73256-^-  1.41  =  .51955) 
or,  log  1'4>/.0003181  =  3.51955  =  log  .0033079 

Hence,  1'4V^003181  =  .  0033079 

497  X.  0181X762 
EXAMPLE  3.  —  Solve,  by  logarithms, 


SOLUTION.— 


3  300X6517 
497  =  2.69636 
.0181  =  2.25768 
762  =  2.88195 


Log 

Log 
Log 


Log  product  =  3.83599 
Log  3,300  =  3.51851 
Log  .6517  =  1.81405 


Hence, 

EXAMPLE 

SOLUTION: 


Log  product  =  3.33256 
3.83599  -  3.33256  =  .50343  =  log  3. 1874 
497  X. 0181X762 
3,300X.65i7~-d'1874: 


Log  504,203  =  5.70260 
Log  507  =  2.70501 

Log  product  =  8.40761 
Log  1.75=  .24304 
Log  71.4  =  1.85370 
Log  87  =  1.93952 


Log  product 
8.40761  -4.03626 


Hence' 


3r 

\ 


L75X74X87 


4.03626 


28-65 


36  MATHEMATICS 

SOLUTION  OF  EQUATIONS  BY  LOGARITHMS 

Logarithms  can  often  be  applied  to  the  solution  of  equations. 
EXAMPLE  1.  —  Solve  the  equation  2.43x5  =  "^.0648. 

SOLUTION.  —  Dividing  by  2  .43  ,  xs  =  —~~r^r  •   Taking  the  logs  of  both  numbers  , 


5  log  x  -         I         -log  2.43;  5  log  x  =  -~-  -.38561  =1.80193  -.38561 

=  1.41632.     Dividing  by  5,  log  x  =  1.88326,  whence  x=  .7643. 
EXAMPLE  2.  —  Solve  the  equatipn  4.5*  =  8. 
SOLUTION.  —  Taking  the  logarithms  of  both  numbers,  x  log  4.5  =  log  8, 

whence,  x  =  .  °g       =  "65321"    Talcmg  logarithms  again,  log  *  =  log  .90309  —  log 

.65321  =  1.95573-1.81505  =  .14068,  and  x=  1.3825. 

REMARKS.  —  Logarithms  are  particularly  useful  in  those  cases  when  the 
unknown  quantity  is  an  exponent,  as  in  the  last  example,  or  when  the  exponent 
contains  a  decimal,  as  in  several  instances  in  the  examples  already  given. 
Such  examples  can  be  solved  without  the  use  of  logarithms,  but  the  process  is 
very  long  and  somewhat  involved,  and  the  arithmetical  work  required  is 
enormous.  To  solve  the  example  last  given  without  using  the  logarithmic 
table  and  obtain  the  value  of  x  correct  to  five  figures  will  require,  perhaps, 
100  times  as  many  figures  as  are  used  in  the  solution  given,  and  the  resulting 
liability  to  error  will  be  correspondingly  increased;  indeed,  to  confine  the  work 
to  this  number  of  figures  will  also  require  a  good  knowledge  of  short-cut  methods 
in  multiplication  and  division,  and  judgment  and  skill  on  the  part  of  the 
calculator,  which  can  only  be  acquired  by  practice  and  experience. 

Formulas  containing  quantities  affected  with  decimal  exponents  are  gener- 
ally of  an  empiric  nature;  that  is,  the  constants  or  exponents  or  both  are  given 
such  values  as  will  make  the  results  obtained  by  the  formulas  agree  with  those 
obtained  by  experiment.  Such  formulas  occur  frequently  in  works  treating 
on  thermodynamics,  strength  of  materials,  machine  design,  etc. 


GEOMETRY 

PRINCIPLES  OF  GEOMETRY 

1.  The  sum  of  all  the  angles  formed  on  one  side  of  a  straight  line  equals 
two  right  angles,  or  180°. 

2.  The  sum  of  all  the  angles  formed  around  a  point  equals  four  right 
angles,  or  360°. 

3.  When  two  straight  lines  intersect  each  other,  the  opposite  or  vertical 
a/igles  are  equal. 

4.  If  two  angles  have  their  sides  parallel,  they  are  equal. 

5.  If  two  triangles  have  two  sides,  and  the  included  angle  of  the  one 
equal  to  two  sides  and  the  included  angle  of  the  other,  they  are  equal  in  all 
their  parts. 

6.  If  two  triangles  have  two  angles,  and  the  included  side  of  the  one  equal 
to  two  angles  and  the  included  side  of  the  other,  they  are  equal  in  all  their  parts, 

7.  In  any  triangle,  the  greater  side  is  opposite  the  greater  angle,  and  the 
greater  angle  is  opposite  the  greater  side. 

8.  The  sum  of  the  lengths  of  any  two  sides  of  a  triangle  is  greater  than 
the  length  of  the  third  side. 

9.  In  an  isosceles  triangle,  the  angles  opposite  the  equal  sides  are  equal. 

10.  In  any  triangle,  the  sum  of  the  three  angles  is  equal  to  two  right 
angles,  or  180°. 

11.  If  two  angles  of  a  triangle  are  given,  the  third  may  be  found  by  sub- 
tracting their  sum  from  two  right  angles,  or  180°. 

12.  A  triangle  must  have  at  least  two  acute  angles,  and  can  have  but  one 
obtuse  or  one  right  angle. 

13.  In  any  triangle,  a  perpendicular  let  fall  from  the  apex  to  the  base  is 
shorter  than  either  of  the  two  other  sides. 

14.  If  a  triangle  is  equilateral,  it  is  equiangular,  and  vice  versa. 

15.  If  a  straight  line  from  the  vertex  of  an  isosceles  triangle  bisects  the  base, 
it  bisects  the  vertical  angle  and  is  perpendicular  to  the  base. 

16.  If  one  side  of  a  triangle  is  extended,  the  exterior  angle  thus  formed, 
is  equal  to  the  sum  of  the  two  interior  and  opposite  angles. 


MATHEMATICS  37 

17.  If  two  triangles  are  mutually  equiangular,  they  are  similar  and  their 
corresponding  sides  are  proportional. 

18.  Triangles  that  have  an  angle  in  each  equal,  are  to  one  another  as  the 
products  of  the  sides  including  those  equal  angles. 

19.  Similar  triangles  are  to  one  another  as  the  squares  of  their  corre- 
sponding sides. 

20.  In  a  right-angled  triangle,  the  square  of  the  hypotenuse  is  equal  to  the 
sum  of  the  squares  of  the  other  two  sides. 

21.  If  a  triangle  is  inscribed  in  a  semicircle,  one  side  being  a  diameter,  it 
is  right-angled. 

22.  In  any  parallelogram,  the  opposite  sides  are  equal;  the  opposite  angles 
are  equal;  it  is  bisected  by  its  diagonals  into  two  equal  triangles,  and  its  diag- 
onals bisect  each  other. 

23.  If  the  sides  of  a  polygon  are  produced  in  regular  order,  the  sum  of  the 
exterior  angles  thus  formed  is  equal  to  360°. 

24.  The  sum  of  the  interior  angles  of  a  polygon  is  equal  to  twice  as  many 
right  angles  as  the  polygon  has  sides,  less  four  right  angles.     For  example,  the 
sum  of  the  interior  angles  of  a  pentagon  is  (2X5)— 4  =  6  right  angles,  or  540°; 
of  an  octagon,  (2X8)  —4  =  12  right  angles,  or  1,080°,  etc. 

25.  The  diagonals  joining  the  vertices  of  a  regular  polygon  intersect  at 
the  center  of  the  inscribed  and  circumscribed  circles. 

26.  The  angle  at  the  center  subtended  by  the  side  of  a  regular  polygon  is 
equal  to  360°  divided  by  the  number  of  sides. 

27.  Plane  figures  are  similar  when  they  are  bounded  by  the  same  number 
of  similar  sides  and  their  correspondingly  situated  angles  are  equal  each  to  each. 

28.  The  perimeters  of  similar  polygons  are  to  one  another  as  any  two 
corresponding  sides;  and  their  areas  are  to  one  another  as  the  squares  of  those 
sides. 

29.  The  circle  is  a  polygon  of  an  infinite  number  of  sides. 

30.  A  circle  may  be  described  about  or  inscribed  within  any  regular 
polygon. 

31.  Through  three  points  not  in  the  same  straight  line  a  circle  may  be  made 
to  pass  and  but  one. 

32.  The  diameter  of  a  circle  is  greater  than  any  chord. 

33.  Any  radius  that  is  perpendicular  to  a  chord,  bisects  the  chord  and  the 
arc  subtended  by  it. 

34.  Arcs  and  chords  of  the  same  circle  are  proportional  to  the  angles  at 
the  center  of  the  circle  subtended  by  them. 

35.  Similar  arcs  are  proportional  to  the  radii  of  their  circles. 

36.  A  tangent  to  a  circle  meets  it  at  one  point  only,  and  is  perpendicular 
to  the  radius  at  that  point. 

37.  If  from  a  point  without  a  circle  tangents  are  drawn  to  touch  the 
circle,  there  are  but  two  such  tangents;  they  are  equal,  and  they  make  equal 
angles  with  the  chord  joining  the  points  of  tangency. 

38.  The  angle  between  a  tangent  and  a  chord  is  equal  to  one-half  the  angle 
at  the  center  subtended  by  the  chord. 

39.  The  perimeters  of  circles  are  to  one  another  as  any  two  corresponding 
dimensions,  and  their  areas  are  to  one  another  as  the  squares  of  such  dimensions. 

40.  Only  five  regular  polyhedrons  are  possible;  the  tetrahedron  with  four 
triangular  faces;  the  cube  with  six  square  faces;  the  octahedron  with  eight 
triangular  faces;  the  dodecahedron  with  twelve  pentagonal  faces;  and  the 
icosahedron  with  twenty  triangular  faces. 

41.  The  sum  of  all  the  angles  of  the  faces  of  any  polyhedron  is  equal  to 
four  right  angles  taken  as  many  times  as  che  polyhedron  has  vertices  less  two. 

42.  The  center  of  any  regular  polyhedron  and  of -its  circumscribed  and 
inscribed  spheres  is  at  the  point  of  intersection  of  the  diagonals  joining  its 
opposite  vertices. 

43.  Solids  are  similar  which  are  bounded  by  the  same  number  of  similar 
faces  similarly  placed,  and  which  have  their  corresponding  polyhedral  angles 
equal. 

44.  The  areas  of  the  surfaces  of  similar  solids  are  to  one  another  as  the 
squares  of  their  similar  dimensions,  and  the  volumes  of  similar  solids  are  to 
one  another  as  the  cubes  of  like  dimensions. 

45.  The  sphere  is  a  regular  polyhedron  of   an  infinite  number  of   sides. 

46.  A  sphere  may  be  described  about  any  regular  polyhedron,  and  its 
radius  is  equal  to  the  distance  from  any  vertex  to  the  center;  and  a  sphere 
may  be  inscribed  within  any  regular  polyhedron,  and  its  radius  is  equal  to  the 
perpendicular  distance  from  the  center  of  any  face  to  the  center  of  the  figure. 


38 


MA  THEM  A  TICS 


47.  Through  four  points  not  in  the  same  plane  a  spherical  surface  may  be 
made  to  pass,  and  but  one. 

48.  From  a  point  without  a  sphere  two  tangents  may  be  drawn  to  a  great 
circle  of  the  sphere,  and  but  two. 

49.  Through  a  line  without  a  sphere  two  tangent  planes  to  the  surface 
of  the  sphere  may  be  drawn,  and  but  two. 

PROBLEMS  IN  GEOMETRICAL  CONSTRUCTION 
1.     To  Bisect  a  Given  Straight  Line  or  the  Chord  or  the  Arc  of  a  Circle. 

Let  AB,  Fig.  1,  be  the  given  line  or  chord  and  ACB  the  arc  of  the  circle.     With  A 
*»  and  B  as  centers  and  with  a  radius  greater  than  one- 

half  the  line  AB  or  the  arc  ACB,  describe  arcs  inter- 
secting at  E  and  F.  The  line  EF  will  bisect  the  line, 
chord,  or  arc. 

COROLLARY. — The  line  EF  will  also  be  perpendicu- 
lar to  the  line  AB  and,  when  prolonged,  will  pass 
through  the  center  of  the  circle  of  which  ACB  is 
the  arc.  _ 

2.    From  a  Given  Point 
C,  Without  a  Straight  Line 
_,  A  B,  to  Draw  a  Perpendicular   <  A 

*IG-  *  to  the  Line.— From  C,  Fig.  2,   ^a— 

as  a  center,  with  a  radius  greater  than  the  distance 
from  C  to  AB,  describe  an  arc  cutting  the  line  AB 
at  A  and  B.  From  A  and  B  as  centers  and  with  a 
radius  greater  than  one-half  of  AB,  describe  arcs 
intersecting  at  D,  and  draw  the  line  CD. 

COR.— The  line  CD  will  bisect  that  portion  of  the  line 
the  points  A  and  B. 

3.  At  a  Given  Point  C  in  a  Straight  Line  AB, 
to  Erect  a  Perpendicular  to  That  Line. — Lay  off 
the  points  A  and  B,  Fig.  3,  equidistant  from  C,  and 
with  A  and  B  as  centers  and,  with  a  radius  greater 
than  one-half  AB,  describe  arcs  intersecting  at  D. 
The  line  DC  will  be  perpendicular  to  AB. 

4.  To  Erect  a  Perpen-    _ 
dicular  at  the  End  A  of  a 
Given    Line   A  B.  —  First 


L 


FIG.  2 
ncluded  between 


FIG.  3 


Method. — From  any  point  C,  Fig.  4,  above  the  line 
AB  and  with  a  radius  AC  describe  the  arc  of  the  circle 
AD,  which  also  cuts  the  line  AB  at  B.  Connect  B 
and  C  and  prolong  the  line  to  intersect  the  circle  at  D. 

The  line  AD  will  be  perpendicular 

to  the  line  AB. 


FIG.  4 


Second  Method. — From  the  given  point  A,  Fig.  5,  set 
off  a  distance  AB  equal  to  three  parts  by  any  scale. 
From  A  and  B  as  centers  and  with  radii  equal,  respec- 
tively, to  four  parts  and  five  parts,  draw  arcs  intersecting 
at  C.  The  line  AC  will  be  the  perpendicular  required. 

NOTE. — This  is  one  of  the  methods  employed  for  laying 
off  the  coordinates  on  mine  maps. 

5.    Through  a  Given 


„    u       Point  A,  to  Draw  a  Straight 

FIG.  5  Line   Parallel  to   a   Given 

Straight  Line  CD. — With  A ,  Fig.  6,  as  a  center 

and  with   a  radius   greater  than   the  shortest 

distance  from  A   to  the  line  CD,  describe  an 

indefinite  arc  DB.     With  D  as  a  center  and  with 

_  ~  the  same  radius 


D 


FIG.  7 


DA  .describe  the  FlG<  6 

arc  AC.  With  D  as  a  center  and  with  the  radius 
AC  describe  an  arc  cutting  the  arc  DB  at  B, 
The  line  AB  will  be  parallel  to  the  line  CD. 

6.     To  Draw  a  Straight  Line  Parallel  to  a 
Given  Line  and  at  a  Given  Distance  From  It. 


First  Method. — Select  any  two  points  A  and  B,  Fig.  7,  on  the  given  line.  With 
these  as  centers  and  with  radii  equal  to  the  distance  apart  of  the  lines  de- 
scribe the  arcs  C  and  D.  Draw  the  line  CD  touching  the  arcs. 


MA  THEM  A  TICS 


39 


1 

* 

f. 

Frc.  9 


Second  Method. — At  any  two  selected  points  A  and  B,  Fig.  8,  in  the  given 
line,  erect  perpendiculars.  With  A  and  B  as  centers  and  with  a  radius  equal 
to  the  distance  apart  of  the  lines,  draw  arcs  of 

circles  cutting  the  perpendiculars  at  C  and  D.          tc  ,/> 

The  line  CD  joining  these  points  of  intersec-    ~ 
tion  will  be  parallel  to  the  line  AB. 

NOTE. — These  methods  are  employed  to 
lay  off  the  coordinates  of  mine  maps. 

7.  To   Divide   a  Straight  Line  Into  Any 
Number  of  Equal  Parts. — Let  AB,  Fig.  9,  be 

.a  straight  line  that  is  to  be  divided  into,  say,  seven  equal  parts.  Draw 
the  parallel  lines  AC  and  BD  making  any  angle  with  A  B,  and  measure 
off  upon  each  of  them  seven  equal  spaces.  Connect  the  points,  1  and  1 ,  2  and  2, 
etc.,  by  lines.  These  lines  will  divide  the  line  A  B  into  seven  equal  parts. 

Or,  but  one  line  AC  need  be  drawn. 
By  connecting  7  and  B,  the  parallel  lines 
drawn  through  6,5,4,  etc.,  will  divide  the 
line  as  required. 

B         NOTE. — This   method  is  available  for 
7    dividing  a  line  into  any  odd  number  of 
parts  when  no  scale  of  such  parts  is  to  be 
had.     Thus,  to  divide  a  line,  2£J  in.  long 
into  sevenths,  seven  i  or  5  in.,  may  be  laid 
off  along  the  line  AC.  The  operation  will,  if 
properly  carried  out,  divide  the  2£fc  in.  into 
seven  equal  parts  of  .3171  in. 
A  line  may  be  divided  into  proportional  parts  by  this  method.     Thus  to 
divide  the  line  AB  in  the  ratio  of  3  to  4-     Lay  off  the  distance  A-3  equal  to 
three  parts,  and  the  distance  4~7  equal  to  four  parts.     The  line  3-3  will  divide 
the  line  AB  in  the  required  ratio. 

8.  At  a  Point  A  on  a  Given  Straight  Line  AB, 
to  Make  an  Angle  Equal  to  a  Given  Angle  EFG. 
From  F,  Fig.  10,  as  a  center  and  with  any  radius  FG 
describe  the  arc  EG.     From  A   as  a  center  and 
with  the  same  radius,  describe  the  arc  CB\  then 
with  a  radius  equal  to  the  chord  EG,  describe  an 
arc  from  B  as  a  center,  cutting  CB  at  D,  and  draw 
the  line  AD.     The  angle  BAD  will  be  equal  to  the 

,  angle  EFG. 

9.  To  Draw  Angles  of  60°  and  30°.— From  any  point 
A,  Fig.  11,  on    the  line  AB  and  with   any  radius  AB 
describe  the  arc  BD.     With  B  as  a  center  and  with  the 
same  radius  AB,  describe  an  arc  cutting  BD  at  D.      The 
line  AD  will  form  an  angle  DAB  with  AB  equal  to  60°. 
The  perpendicular  DC  to  the  base  will  form  the  angle 
ADC  of  30°. 

10.  To  Draw  an  Angle  of  45°. 
Lay  off  any  distance  AB,  Fig.   12, 
and  at  B   erect  a   perpendicular  to 

AB.     With  B  as  a  center  and  with  a  radius  equal  to 

BA    describe   an   arc   cutting  the    perpendicular  at   C. 

The  line  AC  will  form  with  the  line  AB  an  angle  CAB 

equal  to  45°. 

Or,  the  second  method  under  problem  4  may  be  used.  FIG.  12 

11.     To  Bisect  an  Angle  ABC. — With  any  radius  and 

with  B,  Fig.  13,  as  a  center,  describe  an  arc  cutting  the  sides  at  A  and  C. 
With  A  and  C  as  centers,  describe  arcs  of  equal 
radius  intersecting  at  D.  The  line  BD  is  the 
bisector,  and  the  angle  ABD  =  angle  DEC. 

12.  To  Bisect  an  Open  Angle  (Method  by  L.  L. 
LOGAN). — Let  AB  and  CD,  Fig.  14,  be  the  sides  of 
an  open  angle.  With  any  point  O  as  a  center, 
describe  a  circle  cutting  the  sides  at  e,f,  g,  and  h, 
and  with  e  and  /,  and  g  and  h  as  centers  and  any 
radius,  describe  arcs  intersecting  at  k  amd  /, 

respectively.     Draw  Ok  and  Ol  and  mn.     With  p  and  q  as  centers,  and  any 

radius,  describe  arcs  intersecting  at  R  and  S.     The  line  drawn  through  RS  is 

the  required  bisector. 


Q 

•D       11 


FIG.  13 


40 


MATHEMATICS 


13.    To  Find  the  Center  of  a  Given  Circumference  or  Arc. — First    Method. 
Take  any  three  points  A,  B,  and  C,  Fig.  15,  on  the  circumference  and  unite 
them    by    lines    AB    and   BC.     Bisect   these 
chords   by   the   perpendiculars    DO    and  EO\ 
their  intersection  is  the  center  of  the  circle. 

Second  Method. — Take  any  three  points  A ,  B, 
and  C,  Fig.  16,  on  the  circumference  as  far 
apart  as  convenient.  With  these  three  points 


FIG.  14 


FIG.  15 


FIG.  16 


as  centers  and  with  the  same  radius,  draw  a  series  of  intersecting  arcs.  The 
lines  GF  and  DE  through  these  intersections  cut  one  another  at  the  center  H 
of  the  circle. 

NOTE. — This  method  is  employed  to  describe  a  circle  through  any  three 
points  not  in  the  same  straight  line. 

14.  To  Describe  an  Arc  of  a  Circle 
Passing  Through  Three  Given  Points 
When   the   Center  Is   Not  Available. 
Let  A,  B,  and  C,  Fig.  17,  be  the  three 
points.     From  A  and  C  as  centers  and 
with  the  radius  AC  describe  the  arcs  CY 
and  AX.      Through  the  third  point  B 
draw  the  lines  CD  and  AE  cutting  the 
arcs.     Divide  the  distance  AD  into  any 
number    of   equal    parts   and   lay   off 
similar  parts  above  D  on  the  arc  AX. 

Also  lay  off  like  parts  above  and  below  E  on  the  arc  CY.  Draw  lines  CF,  CG, 
etc.,  and  AH,  AL,  etc.  Their  intersection,  1,  and  2,  will  be  points  on  the 
required  circle.  The  curve  may  be  drawn  by  splines.  The  smaller  the  divi- 
sions of  the  arcs,  the  more  points  will  there  be  given  in  the  arc  of  the  circle. 

15.  To  Draw  a  Tangent  to  a  Circle  Through  a  Given  Point  P  in  the  Circum- 
ference.— Find  the  center  C,  Fig.  18,  of  the  circle  by  any  of  the  methods  de- 
scribed and  draw  the  radial  line  CD.     At  P  erect  a  perpendicular  AB  to  this 
line  CD;  the  perpendicular  AB  will  be  tangent  to  the  circle  at  P. 


FIG.  17 


FIG.  18 


FIG.  19 


16.  To  Draw  Tangents  to  a  Circle  From  a  Point  P  Without  the  Circum- 
ference.— First  Method. — If  the  center  of  the  circle  is  not  given  find  it  by  any 
method,  and  draw  the  line  PC,  Fig.  19.  Bisect  this  line  PC  at  E,  and  with  the 
radius  EC  =  PE,  describe  a  circle  cutting  the  given  circle  at  A  and  B.  Con- 
nect A  and  P  and  B  and  P;  the  lines  AP  and  BP  will  be  tangent  to  the  circle. 

Second  Method.— As  before,  let  P,  Fig.  20,  be  the  point.  Find  the  center  C 
of  the  circle  and  draw  the  line  PCD.  With  P  as  a  center  and  with  a  radius  PC, 


M  A  THEM  A  TICS 


41 


describe  the  arc  FCG.  With  C  as  a  center  and  with  a  radius  equal  to  the 
diameter  DE  of  the  circle,  cut  this  arc  at  F  and  G.  Draw  the  lines  FC  and  GC 
cutting  the  circle  at  L  and  K.  Draw  the  lines  PB  and  PA  through  L  and  K 
respectively;  they  will  be  tangents  to 
the  circle. 

17.  To  Draw  an  Arc  of  a  Circle 
Tangent  to  Two  Lines  Inclined  to  Each 
Other,  One  Point  of  Tangency  B 
Being  Given.  —  Produce  the  given  lines, 
AB  and  CD,  Fig.  21,  until  they  inter- 
sect at  E.  Bisect  the  angle  A  EC  by 
the  line  EF.  Draw  a  perpendicular  FlG-  21 

to  the  line  AB  from  the  point  B.     Its  intersection  G  with  the  line  EF,  the 
bisector  of  the  angle,  is  the  center  of  the  required  arc.     The  other  point  of  tan- 
gency  may  be  found  by  dropping  a  perpendicular  GH  upon  the  line  CD. 
NOTE.  —  If  an  intersection  cannot  be  reached,  use  the  method  described 
in  problem  12,  for  bisecting  the  angle. 

18.  To  Construct  a  Triangle,  the  Sides 
Being  Given.  —  Let  A  B,  Fig.  22,  be  one  of  the 
sides.  With  A  as  a  center  and  a  radius  equal 
to  one  of  the  remaining  sides  describe  the  arc 
AC,  and  with  B  as  a  center  and  a  radius  equal 
to  the  third  side  describe  the  arc  BC  cutting 
the  arc  AC  at  C'  Draw  the  lines  AC  and 
BC;  then  ABC  will  be  the  required  triangle. 


pIG>  22 


19.  To  Describe  a  Circle  About  a  Triangle. — Let 
ABC,  Fig.  23,  be  the  triangle.     Bisect  any  two  sides 
as  A  B  and  AC  at  D  and  E  and  at  these  points  erect 
perpendiculars  to  the  sides  intersecting  at  F.     With  F 
as  a  center  and  with  a  radius  equal  to  FA  =  FB  =  FC, 
describe  the  circle  ABC. 

20.  To  Inscribe  a  Circle  in  a  Triangle.— Let  ABC, 

Fig.  24,  be  the  given 


triangle.  Bisect 
any  two  angles,  such 
as  A  and  C,  by  lines  pIG  23 

intersecting    at    D. 

Drop  a  perpendicular  from  D  upon  any  side 
as  DE  upon  the  side  AC,  and  with  D  as  a 
center  and  a  radius  DE,  inscribe  the  circle. 
21.  To  Construct  a  Hexagon  Upon  a 
Given  Straight  Line.— Let  FE,  Fig.  25,  be 


FIG.  24 

the   given  line.     From    its    extremities    F  and  E   as 

centers  and  with  the  radius  FE  describe  arcs  of  circles 

intersecting  at  G.     With  a  radius  GE,  draw  the  cir- 
cumscribing circle  EDCBAF.     With  the  same  radius 

GE  =  FE  set  off  upon  the  circumference  of  this  circle 

the   chords  ED,  DC,  CB,  and   BA.     The  points  so 

found,  when  joined,  will  form  the  required  hexagon. 
NOTE. — The  side  of  any  hexagon  is  equal  to  the 

radius  of  its  circumscribed  circle.      As  the  exterior 

angles  of  a  hexagon  are  each  equal  to  60°,  this  polygon 

is  readily  drawn  with  a  straightedge  and  a  60°-30° 
triangle. 

22.  To  Describe  an  Octagon  Upon  a  Given  Straight 
Line.— Let  AH,  Fig.  26,  be  the  given  line.  Produce 
it  in  both  directions  and  at  A  and  H  erect  the  perpen- 
diculars AD  and  HE.  Bisect  the  angles  DAa  and 
EHh  with  the  lines  AB  and  HG.  With  A  and  H  as 
centers  and  with  a  radius  AH  equal  to  the  length  of 
the  given  side  describe  arcs  cutting  the  bisectors  at 
B  and  G  respectively;  AB  and  HG  will  be  sides  of 
the  octagon.  Draw  BC  and  GF  parallel  to  DA  and 
EH.  Make  them  equal  to  AH  by  cutting  them 
(using  B  and  G  as  centers)  with  the  arcs  of  a  circle  whose 
From  C  and  F  as  centers  and  with  a  radius  equal  to  AH, 


FIG.  26 
radius  is  equal  to  AH. 


describe  arcs  of  circles  intersecting  the  perpendiculars  at  D  and  E.     The  lines, 
CD,  DE,  and  EF,  joining  the  points  thus  determined,  complete  the  octagon. 


42 


MATHEMATICS 


NOTE. — As  the  exterior  angles  of  an  octagon  are  each  45°,  this  polygon  is 

readily  drawn  with  a  straightedge  and  a  45°  triangle. 

23.    To  Construct  an  Ellipse,  the  Axes  Being  Given. — Let   AB   and   CD, 

Fig.  27,  be  the  major  and  minor  axes,  respectively,  intersecting,  bisecting,  and 
perpendicular  to  each  other  at  P.  Using  P 
as  a  center  draw  two  circles  with  radii  equal, 
respectively,  to  one-half  the  axes,  or  PA  and 
PC.  Prom  P,  draw  any  number  of  random 
lines,  as  Pa,  Pb,  ...  P/  to  the  circumfer- 
ence of  the  larger  circle  and  drop  perpendic- 
ulars from  the  extremities,  a,  b,  .  .  .  f.  From 
the  points  of  intersection,  1,  2,  .  .  .  6,  of  the 
lines  Pa,  Pb,  etc.,  with  the  smaller  circle  draw 
lines  parallel  to  the  major  axis  AB.  The 
points  of  intersection  of  these  parallels  with 
the  verticals  previously  drawn  will  be  points 
on  the  ellipse.  This  is  the  most  convenient 
method  of  drawing  an  ellipse  and  is  the  one 
used  very  largely  in  drafting  rooms.  It  will 
be  noted  that  more  points  should  be  deter- 
mined where  the  .direction  of  the  curve  is 


FIG.  27 


changing  rapidly,  as  at  and  near  B,  than  at  C  where,  for  a  considerable  dis- 
tance on  either  side  of  the  minor  axis,  the  change  in  direction  is  slight. 

The  foci  of  the  ellipse  may  be  found  by  drawing,  with  C  or  D  as  a  center 
and  with  PA  =  PB  as  a  radius,  arcs  of  circles  cutting  the  major  axis  at  F  and  F'. 

There  are  numerous  complicated  and  inaccurate  methods  of  drawing  what 
is  called  an  approximate  ellipse,  three  of  which  are  given,  but  they  do  not 
compare  in  simplicity  with  the  exact  method  given. 

24.  To  Construct  an  Approximate  Ellipse,  the  Axes  Being  Given. 
Method  by  Three  Centers. — Let  a,  Fig.  28,  be  the  center,  be  the  major,  and  ae 
one-half  of  the  minor  axis  of  an  ellipse. 
Draw  the  rectangle  bfgc,  and  the  diagonal 
line  be;  at  a  right  angle  to  the  line  be,  draw 
line  fh  cutting  the  line  BB  at  i.  With  radius 
ae,  and  from  a  as  a  center,  draw  the  dotted 
arc  ej,  giving  the  point  j  on  the  line  BB. 
From  k,  which  is  central  between  b  and  j, 
draw  the  semicircle  bmj,  cutting  the  line 
A  A  at  I.  Draw  the  radius  of  the  semicircle 
bmj,  cutting  fg  at  n.  With  radius  mn,  mark 
on  the  line  A  A,  from  a  as  a  center,  the 

rint  o.  With  radius  ho,  and  from  center 
draw  the  arc  poq.  With  radius  al,  and 
from  b  and  c  as  centers,  draw  arcs  cutting 
the  arc  poq  at  the  points  p  and  q.  Draw 
the  lines  hpr  and  hqs,  and  also  the  lines  pit 
and  qvw.  From  h  as  a  center,  draw  that 
part  of  the  ellipse  lying  between  r  and  s 
with  radius  hr.  From  p  as  a  center  draw 


FIG.  28 


that  part  of  the  ellipse  lying  between  r  and  t  with  the  radius  pr.  From  q,  draw 
the  ellipse  from  s  to  w .  With  radius  */,  from  i  as  a  center,  draw  the  ellipse  from 
/  to  b  with  radius  it,  and  from  v  as  a  center,  draw  the  ellipse  from  w  to  c,  and 
one-half  the  ellipse  will  be  drawn.  It  will  be  noted  that  the  whole  construc- 
tion has  been  performed  to  find  the  centers  h,  p,  q,  i,  and  v,  and  that  while  v 
and  *  may  be  used  to  carry  the  curve  around  the  other  side  or  half  of  the 
ellipse,  new  centers  must  be  provided  for  h,  p,  and  q;  these  new  centers  cor- 
respond in  position  to  h,  p,  q. 

INoTE. — This  method  is  the  one  commonly  employed 
to  lay  off  concrete,  or  masonry  arches,  etc. 
Method  by  Straightedge. — On  a  straightedge,  lay  off 
AB,  Fig.  29,  equal  to  one-half  the  shorter  axis  and  AC 
equal  to  one-half  the  longer  axis.  Determine  points 
in  the  ellipse  by  marking  positions  of  A  as  the  point  B 
is  moved  along  the  major  axis,  at  the  same  time  the 
point  C  being  kept  in  the  minor  axis. 

Method  by  Cord. — Lay  off  the  axes  and  find  the  foci 


FIG.  29 


as  described  in  problem  23.     Stick  pins  at  the  foci  F  and  F',  Fig.  27.     To  these 
pins  attach  a  string  making  its  length  equal  to  FC+CF'.     The  point  of  a 


MATHEMATICS  43 

pencil  placed  inside  the  string  may  be  made  to  describe  an  ellipse,  if  the  string 
is  kept  tightly  and  uniformly  stretched  while  the  pencil  is  in  motion. 

NOTE. — This  is  the  method  commonly  employed  to  lay  off  an  ellipse  upon 
the  ground,  as  when  making  garden  beds,  etc. 

The  cord  and  straightedge  methods  are  theoretically  capable  of  describing 
a  true  ellipse.  That  is,  the  methods  are  founded  on  the  mathematical  prin- 
ciples governing  the  ellipse,  but  it  is  not  generally  possible  to  manipulate 
either  the  string  or  straightedge  so  that  perfect  results  may  be  obtained. 


MENSURATION  OF  SURFACES 

TRIANGLES 

A  triangle  is  a  plane  surface  bounded  by  three  straight  lines.     Some  of  the 
different  kinds  of  triangles  are  shown  here. 


a,  b,  c  =  sides  opposite  angles  A,   B, 

andC 

P  =  perimeter 

h  =  perpendicular  upon  base  from 
vertex  of  angle  opposite 


Acute 


Let      A,  B,  C  =  interior  angles 
A',  B',  C'  —  exterior  angles 
6  =  side  called  base 
A  =  area 
m  =  distance  from  foot  of 

h  to  nearest  vertex 
Angles.— A  +B  +  C=  180°.     A  =  180°-  (B+O,  and  similarly  for  B  and  C. 
A+A'  =  18Q°,  and  similarly  for  B  +  B'  and.  C+C'.     A' =180°- A,  and  simi- 
larly for  B'  and  C.     A'  +  B'  +  C'  =  360°.     A'  =  360° -(B'  +  Cr),  and  similarly 
for  B'  and  C'.     A'  =  B+C;  B'  =  A  +  C;  C'  =  A+B. 

Perimeter  and  Sides. — P  =  a+b  +  c.     In  all  acute-angled  triangles,  includ- 

ing  equilateral,  isosceles,  and  right-angled  triangles,  any  side  a=  V&2+c2  —  2bm. 

In  an  obtuse-angled  triangle,  the  side  opposite  the  obtuse  anglea  =  V62+c2+2fc»i. 

Altitude. — In  any  triangle,  the  altitude,  or  perpendicular  distance  from  the 

base  to  the  vertex  of  the  opposite  angle,  is  h=  Vc2  —  m?. 

Area. — In  any  triangle,  the  area  is  equal  to  the  product  of  the  base  by 

one-half  the  altitude,  or  A  =  -=-.     Any  side  may  be  selected  as  the  base.     Thus, 

in  the  obtuse-angled  triangle,  if  the  base  is  the  side  b,  A  =  — ;  if  the  base  is  the 
side  a,  A  =  -^-.     If  the  length  of  the  three  sides  is  given,  let  p  =  one-half  the 

sum  of  the  three  sides,  or  p  =  a+^+-,  and  A  =  ^p(p-a)(p-b)(p-c)\  that  is, 

the  area  is  equal  to  the  square  root  of  one-half  the  sum  of  the  sides  multiplied  by 
this  one-half  sum  less  each  one  of  the  sides,  respectively. 


44 


MATHEMATICS 


Special  Cases.— Equilateral   Triangle.— Angle  A=B  =  C-=GO°.     Side  a  =  b 

=  c. Altitude    h  =  side X. 866025.      Side  =  h -h  .866025  =  h  X  1.154701.      Side 

=  VareaX  1.51967.  .  Area  =  side2X. 443013.  Length  of  side  of  square  having 
same  area  as  an  equilateral  triangle  =  side  of  triangle X. 658037.  Diameter  of 
circle  of  same  area  as  an  equilateral  triangle  =  side  of  triangle  -5- 1.34677.  The 
perpendicular  h  bisects  the  angle  B  and  the  side  b;  and  similarly  for  the  other 
angles  and  sides.  This  triangle  is  also  known  as  the  equiangular  or  60°  triangle. 

Isosceles  Triangle.— Angle  A=C.  B  =  90°  -  A  or  C.  Side  a  =  c.  The  per- 
pendicular h  bisects  the  angle  B  and  the  side  b. 

Right- A  ngled  Triangle.— Angle  A  =  90°.  Angles  B + C  =  90°.  Side  a2  =  b1 + 
c*,  and  o=  V&2+c2,  b  =  Va2-c2,  c=  Va2-R 

For  other  properties  and  methods  of  solving  triangles,  see  under 
Trigonometry. 

PARALLELOGRAMS 

A  parallelogram  is  a  plane  figure  bounded  by  four  straight  lines  which  are 
parallel,  two  and  two.  Some  of  the  different  kinds  of  parallelograms  are 
shown  here. 


A*. 


Square. — Four 

equal  sides 
and  four  right 
angles 


Rectangle. — Four 

right  angles 
and  opposite 
sides  equal 


Rhombus. — Four 
equal  sides 

and 
oblique  angles 


Rhomboid.  —  Four 
oblique  angles 

and 
opposite  sides  equal 


Angles.  —  The  sum  of  the  exterior  angles  =  the  sum  of  the  interior  angles 
<=A+B+C+D  =  A'+B'+Cr+D'  =  36Q°.  In  the  square  and  the  rectangle, 
the  four  angles  are  equal  and  each  is  90°;  in  the  rhombus  and  rhomboid,  A  =C 
and  B  =  D.  In  the  square  and  the  rhombus,  the  diagonals  are  perpendicular 
to  one  another  and  bisect  one  another  and  the  angles  at  their  opposite 
extremities. 

Perimeter  and  Sides.  —  Let  the  sides  be  a,  b,  c,  and  d,  respectively,  then  the 
perimeter,  P  =  a+b  +  c+d.  In  the  square  and  rectangle,  any  side  =  area  -?-  by 
an  adjacent  side.  In  the  rhombus  and  rhomboid,  a  side  =  area  -I-  by  the 
altitude  h.  In  all  four  cases,  the  diagonal  d  =  area-=-by  perpendicular  p. 

Area.  —  In  all  cases,  the  area  A  =  bh  =  dp. 

Square.—  Diagonal  d  =  sideX  1.41421.  Side  =  diagonal  X  .707107.  The  side 
of  a  square  equal  in  area  to  a  given  circle  =  diameter  of  circle  X.  886277.  The 
area  of  the  largest  square  that  may  be  inscribed  in  a  circle  =  2  X  radius  of  circle.2 

It  should  be  noted  that  all  problems  relating  to  parallelograms,  as  well  as 
to  trapezoids,  trapeziums,  and  regular  and  irregular  polygons,  may  be  solved 
by  resolving  these  figures  into  triangles. 

TRAPEZOIDS 

A  trapezoid  is  a  plane  figure  bounded  by  four  straight  lines,  only  two  of 
-  "-1--  —-1-— 


which  are  parallel  one  to  the  other 


One  is  shown  in  the  accompanying  figure. 
Angles.  —  The  sum  of  the  interior 
angles  =  the  sum  of  the  exterior  angles 
=  360°,  or  A+B+C+D  =  A'  +  B'  +  C' 
+D'  =  360°.  A=B':  B  =  A';  C=Df;  D 
=  C'.  A  =  180°-A';  B=  180°  -  B';  and 
similarly  for  C  and  D.  A  +  B  =  C'  +  D'; 
A+C=B'+D';  A+D  =  B'+C';  B+C 
=  A'+D';  and  similarly  for  other  combi- 
nations of  A,  B,  C,  and  D. 

Perimeter.  —  The  sides  being  a,  b,  c,  and 
1     d,  the  perimeter  P  =  a+b+c+d. 
Diagonal.—  The  diagonal  d  =  2  X  area  -^  (p+pf). 
Area.—  Case  /.—Given  the  two  parallel  sides  a  and  c  and  the  perpendicular 

distance  between  them  h,    A= 


MATHEMATICS  45 

Case  II. — Given  the  diagonal  d  and  the  perpendiculars  upon  it  p  and  P'. 


Case  III.  —  Given  the  two  parallel  sides  a  and  c  and  the  angles  adjacent  to 
one  of  them,  A  and  D,  the  area, 

_  c2  —  a2  _  (c  —  o)(c+a)  sin  A  sin  B 

2  (cot  A+cot  B)~~          2  sin  (A+B) 
Case  IV.  —  Given  all  four  sides  a,  b,  c,  and  d.     Let  c  —  a=f,  and 

=  5,  then  area  A  = 


TRAPEZIUMS 

A  trapezium  is  a  plane  figure  bounded  by  four  straight  lines,  no  two  of  which 
are  parallel. 


FIG.  1 


FIG.  2 


Angles. — As  with  trapezoids,  the  sum  of  the  interior  angles  =  the  sum  of 
the  exterior  angles  =  360°.  Also,  A  =  180°  —  A',  and  similarly  for  B,  C,  and  D. 

Perimeter  and  Diagonal. — The  same  relations  prevail  for  the  perimeter 
and  the  diagonal  as  for  trapezoids. 

Area. — In  the  trapezium  shown  in  Fig.  1,  A  =  £  [b(h+h')  +  ah+ch']. 

In  the  trapezium  shown  in  Fig.  2,  A  —-  (p-\-pf). 

POLYGONS 

A  polygon  is  a  plane  figure  bounded  by  three  or  more  straight  lines.     Some 
of  the  more  common  forms  are  shown  in  Fig.  1. 


Pentagon 


Hexagon 


Heptagon 


Octagon 


FIG.  1 


If  all  the  sides  and  angles  are  equal,  each  to  each,  the  figure  is  a  regular 
polygon;  otherwise  it  is  not.  Of  the  figures  previously  discussed,  the 
equilateral  triangle  and  the  square  are  regular  polygons;  the  others  are 
irregular. 

In  any  regular  polygon,  Fig.  2,  let  the  central  angle  (AOB  =  BOC,  etc.)  =C; 
let  the  interior  angle  (ABC  =  BCD,  etc.)  =  /;  let  the  exterior  angle  (A'AB 

=  B'BC,  etc.)  =  £.     Also  let  R  =  -=  =  radius  of  circumscribed  circle,  and  let  r 

=  -  =  radius  of  inscribed  circle  =  apothem.     Likewise,  let  5  =  length  of  a  side 

as  AB,  BC,  etc.,  and  let  N  =  number  of  sides. 

Central  Angle.— The  central  angle  is  equal  to  the  exterior  angle  and  is  equal 

to  360°  divided  by  the  number  of  sides  in  the  polygon,  or  C  =  E  =  -^-.     The 
sum  of  either  the  central  or  the  exterior  angles  of  any  polygon  is  360°. 


46 


MATHEMATICS 


Interior  Angle. — The  interior  angle  is  equal  to  180°  minus  either  the  central 
the  exterior  angle,  or  /  =  180°  —  C=  180°  —  E.     The  sum  of  all  the  interior 

¥ 


'--,€?' 


angles  of  any  polygon  is  equal  to  twice  as  many 
right  angles  as  the  polygon  has  sides,  less  four 
right  angles,  or  27=  (2X-/VX90°)-360°. 

Diagonals.  —  The  diagonals  AD,  BE,  etc.,  of 
a  regular  polygon  bisect  the  interior  angles  /, 
bisect  one  another,  intersect  at  the  center  of 
the  inscribed  and  circumscribed  circles,  divide  the 
polygon  into  as  many  isosceles  triangles  as  it  has 
sides;  also,  they  are  the  diameters  D  of  the  cir- 
cumscribed circle. 

Apothems.  —  The  apothems  LO,  etc.,  of  a 
regular  polygon  are  perpendicular  to  the  sides. 
They  bisect  the  sides,  the  central  angles,  and 
one  another;  divide  the  fundamental  isosceles 
triangles  of  the  polygon  into  two  equal  right 
angled  triangles  BLO+CLO  =  BOC;  and  are 

the  radii  r  of  the  inscribed  circle. 

Perimeter  and  Sides.  —  The  perimeter  of  any  polygon  is  equal  to  the  sum 

of  the  lengths  of  all  its  sides.     The  perimeter  of  a  regular  polygon,  P  =  NS. 

Any  side,  5=  2^R*=r*  =  2R  sin    =  2r  tan     =     . 


p'— 


Area.  —  In  any  polyg9n,  the  area  is  equal  to  the  sum  of  the  areas  of  the 
triangles  into  which  it  is  divided  by  its  diagonals.  The  area  of  a  regular 
polygon  is  equal  to  the  area  of  one  of  the  fundamental  triangles,  as  AOB, 
multiplied  by  the  number  of  sides.  ' 


A  =  Nrz  tan     = 


Likewise, 
sin  C- 


The  accompanying  table  gives,  for  the  more  important  regular  polygons, 
the  number  of  sides;  the  name;  the  central  angle,  which  equals  the  exterior 
angle;  the  interior  angle;  the  length  of  the  side,  in  terms  of  the  radius  of  both 
the  circumscribed  and  inscribed  circles  R  and  r\  and  the  area,  in  terms  of  the 
side  5  and  in  terms  of  the  radius  of  the  circumscribed  and  inscribed  circles  R 
and  r,  respectively. 

NAMES  AND  RELATIONS  OF  REGULAR  POLYGONS 


*6 

L,     05 

Angle 

Side 

Area 

S  <U 

13 

.      Name 

9 

fci 

C  =  E 

7 

R  =  l 

r=l 

5=1 

R=l 

r  =  l 

3 

Equilateral 

120° 

60° 

1.73205 

3.46410 

.43301 

1.29904 

5.19615 

Triangle 

4 

Square 

90° 

90° 

1.41421 

2.00000 

1.00000 

2.00000 

4.00000 

5 
6 

Pentagon 
Hexagon 

72° 
60° 

108° 
120° 

1.17557 
1.00000 

1.45308 
1.15470 

1.720482.37765:3.63271 
2.59808  2.59808  3.46608 

7 

Heptagon 

51°  25.7' 

128°  34.3' 

.86776 

.96315 

3.63391 

2.73641 

3.37106 

8 

Octagon 

45° 

135° 

.76536 

.82842 

4.82842 

2.82840 

3.31368 

9 

Nonagon 

40° 

140° 

:68404 

.72794 

6.18183 

2.89253 

3.27573 

10 

Decagon 

36° 

144° 

.61804 

.64984 

7.69421 

2.93895 

3.24921 

11 

Undecagon 

32°  43.6' 

147°16.4' 

.56346 

.58724 

9.36581 

2.97341 

3.22972 

12 

Dodecagon 

30° 

150° 

.51764 

.53590 

11.19615 

3.00000 

3.21538 

EXAMPLE  1. — What  is  the  length  of  the  side  of  a  triangle  inscribed  in  a 
circle  of  2  in.  radius? 

SOLUTION.— Here  R  =  2  and  the  side  5  =  2X1.73205  =  3.46410. 

EXAMPLE  2. — 'What  is  the  length  of  the  side  of  a  pentagon  circumscribed 
about  a  circle  of  4  in.  radius? 

SOLUTION.— Here  r  =  4  and  side  5  =  4X1.45308  =  5.81232  in. 

EXAMPLE  3. — What  is  the  area  of  a  hexagon  whose  side  is  2  in.  long? 

SOLUTION. — Here  5  =  2  and  area  =  52  or  4X2.59808=10.39232  sq.  in. 

EXAMPLE  4.— What  is  the  area  of  a  dodecagon  that  may  be  inscribed  in  a 
circle  of  3  in.  radius? 


MATHEMATICS 


47 


SOLUTION.— In  this  case,  R  =  3  and  area  =R*  or  9X3.000000  =  27.000000 
sq.  in. 

EXAMPLE  5. — What  is  the  area  of  a  decagon  that  may  be  circumscribed 
about  a  circle  of  4  in.  radius? 

SOLUTION. — In  this  case  r  =  4  and  area  =  r2  or  16X3.24921  =  51.9874  sq.  in. 

EXAMPLE  6. — What  is  the  radius  of  the  circle  that  may  be  circumscribed 
about  a  square  whose  side  is  2  in.? 

SOLUTION. — Here  R  =  2  and  it  is  required  to  find  S.  5  =  2^-1.41421 
=  1.41421. 

Area  of  Irregular  Polygons. — If  the  figure  is  bounded  by  straight  lines,  to 
find  its  area  divide  it  into  triangles;  the  sum  of  the  areas  of  these  will  be  equal 
to  that  of  the  irregular  polygon.  This  method  is  commonly  used  by  engineers 
as  a  useful  check  upon  the  accuracy  of  the  areas  obtained  by  calculation.  In 
many  cases  the  results  thus  obtained  answer  every  purpose. 

If  one  or  more  of  the  boundaries  is  an  irregular  line,  as -would  be  that  of  the 
bank  of  a  river,  the  area  may  be  found  by  one  of  several  methods. 

First  Method.— Lei  A  and  E,  Fig.  3, 
be  two  corners  on  the  river  or  on  any 
other  irregular  boundary.     Draw  the  A] 
lines  AF  and  FE  to  include  as  much 
water  on  the  land  side  as  they  exclude 

land  on  the  water  side.     If  the  map  f  _ 

has  been  platted  by  means  of  coordi-  B\r -' 

natesi,  those  of  F  may  be  found  by 
measurement,  and  the  area  can  then  be 
calculated  by  double  latitudes.  Or  the 
entire  figure  may  be  divided  into  a 
series  of  triangles  as  shown  and  the 
sum  of  their  areas  taken  as  that  of  the  ^  pIG>  3 

Second  Method:  By  Selected  Ordinates.— Draw  perpendiculars  on  AB, 
Fig.  4,  from  the  points  of  the  curve  at  which  its  direction  changes  appreciably, 
and  consider  the  portion  of  the  curve  between  two  consecutive  perpendiculars 
to  be  a  straight  line.  The  figure  is  then  treated  as  if  divided  into  a  number 
of  trapezoids,  whose  areas  can  be  computed  by  the  rules  already  given. 


FIG.  4 


Third  Method:  Trapezoidal  Rule.—  The  ordinates  are  measured  at  regular 
intervals  d  along  the  line,  as  shown  in  Fig.  5.  If  the  end  ordinates  are  a  and  n 

respectively,  the  area  is  A  =  (~^  +  2fe)<f  in  which  2fc  is  the  sum  of  all  the 

intermediate  ordinates. 

EXAMPLE  —  If  the  ordinates  from  the  straight  line  AB  to  the  curved  boun- 
dary DC,  are  19,  18,  14,  12,  13,  17,  and  23  li.,  respectively,  and  are  at  equal 
distances  of  50  li.,  what  is  the  area  included  between  the  curved  boundary  and 

the  straight  line? 

SOLUTION.—  Area  ABCD 


_*-  

1 

—  •—-_ 
2 

4 

„  —  •  — 
5 

6 

3 

a 

h* 

*9 

h2 

'*3 

h2 

k-d-~ 

1—  d—  • 

1—  -d  »1«  cf-— 

FIG.  6 

t—  d— 

l—d-H 

+  18+14  +  12+13+17)  X  50  =  4,750 

^'Fourth  Method:  Simpson's  Rule. 
The  base  line  must  be  divided  into  an 
even  number  of  equal  parts,  as  shown 
in  Fig.  6.  The  area  is  then  equal  to  A 

=  (o+n+42/i2-t-22ft3)^,  in  which  o+n  is  the  sum  of  the  end  ordinates;  42fo  is 
four  times  the  sum  of  all  intermediate  even-numbered  ordinates;  and22As  is 


48  MATHEMATICS 

twice  the  sum  of  all  intermediate  odd-numbered  ordinates.  This  rule  is  more 
accurate  than  the  trapezoidal  rule. 

EXAMPLE. — What  is  the  area  A  BCD  of  the  polygon,  in  the  example  of  the 
Third  Method,  according  to  Simpson's  rule? 

SOLUTION.— A  =  [19+23+4X  (18+12+  17)+2X  (14  +  13)1X^  =  4.733  sq.li. 

Fifth  Method. — Prepare  two  drawings  upon  paper  of  the  same  weight  and 
quality,  one  of  the  tract  of  irregular  outline  and  another  of  about  the  same 
size  but  of  a  tract  whose  area  is  known,  both  drawings  being  to  the  same  scale. 
Cut  each  out  carefully  along  the  boundary  and  weigh  in  a  chemist's  balance 
sensitive  to  milligrams  (1  mg.  =  .015  gr.,  about).  The  area  of  the  irregular 
figure  may  be  calculated  from  the  proportion:  The  unknown  area  :  the  known 
area  =  the  weight  of  the  drawing  of  the  unknown  area  :  the  weight  of  the  drawing 
of  the  known  area. 

Sixth  Method. — Draw  the  figure  upon  cross-section  paper.  If  each  of  the 
small  squares  represents  a  certain  area  to  the  scale  of  the  map,  the  number 
of  whole  squares  and  fractions  thereof  within  the  boundary,  when  multiplied 
by  the  relative  area  of  a  single  square,  will  give  the  area  of  the  figure. 

Seventh  Method. — If  the  area  of  many  irregular  figures  (such  as  a  series  of 
indicator  diagrams)  is  to  be  determined,  a  planimeter  should  be  secured. 
This  instrument,  of  which  there  are  several  types,  and  which  may  be  secured 
through  any  dealer  in  engineer's  supplies,  affords  the  most  rapid  and  accurate 
means  for  determining  the  areas  of  irregular  figures. 

NOTE. — The  accuracy  of  the  results  obtained  by  the  use  of  these  approxi- 
mate methods  for  determining  the  areas  of  _  irregular  figures  depends  almost 
entirely  on  the  skill  and  judgment  of  the  engineer.  Other  things  being  equal, 
the  smaller  the  subdivisions  (in  the  method  involving  ordinates  or  small  squares) 
the  more  accurate  the  results. 

CIRCLES 

A  circle  is  a  plane  figure  bounded  by  a  curved  line  every  point  of  which  is 
equidistant  from  an  interior  point  called  the  center. 

In  the  formulas  relating  to  circles  the  letters  have  the  following  meanings: 
capital  letters  refer  to  the  larger  and  lower-case  letters  to  the  smaller  of  two 
circles  concerned  in  the  same  formula. 

D,  d  =  diameter  .         L,  1  =  length  of  arc 

R,r=  radius  C,  c  =  angle  at  center  subtended  by 

A ,  a  =  area  chord  or  arc 

P,  p  =  circumference  =  perimeter  T,  t  =  thickness  of  circular  ring 

H,  h  =  rise  of  arc  A, B  =  major   and   minor  axes   of 

*•  =  ratio  of  P  to  Z>  =  3.1416  ellipse 

*•  =  3.141592653589793238462  a,  b  =  semi-major  and  semi-minor 

ir2  =  9.86965  axes 

K,  k  =  length  of  chord  ^  =  1.772453 

/>  =  ir<f  =  3.14164  p  p 


••  2  VTTA=  3.5449  \U 
2A     4A  r=\/--.5642VA 


<f  =  2\/^=1.1284VI          *-pr-pd 


2~  4 
1  =  v-  =  -079602 

To  Find  Diameter  of  a  Circle  Equal  in  Area  to  a  Given  Square. — Multiply 
one  side  of  the  square  by  1.12838. 

To  Find  Radius  of  a  Circle  to  Circumscribe  a  Given  Square. — Multiply 
one  side  by  .7071;  or  take  one-half  the  diagonal. 

To  Find  Side  of  a  Square  Equal  in  Area  to  a  Given  Circle. — Multiply  the 
diameter  by  .88623. 

To  Find  Side  of  Greatest  Square  in  a  Given  Circle. — Multiply  the  diameter 
by  .7071. 

To  Find  Area  of  Greatest  Square  in  a  Given  Circle. — Square  the  radius 
and  multiply  by  2. 


MA  THEM  A  TICS 


49 


To  Find  Side  of  an  Equilateral  Triangle  Equal  in  Area  to  a  Given  Circle. 

Multiply  the  diameter  by  1.3468. 

Circumferences  and  areas  of  circles  from  1  to  1,000  units  in  diameter  will  be 
found  in  connection  with  the  table  of  squares,  cubes,  etc.  A  similar  table, 
but  for  diameters  from  ^  to  100,  increasing  by  J,  is  also  given  at  the  end  of 
the  volume.  Circumferences  and  areas  of  circles  whose  diameters  are  not 
exactly  given  in  the  tables,  but  are  within  its  limits,  may  be  found  by  inter- 
polation. If  the  diameters  are  greater  than  those  given  in  the  table,  the 
circumferences  and  areas  may  be  found  by  recalling  that  the  former  are  pro- 
portional to  the  diameters  and  the  latter  to  the  squares  of  the  diameters. 
Thus,  the  circumference  and  area  of  a  circle  9,380  units  in  diameter  are 
respectively  10  and  100  times  those  of  a  circle  938  units  in  diameter. 


Let  5  =  area  and  T 


RINGS 

thickness  of  a  ring. 


2TT 


=  A-a  =  ~~-  =  .079578(P2- 


-  d2)  =  .785398(D*  - 


SECTORS 

A  sector  is  a  portion  of  the  surface  of  a  circle  included 
between  an  arc  AEB  and  two  radii  OA  and  OB. 

A  =  \lr  =  "°™  =  ^-  r*C  =  28.647823  ~  =  .00872666r*C 
IT  C      obU  C 


180  I 
if    C~ 


10.704732  \  9; 


The  central  angle  C  must  be  reduced  to  degrees  and 
decimal  parts  thereof. 


CIRCULAR  SEGMENTS 

A  segment  is  a  portion  of  the  surface  of  a  circle  in- 
cluded between  an  arc  NEM  and  its  chord  NM. 

Area  segment  NEM  =  area  sector  ONEM  —  area 
triangle  NOM. 

The  area  of  the  sector  is  found  from  some  one  of  the 
formulas  already  given  and  that  of  the  triangle  is 
found  from 

A'  =  ^(r-  K)  =  \i*  sin  C=  \k  cot  ~=(k-h)*  tan  § 

Z  £ 


Other  formulas  are  k  =  2  ^h(2r-h)  =  2r  sin  - 


h  =  r- 


-rC- .017453»C 


.    C 
Sm2 


To  determine  the  area  of  a  heading,  the  upper  part  of  which  is  the  arc  of  a 
circle,  the  width  thereof  k  and  the  rise  of  the  arc  h  being  given.     Find  r  from  the 


formula  r  - 


8h 


Then  find  \C  from  sin  -  =  -. 


The  angle  found  is  \C  and 


must  be  multiplied  by  2.     C  is  to  be  expressed  in  degrees  and  decimals  thereof. 
The  area  of  the  sector  ONEM  is  now  found  from  the  formula  A  =  .00872664r2C. 

The  area  of  the  triangle  NM 0  is  found  from  the  formula  A '  -  ^(r  —  K) .     Then  A 

—  A'  =  area  segment  NEM,  which  is  to  be  added  to  that  of  the  lower  rectangular 
portion  of  the  heading. 


SO  MATHEMATICS 

ELLIPSE 

If  A  and  B  are  the  axes  of  an  ellipse  and  c  and  b  are  the  semi-,  or  half,  axes, 
the  area  A  =  7rc6  =  3.141593  ab  =  |A£  =  .  785398  A  B. 

No  simple  formula  has  been  developed  for  finding  the  perimeter  of  an 
ellipse.  In  terms  of  the  semi-axes,  the  formula  for  the  perimeter  involves  the 
summation  of  an  expanding  series  of  an  infinite  number  of  terms: 

i  /(a-fly  ,   1  /(o-&)y 


In  an  ellipse  whose  semi-axes  are  4  and  3,  the  values  within  the  brackets 
become  1  +  .  005102041  +  .000006507  +.000000033.  It  is  apparent,  then,  except 
in  cases,.  involving  great  accuracy,  that  the  terms  beyond  the  second  may 
be  dropped  and  the  formula  for  the  perimeter  of  an  ellipse  may  be  written, 

P  =  ir(o+6)   s1+!'     This,  the  correct  formula,  is  fully  as  simple 


and  is,  naturally,  far  more  accurate  than  any  of  the  so-called  shorter  approxi- 
mations. 


MENSURATION  OF  SOLIDS 

VALUES  USED  IN  FORMULAS 

V  =  volume  of  solid  P  =  perimeter  of  base 

5  =  area  of  convex  surface  p  =  perimeter  of  second  base  or  top 

A  —  area  of  main  base  R,  r,  D,d  =  radius  and  diameter  of  main  base 

a  =  area  of  second  base,  or  top  and  of  secondary  base,  respec- 

T  =  area  of  entire  surface  =  5+A+a  tively;  or,  radius  and  diameter 

h  =  altitude,    or    perpendicular    dis-  of  a  sphere 

tance  from  base  to  top  /  =  slant  height,  or  length  from  base 

to  base  measured  on  surface 

PRISMOID  AND  PRISMOIDAL  FORMULA 

A  prismoid  is  any  solid  having  two  parallel  ends  or  faces  of  any  shape 
similar  or  dissimilar,  regular  or  irregular,  provided  these  ends  are  united  by 

surfaces,  whether  plane  or  curved,  on 
which  and  through  every  point  of  which, 
a  straight  line  may  be  drawn  from  one 
of  the  parallel  ends  to  the  other.     It 
embraces  all  polyhedrons,  parallelepi- 
peds,   prisms,    cylinders,    cones,  pyra- 
mids, etc.,  and  even  the  sphere,  which 
may  be  regarded  as  a  regular  polyhe- 
dron  of   an  infinite  number  of  faces. 
This  is  true  whether  the  solids  are  regular  or  irregular,  right  or  oblique,  and 
applies  to  their  frustums  when  cut  parallel  to  the  base. 
The  formula  for  the  volume  of  a  prismoid  is 
Tr     H(A+4M+B) 

6 
in  which  A  and  B  =  areas  of  two  ends,  respectively; 

M  =  are"a  of  section  taken  midway  between  ends; 
H  =  perpendicular  distance  between  parallel  ends. 

This  is  known  as  the  prismoidal  formula,  and  from  it,  by  making  the  proper 
substitutions  for  A ,  M,  and  B,  an  equation  for  the  volume  of  any  solid  may  be 
deduced,  provided  its  form  is  included  in  the  definition  of  a  trapezoid.  Unless 
the  parallel  ends  are  similar  polygons,  the  mid-section  M ,  is  not  the  mean  of 
the  sections  A  and  B.  This  formula  is  extensively  used  in  calculating  exca- 
vations in  railroad  work. 

REGULAR  POLYHEDRONS 

A  polyhedron  is  a  solid  contained  within  any  number  of  plane  sides.  A 
regular  polyhedron  is  one  whose  bounding  planes  (faces)  are  regular  polygons 
of  the  same  shape  and  area,  and  whose  solid  (polyhedral)  angles  are  equal 
each  to  each.  Unless  the  sphere  is  considered  a  regular  polyhedron  of  an 


MATHEMATICS 


51 


infinite  number  of  sides,  only  five  regular  polyhedrons  are  possible;  these  are 
shown  in  the  accompanying  figure. 


Tetrahedron 


Cube 


Octahedron        Dodecahedron        Icosahedron 


REGULAR  POLYHEDRONS  WHOSE  EDGES  ARE  UNITY 


Name 

Bounding  Polygons 

Surface 

Volume 

Tetrahedron 
Hexahedron  or  cube 
Octahedron 
Dodecahedron 
Icosahedron 

4  equilateral  triangles 
6  squares 
8  equilateral  triangles 
12  pentagons 
20  equilateral  triangles 

1.732051 
6.000000 
3.464102 
20.645729 
8.660254 

.117851 
1.000000 
.471405 
7.663119 
2.181695 

The  surface  of  any  regular  polyhedron  is  equal  to  the  number  of  faces 
multiplied  by  the  area  of  a  single  face.  It  maybe  found  from  the  accompanying 
table  by  squaring  the  length  of  the  edge  of  a  face  and  multiplying  this  by  the 
number,  in  the  column  headed  Surface,  opposite  the  name  of  the  polyhedron. 
Thus,  the  surface  area  of  an  octahedron  whose  edge  is  2  in.  long,  is  22,  or  4X 
3.464102  =  14.856408  sq.  in. 

The  volume  of  any  polyhedron  may  be  obtained  by  taking  the  sum  of  the 
volumes  of  the  pyramids  into  which  it  may  be  divided.  There  will  be  as  many 
pyramids  as  there  are  faces  in  the  polyhedron  and  the  bases  of  these  pyramids 
will  be  the  several  faces  of  the  polyhedron.  The  volumes  of  the  regular  poly- 
hedrons may  be  obtained  from  the  table  by  multiplying  the  cube  of  the  length 
of  the  edge  by  the  number,  in  the  column  headed  Volume,  opposite  the  name 
of  the  polyhedron  concerned.  Thus,  the  volume  of  a  tetrahedron  whose  edge 
is  2  in.  long,  is  2",  or  8X  .117851  =  .942808  cu.  in. 


THE  SPHERE 

The  sphere  may  be  defined  as  a  regular  polyhedron  of  an  infinite  number  of 
sides;  or  as  a  solid  generated  by  the  revolution  of  a  semicircle  about  its  diam- 
eter; or  as  a  solid,  every  point  of  whose  surface  is  equi- 
distant from  a  fixed  interior  point  called  the  center. 

A  great  circle  of  a  sphere  is  the  line  formed  by  the 
intersection  of  a  plane  through  the  center  with  the 
surface  of  the  sphere,  as  A  BCD  or  AbCc.  Its  radius 

and  diameter  r  and  d  are  the  same  as  those  of  the       .,  -„,„._          *„ 

sphere ;  its  area  irR2  may  be  placed  equal  to  Z.  A  * " 


R=\IT-  F  =  . 62035  ^F=\f~-  =  . 2821 VS 

\4ir  \4ir 


p  =  -v/e^F  =  3  8978  %V-- 
5  =  47^2=12.5664^=-^ 


••  1.7725  VS=4 
a 


6 


dZ 


52 


MATHEMATICS 


SPHERICAL  SEGMENTS 

A  spherical  segment  is  that  portion  of  a  sphere  that  is  included  between  its 
surface  and  a  plane  cutting  it,  as  EABCD.  If  the  plane  passes  through  the 
center,  the  sphere  is  divided  into  two  equal  parts,  each  of 
which  is  a  hemisphere.  Let  EF  =  h  =  height  of  segment, 
and  r'  and  d'  be  the  radius  and  diameter  of  the  basal 
plane,  and  R  be  the  radius  of  the  sphere. 


5  =  2irRh  =  6.2832Rh 


.7854(^+4^)  =  Ph 


To  this  must  be  added  the  area  of  the  base,  ^d'2,   if 
the  entire  surface  is  required. 


SPHERICAL  ZONES 

A  spherical  zone  is  that  portion  of  a  sphere  that  is  in- 
cluded between  two  parallel  intersecting  planes. 

Let  d  be  the  diameter  of  the  sphere  and  df  and  d"  be 
the  diameters  AC  and  ac  of  the  two  planes,  whose  distance 
apart  is  EF  =  h. 

S  =  PZ        "  '          •"'-'-«        '  -  * 


V—o- 


vdh  =  surface  of  sphere  X  -. 


V-f 


CYLINDRICAL  RINGS 

A  cylindrical  ring  is  produced  by  bending  a  cylinder  upon 
itself.  Using  the  notation  in  the  accompanying  figure 
5  =  4**Rr  =  39A78GRr  =  ir*Dd  =  9.8Q97Dd.  V  =  2v*Rr* 

d-J  =  19.7393Kr2  =  ^  Dd*  =  2.4674Dd*. 

^*^fopf£MV.'>i'Sft«nff»!  ''•'•'?:"•;: .';;.    ""'"''.^1 

PARALLELOPIPEDS 


Cube 


Rectangular  Prism        Rhombohedron         Rhombic  Prism 


A  parallelepiped  is  a  solid  bounded  by  six  faces,  all  of  which  are  parallelo- 
grams; opposite  faces  being  parallel.  In  the  cube,  there  are  six  equal  faces 
and  eight  equal  solid  angles;  in  the  rectangular  prism,  there  are  three  pairs  of 
equal  opposite  faces  and  eight  equal  solid  angles;  in  the  rhombqhedron,  there  are 
six  equal  faces  and  four  pairs  of  equal  and  diagonally  opposite  angles;  in  the 
rhombic  prism,  there  are  three  pairs  of  equal  opposite  faces  and  four  pairs  of 
equal  and  diagonally  opposite  angles. 

.5  =  sum  of  areas  of  six  faces.     In  the  cube  and  rhombohedron  5  =  6.4. 
In  the  two  prisms  (calling  the  equal  faces  A,  B,  and  C)  S  =  2A+2B+2C. 
V  =  Ah\  that  is,  the  volume  is  equal  to  the  area  of  any  face  multiplied  by 
the  perpendicular  distance  to  the  opposite  face. 

In  the  cube,  F  =  cube  of  length  of  one  edge.  The  diagonal 
joining  opposite  vertices  =  an  edge  X  1.732051.  The  radius  of  the 
inscribed  sphere  =  the  edge  X  .5.  The  radius  of  the  circumscribed1 
sphere  =  one-half  the  diagonal  joining  opposite  vertices  =  the  edge 
X. 866026. 

Frustum  of  Prism. — If  a  section  perpendicular  to  the  edges 
is  a  triangle,  square,  parallelogram,  or  regular  polygon, 

T/     sum  of  lengths  of  edges  vx  ,    .  ,  . 

V  = : r-5 — T— - — - — Xarea  of  right  section 

number  of  edges 


MATHEMATICS 


53 


CYLINDERS 

A  cylinder  of  revolution,  which  is  the  common  form,  is  a  solid  that  may  be 
considered  to  have  been  generated  by  the  revolution  of  a  parallelogram  about 
one  edge. 

S  =  2vrh  =  irdh  =  Ph.     T  =  5+2Xarea  of  base  = 


V=  area  of  base  X  perpendicular  height  h,  or  V  =  Ah 
-d?h  =  ~h  =  3.1416r2/i  =  . 


irr*h 


-          ~ 
4  4x 

Frustum  of  Cylinder.  — 

Let  h  =  one-half  sum  of  greatest  and  least  heights 


T  = 


d2+area  of  elliptic  top. 


Hollow  Cylinders. — The  volumes  of  hollow  cylinders,  as  the 
quantity  of  metal  in  a  pipe,  may  be  found  by  multiplying  the  area 
of  the  ring  made  by  its  cross-section  by  the  length  of  the  cylinder. 
The  area  of  the  cross-section  may  be  determined  by  the  formulas 
given  under  Rings. 

THE  PYRAMID 

A  pyramid,  Fig.  1,  is  a  solid  having  for  its  base  a  plane  figure  of  any  num- 
ber of  sides,  and  for  its  sides,  plane  triangles  terminating  in 
a  common  point,  called  the  apex. 

S  =  iPJ,  and  T  =  %Pl+A,  in  which  P  is  the  perimeter 
of  the  base,  A  its  area,  and  I  the  slant  height.  Note  that 
I,  Fig.  1,  is  not  measured  on  an  edge,  but  from  the  center  of 
one  side  of  the  base  to  the  vertex.  These  formulas  apply  to 
the  right  regular  pyramid  in  which  the  base  is  a  regular  poly- 
gon and  the  axis  is  perpendicular  thereto.  If  the  base  is  not 
a  regular  polygon  and  the  pyramid  is  oblique  (the  axis  is 
inclined  to  the  base),  each  triangular  side  has  different  pIG 

dimensions.     To  find  S,  the  sum  of  the  areas  of  the  different 
triangular  sides  must  be  taken,  to  which  must  be  added  the  area  of  the  irreg- 
ular base  if  T  is  desired. 

The  volume  of  any  pyramid  is  equal  to  the  area  of  the 
base  multiplied  by  one-third  the  altitude,  or  V  =  %Ah. 

Frustum  of  Regular  Pyramid. — If  A  and  a  and  P  and  p 
*  are  the  area  and  perimeter  of  the  lower  and  upper  bases,  re- 
^  |  spectively,  of  a  frustum  of  a  regular  pyramid,  Fig.  2, 

If  the  cutting  p^lane  is  inclined  to  the  base  or  the  frus- 
FIG.  2  *um  is  J-hat  °f  an  irregular  or  oblique  pyramid,  the  surface 

area  5  is  the  sum  of  the  areas  of  the  trapeziums  forming  the 
sides,  to  which  must  be  added  the  areas  of  the  irregular  bases  if  T  is  wanted. 
The  volume  of  the  frustum  of  any  pyramid  is  V  =  ih(A+a- 

THE  WEDGE 

The  wedge,  whether  with  a  blunt  edge 
as  A  BCD-abed,  or  with  a  sharp  edge  as 
ABCD-a'b',  is  a  special  form  of  the  trape- 
zoid,  as  the  ends  abed,  or  a'V  are  parallel 
to  the  base  A  BCD.  In  the  blunt  wedge, 
V  =  %fh(m-\-n)  and  in  the  sharp  wedge 
V=afnh,  as  m-O.  In  the  latter  case,  h 
=  Bb'. 

THE  CONE 

A  cone,  Fig.  1,  is  a  solid  generated  by  a  straight  line,  one  end 
of  which  passes  through  a  fixed  point,  called  the  apex  while  the 
other  end  is  free  to  move  around  the  perimeter  of  a  closed  curve, 
known  as  the  base.  Cones  are  regular  when  the  base  is  a  circle 
and  are  right  of  oblique  according  as  the  axis  is  at  right  angles 
to  or  inclined  to  the  base. 

P  The  common  form  of  cone,  as  shown  in  accompanying 

figure,  is  the  right  regular  cone  of  revolution,  which  may  be 


54 


MATHEMATICS 


considered  to  have  been  generated  by  the  revolution  of  a  right-angled  tri- 
angle about  one  side.  Its  base  is  a  circle  and  its  axis  is  perpendicular  to  the 
center  of  the  base. 

The  surface  of  the  cone  is  S 

Thetotal  surface,  T=  irrl 


The  volume, 


V  = 


vr(l  +  r) 


1  .0472r2/». 


Frustum  of  Cone.  —  When,  as  in  Fig.  2,  the  cutting  plane 
is  parallel  to  the  base  of  the  cone 

,  and  T- 


FIG.  1 


PLANE  TRIGONOMETRY 

DEFINITIONS 

Plane  trigonometry  treats  of  the  solution  of  plane  triangles.  In  every  tri- 
angle there  are  six  parts — three  sides  and  three  angles.  These  parts  are  so 
related  that  when  three  of  the  parts  are  given,  one  being  a  side,  the  other  parts 
may  be  found. 

An  angle  is  measured  by  the  arc  included  between  its  sides,  the  center  of 
the  circumference  being  at  the  vertex  of  the  angle. 

For  measuring  angles,  the  circumference  is  divided  into  360  equal  parts, 
called  degrees;  each  degree  is  divided  into  60  equal  parts  called  minutes;  and 
each  minute  is  divided  into  60  equal  parts  called  seconds.  Divisions  smaller 
than  a  second  are  expressed  in  decimal  parts  of  that  unit;  thus,  24.56". 

A.  quadrant  is  one-fourth  the  circumference  of  a  circle, 
or  90°. 

The  complement  of  an  arc  is  90°  minus  the  arc;  the 
arc  DC,  Fig.  1,  is  the  complement  of  the  arc  BC,  and  the 
angle  DOC  is  the  complement  of  the  angle  BOC. 

The  supplement  of  an  arc  is  180°  minus  the  arc;  the  arc    ^  I 
AE  is  the  supplement  of  the  arc  BDE,  and  the  angle  AOE 
is  the  supplement  of  the  angle  BOE. 

In  trigonometry,  instead  of  comparing  the  angles  of 
triangles  or  the  arcs  that  measure  them,  the  trigonomet- 
ric functions,  known  as  the  sine,  cosine,  tangent,  cotan- 
gent, secant,  and  cosecant,  are  compared. 

The  sine  of  an  arc  is  the  perpendicular  let  fall  from  one  extremity  of  the 
arc  on  the  diameter  that  passes  through  the  other  extremity.  Thus,  CD, 

Fig.  2,  is  the  sine  of  the  arc  AC. 
The  cosine  of  an  arc  is  the 
sine  of  its  complement ;  or  it  is 
the  distance  from  the  foot  of 
the  sine  to  the  center  of  the 
circle.  Thus,  CE  or  OD  equals 
the  cosine  of  arc  AC. 

The  tangent  of  an  arc  is  a 
line  that  is  perpendicular  to 
the  radius  at  one  extremity 
of  an  arc  and  limited  by  a  line 
passing  through  the  center  of 
the  circle  and  the  other  ex- 
tremity .  Thus ,  A  T  is  the  tan- 
gent of  AC. 

The  cotangent  of  an  arc  is 
equal    to   the   tangent   of    the 
•c.       0  complement  of  the  arc.     Thus, 

BT'  is  the  cotangent  of  AC. 

The  secant  of  an  arc  is  a  line  drawn  from  the  center  of  the  circle  through 
one  extremity  of  the  arc,  and  limited  by  a  tangent  at  the  other  extremity. 
Thus,  OT  is  the  secant  of  AC. 


MATHEMATICS  55 

The  cosecant  ot  an  arc  is  the  secant  of  the  complement  of  the  arc.  Thus, 
OT'  is  the  cosecant  of  AC. 

The  versed  sine  of  an  arc  is  that  part  of  the  diameter  included  between  the 
extremity  of  the  arc  and  the  foot  of  the  sine.  DA  is  the  versed  sine  of  AC. 

The  coversed  sine,  is  the  versed  sine  of  the  complement  of  the  arc.  Thus, 
BE  is  the  coversed  sine  of  AC.  •» 


FUNDAMENTAL  RELATIONS 

t 
e 
sin2  x-f  cos2  # 


If  x  is  any  angle,  the  fundamental  relations  that  its  trigonometric  functions 
sustain  to  one  another  are: 


cosec  x- 


sec2  x=  1-f-tan2  x 

_     -  cosec2  x  =1 + cot2  x 

C~tanx  vers*=l-cos* 

covers  x  =  1  —  sin  x 

The  tangent  and  cotangent  of  the  same  angles  are  reciprocals  of  each  other; 
so  also  are  the  secant  and  cosine;  and  the  cosecant  and  sine. 

The  value  of  the  sine  and  cosine  cannot  be  greater  than  1.  Tangents 
and  cotangents  may  have  any  value  from  0  to  00.  Secants  and  cosecants 
may  have  any  value  between  1  and  00.  Versed  sines  and  coversed  sines  may 
have  any  value  between  0  and  2. 

SIGNS  OF  TRIGONOMETRIC  FUNCTIONS 

The  various  trigonometric  functions  have  signs;  that  is,  they  are  +  or  — , 
depending  on  the  magnitude  of  the  angle. 

Sines  and  cosecants  of  angles  between  0°  and  180°  are  +;  and  those  of 
angles  between  180°  and  360°  are  -. 

Cosines  and  secants  of  angles  between  0°  and  90°  and  between  270°  and  360° 
are  -f-;  and  those  of  angles  between  90°  and  270°  are  — . 

Tangents  and  cotangents  of  angles  between  0°  and  90°  and  between  180° 
and  270°  are  + ;  and  those  of  angles  between  90°  and  180°  and  between  270° 
and  360°  are  -. 

Versed  sines  and  coversed  sines  are  always  +  regardless  of  the  magnitude 
of  the  angle. 

FUNCTIONS  OF  ANGLES  BETWEEN  90°  AND  180° 

In  the  solution  of  obtuse-angled  triangles,  it  is  commonly  necessary  to 
have  to  find  the  functions  of  an  angle  of  more  than  90°.  This  may  readily  be 
done  if  it  is  recalled  that  the  sine,  etc.,  of  an  angle  equals  the  corresponding 
function  of  its  supplement.  Thus 

sine  110°  =  sine  of  70°  cosine  110°  =  cosine  70° 

tangent  110°  =  tangent  of  70°  cotangent  110°  =  cotangent  70° 

secant  110°  =  secant  of  70°  cosecant  110°  =  cosecant  70° 

Thus,  if  it  is  desired  to  find  the  sine  of  an  angle  of  120°  30',  look  for  the  sine 
of  180°— 120°  30',  or  59°  30',  and  similarly  for  the  other  functions.  In  deal- 
ing with  angles  of  more  than  90°  attention  should  be  paid  to  the  sign  of  the 
function. 

FUNCTIONS  OF  90°+ A 

sin   (90°+A)  =     cos  A  cot  (90°+A)  =  -tan  A 

tan  (90°+ A)  =  -cot  A  sec  (90°+ A)  =  -esc  A 

cos  (90°+A)  =  -sin  A  esc  (90°+A)=     sec  A 

FUNCTIONS  OF  180°- A  AND  OF  180°+ A 

sin  (180°- A)  =     sin  A  sin  (180°+ A)  = -sin  A 

tan  (180°- A)  =  -tan  A  tan  (180°+A)  =     tan  A 

cos  (180°- A)  =  -cos  A  cos  (180°  +  A)  =  -cos  A 

cot  (180°- A)  =  -cot  A  cot  (180°+A)=     cot  A 

sec  (180°-A)  =  -sec  A  sec  (180°+A)  = -sec  A 

esc  (180°- A)  =     esc  A  esc  (180°+A)  = -esc  A 


56 


MATHEMATICS 
FUNCTIONS  OF  (A+B)  AND  OF  (A-B) 


sin  (A+B)  = 
sin  (A-B)  = 
cos  (A  +B)  = 
cos  (A-B)  = 

tan(A+B)=* 
tan  (A- 


sin  A  cos  B + cos  A  sin  B 
sin  A  cos  B  —  cos  A  sin  B 
cos  A  cos  J3  — sin  A  sin  B 
cos  A  cos  .B+sin  A  sin  J3 

tan  A  +  tan  B 
1-tan  A  tan  B 

tan  A— tan  B 
1-f-tan  A  tan  B 


FUNCTIONS  OF  2A  AND  OF  J. 

sin  2A  =  2  sin  A  cos  A 

sin  $A  = 
cos  2A  =  cos2  A  —  sin2  A 

cos  2A  =2  cos2  A  - 1  cos  *A  = 

cos  2A  =  1  — 2  sin*  A 
2  tan  A 


—  cos  A 


tan  2A  = 


1-tan2  A 


sin  A 


SUMS  AND  DIFFERENCES  OF  FUNCTIONS 


sin  A+sin  B  =  2  sin 
sin  A  —  sin  B  =  2  sin 
cos  A+cos  B  =  2  cos 
cos  A  —  cos  B  =  2  sin 


(A-B) 
(A+B) 
(A-B) 
(B-A) 


R 

cos  B 
sin  (A-B) 
cos  A  cos  B 
sin2  A  —  sin2  B  =  sin  (A  +  B)  sin 
cos2  A  -  cos2  B  =  sin  (A  +  B)  sin 


tan  A  -tan  B  = 


(A-, 
[B-. 


cos2  A  -  sin2  B  =  cos  (A  +  B)  cos  (A  -  B) 


Side  adjacent 


SOLUTION  OF  RIGHT-ANGLED  TRIANGLES 

There  are  six  parts  in  every  triangle  and  if 
three  of  them  are  known  the  other  three  may  be 
u  determined  by  calculation,  provided  one  of  the 
three  known  parts  is  a  side.  In  the  case  of  a  right- 
angled  triangle,  one  of  the  angles  is  90°,  but 
two  other  parts,  one  of  them  a  side,  are  necessary 
§.  for  its  solution.  Three  angles  do  not  determine 
a  triangle,  because  all  triangles  whose  sides  are 
parallel  each  to  each  have  the  same  angles  but 
sides  of  different  length. 

In  right-angled  triangles,  the  following  rela- 
tions between  the  angles  and  sides  prevail: 


cos  A 


.  =  side  opposite  _  a 
=  hypotenuse  ~  c 
side  adjacent  _  b 
hypotenuse      c 

A  _side  opposite _a 

ia,n  si  —  — — — —  — 

side  adjacent     b 


versA=l-- 


cot  A  = 


sec  A 


side  adjacent  _  b 
side  opposite     a 
hypotenuse  _^ 
side  adjacent     b 
.  _  hypotenuse  _  c 
side  opposite     a 


covers  A  =  l  — - 


MA  THEM  A  TICS 

RELATIONS  BETWEEN  ANGLES  AND  SIDES  OF  RIGHT- 
ANGLED  TRIANGLES 


57 


Given 

Required 

Formula 

Given 

Required 

Formula 

a,  A 

B,b,c 

{b  =  a  cot  A 
a 

tan  B  =  -, 

sin  A 

a,B 

A,b,c 

!'b  =  ata.nB 
C  =  cosB  =  aSeC  B 

a,  b 

A,  B,  c 

:3?°  L 

c,A 

B,a,b 

<   a  =  c  sin  A 
I  b  =  c  cos  A 

sin  A  —- 
c 

cos  B  =  - 

a,  c 

A,B,b 

c 

=  V(c+o)(c  —  a] 
b  =  a  cot  A 

Area. — The  area  ot  a  right-angled  triangle  is  equal  to  one-half  the  product 
of  the  base  by  the  altitude,  or  area  =  \  ab. 

The  area  is  also  equal  to  one-half  the  product  of  any  two  sides  into  the  sine 
of  the  angle  between  them.  Thus,  if  the  angle  A  and  the  sides  c  and  b  are  given, 
area=jcfc  sin  A. 

SOLUTION  OF  OBLIQUE-ANGLED  TRIANGLES 

The  following  relations  between  the  sides  and  angles  apply  to  all  triangles, 
but  are  of  particular  service  in  solving  those  with  oblique  angles: 


1.  The  sides  of  any  plane  triangle  are  proportional  to  the  sines  of  the  angles 
opposite. 

a  :  b  =  sin  A  :  sin  B 
a  :  c  =  sin  A  :  sin  C 
b  :  c  =  sin  B  :  sin  C 

2.  Any  side  of  a  plane  triangle  equals  the  sum  of  the  products  of  each  of  the 
other  sides  into  the  cosine  of  the  angle  that  it  makes  with  the  first  side. 

a  =  b  cos  C+c  cos  B 
b  =  a  cos  C+c  cos  A 
c  =  a  cos  B  +  b  cos  A 

3.  The  square  of  any  side  of  a  plane  triangle  equals  the  sum  of  the  squares 
of  the  other  two,  minus  twice  their  product  into  the  cosine  of  their  included  angle. 

2  —  2  be  cos  A 


C2  =  c2-f-fc2  —  2afe  cos  C 

4.  The  sum  of  any  two  rides  of  a  plane  triangle  is  to  their  difference,  as  the 
tangent  of  one-half  the  sum  of  the  angles  opposite  them  is  to  the  tangent  of  one-half 
their  difference. 

a+b  :  a-&  =  tan  i(A+J3)  :  tan  $(A-B) 
a+c  :  a-c  =  tan  JU+C)  :  tan  $(A-C) 
b+c  :  b-c  =  t&n  $(B+C)  :  tan  $(B-C) 


58  MATHEMATICS 

5.  The  cosine  of  any  angle  of  a  plane  triangle  is  equal  to  the  sum  of  the  squares 
of  the  adjacent  sides  minus  the  square  of  the  side  opposite,  the  whole  divided  by 
twice  the  product  of  the  adjacent  sides. 

ros    A 

COSA 


2bc 

02  +  CZ 

cos  B=  —  -n  — 
2ac 


6.  The  area  of  any  plane  triangle  is  equal  to  one-half  the  product  of  any  two 
sides  into  the  sine  of  the  included  angle. 

Area  =  \d>  sin  A  =  %ac  sin  B  =  \ab  sin  C 

7.  The  area  of  any  plane  triangle  is  equal  to  the  square  root  of  the  continued 
product  of  one-half  its  perimeter  into  one-half  its  perimeter  minus  each  side  sep- 
arately. 

If  the  perimeter,  a+b+c  =  p,  then, 


Area 

PRACTICAL  EXAMPLES 

1.     Having  given  two  sides  and  the  included  angle,  to  find  the  other  side  and 

remaining  angles.  —  Let  &  =  30,  c  =  20,  and  A  =  38°  20';  required  a,  B,  and  C. 

Find  the  angle  B  from  the  third  formula  of  the  fourth  relation,  which  may 

be  transposed  to  tan  KB-C)=tan  ^(B+C)X^~.     In  this  B+C=180°-A 

=  180°-38°  20'=  141°  40',  and  £(5+0  =  70°  50';  B-C  is  unknown;  b  +  c 
=  30+20  =  50,  and  &-c  =  30-20  =  10.  By  substitution,  tan  JCB-O  =2.87700 
X  £8  =  .57540.  From  this  $(B  -  C)  =  29°  55'  (very  nearly)  ,  and  B  -  C  =  29°  55' 
X2  =  59°50'. 

B  +  C  =  141°  40' 

B-C=   59°  50' 

By  addition,  2B        =201°  30' 

By  division,  B  =  100°  45' 

From  this  A+B  =  38°  20'  +100°  45'  =139°  5',  and  C=180°-(A+B)  =  180° 
-139°  5'  =  40°  55'. 

Find  the  side  a  from  the  first  formula  of  the  first  relation,  which  may  be 


transposed  to  read,  ..»x-30X-<.lM«.     Re- 


member  that  sin  100°  45'  =  sin  (180°-  100°  45')=  sin  79°  15'. 

2.  Having  given  two  sides  and  the  angle  opposite  one  of  them,  to  find  the  other 
side  and  remaining  angles.—  Let  the  given  parts  of  the  triangle  shown  in  Fig.  1, 
be  A  =38°  20',  6  =  30,  and  a  =  18.94;  from  which  it  is  required  to  find  c,  B, 
and  C. 

Find  the  angle  B  from  the  first  formula  of  the  first  relation,  which  trans- 


posed is  sin  B  =  -Xsin  A  =Xsin  38°  20'  =  X.  62024  =  .98245;  whence 


1  =  79°  15'  or  100°  45'.  Unless  the  shape  of  the  triangle  is  actually  known 
it  is  impossible  to  tell  which  of  these  values  of  B 
should  be  taken.  In  fact,  both  of  them  are  correct, 
as  a  study  of  the  accompanying  figure  will  show. 
As  only  A,  b,  and  a,  are  fixed,  it  is  apparent  that  a 
may  occupy  either  position  CB  or  CB'  and  yet  have 
the  same  value,  18.94.  Such  being  the  case,  the  angle 
at  B  may  be  (for  the  position  CB  =  a'  =  18.94)  CBA 
=  79°  15',  or  (for  the  position  CB'  =  a=  18.94)  CB'A 
=  100°  15'.  Hence,  angle  C=180°-(A+£)  =180° 
-  (38°  20'+79°  15')  =  180°- 117°  35' =  62°  25',  or 
C=180°-(38°  20'+100°  45')  =  180° -.139°  5'  =  40°  55' 
The  side  c  may  now  be  found  from  the  second  formula  of  the  first  relation, 

which  may  be  transposed  to  read  c  =  a  —. — - ,  and  taking  the  two  values  of  the 

sin  A 


I 


MATHEMATICS 


Thus  two  solutions  of  this  triangle  are  possible;  in  the  first  case,  B  =  79°  15', 
C  =  62°  25',  c  =  27.07,  and  in  the  second  case,  £=100°  45',  C  =  40°  55',  c  =  20. 

3.  Having  given  two  angles  and  any  side,  to  find  the  other  angle  and  the  other 
two  sides.—  Let  A  =  38°  20',  5  =  100°  45',  a  =  18.94;  to  find  the  remaining 
angle  C  and  the  other  sides  b  and  c. 

Find  C  from  the  relation  C  =  180°-(A+.B)  =  180°-  (38°  20'+100°  45') 
=  180°  -139°  5'  =  40°  55'. 

The  sides  may  now  be  found  from  the  first  and  second  formulas  given  in 
the  first  relation  after  these  have  been  transposed. 

sin  £5  smOO    45'  98245 


4.  Having  given  the  three  sides  to  find  the  three  angles.—  Let  a  =18.94, 
b  =  30,  and  c  =  20;  required  the  angles  A  ,  B,  and  C.  Using  the  formulas  given  in 
the  fifth  relation  to  find  A  and  B,  then  C  may  be  found  from  C=  180°-  (A  +  B). 


tc=  180°-  (A+B)  =  180°-  (38°  20'+ 100°  45')  =40°  55' 
Note  that  the  angle  corresponding  to  the  cosine  .18648  is  either  79°  15' 
or  100°  45'.     By  referring  to  the  section  Signs  of  Trigonometnc  Functions, 
it  will  be  seen  that  when  the  cosine  is  minus,  as  it  is 
in  this  case  (-.18648),  the  angle  is  between  90°  and 
270°;  hence,  the  value  B  =  100°  45'  is  taken. 

This  example  is  readily  solved  by  the  solution  of  two 
right-angled  triangles,  as  shown  in  Fig.  2.     Let  fall  a  h, 

perpendicular  CD  from  the  opposite  vertex  C  upon  the 
longest  side  AB  dividing  it  into  two  segments  AD 
=  m  andDjB  =  n.  From  geometry,  m  +  n  :  b+a  =  b  —  ( 

(b+a)(b-a) 
:m  —  n,  and  as  m  +n  =  c,m  —  n  = . 

bining  the  value  of  m  —  n  thus  obtained  with  that  of 
w  +  n  =  c,  the  values  of  m  and  n  may  be  found.  In  the  right-angled  triangles 
ACD  and  BCD,  b  and  m  and  a  and  n,  respectively,  are  given,  from  which  the 
angles  A  and  B  may  be  calculated;  angle  C  found  by  subtracting  the  sum  of 
angles  A  and  B  from  180°. 

Using  the  values  for  the  sides,  a  =  18.94,  &  =  30,  and  c  =  27.066 
(30 + 18.94)  X  (30  - 18.94)     48.94  X 1 1 .06 


m—  n=  — 

Then 
1 
i 

27.066 

n  +  n  =  27.066 
w-n=  19.998 

27.066 

m+«  =  27.066 
m-n=  19.998 

By  addition 

2w  =  47.064 
w  =  23.532 

By  subtraction       2n=   7.068 
n=   3.534 

In  the  triangle  A  CD,  cos  A  =     =         -  =  .78440.     Whence  A  =  38°  20'. 


In  the  triangle  DCB,  cos  5  =  -=  =  .  18659.     Whence  £  =  79°  15'. 

a    is.y4 

C  =  180°  -  (A  +  B)  =  180°  -  1  17°  35'  =  62°  25' 

Tables  of  natural  and  logarithmic  trigonometric  functions  will  be  found 
at  the  end  of  the  volume;  each  table  is  preceded  by  the  necessary  explanations 
for  its  use. 


60  SURVEYING 


SURVEYING 


THE  COMPASS 

GENERAL  DESCRIPTION 

Surveying  is  an  extension  of  mensuration,  and,  as  ordinarily  practiced, 
may  be  divided  into  surface  work,  or  ordinary  surveying,  and  underground 
work,  or  mine  surveying.  With  slight  modifications,  the  instruments  employed 
in  both  are  the  same,  and  consist  of  a  compass — if  the  work  is  of  little  impor- 
tance, and  accuracy  is  not  required — a  transit,  level,  transit  and  level  rods, 
steel  tape  or  chain,  and  measuring  pins,  and  sometimes  certain  accessory  instru- 
ments, as  clinometers  or  slope  levels,  dipping  needles,  etc.,  as  will  be  described 
later. 

The  compass  may  be  either  a  pocket  compass,  or  a  surveyor's  compass, 
and  may  be  used  while  held  in  the  hand,  or  upon  a  tripod.  The  Jacob's  staff, 
convenient  for  use  on  the  surface,  is  useless  in  the  mine.  As  the  compass  can- 
not be  sighted  accurately  on  an  object,  cannot  be  read  closer  than  30',  except 
by  guess,  and  may  be  deflected  from  its  true  course  as  much  as  2°  or  3°  by  the 
iron  in  the  rails  or  water  pipes  or  by  electric  currents,  it  is  obvious  that  bear- 
ings and  angles  determined  through  its  use  cannot  be  relied  on  as  being  within 
15'  of  the  truth  and  they  may  be  very  much  more  in  error.  As  present  day 
surveying  requires  that  any  angle  be  known  within  1  min.  and  in  special  cases, 
such  as  tunnel  work,  within  30"  or  even  20"  or  15",  the  compass  is  now  no 
longer  used  except,  in  emergencies,  when  a  transit  is  not  available.  However, 
in  driving  room  necks  far  enough  for  the  permanent  sights,  in  obtaining  a  rough 
idea  of  the  direction  of  a  heading,  and,  on  the  surface,  in  connection  with  the 
rerunning  of  old  land  lines,  the  compass  has  its  uses. 

Owing  to  the  length  of  time  taken  by  the  needle  to  settle  so  that  it  can  be 
read,  an  accurate  transit  survey  can  commonly  be  made  in  less  time  than  an 
inaccurate  one  with  the  compass. 

COMPASS  ADJUSTMENTS 

When  adjusting  the  levels,  first  bring  the  bubbles  into  the  center  by  the 
pressure  of  the  hand  on  different  parts  of  the  plate,  and  then  turn  the  compass 
half  way  around.  Should  the  bubbles  run  to  the  ends  of  the  tubes,  those  ends 
are  the  higher;  these  should  then  be  lowered  by  tightening  the  screws  imme- 
diately under,  and  loosening  those  under  the  lower  ends  until,  by  estimation, 
the  error  is  half  removed.  The  plate  should  again  be  leveled  and  the  first 
operatipn  repeated  until  the  bubbles  will  remain  m  the  center  during  an  entire 
revolution  of  the  compass. 

The  sights  may  next  be  tested  by  observing,  through  the  slits,  a  fine  hair 
or  thread,  made  exactly  vertical  by  a  plumb.  Should  the  hair  appear  on  one 
side  of  the  slit,  the  sight  must  be  adjusted  by  filing  off  its  under  surface  on 
the  side  that  seems  the  higher. 

The  needle  is  adjusted  in  the  following  manner:  Having  the  eye  nearly  in 
the  same  plane  with  the  graduated  rim  of  the  compass  circle,  with  a  small 
splinter  of  wood,  or  a  slender  iron  wire,  bring  one  end  of  the  needle  in  line 
with  any  prominent  division  of  the  circle,  as  the  0  or  90°  mark,  and  notice 
if  the  other  end  corresponds  with  the  degree  on  the  opposite  side.  If  it  does, 
the  needle  is  said  to  cut  opposite  degrees;  if  not,  bend  the  center  pin  by  apply- 
ing a  small  brass  wrench,  furnished  with  most  compasses,  about  £  in.  below 
the  point  of  the  pin,  until  the  ends  of  the  needle  are  brought  into  line  with  the 
opposite  degrees.  Then,  holding  the  needle  in  the  same  position,  turn  the 
compass  half  way  around,  and  note  whether  it  now  cuts  opposite  degrees; 
if  not,  correct  half  the  error  by  bending  the  needle,  and  the  remainder  by  bend- 
ing the  center  pin.  The  operation  must  be  repeated  until  perfect  reversion 
is  secured  in  the  first  position.  This  being  obtained,  it  may  be  tried  on  another 
quarter  of  the  circle;  if  any  error  is  there  manifested,  the  correction  must  be 
made  in  the  center  pin  only,  the  needle  being  already  straightened  by  the  pre- 
vious operation.  When  again  made  to  cut,  it  should  be  tried  on  the  other 
quarters  of  the  circle,  and  corrections  made  in  the  same  manner  until  the  error 
is  entirely  removed,  and  the  needle  will  reverse  in  every  point  of  the  divided 
circle. 


SURVEYING  61 

USING  THE  COMPASS 

When  using  the  compass,  the  surveyor  should  keep  the  south  end  toward 
his  person,  and  read  the  bearings  from  the  north  end  of  the  needle.  In  the 
surveyor's  compass  the  position  of  the  E  and  W  letters  on  the  face  of  the  com- 
pass are  reversed  from  their  natural  position,  in  order  that  the  direction  of  the 
sight  may  be  correctly  read. 

The  compass  circle  being  graduated  to  |°,  a  little  practice  will  enable  the 
surveyor  to  read  the  bearings  to  quarters — estimating  with  his  eye  the  space 
bisected  by  the  point  of  the  needle. 

The  compass  is  divided  into  quadrants,  and  0  is  placed  at  the  north  and 
south  ends;  90°  is  placed  at  the  E  and  W  marks,  and  the  graduations  run  right 
and  left  from  the  0  to  90°.  When  reading  the  bearing,  the  surveyor  will 
notice  that  if  the  sights  are  pointed  in  a  NW  direction,  the  north  end  of  the 
needle,  which  always  points  approximately  north,  is  to  the  right  of  the  front 
sight  or  front  end  of  the  telescope,  and,  as  the  number  of  degrees  is  read  from 
it,  the  letters  marking  the  cardinal  points  of  the  compass  read  correctly.  If 
the  E,  or  east.^mark  were  on  the  right  side  of  the  circle,  a  NW  course  would 
read  NE.  This  same  remark  applies  to  all  four  quadrants.  The  compass 
should  always  be  in  a  level  position. 

If  all  the  corners  of  a  field  can  be  seen  from  a  central  point,  the  survey 
can  be  made  by  setting  up  at  that  point,  and  with  one  corner  as  a  backsight, 
taking  all  the  other  corners  as  foresights,  and  by  measuring  from  this  point 
to  all  of  the  corners;  or  the  compass  can  be  set  up  at  any  corner  and  a  line  of 
survey  run  around  the  field.  This  latter  method  is  called  meandering.  Both 
methods  will  give  the  same  result  when  plotted;  but  the  first  is  much  quicker, 
as  the  boundaries  of  a.  tract  are  frequently  oyergrown  with  bushes  that  must 
be  cleared  to  allow  a  sight;  while  a  central  point  can  frequently  be  found  that 
will  allow  a  free  sight  to  all  the  corners,  and  the  distance  can  be  measured  by 
tape,  or  stadia.  As  the  central  point  is  nearer  the  corners  than  they  are  to 
one  another,  a  shorter  distance  must  be  chained  or  cut  in  the  case  of  a  central 
set-up. 

MAGNETIC  VARIATION 

Magnetic  declination,  or  variation,  of  the  needle  is  the  angle  made  by  the 
magnetic  meridian  with  the  true  meridian  or  true  north  and  south  line.  It 
is  east  or  west  according  as  the  north  end  of  the  needle  lies  east  or  west  of  the 
true  meridian.  It  is  _not  constant,  but  changes  from  year  to  year,  and,  for 
this  reason,  in  rerunning  the  lines  of  a  tract  of  land,  from  field  notes  of  some 
years'  standing,  the  surveyor  makes  an  allowance  in  the  bearing  of  every  line 
by  means  of  a  vernier. 

The  declination,  where  a  knowledge  of  it  is  necessary,  should  always  be 
determined  for  the  particular  place  and  at  the  particular  time  where  and  when 
it  is  needed.  Quite  a  number  of  the  States  in  cooperation  with  the  United 
States  Coast  and  Geodetic  Survey  have  established  a  true  meridian  by  astro- 
nomical observations  at  each  county  seat.  Information  as  to  the  location,  etc., 
of  the  monuments  marking  the  meridian  may  be  obtained  from  the  county  sur- 
veyor, the  recorder  of  deeds,  or  some  one  else  in  authority  at  the  county  court 
house.  However,  the  variation  thus  obtained  is  only  available  for  use  a  com- 
paratively short  distance  either  east  or  west  of  the  county  seat  (assuming  that 
the  highest  accuracy  is  desired),  because  on  the  average,  there  is  in  the  United 
States,  a  change  in  the  value  of  the  declination  of  1'  per  mi.  in  the  foregoing 
directions.  From  this,  it  is  apparent  that  the  declination  at  a  place  30  mi. 
east  or  west  of  the  county  seat  will  probably  vary  30'  from  that  at  the  monu- 
ments referred  to.  This  difference  of  30'  is  within  the  limits  between  which 
the  compass  is  ordinarily  read.  In  proceeding  north  or  south  from  the  county 
seat,  the  change  in  declination  is  very  much  less  than  in  an  east  or  west  direc- 
tion. If  the  declination  cannot  be  determined,  a  note  should  be  made  of  the 
date  of  the  survey,  with  a  statement  to  the  effect  that  the  bearings  are  referred 
to  the  magnetic  meridian,  and  these  notes  should  appear  on  the  map  and  should 
be  incorporated  in  the  deed  if  the  survey  was  made  preliminary  to  a  transfer 
of  property. 

The  United  States  Coast  and  Geodetic  Survey,  Washington,  District  of 
Columbia,  issues  from  time  to  time  tables  and  charts  showing  the  declination 
at  many  points  in  the  United  States  and  outlying  possessions,  together  with 
formulas  by  means  of  which  the  declination  may  be  calculated  with  a  high 
degree  of  accuracy  at  future  times.  These  may  be  obtained  from  the  Super- 
intendent of  the  Survey. 


62 


SURVEYING 


Reading  the  Vernier. — The  compass  vernier,  shown  in  the  accompanying 
illustration,  is  usually  so  graduated  that  30  spaces  on  it  equal  31  on  the  limb 
of  the  instrument  and,  commonly,  there  are  15  spaces  on  each  side  of  the  0  mark. 
It  is  read  as  follows:  Note  the  degrees  and  half  degrees  on  the  limb  of  the 

instrument.  If  the  space  passed 
beyond  the  degree  or  half-degree 
mark  by  the  zero  mark  on  the 
vernier  is  less  than  one-half  the 
space  of  |°  on  the  limb,  the  num- 
ber of  minutes  is,  of  course,  less 
than  15,  and  must  be  read  from  the 
lower  row  of  figures.  If  the  space 
passed  is  greater  than  one-half  the 
spacing  on  the  limb,  the  upper  row  of  figures  must  be  read.  The  line  on  the 
vernier  that  exactly  coincides  with  a  line  on  the  limb  is  the  mark  that  denotes 
the  number  of  minutes.  If  the  index  is  moved  to  the  right,  the  minutes  are  read 
from  the  left  half  of  the  vernier;  if  moved  to  the  left,  they  are  read  from  the 
right  side  of  the  vernier. 

Turning  Off  the  Variation. — Moving  the  vernier  to  either  side,  and  with  it, 
of  course,  the  compass  circle  attached,  set  the  compass  to  any  variation  by 
placing  the  instrument  on  some  well-defined  line  of  the  old  survey,  and  by 
turning  the  tangent  screw  (slow-motion  screw)  until  the  needle  of  the  compass 
indicates  the  same  bearing  as  that  given  in  the  old  field  notes  of  the  original 
survey.  Then  screw  up  the  clamping  nut  underneath  the  vernier  and  run  all 
the  other  lines  from  the  old  field  notes  without  further  alteration.  The  read- 
ing of  the  vernier  on  the  limb  gives  the  amount  of  variation  since  the  original 
survey  was  made. 

FIELD  NOTES  FOR  AN  OUTSIDE  COMPASS  SURVEY 

Call  place  of  beginning  Station  1. 

Stations  Bearings  Distances 

1-2  N  35°  E  270.0 

At  1+  37  ft.  crossed  small  stream  3  ft.  wide. 
At  l-i-116  ft.  =  first  side  of  road. 
At  1  +  131  ft.  =  second  side  of  road. 

At  1  +  137  ft.  =  blazed  and  painted  pine  tree,  3  ft.  left,  marked  for  a  go-by. 
Station  2  is  a  stake  at  foot  of  white-oak  tree,  blazed  and  painted  on  four 
sides  for  corner. 

2-3  N  83 £°  E  129.0 

Station  3  is  a  stake-and-stones  corner. 

3-4  S  57°  E  222.0 

3+64  ft.  =  center  of  small  stream  2  ft.  wide. 
3  +  196  ft.  =  white  oak  go-by,  2  ft.  right. 
Station  4,  cut  stone  corner. 

4-5  S  341°  W  355.0 

4+174  ft.  =*  ledge  of  sandstone  10  ft.  thick,  dipping  27°  south. 

5-1  N  56i°  W  323.0 

5+274  ft.  =  ledge  of  sandstone  10  ft.  thick,  dipping  25°  south  (evidently 

continuation  of  same  ledge  as  at  4  +  174). 
Station  1  =  place  of  beginning. 


THE  TRANSIT 

GENERAL  DESCRIPTION 

The  transit  is  the  only  instrument  that  should  be  used  for  measuring  angles 
in  any  survey  where  accuracy  is  desired.  The  advantages  of  a  transit  over  a 
vernier  compass  are  mainly  due  to  the  use  of  a  telescope.  By  its  use,  angles 
can  be  measured  either  vertically  or  horizontally,  and,  as  the  vernier  is  used 
throughout,  extreme  accuracy  is  secured. 

Fig.  1  shows  the  interior  construction  of  the  sockets  of  a  transit  having 
two  verniers  to  the  limb,  the  manner  in  which  it  is  detached  from  its  spindle, 
and  how  it  can  be  taken  apart  when  desired.  The  limb  b  is  attached  to  the 
main  socket  c,  which  is  carefully  fitted  to  the  conical  spindle  h,  and  held  in 
place  by  the  spring  catch  s. 

The  upper  plate  a,  carrying  the  compass  circle,  standards,  etc.,  is  fastened 
to  the  flanges  of  the  socket  k,  which  is  fitted  to  the  upper  conical  surface  of  the 


SURVEYING 


63 


main  socket  c.  The  weight  of  all  the  parts  is  supported  on  the  small  bearings 
of  the  end  of  the  socket,  as  shown,  so  as  to  make  as  little  friction  as  possible 
where  such  parts  are  be- 
ing turned  as  a  whole. 
A  small  conical  cen- 
ter, in  which  a  strong 
screw  is  inserted  from 
below,  is  brought  down 
firmly  on  the  upper  end 
of  the  main  socket  c, 
thus  holding  the  two 
plates  of  the  instrument 
securely  together,  and, 
at  the  same  time,  allow- 
ing them  to  move  freely 
around  each  other.  The 
steel  center  pin  on  which 
the  needle  rests  is  held 
by  the  small  disk  fas- 
tened to  the  upper  plate 
by  two  small  screws 
above  the  conical  cen- 
ter. The  clamp  to  limb 
df,  with  clamp  screw,  is 
attached  to  the  main 
socket.  The  instrument 


FIG.  1 


is  leveled  by  means  of  the  leveling  screws  /  and  placed  exactly  over  a  point  by 
means  of  the  shifting  center.     The  plummet  is  attached  to  the  loop  p. 

Transit  Verniers. — In  transits,  the  limb  or  plate  has  two  sets  of  concentric 
graduations,  as  shown  in  part  in  Fig.  2.  The  style  of  marking  these  gradua- 
tions may  be  varied  to  suit  the  ideas  of  the  surveyor,  but  the  arrangement 
shown  is  a  common  and  a  good  one.  The  same  0°  point  is  used  for  both  sets 
of  the  graduations  and  is  placed  near  or  under  the  eye  end  of  the  telescope. 
One  set  of  graduations  is  continuous  from  this  0°  to  360°  toward  the  left. 
The  other  set  begins  at  the  same  0°  point  and  increases  to  90°  at  the  left, 
decreases  to  0°  directly  opposite  the  starting  point,  increases  to  90°  at  the 


mark  at  the  right;  and  then  decreases  by  10°  to  the  starting  point.  This  last 
set  of  graduations,  known  as  quadrant  graduations,  is  marked  with  an  N  at  the 
0°  point,  with  E  at  the  90°  point;  and  similarly  with  S  and  W  at  the  second  0° 
and  second  90°  points,  respectively.  Further,  as  shown,  at  each  marking, 
the  letters  N  E,  S  E,  S  W,  or  N  W  are  stamped  on  the  plate  at  its  proper  quad- 
rant. Thus  the  0°  of  the  continuous  graduation  is  the  same  as  the  N  on  the 
quadrant  graduation,  the  90°  of  the  continuous  graduation  is  the  same  as  the  E 
of  the  quadrant,  the  180°  of  the  continuous  graduation  is  the  S  of  the  quadrant, 
and  the  270°  of  the  continuous  graduation  is  the  W  of  the  quadrant. 

There  are  two  transit 
verniers;  one,  known  as  ver~ 
nier  A,  is  placed  as  near  as 
possible  under  the  eye  end 
of  the  telescope,  and  the 
other,  known  as  vernier  B, 
is  placed  directly  opposite. 
These  verniers  are  double, 
that  is,  they  read  both 
ways  from  the  0  mark  so 
that  angles  deflected  either 
to  the  right  or  left  may  be 
read.  The  vernier  is  com- 
monly divided  so  that  30 


spaces  on  i 
vernier  is 


it  are  equal  to  29  spaces  on  the  limb  of  the  transit.  Each  division  of  the 
,  therefore,  ^,  or,  in  other  words,  1'  shorter  than  the  £°  graduations  on 
the  limb.  In  Fig.  2,  the  reading  is  S  60°  30'  E  (from  the  limb)  + 13'  (from  the  ver 
nier)  =  S  60°  43' E.  This  is  the  quadrant  reading  from  the  inner  row  of  gradu- 
ations. The  continuous  vernier  (outer  row)  reading  is  119°  (from  the  limb) 


64  SURVEYING 

+  17'  (from  the  vernier)  =  119°  17'.  It  will  be  noted  that  the  sum  of  the  two 
readings  is  60°  43'+ 119°  IT  =  180°.  This  summation  proves  and  checks  the 
readings.  Had  the  quadrant  reading  been  N  33°  18'  E,  the  continuous  vernier 
should  read  33°  18'.  Had  the  quadrant  reading  been  S  56°  39'  W,  the  con- 
tinuous vernier  should  read  180°+56°  39' =  236°  39';  and  had  the  quadrant 
reading  been  N  76°  29'  W,  the  continuous  vernier  should  read  360°  — 76°  19' 
=  283°  31'.  In  other  words,  when  the  continuous  vernier  reads  from  0°  to  90°, 
the  quadrant  reading  will  be  NE;  when  the  continuous  is  between  90°  and 
180°  the  quadrant  is  SE;  when  the  continuous  is  between  180°  and  270°  the 
quadrant  is  SW;  and  when  the  continuous  is  between  270°  and  360°  (or  0°), 
the  quadrant  is  NW. 

Transit  Telescope. — The  interior  of  the  telescope  is  fitted  up  with  a  dia- 
phragm or  cross-wire  ring  to  which  cross-wires  are  attached.  These  cross- 
wires  are  either  of  platinum  or  are  strands  of  spider  web.  •  For  inside  work, 
platinum  should  be  used,  as  spider  web  is  translucent  and  cannot  readily  be 
seen.  They  are  set  at  right  angles  to  each  other  and  are  so  arranged  that  one 
can  be  adjusted  so  as  to  be  vertical  and  the  other  horizontal.  This  diaphragm 
is  suspended  in  the  telescope  by  four  capstan-headed  screws,  and  can  be  moved 
in  either  direction  by  working  the  screws  with  an  ordinary  adjusting  pin. 
The  transit  should  not  be  subjected  to  sudden  changes  in  temperature  that 
may  break  the  cross-hairs.  In  case  of  a  break,  the  cross-hair  diaphragm 
must  be  removed  and  the  broken  wire  replaced. 

The  intersection  of  the  wires  forms  a  very  minute  point,  which,  when 
they  are  adjusted,  determines  the  optical  axis  of  the  telescope,  and  enables 
the  surveyor  to  fix  it  upon  an  object  with  the  greatest  precision. 

The  imaginary  line  passing  through  the  optical  axis  of  the  telescope  is 
termed  the  line  of  collimation,  and  the  operation  of  bringing  the  intersection  of 
the  wires  into  the  optical  axis  is  called  the  adjustment  of  the  line  of  collimation. 

All  screws  and  movable  parts  should  be  covered,  so  that  acid  water  and  dust 
will  be  kept  out.  If  this  is  not  done,  the  mine  work  will  destroy  a  transit. 
The  vertical  circle  on  the  transit  may  be  a  full  circle  or  a  segment.  The  for- 
mer is  to  be  preferred,  as  it  is  always  ready  without  intermediate  clamp  screws. 

TRANSIT  ADJUSTMENTS 

The  use  of  a  transit  tends  to  disarrange  some  9f  its  parts,  which  detracts 
from  the  accuracy  of  its  work,  but  in  no  way  injures  the  instrument  itself. 
Correcting  this  disarrangement  of  parts  is  called  adjusting  the  transit. 

1.  To  make  the  level  tubes  parallel  to  the  vernier  plate. — Plant  the  feet  of 
the  tripod  firmly  in  the  ground.     Turn  the  instrument  until  one  of  the  levels 
is  parallel  to  a  pair  of  opposite  leveling  screws;  the  other  level  will  be  parallel 
to  the  other  pair.     Bring  the  bubble  in  each  tube  to  the  middle  with  the  pair 
of  leveling  screws  to  which  the  tube  is  parallel.     Next  turn  the  vernier  plate 
half  way  around;  that  is,  revolve  it  through  an  angle  of  180°.     If  the  bubbles 
have  remained  in  the  middle  of  the  tubes,  the  levels  are  in  proper  adjustment. 
If  they  have  not  remained  so,  but  have  moved  toward  either  end,  bring  them 
half  way  back  to  the  middle  of  the  tubes  by  means  of  the  capstan-headed  screws 
attached  to  the  tubes,  and  the  rest  of  the  way  back  by  the  leveling  screws. 
Again  turn  the  vernier  plate  through  180°,  and  if  the  bubbles  do  not  remain 
at  the  middle  of  the  tubes,  repeat  the  correction.     Sometimes  the  adjustment 
is  made  by  one  trial,  but  usually  it  is  necessary  to  repeat  the  operation.     Each 
level  must  be  adjusted  separately. 

2.  To  make  the  line  of  collimation  perpendicular  to  the  horizontal  axis  that 
supports  the  telescope. — With  the  instrument  firmly  set  at  A,  Fig.  1,  and  care- 
fully leveled,  sight  to  a  pin  or  tack  set  at  a  point  B,  about  400  ft.  distant,  and 
on  level,  or  nearly  level,  ground.     Reverse  the  telescope;  that  is,  turn  it  over  on 

its  axis  until  it  points  in  the 

O A       '&  opposite  direction,  and  set  a 

B  .  u  i-^^~^ F       point  at  about  the  same  dis- 

400*~~ C  *  tance,   which   will  be  at   D, 

FiG.  1  for  example,   if  this  adjust- 

ment needs  correction.     Un- 

clamp  the  vernier  plate,  and,  without  touching  the  telescope,  revolve  the  instru- 
ment about  its  vertical  axis  sufficiently  far  to  take  another  sight  upon  the 
point  B.  Then  turn  the  telescope  on  its  axis  and  locate  a  third  point,  as  at  C. 
Measure  the  distance  CD,  and  at  E,  one-fourth  of  the  distance  from  C  to  D, 
set  the  pin  or  tack.  Move  the  cross-hairs,  by  means  of  the  capstan-headed 
screws,  until  the  vertical  hair  exactly  covers  the  pin  at  E,  being  careful  to 
move  it  in  the  opposite  direction  from  that  in  which  it  appears  it  should  be 


SURVEYING  65 

moved.  Having  done  this,  and  then  having  reversed  the  telescope,  the  line  of 
sight  will  not  be  at  the  point  B,  but  at  G,  a  distance  from  B  equal  to  CE.  Again 
sight  to  B,  then  reverse,  and  the  pin  will  be  at  F  in  the  same  straight  line  with 
A  B.  It  may  be  necessary  to  repeat  the  operation  to  secure  an  exact  adjustment. 

3.  To  make  the  horizontal  axis  of  the  telescope  parallel  to  the  vernier  plate, 
so  that  the  line  of  collimation  will  revolve  in  a  vertical  plane. — Sight  to  some  point 
A,  Fig.  2,  at  the  top  of  a  building,  so  that  the  teleg&ope  will  be 
elevated  at  a  large  angle.     Depress  the  telescope  and  set  a  pin 

on  the  ground  below  at  a  point  B.  Loosen  the  clamp,  turn  over 
the  telescope,  and  turn  the  plate  around  sufficiently  far  to  take 
an  approximately  accurate  sight  upon  the  point  A.  Then  clamp 
the  instrument  and  again  take  an  exact  sight  to  the  point  A.  Next 
depress  the  telescope,  and  set  another  pin  on  the  ground,  which 
will  come  at  C.  The  distance  BC  is  double  the  error  of  adjust- 
ment. Correct  the  error  by  raising  or  lowering  one  end  of  the 
telescope  axis  by  means  of  a  small  screw  placed  in  the  standard  for 
that  purpose.  The  amount  the  screw  must  be  turned  is  deter- 
mined only  by  repeated  trials. 

4.  To  make  the  axis  of  the  attached  level  of  the  telescope  parallel 
to  the  line  of  collimation. — Drive  two  stakes  at  equal  distances  from 
the  instrument  and  in  exactly  opposite  directions.     Level  the  plate 
carefully,  and  clamp  the  telescope  in  a  horizontal  position,  or  as         pIG 
nearly  so  as  possible.     Sight  to  a  rod  placed  alternately  upon  each 

stake,  and  have  the  stakes  driven  down  until  the  rod  reading  is  the  same  on 
both  stakes.  When  this  condition  is  reached,  the  heads  of  the  stakes  are  at 
the  same  level.  Then  move  the  instrument  beyond  one  stake  and  set  it  up  so 
that  it  will  be  in  line  with  both  stakes.  Level  the  plate  again  and  elevate  or 
depress  the  telescope  so  that,  when  a  sight  is  taken  to  the  rod  held  on  first 
one  stake  and  then  on  the  other,  the  reading  will  be  alike  on  both.  In  this 
position,  the  line  of  collimation  is  level,  and  the  bubble  in  the  level  attached 
to  the  telescope  should  stand  in  the  center  of  the  bubble  tube.  If  it  does 
not,  bring  it  to  the  center  by  turning  the  nuts  at  the  ends  of  the  tube,  being 
careful  at  the  same  time  to  keep  the  telescope  in  the  position  that  gives  equal 
rod  readings  on  both  stakes.  

CHAIN,  STEEL  TAPE,  AND  PINS 

The  chain  is  probably  the  earliest  form  of  distance-measuring  instrument. 
The  original  surveyor's  or  Gunters  chain,  was  66  ft.  or  4  rd.  in  length  and  was 
composed  of  100  li.,each  7.92  in.  long.  This  form  of  chain  is  no  longer  used, 
but  is  useful  in  preliminary  work  in  locating  old  corners  from  descriptions  in 
early  deeds  where  distances  are  expressed  in  rods  (poles,  perches,  or  chains). 
The  engineer's  chain  composed  of  100  li.  each  1  ft.  long  is  also  falling  into  dis- 
use except  for  railroad  work.  Any  chain  is  so  liable  to  abrasion  at  the  numer- 
ous joints  and  to  bending,  that  distances  measured  with  it  cannot  be  relied 
on  to  be  accurate  within  the  limits  demanded  by  modern  engineering.  A 
100-ft.  chain  has  800  wearing  surfaces,  and  should  each  one  of  these  be  worn 
but  Tfo  in.  after  several  season's  work,  the  chain  will  be  100  ft.  8  in.  (100.67  ft.) 
in  length,  and  each  full  100  ft.  measured  with  it  will  be  recorded  as  but  99.34  ft. 
Similarly,  bends  or  kinks  shorten  the  chain  so  that  the  distances  measured 
with  it  are  recorded  as  being  too  great. 

When  used  at  all,  the  chain  should  be  made  of  annealed  steel  wire,  each 
link  exactly  1  ft.  in  length.  The  links  should  be  so  made  as  to  reduce  the  liabil- 
ity to  kink  to  a  minimum.  All  joints  should  be  brazed,  and  handles  at  each 
end  of  D  shape,  or  modifications  of  D  shape,  should  be  provided.  These 
handles  should  be  attached  to  short  links  at  eacn  end,  and  the  combined  length 
of  each  of  these  short  links  and  one  handle  should  be  exactly  1  ft.  The  handles 
should  be  attached  to  the  short  link  in  such  a  manner  that  the  chain  may  be 
slightly  lengthened  or  shortened  by  screwing  up  a  nut  at  the  handle.  It  should 
be  divided  every  10  ft.  with  a  brass  tag,  on  which  either  the  number  of  points 
represents  the  number  of  tens  from  the  front  end,  or  the  number  of  tens  may 
be  designated  by  figures  stamped  on  the  tags. 

When  a  chain  is  purchased,  one  that  has  been  warranted  as  Correct,  U.  S. 
Standard,"  should  be  selected,  and,  before  using  it,  it  should  be  stretched  on 
a  level  surface,  care  being  taken  that  it  is  straight,  and  no  kinks  in  it,  and 
the  extremities  marked  by  some  permanent  mark.  These  marks  can  be  used 
in  the  future  to  test  the  chain.  It  slumld  be  tested  frequently,  and  the  length 
kept  to  the  standard  as-  marked  when  it  was  new. 


66  SURVEYING 

Ordinarily,  the  chain  should  be  held  horizontally,  and  if  either  end  is  held 
above  the  ground,  a  plumb-bob  and  line  should  be  used  to  mark  the  end  of  the 
chain  on  the  ground.  If  used  on  a  regular  slope,  the  chain  may  be  stretched 
along  the  ground,  and,  by  having  the  amount  of  inclination,  the  horizontal 
and  vertical-1  distances  may  either  be  calculated  or  found  in  the  Traverse  Table. 

The  steel  tape,  which  has  superseded  the  chain,  is  simply  a  ribbon  of  steel 
not  so  high  in  carbon  as  to  be  brittle  and  liable  to  snap  on  a  short  bend,  nor 
of  so  soft  a  steel  that  it  will  stretch  when  strongly  pulled.  Tapes  are  made 
of  a  standard  or  exact  length  at  a  given  temperature,  say  60°  F.,  and  under  a 
certain  tension,  say,  15  Ib.  At  higher  temperatures  or  under  greater  pull  the 
tape  expands,  and  distances  measured  with  it  are  less  than  the  true  ones.  At 
lower  temperatures  or  under  less  tension,  the  tape  contracts  and  distances 
measured  with  it  are  too  long.  When  a  tape  is  hung  unsupported  between  two 
points  it  forms  a  curve,  called  a  catenary,  and  measures  a  greater  distance 
between  the  points  than  if  the  tape  formed  a  straight  line.  However,  the 
apparent  shortening  of  the  distance  between  two  points,  owing  to  the  tape 
being  subject  to  more  than  the  normal  tension,  may  be  offset  by  the  lengthen- 
ing of  the  distance  due  to  sag  in  the  unsupported  tape.  For  every  span,  there 
is  a  corresponding  tension  where  the  errors  balance,  and  this  tension  should 
be  ascertained  and  used  in  practice.  The  errors  due  to  expansion  and  contrac- 
tion, arising  from  changes  in  temperature,  cannot  be  compensated  and  must  be 
corrected  for  in  all  accurate  work.  It  should  be  noted  that  the  temperature 
of  the  average  mine  is  about  65°  and  being  essentially  the  same  as  that  at  which 
the  tape  was  graduated,  no  allowance  for  expansion  or  contraction  is  generally 
necessary  in  mine  work. 

Steel  tapes  are  of  two  general  kinds,  and  are  commonly  named  from  their 
length,  as  a  100-ft.  tape,  a  400-ft.  tape,  etc.  The  50-ft.  and  100-ft.  tapes  are 
about  |  in.  wide,  coil  or  wind  up  in  a  leather  case  or  upon  a  small  single-handed 
reel,  and,  for  surveyor's  use,  are  divided  throughout  their  length  into  feet, 
tenths,  and  hundredths. 

The  steel  tape,  proper,  is  a  narrow  band  of  metal  about  one-third  the  width 
of  the  100-ft.  tape  and  considerably  thicker,  which  is  wound  upon  a  wooden 
or  iron  reel  like  a  spool.  These  tapes  may  be  made  in  any  length,  but  those 
400  ft.  long  appear  to  be  in  most  general  use.  The  tape  is  commonly  graduated 
every  5  ft.  on  brass  sleeves  soldered  upon  it.  Distances  are  read  to  the  nearest 
5  ft.  from  the  tape  and  intermediate  distances  measured  with  a  pocket  tape 
graduated  in  hundredths  of  a  foot.  Sometimes  before  the  0  mark  there  is  an 
extra  set  of  divisions  into  feet,  the  first  foot  being  further  divided  into  tenths. 
In  this  case,  the  scale  for  determining  the  hundredths  need  be  very  short,  say 
a  tenth  or  two  in  length.  In  use,  a  handle  with  a  swivel  joint  is  fixed  in  an  eye 
at  the  0  end  and  the  tape  unwound  from  the  reel  for  the  desired  or  required 
distance,  but  is  not  removed  from  the  reel  unless  a  distance  equal  to  that  of  the 
tape  is  to  be  measured  many  times.  In  this  case,  a  second  handle  may  be 
fixed  in  the  eye  at  the  outer  end  of  the  tape. 

In  order  to  repair  breaks  that  may  occur  in  the  field,  clamps  are  made  to 
hold  the  broken  ends  together.  Brass  sleeves  that  may  be  brazed  around 
broken  ends  by  the  surveyor  or  by  a  competent  gunsmith  may  be  purchased. 
To  keep  a  mark  upon  the  tape  for  frequent  reference,  a  clip  (made  by  bending 
sharply  upon  itself  a  piece  of  steel  Jm.  X3in.)  is  slipped  upon  the  tape,  where 
it  will  remain  unless  subject  to  considerable  force. 

What  are  known  as  metallic  tapes,  are  made  in  lengths  of  25,  50,  and  100  ft., 
and  are  graduated  in  hundredths  of  a  foot  for  surveyors  and  into  inches  and 
eighths  for  mine  foremen.  These  are  similar  to  the  100-ft.  steel  tape  but  are 
made  of  linen,  with  threads  df  copper  woven  in  to  overcome  the  tendency  to 
stretch.  One  of  these  tapes,  100  ft.  long,  is  part  of  every  surveying  outfit 
and  it  should  be  used,  wherever  possible,  to  save  the  more  costly  100-ft.  steel 
tape.  The  metallic  tape  answers  every  purpose  in  measuring  the  dimensions 
of  buildings  that  must  appear  on  the  map,  the  width  of  small  streams,  roads, 
etc.,  and  the  distance  to  a  property  corner,  if  it  is  a  nearby  tree  or  other  not 
sharply  defined  point. 

Pins  are  now  but  little  used  except  in  those  classes  of  work  where  the  use 
of  the  chain  is  permissible.  Pins  should  be  from  15  to  18  in.  long,  made  of 
tempered-steel  wire,  and  should  be  pointed  at  one  end,  and  turned  with  a  ring 
for  a  handle.  When  using  a  50-ft.  chain,  a  set  of  pins  should  consist  of  eleven, 
one  of  which  should  be  distinguished  by  some  peculiar  mark.  This  should  be 
the  last  pin  stuck  by  the  front  chainman.  When  all  eleven  pins  have  been 
stuck,  the  front  chainman  calls  "Out! "  and  the  back  chainman  comes  forwards 
and  delivers  him  the  ten  pins  that  he  has  picked  up,,  and  he  notes  the  out. 


SURVEYING  67 

When  giving  the  distance  to  the  transitman,  he  counts  his  outs,  each  of  which 
consists  of  500  ft.,  and  adds  to  their  sum  the  number  of  fifties  as  denoted  by 
the  pins  in  his  possession,  and  the  odd  number  of  feet  and  fractional  parts  of 
a  foot  from  the  last  pin  to  the  front  end  of  the  chain.  Pins  cannot  be  used 
in  underground  work  as  they  cannot  be  stuck  in  the  floor.  If  the  distance 
to  be  measured  is  longer  than  the  tape,  a  tack  is  placed  in  a  tie  between  the 
stations  and  a  measurement  taken  t9  it  from  each  station  with  the  dip  of  the 
sights.  In  outside  work,  a  stake  with  a  tack  is  used  for  the  same  purpose, 
and  is  lined  in  with  the  transit. 

The  clinometer,  or  slope  level,  is  a  valuable  instrument  for  side-note  work; 
but  it  is  not  accurate  enough  for  a  survey,  and  its  place  is  taken  by  the  ver- 
tical circle  on  the  transit.  There  are  two  styles  of  clinometer,  with  a  bubble 
and  with  a  pendulum.  The  latter  is  the  old-fashioned  and  more  accurate 
German  gradbogen  that  is  used  by  some  old  corps.  The  bubble  variety  is 
much  more  easily  rendered  worthless  by  the  breaking  of  the  bubble  tube,  and, 
in  general,  is  not  so  accurate  as  the  other  style,  which  consists  of  a  semicircular 
protractor  cut  out  of  thin  brass  and  furnished  with  hooks  at  each  end,  that  it 
can  be  hung  on  a  stretched  string  so  that  the  string  will  pass  through  the  0° 
and  180°  points.  The  dip  is  read  by  a  pendulum  swung  from  the  center  of  the 
circle.  If  made  sufficiently  large,  it  will  readily  read  to  quarter  degrees.  By 
inclining  the  string  parallel  to  the  surface  and  hanging  the  clinometer,  the  dip 
will  be  obtained.  A  pocket  instrument  combining  a  compass  and  clinometer 
can  be  obtained  from  any  dealer  in  surveying  instruments. 


TRANSIT  SURVEYING 

READING  ANGLES 

The  angle  read  may  be  included  or  deflected.  If  the  transit  is  set  up  at  0, 
and  a  backsight  taken  on  B  and  a  foresight  taken  on  C,  it  will  be  noted  that 
there  are  two  angles  made  by  the  line  CO  with  the  line  BOA ,  namely  the  included 
angle  BOC,  and  the  deflected  angle  AOC.  It  will  be  further  noted  that  AOC 
=  180°  —  BOC,  and  vice  versa. 

Reading  the  Included  Angle. — To  read  the  included  angle,  set  the  zeros 
of  the  vernier  and  the  limb  as  near  together  as  possible  by  the  eye,  clamp  the 
upper  plate  and  bring  the  zeros  into  exact  coincidence  by  means  of  the  upper 
tangent  screw.  Set  the  vertical  hair  approximately  upon  the  backsight,  clamp 
the  lower  motion,  and  by  the  lower  tangent  screw,  make  the  setting  exact. 
Loosen  the  upper  clamp,  set  approximately  on  the  foresight,  tighten  the  upper 
clamp,  and  by  means  of  the  upper  tangent  screw  make  the  setting  exactly. 
The  vernier  will  read,  say  45°,  which  is  the  included  angle 
BOC. 

Reading  the  Deflected  Angle.— -After  arranging  the 
verniers  as  just  explained,  to  read  the  deflected  angle,  in- 
vert the  telescope  so  that  the  level  bubble  is  above,  and 
set  upon  the  backsight  as  before.  Turn  the  telescope  back 
to  its  normal  position  (this  is  called  plunging  the  telescope) 
and  sight  to  the  foresight  as  explained.  The  vernier  will 
read  a  right  angle  of  135°.  As  noted,  the  sum  of  the  in- 
cluded and  deflected  angles  must  always  be  180°,  and  in  the  case  given  45° 
+  135°  =  180°. 

MAKING  A  SURVEY  WITH  A  TRANSIT 

Meridians,  or  Base  Lines. — Every  survey  must  start  from  some  fixed  point 
and  the  angles  measured  in  the  course  thereof  must  be  referred  to  some  line 
as  a  base.  The  nature  of  the  base  line  depends  on  the  use  to  which  the  sur- 
vey of  the  property  is  to  be  put.  When  surveying  small  tracts  of  land,  such 
as  city  or  town  lots,  the  starting  point  may  be  a  stake  driven  into  the  ground 
or  a  corner  of  the  property  itself  and  the  base  line  may  be  one  of  the  sides  of  the 
tract.  When  surveying  farms,  it  is  customary  to  make  one  of  the  property 
corners  the  starting  point  and  to  use  as  a  base  line  the  magnetic  meridian, 
noting  the  date  on  which  the  survey  is  made,  so  that  at  any  subsequent  time  an 
allowance  may  be  made  for  the  variation  of  the  needle.  When  surveying  large 
tracts  of  land,  or  even  comparatively  small  ones,  upon  which  mines  are  to  be 
opened,  the  starting  point  is  commonly  some  firmly  planted  artificial  object, 
and  the  base  line  is  the  true  meridian,  as  determined  by  astronomical  observa- 
tions on  the  North  Star  (Polaris),  or  on  the  sun,  by  methods  given  under  the 


68  SURVEYING 

head  of  Latitude  and  Longitude.  The  true  meridian  is  the  only  invariable 
base  line  that  can  always  be  determined  at  any  time  or  place  by  means  of  the 
engineer's  transit. 

Monuments. — When  establishing  a  reference  meridian  or  base  line  for 
any  large  coal  property,  it  is  not  customary  to  place  the  monuments  marking 
its  extremities  exactly  in  the  true  north-and-south  line;  in  fact,  it  is  not  gen- 
erally possible  to  do  39.  The  monuments  should  be  placed  where  they  will 
not  be  disturbed  by  mining  operations;  where  the  line  of  sight  between  them 
will  not  become  obstructed  by  subsequent  building  operations;  and  where  they 
will  be  convenient  for  use.  Hence,  monuments  should  be  placed  outside  the 
crop  line  if  this  comes  upon  the  property  so  that  pillar  drawing,  followed  by  set- 
tling of  the  surface,  will  not  throw  them  out  of  line.  If  the  property  is  opened 
by  a  shaft,  one  monument  may  be  placed  upon  that  portion  of  the  surface  that 
will  be  sustained  by  the  shaft  pillar,  and  the  other  monument  or  monuments 
may  be  placed  upon  reservations  from  under  which  the  coal  will  not  be  mined, 
or  may  be  placed  entirely  outside  the  boundaries  of  the  property.  If  no  place 
that  will  remain  undisturbed  during  the  life  of  the  mine  can  be  found  for  the 
second  monument,  sights  may  be  taken  to  a  number  of  prominent  buildings 
or  natural  objects  within  or  without  the  boundaries  of  the  property.  The 
angles  made  by  the  lines  joining  these  objects  with  the  monument  as  a  vertex 
should  be  repeatedly  read,  and  the  mean  of  the  readings  taken  as  the  true  angle. 
Reference  points  so  selected  will  determine  the  direction  of  the  meridian  at 
any  later  date,  as  it  is  improbable  that  all  of  the  five  or  ten  reference  points  will 
be  disturbed  or  destroyed. 

The  cheapest  monuments  may  be  made  from  mine-car  axles  or  from  old 
railroad  iron  of,  say,  60  to  70  Ib.  to  the  yd.,  cut  into  lengths  of  from  4  to  8  ft., 
depending  on  the  nature  of  the  soil.  One  end  should  then  be  sharpened  and 
the  axle  or  rail  driven  into  the  ground  until  about  6  in.  project  above  the  sur- 
face. A  bole  is  then  deeply  marked  in  the  top  by  a  center  punch  and  its  dis- 
tance from  three  or  four  nearby  points  is  measured.  These  distances,  or 
references,  will  enable  the  monument  to  be  found  in  event  of  its  being  subse- 
quently covered  with  dirt. 

Monuments  made  of  rails,  unless  the  ends  are  driven  well  below  the  frost- 
line,  are  apt  to  be  moved  out  of  line  through  the  alternate  freezing  and  thaw- 
ing of  the  soil;  therefore,  a  better  way  is  to  place  the  monuments  in  solid,  out- 
cropping rock.  In  this  case,  a  hole  some  12  in.  deep  is  drilled  in  the  rock  and 
a  bolt  of  1-in.  or  IJ-in.  round  iron  is  leaded  into  it,  the  head  of  the  bolt  being 
allowed  to  project  1  or  2  in.  above  the  rock.  The  bolt  is  center-punched  the 
same  as  would  be  a  rail.  Sometimes  the  projecting  end  of  the  bolt  is  threaded 
so  that  a  cap  may  be  screwed  upon  it  to  protect  the  center.  This  is  a  good  plan 
in  damp  climates  if  the  monument  is  intended  to  last  many  years. 

Excellent  monuments  may  be  made  of  dressed  stone  in  which  a  center- 
punched  bolt  is  set  to  mark  the  exact  point.  The  upper  foot,  in  length,  of 
the  stone,  about  6  in.  of  which  projects  above  the  surface,  is  dressed  square 
with  a  side  of  6  to  8  in.  The  lower  portion  beneath  the  ground  should  be  as 
large,  and  consequently  as  heavy,  as  possible.  The  length  should  be  4  ft.  or 
more,  so  that  the  bottom  is  set  well  below  the  frost  line.  Concrete  monuments 
are  cheaper  than  stone  and  may  be  constructed  of  any  size.  They  are,  of 
course,  built  up  in  a  pit  of  good  depth,  the  center  bolt  being  placed  before  the 
cement  has  had  time  to  set. 

The  boundary  of  a  large  property  may  be  5,  10,  or  more  mi.  in  length. 
As  it  is  impossible  to  tell,  in  advance,  when  and  where  new  property  will  be 
acquired,  necessitating  an  extension  of  the  original  survey,  it  is  a  most  excel- 
lent plan  to  set  a  pair  of  monuments  at  intervals  of  about  1  mi.  along  the  line 
of  the  survey.  The  wooden  pegs  used  as  stations  in  the  original  survey,  will 
disappear  in  12  to  18  mo.  or  will  have  been  so  displaced  by  the  action  of  frost 
as  to  be  useless.  If  two  consecutive  stations  are  made  of  rails  placed  in  the 
fashion  of  monuments,  they  will  serve  at  any  future  time  as  a  base  for  the 
extension  of  the  survey.  These  permanent  stations,  as  they  are  frequently 
called,  should  be  carefully  witnessed  and  referenced. 

OUTSIDE  SURVEYS 

Preliminary  Work. — Before  the  survey  of  a  property  is  undertaken,  it 
is  highly  advisable  that  the  surveyor  should  go  over  the  ground  and  familiarize 
himself  with  the  location  of  all  the  corners,  roads,  streams,  houses,  outcrops, 
reservations,  and  other  features  that  are  to  appear  upon  the  map.  While  in 
some  cases  a  map  of  the  property  is  furnished  the  surveyor,  it  is  usually  neces- 
sary for  him  to  prepare  one  from  the  deeds  to  its  component  tracts  as  recorded 


SURVEYING  69 

at  the  county  seat.  A  large  property  is  usually  made  up  of  from  10  to  100  or 
more  tracts  varying  in  size  from  a  fraction  of  1  A.  to  100  A.  or  more.  As  the 
surveys  found  in  the  deeds  were  made  at  widely  different  dates,  the  bearing 
of  a  line  common  to  two  or  more  properties  is  commonly  different  in  each  deed 
in  which  it  is  mentioned.  In  such  cases,  the  surveyor  should  mark  on  his 
tracing  the  different  bearings  given,  as  well  as  the  different  lengths  for  each  line. 
With  this  map,  a  good  pocket  compass,  and  a  100-ft.  tape,  together  with  what 
information  may  be  picked  up  from  residents  along  the  line,  the  surveyor  and 
his  assistant  can  locate  and  mark  the  various  corners. 

Angular  Measurements. —  The  angular  measurements  in  a  survey  may  be 
made  by  one  of  two  methods.  In  one,  the  angle  at  any  station  is  read  but 
once,  the  method  commonly  used  being  known  as  the  continuous  vernier;  in 
the  other  method,  the  angle  at  each  station  is  read  twice.  By  the  first  method, 
no  check  on  the  accuracy  of  the  wprk  is  afforded  until  the  initial  station  of  the 
survey  is  occupied  with  the  transit  and  the  azimuth  of  the  first  line  redeter- 
mined,  affording  what  is  known  as  a  close.  As  the  bulk  of  the  time  in  the  field 
is  employed  in  setting  up  the  transit,  it  would  seem  but  ordinary  good  sense 
to  repeat  or  check  the  angles  at  each  station  that  the  accuracy  of  the  work  may 
be  certain  as  the  survey  proceeds.  In  no  case  should  the  results  of  a  single- 
angle  survey  be  accepted  as  correct  until  such  a  close  has  been  made. 

When  making  a  survey  by  single  angles,  the  procedure  is  as  follows:  Set 
the  transit  over  the  monument  marking  one  end  of  the  base  line,  which  is  called 
Sta.  0.  Assuming  that  the  base  line  makes  an  angle  of  48°  21'  to  the  right  of 
the  meridian,  this  angle  is  the  azimuth  of  the  base  line;  and  as  it  is  to  right 
of  the  meridian,  its  bearing  is  N  48°  21'  E.  Set  off  this  azimuth  on  the  limb  of 
the  transit  and  focus  the  vertical  hair  on  the  second  mounment;  the  line 
of  collimation  of  the  transit  will  now  be  in  a  line  directed  N  48°  21'  E,  and 
if  the  upper  plate  is  loosened  and  the  instrument  set  on  any  distant  object, 
the  azimuth  and  bearing  of  that  point  from  Sta.  0,  may  be  read  from  the  grad- 
uated limb.  Suppose  the  sight  is  taken  to  Sta.  1  of  the  survey.  If  the  read- 
ing on  one  set  of  graduations  is  326°  48',  which  is  the  azimuth  of  the  line  0-1, 
the  reading  on  the  other  set  will  be  N  33°  12'  W,  which  is  the  bearing  of  the 

Setting  up  the  instrument  over  Sta.  1,  the  vernier  is  read,  to  see  that  it  still 
reads  326°  48'.  Then  invert  the  telescope  so  that  the  level  tube  is  on  top,fand 
by  means  of  the  lower  motion,  take  a  backsight  on  Sta.  1.  When  the  telescope 
is  plunged  into  its  normal  position  (level  tube  below) ,  the  line  of  sight  is  in  the 
line  0-1  produced  with  an  azimuth  of  326°  48'.  Loosen  the  upper  motion 
and  sight  on  Sta.  2  of  the  survey.  If  the  azimuth  from  one  set  of  graduations 
is,  say,  266°  10',  the  bearing  from  the  other  set  will  be  S  86°  10'  W.  Continue 
this  work  from  station  to  station  until  the  transit  finally  reoccupies  Sta.  0, 
the  monument  at  one  end  of  the  base  line.  If,  now,  the  azimuth  of  the  base 
line  as  determined  by  reference  to  the  last  line  of  the  survey  is  found  to  be 
48°  21'  as  determined  astronomically,  all  of  the  angles  of  the  survey  have  been 
measured  correctly,  and  the  survey  is  said  to  close  in  angle. 

When  making  a  survey  by  double  angles  at  each  station,  assume  that  the 
azimuths  of  the  lines  are  the  same  as  those  just  used  for  illustration  and  that 
the  transit  is  set  up  at  Sta.  1.  Set  the  vernier  at  0°  and  take  a  backsight  on 
Sta.  0.  If  the  upper  motion  is  loosened  and  the  telescope  revolved  180°  around 
its  vertical  axis,  the  line  of  sight  will  be  in  the  line  0-1  produced.  Continue 
revolving  the  telescope  until  it  is  set  upon  Sta.  2,  when  it  will  have  been  turned 
to  the  left  of  the  line  1-0  produced  and  the  angle  made  by  the  line  1-2  with  this 
line  (0-1  produced)  is  a  deflection  angle  to  the  left,  or  a  left  angle  commonly 
called.  This  will  be  found  to  be  (in  the  assumed  case)  60°  38'.  Next,  set  the 
vernier  on  the  azimuth  of  the  line  0-1,  viz.:  326°  48'  (bearing  N  33°  12'  W), 
and  with  the  telescope  inverted  take  a  backsight  upon  Sta.  0.  Plunge  the 
telescope  and  by  the  upper  motion  set  on  Sta.  2.  The  azimuth  will  be  found 
to  be  266°  10'  (bearing  S  86°  10'  W).  As  the  deflection  angle  subtracted  from 
the  azimuth  of  the  line  0-1  gives  the  azimuth  of  the  line  1-2,  the  angles  have 
been  correctly  read.  Thus  326°  48'  (azimuth) -60°  38'  (deflection  angle) 
=  266°  10'  (azimuth  line  1-2).  Similarly  N  33°  12'  W  (bearing  line  071) 
+60°  38'  (left  deflection  angle)  =  N  93°  50'  W  =  S  86°  10'  W  (bearing  of  line 
1-2). 

It  is  customary  to  read  and  record  the  deflection  angle  first,  and  then  to  read 
and  record  the  azimuth  or  bearing.  After  the  main  angles  by  which  the  sur- 
vey is  continued  have  been  noted,  before  moving  to  the  next  station,  all  the  cor- 
ners, houses,  roads,  streams,  etc.,  that  can  conveniently  be  reached  from  the 
instrument  should  be  located  and  entered  in  the  notebook. 


70  SURVEYING 

Whether  the  direction  of  a  line  of  a  survey  shall  be  recorded  and  described 
by  its  azimuth  or  by  its  bearing  is  a  matter  of  choice.  Few  of  those  for  whom 
the  map  is  chiefly  made  are  familiar  with  the  former  term,  and  the  statement 
that  a  certain  property  line  or  heading  has  an  azimuth  of,  say,  286°  10'  does 
not  give  them  any  idea  as  to  its  direction ;  whereas,  every  layman  understands 
the  meaning  of  the  equivalent  bearing,  S  86°  10'  W.  For  this  reason  it  seems 
better  to  give  the  bearings  of  lines  instead  of  their  azimuths. 

Distance  Measurements. — A  general  rule  that  should  not  be  broken  is 
that  all  operations  necessary  to  carry  on  the  main  line  of  the  survey  must  be 
done  before  anything  else  is  attempted.  Therefore,  after  reading  and  record- 
ing the  angle  between  the  lines  of  the  survey,  and  checking  it  by  the  method 
just  explained,  the  distance  to  the  next,  or  foresight,  station  must  be  read. 
The  method  of  doing  this  will  depend  on  whether  a  100-ft.  tape  or  chain  is  used, 
or,  as  is  the  better  practice,  a  400-ft.  tape  is  employed. 

The  method  of  using  a  chain  on  level  ground  has  been  described.  On 
ground  sloping,  say,  down  hill  from  the  instrument,  one  end  of  the  chain  is 
held  at  the  tack  in  the  stake  marking  the  station,  and  as  much  of  the  tape  as 
can  be  held  horizontal  is  stretched  out  in  the  line  to  the  next  station.  The  end 
of  the  horizontal  portion  of  the  chain  is  marked  on  the  ground  by  dropping 
a  plumb-line  from  it.  The  length  of  this  level  portion  is  noted  on  a  piece  of 
paper;  the  end  of  the  tape  held  at  the  plumb-bob  in  the  ground  and  another 
length  of  level  tape  stretched  out  and  its  end  marked,  and  length  noted  as 
before.  This  is  kept  up  until  the  distance  between  the  stations  has  been  cov- 
ered, when  the  sum  of  the  single  measurements,  is  equal  to  the  entire  measure- 
ment. This  is  a  slow,  laborious,  and  generally  inaccurate  method  that  has,  by 
mine  surveyors,  at  least,  given  way  to  the  use  of  the  long  steel  tape. 

If  the  distance  between  stations  is  less  than  the  length  of  the  tape  and  the 
ground  is  level  or  uniformly  sloping,  the  0  end  of  the  tape  is  held  at  the  tack 
in  the  stake  at  the  instrument  and  the  distance  to  the  tack  in  the  foresight  stake 
read,  as  previously  explained.  If  the  ground  slopes  either  up  or  down  hill, 
the  angle  of  elevation  or  depression  of  the  slope  must  be  taken  and  recorded 
as  a  plus  (+)  angle  if  one  of  elevation,  or  as  a  minus  (  — )  angle,  if  one  of  depres- 
sion. If  the  tape  has  been  stretched  along  a  plane  surface,  as  explained,  the 
line  of  sight  when  the  so-called  vertical  angle  is  read  must  be  parallel  to  the  tape. 
To  do  this,  a  sight  must  be  taken  at  a  point  on  the  foresight  rod  as  far  above 
the  ground  as  is  the  center  of  the  telescope  axis  at  the  instrument  station.  If 
the  ground  is  not  uniformly  sloping,  the  0  end  of  the  tape  is  held  at  the  hole 
marking  the  end  of  the  horizontal  axis  of  the  telescope,  and  the  measurement 
is  made  to  the  tack  in  the  foresight  stake.  In  this  case  the  vertical  angle  is 
measured  directly,  exactly  as  the  horizontal  cross-hair  cuts  the  station  tack. 
Distance  on  slope  X  cos  vertical  angle  =  horizontal  distance  (1) 

Distance  on  slope  X  sin  vertical  angle  =  difference  in  elevation        (2) 

The  reduction  of  the  slope  distances  to  horizontal  ones  is  made  in  the  office, 
not  in  the  field.  If  the  elevation  of  the  first  survey  station  is  known,  that  of 
all  the  other  stations  is  obtained  by  adding  continuously  to  it  the  difference 
in  elevation,  as  obtained  from  formula  2.  While  elevations  thus  obtained 
are  not  so  accurate  as  those  secured  through  the  use  of  leveling  instruments, 
they  answer  every  purpose  as  a  basis  for  a  topographical  survey  made  with  the 
stadia. 

If  the  distance  is  greater  than  the  length  of  the  tape,  but  less  than  twice 
as  great,  say  790  ft.,  a  stake  with  a  tack  is  placed  about  half  way  between  the 
stations  and  in  the  line  joining  them.  The  distance  and  vertical  angle  to  the 
stake  are  read  after  making  the  foresight,  and  again  from  the  next  station,  after 
taking  the  backsight.  The  sum  of  these  distances,  after  reduction  to  the  hori- 
zontal, is  the  total  distance  between  the  two  stations. 

If  the  distance  is  greater  than  two  tape  lengths,  say,  1,000  ft.,  two  stakes 
must  be  set.  The  first  stake  a  may  be  placed,  say,  350  ft.  from  the  instrument, 
and  the  second  stake  b,  350  ft.  beyond  that.  Before  moving  the  transit  the 
distance  and  vertical  angle  to  a  must  be  read  and  the  transit  set  up  roughly 
over  a  and  the  distance  and  vertical  angle  to  b  read.  At  the  next  station  and 
on  the  backsight,  the  distance  and  vertical  angle  to  b  must  be  read.  The  sum 
of  these  three  distances  reduced  to  the  horizontal  is  the  distance  between  the 
stations. 

Locating  Corners,  Etc. — After  the  main-line  angle  is  read  and  checked 
and  the  distance  to  the  next  station  measured  (or  such  part  of  it  as  is  possible 
without  moving  the  transit)  a  sight  or  sights  should  be  taken  to  any  nearby 
property  corner  or  corners  and  the  azimuth  or  bearing,  as  well  as  the  distance 
and  the  vertical  angle  thereto  recorded.  It  should  be  noted  that  the  deflection 


SURVEYING 


71 


angle  between  the  lines  joining  stations  should  be  read  first,  as  the  instru- 
ment must  be  properly  oriented  before  corners,  etc.,  can  be  located  and  this 
orientation  is  secured  at  each  station  by  using  as  a  backsight  for  the  second 
reading,  the  azimuth  of  the  line  joining  the  backsight  and  instrument  stations 
as  determined  from  the  previous  set-up.  After  the  corners  have  been  located 
stadia  sights  are  taken  to  any  houses,  streams,  roads,  topographic  features' 
etc.,  that  should  appear  upon  the  map. 

Keeping  Notes.— The  various  ways  of  keeping  the  main-line  and  side  notes 
of  an  outside  survey  arrange  themselves  into  four  groups:  (1)  The  side  notes 
of  each  sight  follow  the  transit  notes  of  that  sight,  and  on  the  same  paee 
(2)  They  are  entered  in  the  same  book  on  opposite  pages.  (3)  The  transit 
notes  of  the  whole  survey  come  first,  and  are  followed  by  the  side  notes  in  the 
same  book.  (4)  Each  set  of  notes  has  a  separate  book. 

Of  these  methods,  the  second  and  third  are  in  common  use.  For  a  survey 
made  by  the  methods  just  explained,  the  accompanying  form  of  transit  notes 
is  the  usual  one.  The  columns  are  headed  for  station  (Sta.),  Bearing  Anele 
(deflection  angle)  which  may  be  either  R  (right)  or  L  (left),  distance  (Dist ) 
and  Slope  (vertical  angle,  or  pitch). 

TRANSIT  NOTES 


Angle 

Sta. 

Bearing 

Dist. 

Slope 

R 

L 

Mt-Mz 
Mi-1 

N  48.21  E 
S  26.30  W 

(Bea 

ring  of  base 
21.51 

line) 
262.83 

—  4.16 

1-2 

S  67.49  W 

41.19 

387.62 

—  2  18 

2-3 

3-4 

N  86.11  W 
S  55.28  W 

26.00 

38.21 

316.99 
365.34 

+0.16 
+  1.56 

The  bearing  of  the  base  line,  or  that  joining  the  two  monuments,  Mi  and 
M2,  is  N  48.21  E.  It  will  be  noted  that  the  signs  °  and  '  are  not  used,  a  period 
serving  to  separate  the  degrees  and  minutes.  This  saves  time.  The  notes  are 
simple  and  self-explanatory.  The  transit  is  always  assumed  to  be  at  the  sta- 
tion whose  number  or  letter  is  given  first  in  the  station  column.  Thus,  the 
instrument  is  at  Sta.  Mi,  1,  2,  and  3.  The  foresight  follows  the  instrument 
station  in  the  same  horizontal  line.  Thus,  the  foresights  to  Sta.  1,  2,  3,  and  4, 
are  made  from  Sta.  Mi,  1,  2,  and  3,  respectively.  The  backsight  at  Sta.  1  is, 
of  course,  Mi,  at  Sta.  2,  it  is  1,  and  similarly.  It  should  be  noted  at  Sta.  Mi, 
when  the  vernier  is  set  for  the  purpose  of  taking  the  azimuth  or  bearing  of  the 
line  1-2,  that  the  setting  S  48.21  W  and  not  N  48.21  E  is  used.  This  is  because 
the  line  M^-Mi  runs  in  exactly  the  opposite  direction  from  the  line  Mi-Mz, 
and  the  survey  is  moving  forwards  in  the  former  line. 

As  stated,  the  side  notes  are  entered  in  the  same  book  as  the  main-line 
notes,  but  usually  in  the  back.  It  is  well  to  head  a  certain  page,  say,  Sta.  1, 
and  then  to  follow  with  all  the  side  notes  taken  at  that  station,  and  similarly 
for  the  succeeding  stations.  The  condition  of  all  property  corners  should  be 
carefully  described,  as  their  present  state  is  often  very  different  from  what 
it  was  at  the  time  the  original  deeds  were  made.  Thus,  a  corner  described  as  a 
hemlock  sapling  in  a  deed  dated  1790,  may  now  be  a  tree  2  or  3  ft.  in  diameter, 
may  be  a  stump,  may  have  entirely  rotted  away  so  that  only  an  expert  can  tell 
from  the  decayed  remains  that  a  hemlock  once  marked  the  corner,  or  a  good- 
sized  oak,  sugar  maple,  or  hickory  may  have  replaced  it,  the  hemlock  having 
been  destroyed  but  a  few  years  after  the  deed  was  made  and  a  tree  of  another 
species  grown  in  its  place. 

Frequently  there  are  reservations  around  farm  houses  from  under  which 
the  coal  may  not  be  mined.  Sometimes  the  corners  of  these  reserves  (as  they 
are  often  called)  can  be  reached  in  a  single  sight;  if  not,  a  branch  line  must  be 
run  to  them  from  the  line  of  the  main  survey. 

When  locating  houses  by  stadia  sights,  two  men  are  necessary.  One  can 
hold  the  stadia  rod  at  the  opposite  corners  of  the  house,  but  a  second  is  required 
to  hold  the  tape  by  which  the  dimensions  of  the  buildings  are  secured.  Roads 
are  located  by  the  fences  on  either  side,  the  road  legally  occupying  all  the  space 
between  the  fences,  even  if  part  of  it  is  grown  up  in  weeds  and  the  wagons 


72  SURVEYING 

have  maderbut  a  single  line  of  ruts.  Roads  are  commonly  either  1  or  2  rd., 
that  is,  16.5  or  33  ft.  in  width,  and  should  be  so  mapped. 

Small  brooks  are  located  by  taking  a  stadia  sight  to  their  center  at  each 
.  important  bend.  Larger  creeks  should  have  one  bank  located  with  the  stadia, 
the  stadia  rodman  estimating  the  width  of  the  stream,  which  should  be  entered 
in  the  notes.  Large  rivers  should  have  a  regular  traverse  run  along  the  bank, 
the  opposite  side  being  located  by  stadia  sights.  In  the  case  of  very  large 
rivers,  a  transit  line  must  be  run  along  each  bank  and  the  shore  line  located  by 
stadia  sights.  Stadia  sights  should  be  taken  to  points  along  the  bpttoms  of  all 
dry  gulleys,  to  the  summits  of  all  ridges,  and  to  any  marked  change  in  the  degree 
of  slope  of  a  hill. 

If  the  vertical  angles  have  been  taken  when  the  distances  between  the  sta- 
tions were  measured  and  the  stadia  sights  taken  as  just  explained,  there  will  be 
gathered  in  the  course  of  the  survey  enough  data  to  make  a  very  complete 
topographic,  or  contour,  map  of  the  property.  This  will  particularly  be  true, 
if,  as  is  customary,  the  boundaries  of  the  individual  farms  making  up  the  entire 
property  are  surveyed.  The  reason  for  surveying  the  single  farms  is  that  very 
frequently  the  operating  coal  company  has  not  the  same  rights  in  all  of  them, 
so  that  the  method  of  mining  is  affected  by  what  the  company  can  and  cannot  do. 

The  kind,  dip,  and  strike  of  all  outcropping  ledges  or  other  exposures  of 
rock  should  be  noted  and  mapped.  The  information  thus  obtained,  combined 
with  the  elevations  obtained  with  the  stadia,  etc.,  furnishes  the  data  from  which 
geological  cross-sections  may  be  made. 

The  first  page  of  the  notebook  should  give  the  name  of  the  company  for 
whom  the  work  is  done,  the  location  of  the  property,  name  of  the  engineer  in 
charge  of  the  work,  the  names  of  the  helpers,  and  each  day's  work  should  be 
dated;  and  if  the  members  of  the  corps  have  changed,  this,  too,  should  be  a 
matter  of  record. 

If  more  than  one  property  is  being  surveyed  from  the  same  office,  a  separate 
set  of  field  books  should  be  devoted  to  each.  It  is  an  excellent  plan  at  night 
to  copy  at  least  the  main-line  notes  in  a  permanent  notebook,  which  is  left  at 
the  office,  or  at  the  farmhouse  if  the  corps  is  in  the  field.  Sometimes  the  side 
notes  are  also  copied.  These  copies  are  made  so  that  all  the  records  may  not  be 
destroyed,  necessitating  an  entirely  new  survey,  should  anything  serious  happen 
to  the  field  book.  When  not  in  use,  all  field  books,  both  originals  and  copies, 
should  be  kept  in  a  fireproof  vault. 

Closing  Surveys. — To  diminish  the  chance  of  error,  even  if  double  angles 
have  been  read,  the  survey  must  be  closed  upon  itself  or  some  part  of  a  former 
closed  survey.  That  is,  the  transit  must  a  second  time  occupy  the  initial 
station,  so  that  the  first  azimuth  read  may  be  referred  back  to  the  last  line  of 
the  survey.  If  the  azimuth  (or  bearing)  as  read  the  second  time  agrees  with 
that  obtained  at  the  first  reading,  the  angular  readings  are  proved  to  have  been 
correctly  made.  If  the  error  in  closure  is  not  more  than  1'  to  3'  in  a  line  4  or 
5  mi.  in  length,  most  surveyors  will  balance  the  survey,  but  in  important  work 
the  error  must  (or  should)  be  located  so  that  the  survey  will  close  exactly 
in  angle.  Usually  one  or  more  stations  will  be  selected  as  the  most  probable 
ones  at  which  the  error  (all  or  in  part)  was  made.  These  stations  will  be  those 
at  which  good  sights  were  not  to  be  had  owing,  say,  to  smoke  obscuring  the 
point  of  the  plumb-bob  underground  or,  in  the  case  of  surface  surveys,  to  the 
station  stake  on  either  backsight  or  foresight  being  beyond  a  roll  in  the  ground 
so  that  the  tack  or  the  point  of  the  rod  was  not  visible.  These  doubtful  sta- 
tions may  be  reoccupied  and  the  angles  remeasured  with  special  care.  If  not 
located  at  the  probable  places  of  error,  the  survey,  so  far  as  the  angle  measure- 
ments are  concerned,  may  be  rerun  in  its  entirety;  but  this  is  rarely  necessary. 
If  the  angles  cannot  be  made  to  close  upon  resurvey,  the  failure  to  do  so  is  prob- 
ably caused  by  cumulative  errors,  a  few  seconds  at  each  station.  These  errors 
are,  singly,  too  small  to  measure,  but  in  a  survey  of  40  or  50  stations  may 
amount  to  1'  or  more.  Errors  in  linear  measurement  are  far  more  common 
than  errors  in  angular  measurement,  as  there  is  no  field  check  upon  the  work 
with  the  tape  unless  the  distances  are  read  twice,  on  the  foresight  from  the  one 
station  and  on  the  backsight  from  the  next.  A  wrong  reading  of  the  vertical 
angle  will,  of  course,  affect  the  horizontal  distance.  Errors  in  measurement 
are  often  of  5  or  10  ft.  due  to  incorrectly  reading  the  graduations  on  the  tape. 
Perfect  linear  measurements  are  far  more  difficult  to  make  than  perfect  angular 
measurements.  This  is  because  the  correct  length  of  a  line  is  very  materially 
affected  by  variations  in  the  length  of  the  tape  due  to  the  effects  of  sag,  ten- 
sion, changes  in  temperature,  etc.  In  highly  accurate  work,  corrections  should 
be  made  for  all  of  these. 


SURVEYING  73 

The  allowable  error  in  closure  depends  on  many  things,  the  chief  of  which 
is  financial.  If  it  will  C9st  more  to  locate  and  correct  the  error  than  the  value 
of  the  land  saved,  it  will  not  pay  to  do  so.  In  other  words,  far  more  time 
(consequently,  money)  may  be  spent  upon  a  survey  of  coal  land  worth  $2,500 
an  A.  than  upon  land  costing  but  $5  an  A.  In  ordinary  rolling  country,  such 
as  prevails  in  the  coal  fields  of  the  eastern  states,  with  instruments  in  good 
adjustment  and  using  ordinary  precautions,  the  error  in  closure  should  not  be 
greater  than  1  ft.  in  3,000  ft.  to  1  ft.  in  5,000  ft.,  and  trained  corps  will  do  better. 
In  bituminous  mines,  which  are  commonly  in  flat  coal,  underground  surveys 
may  easily  be  closed  within  1  ft.  in  10,000  ft.  to  1  ft.  in  20,000  ft.  The  higher 
accuracy  obtainable  underground  is  due  chiefly  to  the  fact  that  mine  temper- 
atures are  extremely  uniform  so  that  corrections  for  expansion  or  contraction 
of  the  tape  are  unnecessary.  Likewise,  the  tape  is  stretched  on  the  ground 
and  errors  due  to  sag  are  thus  eliminated. 


LEVELING 

DESCRIPTION  OF  INSTRUMENTS 

In  leveling,  but  two  instruments  are  used,  the  level  and  a  leveling  rod. 

The  level  consists  of  a  telescope  to  which  is  fitted,  on  the  under  side,  a  long 
level  tube.  The  telescope  rests  in  a  Y  at  each  end  of  a  revolving  bar,  which  is 
attached  to  a  tripod  head  very  similar  to  that  used  for  a  transit.  The  tele- 
scope is  similar  to  the  telescope  of  a  transit. 

The  leveling  rod  is  merely  a  straight  bar  of  wood,  6  ft.  or  more  in  length, 
divided  into  feet  and  tenths  of  a  foot.  A  target  divided  into  four  equal  parts 
by  two  lines,  one  parallel  with  the  staff,  and  the  other  at  right  angles  to  it, 
and  painted  red  and  white,  so  as  to  make  it  prominent  at  a  distance,  slides  on 
the  rod  and  is  provided  with  a  clamp  screw.  The  center  of  the  target  is  cut 
out  and  a  vernier,  graduated  decimally,  is  set  in,  which  enables  the  rodman  to 
read  as  close  as  ^^7  ft-  If  a  long  rod  is  required,  it  is  made  of  two  sliding  bars, 
which,  when  closed,  are  similar  to  a  single  rod,  as  described  above.  When  used 
at  points  where  it  is  necessary  to  shove  the  target  to  a  greater  height  than  6  or 
65  ft.,  the  target  is  clamped  at  the  highest  graduation  on  the  front  of  the  rod, 
and  the  rod  is  extended  by  pushing  up  the  back  part,  which  carries  the  target 
with  it.  The  readings,  in  this  case,  are  made  either  from  the  vernier  on  a 
graduated  side,  or  a  vernier  on  the  back.  The  rodman  must  always  hold  his 
rod  perfectly  plumb  or  perpendicular. 

LEVEL  ADJUSTMENTS 

The  proper  care  and  adjustment  of  the  level  is  of  great  importance.  A  very 
slight  error  in  adjustment  will  completely  destroy  the  utility  of  any  work  done. 

1.  To  Adjust  the  Line  of  Collimation. — Set  the  tripod  firmly,  remove  the 
Y  pins  from  the  clips,  so  as  to  allow  the  telescope  to  turn  freely,  clamp  the  instru- 
ment to  the  tripod  head,  and,  by  the  leveling  and  tangent  screws,  bring  either 
of  the  wires  upon  a  clearly  marked  edge  of  some  object,  distant  from  100  ft. 
to  500  ft.     Then  with  the  hand,  carefully  turn  the  telescope  half  way  around, 
so  that  the  same  wire  is  compared  with  the  object  assumed.     Should  it  be 
found  above  or  below,  bring  it  half  way  back  by  moving  the  capstan-headed 
screws  at  right  'angles  to  it,  remembering,  always,  the  inverting  property  of  the 
eyepiece;  now  bring  the  wire  again  upon  the  object,  and  repeat  the  first  oper- 
ation until  it  will  reverse  correctly.     Proceed  in  the  same  manner  with  the 
other  wire  until  the  adjustment  is  completed.     Should  b9th  wires  be  much 
out,  it  will  be  well  to  bring  them  nearly  correct  before  either  is  entirely  adjusted. 

2.  To  Adjust  the  Level  Bubble. — Clamp  the  instrument  over  either  pair  of 
leveling  screws,  and  bring  the  bubble  into  the  center  of  the  tube.     Now  turn 
the  telescope  in  the  wyes,  so  as  to  bring  the  level  tube  on  either  side  of  the  cen- 
ter of  the  bar.     Should  the  bubble  run  to  the  end,  it  shows  that  the  vertical 
plane,  passing  through  the  center  of  the  bubble,  is  not  parallel  to  that  drawn 
through  the  axis  of  the  telescope  rings.     To  rectify  the  error,  bring  it  by  esti- 
mation half  way  back,  with  the  capstan-headed  screws,  which  are  set  in  either 
side  of  the  level  holder,  placed  usually  at  the  object  end  of  the  tube.     Again 
bring  the  level  tube  over  the  center  of  the  bar,  and  adjust  the  bubble  in  the 
center,  turn  the  level  to  either  side,  and,  if  necessary,  repeat  the  correction 
until  the  bubble  will  keep  its  position,  when  the  tube  is  turned  £  in.  or  more 
to  either  side  of  the  center  of  the  bar.     The  necessity  for  this  operation  arises 
from  the  fact  that  when  the  telescope  is  reversed,  end  for  end,  in  the  wyes  in 
the  other  and  principal  adjustment  of  the  bubble,  it  is  not  easy  to  place  the 


74  SURVEYING 

level  tube  in  the  same  vertical  plane,  and,  therefore,  it  is  almost  impossible 
to  effect  the  adjustment  without  a  lateral  correction. 

Haying  now,  in  a  great  measure,  removed  the  preparatory  difficulties,  it 
is  possible  to  proceed  to  make  the  level  tube  parallel  with  the  bearings  of  the 
Y  rings.  To  do  this,  bring  the  bubble  into  the  center  with  the  leveling  screws, 
and  then,  without  jarring  the  instrument,  take  the  telescope  out  of  the  wyes 
and  reverse  it  end  for  end.  Should  the  bubble  run  to  either  end,  lower  that 
end,  or,  what  is  equivalent,  raise  the  other  by  turning  the  small  adjusting  nuts, 
on  one  end  of  the  level,  until,  by  estimation,  half  the  correction  is  made;  again 
bring  the  bubble  into  the  center  and  repeat  the  whole  operation,  until  the 
reversion  can  be  made  without  causing  any  change  in  the  bubble.  It  is  well 
to  test  the  lateral  adjustment,  and  make  such  correction  as  may  be  necessary 
in  that,  before  the  horizontal  adjustment  is  entirely  completed. 

3.'  To  Adjust  the  Wyes. — To  adjust  the  wyes,  or,  more  precisely,  to  bring 
the  level  into  a  position  at  right  angles  to  the  vertical  axis,  so  that  the  bubble 
will  remain  in  the  center  during  an  entire  revolution  of  the  instrument,  bring 
the  level  tube  directly  over  the  center  of  the  bar,  and  clamp  the  telescope 
firmly  in  the  wyes.  Place  it,  as  before,  over  two  of  the  leveling  screws,  unclamp 
the  socket,  level  the  bubble,  and  turn  the  instrument  half  way  around,  so  that 
the  level  bar  may  occupy  the  same  position  with  respect  to  the  leveling  screws 
beneath.  Should  the  bubble  run  to  either  end,  bring  it  half  way  back  by  the 
Y  nuts  on  either  end  of  the  bar;  now  move  the  telescope  over  the  other  set  of 
leveling  screws,  bring  the  bubble  again  into  the  center,  and  proceed  precisely 
as  just  described,  changing  to  each  pair  of  screws,  successively,  until  the  adjust- 
ment is  very  nearly  perfected,  when  it  may  be  completed  over  a  single  pair. 

The  object  of  this  approximate  adjustment  is  to  bring  the  upper  parallel 
plate  of  the  tripod  head  into  a  position  as  nearly  horizontal  as  possible,  in 
order  that  no  essential  error  may  arise,  in  case  the  level,  when  reversed,  is  not 
brought  precisely  to  its  former  situation.  When  the  level  has  been  thus 
completely  adjusted,  if  the  instrument  is  properly  made  and  the  sockets  are 
well  fitted  to  one  another  and  the  tripod  head,  the  bubble  will  reverse  over 
each  pair  of  screws  in  any  position.  Should  the  engineer  be  unable  to  make  it 
perform  correctly,  he  should  examine  the  outside  socket  carefully,  to  see  that 
it  sets  securely  in  the  main  socket,  and  also  notice  that  the  clamp  does  not 
bear  upon  the  ring  that  it  encircles.  When  these  are  correct,  and  the  error 
is  still  manifested,  it  will  probably  be  in  the  imperfection  of  the  interior  spindle. 

After  the  adjustments  of  the  level  have  been  effected  and  the  bubble  remains 
in  the  center  in  any  position  of  the  socket,  the  engineer  should  carefully  turn 
the  telescope  in  the  wyes,  and  sighting  upon  the  end  of  the  level,  which  has 
the  horizontal  adjustment  along  each  side  of  the  wye,  make  the  tube  as  nearly 
vertical  as  possible.  When  this  has  been  secured,  he  may  observe,  through  the 
telescope,  the  vertical  edge  of  a  building,  noticing  if  the  vertical  hair  is  parallel 
to  it;  if  not,  he  should  loosen  two  of  the  cross- wire  screws  at  right  angles  to 
each  other,  and  with  the  hand  on  these,  turn  the  ring  inside,  until  the  hair  is 
made  vertical;  the  line  of  collimation  must  then  be  corrected  again,  and  the 
adjustments  of  the  level  will  be  complete. 

USING  THE  LEVEL 

When  the  instrument  is  being  used,  its  legs  must  be  set  .firmly  into  the 
ground,  and  neither  the  hands  nor  person  of  the  operator  be  allowed  to  touch 
them.  The  bubble  should  then  be  brought  over  each  pair  of  leveling  screws 
successively,  and  the  instrument  leveled  in  each  position,  any  correction  being 
made  in  the  adjustments  that  may  appear  necessary.  Care  should  be  taken 
to  bring  the  wires  precisely  in  focus,  and  the  object  distinctly  in  view,  so  that 
all  errors  of  parallax  may  be  avoided. 

An  error  of  parallax  is  seen  when  the  eye  of  an  observer  is  moved  to  either 
side  of  the  center  of  the  eyepiece  of  a  telescope,  in  which  the  foci  of  the  object 
and  eyeglasses  are  not  brought  precisely  upon  the  cross-wires  and  object;  in 
such  a  case,  the  wires  will  appear  to  move  over  the  surface  and  the  observation 
will  be  liable  to  inaccuracy.  In  all  instances,  the  wires  and  object  should  be 
brought  into  view  so  perfectly  that  the  spider  lines  will  appear  to  be  fastened 
to  the  surface,  and  will  remain  in  that  position  however  the  eye  is  moved. 

If  the  socket  of  the  instrument  becomes  so  firmly  set  in  the  tripod  head  as 
to  be  difficult  of  removal  in  the  ordinary  way,  the  engineer  should  place  the 
palm  of  the  hand  under  the  Y  nuts  at  each  end  of  the  bar,  and  give  a  sudden 
upward  shock  to  the  bar,  taking  care,  also,  to  hold  his  hands  so  as  to  grasp  it 
the  moment  it  is  free. 


SURVEYING 


75 


FIELD  WORK 

If  the  survey  has  been  carefully  made  and  vertical  angles  taken  at  every 
sight,  leveling  will  be  necessary  only  in  cases  where  extreme  accuracy  in  regard 
to  vertical  heights  is  necessary.  In  most  cases  of  practical  work  at  collieries, 
particularly  in  determining  thickness  of  strata,  general  rise  or  fall  of  an  inside 
road,  etc.,  the  elevations  calculated  by  the  use  of  the  vertical  angle  will  be  close 
enough,  but  there  are  frequently  instances  when  leveling  must  be  done,  to 
insure  success  in  certain  work.  In  this  connection,  it  is  well  to  state  that  if  the 
transit  telescope  is  supplied  with  a  long  level  tube,  and  it  is,  as  a  whole,  in 
first-class  adjustment,  levels  can  be  successfully  run  with  it  if  the  transitman 
uses  due  care.  Having  his  instrument  in  proper  adjustment  and  his  notebook 
ruled,  the  levelman  is  ready  to  proceed  with  the  work. 

The  rodman  holds  the  rod  on  the  starting  point,  the  elevation  of  which  is 
either  known  or  assumed.  The  levelman  sets  up  his  instrument  somewhere 
in  the  direction  in  which  he  is  going,  but  not  necessarily,  or  usually,  in  the 
precise  line.  He  then  sights  to  the  rod  and  notes  the  reading  as  a  backsight 
or  +  (plus)  sight,  entering  it  in  the  proper  column  of  his  notebook,  and  adding 
it  to  the  elevation  of  the  starting  point  as  the  "height  of  instrument."  The 
rodman  then  goes  ahead  about  the  same  distance,  sets  his  rod  on  some  well- 
defined  and  solid  point,  and  the  levelman  sights  again  to  the  target,  which 
the  rodman  moves  up  or  down  the  rod  until  it  is  exactly  bisected  by  the  hori- 
zontal cross-hair  in  the  telescope,  as  he  did  when  giving  the  backsight.  This 
reading  is  noted  as  a  foresight  or  —  (minus)  sight.  The  foresight  subtracted 
from  the  height  of  instrument  gives  the  elevation  of  the  second  station.  The 
rodman  holds  this  latter  point,  and  the  levelman  goes  ahead  any  convenient 
distance,  backsights  to  the  rod,  and  proceeds  as  before.  In  this  case,  it  is 
assumed  that  levels  are  only  being  taken  between  regular  stations  or  two 
extreme  points. 

If  a  number  of  points  in  close  proximity  to  each  other  are  to  be  taken,  the 
rodman,  after  giving  the  backsight,  holds  his  rod  at  each  point  desired.  The 
readings  of  any  number  in  convenient  sighting  distance  are  taken  and  recorded 
as  foresights,  and  any  descriptive  notes  are  made  in  the  column  of  remarks. 
These  are  each  subtracted  from  the  height  of  instrument,  and  the  elevation 
found  is  noted  in  column  headed  Elevation.  After  all  the  intermediate  points 
are  taken,  the  rodman  goes  ahead  to  some  well-defined  point,  which  is  called 
a  turning  point  (T.  P.)  in  the  notes.  The  elevation  of  this  is  found  and  recorded . 
The  rodman  remains  at  this  point  until  the  levelman  goes  ahead,  sets  up  and 
takes  a  backsight.  This  backsight  reading,  added  to  the  elevation  of  the 
turning  point,  gives  a  new  height  of  instrument  from  which  to  subtract  new 
foresights,  and  thus  obtain  the  elevation  of  the  next  set  of  points  sighted  to. 

When  running  levels  over  a  long  line,  the  levelman  should  set  frequent 
bench  marks  (B.  M.).  These  are  any  permanent  well-defined  marks  that  can 
be  readily  found  and  identified  at  any  future  time.  By  leveling  to  them  he 
has  secured  the  elevation  of  points  from  which  to  start  any  subsequent  levels 
that  may  be  necessary.  A  good  bench  mark  can  always  be  made  on  the  side 
or  root  of  a  large  tree  or  stump  by  chopping  it  away  so  as  to  leave  a  wedge- 
shaped  projection  with  the  point  up.  A  nail  should  be  driven  in  the  highest 
point  of  this,  to  mark  where  the  rod  was  held,  and  the  tree  or  stump  blazed 

LEVEL  NOTES 


Station 

B.  S. 

P.  S. 

H.  Inst. 

Elev. 

Remarks 

1 

100. 

Assumed  elevation  of  Sta.  1. 

3.412 

103.412 

2 

4.082 

99.33 

Sta.  2  of  survey.     See  page  

Vol.—  - 

6.791 

96.621 

Sight  taken  to  ground  at  N.  E. 
cor.  John  Smith's  house. 

3  =  T.  P. 

4.862 

98.55 

Sta.  3  of  survey  noted  above. 

11.698 

110.248 

4 

9.817 

100.431 

Sta.  4  of  survey  noted  above. 

B.  M.  1 

6.311 

103.937 

B.  M.  1  is  on  north  side  of  large 

white  oak. 

5 

6.427 

103.821 

Sta.  5  of  survey  noted  above. 

70 


SURVEYING 


above  the  bench  mark.  In  this  blaze,  the  number  of  the  bench  mark,  which 
should,  of  course,  correspond  with  the  number  in  the  notebook,  should  be  cut 
or  painted.  In  the  mines,  prominent  frogs  or  castings  in  the  main  roads,  if 
permanent,  make  good  bench  marks. 

In  underground  leveling,  extreme  care  must  be  observed  to  record  the 
algebraic  signs  of  .the  readings,  which  show  whether  the  level  rod  was  held 
in  its  usual  position,  indicated  by  a  -f-  sign  or  the  absence  of  any  sign,  or  upside 
down,  indicated  by  the  —  -sign. 

Proof  of  Calculations. —  The  calculations  are  proved  by  adding  together 
the  backsights  and  also  the  foresights  taken  to  turning  points  and  last  station. 
Their  difference  equals  the  difference  of  level  between  the  starting  point  and 
last  station.  Thus: 

Foresights  Backsights 

4.S62  3.412 

6.427  11.698 

11.289  15.110 

11.289 

3.821  =  103.821  - 100.0  or  3.821 
TRIGONOMETRIC  LEVELING 

Trigonometric  leveling  determines  the  difference  in  elevation  between  two 
points  from  the  measurement  of  the  distance  between  the  points,  and  from  the 
vertical  angle  between  them.  Although  generally  less  accurate  than  level- 
ing with  a  Y  level,  it  is  much  more  rapid  and  is  especially  adapted  for  pre- 
liminary work  in  a  hilly  country,  or 
for  the  leveling  of  mine  slopes  and 
pitching  rooms  where  the  Y  level  can- 
not be  used  with  any  advantage  or 
accuracy.  By  reading  the  angles  and 
by  checking  the  measurements,  a  very 
high  degree  of  accuracy  can  be  ob- 
tained in  trigonometric  leveling. 

Case  1. — Assume  the  elevation  of 
A,  Fig.  1,  to  be  100  ft.  above  tide. 
With  the  transit  set  up  over  A  and  prop- 
erly leveled,  sight  to  a  point  C  on  a  rod 
so  that  BC  equals  AD.  Measure  the 
vertical  angle  Z  and  the  inclined  distance  DC,  then  the  difference  in  the  eleva- 
tion between  A  and  B  equals  BC  =  CDXsin  Z,  and  the  elevation  of  B  equals 
100 +BC. 

Case  2. — Assume  the  elevation  of 
station  A,  Pig.  2,  in  the  roof  of  a  mine 
to  be  100  ft.  above  tide.  Then,  with  the 
transit  set  up  directly  under  A  and 
properly  leveled  sight  to  a  point  C  upon 
the  plumb-line  suspended  from  the  sta- 
tion B,  measure  the  vertical  angle  X, 
inclined  distance  DC,  and  roof  distance 
BC.  From  this,  the  distance  CY  =  DC 
X  sin  X.  The  elevation  of  B  is  then 
found  as  follows:  The  elevation  of 
B  =  elevation  of  A-AD+(DCXsin  X) 
+  BC. 

There  are  many  modifications  of  this 
simple   method,   but   from   these   dia- 
grams the  most  complex  modifications  can  be  worked  out. 
TRIGONOMETRIC  LEVEL  NOTES 


FIG.  1 


FIG.  2 


Station 

Vertical 
Angle 
Degrees 

Inclined 
Distance 

100 
100 
100 
100 

Vertical 
Distance 

Height  of 
Instrument 
Feet 

Roof 
Distance 
Feet 

Elevation 
Feet 

A 
A-B 
B-C 
C-D 
D-E 

+  5 
+2 
-3 
-4 

+8.72 
+  3.49 
-5.23 
-6.98 

2 
3 
4 
2 

3 
2 
3 
1 

+  100.00 
109.72 
112.21 
105.98 
98.00 

SURVEYING  77 

CONNECTING  OUTSIDE  AND  INSIDE  WORK  THROUGH 
SHAFTS  AND  SLOPES 

SURVEYING  SHAFTS 

As  the  dip  of  the  bed  increases,  it  becomes  more  difficult  to  make  a  connec- 
tion and  the  chances  of  accuracy  diminish.  In  the  survey  of  a  pitching  plane, 
one  station  is  located,  with  respect  to  the  adjacent  ones,  by  multiplying  the 
distance  by  the  cosine  of  the  vertical  angle.  The  greatest  angular  accuracy 
for  a  given  distance  is  where  the  vertical  angle  is  0°.  As  the  pitch  or  vertical 
angle  of  sight  increases  the  cosine  diminishes  until,  at  a  vertical  sight,  distance 
Xcos.  vertical  angle  =  0°. 

In  the  case  of  an  adit  level,  or  a  slope  of  less  than  45°,  there  is  no  difficulty 
beyond  the  want  of  absolute  rigidity  in  setting  up  the  transit,  and  the  danger 
of  moving  it  in  going  about  it.  The  difficulty  increases  more  rapidly  than  does 
the  pitch,  and  as  the  distance  X  cos.  vertical  angle  diminishes,  though  the  dis- 
tance is  fixed,  the  chances  of  error  increase.  When  the  slope  reaches  60°,  there 
is  an  impracticability  in  running  a  line  down  a  slope,  as  the  line  of  collimation 
of  the  telescope  strikes  the  graduated  limb  of  the  instrument.  A  person  can 
use  a  prismatic  eyepiece  and  see  up  the  slope;  but  cannot  look  down.  As  it 
is  assumed  that  it  is  unnecessary  to  use  an  additional  telescope,  the  line  must 
be  run  by  intermediates.  To  do  this,  the  transit  should  be  set  up  at  the  bot- 
tom of  the  slope  where  the  longest  sight  up  the  same  can  be  secured  and  a  back- 
sight taken  on  a  station  of  the  underground  work;  or  a  backsight  should  be  set 
for  the  occasion  (both  stations  will  afterwards  be  connected  with  the  work 
below).  With  the  prismatic  eyepiece,  a  sight  should  be  taken  up  the  slope  on 
a  line  that  will  give  the  longest  sight  and,  at  the  same  time,  afford  a  good 
intermediate  place  to  set  up  the  transit,  as,  on  a  pitch  of  60°  or  more,  it  is 
absolutely  necessary  that  the  legs  of  the  transit  should  be  set  solidly  (in  holes 
in  the  floor,  or  between  the  sills  of  the  track)  so  that  they  will  not  be  moved  by 
subsequent  walking  about  it.  By  this  method,  all  the  sights  will  be  taken  from 
one  side  alone,  and  the  tripod  legs  can  be  shortened  to  make  the  sight  possible 
without  building  a  standing  place — if  the  man  is  short. 

Call  this  station  A ;  at  the  foot  of  the  slope  locate  B,  where  the  transit  can 
be  readily  set  up,  and  as  far  up  the  slope  as  possible  (this  distance  must  be 
at  least  100  ft.),  and  in  a  continuation  of  A  B,  locate  C.  Set  up  at  B  and  take 
foresight  to  C;  locate  D  under  the  same  conditions  that  governed  the  placing 
of  B,  and,  in  a  continuation  of  the  line  BD,  place  E.  Set  up  at  D  with  fore- 
sight at  E,  and  locate  F  and  G  as  before.  The  survey  is  carried  by  the  inter- 
mediates B,  D,  F,  etc.,  to  the  top,  by  a  series  of  foresights  to  C,  E,  G,  etc. 

The  term  shaft  in  American  coal-mining  practice  is  applied  only  to  ver- 
tical openings,  though  in  metal  mining,  both  in  the  United  States  and  abroad, 
it  is  also  applied  to  highly  inclined  slopes.  For  such  shafts,  most  of  the  methods 
given  in  the  textbooks  are  worthless,  as  they  are  for  transit  work  and  the  dis- 
tance Xcos.  vertical  angle  in  rare  cases  may  be  as  great  as  20  ft.,  while  the 
distance  varies  from  100  to  1,500  ft.  Again,  to  sight  down  a  shaft  neces- 
sitates the  erection  of  a  temporary  (and  therefore  more  or  less  unsteady)  sup- 
port for  the  tripod  of  the  transit,  and  the  chances  of  variation  in  its  position 
as  the  different  sights  are  made  are  so  great  that  it  is  difficult  to  say  when  a 
movement  has  not  taken  place  that  will  vitiate  the  work. 

In  sighting  up  a  shaft  of  greater  depth  than  100  ft.,  there  is  annoyance — if 
not  danger — from  dripping  water  or  the  fall  of  more  solid  substances.  _  In  a 
wet  shaft  the  object  glass  is  instantly  covered  with  water,  and  a  sight  is  impos- 
sible. Also,  it  is  necessary  to  stand  upon  a  platform,  and  it  is  hard  to  tell  when 
this  is  perfectly  rigid.  From  all  these  considerations  the  methods  with  a  transit 
are  never  used  by  engineers  in  the  anthracite  regions,  and  the  connections  are 
made  as  follows: 

When  the  bottom  of  the  shaft  can  be  reached  by  an  adit  or  a  slope  in  a 
roundabout  route  of  such  length  as  to  render  errors  in  measurement  of  dis- 
tance of  great  importance,  the  angles  are  carried  by  a  transit  with  as  long 
sights  as  possible,  and  no  distances  are  measured,  from  a  point  on  the  surface 
in  the  shaft  to  a  point  vertically  below  it  in  the  mine.  Sometimes  the  guide 
of  the  cage  is  taken  when  it  has  been  recently  set,  as  the  guides  are  plumbed 
into  position;  but  the  better  way  is  to  suspend  an  iron  plummet  by  a  copper 
wire:  sink  the  former  in  a  barrel  of  water  or  bucket  of  oil  so  as  to  lessen  the 
tendency  to  swing  on  account  of  the  pull  upon  the  bob  and  wires  from  the 
air-currents,  or  falling  drops  in  a  wet  shaft.  The  top  of  the  barrel  should  be 


78  SURVEYING 

covered  with  two  pieces  of  plank  with  a  semicircular  groove  of  3  in.  radius  cut 
out  of  the  middle  for  the  passage  of  the  wire,  to  catch  the  substances  whose  fall 
upon  the  water  would  cause  waves.  The  heavier  the  plummet  and  the  lighter 
the  wire,  the  less  the  tendency  to  swing.  This  wire  can  be  sighted  at  by 
parties  above  and  below  at  the  same  time,  and  the  swing  can  be  bisected 
to  get  the  position  of  the  wire.  A  number  of  sights  that  agree  can  be  taken 
as  accurate. 

When  the  shaft  is  the  only  way  to  get  below  from  above,  it  must  be  plumbed 
with  two  or  more  wires  suspended  as  just  described.  When  two  wires  are  used, 
the  wires  should  be  so  hung  that  an  instrument  can  be  set  up  below  in  a  line 
passing  through  them  produced,  and  at  a  sufficient  distance  from  them  to 
insure  an  accurate  sight.  When  more  than  two  wires  are  used,  the  under- 
ground station  can  be  located  at  any  point  at  which  all  the  wires  can  be  seen 
from  the  instrument. 

Case  1. — Two  wires  are  used,  which  are  located  as  far  apart  as  possible. 
Two  pieces  of  scantling  cd  and  ef,  Fig.  1,  are  spiked  across  the  opposite  cor- 
ners of  two  compartments  of  a  shaft  to  allow  the  cages  to  pass  up  and  down 
without  interference.  The  station  X  is  (roughly)  located  in  a  line  through 
the  corners  x,  and  is  connected  with  the  outside  survey.  From  this  station 
locate  in  the  line  Xxx  two  spads  for  holding  the  wires  of  the  plumb-bobs. 
These  are  driven  up  to  the  head  in  the  scantlings  in  such  a  way  that  the  line 
of  sight  passes  through  the  center  of  the  holes  in  their  heads.  When  the 
distances  Xa  and  ab  are  measured,  the  work  of  the  survey  above  ground  is  com- 
pleted. The  light  copper  wire  is  rolled 
upon  a  reel,  and  one  end  is  fastened  to  a 
light  plumb-bob  to  keep  it  free  from 
coils  or  kinks  in  descending.  It  can 
thus  be  readily  lowered  without  acci- 
dent. When  at  the  bottom,  the  upper 
end  is  fastened  in  the  spad  and  the 
Jieavy  bob  applied  to  the  bottom  and 

FIG.  1  placed  in  the  empty  barrel.    The  cages 

are  then  run  slowly  up  and  down, 
with  an  observer  on  each,  to  see  that  the  wires  hang  free  from  top  to  bot- 
tom. By  this  time  the  wire  will  have  stretched  so  that  it  will  be  straight, 
all  slack  is  taken  up,  the  barrel  filled  with  water,  and  the  top  boards  put  in 
place.  As  a  last  check,  the  distance  between  the  wires  below  is  measured,  to 
see  if  it  agrees  with  the  distance  above. 

Lining  in  below  a  point  Y  on  the  line  ab,  make  a  hole  in  the  roof  2  in.  in 
diameter,  and  drive  in  a  broad  plug.  Setting  up  the  transit  under  Y,  sight" 
at  the  wires  a  and  b  alternately.  A  number  of  methods  for  illuminating  the 
wires  have  been  used.  But  the  most  satisfactory  method  is  to  place  a  large 
white  target  behind  both  wires  and  illuminate  them  by  a  large  lamp  with  a 
reflector  behind  it.  The  wire  stands  out  black  against  the  target,  and  can  be 
followed  across  it.  As  there  is  considerable  distance  between  the  wires,  and 
as  the  transit  is  comparatively  near  them,  there  is  little  chance  of  getting  a 
sight  of  one,  when  the  telescope  is  focused  upon  the  other,  and  so  the  focus 
has  to  be  set  between  them.  This  gives  a  hazy  sight  at  each;  but  both  are 
shown  against  the  white  background  in  strong  relief.  After  the  transit  head 
is  shifted  so  that  the  line  of  sight  coincides  approximately  with  both,  they  should 
be  focused  upon  alternately  so  as  to  see  if  the  line  bisects  the  swing  of 
each.  If  so,  the  work  is  done;  if  not,  the  shifting  of  the  transit  head  must  fol- 
low until  the  end  is  attained.  It  frequently  requires  2  hr.  or  more  of  steady 
observation  to  complete  the  work,  and,  when  it  seems  as  if  the  proper  point 
were  secured,  one  of  the  wires  will  show  by  its  swaying  that  it  has  been  deflected 
from  the  vertical  by  a  peculiar  slant  of  wind,  and  the  result  obtained  must  be 
checked  again.  When  through,  there  is  no  absolute  certainty  that  the  point 
marked  is  in  the  accurate  extension  of  the  line  ab  at  the  surface.  Having  de- 
cided on  the  proper  place,  a  spad  must  be  driven  into  the  plug  overhead  and 
a  plumb-bob  hung  to  it  to  see  if  it  is  over  the  axis  of  the  transit,  as  shown  by 
the  screw  on  the  telescope.  If  not,  the  spad  must  be  driyen  so  that  the  point 
of  the  bob  does  so  hang,  and  the  station  Y  is  said  to  be  in  the  line  ab.  The 
distance  Ya  and  the  angles  to  any  station  of  the  underground  survey  must  then 
be  measured  and  when  the  line  ab  is  connected  with  the  surveys  at  daylight 
and  below,  the  plumb-bobs  may  be  removed. 

The  disadvantages  of  this  method  are  that  there  is  no  absolute  certainty 
that  the  point  Y  is  in  the  line  ab  prolonged,  and  this  want  of  certainty  should 
not  exist  in  so  important  a  measurement. 


SURVEYING 


79 


The  work  must  be  performed  by  daylight,  and  the  length  of  time  neces- 
sary to  complete  it  makes  it  impossible  to  work  the  shaft  for  at  least  5  da., 
and  may  cause  annoyance  to  the  operators,  or,  if  you  are  working  for  a  lessee, 
lead  them  to  refuse  to  let  you  have  the  use  of  the  shaft  at  the  time  most  suit- 
able for  your  purpose. 

Underground  it  may  be  hard  to  obtain  a  long  sight  on  any  line  running 
through  the  larger  axis  of  the  shaft.  Any  shorter  line  will  give  too  short  a 
base  line  and  will  increase  the  chances  of  error. 

Case  2. — Fig.  2  shows  the  top  set  of  timbers  in  a  shaft  of  two  hoisting  com- 
partments, down  which  it  is  desired  to  carry  a  known  course  or  meridian  on  the 
surface  to  the  entry  below.  It  is  necessary  first,  to  find  out  which  side  of  the 
shaft  is  best  adapted  for  setting  up  the  transit,  as  the  point  to  be  marked  in 
the  mines  will  be  vertically  under  the  point  on  the  surface;  consequently, 
the  side  with  the  widest  opening  leading  from  the  foot  of  the  shaft  should  be 
selected. 

Having  carried  the  meridian  to  a  convenient  point  near  the  top  of  the 
shaft,  and  having  found  that  the  south  side  of  the  shaft  is  the  most  accessi- 
ble, determine,  with  an  ordinary  string,  the  location  of  the  point  A,  from 
which  the  hangers  for  the  plumb-lines  will  be  exactly  located,  by  means  of 
the  transit.  Now  mark  with  chalk  on 
the  timbers  where  the  strings  cross. 
These  marks,  though  not  accurate, 
serve  as  guides  in  setting  the  hangers. 
Make  a  permanent  station  at  the  point 
A  and  carry  the  meridian  to  it. 

The  hangers  can  be  made  of  strap 
iron,  5  in.  thick  by  2  in.  wide,  and  at 
least  16  in.  long.  In  one  end  of  the 
iron,  have  a  jaw  with  a  fine  cut  at  the 
apex,  or  a  drill  hole  just  large  enough 
to  contain  the  wire  to  be  used  for 
plumbing.  There  should  be  two  or 
three  countersunk  holes  in  the  hanger, 
through  which  to  fasten  it  to  the  tim- 
bers by  means  of  heavy  wire  nails.  A 
top  view  of  the  hanger  is  shown  in 
Fig.  2.  In  most  shafts  there  is  a  space 
from  2  to  4  in.  wide  between  the  ends 
of  the  cage  and  the  sides  of  the  tim- 
bers. In  order  to  hoist  and  lower  the 
cage  to  see  that  the  wires  are  hanging  freely,  it  is  best  to  set  the  hangers  in 
such  a  position  on  the  timbers  that  the  wires  will  hang  in  the  middle  of  the 
space.  The  hangers  should  be  permanently  fastened  over  the  chalk  marks 
previously  made  on  the  north  side  of  the  shaft,  with  the  jaws  pointing  toward 
A ,  and  on  the  south  side  of  the  shaft  the  outer  end  of  the  hanger  may  be  fastened 
temporarily. 

Now,  set  the  transit  over  the  station  at  A,  take  the  backsight,  foresight  on 
the  wire  hole  of  the  hanger  C  and  set  the  wire  hole  of  the  hanger  B  on  the 
same  line.  Record  this  course  and  foresight  on  the  wire  hole  of  the  hanger 
E,  fixing  as  before  the  wire  hole  of  the  hanger  D  in  the  same  line.  Record 
this  course,  and  then  the  meridian  to  be  carried  into  the  workings  below  is 
established.  Measure  carefully  and  record  the  distances  A  to  B,  A  to  C, 
B  to  C,  A  to  D,  AtoE,D  to  E,  B  to  D,  and  C  to  E,  in  order  to  establish  a  point 
at  the  bottom  of  the  shaft  vertically  below  A,  and  check  the  work  in  the 
office. 

The  transit  party  can  now  descend  to  the  bottom  of  the  shaft,  taking  with 
it  four  buckets  of  oil,  the  weights  or  plumb-bobs  to  be  attached  to  the  wire, 
and  all  the  surveying  instruments,  leaving  a  responsible  person  on  the  surface 
to  handle  the  wires.  Having  arrived  at  the  bottom  of  the  shaft,  the  transit- 
man  should  have  the  cage  hoisted  3  ft.  above  the  landing,  throw  several  planks 
across  the  timbers  on  which  to  set  the  buckets  of  oil,  signal  to  the  man  on  top 
to  lower  a  wire  and  fasten  it  securely,  passing  it  through  the  wire  hole  of  the 
hanger,  attach  the  plumb-bob  and  adjust  the  wire  to  such  length  that,  when 
sustaining  the  full  weight  of  the  plumb-bob,  the  latter  will'  not  touch  the  bot- 
tom of  the  bucket.  He  should  then  place  the  weight  in  the  oil,  using  care 
not  to  let  the  full  weight  come  upon  the  wire  with  a  jerk,  but  should  let  the 
weight  down  slowly,  so  that  the  wire  will  receive  the  full  strain  gradually. 
The  three  remaining  wires  should  be  set  in  a  similar  way. 


FIG.  2 


80 


SURVEYING 


After  the  wires  have  been  hanging  a  few  minutes  with  the  weights  attached, 
the  latter  may  move  from  one  side  to  the  other  of  the  buckets.  They  should 
be  watched  carefully  and  the  buckets  moved  until  all  the  weights  hang  per- 
fectly free,  then  everything  should  be  let  alone  until  the  wires  become  steady. 
The  cages  can  now  be  hoisted  and  lowered  for  the  purpose  of  examining  the 
wires  to  see  that  they  hang  free  and  plumb,  care  being  taken  that  the  cages 
are  not  brought  so  close  to  the  landings  as  to  disturb  the  hangers  at  the  top, 
or  the  buckets  at  the  bottom. 

To  find  a  point  vertically  below  A,  a  string  may  be  stretched  along  the 
wires  B  and  C,  care  being  taken  not  to  touch  them;  another  may  be  stretched 
along  the  wires  D  and  £;  then,  with  a  plumb-line,  a  point  on  the  bottom  ver- 
tically below  the  intersection  of  the  strings  may  be  determined.  The  dis- 
tances AB,  AD,  BD,  and  CE  should  then  be  measured  and  compared  with  the 
corresponding  distances  at  the  top  of  the  shaft.  If  these  distances  compare 
favorably,  the  wires  are,  in  all  probability,  steady,  and  the  work  of  determin- 
ing the  desired  course  with  the  transit  may  be  begun. 

Set  the  transit  up  over  the  point  of  intersection  just  found;  backsight  on 
the  wires  B  and  C;  foresight  on  the  wires  D  and  E,  and  compare  the  included 
angle  and  the  distances  with  the  corresponding  angle  and  distances  at  the 
surface.  If  these  do  not  correspond,  move  the  transit  in  the  direction 
necessary  to  increase  or  decrease  the  angle 
or  distances,  as  the  case  may  be.  Repeat 
this  operation  until  the  exact  point  vertically 
below  A  is  determined. 

A  simple  device  that  is  of  great  advantage 
_jj  is  to  have  three  links  from  an  ordinary 
trace  chain  placed  in  the  wires  on  the  side 
toward  the  transit,  and  a  few  feet  above 
the  buckets.  This  not  only  enables  the 
wires  to  turn  freely,  but  also  enables  the 
transitman  to  sight  through  one  of  the  links 

I  to  the  wire  beyond,  whereby  he  can  place 

Q  the  transit  in  exact  line  with  the  wires  more 

A  easily  than  if  the  links  were  not  there, 

/h  Case    3. —  Two,     three,    or    four    wires 

;|\\  may  be  used,   being  secured   and   hung  as 

/  l\\  ^B  before.    They  are  located  in  the  angles  of  the 

/   l\\    I  compartments    x.    Pig.    3.     These   are    con- 

/      \  \  IBM  nected  with  four  stations  A,  B,  C,  and  D, 

ve  \ux\  I  the  lines  AB  and  CD  being  at  right  angles  to 

\  Ml   A|  each   other   for    convenience    in   the    subse- 

\  ||/    /•••  quent  calculation,   and  are  connected  with 

\  I  /  I  the  outside  survey.     From  A  and  B,  taking 

\  i  /  AB  as  a  base  line,  the  points  x  are  located. 

W/  The  same  is  repeated  from  C  and  D,  taking 

CD  as  a  base  line.  Thus  are  obtained  four 
locations  of  each  wire;  these  are  tabulated, 
and  any  variations  in  a  reading  must  be 
followed  by  a  repetition  of  the  same.  The 
mean  of  the  readings  gives  the  location. 
(Subsequently,  the  subject  of  calculating 
work  will  be  taken  up.)  It  can  be  briefly 
stated  that  the  bearings  of  each  wire  to  each 
of  the  others,  as  referred  to  the  base  line 
of  the  survey,  are  then  calculated  and  the 
distance  between  the  wires  accurately  meas- 
ured. This  finishes  the  work  at  daylight. 

There  may  be  two  general  types  of  ar- 
rangements of  the  bottom  of  the  shaft,  and 
both  arrangements  have  been  sketched  and 
lettered  similarly.  The  first  is  a  case  when 
the  shaft  is  arranged  across  the  dip  of  the 
bed,  and  the  second  is  parallel  to  the  same. 
In  both  cases  0  and  7  are  taken  as  far  apart  as 
possible,  and  all  the  wires  x  are  located  from 
each  station  with  reference  to  the  other.  The 
distances  between  the  wires  above  and  below  are  also  accurately  measured 
as  a  check.  There  will  be  four  locations  of  0  and  7  from  the  four  wires, 


FIG.  3 


SURVEYING 


81 


and  the  mean  of  these  is  taken  as  the  correct  one.  In  every  case  of 
angle  measurement,  a  series  of  readings  of  each  angle  is  taken  on  different 
parts  of  the  graduated  limb,  to  avoid  instrumental  errors,  and  the 
mean  of  these  is  taken  as  the  true  reading.  From  the  locations  of  0  and  7, 
the  course  between  them,  as  referred  to  the  mean  base  line,  is  calculated,  and 
07  is  the  base  line  for  the  underground  work.  The  angle  readings  above  and 
below  can  be  made  at  the  same  time  with  different  instruments,  and,  in  taking 
the  readings  below,  it  is  not  necessary  to  wait  for  absolute  quiet  in  the  wires, 
as  that  is  seldom  found.  A  small  swing  can  be  bisected  by  the  cross-hair, 
and  the  readings  are  duplicated  until  a  constant  result  is  secured.  By  this 
method  a  greater  accuracy  and  speed  is  obtained,  and  the  angles  below  can  be 
accurately  measured,  no  matter  how  the  shaft  may  be  arranged. 

The  T-Square  Method.  —  'The  T-square  method  of  taking  the  line  under- 
ground is  especially  valuable  in  shafts  with  several  small  compartments  or 
in  cramped  places  where  one  cannot  line  in 
with  the  wires.  The  wires  are  placed  in  sep- 
arate compartments  and  as  far  apart  as  pos- 
sible. The  apparatus  is  made  by  the  car- 
penter, and  consists  of  a  straightedge  and 
T  squares.  The  former  is  merely  a  planed 
pine  board  about  8  in.  X  I  in.  and  1  ft.  longer 
than  the  distance  between  the  wires.  It  rests 
approximately  horizontally  on  slats  tacked 
across  the  shaft  for  supports.  It  is  brought 
to  about  \  or  fg  in.  from  each  wire  and 
then  nailed  to  the  slats  sufficiently  to  pre- 
vent slipping.  One  man  should  be  at  each 
wire.  The  I  squares  are  most  serviceable  if 
made  with  a  movable  head  clamped  by  a 
thumbscrew,  and  of  planed  pine,  about  2  5  in. 
XI  in.  Except  in  cramped  quarters,  the 
T  squares  will  be  set  at  right  angles,  and 
should  be  placed  together  in  clamping,  to 
insure  that  each  set  is  at  precisely  the  same  angle. 

Fig.  4  shows  a  cramped  position,  similar  to  what  sometimes  arises,  in  which 
the  movable  head  gives  more  latitude  in  working.  After  clamping,  the 
T  squares  are  slid  along  the  straightedge  until  close  to  the  wire,  but  not  touch- 
ing it,  and  are  there  clamped  by  a  G  clamp,  both  men  working  at  one  T  square. 
The  ends  of  the  T  squares  C  and  D  must  be  supported  on  blocks  so  that  the 
T  squares  lie  approximately  in  the  same  horizontal  plane.  Everything  up 
to  the  next  step  need  be  only  approximately  and  quickly  placed,  but  the  great- 
est care  must  be  exercised  in  measuring  out  equal  distances  AC  and  BD  from 
the  wires.  If  the  wire  vibrates,  the  middle  of  its  swing  must  be  determined 
by  a  pencil  or  pin.  When  holding  a  foot-mark  (not  the  end  of  the  tape)  oppo- 
site the  wire  on  the  T  square,  an  even  number  of  feet  should  be  measured,  the 
point  marked  with  a  sharp  pencil,  and  a  pin  inserted.  When  this  has  been 
done  for  both  wires  the  parallelogram  ABDC  is  obtained,  in  which  the  only 
essential  is  that  CD  shall  be  exactly  parallel  to  AB,  the  line  of  the  wires.  The 
transit  should  now  be  set  over  the  most  convenient  of  the  two  points,  as  D. 
To  get  the  azimuth  of  DC,  and,  consequently,  the  line  of  the  wires,  sight  must 

be  taken  on  a  known 


FIG.  4 


A 

d 

•    I 
•  1 
•  1 

I  /] 
ayw  —  !/  !  — 

point  E  for  a  backsight, 
and  the  angle  EDC 
measured.  Another 
point  F  must  be  estab- 
lished on  the  line  of  the 



L       j  L          ?*. 

'"~~:Y~~7/~]  r~~ 

backsight,  in  order  that 
its  course  may  be  pre- 

served after  the  instru- 

  ---1     r~~ 
i     i 

ment  and  T  square  are 
removed. 

. 

FIG.  5  By  this  means  the 

closing  angle  at  E  may  be  read  after  the  wires  are  removed  from  the  shaft.  Un- 
derground, the  method  is  the  same,  except  that  DC  is  the  known  course,  and 
is  used  as  the  backsight.  To  give  the  coordinates  of  the  instrument  at  D  with 
the  greatest  precision,  the  angle  ADC  and  the  distance  AD  should  be  measured. 
Check  Methods.  —  The  results  obtained  by  the  use  of  the  methods  just 
described  should  be  checked  as  soon  as  an  underground  connection  between 


82  SURVEYING 

the  hoisting  shaft  and  air-shaft  has  been  driven.  Single  wires  are  hung,  one 
in  each  shaft,  and  the  distance  between  them  on  the  surface  is  measured.  The 
latitude  and  departure  of  both  A  and  B,  Fig.  5,  are  known  as  they  are  tied 
in  to  the  outside  survey.  In  the  mine,  the  stations  a  and  b  are  occupied  by  the 
transit  and  the  angles  Aab  and  abB  repeatedly  measured.  The  underground 
distances  Aa,  ab.  and  bB  are  carefully  measured.  With  these  data,  it  is  easily 
possible  to  calculate  the  latitude  and  departure  of  the  mine  stations  a  and  b, 
and  consequently  the  azimuth  of  the  line  ab,  which  serves  as  a  base  for  all  future 
extensions  of  the  mine  suryey.  It  should  be  noted  that  Fig.  5  shows  the  sim- 
plest arrangement  of  the  sights  that  is  possible,  but  two;  ordinarily  there  will 
be  anywhere  from  four  to  ten  or  more  stations  required  to  carry  the  line  from 
one  shaft  to  another.  As  the  surface  and  mine  temperatures  may  be  very  dif- 
ferent, particularly  during  the  winter  and  summer  months,  a  correction  should 
be  made  for  the  expansion  or  contraction  of  the  tape. 

SURVEYING  SLOPES  OR  INCLINED  SHAFTS 

Where  a  single  sight  reaches  from  top  to  bottom  of  the  slope,  the  problem 
is  simple  enough.  A  station  can  be  established  on  the  inside  of  the  foot-wall 
plate  at  the  collar  and  others  in  similar  positions  at  each  level.  The  instru- 
ment set  up  over  any  station  can  command  the  whole 
slope  and  the  level  opposite. 

Where  the  slope  is  sunk  on  several  dips,  the  survey 
is  a  much  more  difficult  matter.  Fig.  1  illustrates 
cases  of  common  occurrence.  The  slope  may  be 
divided  into  sections  like  A  DEB,  which  are  convex 
downwards,  and  others  such  as  EBC,  which  are  con- 
cave downwards.  As  a  rule  a  set-up  can  be  avoided 
at  the  convex  knuckles  if  desired,  and  need  only  be 
made  at  those  that  are  concave. 

Bent  Plumb-Line  Method. — Point  A  may  be  invisi- 
ble from  point  B,  but  the  survey  may  be  carried  from 
FIG   1  ~  one  P9int  to  the  other  by  the  bent  plumb-line  method. 

In  this  case,  establish  a  station  at  A,  the  foot-wall 
side  of  the  collar,  the  center  point  being  a  small  nail  head  projecting  hori- 
zontally. Attach  a  long  plumb-line  to  this  and  carry  the  other  end  to  B. 
Here  it  will  probably  be  necessary  to  use  a  small  screw-eye,  with  its  head  turned 
into  the  vertical  plane  of  the  slope  for  the  center  point.  Pass  the  plumb-line 
through  this  and  draw  it  fairly  tight.  Now  attach  a  plumb-bob  at  an  inter- 
mediate point  and  regulate  the  tautness  so  that  the  line  is  clear  at  all  points. 
The  curves  in  the  slope  may  be  such  that  two  plumb-bobs  may  have  to  be 
hung,  as  at  D  and  E,  and  even  a  third  may  become  necessary. 

As  the  plumb-line,  perhaps  100  ft.  long,  is  apt  to  be  disturbed  by  the  air- 
currents,  it  is  often  better  to  mark  a  point  on  a  convenient  timber  near  D, 
and  another  near  E,  so  close  to  the  string  that  there  is  no  doubt  of  the  points 
lying  in  exactly  the  same  vertical  plane  as  the  plumb-line.  If  these  points 
are  once  established,  the  string  and  weights  can  be  taken  out  of  the  slope, 
leaving  four  points  in  the  same  vertical  plane,  and  whose  horizontal  projections 
lie  in  the  same  course. 

Now  set  up  the  transit  at  A  and  measure  the  azimuth  angle  from  the  back- 
sight to  D,  thereby  giving  the  bearing  from  A  to  B.  If  D  should  be  invisible 
from  B,  depress  the  telescope  after  sighting  on  D  and  locate  the  point  N  in 
the  same  vertical  plane,  and  so  situated  that  it  is  visible  from  both  A  and  B. 
Measure  the  vertical  angle  and  distance  to  N.  Now  set  up  the  transit  at  B, 
use  the  course  BE  for  a  backsight,  and  foresight  to  C.  Measure  the  vertical 
angle  and  distance  BN.  The  line  BN  might  have  been  used  as  a  backsight, 
and  E  serve  as  an  additional  check.  The  point  N  is  really  an  intermediate 
station,  but  as  it  lies  in  the  course  AB,  a  set-up  there  is  unnecessary.  In 
simple  cases,  the  bent  plumb-line  method  is  a  very  convenient  one  for  carrying 
a  survey  from  the  surface  to  the  first  level,  and  a  longer  horizontal  projection 
of  the  sight  AD  can  be  secured  than  if  a  set-up  were  made  in  the  shaft  at  D; 
but  in  complicated  cases,  such  as  the  one  shown,  it  may  often  be  quicker  to 
make  the  extra  set-up  than  to  use  the  plumb-line.  In  all  sights  for  determin- 
ing azimuth,  the  vertical  angles  must  be  kept  as  low  as  possible,  and  the  hori- 
zontal projection  of  the  course  long. 

Method  by  a  Single  Wire  in  the  Slope. — When  surveying  a  slope  by  using  a 
single  wire,  stretch  a  rather  fine  wire,  free  from^kinks,  down  the  slope,  as  shown 
in  Fig.  2,  being  careful  that  it  touches  nowhere  in  the  slope.  Take  two  plumb- 
bobs  provided  with  fine  round  strings  and  suspend  one  from  A  and  the  other 


SURVEYING  83 

from  B  so  that  they  nearly  touch  the  same  side  ,of  the  wire  MN.     In  order  to 
have  the  plumb-lines  as  far  apart  as  possible,  the  line  at  B  must  be  quite  long 
and  a  can  of  water  provided  to  keep  the  bob  from  swinging.     The  plumb-line 
is  fastened  to  a  nail  B  nearly  in  the  proper  position.     A  bar  of  wood,  with  a 
block  fastened  to  it,  should  be  placed  to  one  side  and  a  little 
below  B.     The  block  must  have  a  hole  through  which  a  small 
screw  bolt  can  easily  screw.     On  this  bolt  is  placed  a  spool  in 
which  a  groove  is  turned  and  which  is  sandpapered  and  greased 
so  that  the  string  will  slip  easily  as  the  bolt  is  turned.     Now, 
place  the  transit  in  line  with  the  two  plumb-bobs,  as  in  an  ordi- 
nary  case   of   shaft   plumbing.     Repeat   this   operation   below. 
The  plumb-bobs  in  both  cases  hang  in  the  same  vertical  plane 
and  thus  the  true  bearings  are  found  underground.     Even  the 
plumb-lines  may  be  dispensed  with,  but  the  method  will  not 
then  be  so  accurate.     The  instrument  will  be  set  nearly  in  the 
vertical  plane  passing  through  the  wire,  leveled  and  sighted  at  M. 
The  telescope  should  be  dipped  until  the  lowest  point  on  the 
wire  is  visible  and  the  amount  by  which  the  cross-hair  and  wire         FIG.  2 
fail  to  coincide  noted  and  the  instrument  shifted  accordingly. 
But  if  this  method  is  tried,  the  two  points  sighted  at  will  not  be  nearly  so 
far  apart  horizontally  as  the  plumb-lines,  and  any  error  in  leveling  will  also 
vitiate  the  result.     This  method  of  the  single  wire,  however,  provides  no  way 
of  obtaining  the  coordinates. 


UNDERGROUND,  OR  MINE,  SURVEYING 

INTRODUCTION 

The  same  instruments  and  the  same  methods  of  measuring  and  recording 
angles  and  distances  are  used  on  the  surface  and  in  the  mine.  The  chief  dif- 
ference between  surface  and  underground  work  is  one  of  detail  9nly.  In  the 
mine,  lamps  are  needed  to  give  light,  sights  are  taken  to  a  string  or  to  the 
point  of  a  plumb-bob,  and  stations  are  placed  in  the  roof  and  not  in  the  ground. 
The  main-line  notes  are  kept  in  the  same  way  above  and  below  ground,  but 
the  method  of  taking  and  recording  side  notes  is  materially  different. 

Mine  surveying  in  flat  coal  seams  differs  in  minor  details  from  that  used  in 
pitching  seams,  and  this  difference  in  detail  has  been  greatly  exaggerated  until 
it  has  become  a  prevailing  belief  that  anthracite  (pitching)  and  bituminous 
(flat,  usually)  mine  surveying  methods  are  absolutely  distinct.  There  is,  in 
all  underground  work,  a  difference  in  the  organization  of  the  corps  and  con- 
sequently in  some  minor  details  in  carrying  on  the  work,  depending  on  whether 
the  survey  of  an  entire  and  extensive  mine  is  to  be  undertaken  or  whether, 
as  is  commonly  the  case,  the  survey  is  made  merely  to  connect  recent  develop- 
ments with  those  previously  surveyed. 

FLAT  WORK 

Because  it  is  necessary  for  the  gangways,  or  entries,  in  pitching  work  to 
follow  the  foldings  and  twistings  of  the  seam,  the  physical  difficulties  in  the 
way  of  the  surveyor  are  greater  in  that  kind  of  work  than  in  flat  seams.  In 
pitching  seams,  short  sights  and  many  of  them  are  the  rule;  in  flat  work,  long 
sights  and  few  are  general.  In  fact,  in  flat  seams  the  headings  or  entries  are 
commonly  driven  on  points;  that  is,  they  are  driven  upon  some  predetermined 
course  for  long  distances,  even  2  or  3  mi.  in  the  case  of  large  properties.  At 
regular  intervals,  pairs  of  cross-,  or  butt,  entries  are  driven  at  right  angles  to 
the  main  entries;  from  these,  in  turn,  the  rooms  are  driven.  Hence,  the  sur- 
veyor in  the  average  bituminous  mine  (bituminous  mines  are  commonly  flat) 
is  chiefly  concerned  with  prolonging  straight  lines  for  several  thousand  feet 
in  the  case  of  butt  entries,  and  up  to  2,  3,  or  4  mi.  and  more  in  the  case  ot 
long  main  entries.  The  angles  measured  are  chiefly  right  angles  at  the  points 
where  a  butt  entry  intersects  the  main  entry,  or  at  the  mouths  of  rooms 
driven  from  a  butt  entry. 

The  bituminous-mine  surveyor  is  very  rarely  called  on  to  make  a  com- 
plete survey  of  underground  workings.  He  usjually  moves  up  the  points  (sights) 
at  more  or  less  regular  intervals  of  time  or  of  distance  driven,  measures  the 
distance  from  the  old  set  of  points  to  the  new,  takes  the  necessary  side  notes, 
and  at  once  plots  them;  the  mine  map,  so  far  as  the  main  headings  and  cross- 
entries  are  concerned,  is  thus  up  to  date  within  a  month  or  so  at  the  most. 


84  SURVEYING 

In  fact,  whether  the  sights  are  moved  up  with  regularity  or  not,  the  mine  fore- 
man is  always  able  to  determine  the  position  of  the  working  face  by  measur- 
ing back  from  it  to  the  last  survey  station  appearing  on  the  tracing  or  blue- 
print furnished  him,  and  adding  this  distance  thereto,  laying  it  off  in  the  direc- 
tion the  heading  is  being  driven. 

Stations. — An  essential  part  of  the  equipment  of  the  mine  surveyor  is  a 
carpenter's  brace  and  from  three  to  six  bits,  or  drills,  which  can  be  made  from 
files  thrown  away  by  the  miner.  With  these,  a  hole  from  f  to  1  in.  in  diameter 
and  from  1  to  1?  in.  deep  may  be  drilled  in  the  roof  where  a  station  is  neces- 
sary. From  ten  to  fifty  plugs  should  also  be  carried  by  the  corps.  These 
plugs  are  pieces  of  poplar  or  other  softwood  about  *|  to  f  in.  longer  than  the 
drill  hole.  They  are  square  in  section,  the  side  being  a  little  longer  than  the 
diameter  of  the  hole  in  which  they  are  to  be  used;  the  lower  end  may.be  roughly 
rounded.  After  the  hole  is  drilled,  one  of  these  plugs  is  fitted  in  and  driven 
home  by  blows  from  the  hatchet  until  from  £  to  f  in.  projects  below  the  roof. 
A  spad,  spud,  or  as  sometimes  called  a  nail,  is  then  driven  into  the  plug.  The 
spads  or  nails  are  made  from  mule-shoe  nails,  through  the  flattened  heads  of 
which  |-in.  holes  have  been  drilled  or  punched.  These  spads  may  also  be  pur- 
chased from  dealers  in  surveyors'  supplies,  but  are  commonly  made  by  the 
'blacksmith's  helper  at  odd  times. 

Sometimes  stations  are  made  by  driving  a  tack  or  nail  in  a  tie,  which  has 
been  notched  or  flattened  with  a  hatchet  to  receive  it,  or  by  driving  a  spad  in 
the  collar  or  cap-piece  of  a  set  of  timbers.  Neither  of  these  methods  is  to  be 
recommended,  as  the  position  of  a  tie,  and  with  it  that  of  the  station  tack, 
is  practically  sure  to  be  changed  in  a  few  months  from  the  pounding  it  receives 
from  passing  cars,  mules,  and  men,  or  from  alining  the  track.  Stations  in 
collars  are  less  liable  to  be  shifted  than  those  in  the  track,  but  as  the  pressure 
due  to  mining  operations  comes  upon  the  timbers  they,  too,  are  apt  to  be  shifted 
out  of  line.  Sometimes  stations  that  must  be  set  at  an  exact  distance  from  a 
previous  station  (as  when  a  butt  entry  is  to  be  started,  say,  225.25  ft.  from  the 
main  entry  station)  are  of  necessity  made  in  a  tie  if  the  roof  at  the  exact  spot 
is  not  in  condition  to  hold  a  plug  (or  has  been  shot  down  for  an  overcast) .  In 
such  a  case  the  station  is  placed  in  the  tie  and  as  soon  as  the  butt  entry  or  other 
place  has  advanced  sufficiently  to  have  sight  plugs  set  in,  these  are  placed, 
and  the  use  of  the  tack  abandoned. 

In  longwall  work,  much  difficulty  is  experienced  at  times  through  the  sta- 
tions being  shifted  out  of  line  through  the  settling  of  the  overlying  rocks.  This 
settling  may  extend  over  a  period  of  years  or  may  stop  after  a  few  months. 
While  the  setth'ng  is  in  progress,  the  timbers  must  frequently  be  renewed,  so 
that  they  and  the  constantly  disturbed  roof  and  floor  afford  a  poor  place  for 
permanent  stations.  Hence,  during  the  period  of  settlement  at  least,  stations 
m  longwall  mines  must  be  placed  in  the  floor.  For  the  foregoing  reasons, 
combined  with  heavings  of  the  floor  as  the  weight  comes  unevenly  upon  the 
pillars,  these  stations  are  almost  certain  to  be  disturbed,  and  should  not  be 
used  to  extend  a  previous  survey  until  one  or  more  older  stations  have  been 
reoccupied  by  the  transit  and  the  angles  and  distances  remeasured  to  be  abso- 
lutely certain  that  no  such  disturbance  has  taken  place.  If  displacement  has 
occurred,  it  will  be  necessary  to  go  back  along  the  line  until  three  stations 
have  been  found  in  their  original  position.  From  these  a  new  set  of  lines 
must  be  run,  using  the  old  stations  if  solid  enough,  remeasuring  the  angles  and 
distances,  but  not  necessarily  retaking  the  side  notes. 

Stations  are  commonly  marked  by  enclosing  them  in  a  circle,  square,  or 
triangle,  or  by  a  +  mark  of  white  paint.  >  White  lead,  or  Dutch  white,  thinned 
with  linseed  oil  is  ordinarily  used,  and  is  applied  with  an  ordinary  sash  tool. 
If  the  paint  has  to  be  kept  a  number  of  days,  it  should  be  covered  with  water, 
which  should  be  poured  off  before  the  paint  is  used. 

In  addition  to  marking  the  station  itself  so  that  it  may  readily  be  found, 
some  system  of  lettering  or  numbering  must  be  devised  so  that  the  stations 
may  be  distinguished  one  from  the  other.  Stations  on  the  main  entry  fre- 
quently have  the  letter  M  prefixed  and  are  numbered  in  regular  order  from  the 
drift  mouth,  thus,  M-l,  M-2,  etc.  Or  the  stations  on  the  main  entry  may  use 
the  letter  A,  those  on  its  air-course  the  letter  B,  those  on  the  manway  the  let- 
ter C,  and  similarly  for  other  parallel  entries.  As  butt  entries  are  usually 
known  by  a  number  corresponding  to  the  order  in  which  they  were  turned  off 
from  the  main  entry,  the  stations  on  such  entries,  while  numbered  consecu- 
tively, have  prefixed  to  them  the  letter  R  or  L  to  indicate  whether  the  entry 
is  turned  to  the  right  or  the  left  of  the  main  entry,  as  well  as  the  serial  num- 
ber proper  to  the  entry.  Thus,  Ll-12  or  1L-12  indicates  the  twelfth  station 


SURVEYING  85 

on  the  first  left-hand  cross-entry,  or,  as  commonly  said,  on  the  first  left.  Sim- 
ilarly R5-6,  R-56,  or  5R-6,  is  the  sixth  station  on  the  fifth  cross-entry  to  the 
right.  If  entries  are  driven  from  one  side  only  of  the  main  entry,  the  pre- 
fixed letters  R  and  L  may  be  omitted.  In  this  case,  the  foregoing  stations 
will  be  numbered  1-12  and  5-6,  respectively.  Air-courses  are  not  usually 
run  on  sights.  If  they  are,  the  stations  in  them  may  be  numbered  in  the  same 
way  as  those  on  the  heading  proper  with  a  letter,  such  as  A,  to  denote  the  fact 
that  they  are  on  the  air-course.  Stations  coming  between  regular  stations  on 
an  entry  commonly  receive  the  number  of  the  preceding  station  with  some 
letter  added.  Thus  56  D  is  a  station  on  the  fifth  cross-entry  at  a  point 
between  regular  stations  6  and  7. 

Some  corps  number  the  stations  in  a  heading  as  are  stakes  in  a  railroad 
survey.  The  station  at  the  mouth  of  the  heading  on  the  main  entry  is  called  0, 
and  the  first  station  in  the  heading  will  be,  say,  2+56.29,  the  second  4+81.96, 
etc.  This  means  that  these  stations  are  256.29  and  481.96  ft.,  respectively, 
from  the  mouth  of  the  entry.  The  distance  between  the  stations  is  of  course 
481.96  -  256.29  =  225.67  ft.  While  this  system  of  numbering  shows  at  a  glance 
the  exact  distance  an  entry  has  been  driven,  such  large  numbers  may  be  a 
source  of  trouble  and  of  possible  error  when  used  to  describe  the  backsight, 
instrument,  and  foresight  stations  as  entered  in  the  field  notes. 

Rarely  are  stations  numbered  in  the  order  in  which  they  chance  to  be 
placed.  It  may  happen  that  station  56  will  be  on  the  main  entry,  57  on  the 
fifth  right,  and  58  on  the  tenth  left  and  follow,  say,  stations  numbered  36,  48, 
and  51.  This  system,  or  want  of  system,  is  not  commended,  as  it  leads  to 
confusion. 

While  the  numbers  of  stations  are  frequently  painted  on  the  roof  along- 
side the  station  mark,  it  is  better  practice  to  paint  them  on  the  rib  a  short 
distance  before  the  station  is  reached.  In  this  way  the  foresight  man  can 
see  them  without  having  to  walk  in  a  stooping  posture. 

Sighting. — Sights  in  underground  work  are  commonly  taken  either  to  the 
point  of  a  plumb-bob  suspended  by  a  cord  passed  through  the  hole  in  the  head 
of  the  spad  marking  the  station,  or  to  the  cord  itself.  In  the  first  case,  a  lamp 
is  held  a  short  distance  back  of  the  point  of  the  bob  to  render  it  visible  against 
a  background  of  flame.  In  the  latter  case,  the  cord  is  best  illuminated  by 
placing  a  white  paper  or  cardboard  behind  it  and  holding  the  lamp  in  front 
and  to  one  side.  The  string  shows  as  a  dark  line  against  a  white  ground,  but 
care  must  be  taken  not  to  confuse  the  string  with  the  shadow  it  casts  upon  the 
paper. 

What  are  known  as  plumb-lamps,  or  plummet  lamps,  are  a  great  convenience. 
These  are  very  heavy  plumb-bobs,  suspended  in  gimbals  to  ensure  verticality, 
which  are  hollowed  to  form  an  oil  chamber,  and  are  provided  with  a  wick. 
The  bisection  of  the  lamp  flame,  if  the  wick  is  turned  low,  affords  a  sufficiently 
accurate  setting  of  the  transit  when  placing  room  sights,  surveying  rooms,  and 
even  in  moving  up  sights  in  a  butt  entry,  provided  the  backsight  is  not  too 
close  to  the  instrument  and  the  flame  is  not  greatly  disturbed  by  the  ventilat- 
ing current.  It  is  obvious  that  the  use  of  the  plummet  lamp,  which  will  burn 
for  several  hours  and  is  always  ready  for  backsighting  on,  saves  the  labor  of 
one  man.  In  accurate  sighting,  the  point  or  the  cord  of  the  plumb-lamp  may 
be  used  as  just  explained.  Where  the  velocity  of  the  air  is  great  enough  to 
cause  the  plumb-bob  to  oscillate,  long  narrow  bobs  must  be  used,  and  these 
must  be  shielded  from  the  direct  current  by  the  backsight  man.  In  drafty 
places,  a  hole  may  be  dug  out_  in  the  ballast  between  the  ties  and  the  bob  let 
into  this  shelter,  the  sight  being  taken  to  the  string.  Cords  for  suspending 
plumb-bobs  should  be  braided  to  avoid  twisting  under  the  weight  of  the  bob, 
should  be  well-oiled,  and  should  be  hung  with  a  slip  knot  so  that  the  point 
may  be  raised  or  lowered. 

Various  means  are  employed  to  illuminate  the  cross-hairs  in  the  telescope. 
Commonly  this  is  done  by  holding  a  lamp  a  little  beyond,  above,  and  to  one 
side  of  the  object  glass.  Sometimes  a  reflector  is  provided.  This  con- 
sists of  a  piece  of  silvered  metal,  inclined  at  an  angle  of  about  30°,  that  is 
soldered  on  one  edge  to  a  metal  ring  that  fits  around  the  object  end  of  the 
telescope.  The  reflector  has  an  oval  hole  through  it  t9  permit  the  passage 
of  the  line  of  sight.  The  reflection  of  the  light  carried  in  the  surveyor's 
cap  sufficiently  illuminates  the  hairs  to  permit  their  being  centered  upon 
an  object.  In  some  rare  cases,  transits  have  the  horizontal  axis  pierced  (the 
opening  being  closed  by  a  piece  of  glass),  through  which  hole  a  lamp  held 
at  the  end  of  the  telescope  axis  will  throw  enough  light  to  render  the 
cross-hairs  visible. 


86  SURVEYING 

Centers. — If  stations  are  made  in  the  ties,  the  transit  may  be  set  up  over 
them  exactly  as  in  outside  work.  However,  stations  are  commonly  made  in 
the  roof.  The  transit  may  be  set  under  a  station  if  a  center  mark  is  punched 
in  the  collar  surrounding  the  telescope  and  to  which  the  transverse  axis  is 
attached.  When  the  telescope  is  level,  this  mark  is  immediately  above  the 
point  of  a  plumb-bob  suspended  from  beneath  the  instrument.  By  slightly 
loosening  the  leveling  screws,  the  plate  may  be  shifted  until  the  center  of  the 
instrument  is  exactly  below  the  P9int  of  a  bob  suspended  from  the  station  spad. 
However,  care  must  be  taken  in  tightening  the  leveling  screws,  that  the  instru- 
ment is  not  thrown  out  of  line.  Commonly,  the  station  in  the  roof  is  trans- 
ferred to  what  is  called  a  center  placed  on  the  floor,  and  over  this  center  the 
instrument  is  set  in  the  ordinary  way. 

The  center  may  be  made  from  a  large  square  or  hexagonal  nut  some  2  in. 
across.  A  wire  nail  or  spad  is  set  in  the  center  of  the  hole  in  the  nut,  which 
is  filled  with  melted  lead  or  Babbitt  metal.  The  point  of  the  nail  is  cut  off 
about  $  in.  above  the  top  of  the  nut  and  sharpened  with  a  file.  Or  a  very 
satisfactory  center  may  be  made  by  boring  a  hole  11  in.  in  diameter  and  1  in. 
deep  in  a  thick  plank,  setting  a  brad  in  the  center  with  its  head  down,  and 
filling  in  with  melted  lead,  at  the  same  time  holding  the  brad  in  a  vertical  posi- 
tion with  its  end  projecting  slightly  above  the  top  of  the  plank.  After  cooling, 
the  brad  may  be  sharpened  as  before. 

A  plumb-bob  is  hung  from  the  station  and  the  string  adjusted  until  the 
point  of  the  bob  just  clears  the  point  of  the  center.  By  sighting  across  the 
two  points  at  an  angle  of  90°,  the  point  in  the  center  may  be  shifted  into  coin- 
cidence with  the  point  of  the  bob.  If  the  center  has  been  lost  or  forgotten, 
a  plank  may  be  laid  across  the  rails  under  the  station  and  the  position  of  the 
point  of  the  plumb-bob  marked  upon  it  with  a  pencil.  After  removing  the 
plumb-bob  and  its  cord,  the  transit  may  be  set  over  the  center  or  pencil  mark 
in  the  usual  way. 

Placing  Stations  on  Line. — Two  cases  of  placing  stations  on  line  may  arise: 
(1)  The  station  may  be  on  the  prolongation  of  the  heading  line  and  at  any 
indefinite  distance  from  the  instrument.  (2)  The  station  may  (or  may  not) 
be  on  the  line  of  the  heading,  but  is  at  a  fixed,  definite  distance  from  the  instru- 
ment. 

The  first  is  the  common  case  when  the  last  station  on  a  straight  heading 
is,  say,  200  to  250  ft.  back  from  the  face,  and  a  new  station  must  be  set  ahead 
and  on  line  so  that  sight  plugs  may  be  placed  from  it.  The  transit  should  be 
set  up  at  the  station  nearest  the  face,  a  backsight  taken  on  an  outer  station 
on  the  line,  and  the  telescope  plunged.  Where  the  roof  is  solid  and  from  25  to 
50  ft.  back  from  the  face,  the  foresight  man  should  hold  his  lamp  against  the 
roof  so  that  its  flame  may  be  lined  in  by  the  surveyor,  a  smear  with  the  lamp- 
wick  or  an  X  with  a  piece  of  chalk  should  then  be  made  on  the  roof  when  the 
line  is  secured..  The  point  of  the  drill  may  be  placed  on  this  mark  and  the 
lamp  held  behind  it.  If  not  in  line,  the  drill  may  be  shifted  to  the  right  or  left 
until  it  is.  The  hole  should  then  be  started  by  pressing  upwards  and  turning 
the  brace.  As  the  point  of  the  drill  is  apt  to  slip  on  smooth  rock,  as  soon  as 
the  hole  has  a  grip,  another  sight  should  be  taken  to  make  sure  that  the  drill 
is  still  in  line.  If  it  is  not  in  line,  a  new  sight  should  be  taken  and  a  new  hole 
started  a  few  inches  away.  The  hole  should  be  drilled  to  the  required  depth 
and  the  plug  driven  firmly  home.  The  point  of  a  spad  should  then  be  stuck 
in  the  plug  near  its  center  with  the  head  hanging  vertically  and  the  eye  facing 
the  transit..  Holding  the  flame  9f  the  lamp  behind  the  spad,  it  must  be  moved 
to  the  right  or  left  until  its  point  is  exactly  in  line.  Still  holding  the  lamp 
behind  it,  the  spad  should  be  driven  firmly  home,  the  blows  of  the  hatchet  being 
inclined  so  that  the  head  of  the  spad  may  be  driven  to  the  right  or  the  left  as 
the  transitman,  who  is  following  the  work,  may  direct.  When  the  spad  is 
driven  home,  the  lamp  should  be  held  behind  its  eye  and,  with  gentle  taps  of 
the  hatchet,  it  should  be  knocked  to  the  right  or  left  until  the  vertical  hair 
exactly  bisects  the  hole.  For  many  purposes,  the  alinement  is  now  sufficiently 
accurate.  For  important  work,  however,  the  plumb-bob  should  be  hung  from 
the  spad  and  the  final  and  exact  alinement  made  by  sighting  to  its  point  or 
to  the  cord.  The  distance  between  the  old  and  new  stations  should  be  measured 
and  if,  in  addition,  the  side  notes  are  taken  the  work  may  be  placed  upon  the 
mine  map  at  once. 

The  second  case  arises  when  a  branch  or  cross-entry  is  driven  from  the 
main  entry,  either  to  meet  a  similar  place  being  driven  toward  it  or  to  inter- 
sect another  place  at  a  fixed  point.  The  instrument  is  set  up  on  the  main 
entry  at  .the  point  nearest  to  that  from  which  the  branch  road  is  to  be  driven, 


SURVEYING  87 

a  backsight  is  taken  upon  an  outer  station,  and  the  telescope  plunged.  The 
foresight  must  now  be  placed  not  only  on  the  entry  line,  but  at  an  exact  dis- 
tance, say,  186.27  ft.,  from  the  transit.  The  tape  must  be  stretched  in  line, 
and  at  the  exact  distance  from  the  station,  a  pencil  mark  3  or  4  in.  long  made 
at  right  angles  to  the  line  of  sight.  This  mark  may  be  made  on  the  face  of 
a  tie  that  has  been  cleaned  off,  if  one  is  at  the  right  distance;  or  on  a  piece  of 
plank  made  to  span  the  space  between  two  ties.  The  point  of  a  tack  or  a 
brad  should  be  placed  in  this  line  and  a  lamp  held  behind  it.  The  tack  must 
then  be  shifted  until  it  is  in  line  and  driven  home.  If  the  distance  the  branch 
road  is  to  be  driven  is  short  and  the  station  at  its  mouth  will  not  be  needed 
again,  the  instrument  may  be  set  over  the  tack,  and  after  setting  the  vernier 
at  0  or  at  the  back  azimuth  or  bearing  of  the  entry  line,  the  deflection  angle, 
azimuth,  or  bearing  on  which  the  new  place  is  to  be  driven  may  be  set  off  on 
the  upper  plate  and  upon  this  line  the  sight  plugs  may  be  placed.  The  sur- 
veyor is  recommended  to  always  use  the  system  of  reading  and  recording 
angles  with  which  he  is  most  familiar,  except,  of  course,  when  the  system  is 
inaccurate. 

If  the  station  must  be  preserved  (which  is  commonly  the  case) ,  the  position 
of  the  tack  just  placed  in  the  tie  must  be  transferred  to  a  permanent  station 
in  the  roof.  To  do  this,  leave  the  transit  as  it  was  after  setting  the  tack. 
Suspend  a  plumb-bob  from  the  roof,  holding  the  string  in  such  a  way  between 
the  thumb  and  forefinger  that  when  the  helper  says  the  point  is  directly  over 
the  tack,  a  smear  of  chalk  (previously  applied  to  the  thumb)  may  easily  be 
made  on  the  roof.  Hold  the  drill  on  the  mark  and  have  it  lined^in  from  the 
transit.  After  the  bit  grips  the  rock,  again  line  in  from  the  transit  and  check 
the  distance  measurement  by  again  dropping  a  plumb-line  upon  the  tack. 
Drill  the  hole  and  drive  home  a  plug,  which  may  be  of  somewhat  larger  sur- 
face area  than  the  prdinary  station  plug.  Draw  a  pencil  line  across  the  face 
of  the  plug  by  joining  the  holes  left  by  the  points  of  two  brads  set  near  the 
inner  and  outer  edges  thereof  and  which  have  been  lined  in  from  the  transit. 
(These  brads  need  not  be  driven  up,  as  they  are  used  only  for  giving  the  ends 
.  of  the  line.)  Next  suspend  the  plumb-bob  over  the  edge  of  a  knife  blade  (the 
thumb  is  too  blunt),  so  that  the  cord  is  on  the  pencil  line,  and  when  the  helper, 
by  sighting  across  the  point  and  the  tack,  announces  that  they  are  directly 
over  one  another  (that  is,  the  distance  is  exact)  make  a  mark,  with  a  pencil, 
on  the  plug.  A  spad  may  now  be  placed  in  this  mark  and  should  be  on  the 
entry  line  and  at  the  proper  distance  from  the  instrument.  However,  before 
driving  it  home,  check  the  alinement.  After  driving  home,  perfect  the  aline- 
ment  by  sighting  to  the  point  of  the  bob  or  to  its  cord.  Some  prefer,  after 
the  plug  is  driven  up,  to  suspend  the  plumb-bob  from  a  spad,  which  is  shifted 
by  the  transitman  to  the  right  or  left  until  in  the  line  of  the  heading,  and  by 
the  foresight  man's  helper  inbye  and  outbye  along  the  heading  line  until  at 
the  exact  distance,  after  which  it  is  slpwly  driven  up,  being  checked  during  the 
process.  By  the  first  method,  there  is  no  trouble  in  placing  spads  within  less 
than  T&T  ft.  of  the  exact  spot  and  any  desired  degree  of  accuracy  may  be 
obtained  by  taking  time. 

Placing  Sights.— The  entries  always  and  the  rooms  usually,  in  flat  seams, 
are  driven  on  sights.  These  sights  are  a  pair  of  plugs  set  on  the  pre- 
determined line  about  2  ft.  apart  in  which  are  driven  spads  that  are  set  exactly 
on  line.  Pieces  of  coal,  iron  nuts,  or  other  weights  are  hung  from  the  spads 
and  before  an  undercut  is  made  the  foreman,  miner,  or  machine  runner  sights 
across  the  strings  and  marks  the  center  line  on  the  face  with  a  piece  of  chalk. 
Under  ordinary  conditions,  sights  should  be  moved  up  about  every  200  ft. 
of  advance  in  the  working  face;  although  this  distance  may  be  increased  where 
the  ventilation  is  good  and  lessened  where  it  is  poor.  While  a  pair  of  sights 
may  be  placed  near  the  face  from  an  instrument  _station  200  ft.  or  more  back 
therefrom,  the  better  practice  is  to  place  a  station  ahead  as  just  explained. 
The  transit  is  then  moved  to  this  station,  a  backsight  taken  as  before,  the 
telescope  plunged  and  the  two  sight  plugs  placed  some  10  to  15  ft.  ahead  of  the 
instrument,  the  final  alinement  being  effected  by  bisecting  the  two  eyes._  This 
makes  the  survey  station  independent  of  the  sight  plugs  and  the  spad  in  it  is 
not  apt  to  be  pulled  out  of  line,  as  will  be  the  case  if  the  station  is  one  of  the 
sight  plugs.  The  practical  certainty  of  finding  the  station  in  good  condition 
more  than  repays  for  the  labor  of  setting  the  extra  plug  and  making  the  extra 

While  entry  sights  are  commonly  and  naturally  placed  in  the  center  of  the 
opening,  many  consider  it  better  to  place  them  to  one  side  and  over,  say,  the 
right-hand  rail.  By  so  doing,  a  conscientious  track  foreman  can  use  them  to 


88  SURVEYING 

keep  his  own  work  in  line  and,  being  proud  of  a  fine  piece  of  work,  will  urge 
the  miners  to  drive  the  headings  straight.  With  heavy  trains  and  motors 
and  the  high  speed  required  for  large  outputs,  the  importance  of  a  straight 
track  is  apparent. 

When  rooms  are  driven  on  sights,  usually  each  room  is  given  a  pair  of  sight 
plugs,  but  in  some  cases  only  every  other  room  is  so  provided,  the  intermediate 
room  being  kept  in  line,  as  well  as  possible,  by  leaving  a  pillar  of  constant 
thickness  on  each  side,  which  thickness  is  determined  by  measuring  through 
the  cross-cuts.  As  the  direction  of  rooms  is  rarely  of  prime  importance,  sights 
in  them  are  not  moved  up,  unless  it  is  absolutely  impossible  to  see  the  face 
from  them  by  reason  of  smoke,  roof  falls,  etc.  Room  sights  are  commonly 
placed  in  the  necks  anywhere  from  8  to  20  ft.  from  the  entry  line.  Surveyors 
prefer  to  wait  until  the  necks  have  been  turned  for  a  number  of  rooms  before 
placing  the  sights  in  any  of  them.  The  instrument  is  then  set  up  at  any  con- 
venient station  and  the  line  of  sight  made  to  coincide  with  that  of  the  entry. 
A  series  of  tacks  is  placed  in  line  the  proper  distance  apart  (when  rooms  are 
turned  at  90°,  distance  =  width  of  room + width  of  pillar)  and  are  driven  down 
into  the  tie  or  into  a  plank  laid  across  the  rails,  one  tack  for  each  room.  The 
instrument  is  set  up  over  each  tack  in  succession  and  a  right  angle  to  the  head- 
ing line  is  turned  and  two  sight  plugs  are  placed  in  the  room  neck  as  far  from 
the  entry  as  possible.  The  distance  of  each  tack  from  the  entry  station  is 
noted  and  the  distance  from  the  line  of  the  entry  to  the  outbye  room  sight  plug 
is  also  measured  and  recorded.  Room  sights  may  be  set  by  bisecting  the  eye 
of  the  spad  and  are  commonly  placed  18  in.  to  2  ft.  from  the  rib.  Where  rooms 
are  inclined  to  the  entry,  the  distance  between  their  centers  measured  along 
the  line  of  the  entry  is  found  from  the  formula: 

_..  ,  width  of  room + thickness  of  pillar 

Distance  =  —  — V^ — r = 

sin  angle  of  inclination 

Surveying  and  Note  Keeping. — The  laws  of  most  states  require  that  the 
mine  workings  be  surveyed  and  mapped  at  least  once  every  6  mo.  If  the  neces- 
sary measurements  and  side  notes  have  been  taken  at  the  times  the  entry 
sights  have  been  moved  up  and  have  been  mapped,  the  mine,  so  far  as  the  main 
roads  are  concerned,  is  always  within  a  few  weeks  of  being  up  to  date.  If 
this  has  not  been  done,  the  procedure  will  depend  on  whether  lines  of  sight 
are  carried  up  one  or  both  entries  of  a  pair.  If  each  entry  has  its  sights,  the 
0  end  of  the  tape  should  be  held  at  the  last  station  appearing  on  the  map  and 
the  tape  stretched  out  to  the  next  station.  The  surveyor  may  then  walk 
along  the  tape  and,  when  opposite  a  break-through,  note  the  distance  to  both 
sides  of  the  opening  as  say  +256  to  +267  (the  opening  being  11  ft.  wide). 
The  assistant  should  carry  the  0  end  of  a  tape  (usually  a  50-ft.  metallic  tape) 
to  the  rib  at  each  side  of  the  cross-cut,  and  the  surveyor  should  measure  the 
distance  to  the  nearest  J-ft.  mark  to  these  points  from  the  entry  line  and  note 
whether  the  break-through  has  been  driven  to  the  right  or  left  from  the  entry. 
Room  necks  may  be  located  in  the  same  way. 

It  is  advisable,  where  the  entry  is  crooked,  to  note  the  places  where  the  tape 
comes  nearest  and  farthest  from  the  rib.  Many  surveyors  do  not  take  offsets 
to  the  corners  of  the  pillars  made  by  the  various  openings,  merely  noting  the 
plusses,  or  distance  measured  along  the  tape  opposite  which  these  openings 
come.  When  so  mapped,  the  entries  appear  perfectly  straight,  which  makes  an 
attractive  but  inaccurate  map.  When  the  exact  distance  between  stations 
as  well  as  the  necessary  vertical  angles  have  been  taken  at  the  time  the  stations 
were  moved  up,  the  use  of  a  transit  is  unnecessary  when  making  the  entry  sur- 
veys, but  it  is  highly  advisable  to  remeasure  these  distances  as  a  valuable, 
in  fact  as  the  only  possible,  check  on  the  original  distance  measurements  until 
a  close  is  made  and  the  survey  calculated. 

After  taking  the  notes  between  the  first  pair  of  stations,  those  between  the 
next  pair  should  be  taken,  and  similarly  until  the  foresight  man  with  the  tape 
reel  is  at  the  last  station.  This  may  be  anywhere  from  25  to  200  ft.  from  the 
face.  To  get  the  entry  line,  the  foresight  man,  carrying  the  reel,  should  be  sent 
ahead;  and  when  he  is  at  the  face,  the  tape  may  be  brought  in  line  by  sighting 
over  the  entry  sight  plugs  to  a  lamp  held  on  the  reel.  After  completing  the 
side  notes  on  one  entry,  those  on  the  parallel  entry  or  entries  are  taken.  These 
notes  are  entered  in  tabular  form  as  taken,  beginning  at  the  bottom  of  the 
page  and  working  toward  the  top.  The  plusses,  or  distances  from  the  instru- 
ment, are  in  one  column  and  in  other  columns  are  the  offsets  to  the  corners 
of  the  openings,  each  placed  in  the  horizontal  line  of  the  proper  plus. 


SURVEYING 


89 


Each  surveyor  will  have  his  own  set  of  abbreviations:  Common  ones  are 
Bt  for  break-through  (or  cc  for  cross-cut) ,  Rm  for  room,  r  or  rb  for  rib  Thus 
-f-256,  5.5  Btr,  means  that  at  256  ft.  from  the  station  and  5.5  from  the  line 
is  the  corner  of  a  break-through,  which  is  driven  to  the  right.  Sometimes 

these  notes  are  amplified  and  illustrated  by  sketches   x 

as  shown  in  Figs.  1  and  2.  In  most  mines,  particu- 
larly in  the  case  of  butt  entries,  only  the  room 
entry  is  driven  on  points,  the  air-course  being  kept 
as  nearly  on  a  parallel  line  as  possible  by  main- 
taining a  constant  thickness  of  pillar  between  it 
and  the  room  entry.  In  this  case,  the  distance 
from  the  tape  or  the  offset  is  measured  not  only  to 
the  edge  of  the  cross-cut,  but  also  to  the  correspon- 
ding edge  of  it  on  the  air-course  and  to  the  far  side 
of  the  air-course  as  well.  These  three  measure- 
ments might  be  recorded  as  follows:  +  254 
5-26-37  and  +263,  6-26-36.  The  plusses  are  at 
254  and  263  ft.  from  the  station  and  show  that  the 
break  through  is  9  ft.  wide.  At  the  first  plus,  the 
distance  to  the  corner  of  the  break-through  is  5  ft., 
the  distance  to  the  corresponding  corner  on  the  air- 
course  is  26  ft.  (the  pillar  being  26  —  5  =  21  ft.  thick) , 
and  37  ft.  to  the  rib  of  the  air-course,  which  is  37 
—  26  =  11  ft.  wide.  At  the  inner  side  of  the  cross- 


in 

.•.i.    5   —  AC-  —  r 

];;:..  LJ 


16*61 
5  - 135  -S 
•* 

3  -110—6 
4-  -9f  -6 

5  -n  -r 


FIG.  1 


+  */  — J 


cut  the  pillar  is  26- 6  =  20  ft.  thick,  and  the  air-course  36-26=10  ft.  wide. 
The  advantage  in  measuring  continuously  out  from  the  tape  is  twofold:  The 
surveyor  does  not  have  to  leave  the  entry,  and  consequently  has  time  to  enter 
his  notes  in  a  concise  and  cleanly  way  as  the  foresight  man  does  the  running 
around  and,  above  all,  by  standing  on  the  entry  he  is  able  to  keep  the  small 
tape  with  which  the  side  notes  are  taken,  exactly  at  right  angles  to  the  large 
tape;  further,  notes  thus  kept  are  easier  to  map,  requiring  but  one  setting  of 
the  scale,  regardless  of  the  number  of  offsets  taken  from  any  plus. 

It  is  usual  to  make  sketches  as  the  side  notes  are  taken,  in  order  to  illustrate 
and  make  plain  any  points  that  might  be  obscure  to  the  office  man  that  plots 
the  notes.  Two  forms  of  such  notes  are  shown  in  Figs.  1  and  2;  both  are  of  the 
same  entry,  the  air-course  parallel  to  which  is  located  by  measurements  through 
the  break-throughs.  Such  notes  are  begun  at  the  bottom  of  a  page  and 
sketched  upwards  in  the  order  in  which  they  are  taken.  The  form  shown  in 
Fig.  2  is  preferable  as  being  the  clearer.  It  will  be  noticed  that  in  both  cases 
the  air-course  is  located  not  by  continuous  offsets,  but 
by  single  measurements  through  the  pillar,  the  disad- 
vantages of  which  method  have  been  explained.  The 
ends  of  pillars  are  so  rarely  square  that  it  is  commonly 
difficult  to  decide  at  just  what  point  a  break-through 
begins.  This  is  illustrated  at  a  and  b,  Fig.  2.  The 
proper  way  to  locate  such  a  rounded  pillar  is  to  take  a 
plus  and  offset  at  the  point  where  the  pillar  begins  to 
round  (+155,  a)  and  a  second  plus  and  offset  where  a 
sight  tangent  to  the  end  of  the  pillar  may  be  had 
(  +  157,  b).  The  distance  between  the  stations  is  al- 
ways noted  on  the  sketch.  In  the  case  illustrated,  the 
distance  from  the  last  station  to  the  face  is  shown  (8  ft.) 
beyond  the  figures  for  the  length  of  the  line. 

The  survey  of  a  series  of  rooms  in  which  sights  have 
been  placed  is  a  comparatively  simple  matter.  The 
sight  strings  are  lowered  (the  miner  generally  keeps 
them  hung  up  against  the  rib),  and  the  helper  goes  to 
the  face,  unwinding  the  400-ft.  tape  as  he  goes.  The  0 
end  of  the  tape  is  held  at  the  first  or  outer  sight  plug, 
the  distance  of  which  from  the  line  of  the  entry  was 
measured  when  the  sights  were  placed.  The  transit- 
man,  by  means  of  the  room  sights,  places  the  man  at 
the  face  in  line  and  takes  the  side  notes  in  the  manner 
explained.  If  the  rooms  have  not  been  driven  on  sights, 
it  is  customary  to  place  a  tack  in  a  tie  at  the  mouth  of  each  room,  the  tacks 
all  being  on  the  entry  line,  but  at  irregular  distances  apart  as  they  are  placed 
so  that  the  instrumentman  may  see  the  face.  After  the  tacks  are  lined  in, 
their  respective  distances  from  the  instrument  are  measured  and  recorded. 


0 


J. 

:n" 


FIG.  2 


90  SURVEYING 

The  instrument  is  set  over  the  tack  at  the  first  1-09111,  the  vernier  is  set  at  the 
azimuth  or  bearing  of  the  entry,  and  a  backsight  is  taken  upon  some  station. 
The  foresight  man  unwinds  the  tape  on  his  way  to  the  face,  where.he  holds  the 
reel  on  an  X  he  has  marked  on  the  coal  in  chalk,  and  to  which  the  transitman 
takes  a  sight.  The  0  of  the  tape  being  at  the  instrument,  a  line  is  established 
to  the  face,  and  the  side  notes  may  be  taken  as  before  explained.  In  many  in- 
stances a  line  is  run  up  every  other  room  only  (thus,  up  rooms  1,  3,  5,  7,  etc.) 
the  intermediate  rooms  being  located  with  sufficient  accuracy  by  offsets  through 
the  cross-cuts. 

It  sometimes  happens  that  practically  all  the  rooms  on  an  entry  are  so 
blocked  with  falls  of  slate  that  it  is  impossible  to  see  to  the  face  and  thus  sur- 
vey each  room  separately.  In  such  a  case,  a  line  is  run  from  the  entry  up 
some  room  not  blocked  by  falls  and  a  survey  made  of  the  faces  of  the  rooms  by 
running  a  line  along  them  through  the  break-throughs.  If  desired,  stations 
may  be  established  in  ties  in  each  room  near  the  face,  and  sights  taken  down 
the  room  until  stopped  by  the  falls;  or  a  line  may  be  run  down  every  other  room. 
Usually,  offsets  from  the  line  along  the  face  will  locate  the  pillars  and  face  line 
with  sufficient  accuracy  for  all  practical  purposes,  particularly  if  a  good  por- 
tion of  the  rooms  have  been  mapped  from  surveys  made  before  the  fall  of  roof 
took  place. 

Level  Notes. — All  level  notes  are  kept  as  in  outside  work,  with  the  exception 
that,  as  the  rod  is  reversed  in  getting  the  elevation  of  a  station  in  the  roof, 
the  record  of  the  reading  is  prefixed  with  a  minus  sign.  A  record  of  such  a 
reversed  rod,  when  the  target  is  3.78  ft.  below  the  station,  is  recorded  —3.78. 

A  shaft  is  measured  (if  deep)  by  a  fine  steel  wire  running  about  an  accu- 
rately graduated  wheel  (a  sufficient  number  of  turns  being  laid  to  prevent 
slipping)  and  noting  the  number  of  turns  before  the  bottom  is  reached.  The 
wire  may  be  measured  before  and  after  the  operation,  to  insure  against  stretch- 
ing. An  aneroid  mining  barometer,  if  in  good  condition,  will  give  quite  accurate 
results  if  a  number  of  trips  are  made  between  top  and  bottom,  to  give  an  aver- 
age. In  this  case  the  barometer  must  be  left  quiet  10  or  15  min.,  to  be  sure 
that  it  has  expanded  or  contracted  to  the  proper  degree.  For  rough  measure- 
ments, the  length  of  the  winding  rope  between  top  and  bottom  is  taken. 

By  one  of  these  methods  a  bench  mark  should  be  located  below,  connected 
with  the  outside  work,  and  referred  to  tide  water.  The  rod  must  be  reversed 
to  get  the  elevation  of  all  stations  in  the  roof,  and  all  such  readings  are  noted 
with  the  minus  sign,  as  —4.32'  (read  4.32  ft.  below  station).  Roof  stations 
are  almost  certain  to  settle,  from  the  pressure  of  the  superincumbent  rocks. 
To  check  such  settling,  the  distance  from  roof  to  floor  must  be  accurately  meas- 
ured. Some  measure  from  floor  to  rail  of  track;  this  i,s  inaccurate,  as  the  track 
may  be  shifted  or  the  grade  changed  in  making  repairs,  or  to  take  out  a  sag. 

Whenever  a  level  survey  is  begun  the  distance  between  roof  and  floor  should 
be  measured  to  see  if  it  agrees  with  the  notes.  If  it  differs,  the  fact  should  be 
stated  under  the  original  notes,  as  a  check  for  future  work. 

PITCHING  WORK 

The  survey  of  workings  in  highly  inclined  coal  seams  does  not  differ  in 
methods  from  those  employed  in  surveying  mines  in  flat  seams,  but  there  are 
sundry  minor  modifications  in  detail  varying  from  mine  to  mine,  as  peculiar 
or  local  difficulties  have  to  be  overcome. 

Stations. — The  seams  are  usually  folded  along  the  line  of  strike  so  that  the 
entnes,  or  gangways,  that  are  driven  approximately  upon  a  water-level,  are 
curved  and  crooked  to  the  same  extent  as  the  seam.  For  this  reason,  gang- 
ways cannot  be  driven  upon  sights,  and  stations  are  established  as  needed  as 
the  survey  proceeds.  As  these  stations  are  placed  solely  with  a  view  to  obtain- 
ing as  long  or  as  many  sights  from  one  point  as  possible  and  as  the  spads  used 
do  not  have  to  be  set  exactly  on  line,  much  smaller  drills  and  plugs  may  be  used 
in  pitching  than  in  flat  work.  In  some  cases,  the  holes  are  only  $  to  \  in.  in 
diameter  and  but  \  in.  to  1  in.  long  as  a  maximum.  Various  devices  for  quickly 
establishing  these  more  or  less  temporary  stations  have  been  adopted  in  the 
anthracite  regions  of  Pennsylvania,  some  of  which  are  here  given. 

1.  The  simplest  top  station  is  a  shallow  conical  hole,  made  with  the  point 
of  the  foresight  man's  hatchet,  which  is  dug  into  the  top  rock  and  rotated, 
and  is  called  by  some  a  jigger  station.  Corps  using  these  entirely  have  a 
jigger  consisting  of  a  steel-pointed  extension  rod,  with  an  offset  holding  a 
paint  brush.  The  rod  is  long  enough  to  allow  the  point  to ,  be  driven 
into  the  roof  at  any  height,  and  its  rotation  marks  a  circle  with  the  brush, 
which  is  also  used  to  mark  the  number  beside  it.  Centers  are  set  under  such 


SURVEYING  91 

stations  and  sights  are  given  by  another  tool — also  called  a  jigger.  This  is  an 
extension  rod,  beyond  the  upper  end  of  which  projects  a  piece  of  sheet  iron 
shaped  like  an  isoceles  triangle,  with  the  upper  and  smaller  angle  cut  off  so  as 
to  form  an  end  i  in.  broad,  and  in  this  end  is  cut  a  U-shaped  groove. 

The  sights  are  given  and  the  centers  set  by  putting  the  plummet  cord  in 
this  groove,  and  placing  the  end  in  the  jigger  hole  in  the  roof.  The  cord 
must  be  more  than  twice  the  length  of  the  section  of  the  place,  as  it  must 
be  held  in  the  hand,  run  over  the  jigger  notch,  and  hung  vertically  to  the  plum- 
met, which  must  come  to  the  floor  when  the  stations  are  set.  The  rod  and 
cord  are  held  in  the  left  hand,  and  the  right  is  free  to  steady  the  bob,  give  sight, 
or  set  the  center. ;  The  advantages  are  the  quickness  with  which  the  centers 
are  set  and  the  sights  given,  and  the  ease  with  which  the  highest  stations 
are  reached.  The  disadvantages  are  the  impossibility  of  making  the  jigger 
hole  perfectly  conical,  so  that  the  jigger  can  be  set  in  the  same  place  on  two 
successive  sights,  and  the  plummet  cord  will  hang  exactly  in  the  same  place. 

2.  A  twist  drill  ^  in.  in  diameter  is  used  to  make  a  hole  in  the  roof;  a 
piece  of  cord — <>T,  better,  a  copper  wire — is  placed  across  this,  and  a  hardwood 
shoe  peg  is  driven  into  the  hole  and  binds  the  cord  tight.     The  plummet  is 
tied  to  the  lower  end.     A  cord  will  soon  rot,  and,  if  in  the  gangway,  is  pulled 
out  by  the  drivers  for  whip  lashes,  while  the  wire  is  more   permanent;   but 
even  this  will  be  pulled  out  by  catching  in  the  topping  of  a  car  in  a  low  place. 

3.  The  use  of  spads  is  dispensed  with,  and  all  the  stations  put  in  rock 
roof  where  possible.     A  i-in.  twist  drill  makes  a  vertical  hole  1  in.  deep.    Into 
this,  when  a  sight  is  to  be  taken,  the  foresight  man  puts  a  steel  clip  with  ser- 
rated edges.     This  is  made  by  bending  upon  itself  a  thin  piece  of  steel  ^  in. 
wide.     When  the  ends  are  pressed  together  it  will  go  into  the  hole,  and  the 
spring  of  the  sides  and  the  serrated  edges  hold  the  clip  in  the  hole  so  that  it 
is  hard  to  pull  out.     The  cord  passes  through  a  hole  in  the  center  of  the  bend 
and  is,  therefore,  in  the  center  of  the  hole — no  matter  how  the  clip  is  inserted. 
It  is  removed  by  pressing  together  the  ends  of  the  clip.     This  is  the  easiest 
and  quickest  way  of  working,  as  there  is  no  eyehole  to  be  freed  from  dirt  and 
no  knot  to  be  tied  and  untied.     The  hanging  of  the  plummet  takes  a  fraction 
of  a  second,  and  the  station  will  remain  as  long  as  the  roof  keeps  up.     The 
disadvantages  are  the  putting  of  the  holes  inclined  to  the  vertical  by  a  care- 
less man,  and  the  many  roofs  that  are  unfit  for  piercing  with  a  twist  drill. 

Stations  are  generally  marked  upon  some  regular  system,  as  in  flat  work, 
although  in  some  mines  the  objectionable  practice  of  numbering  stations  at 
random  as  they  happen  to  be  placed  still  prevails.  In  the  case  of  leased  prop- 
erties two  surveys  will  commonly  be  made,  one  by  the  operator  and  another 
by  the  land  owner.  When  this  happens,  each  corps  will  have  its  distinctive 
mark  as,  for  example,  the  one  a  circle  and  the  other  a  cross  (+),  with  possibly 
a  distinguishing  letter  selected  from  the  name  of  the  corps  as  a  further  means 
of  identification.  If  both  corps  use  the  same  station  each  will  place  about 
it  its  distinguishing  sign  and  number,  and  the  notes  will  state  "  Sta.  617  =  Sta.  432 
of  (  )  Corps." 

Surveying  Methods. — The  method  of  surveying  gangways  and  keeping 
notes  does  not  differ  from  that  employed  in  flat  seams,  except  from  the  fact 
that  three  consecutive  stations  not  being  in  line,  a  deflection  angle  and  bear- 
ing or  azimuth  must  be  read  at  each  set  up.  As  the  grade  between  stations 
may  be,  in  fact  commonly  is,  pronounced,  particular  attention  must  be  paid 
to  reading  the  vertical  angle.  Parallel  entries  (room  entry  and  its  air-course) 
are  commonly  at  such  a  distance  above  or  below  one  another  that  it  is  not 
usually  possible  to  locate  the  one  by  measurements  made  through  the  cross- 
cuts from  the  other  and  a  separate  line  must  be  run  in  each.  In  case  it  is 
possible  to  locate  the  air-course  by  means  of  offsets  from  the  main  gangway, 
a  clinometer,  frequently  a  brass  protractor  with  a  plummet  attached,  must  be 
hung  from  the  stretched  tape  to  give  its  angle  of  inclination.  All  such  inclined 
offset  sights  must  be  reduced  to  the  horizontal  before  being  mapped. 

If  the  seam  pitches  more  than  30°,  the  rooms  are  worked  with  batteries; 
the  heavy  timbers  forming  these  usually  preclude  the  possibility  of  sighting 
from  the  'gangway  to  the  face.  Work  of  this  kind  is  surveyed  by  lines  out  the 
gangway  and  back  through  the  faces  of  the  rooms,  which  are  generally  clear 
of  timber.  The  line  along  the  face  should  be  tied  into  the  gangway  line  as 
soon  as  opportunity  offers. 

If  the  seam  makes  much  gas,  sights  must  be  taken  to  safety  lamps  unless 
the  portable  battery  hat  lamps  are  used.  The  latter  afford  a  very  satisfactory 
light  and,  being  absolutely  clean,  are  preferable  not  only  to  the  ordinary  safety 
lamp  in  gaseous  mines,  but  to  the  oil  lamp  in  any  mine. 


92  SURVEYING 

The  angle  of  dip  of  the  seam  should  be  taken  at  each  station  and  at  inter- 
mediate points  if  it  changes  radically.  The  thickness  and  quality  of  the  coal 
should  be  observed  frequently  and  changes  of  importance  noted  on  the  map. 

Locating  Pillars  for  Surface  Support. — It  is  customary  to  leave  unmined 
pillars  of  coal  to  support  important  buildings,  reservoirs,  etc.,  on  the  surface. 
The  usual  method  of  locating  these  pillars  is  to  extend  vertical  planes  through 
the  boundary  lines  of  such  objects,  and  leave  untouched  all  parts  of  the  super- 
incumbent beds  embraced  by  those  planes.  This  is  accurate  only  when  the 
strata  are  horizontal  or  vertical,  as  beds  settle  normally  to  the  planes  of  the 
strata  and  not  in  a  vertical  line  in  case  the  open  spaces  are  stowed.  If  the 
spaces  are  left  open,  they  are  first  filled  by  falls,  and  then  the  settling  goes  on 
according  to  the  above  rule.  No  cut  is  necessary  to  show  the  method  of  set- 
tling, and  the  place  where  the  bed  is  to  be  left  untouched  may  be  found  as 
follows:  Draw  a  vertical  section  through  the  point  to  be  supported,  and  also  the 
underlying  bed  on  the  line  of  the  dip  of  the  bed — the  section  being  accurately  drawn 
to  any  scale.  Draw  through  the  extremities  of  the  object  to  be  supported,  lines  to 
the  bed,  which  will  make  right  angles  with  it.  The  space  included  will  give  the 
dimension  of  the  pillar  measured  along  the  dip  of  the  bed,  and  the  dimensions 
of  the  object  taken  at  right  angles  to  the  first  plane  will  give  the  other  dimension  of 
the  pillar. 

MINE  CORPS 

The  number  of  men  required  in  making  a  mine  survey  and  the  nature  of 
their  duties  depend  on  the  nature  of  the  work  to  be  performed.  If  sights 
are  to  be  moved  up  two  men,  the  transitman  and  foresight  man,  can  do  the 
work;  but  if  distances  are  to  be  measured,  a  third  man  is  advisable  to  assist 
with  the  tape  if  time  is  an  object.  The  third  man  is  essential  if  stations  are 
to  be  set  at  exact  distances  from  the  instrument.  In  all  ordinary  survey  work 
where  offsets  are  to  be  taken,  four  men  are  essential  and  five  are  advisable. 
There  must  be  two  men  to  hold  the  long  tape  between  stations  on  the  entry, 
and  two  to  hold  the  tape  with  which  the  offsets  are  taken,  one  of  whom  may 
be  the  transitman,  but  it  is  better  to  have  a  special  crew  for  taking  offsets, 
leaving  the  surveyor  free  to  record  the  notes,  determine  the  position  of  the 
stations,  etc.  Much  time  will  be  saved  if  one  of  the  four  men  can  set  up  the 
transit  and  read  the  angles. 

When  making  a  complete  survey  of  an  extensive  property,  particularly 
in  pitching  work  where  short  sights  are  the  rule  and  branch  gangways  on 
divers  grades  are  common,  it  is  a  material  help  to  place  the  survey  stations 
before  an  attempt  is  made  to  measure  the  angles  or  distances.     To  do  this, 
the  transitman  will  require  two  assistants  and  the  services  of 
a  mine  foreman  or  other  official  familiar  with  the  workings  and 
I  who  will,  in  emergencies,  hold  a  lamp  where  needed.     The 

backsight  man  remains  at  the  station  from  which  the  survey 
>.        I   .         is  to  start  and  the  party  goes  ahead  to  the  most  distant  point 
>v— '   7         therefrom  that  the  lamp  is  visible.      At  this  point,  a  station  is 
established  in  the  roof  with  the  drill,  plug,  and  spad,  and  its 
proper  number  painted  on  the  rib  or  roof.    The  backsight  man 
comes  up  to  the  new  station  and  the  party  g9es  ahead  loca- 
ting a  second  and  succeeding  station  or  stations  as  may  be 
needed.     Very  frequently  several  sights  must  be  taken  from 
one  station,  a  common  case  being  that  shown  in  the  accom- 
panying figure,  where  the  road  forks.     Here  a  helper  is  sent  up 
each  branch,  the  mine  foreman  holding  his  lamp  at  the  back- 
sight, and  the  transitman  shifts  his  position  until  he  finds  a  point  from  which 
the  three  lamps  are  visible  and  there  establishes  a  station.     For  this  work  the 
transit  is  not  necessary,  only  a  bucket  holding  the  brace,  and  drills,  plugs 
spads,  and  a  hatchet,  and  possibly  a  100-ft.  tape,  being  taken  into  the  mine. 

CARE  OF  INSTRUMENTS 

The  transit  should  be  removed  from  the  tripod  and  placed  in  the  instru- 
ment box  with  its  plates  undamped  when  not  in  use.  When  going  to  and 
from  work,  the  transit  should  not  be  carried  on  the  transit  head,  or  the  spindle 
will  become  sprung.  Nor  should  it  be  carried  with  the  arm  crooked  under 
the  telescope  as  the  weight  comes  on  the  axis,  and  that  soon  gets  sprung  so 
that  all  the  adjusting  in  the  world  will  not  make  it  work  right.  When  carried 

the  hand,  it  should  be  reversed  and  the  hand  slipped  under  the  compass 
plate  and  brought  over  so  as  to  clamp  both  plates.  In  this  way  there  will  be 
no  strain  on  any  part.  The  person  carrying  the  transit  should  be  the  first  to 


SURVEYING  93 

ascend  a  slope  or  any  pitching  place  and  the  last  to  descend,  so  that  loose  stones 
or  dirt  that  may  be  dislodged  may  not  affect  or  endanger  the  instrument  or 
trip  the  carrier.  He  must  be  sure  that  the  tripod  head  is  screwed  firmly  on 
the  tripod.  The  possible  slip  of  the  instrument  through  not  observing  this 
caution  may  be  a  source  of  trouble  in  the  failure  to  agree  of  the  duplicate  angles 
read  at  each  station.  As  soon  as  the  corps  comes  back  from  the  mine,  the  tape 
must  be  stretched,  tested,  wiped,  and  piled.  It  can  be  inspected  to  see  if 
marks  are  too  much  worn,  or  it  stands  in  need  of  mending,  the  marking  pot 
is  cleared  of  muck,  and  fresh  white  paint  is  mixed,  if  the  corps  is  going  out  in 
24  hr.;  the  plummets  will  have  their  strings  overhauled  and  freed  from  knots; 
hatchets  will  be  sharpened,  and  axes  ground,  pouches  overhauled,  and  a  supply 
of  tacks  or  spads  taken.  The  transit  is  set  up  and  wiped  with  a  cloth  wet  with 
alcohol,  so  as  to  remove  dirt,  oil,  and  paint.  If  water  has  gotten  between  the 
graduated  limb  and  compass  box,  the  verniers  must  be  uncovered  and  the  whole 
wiped  dry.  If  sulphureted  hydrogen  from  the  powder  smoke  has  tarnished 
the  silver  surfaces  of  any  of  the  graduated  circles,  it  must  be  removed  with 
whiting.  Alcohol  should  be  always  used  instead  of  water,  as  it  will  quickly 
evaporate  and  leave  the  parts  dry.  The  telescope  glasses  are  then  wiped  with 
soft  chamois  leather,  and  the  instrument  is  tested  for  want  of  adjustment  before 
it  is  put  away  in  its  box. 

How  often  the  transit  will  require  adjusting  depends  on  the  quality  of 
the  instrument  and  the  care  it  receives  when  in  use.  When  moving  up  sights 
by  backsighting  and  plunging  the  telescope,  the  adjustment  of  the  vertical 
hair  must  be  perfect  or  the  fpresight  will  be  to  the  right  or  to  the  left  of  the 
prolongation  of  the  line  joining  the  backsight  and  instrument  stations;  this 
adjustment  is,  thence,  of  prime  importance  to  the  surveyor  in  flat  work,  who 
is  chiefly  occupied  in  moving  up  sights  as  the  workings  advance.  This  adjust- 
ment is  also  of  importance  when  reading  deflection  angles  by  the  methods 
explained.  Sights  may  be  set  without  regarding  the  adjustment  of  the  ver- 
tical hair,  by  setting  the  vernier  at  0°,  backsighting,  and  turning  off  an  angle 
of  180°,  but  this  involves  two  accurate  readings  and  settings  of  the  yernier. 
Deflection  angles  may  be  determined  in  the  same  way,  by  subtracting  the 
included  angle  from  180°,  and  with  the  same  objections  to  the  method.  A 
method  sometimes  employed  to  move  up  sights,  which  is  independent  of  the 
cross-hair  adjustment  and  does  not  require  the  reading  of  an  angle  is  as  fol- 
lows: Assume  that  stations  numbered,  say,  200  and  201  are  those  nearest 
the  face  and  that  Sta.  202  is  to  be  placed  on  the  line  200-201  prolonged.  Set 
up  at  Sta.  200,  and  foresight  upon  Sta.  201,  remove  the  plumb-bob  and  cord 
from  Sta.  201  and  set  Sta.  202  at  the  proper  distance  ahead  on  the  line  thus 
prolonged. 

For  plumbing  wet  shafts,  kerosene  resists  the  extinguishing  power  of  water 
better  than  fish  oil,  and  is  less  readily  blown  out  by  a  strong  ventilating  cur- 
rent. It  makes  more  smoke,  and,  in  tight  headings,  or  mines  with  poor  ven- 
tilation, with  a  large  party,  fouls  the  air  much  more  readily  than  fish  oil.  Some- 
times a  mixture  of  the  two  is  burnt  in  very  drafty  places,  where  it  is  hard  to 
maintain  a  light.  Kerosene  is  burned  in  the  plummet  lamp  unless  it  is  used 
with  the  safety  attachment.  Sweet  oil,  or  any  oil  burning  without  smoke, 
must  then  be  used.  Smoke  clogs  the  openings  in  the  gauze,  restricts  the 
entry  and  escape  of  gases,  and,  especially  if  the  gauze  is  damp  with  oil,  may 
ignite  and  communicate  the  flame  from  within  to  the  outside  body  of  gas. 


TRAVERSING  AND  MAPPING 

TRAVERSING 

The  latitude  of  a  point  is  its  distance  north  or  south  of  some  parallel  of 
latitude,  or  line  running  east  and  west.  The  departure  of  a  point  is  its  distance 
east  or  west  of  some  meridian,  or  line  running  north  and  south;  it  is  the  same 
as  the  longitude  of  the  point.  Latitudes  are  measured  in  a  direction  at  right 
angles  to  the  departures.  The  distance  that  one  end  of  a  line  is  due  north 
or  south  of  the  other  end  is  the  difference  of  latitude  of  the  two  ends  of  the 
line,  and  is  called  the  northing  or  southing,  or  simply  the  latitude  of  the  end 
considered.  The  distance  that  one  end  of  a  line  is  due  east  or  west  of  the  other 
end  is  the  difference  in  longitude  of  the  two  ends  of  the  line,  and  is  called  the 
easting  or  westing,  or  simply  the  departure. 

The  process  of  calculating  and  tabulating  the  latitudes  and  departures  of  the 
courses  of  a  survey  is  known  as  traversing  the  survey.  To  do  this,  all  distances 


94 


SURVEYING 


must  either  be  measured  horizontally  or  be  reduced  to  horizontal  distances 
by  means  of  the  vertical  angle.  The  horizontal  angles  must  either  be  read  as 
auadrant  courses,  or  must  be  reduced  from  azimuth  to  quadrant  courses. 

Latitude-=  distance  X  cos  of  bearing 
Departure  =  distance  X  sin  of  bearing 

Below  is  given,  in  tabular  form,  the  calculated  notes  of  a  closed  com- 
nass  survev  All  the  work  shown  should  be  kept  in  ink  m  the  permanent, 
office  record  books.  The  notes  in  the  first  three  columns,  headed  Station 
Bearing  Distance,  are  the  same  as  the  corresponding  columns  of  the  held 
notes.  If  the  field  notes  show  that  the  distances  were  measured  along  the 

TRAVERSED  SURVEY  NOTES 


Latitude 

Departure 

Total 
Latitude 

Total 
Departure 

tion 

Bearing 

tance 

A 

.g 

^ 

tn 

£ 

£ 

| 

% 

3 

a 
W 

£ 

S 

& 

£ 

1-2 

N35°E 

270.00 

221 

155 

221 

155 

2-3 

N  83°  30'  E 

129.00 

15 

128 

236 

283 

3-4 

S57°E 

222.00 

121 

186 

115 

469 

4-5 

S  34°  15'  W 

355.00 

293 

200 

178 

269 

5-1 

N  56°  30'  W 

322.56 

178 

269 

0 

0 

0 

0 

414 

414 

469 

469 

slope,  as  would  be  the  case  in  an  ordinary  transit  survey,  two  extra  columns 
should  be  provided,  one  for  the  measured  distances  and  another  for  the  ver- 
tical angles.  If  the  elevations  are  to  be  deduced  from  the  vertical  angles, 
something  that  is  necessary  if  a  topographic  map  of  the  property  is  to  be  made, 
two  additional  columns  will  be  needed,  in  one  of  which  should  be  placed  the 
differences  in  elevation  of  consecutive  stations,  and  in  the  other,  the  total  ele- 
vation of  each  station  above  sea  level. 

From  the  latitudes  and  departures  of  the  individual  stations,  it  is  customary 
to  determine  the  latitude  and  departure  of  each  station  with  reference  to  the 
first  station  of  the  survey.  These  are  commonly  called  the  total  latitudes  and 
total  departures,  or  total  northings,  southings,  eastings,  or  westings,  as  may  be. 

The  latitudes  and  departures  of  the  individual  stations  are  calculated  by 
the  formulas  given.  The  total  latitudes  and  departures  are  obtained  by  adding 
continuously  and  algebraically  to  the  assumed  latitude  and  departure  of  the 
first  station,  the  latitudes  and  departures  of  the  individual  stations.  The  first 
station  is  frequently  called  the  origin  of  coordinates,  and  its  northing,  southing, 
easting,  and  westing  are  commonly  taken  as  zero  (0).  As  a  check  on  entering 
the  latitudes  and  departures  in  the  right  columns,  it  should  be  noted  that 
when  the  bearing  is  less  than  45°,  the  departure  is  less  than  the  latitude; 
and  when  the  bearing  is  greater  than  45°,  the  departure  is  greater  than  the 
latitude. 

Errors  in  Closure. — If  the  survey  is  a  continuous  one  around  a  tract,  and 
ending  at  the  place  of  beginning,  the  sum  of  the  northings  should  equal  the 
sum  of  the  southings,  and  the  sum  of  the  eastings  should  equal  the  sum  of  the 
westings.  Or,  in  other  words,  the  sum  of  all  the  latitudes  north,  should  equal 
the  sum  of  all  the  latitudes  south;  and  the  sum  of  all  the  departures  east, 
should  equal  the  sum  of  all  the  departures  west.  It  is  evident  that  by 
coming  back  to  the  place  of  beginning  the  surveyor  has  traveled  the  same 
distance  north  as  he  has  south,  and  the  same  distance  east  as  he  has  west. 
However,  in  practice,  as  has  been  intimated  under  the  heading  Closing  Sur- 
veys, no  such  agreement  is  possible.  In  fact,  should  a  survey  actually  bal- 
ance or  close,  it  should  be  assumed  that  the  closure  is  apparent  and  not  real; 
the  sum  of  the  errors  in  one  direction  being  exactly  offset  by  the  sum  of  the 
errors  in  the  opposite  direction. 

.  The  error  in  closure  of  a  survey  is  the  ratio  that  the  length  of  the  line  join- 
ing the  initial  and  final  stations  (as  determined  by  the  survey)  bears  to  the 


SURVEYING  95 

entire  distance  run.  The  length  of  this  line  is  that  of  the  hypotenuse  of  a 
right-angled  triangle  of  which  the  errors  in  latitude  and  departure  are  the  two 
sides.  Thus,  if  the  coordinates  of  the  starting  point  are  0,  and  after  running 
around  a  tract  of  land  a  distance,  by  survey  of,  say,  25,000  ft.,  it  is  found  that 
the  total  eastings  exceed  the  total  westings  by  4.25  ft.,  and  that  the  total 
northings  exceed  the  total  southings  by  1.5  ft.,  the  survey  will  have  failed  to 
close  by  V4.252+1.502=4.51  ft.  The  error  in  closure  will  be  25,000-^-4.51 
=  1  ft.  in  5,543ft.  (about).  The  bearing  of  the  line  of  error  (as  it  may  be  called) 
may  be  found  from  the  formula: 

Tan  bearing    err°r  in 


error  in  latitude  l.o 
from  which  the  bearing  is  N  70°  34'  E.  That  is  to  say,  owing  to  errors  in 
measurement,  the  final  point  instead  of  coinciding  with  the  initial  point,  is 
found  to  be  N  70°  34'  E,  4.51  ft.  from  it. 

Balancing  Surveys.  —  In  surveys  made  with  the  compass  and  chain,  it  may 
be  safely  assumed  that  the  failure  to  close  is  as  much  due  to  errors  in  angular 
measurement  as  in  chaining.  In  this  case,  the  latitudes  and  departures  may 
each  be  corrected  by  certain  amounts,  some  being  increased  and  other  being 
decreased,  until  a  perfect  balance  is  secured  between  the  northings  and  south- 
ings on  the  one  hand  and  between  the  eastings  and  the  westings  on  the  other 
by  means  of  the  following  rule: 

Rule  I.  —  The  correction  to  be  applied  to  any  particular  latitude  or  departure 
is  to  the  total  error  in  latitude  or  departure  as  the  corresponding  distance  is  to  the 
entire  distance  covered  by  the  survey. 

Each  correction  is  to  be  applied  in  such  a  way  as  to  diminish  the  whole 
error  at  the  particular  station. 

In  the  case  of  surveys  made  with  the  transit,  the  angular  measurements 
are  highly  accurate  and  it  is  very  probable  that  errors  in  closing  are  due  almost 
entirely  to  incorrect  chaining.  This  is  particularly  so  if  the  sum  of  the  deflec- 
tion angles  is  360°  (in  which  case  the  survey  closes  exactly  in  angle)  or  is  not 
more  than  1'  different  for  each  mile  or  two  (averaging,  say,  fourteen  stations 
per  mile)  surveyed.  In  this  case  the  rule  for  determining  the  corrections  to 
be  applied  to  each  individual  latitude  or  departure  is: 

Rule  II.  —  The  correction  to  be  applied  to  any  particular  latitude  or  departure 
is  to  the  whole  error  in  latitude  or  departure  as  the  corresponding  latitude  or  depar- 
ture is  to  the  arithmetical  sum  of  all  the  latitudes  or  departures. 

As  before,  each  correction  should  be  so  applied  as  to  diminish  the  whole 
error  at  each  station. 

Locating  Special  Work.—  The  rules  given  for  finding  the  error  in  closure  of 
a  survey,  as  well  as  its  bearing,  are  applied  to  determine  the  length  and  bearing 
of  a  line  (as  that  of  a  tunnel  or  entry)  required  to  connect  two  points  whose 
latitudes  and  departures  are  known.  Thus,  suppose  that  it  is  required  to  connect 
Sta.  57,  whose  latitude  is  2,046,25  N  and  departure  18.76  E,  with  Sta.  49  whose 
latitude  is  1,625.75  N  and  departure  159.26  E.  It  is  apparent  that  Sta.  49  is 
2,046.25-1,625.75  =  420.50  ft.  south,  and  159.26-18.76=140.50  ft.  east  of 
Sta.  57.  The  distance  between  the  two  stations  is  V420.502-f-  140.502  =  443.35  ft. 
Again, 

_      ,        .         difference  in  departures     140.5      00.10 
Tan  bearing  =    ,.„  —  =  77^-5.  =  .33413 

difference  in  latitudes      420.5 

whence  the  angle  is  18°  29'.     As  Sta.  49  is  south  and  east  of  Sta.  57,  the  bear- 

ing and  length  of  the  line  joining  Sta.  57  and  Sta.  49  is  S  18°  29'  E,  443.35  ft. 

It  must  be  noted  that  the  exact  tangent  of  18°  29'  is  .33427,  or  .00014  more 

than  the  calculated  one.     In  the  distance  between  the  stations,  443.35  ft., 

a  line  run  on  a  bearing  of  S  18°  29'  E  will  miss  Sta.  49  by  .06  ft.     Hence,  an 

exact  closure  cannot  generally  be  obtained  with  an  instrument  graduated  to 

minutes  only.     The  distance  between  the  stations  may  be  found  without  having 

to  extract  the  square  root,  the  bearing  having  been  obtained,  by  the  formula 

_.  difference  in  latitudes      420.5  -„  - 

Distance  =  —  —  =  -^  -r^  =  443.36  ft. 

cos  of  bearing  .94842 

MAPPING 

Laying  Off  a  Map.  —  It  is  very  commonly  the  case  that  a  mining  property  has 
its  greatest  linear  dimension  in  any  other  direction  than  an  east-and-west 
line.  Thus  a  property  containing,  say,  2,000  A.,  might  have  approximate 
dimensions  of  2$  mi.  in  a  general  northeast  and  southwest  direction,  and  of 


96  SURVEYING 

H  mi.  at  right  angles  thereto.  Mine  maps  are  required  by  the  .laws  of  most 
states  to  be  on  a  scale  of  100  ft.  to  1  in.,  although  200  ft.  to  1  in.  is  permissible 
in  some  cases.  On  the  larger  scale,  the  property  just  described  would  have  a 
northeast  and  southwest  length  of  128  in.  (10  ft.  8  in.)  and  a  length  at  right 
angles  thereto  of  79.2  in.  (6  ft.  7.2  in.).  It  is  apparent  that  if  such  a  property 
is  mapped  with  its  meridian  at  right  angles  to  the  length  of  the  paper  (that 
is  like  ordinary  maps  in  an  atlas  with  the  north  toward  the  top)  a  goodly 
portion  of  the  survey  will  extend  both  above  and  below  the  top  and  bottom 
edges  of  any  paper  now  made  for  draftsmen's  use.  Such  a  property  must  be 
laid  down  with  its  longest  dimension  parallel  to  the  longest  dimension  ot  the 
paper,  regardless  of  the  direction  of  the  meridian. 

To  determine  the  best  way  to  lay  off  the  map  on  the  paper,  it  is  customary 
to  make  a  skeleton  map  of  the  property  on  a  small  scale,  say,  on  one  of  1,000  ft. 
to  1  in.  (in  the  foregoing  case  the  dimensions  would  be  12.8  in.  X  7.92  in.)  and  lay 
this  upon  a  sheet  of  paper  that  represents,  on  the  same  scale,  the  paper  to 
be  used  for  the  finished  map.  By  shifting  one  upon  another,  a  position  will 
eventually  be  found  where  the  property  may  be  drawn  upon  the  sheet.  By 
pricking  through  with  a  needle  point,  the  stations  may  be  transferred  from  the 
skeleton  map  to  the  sheet  representing  the  drawing  paper,  and  the  connecting 
lines  drawn.  A  border  should  be  drawn  around  this  minature  map  at  one-tenth 
the  distance  from  the  edge  that  the  border  will  be  from  the  edge  of  the  large  map. 
There  will  now  be  available  for  laying  off  the  paper,  a  minature  reproduction  of 
the  outlines  of  the  finished  map.  To  draw  the  coordinate  lines,  lay  off  upon  the 
large  sheet,  using  their  location  on  the  small  map  as  a  guide,  the  most  easterly 
and  most  westerly  corners  of  the  property.  Any  other  two  corners  will  do,  pro- 
vided they  are  separated  by  as  long  a  distance  as  is  conveniently  possible. 
Connect  the  selected  corners  by  a  line  and  calculate  the  bearing  there9f.  If 
it  is  assumed  that  this  line  has  a  bearing  of  N  58°  30'  E,  all  lines  making  an 
angle  of  58°  30'  to  the  left  of  this  base  will  be  north-and-south  lines,  or 
meridians. 

When  mapping  extensive  surveys,  it  is  a  slow  and  usually  an  inaccurate 
process  to  measure  from  the  initial  station  the  total  latitude  and  departure  by 
which  every  other  station  is  located,  as  many  of  the  distances  will  be  very  long, 
from  5,000  to  10,000  ft.  or  more  (from  50  to  100  in.  on  the  scale  of  the  map) ; 
therefore,  mine  maps  are  laid  off  in  a  series  of  squares  1,000  ft.  (10  in.)  on 
edge  with  their  sides  in  the  meridian.  To  locate  a  station  whose  coordinates 
are,  say,  latitude  8,250  N  and  departure  6,500  E,  measure  along  the  meridian 
marked  6,000  a  distance  250  ft.  north  of  its  intersection  with  the  parallel 
marked  8,000.  At  this  point  erect  a  perpendicular  to  the  meridian  (or  draw 
a  line  parallel  to  the  latitude)  and  lay  off  along  it  a  distance  of  500  ft.  to  the 
east.  The  point  thus  plotted  will  have  the  coordinates  in  question. 

To  draw  these  squares,  place  a  meridian,  determined  by  the  method  ex- 
plained, upon  the  map  somewhere  near  the  middle.  Upon  this,  mark  a  series 
of  points  exactly  10  in.  apart.  Through  the  extreme  points  draw  perpendiculars 
to  the  meridian  by  any  of  the  methods  of  geometry.  Upon  these  parallels 
lay  off  spaces  of  10  in.  both  east  and  west  from  the  meridian  and  through  these 
points  draw  the  remaining  meridians.  On  the  most  eastern  and  western  mer- 
idian thus  established,  lay  off  further  spaces  of  10  in.,  the  points  marking  which 
may  be  connected  with  those  on  the  first  meridian  laid  down  upon  the  map, 
thus  completing  the  work.  These  squares  should  be  laid  off  in  pencil  and 
lightly  inked  in  with  the  utmost  accuracy.  The  work  should  be  done  during 
a  single  day  when  conditions  of  temperature  and  humidity  are  as  nearly  con- 
stant as  possible,  as  atmospheric  changes  will  cause  paper  to  expand  or  con- 
tract and  thus  change  the  size  of  the  squares.  In  the  case  of  large  properties, 
the  proper  placing  of  the  meridians  and  parallels  so  that  all  the  corners,  etc. 
will  come  on  one  sheet  of  paper  is  a  matter  of  painstaking  work.  Often  the 
shifting  of  the  meridians  or  parallels  1  or  2  in.  either  way  will  accomplish  this 
much  to  be  desired  result;  and  this  can  only  be  done  by  cut-and-try  methods 
combined  with  more  or  less  calculation  and  recalculation  of  the  coordinates 
of  the  extreme  points  as  the  meridians  and  parallels  are  shifted.  If  the  map 
will  extend  over  upon  a  second  sheet,  this  should  be  laid  off  in  squares  in  a  sim- 
ilar manner  to  the  first,  and  should  have  laid  down  upon  it  enough  of  the  work- 
ings, etc.,  appearing  last  upon  the  first  sheet,  that  it  may  be  used  independently 
of  it.  In  other  words,  the  second  sheet  of  the  map  should  overlap  for  2  or  3  in. 
on  that  of  the  first  sheet. 

The  question  of  numbering  the  meridians  and  parallels  or,  what  is  in 
effect  the  same  thing,  determining  the  location  of  the  zero  of  coordinates,  is  a 
matter  of  importance.  In  most  maps,  some  one  meridian  will  be  marked  0, 


SURVEYING  97 

those  to  the  right  of  it  will  be  designated  as  1  E,  2  E,  3  E,  etc.,  and  those  to 
the  left,  1  W,  2  W,  3  W,  etc.  Similarly,  some  one  parallel  will  be  marked  0, 
and  those  above  and  below  it  will  be  respectively  1  N,  2  N,  3  N,  etc.,  and  1  S, 
2  S,  3  S,  etc.  A  better  plan  is  to  call  the  most  westerly  meridian  and  most 
southerly  parallel  0.  In  this  way  all  the  latitudes  will  be  north  and  all  the 
departures  will  be  east,  all  additions  made  to  determine  the  total  latitudes  and 
departures  will  be  algebraic  without  shifting  from  one  column  to  another  and 
there  will  be  but  two  columns  for  the  total  latitudes  and  departures  instead  of 
four.  Under  this  plan,  there  is  much  less  liability  to  error  when  making  cal- 
culations involving  differences  in  latitudes  and  departures,  for  these  differences 
will  always  be  obtained  by  subtraction  and  never  by  addition,  as  is  fre- 
quently the  case  when  the  first  system  of  numbering  the  meridians  and 
parallels  is  used.  For  example,  under  the  first  system  two  points  having 
latitudes  of  200  N  and  300  S,  respectively,  will  differ  in  latitude  by  200  +  300 
=  500  ft.;  under  the  second  system,  these  same  points  will  have  latitudes  of, 
say,  800  N  and  300  N,  the  difference  being  800-300  =  500,  as  before. 

Mapping  the  Field  Notes. — The  stations  made  to  determine  the  bounda- 
ries of  the  property  are  first  placed  upon  the  map,  using  the  total  latitude 
and  departure  of  each  for  this  purpose;  the  method  having  been  described. 
After  two  consecutive  stations  have  been  plotted,  as  a  check  on  the  work, 
the  distance  between  them  should  be  measured.  This  should  agree  with  the 
horizontal  distance  reduced  from  the  field  measurements.  After  the  survey 
stations  are  plotted,  the  property  corners  should  be  mapped  in  the  same  way, 
checking  up  the  plotted  distance  between  them  and  the  survey  station  from 
which  they  were  determined.  By  joining  these  corners,  the  outer  boundaries 
of  the  property  will  now  appear  upon  the  map.  Preferably  by  means  of  a  pro- 
tractor reading  to  minutes  and  using  any  convenient  meridian  as  a  base,  the 
side  shots  to  buildings,  runs,  etc.,  as  determined  from  each  station,  should 
be  laid  off.  These  directions  should  be  transferred  to  the  proper  station  and 
the  distance  measurements  laid  off  thereupon;  this  gives  all  the  points  taken 
from  that  station.  After  all  the  side  shots  are  taken,  the  map  may  be  inked 
in,  provided  all  possible  checks  prove  that  the  penciled  work  is  correct.  If  a 
topographic  map  is  desired,  the  stadia  sights  taken  to  determine  the  topography 
may  be  located  and  contours,  10,  20,  25,  or  50  ft.  apart  drawn  in.  The  flatter 
the  country,  the  smaller  should  be  the  contour  interval.  In  ordinary  rolling 
country,  where  the  contours  merely  serve  as  a  guide  to  determine  the  width 
of  pillar  in  the  mine,  a  contour  interval  of  25  ft.  suffices;  in  mountainous  coun- 
try, 50  ft.  is  close  enough. 

The  mine  workings  are  mapped  in  exactly  the  same  way  as  the  surface 
features  so  far  as  survey  lines  are  concerned,  but  there  is  a  difference  in  mapping, 
as  there  is  in  taking,  the  side  shots.  On  the  surface,  points  are  determined  by 
noting  their  bearing  and  distance  from  some  station;  underground,  points  are 
located  by  offsets  at  right  angles  to  the  line  of  sight  and  must  be  so  mapped. 

Property  corners  are  marked  by  a  small  circle  in  black  and  property  lines 
are  reasonably  heavy  ones  joining  adjacent  circles,  but  not  passing  within  the 
circumference,  the  exact  corner  being  a  pin  point  at  the  center  of  the  circle. 
On  the  map  should  appear  the  bearing  and  length  of  all  property  lines.  A 
description  of  the  corner  should  be  given  as  W.  O.  (for  white  oak),  stone,  etc. 
If  the  original  corner  is  gone  and  something  else  is  in  place  the  description 
should  say  "W.  O.,  now  stone,"  or  "Stone,  orig.  W.  O.,"  or  "Stone  (W.  O.)," 
the  original  corner  being  placed  in  parentheses. 

The  boundaries  of  all  the  individual  properties  making  up  the  entire  tract 
should  appear  on  the  map,  as  well  as  the  name  of  the  owner  of  each  and  the 
acreage.  All  reservations  from  under  which  the  coal  cannot  be  mined  or  to 
which  the  company's  rights  are  unusual  or  peculiar,  must  be  carefully  mapped. 
The  names  of  the  owners  of  adjacent  properties  should  appear.  The  outcrop 
of  all  workable  seams  should  be  given  in  brown,  as  well  as  the  location  of  all 
test  openings  thereon  and  the  thickness  and  character  of  the  coal.  The  posi- 
ti9n  of  all  oil  and  gas  wells  should  be  accurately  determined  and  mapped, 
with  memoranda  as  to  their  opera'tion,  production  (if  any)  etc.  Abandoned 
and  improperly  plugged  wells  are  a  constant  source  of  danger  in  some  parts 
of  the  country  and  too  much  time  cannot  be  spent  in  accurately  locating  them. 
The  base-line  monuments,  together  with  the  azimuth  or  bearing  of  the  line 
joining  them  should  be  given,  as  well  as  all  meridian  reference  lines  connected 
therewith. 

Mine  workings  should  be  shown  in  black,  the  stations  being  denoted  by 
small  circles  in  the  same  color.  The  numbers  of  all  stations  and  their  eleva- 
tion above  sea  level  should  appear.  If  more  than  one  seam  is  worked,  the 


98  SURVEYING 

operations  in  the  separate  seams  should  be  given  a  distinctive  color,  none  of 
which  (except  the  principal  workings  which  may  be  shown  in  black)  should 
be  used  in  mapping  any  surface  feature. 

When  mapping  the  operations  in  a  single  seam,  it  is  not  unusual  to  outline 
the  work  done  by  different  colors  to  represent  the  extraction  during  each  semi- 
annual period.  Thus,  the  workings  advanced  between  January  1  and  June  30, 
1914,  would  be  shown,  say,  in  blue;  those  from  July  1  to  December  31,  1914, 
in  red;  those  from  January  1  to  June  30,  1915,  in  green;  and  similarly  for  each 
succeeding  period  9f  6  mo.  While  this  serves  to  show  the  extent  of  the  oper- 
ations for  any  semiannual  peripd,  and  this  is  desirable,  it  makes  an  ugly  map, 
and  many  prefer  to  plat  the  mine  workings  in  one  single  color,  drawing  a  dash 
across  the  face  of  the  working  places  after  each  semiannual  posting  has  been 
made.  The  date,  as  6-30-1914,  placed  by  a  dash  indicates  the  date  at  which 
the  posting  was  made.  If  many  seams  are  worked  under  the  one  property 
and  all  are  platted  on  the  same  sheet,  it  leads  to  confusion  and  it  is  a  better 
plan  not  to  map  them  this  way,  but  to  make  a  series  of  property  maps,  one 
for  the  workings  of  each  seam,  or  at  the  most,  for  the  workings  of  two  adjacent 
seams.  Then,  if  it  is  desired  to  note  the  relationship  between  the  workings 
of  all  the  seams,  a  tracing  may  be  made  upon  which  the  workings  in  all  the 
seams  are  given. 

Coloring  a  Map. — 'The  survey  line  by  which  the  corners  were  determined 
is  frequently  placed  on  the  map  in  red  ink.  It  is  not  necessary  to  give  the  bear- 
ings and  distances  of  the  lines,  but  the  stations  should  be  numbered  and  their 
elevation  above  sea  level  given  if  this  has  been  determined.  Contour  lines 
appear  in  brown,  those  marking  even  hundreds  of  feet  aboye  sea  level  being 
heavier  than  intermediate  ones.  Small  brooks  appear  as  a  single  line  of  Prus- 
sian blue;  larger  ones  are  shown  by  two  parallel  lines;  and  creeks  and  rivers 
have  their  banks  shown  as  they  actually  exist.  If  a  creek  is  named,  this  name 
should  appear  on  the  map.  Roads  are  denoted  in  brown  and  should  appear 
in  their  legal  width.  Houses  are  commonly  outlined  in  black,  as  are  tipples, 
coke  ovens,  etc.  Railroads  are  denoted  by  fine  parallel  lines,  marked  with  black 
dashes  about  fg  in.  in  length;  black-and-white  dashes  of  the  same  length  alter- 
nating. 

It  is  a  question  whether  it  is  advisable  to  tint  a  map  with  water  colors  or 
not.  If  the  map  is  a  final  or  finished  one  upon  which  no  further  operations 
will  appear  it  is  advisable  to  tint  it  properly;  but  in  the  case  of  a  working  map, 
there  will  be  so  many  erasures  as  the  workings  advance,  as  pillars  are  drawn, 
as  new  lines  of  railroad  are  constructed,  etc.,  that  the  effect  of  the  tinting  is  soon 
spoiled.  When  tinting  is  used,  the  inner  edge  of  the  property  lines  should 
receive  a  wash  in  India  ink  (which  will  appear  in  dark  gray-black)  about  i  in. 
wide.  Crop  lines  should  receive  a  similar  but  narrower  band  in  brown.  Roads 
should  have  a  light  wash  in  yellow  ocher,  and  narrow  streams,  those  appear- 
ing less  than  1  in.  in  width  (100  ft.  wide  in  nature)  a  light  wash  in  Prussian 
blue.  Large  ponds  and  wide  streams  if  tinted  for  their  full  width  should  be 
colored  with  indigo,  as  the  Prussian  blue  is  rather  too  vivid.  Frequently, 
streams  and  lakes  are  not  colored  for  their  full  width  with  a  flat  tint;  instead 
the  color  is  applied  with  the  maximum  intensity  at  the  shore  line,  being  grad- 
ually drawn  out  to  nothing  1  in.  or  less  therefrom.  The  projections  of  houses, 
barns,  tipples,  etc.,  should  receive  a  light  wash  of  crimson  lake.  Theoretically, 
unworked  areas  of  coal  should  be  given  a  flat  tint  of  India  ink,  the  tint  being 
removed  to  correspond  to  the  mining  operations.  This  is,  of  course,  not 
practicable,  so  it  is  customary  to  leave  the  unworked  coal,  white,  and  to  color 
the  excavations  made  in  mining.  As  stated,  this  makes  an  attractive  map  when 
first  completed,  but  as  the  workings  advance  and  pillars  are  drawn,  the  scratch- 
ing out  of  previously  applied  tints,  produces  an  unpleasant  effect. 

I  he  paper  upon  which  a  mine  map  is  made  should  be  the  very  best  eggshell, 
linen  mounted,  obtainable.  When  not  in  use  it,  with  all  other  permanent 
records,  should  be  kept  in  a  fireproof  vault. 


SURVEYING 


99 


DETERMINATION  OF  MERIDIAN 

LATITUDE  AND  LONGITUDE 

If  a  meridian,  that  is,  a  circle  passing  through  the  axis  of  the  earth,  is  passed 
through  a  given  point  of  the  earth's  surface,  the  angular  distance  of  the  point 
from  the  equator,  measured  on  the  meridian,  is  the  latitude  of  that  point.  A 
plane  parallel  to  the  equator  cuts  the  earth's  surface  in  a  circle  called  a  par- 
allel of  latitude.  All  the  points  on  a  parallel  of  latitude  have  the  same  latitude. 
The  longitude  of  a  place  is  the  angle  that  the  plane  of  the  meridian  of  the 

S'ace  makes  with  the  plane  of  a  reference  meridian  (usually  the  meridian  of 
reenwich).     This  angle  may  be  measured  on  the  equatorial  circle  or  on  the 
parallel  of  latitude  of  the  given  place.     Longitude  is  counted  from  the  reference 
meridian  toward  the  west. 

CELESTIAL  SPHERE 

The  celestial  sphere  is  an  imaginary  sphere  enclosing  all  the  heavenly  bodies. 
It  is  of  such  enormous  dimensions  that,  in  comparison  with  it,  the  earth  may 
be  considered  as  a  mere  dot.  The  earth's  axis  produced  indefinitely  is  called 
the  axis  of  the  celestial  sphere.  This  axis  intersects  the  celestial  sphere  in  two 
points,  called  the  north  pole  and  the  south  pole  of  the  heavens.  All  the  great 
circles  of  the  celestial  sphere  passing  through  this  axis  are  called  hour  circles. 
The  circle  in  which  the  plane  of  the  equator  intersects  the  celestial  sphere  is 
called  the  celestial  equator.  The  point  on  the  equator  that  the  sun  in  its 
apparent  motion  over  the  celestial  sphere  crosses  on  March  21,  as  it  passes 
from  the  southern  to  the  northern  hemisphere,  is  called  the  vernal  equinox. 

REFERENCE  CIRCLES 

The  accompanying  illustration,  which  represents  the  celestial  hemisphere, 
shows  all  the  reference  circles  that  are  used  for  determining  the  position  of  a 
heavenly  body.  O  is  the  position  of  the  earth;  OP,  one-half  of  the  axis  of  the 
celestial  sphere,  P  being  the  north  pole;  VQV '  L,  part  of  the  celestial  equator; 
X,  the  vernal  equinox;  and  YXC,  part  of  the  sun's  path.  PX  is  the  hour 
circle  passing  through  X,  called  the  equinoctial  colure.  S  is  any  star,  and  PSA 
is  the  hour  circle  passing  through  it.  XA  is  the  right  ascension  of  the  star. 


which  is  the  arc  on  the  equator  measured  eastwards  from  the  vernal  equinox 
to  the  hour  circle  passing  through  the  star.  A  S  is  the  declination  of  the  star; 
that  is,  its  angular  distance  from  the  equator.  The  declination  is  considered 
positive  when  the  star  is  north  and  negative  when  south  of  the  equator.  The 
complement  angle  of  the  declination,  SP,  is  called  the  polar  distance  of  the  star. 

The  zenith  of  a  point  on  the  earth's  surface  is  the  point  Z  in  which  the  line 
passing  through  the  center  of  the  earth  and  the  given  point  intersects  the  celes- 
tial sphere  above  the  given  point.  The  horizon  is  the  plane  NYM  passing 
through  the  given  point  and  perpendicular  to  this  line. 

The  celestial  meridian  of  a  given  point  is  a  great  circle  passing  through  the 
zenith  of  the  point  and  the  poles.  The  celestial  meridian  cuts  the  horizon  in 
two  points  2V  and  M,  called,  respectively,  the  north  point  and  the  south  point. 


100  SURVEYING 

A  vertical  circle  is  one  that  passes  through  the  zenith  and  is  perpendicular 
to  the  horizon. 

The  prime  vertical  is  the  vertical  circle  at  right  angles  to  the  meridian;  it 
intersects  the  horizon  in  two  points  V  and  V,  called  the  west  and  the  east  point, 

The  altitude  of  a  heavenly  body  is  its  angular  distance  DS  from  the  horizon, 
measured  along  the  vertical  circle  passing  through  the  body.  The  zenith 
distance,  is  the  angular  distance  SZ  of  the  star  from  the  zenith,  measured  along 
the  same  circle.  The  zenith  distance  is  the  complement  of  the  altitude. 

The  azimuth  of  a  star  is  the  angle  in  the  plane  of  the  horizon  intercepted 
by  the  planes  of  the  meridian  and  the  vertical  circle  passing  through  the  star. 
It  is  measured  from  the  north  point  toward  the  east  or  from  the  south  point 
toward  the  west.  NMD  is  the  azimuth  of  S,  measured  from  the  north  toward 
the  east,  and  MD  is  the  azimuth  of  5  when  measured  from  the  south  toward  the 
west. 

The  hour  angle  of  a  star  is  the  arc  QA  intercepted  on  the  equator  between 
the  meridian  and  the  foot  of  the  hour  circle  passing  through  the  star;  it  is 
measured  from  the  meridian  toward  the  west. 

TIME 

The  passing  of  a  heavenly  body  across  the  meridian  of  a  place  is  called  its 
culmination,  or  transit.  It  is  upper  or  lower  culmination,  according  as  it  is  then 
occupying  the  highest  or  the  lowest  position  with  regard  to  the  horizon. 

The  interval  of  time  that  elapses  between  two  successive  upper  or  lower 
transits  of  a  star  over  the  same  meridian  is  called  a  sidereal  day.  This  day 
begins,  for  any  place,  when  the  vernal  equinox  crosses  the  meridian  above  the 
pole;  this  instant  is  called  sidereal  noon.  Sidereal  hours,  minutes,  and  sec- 
onds are  reckoned  from  0  to  24  hr.,  starting  from  sidereal  noon.  Time 
expressed  in  sidereal  days  and  fractions  (hours,  minutes,  seconds)  is  called 
sidereal  time. 

Prom  this,  it  follows  that  sidereal  time  is  the  hour  angle  of  the  vernal 
equinox;  also,  that  the  right  ascension  of  a  star  is  equal  to  the  sidereal  time  of 
its  transit,  or  culmination.  For  any  other  position  of  the  star,  the  sidereal 
time  equals  the  algebraic  sum  of  the  right  ascension  and  the  hour  angle  of  the 
star. 

The  interval  between  two  successive  upper  transits  of  the  sun  is  called  a  true 
solar  day,  or  an  apparent  day.  Owing  to  the  fact  that  the  motion  of  the  sun  is 
not  uniform  and  that  the  solar  days  are  not  of  equal  duration,  apparent  time 
is  not  used  for  the  ordinary  affairs  of  life. 

The  mean  sun  is  an  imaginary  body  supposed  to  start  from  the  vernal 
equinox  at  the  same  time  as  the  true  sun,  and  to  move  uniformly  on  the  equator, 
returning  to  the  vernal  equinox  with  the  true  sun.  The  time  between  two  suc- 
cessive upper  transits  of  the  mean  sun  is  called  a  mean  solar  day,  and  time 
expressed  in  mean  solar  days  is  called  mean  solar  time,  or  simply  mean  time. 
This  is  the  time  shown  by  ordinary  clocks  and  watches. 

A  mean  solar  day  is  the  mean  of  the  duration  of  all  the  true  solar  days  in  a 
year  (a  year  being  the  time  in  which  either  the  true  or  the  mean  sun  makes 
a  complete  circuit  of  the  heavens).  As  there  are  365.2422  true  solar  days  and 
366.2422  sidereal  days  in  a  year.  1  mean  solar  da.  =  366.2422-:- 365.2422 
=  1.0027379  sidereal  day  =24h  3m  56.55s,  sidereal  time. 

Likewise,  1  sidereal  day  =  365.2422 -J- 366.2422  =  .99726957  mean  solar  day 
=  23h  56m  4.09s,  mean  solar  time. 

The  equation  of  time  is  a  certain  quantity  that  must  be  added  algebraically 
to  the  apparent  solar  time  to  obtain  the  corresponding  mean  time.  The  value 
of  this  quantity  for  each  day  of  the  year  is  given  in  the  American  Ephemeris.* 

Civil  Time  and  Astronomical  Time.— By  civil  time  is  meant  the  time  that 
is  usually  reckoned  in  ordinary  life.  For  astronomical  purposes,  the  day  is 
considered  to  begin  at  noon,  and  hours  counted  from  0  to  24.  When  time  is 
reckoned  in  this  manner  it  is  called  astronomical  time.  The  civil  day  begins 
at  12  o'clock  at  night,  and  the  astronomical  day  begins  12  hr.  later.  For 
instance,  the  date  October  17,  7h  14m  3s,  astronomical  time,  means  7h  14m  3s 
after  noon  of  the  civil  date  October  17,  and  is  in  civil  time,  7h  14™  3s  P.  M. 
The  astronomical  date  February  20,  18h  6m  12<*  means  18^  6™  12"  after  noon 

*The  American  Ephemeris  and  Nautical  Almanac  may  be  obtained  from 
the  Director  of  the  Nautical  Almanac,  Naval  Observatory,  Washington,  D.  C. 
Remittance  must  be  made  in  cash  or  a  post-office  money  order  for  $1.25. 
Stamps  and  checks  are  not  taken. 


SURVEVlftG'   J  101 

of  the  civil  date  February  20,  or  6h^6m  ISP-after  Tr^iduiJht-'o*  •Jfelor'uArV  2i/'  that 
is,  February  21,  6h  6°»  12*  A.  M.        '-,•-'','  ,  -  <  '    •  * 

Longitude  and  Time.  —  The  mean  sun  describes  a  complete  circle  in  24  mean 
solar  hours.  In  1  hr.  it  moves  over  360°  ^24=  15°  of  arc;  in  1  min.  of  time, 
over  15'  of  arc;  and  in  1  sec.  of  time,  15"  of  arc. 

Relation  Between  Time  and  Longitude.  —  Let  A  and  B  be  two  places  on  the 
earth's  surface,  B  being  west  of  A.  Let  their  respective  longitudes  be  ha  and 
hf,,  and  let  the  difference  between  ha  and  hi,,  expressed  in  measure  of  time,  be  dg, 
Let,  also,  Ta  be  the  time  at  A  when  the  time  at  B  is  Tb.  Then, 

Ta  =  Tb+dp  (1) 

and  Tb  =  Ta-d?          (2) 

EXAMPLE  1.  —  The  longitude  of  Washington,  west  of  Greenwich,  is  5h  8m  1s; 
that  of  San  Francisco,  8b  9m  473.  What  is  the  time  at:  (a)  Washington  when 
it  is  9h  3m  at  San  Francisco?  (b)  San  Francisco  when  it  is  19h  54m  30s  at 
Washington? 

SOLUTION.  —  (a)  Here  A,  the  eastern  locality,  is  Washington  and  B  is 
San  Francisco;  also,  <fc=8l»  9m  47*-5b  8m  l"  =  3h  lm  46s.  Therefore,  applying 
formula  1,  Ta  =  9h  3m+3h  lm  463=  12h  4m  46s 

(b)     Applying  formula  2, 

ra  =  19h  541*1  30s  _3h  lm  46s  =  16h  52™  44s. 

Standard  Time.  —  Time  referred  to  the  meridian  of  a  given  place  is  called  the 
local  time  of  that  place.  To  obviate  complications  in  comparing  local  times 
of  different  localities,  for  use  in  ordinary  affairs  of  life  standard  times  have 
been  adapted  for  regions  between  certain  longitudes.  The  United  States  is 
divided  into  four  zones,  or  sections  of  standard  time.  The  time  in  each  zone 
is  referred  to  the  meridian  passing  through  its  center.  These  central  meridians 
are  15°  or  lh  distant  from  one  another  and  are,  respectively,  75°,  90°,  105°, 
and  120°  west  of  Greenwich;  or,  in  hours,  5h,  6h,  7h,  and  8h  west  of  Greenwich. 
Each  of  these  meridians  controls  the  watch  time  of  all  places  within  7  £°  on 

S*  3°m    8*     7h3°m     7"     6*30"    6"     5^30™    6*    4*30™ 


fThnIS  refer-      [   Pac\fic     \Mountain\  Central     |   Jgq«tern[ 

70  12730'   I20P    irfdrf    105    97  3O     9O°     82°  3O      75°     67°30 


_ 

called  eastern  time;  to  the  90°  meridian,  central  time;  to  the  105°  meridian, 
mountain  time;  and  to  the  120°  meridian,  Pacific  time. 

To  Change  Standard  Time  Into  Local  Time  and  Vice  Versa.  —  Standard 
time  can  be  changed  into  local  time  or  local  time  can  be  changed  into  standard 
time  by  applying  formula  1  or  formula  2,  according  as  the  given  place  is  east 
or  west  of  the  reference  meridian  of  the  zone  in  which  the  place  is  located. 

EXAMPLE.  —  The  standard  time,  by  a  watch,  at  a  place  whose  longitude  is 
81°  37',  is  9h  37m  45s  A.  M.;  what  is  the  local  time? 

SOLUTION.  —  As  the  longitude  is  81°  37',  the  place  lies  within  the  zone  of  the 
75°  meridian;  and  being  west  of  the  latter,  formula  2  must  be  applied.  In  this 
case,  r«  =  9h  37™  45"  and  dp-  =  81°  37'  -75°  =  6°  37'  =  26m  28s.  Therefore, 
r*  =  9h  37m  45s  -26m  28s  =  9&  llm  17"  A.  M. 

DETERMINATION  BY  OBSERVING  POLARIS  AT  CULMINATION 

The  position  of  Polaris,  or  the  north  star,  can  easily  be  ascertained  by  means 
of  the  group  of  stars  called  the  Dipper,  or  the  Great  Bear.  As  shown  in  the 
accompanying  illustration,  a  straight  line  joining  the  stars,  a  and  /3,  called 
the  -pointers,  nearly  intersects  Polaris.  There  are  two  times  during  the  day 
when  the  star  crosses  the  meridian.  It  is  then  said  to  be  at  its  upper  or 
lower  culmination,  as  the  star  is  then  occupying  either  the  highest  or  the  lowest 
position  with  reference  to  the  horizon.  When  the  star  is  in  either  of  these 
positions,  the  vertical  plane  passing  through  it  and  the  observer's  station  is  the 
meridian  of  the  place,  and  its  intersection  with  the  horizon  is  therefore  a  true 
north-and-south  line. 

Field  Work.  —  Select  a  date  on  which  Polaris  is  at  either  lower  or  upper 
culmination  during  the  night  (preferably  during  the  early  part  of  the  evening)  . 
Determine,  by  means  of  the  accompanying  table,  the  exact  time  of  culmination, 
being  careful  to  reduce  the  tabular  values  to  standard  civil  time.  It  is  safer, 
in  order  to  avoid  confusion,  for  the  observer  to  set  his  watch  to  show  local  time. 
About  15m  before  the  time  of  culmination,  set  the  transit  in  such  a  position  that 
an  unobstructed  view  toward  the  north  may  be  obtained  for  a  distance  of 
between  300  and  500  ft.  Drive  a  stake,  and  mark  by  a  tack  the  exact  point 


102 


Q-<S_ 

§          S 

rfj 

a  4 

.d 

e    ili!;;ils5g33as8S83asg3asg3^ 

.      |      CO  »C  Tt<  CO  <N  i-<  ( 

OS  6 

_d 

2        8 

OS  _ 

J3 

^  S 

^  COiO-^cOCNi-^OCON^O! 

i-J  00  t-;  •*  (N  OS  CO  CO  IO  CO  00  O  •*  l>  rH  CO  CD  b-  OS  OS  rH  O  00  CO 

co          g        ooc ' 

r^lOTjtiQkCiOTjtiOT^iO-^iOTjflOrJtiCT^iCT^iC-^iC^iO 
^      I      CO  1C  •*  CO  W  »H  O  CO  <N  T-I  O  TO  00  b- CO  »C  •*  CO  (N —I  O  OS  00  b- 

1    i>  TJ<  co  q  oo  cq  oo  oo  q  rH  co  ic  os  c<i  cp  op  i-i  CM  T»<  TJ<  CD  10  co  i-< 

I      ^  1C  •*  Tj(  O  1C  1C  iO  >O  »C  ••*  1C  »C  »C  Tj<  iC  TJ<  »C  »C  «5  Tjt  1C  »C  iC 
CO  »C  Tf  CO  M  rH  O  CO  M  ^H  O  OS  00  b- CO  »C  ^  CO  (N  <-H  O  OS  00  b- 

(NOSOqiCiCrHCOCOOt^OSrHlCOOC 

CDiCTjtcOCNrHOCO(NrHOOSOOb-CO»C-*CO<NrHOOSOOb. 
NC<IC^C<|rHrHi-(rHrHrHrHi-(rHi-l 

oo^T^rHos^ososNco»ci>:rHTjHoqqcorjjcqcDooi>:»cco 

COlC-<i*CO(NrHOCO(NrHOOSOOb-CDlCTHCO<NrHOOSOOb- 
<N(N<NC<JrHrHrHrHrHrHrHrHrHrH 


SURVEYING  103 

occupied  by  the  instrument.     About  &&  before  tlie  tifna  of  jCirlnaination,  direct 
the  telescope  to  the  star,  holding  a.' lamp  ia  front  irid  a  littlest o\/ftrd jOiie  side 
of  the  objective  glass  to  illuminate  tha  cross-hairs.     Set  both  clamps,  and  with 
either  tangent  screw  set  the  vertical  cross-hair  exactly  on  the  star.     The  star 
will  appear  to  be  moving  toward  the  left  or  toward  the  right  according  as  it  is 
approaching  upper  or  lower  culmination.     Follow  it  in  its  motion  by  turning 
the  tangent  screw  until  the  exact  time  of  culmination   (which,  preferably, 
should  be  called  out  by  an  assistant).     This  completes  the  observation  of  the 
star.     Now  depress  the  telescope,  direct  it  to  a  point  on  the  ground  about 
400  or  500  ft.  from  the  instrument,  and  have  an  assist-  j>  ,      ,,  .     . 
ant  drive  a  tack  in  the  top  of  a  stake  in  line  with  the  *Ofe  [\     ' 
line  of  sight;  this  completes  the  operation.     The  line          j  V 
between  tthe  two  stakes  is  a  true  north-and-south          |  \. 
line,  or  true  meridian.  [     y 

Time  of  Culmination  of  Polaris. — -The  accom-  \ 

panying  table  contains  the  times  of  upper  culmina-  \ 

tion  of  Polaris  for  the  dates  given.     The  lower  culmi-  \ 

nation  occurs  nearly  lib  58m  before  and  after  the  \ 

upper  culmination,  and  can  be  determined  from  the  \ 

latter.     In  the  table  the  extreme  right-hand  column  •  \ 

contains  the  difference  between  the  times  of  culmi-  \ 

nation  for  any  two  succeeding  days.     Each  difference  \ 

applies  to  any  day  between  the  date  horizontally  \ 

opposite   that   difference  in  the  left-hand  column,  \ 

and  the  following  date.     Thus,  the  difference  3.95m,  \ 

which  is  horizontally  opposite  January  1,  indicates  V 

that,  between  January  1  and  January  15,  the  time  of  \ 

culmination  decreases  by  3.95m  per  da.    For  instance,  \a 

the  time  of  culmination  on  January  8  is   obtained  x 

by  subtracting  from  the  time  of  culmination  for  Jan-  I  _. •  ±a 

uary  1  the  product  3.95™  X  7  =27.65™,  the  number        ^i  "  \    ,' 

of  days  elapsed  from  January  1  to  January  8  being  ^/ 

seven. 

It  should  be  borne  in  mind  that  the  times  given   #9#per  or  Great  Meat* 
in  the  table  are  mean  local  times  counted  in  the  astronomical  way;  that  is, 
from  0^  to  24h,  beginning  at  noon. 

EXAMPLE. — Find  the  time  of  upper  culmination  of  Polaris  on  September 
6,  1913. 

SOLUTION. — Referring  to  the  table, 

Upper  culmination,  Sept.  1,  1913 =  14^45.3™ 

Difference  for  1  da =3.92m 

Correction  for  5 da =3.92mX5=        19.6m 

Time  of  culmination  on  Sept.  6 =  14t25.7m 

This  means  that  upper  culmination  will  occur  when  14h  25.7m  have  elapsed 
since  local  noon  Sept.  6;  that  is,  at  2b  25.7m  A.  M.,  Sept.  7. 

DETERMINATION  BY  OBSERVING  POLARIS  AT  ELONGATION 

When  a  star  is  at  its  extreme  westerly  or  easterly  position,  it  is  said  to  be 
at  western  or  eastern  elongation.  This  position  with  reference  to  the  meridian 
of  the  place  is  determined  by  the  angle  that  a  vertical  plane  passing  through 
the  star  and  the  point  of  observation  is  making  with  the  meridian.  This 
angle  is  called  the  azimuth  of  the  star,  and  its  values  for  Polaris,  for  the  years 
1913  to  1922  and  latitudes  5°  to  74°,  are  given  in  the  accompanying  table. 

Polaris  is  at  eastern  elongation  about  5h  55m  before  it  reaches  its  upper  cul- 
mination; and  at  western  elongation,  5&  55m  after  upper  culmination.  The 
times  of  elongation  can,  therefore,  be  readily  determined  from  those  of  culmi- 
nation taken  from  the  table. 

EXAMPLE. — Find  the  time  of  western  elongation  of  Polaris  on  March  1, 
1914. 

SOLUTION. — On  referring  to  the  table,  it  is  found  that  the  upper  culmination 
is  at  2h  52.5m,  local  astronomical  time,  or  2h  52.5m,  P.  M.,  local  civil  time.  Polaris 
is  at  western  elongation  5h  55m  later  or  at  8h  47.5™,  p.  M.,  local  civil  time. 

Making  the  Observation  and  Marking  the  Meridian. — Determine  the 
approximate  time  of  elongation  as  just  explained.  About  20m  before  that 
time,  set  the  transit  over  a  point  properly  marked,  and  level  it  carefully.  Set 
the  vernier  at  0.  Direct  the  telescope  to  the  star,  and,  with  both  clamps  set, 
follow  the  star  by  means  of  the  lower  tangent  screw.  If  the  star  is  approaching 


.. 


SURVEYING 


104 

eastern-  eitmgati&m  tt  \nlL*  Be  movmg  to -the  right;  if  western,  to  the  left. 
About't'ho  tlmo  t,t  .efor-gattort,  it-wfll  be,  noticed  that  the  star  ceases  to  move 
horizontally,  and  that  its  image  appears  to  follow  the  vertical  cross-hair  of  the 
instrument.  The  star  has  then  reached  its  elongation  and  the  observation  is 
completed.  Take  the  azimuth  from  the  table.  Depress  the  telescope,  and 
turn  it  through  an  angle  equal  to  the  azimuth,  to  the  west  or  to  the  east,  accord- 
ing as  the  star  was  at  eastern  or  western  elongation.  The  line  of  sight  will  then 

AZIMUTHS  OF  POLARIS  AT  ELONGATION 

i 

Year 


Q 

li 

313 

1 

914 

1 

915 

1 

916 

1 

317 

1 

918 

1 

)19 

1 

920 

1 

321 

1 

922 

ri 

i-J 

K£ 

g 

S£ 

c 

b£ 

.s 

bo 

£ 

b£ 

G 

a 

G 

M 

.H 

M 

B) 

c 

u 

_c 

Q 

2 

Q 

Q 

Q 

3 

G 

2 

Qj 

Q 

2 

o 

c 

3 

C 

2 

Q 

2 

O 

G 

5 

1 

9.8 

1 

9.5 

j 

9.2 

1 

8.8 

1 

8.5 

1 

8.2 

1 

7.9 

1 

7.6 

1 

7.3 

1 

7.0 

6 

9.9 

9.6 

9.3 

9.0 

8.6 

8.3 

8.0 

7.7 

7.4 

7.1 

8 

10.2 

9.8 

9.5 

9.2 

8.9 

8.6 

8.3 

7.9 

7.7 

7.4 

10 

1 

10.6 

1 

10.3 

1 

10.0 

1 

9.7 

1 

9.3 

1 

9.0 

1 

8.7 

1 

8.4 

1 

8.1 

1 

7.8 

12 

11.0 

10.7 

10.4 

10.1 

9.7 

9.4 

9.1 

8.8 

8.5 

8.2 

14 

11.6 

11.3 

11.0 

10.6 

10.3 

10.0 

9.7 

9.4 

9.0 

8.7 

16 

12.3 

12.0 

11.7 

11.3 

11.0 

10.7 

10.4 

10.1 

9.7 

9.4 

18 

13.1 

12.8 

12.4 

12.1 

11.8 

11.5 

11.1 

10.8 

10.5 

10.2 

20 

1 

14.0 

1 

13.7 

L 

13.4 

1 

13.0 

1 

12.6 

1 

12.3 

1 

11.9 

1 

11.6 

1 

11.3 

1 

10.9 

22 

15.0 

14.7 

14.4 

14.1 

13.8 

13.4 

13.1 

12.7 

12.4 

12.1 

24 

16.0 

15.7 

15.4 

15.1 

14.8 

14.5 

14.1 

13.8 

13.5 

13.2 

26 

17.4 

17.0 

16.7 

16.3 

16.0 

15.7 

15.3 

14.9 

14.6 

14.3 

28 

18.8 

18.5 

18.1 

17.8 

17.4 

17.0 

16.7 

16.3 

16.0 

15.7 

30 

1 

20.3 

1 

19.9 

1 

19.6 

1 

19.2 

1 

18.9 

1 

18.5 

1 

18.2 

1 

17.9 

1 

17.5 

1 

17.1 

32 

22.0 

21.6 

21.2 

20.9 

20.5 

20.1 

19.8 

19.4 

19.0 

18.7 

34 

23.8 

23.5 

23.1 

22.8 

22.4 

22.1 

21.7 

21.3 

21.0 

20.6 

36 

26.0 

25.6 

25.2 

24.9 

24.5 

24.1 

23.8 

23.4 

23.0 

22.6 

38 

28.2 

27.8 

27.5 

27.1 

26.8 

26.4 

26.0 

25.6 

25.2 

24.8 

40 

1 

30.7 

1 

30.3 

1 

30.0 

1 

29.6 

1 

29.2 

1 

28.8 

1 

28.4 

1 

28.0 

1 

27.6 

1 

27.2 

42 

33.6 

33.2 

32.8 

32.4 

32.0 

31.6 

31.1 

30.7 

30.3 

29.9 

44 

36.7 

36.3 

35.8 

35.4 

35.0 

34.6 

34.1 

33.6 

33.2 

32.8 

46 

40.1 

39.7 

39.2 

38.8 

38.4 

37.9 

37.5 

37.1 

36.6 

36.2 

48 

43.9 

43.4 

43.0 

42.5 

42.2 

41.8 

41.3 

40.8 

40.3 

39.9 

50 

1 

48.1 

1 

47.7 

1 

47.2 

1 

46.8 

1 

46.3 

1 

45.9 

1 

45.4 

1 

44.9 

1 

44.4 

1 

43.9 

52 

52.9 

52.4 

52.0 

51.5 

51.0 

50.5 

50.0 

49.5 

49.0 

48.5 

54 

58.3 

57.8 

57.3 

56.8 

56.3 

55.8 

55.2 

54.7 

54.2 

53.7 

56 

4.4 

3.8 

3.3 

2 

2.7 

2 

2.2 

2 

1.7 

2 

1.1 

2 

0.5 

2 

0.0 

1 

59.4 

58 

11.3 

10.7 

10.1 

9.6 

9.0 

8.4 

7.8 

7.2 

6.6 

6.0 

60 

2 

19.0 

2 

18.4 

2 

17.8 

2 

17.2 

2 

16.6 

2 

16.0 

2 

15.3 

2 

14.7 

2 

14.0 

2 

J3.4 

62 

28.1 

27.4 

26.7 

26.0 

25.4 

24.7 

24.0 

23.4 

22.7 

22.0 

64 

38.7 

38.0 

37.3 

36.5 

35.9 

35.2 

34.5 

33.8 

33.0 

32.3 

66 

50.9 

50.1 

49.4 

48.6 

47.8 

47.0 

46.2 

45.5 

44.7 

43.9 

68 

3 

5.7 

3 

4.8 

:? 

4.0 

3 

3.1 

3 

2.2 

3 

1.3 

3 

0.4 

59.6 

58.7 

57.7 

70 

3 

22.8 

3 

21.8 

3 

20.8 

3 

19.9 

3 

18.9 

3 

17.9 

3 

16.9 

3 

15.9 

3 

15.0 

3 

14.0 

72 

45.2 

44.2 

43.1 

42.0 

41.0 

40.0 

38.9 

37.8 

36.8 

35.7 

74 

4 

12.1 

4 

11.0 

1 

9.8 

4 

8.7 

4 

7.5 

4 

6.4 

4 

5.2 

4 

4.1 

4 

3.0 

4 

1.8 

be  directed  along  the  true  meridian,  and  by  marking  another  point  400  or  500  ft 
from  that  occupied  by  the  instrument,  the  direction  of  the  true  meridian  will 
be  established. 

This  is  the  most  accurate  method  of  determining  the  true  meridian,  and, 
where  possible,  should  be  used  in  preference  to  others. 

u**»      u       m?-rkLlng  m°numents  are  not  commonly  set  in  the  meridian,  some 

change  in  the  method  of  making  the  observations  from  that  described  is 

necessary.     Having  the  cross-hair  on  Polaris  at  the  point  of  greatest  elongation, 


SURVEYING  105 

the  telescope  is  brought  down  and  the  angle  between  the  star  and  the 
monument  is  read.  The  telescope  is  inverted  and  again  set  on  Polaris  and  the 
angle  to  the  monument  read.  This  angle  may  be  read  four  or  six  times,  even 
more,  as  the  change  in  position  of  the  pole  star  for  15m  before  and  after  elonga- 
tion is  not  measurable  by  an  ordinary  transit.  The  mean  of  the  two,  four,  or 
six  readings  of  the  angle  is  taken  as  the  true  angle.  By  making  a  sketch  of 
the  position  of  Polaris  with  reference  to  the  meridian  and  of  the  position  of 
the  monuments  with  reference  to  Polaris,  it  will  be  apparent  whether  the  azi- 
muth of  the  star  is  to  be  added  to  or  subtracted  from  the  angle  between  it 
and  the  monuments  to  give  the  azimuth  of  the  line  joining  said  reference  points. 
As  the  determination  of  the  meridian  is  of  great  importance  it  is  well,  unless 
the  engineer  has  had  experience  in  the  work,  to  repeat  the  observations  on  a 
second  night. 

DETERMINATION  BY  SOLAR  OBSERVATION 

Formula  for  Azimuth  of  the  Sun. — One  of  the  most  convenient  methods  of 
determining  the  meridian  is  to  measure  the  altitude  of  the  sun  at  any  hour 
angle  with  a  transit.  At  the  same  time  that  the  altitude  is  measured,  deter- 
mine, also,  the  horizontal  angle  between  the  sun  and  a  fixed  object,  or  refer- 
ence mark.  Then,  the  azimuth  of  the  sun  is  calculated  "by  the  formula  that 
follows.  The  azimuth  of  the  reference  mark  is  then  equal  to  the  algebraic 
sum  of  the  azimuth  of  the  sun  and  the  measured  angle  between  the  sun  and 
the  mark.  Finally,  the  true  north-and-south  line  may  be  located  from  the 
azimuth  of  the  reference  mark. 

Let  a  =  required  azimuth  counted  from  north  toward  east; 

2  =  zenith  distance  of  sun,  which  is  equal  to  90°  minus  altitude; 
8  =  declination  of  sun;  and 
<J>  =  latitude  of  observer;  then 


2       \  sin  z  cos  </> 

Two  values  of  „  will  correspond  to  the  computed  sin  -;  one  angle  will  be 

acute  and  the  other  obtuse.     The  acute  angle  should  be  used  for  morning 
observations  and  the  obtuse  for  afternoon  observations. 

Values  of  8  and  <J>. — The  method  just  described  requires  that  the  declina- 
tion of  the  sun  at  the  time  of  observation,  and  the  latitude  of  the  place  be  known. 
The  declination  of  the  sun  for  every  day  of  the  year  at  the  instant  of  Wash- 
ington noon,  together  with  the  hourly  change,  is  given  in  the  Ephemeris,  and 
has  to  be  reduced  to  the  time  of  observation  as  follows: 

Rule. — Change  the  local  time  to  Washington  time  by  adding  algebraically  to  the 
former  the  longitude  of  the  place  counted  from  Washington.  Take  from  the  Ephem- 
eris the  declination  corresponding  to  the  preceding  Washington  noon  and  add 
algebraically  the  product  of  the  hourly  change  by  the  time  elapsed  since  Washing- 
ton noon. 

EXAMPLE. — Find  the  true  declination  of  the  sun  for  9  A.  M.  January  5,  1903, 
at  Philadelphia. 

SOLUTION. — Jan.  5,  9  A.  M.,  civil  time  =  Jan.  4,  21h,  astronomical  time. 
The  longitude  of  Philadelphia  is  —  7m  378=  —.127^.  The  Washington  time 
corresponding  to  9  A.  M.  is  21t-.127h  =  20.873h.  From  the  Ephemeris,  the 
declination  at  Washington  at  noon  Jan.  4  is  —22°  47'  43",  and  the  hourly 
change  is  15.06".  The  algebraic  increase  is,  therefore.  15.06X20.873  =  5'  14"; 
thus,  the  declination  at  9  A.  M.  is  -22°  47'  43"+5'  14"=  -22°  42'  29". 

DETERMINATION  OF  LATITUDE,  AND  CORRECTIONS  FOR 
ALTITUDE 

Approximate  Determination  of  Latitude  From  Polaris. — In  nearly  all 
methods  of  determining  the  true  meridian,  the  latitude  of  the  place  of  obser- 
vation must  be  known,  at  least  approximately.  In  the  majority  of  cases 
the  latitude  can  be  taken  from  a  map  or  book  of  reference.  In  case  this  can- 
not be  done,  a  sufficiently  close  value  may  be  obtained  by  measuring,  with  a 
transit,  the  altitude  of  Polaris,  which  is  very  nearly  (within  about  1°)  equal 
to  the  latitude  of  the  place. 

This  method  of  determining  latitude  is  founded  on  the  following  very  sim- 
ple and  useful  principle: 

Principle. — The  latitude  of  any  place  on  the  earth's  surface  is  equal  to  the  alti- 
tude of  the  pole  with  respect  to  the  horizon  of  that  place. 


106 


SURVEYING 


For  more  accurate  work,  the  tables  given  in  the  Ephemeris,  entitled,  For 
Finding  the  Latitude  by  Polaris,  may  be  used.  The  simple  directions  for  using 
them  are  there  given  in  full. 

Latitude  by  Solar  Observation. — Latitude  may  be  determined  by  measur- 
ing the  sun's  altitude,  with  the  sextant  or  transit,  at  the  instant  of  its  passage 
across  the  meridian;  that  is,  at  apparent  noon.  The  time  of  apparent  noon 
may  be  determined  by  adding  algebraically  the  equation  of  time  to  the  noon 
of  local  mean  time,  as  previously  explained.  Then  begin  the  observations 
about  15m  before  apparent  noon  and  repeat  them  every  minute  or  two.  At 
first  the  altitude  will  be  increasing;  then,  it  will  be  decreasing.  The  maximum 
altitude  obtained  will  be  the  apparent  meridian  altitude.  To  this  the  correc- 
tions that  follow  must  be  applied,  giving  the  true  altitude.  _  The  true  altitude 
is  then  subtracted  from  90°,  and  the  remainder  is  the  zenith  distance.  The 
latitude  is  then  equal  to  the  algebraic  sum  of  the  zenith  distance  and  the  declina- 
tion of  the  sun  at  the  instant  of  apparent  noon. 

Corrections  for  Altitude. — The  observed  altitude  of  a  heavenly  body  must 
be  corrected  for:  (1)  refraction,  (2)  parallax,  and  (3)  semi-diameter. 

1.  Refraction  is  the  change  of  direction  of  the  rays  of  light  when  they  pass 
from  one  medium  into  another  of  different  density.     Its  amount  for  different 
altitudes  is  given  in  the  table  on  page  107.      It  is  subtractive.      When  the 
altitude  is  less  than  about  8°  to  10°,  the  refraction  becomes  so  uncertain  that 
the  measurement  is  of  no  value  for  accurate  work. 

2.  Parallax  is  the  difference  in  direction  of  a  heavenly  body  as  actually 
observed  and  the  direction  it  would  have  if  seen  from  the  earth's  center.     This 
correction  is  necessary  when  the  sun  is  observed;  its  values  for  different  alti- 
tudes are  given  in  the  accompanying  table.     It  is  additive. 

SUN'S  PARALLAX  IN  ALTITUDE  TO  BE  APPLIED.  TO  ALL  MEASURED 

(Additive  to  observed  altitude) 


Altitude 
Degrees 

Parallax 
Seconds 

Altitude 
Degrees 

Parallax 
Seconds 

Altitude 
Degrees 

Parallax 
Seconds 

0 

9 

40 

7 

69 

3 

6 

9 

45 

6 

72 

3 

12 

9 

48 

6 

75 

2 

16 

8 

51 

5 

78 

2 

20 

8 

54 

5 

81 

1 

25 

8 

57 

5 

84 

1 

30 

8 

60 

4 

87 

o 

34 

7 

63 

4 

90 

0 

36 

7 

66 

3 

3.     The  correction  for  semi-diameter  is  also  necessary  when  the  sun  is 

1  nf°tTg  t0tthe  -aCVthat  *$*»&*  uPPer  or  the  lower  edge  of  thfdisk! 
Fnvf,  n    •   the+ center,  is  observed.     This  correction  may  be  taken  from  the 
fcphemeris  in  the  same  manner  as  the  sun's  declination.     For  the  purpose  of 
ordinary  calculations,  however,  this  may  be  taken  from  the  following  table: 
fime  of  year  (approx.)...  Jan.  1,          Apr.  1,          July  1  Get   1 

Sun's  semi-diameter 16'  18"          16'  2"          15'  45"          16'  2" 

upper  oneisobTerved.11  **  *m  ""*  *  °bserved'  and  Attractive  when  the 
nh  Corr,ecftions  .for  Observation  of  the  Sun  for  Azimuth.— When  the  sun  is 
?hfr7^;n°r  faZAmiith'-a  COITec.tion  for  semi-diameter  must  also  be  applied  to 
the  reading  of  the  horizontal  circle;  this  may  be  found  by  dividing  the  correc- 

add  J ftn tli  Sy  the*(Sfmf  of-  the  sun>s  altitude-  This  correction  is  to  be 
added  to  the  reading  of  the  horizontal  circle  if  the  hair  is  placed  tangent  to 

ch-cll  if  tehegehaf  '   e!SUnA  and  subtractued  'rom  the  readingPof  the  horizontal 

Wh™  ™v?    1S  Pjaced +tangent  to  the  right  edge  of  the  sun. 
ment  t£  r 3      g  observatlons  of  the  sun  for  azimuth,  the  errors  of  adjust- 
b^  the  Wlowfrfc,6""0^  a,?d  tj.e  correction  for  semi-diameter  may  be  eliminated 
£  complete"  '        °h  aSSUmes  that  the  vertical  circle  of  the  transit 

at  theVztauTmLt  SeVUP  fWith  the  hori?ontal  Pla*e  reading  0°  when  sighting 
uth  mark.     For  forenoon  work,  the  sun  should  be  so  sighted  that 


SURVEYING 

MEAN  REFRACTION  TO  BE  APPLIED  TO  ALL  MEASURED 
ALTITUDES 

(Subtractive  from  apparent  altitude) 


107 


App. 
Alti- 
tude 

Re- 
frac- 
tion 

App. 
Alti- 
tude 

Re- 
frac- 
tion 

te 

tude 

Re- 
frac- 
tion 

App. 
Alti- 
tude 

Re- 
frac- 
tion 

App. 
Alti- 
tude 

Re- 
frac- 
tion 

0  0 

33  0 

5  0 

9  54 

10  0 

5  15 

20  0 

2  35 

34  0 

24 

10  10 

5  10 

20  10 

2  34 

34  30 

23 

10  20 

5  5 

20  20 

2  32 

35  0 

21 

10  30 

5  0 

20  30 

2  31 

35  30 

20 

5  20 

9  23 

10  40 

4  56 

20  40 

2  29 

36  0 

18 

10  50 

4  51 

20  50 

2  28 

36  30 

17 

11  0 

4  47 

21  0 

2  27 

37  0 

16 

11  10 

4  43 

21  10 

2  26 

37  30 

14 

5  40 

8  54 

11  20 

4  39 

21  20 

2  25 

38  0 

13 

11  30 

4  34 

21  30 

2  24 

38  30 

11 

11  40 

4  31 

21  40 

2  23 

39  0 

10 

11  50 

4  27 

21  50 

2  21 

39  30 

9 

1  0 

24  29 

6  0 

8  28 

12  0 

4  23 

22  0 

2  20 

40  0 

8 

12  10 

4  20 

22  10 

2  19 

41  0 

5 

12  20 

4  16 

22  20 

2  18 

42  0 

3 

12  30 

4  13 

22  30 

2  17 

43  0 

1 

6  20 

8  3 

12  40 

4  9 

22  40 

2  16 

44  0 

0  59 

12  50 

4  6 

22  50 

2  15 

45  0 

0  57 

13  0 

4  3 

23  0 

2  14 

46  0 

0  55 

13  10 

4  0 

23  10 

2  13 

47  0 

0  53 

6  40 

7  40 

13  20 

3  57 

23  20 

2  12 

48  0 

0  51 

13  30 

3  54 

23  30 

2  11 

49  0 

0  49 

13  40 

3  51 

23  40 

2  10 

50  0 

0  48 

13  50 

3  48 

23  50 

2  9 

51  0 

0  46 

2  0 

18  35 

7  0 

7  20 

14  0 

3  45 

24  0 

2  8 

52  0 

0  44 

14  10 

3  43 

24  10 

2  7 

53  0 

0  43 

14  20 

3  40 

24  20 

2  6 

54  0 

0  41 

14  30 

3  38 

24  30 

2  5 

55  0 

0  40 

7  20 

7  2 

14  40 

3  35 

24  40 

2  4 

56  0 

0  38 

14  50 

3  33 

24  50 

2  3 

57  0 

0  37 

15  0 

3  30 

25  0 

2  2 

58  0 

0  35 

15  10 

3  28 

25  10 

2  1 

59  0 

0  34 

7  40 

6  45 

15  20 

3  26 

25  20 

2  0 

60  0 

0  33 

15  30 

3  24 

25  30 

1  59 

61  0 

0  32 

15  40 

3  21 

25  40 

1  58 

62  0 

0  30 

15  50 

3  19 

25  50 

1  57 

63  0 

0  29 

3  0 

14  36 

8  0 

6  29 

16  0 

3  17 

26  0 

1  56 

64  0 

0  28 

16  10 

3  15 

26  10 

1  55 

65  0 

0  26 

8  10 

6  22 

16  20 

3  12 

26  20 

1  55 

66  0 

0  25 

16  30 

3  10 

26  30 

1  54 

67  0 

0  24 

8  20 

6  15 

16  40 

3  8 

26  40 

1  53 

68  0 

0  23 

16  50 

3  6 

26  50 

1  52 

69  0 

0  22 

3  30 

13  6 

8  30 

6  8 

17  0 

3  4 

27  0 

1  51 

70  0 

0  21 

17  10 

3  3 

27  15 

1  50 

71  0 

0  19 

8  40 

6  1 

17  20 

3  1 

27  30 

1  49 

72  0 

0  18 

17  30 

2  59 

27  45 

1  48 

73  0 

0  17 

8  50 

5  55 

17  40 

2  57 

28  0 

1  47 

74  0 

0  16 

17  50 

2  55 

28  15 

1  46 

75  0 

0  15 

4  0 

11  51 

9  0 

5  48 

18  0 

2  54 

28  30 

1  45 

76  0 

0  14 

18  10 

2  52 

28  45 

1  44 

77  0 

0  13 

9  10 

5  42 

18  20 

2  51 

29  0 

1  42 

78  0 

0  12 

18  30 

2  49 

29  30 

1  40 

79  0 

0  11 

9  20 

5  36 

18  40 

2  47 

30  0 

1  38 

80  0 

0  10 

18  50 

2  46 

30  30 

1  37 

81  0 

0  9 

4  30 

10  48 

9  30 

5  31 

19  0 

2  44 

31  0 

1  35 

82  0 

0  8 

19  10 

2  43 

31  30 

1  33 

83  0 

0  7 

9  40 

5  25 

19  20 

2  41 

32  0 

1  31 

84  0 

0  6 

19  30 

2  40 

32  30 

1  30 

86  0 

0  4 

9  50 

5  20 

19  40 

2  38 

33  0 

1  29 

88  0 

0  2 

19  50 

2  37 

33  30 

1  26 

90  0 

0  0 

108 


SURVEYING 


it  occupies  position  1,  Fig.  1,  with  reference  to  the  cross-hairs;  the  time,  ver- 
tical angle,  and  horizontal  angle  are  noted.  Then  the  upper  plate  is  loosened, 
the  instrument  turned  180°  in  azimuth,  the  telescope  inverted,  and  the  sun 
.  sighted  again,  as  in  position  2.  In  position  1 ,  the  sun  is  moving  toward  both 
hairs;  in  position  2,  the  telescope  should  be  set  approximately  as  shown  by 
the  dotted  circle,  so  that  the  sun  will  clear  both  hairs  at  the  same  instant.  For 


rfffernoon 


FIG.  1 


FIG.  2 


afternoon  work,  the  positions  shown  in  Fig.  2  should  be  used.  The  observa- 
tions are  taken  in  pairs;  if  the  second  observation  of  a  pair  cannot  be  obtained 
promptly  after  the  first  one  (owing  to  a  passing  cloud,  or  some  other  cause), 
the  first  must  be  ignored  and  considered  as  useless. 

It  should  be  noted  that  the  reversal  of  the  transit  between  the  observations 
eliminates  the  index  error  of  the  vertical  circle,  the  error  of  level  in  the  horizon- 
tal axis  of  the  telescope,  and  the  error  of  collimation  of  the  telescope.  By 
sighting  in  diagonal  corners  of  the  field  of  view  and  taking  the  mean  of  the  obser- 
vations, the  corrections  (both  horizontal  and  vertical)  due  to  the  semi-diameter 
of  the  sun  are  eliminated.  To  simplify  the  notes,  180°  should  be  added  to 
(or  subtracted  from)  the  horizontal  plate  reading  when  the  instrument  is 
inverted. 

EXAMPLE. — The  following  measurements  were  taken  in  the  manner  just 
described.  The  four  means  of  the  circle  readings  were  formed  in  the  field. 
The  declination  of  the  sun  was  —9°  30'  5",  and  the  approximate  latitude 
+39°  57'.  Find  the  azimuth  of  the  reference  mark. 


Telescope 

Time 

P.  M. 

Vertical 
Circle 

Horizontal 
Circle 

Direct  

3:27 

19°  39'    00" 

99°  52'    00" 

Inverted 

3-29 

19     52     00 

99     49     00 

Mean  

3:28 

19     45     30 

99     50     30 

Direct  

3:32 

18     46     00 

100     55     30 

Inverted  .  .  . 

3:34 

19       3     00 

100     49     00 

Mean 

3-33 

18     54     30 

100     52     15 

Direct     .  . 

3-36 

18       4     30 

101     46     00 

Inverted  .  .  . 

3:38 

18     23     30 

101     35     00 

Mean  

3-37 

18     14     00 

101     40     30 

Direct  

3-40 

17     26     30 

102     29     30 

Inverted  . 

3-42 

17     43     00 

102     21     00 

Mean  

3-41 

17     34-    45 

102     25     15 

SOLUTION. — 

Mean  of  the  four  vertical  circle  readings .    18°     37'     11 

Refraction _2      48 

Parallax 


True  altitude  of  center 18°     34'     31" 

Zenith  distance  =  90°- true  altitude .' . .'    71°     25'     29" 

To  find  the  azimuth  of  the  sun:  3  =  71°  25'  29";  4>  =  39°  57'  0"; 
5=  T90  30'  5";  J(8+$+«)  =  50°  56'  12";  iOH-0-8)  =  60°  26'  17".  Sub- 
stituting these  values  in  the  formula  for  the  azimuth  of  the  sun. 

50°  56'  12"  sin  60°  26'  17" 


sin  71°  25'  29"  cos  39°  57' 


SURVEYING 


109 


The  two  values  of  fa  are  60°  17'  15"  and  119°  42'  45"  (  =  180°- 60°  17'  15"). 
As  the  observations  were  made  in  the  afternoon,  the  obtuse  angle  should  be 
used.  This  gives  0  =  2X119°  42' 45"  =  239°  25'  30".  The  mean  of  the  four 
horizontal  readings  is  101°  12'  8".  Subtracting  this  from  the  azimuth  of  the 
sun,  the  azimuth  of  the  reference  mark  is  found  to  be  239°  25'  30"  — 101°  12'  8' 
=  138°  13'  22".  

RAILROAD  SURVEYING 

DEFINITIONS  OF  CIRCULAR  CURVES 

The  line  of  a  railroad  consists  of  a  series  of  straight  lines  connected  by 
curves.  Each  two  adjacent  lines  are  united  by  a  curve  having  the  radius 


FIG.  3 

best  adapted  to  the  conditions  of  the  surface.     The  straight  lines  are  called 
tangents,  because  they  are  tangent  to  the  curves  that  unite  them. 

Railroad  curves  are  usually  circular  and  are  divided  into  three  general 
classes,  namely,  simple,  compound,  and  reverse  curves. 

A  simple  curve  is  a  curve  having  but  one  radius,  as  the  curve  AB,  Fig.  1, 
whose  radius  is  AC. 

A  compound  curve  is  a  continuous  curve  composed  of  two  or  more  arcs 
of  different  radii,  as  the  curve  CDEF,  Fig.  2,  which  is  composed  of  the  arcs  CD, 
DE,  and  EF,  whose  respective  radii  are  GC,  HD,  and  KE.  In  the  general 
class  of  compound  curves  may  be  included  what  are  known  as  easement  curves, 
transition  curves,  and  spiral  curves,  now  used  very  generally  on  the  more  impor- 
tant railroads. 

A  reverse  curve  is  a  continuous  curve  composed  of  the  arcs  of  two  circles 
of  the  same  or  different  radii,  the  centers  of  which  lie  on  opposite  sides  of  the 
curve,  as  in  Fig.  3.  The  two  arcs  composing  the  curve  meet  at  a  common 
point  or  point  of  reversal  M,  at  which  point  they  are  tangent  to  a  common  line 
perpendicular  to  the  line  joining  their  centers.  Reverse  curves  are  becoming 
less  common  On  railroads  of  standard 
gauge. 
GEOMETRY  OF  CIRCULAR  CURVES 

The  following  principles  of  geometry 
are  of  special  importance  as  relating  to 
curves: 

1.  A  tangent  to  a  circle  is  perpen- 
dicular to  the   radius   at   its  tangent 
point.     Thus,  in  Fig.  4,  AF  is  perpen- 
dicular to  BO  at  its  tangent  point  B, 
and  ED  is  perpendicular  to  CO  at  C. 

2.  Two  tangents  to  a  circle  from 
any  point  without  the  circle  are  equal 
in  length,  and  make  equal  angles  with 
the  chord  joining  their  points  of  tan- 
gency.     Thus,  BE  and  CE  are  equal, 
and   the   angles   EEC  and    ECB    are 
equal. 

3.  An    angle    not    exceeding   90° 
formed  by  a  chord  and  the  tangent  at 

one  of  its  extremities,  is  equal  to  one-half  the  central  angle  subtended  by  the 
chord.     Thus,  the  angle  EBC  =  ECB  =  *  BOC. 

4.  An  angle  not  exceeding  90°  having  its  vertex  in  the  circumference  of  a 
circle  and  subtended  by  a  chord  of  the  circle,  is  equal  to  one-half  the  central 
angle  subtended  by  the  chord.     Thus,  the  angle  GBH,  whose  vertex  B  is  in  the 


110  SURVEYING 

circumference,  is  subtended  by  the  chord  GH  and  is  equal  to  one-half  the  cen- 
tral angle  GOH,  subtended  by  the  same  chord  GH. 

5  Equal  chords  of  a  circle  subtend  equal  angles  at  its  center  and  also  in 
its  circumference,  if  the  angles  lie  in  corresponding  segments  of  the  circle. 
Thus   if  BG,  GH,  HK,  and  KC  are  equal,  BOG  =  GOH,  GBH  =  HBK,  etc. 

6  '    The  angle  of  intersection  FEC  of  two  tangents  of  a  circle  is  equal  to 
the  central  angle  subtended  by  the  chord  joining  the  two  points  of  tangency. 
Thus,  the  angle  CEF  =  BOC. 

7  A  radius  that  bisects  any  chord  of  a  circle  is  perpendicular  to  the  chord. 
8.     A  chord  subtending  an  arc  of  1°  in  a  circle  having  a.  radius  =  100  ft.  is 

very  closely  equal  to  1.745  ft. 

ELEMENTS  AND  METHODS  OF  LAYING  OUT  A  CIRCULAR  CURVE 

The  degree  of  curvature  of  a  curve  is  the  central  angle  subtending  a  chord 
of  100  ft.  Thus,  if,  in  Fig.  4,  the  chord  BG  is  100  ft.  long  and  the  angle  BOG 
is  1°  the  curve  is  called  a  one-degree  curve;  but  if,  with  the  same  length  of  chord, 
the  angle  BOG  is  4°,  the  curve  is  called  a  four-degree  curve. 

The  deflection  angle  of  a  chord  is  the  angle  formed  between  any  chord  of 
a  curve  and  a  tangent  to  the  curve  at  one  extremity  of  the  chord.  It  is  equal 
to  one-half  the  central  angle  subtended  by  the  chord.  The  deflection  angle  for 
a  chord  of  100  ft.  is  called  the  regular  deflection  angle,  and  is  equal  to  one-half  the 
degree  of  curvature.  The  deflection  angle  for  a  subchord  —  that  is,  for  a  chord 
less  than  100  ft.  —  is  equal  to  one-half  the  degree  of  curvature  multiplied  by  the 
length  of  the  subchord  expressed  in  chords  of  100  ft.  The  length  c  of  a  sub- 
chord  or  of  any  chord  is  given  by  the  formula 
in  which  c  =  2R  sin  D 

R  =  radius; 
D  =  deflection  angle  of  that  chord. 

Relation  Between  Radius  and  Deflection  Angle.  —  From  the  formula  just 
given,  „  _  c 

2smD 

If  Dioo  is  the  deflection  angle  for  a  chord  of  100  ft.,  then 
g_      50 

/V  —  ~:  -  ^r  — 

sin    Dim 
For  a  1°  curve,  Dioo  =  30'  and  R  =  5,730,  nearly.     For  curves  less  than  10°, 

the  radius  may  be  taken  as    '       ,  in  which  DC  is  the  degree  of  curvature.     The 

DC 

accompanying  table  gives  the  length  of  the  radius,  in  feet,  for  degrees  of  curva- 
ture ranging  by  intervals  of  5'  and  10'  from  0'  to  20°. 

Tangent  Distance.  —  The  point  where  a  curve  begins  is  called  the  point  of 
curve,  and  is  designated  by  the  letters  P.  C.;  and  the  point  where  the  curve 
terminates  is  called  the  point  of  tangency,  and  is  designated  by  the  letters  P.  T. 
The  point  of  intersection  of  the  tangents  is  called  the  point  of  intersection;  it 
is  designated  by  the  letters  P.  I. 

The  distance  of  the  P.  C.  or  P.  T.  from  the  P.  I.  is  called  the  tangent  dis- 
tance, and  the  chord  connecting  the  P.  C.  and  P.  T.  of  a  curve  is  commonly 
called  its  long  chord.  This  term  is  also  applied  to  chords  more  than  one  sta- 
tion long. 

If  /  denotes  the  angle  of  intersection  and  R  the  radius  of  the  curve,  then  the 
tangent  distance 


Laying  Out  a  Curve  With  a  Transit.  —  When  the  angle  of  intersection  /  has 
been  measured  and  the  degree  of  curve  decided  upon,  the  radius  of  the  curve 
can  be  taken  from  the  Tablebf  Radii  and  Deflections  or  it  can  be  figured  by  the 
formula  5,730 

*"~nT 

The  tangent  distance  is  then  computed  and  measured  back  on  each  tangent 
from  the  P.  I.,  thus  determining  the  P.  C.  and  P.  T.  Subtracting  the  tangent 
distance  from  the  station  number  of  the  P.  I.  will  give  the  station  number 
of  the  P.  C.  Ordinarily,  this  will  not  be  an  even  or  full  station.  The  length 
of  the  curve  is  then  computed  by  dividing  the  angle  /  by  the  degree  of  curve, 
the  quotient  giving  the  length  of  the  curve  in  stations  of  100  ft.  and  decimals 
thereof.  After  having  found  the  length  of  the  curve,  compute  the  deflection 
angles  for  the  chords  joining  the  P.  C.  with  all  the  station  points;  set  the  transit 
at  the  P.  C.;  set  the  vernier  at  0,  sight  to  the  intersection  point,  and  turn  off 


SURVEYING 


111 


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112 


SURVEYING 


successively  the  deflection  angles,  at  the  same  time  measuring  the  chords  and 
marking  the  stations.  The  station  of  the  P.  T.  is  found  by  adding  the  length 
of  curve  in  chords  of  100  ft.  to  the  station  of  the  P.  C. 

If  the  entire  curve  cannot 

X  be  run  from  the  P.  C.  on  ac- 

count of  obstructions  to  the 
view,  run  the  curve  as  far  as 
the  stations  are  visible  from  the 
P.  C.  and  run  the  remainder  of 
the  curve  from  the  last  station 
that  can  be  seen.  Suppose  that  ' 
in  the  10°  curve  shown  in  Fig.  1 
the  station  at  H,  200  ft.  from 
the  P.  C.,  which  is  at  B,  is  the 
last  point  on  the  curve  that  can 
be  set  from  the  P.  C.  A  plug 
is  driven  at  H  and  centered 
carefully  by  a  tack  driven  at 
the  point.  The  transit  is  now 
moved  forward  and  set  up  at  H. 
As  the  deflection  angle  EBH  is 
10°  to  the  right,  an  angle  of  10° 
is  turned  to  the  left  from  0  and 
the  vernier  clamped.  The  in- 
strument is  then  sighted  to  a  flag  at  B,  the  lower  clamp  set,  and  by 
means  of  the  lower  tangent  screw  the  cross-hairs  are  made  to  bisect  the 
flag  exactly.  The  vernier  clamp  is  then  loosened,  the  vernier  set  at  0,  and 
the  telescope  plunged.  The  line  of  sight  will  then  be  on  the  tangent  IP,  and 
the  deflection  angles  to  K  and  C  can  be  turned  off  from  this  tangent,  and 
the  stations  at  K  and  C  located  in  the  same  manner  that  the  stations  at  G  and 
H  were  located  from  B,  because  the  angle  at  IHB  between  the  tangent  IH  and 
the  chord  BH  is  equal  to  the  angle  EBH  between  the  tangent  EB  and  the 
same  chord. 

This  method  of  setting  the  vernier  for  the  backsight  when  the  instrument 
is  moved  forwards  to  a  new  instrument  point  on  the  curve  is  sometimes  called 
the  method  by  zero  tangent.  The  essential  principle  of  the  method  is  that  the 
vernier  always  reads  zero  when  the  instrument  is  sighted  on  the  tangent  to 
the  curve  at  the  point  where  the  instrument  is  set,  and  the  deflection  angles  are 
made  to  read  from  the  tangent  to  the  curve  at  this  point  in  the  same  manner 
as  if  this  point  were  the  P.  C.  of  the  curve. 

Tangent  and  Chord  Deflections.  —  Let  A  B,  Fig.  2,  be  a  tangent  joining  the 
curve  BCEH  at  B.  If  the  tangent  AB  is  prolonged  to  D,  the  perpendicular 
distance  DC  from  the  tangent  to  the  curve  is  called  a  tangent  deflection.  If  the 
chord  BC  is  prolonged  to  the  point  G,  so  that  CG  =  CE,  the  distance  GE  is  called 
a  chord  deflection.  If  the 
radius  R  of  the  curve  and 
the  length  of  the  chord  c  are 
known,  the  tangent  deflection  / 
can  be  determined  by  the 
formula 

fc*. 

J     2R 

This  formula  can  be  used  A. 
for  any  length  of  chord  or  ra- 
dius.    If   CE  =  BC,   the  chord 


deflection 


=  -.     For  this 


condition  the  Table  of  Radii 
and  Deflections  gives  the  ch9rd 
deflection  and  tangent  deflection 
for  100-ft.  chords  and  for  de- 
grees of  curvature  varying  by 
intervals  of  5'  and  10'  from  5' 
to  20°. 

When  the  two  chords  preceding  the  station  considered  are  of  unequal 
lengths,  the  chord  deflection  =  Cl(ci+c*) ,  where  ci  is  the  length  of  the  first  chord 


SURVEYING  113 

and  cz  the  length  of  the  second  chord  preceding  the  station  considered.    When 
the  tangent  deflection  /  is  known,  the  chord  deflection 


*-/('+;) 


Special  Values  of  Chord  and  Tangent  Deflection. — For  a  chord  of  100  ft. 
preceded  by  one  of  the  same  length  the  chord  deflection  for  a  1°  curve  is  1.745; 
for  a  2°  curve,  it  is  twice  that  amount,  or  3.49;  and  so  on.  The  tangent 
deflection,  being  half  the  chord  deflection,  will  be  .873  ft.  for  a  1°  curve,  1.745 
for  a  2°  curve,  etc.  The  tangent  deflection  for  a  chord  of  any  length  equals 
the  tangent  deflection  for  a  chord  of  100  ft.  multiplied  by  the  square  of  the 
given  chord  expressed  as  the  decimal  part  of  a  chord  of  100  ft. 

Application  of  Chord  and  Tangent  Deflection. — Let  it  be  required  to  restore 
center  stakes  on  the  4°  curve,  Fig.  3,  at  each  full  station.  The  points  A  and  B 
determine  the  direction  of  the  tangent,  the  point  B  being  the  P.  C.,  which  is  at 
Sta.  8+25.  For  a  4°  curve  the  regular  chord  deflection  for  100  ft.  is  4  X  1.745 
=  6.98  ft.,  and  the  tangent  deflection  is  3.49  ft.  The  distance  from  P.  C.  to  the 
next  full  station  is  75  ft.;  hence,  the  tangent  deflection  CF  =  .752X3.49  =  1.96  ft. 
The  point  F  is  found  by  first  measuring  75  ft.  from  B,  thus  locating  the  point  C 
in  the  line  AB  prolonged,  then  from  C  measuring  CF  =  1.96  ft.,  at  right  angles  to 
BC;  the  point  F  thus  determined  will  be  Sta.  9.  Next,  the  chord  BF  is  pro- 
longed 100  ft.  to  D;  BF  is  only  75  ft.,  DG  is  computed  from  the  preceding 
formula;  thus,  do  =  3.49 
(1  + flW  =  6.11.  This  A  &  _i__C 

distance  is  measured  at  8+25]  jf<X     y"**^r -r 

right  angles  to  BD;  the        -  p 

point  G  thus  deter- 
mined will  be  Sta.  10.  [ 
The  point  H,  which  is 
Sta.  11,  and  the  P.  T.  of 
the  curve,  is  determined 
in  the  same  manner,  ex- 
cept that,  as  the  chords  pir 
FG  and  GH  are  each 
100  ft.  long,  the  regular 
chord  deflection  of  6.98  ft.  is  used  for  EH.  A  stake  is  driven  at  each  station 
thus  located.  Although  a  chord  deflection  is  not  at  right  angles  to  the  chord 
theoretically,  yet  the  deflection  is  so  small,  as  compared  with  the  length  of  the 
chord,  that  for  curves  of  ordinary  degree  it  is  usually  measured  at  right  angles. 

Middle  Ordinate. — The  middle  ordinate  of  a  chord  is  the  ordinate  to  the 
curve  at  the  middle  point  of  the  chord.  The  following  formulas  give 
the  relation  between  the  length  of  the  chord  c,  the  radius  of  the  curve  R,  and 
the  middle  ordinate  m. 


To  Determine  Degree  of  Curve  From  Middle  Ordinate. — It  is  sometimes 
necessary  to  determine  the  radius  or  the  degree  of  a  curve  in  an  existing  track 
when  no  transit'  is  available.  By  measuring  the  middle  ordinate  of  any  con- 
venient chord,  the  degree  of  the  curve  can  be  calculated  from  the  relative  values 
of  the  ordinate  and  chord.  As  the  track  is  likely  not  to  be  in  perfect  aline- 
ment,  it  is  well  to  measure  the  middle  ordinate  of  different  chords  in  different 
parts  of  the  curve;  also,  as  the  middle  ordinate  of  a  chord  measured  to  the 
inner  rail  will  somewhat  exceed  the  middle  ordinate  of  the  same  chord  measured 
to  the  outer  rail,  the  ordinate  of  each  chord  should  be  measured  to  both  rails 
and  the  average  of  the  two  taken  as  the  value  of  the  ordinate.  Having  meas- 
ured the  middle  ordinate  of  one  or  more  chords,  the  degree  of  curve  De  can  be 
found  by  the  formula 

_  _  45,840w 

De~        ~&~ 

The  following  rule  is  sometimes  applied  in  determining  the  degree  of  curve: 

Rule. — Measure  the  middle  ordinate  to  a  chord  of  67.71  ft.;  express  it  in  feet 

and  decimals  of  a  foot,  and  multiply  by  10;  the  result  will  be  the  degree  of  the  curve. 


114 


SURVEYING 


Rules  for  Measuring  the  Radius  of  a  Curve. — Stretch  a  string,  say  20  ft. 
long,  or  longer  if  the  curve  is  not  a  sharp  one,  across  the  curve  corresponding 
to  the  line  from  A  to  C,  in  Fig.  4.     Then  measure 
from  B  the  center  of  the  line  AC,  and  at  right  angles 
with  it,  to  the  rail  at  D.     Multiply  the  distance  A  to 
B,  or  one-half  the  length  of  the  string,  in  inches,  by 
B  itself;  measure  the  distance  D  to  B  in  inches,  and  multi- 

„  ply  it  by  itself .    Add  these  two  products,  and  divide  the 

sum  by  twice  the  distance  from   B  to  D,  measured 

exactly  in  inches  and  fractional  parts  of  inches.     This  will  give  the  radius  of 
the  curve  in  inches. 

It  may  be  more  convenient  to  use  a  straightedge  instead  of  a  string.  Care 
must  be  taken  to  have  the  ends  of  the  string  or  straightedge  touch  the  same 
part  of  the  rail  as  is  taken  in  measuring  the  distance  from  the  center.  If  the 
string  touches  the  bottom  of  the  rail  flange  at  each  end,  and  the  center  measure- 
ment is  made  to  the  rail  head,  the  result  will  not  be  correct. 

In  practice,  it  will  be  found  best  to  make  trials  on  different  parts  of  the 
curve,  to  allow  for  irregularities. 

ILLUSTRATION. — Let  AC  be  a  20-ft.  string;  half  the  distance,  or  AB,  is  then 
10  ft.,  or  120  in.  Suppose  BD  is  found  on  measurement  to  be  3  in.  Then  120 
X 120  =14,400,  and  3X3  =  9;  14,400+9  =  14,409,  which,  divided  by  2X3  =  6, 
equals  2,401$  in.,  or  200  ft.  1J  in.,  which  is  the  radius  of  the  curve.  The 

formula  — ^  „    —  =  R,  applied  to  the  example  is 


2BD 


12Q2+9 
2X3 


=  2,40Uin.  = 


1J  in. 


Other  Ordinates. — Any  ordinate  y  to  the  curve  at  a  distance  a  from  the 
middle  point  of  a  chord  may  be  determined  by  means  of  the  formula: 


By  using  long  chords,  a  curve  may  be  laid  out  or  obstacles  passed  by  means 
of  ordinates.  Suppose  that  it  is  required  to  run  out  the  curve  A  EH,  Fig.  5, 
with  several  obstacles  in  the  direct  line  of  the  curve,  as  shown,  Sta.  3  being  the 
P.  C.,  and  the  regular  stations  on  the  curve  being  in  the  positions  indicated  by 
the  numbers  4,  7,  8,  etc.  The  positions  of  Stas.  5  and  6  are  indicated  by  the 
letters  C  and  D.  The  stations  are  to  be  located  in  their  proper  positions  on  the 
curve,  between  the  obstructions, 
wherever  it  is  possible  to  do  so. 
In  addition  to  this,  it  is  customary 
to  mark  with  a  tack  or  otherwise 
the  point  where  the  line  of  the 
curve  intersects  each  obstruction. 

Beginning  at  the  point  of  / 

curve  A ,  which  is  at  Sta.  3,  the 
curve  can  be  run  in  as  far  as  the 
first  obstruction,  which  is  the 
building  P,  setting  the  stakes  on 
the  curve  at  Stas.  4  and  5,  and 
a  tack  in  the  side  of  the  building 
P  at  the  point  where  the  line  of 
curve  intersects  it,  according  to 
the  deflection  angle  as  deter- 
mined by  its  distance  from  Sta.  5. 
It  is  not  possible  to  proceed  fur- 
ther in  the  regular  manner,  how- 
ever, because  Sta.  6  cannot  be 
seen  from  the  P.  C.  Therefore, 
it  is  necessary  to  locate  Sta.  7  by 
deflection  angle  V'BE,  from  B  or  » 
Sta.  4,  to  determine  the  chord 
4-7,  which,  in  this  case,  is  a  long 
chord  of  three  stations,  and  to  calculate  the  ordinates  D'D  and  C'C  by  sub- 
stituting for  a  in  the  preceding  formula  the  value  of  MC  =  MD'  =  half  a  station 
or  50  ft.  ' 

Fig.  5  shows  also  another  method  of  passing  a  building  S,  namely  by 
running  an  equilateral  triangle  FLG.  In  this  method,  the  instrument  is  set 
3P  *i  «  a;-8  and  S,lghtei back  -to  the  P"  C-  Then'  the  telescope  is  reversed  and 
the  deflection  angle  for  Sta.  9  is  turned  off  the  same  as  if  no  obstruction  existed 


FIG.  5 


SURVEYING 


115 


The  telescope  will  then  be  sighted  on  the  line  FG,  although  the  point  G  will  not 
be  visible.  The  angle  GFL,  equal  to  60°,  is  then  turned,  and  the  point  L  is 
located  so  that  FL  =  FG  =  100  ft.  The  instrument  is  next  moved  to  L,  and  the 
line  LG  is  run,  making  60°  with  FL.  On  this  line  the  distance  LG  =  100  ft.  is 
measured,  giving  the  point  G,  which  is  Sta.  9.  The  transit  is  then  set  up  at  this 
point  and  sighted  to  L,  and  an  angle  of  60°  is  turned  off  to  the  right,  giving  the 
direction  of  the  line  9-8,  the  intersection  of  which  with  5  is  marked.  The 
remainder  of  the  curve  may  be  run  in  the  following  manner:  Set  the  vernier 
at  an  angle  equal  to  the  deflection  angle  of  the  chord  9-8  to  the  left  from  the  0; 
clamp  the  upper  plate,  sight  at  the  point  set  in  the  line  9-8;  then  clamp  the 
lower  plate  and  set  vernier  at  0.  The  line  of  sight  will  then  be  in  the  tangent 
at  point  9,  and  by  plunging  the  telescope  the  remainder  of  the  curve  can  be 
run  as  if  the  point  9  were  the  P.  C. 

FIELD  NOTES  FOR  CURVES 

Various  styles  of  field  notebooks  are  published,  in  which  the  pages  are 
ruled  to  suit  the  different  kinds  and  methods  of  field  work.  The  accompany- 
ing, which  are  the  field  notes  of  a  portion  of  a  line  containing  a  curve,  represent 
a  good  form  for  recording  the  field  notes  of  a  curve  that  is  run  in  by  the  method 
of  zero  tangent. 

In  the  first  column  are  recorded  the  station  numbers;  in  the  second  column, 
the  deflections  with  the  abbreviations  P.  C.  and  P.  T.,  together  with  the  degree 
of  curve  and  the  abbreviation  R  or  L,  according  as  the  line  curves  to  the  right 
or  left.  At  each  transit  point  on  the  curve,  the  total  or  central  angle  from  the 
P.  C.  to  that  point  is  calculated  and  recorded  in  the  third  column.  This  total 
angle  is  double  the  deflection  angle  between  the  P.  C.  and  the  transit  point.  In 


these  notes,  there  is  but  one  intermediate  transit  point  between  the  P.  C.  and 
the  P.  T.  The  deflection  from  the  P.  C.  at  Sta.  3+20  to  the  intermediate 
transit  point  at  Sta.  4+50  is  2°  36'.  The  total  angle  is  double  this  deflection, 
or  5°  12',  which  is  recorded  on  the  same  line  in  the  third  C9lumn.  The  record 
of  total  angles  at  once  indicates  the  stations  at  which  transit  points  are  placed. 
The  total  angle  at  the  P.  T.  will  be  the  same  as  the  angle  of  intersection,  pro- 
vided the  work  is  correct.  When  the  curve  is  finished,  the  transit  is  set  up  at 
the  P.  T.,  and  the  bearing  of  the  forward  tangent  taken,  which  affords  an 
additional  check  upon  the  previous  calculations.  The  magnetic  bearing  is 
recorded  in  the  fourth  column,  and  the  deduced,  or  calculated,  bearing  is  re- 
corded in  the  fifth  column. 

EARTHWORK 

Cuts  and  Fills. — When  building  a  railroad,  cuts  and  fills  are  introduced 
to  equalize  the  irregularities  of  the  natural  soil.  Figs.  1  and  2  show  a  typical 
fill  and  cut  in  ordinary  firm  earth  or  gravel. 

Slope  Ratio. — In  cuts  in  the  hardest  rock,  the  average  slope  is  made  usually 
1:1;  that  is,  \  horizontal  to  1  vertical.  As  the  soil  becomes  less  firm,  the  slope 
must  be  flattened  until,  for  a  soil  of  firm  earth  or  gravel,  a  slope  of  1  to  1  may  be 
permissible,  although  a  slope  of  \\:\  is  commonly  adopted.  In  very  soft  soil, 
the  slope  ratio  is  sometimes  cut  down  even  as  far  as  4  horizontal  to  1  vertical. 


116 


SURVEYING 


The  standard  practice  in  a  fill  is  1J  horizontal  to  1  vertical.  When  a  fill  is 
made  of  the  material  from  a  rock  cut,  it  is  possible  to  make  a  stable  embank- 
ment with  a  slope  ratio  of  1:1.  On  side-hill  work,  where  a  slope  ratio  of  1^:1 
or  even  1:1  might  require  a  very  long  slope,  it  is  often  advisable  to  make  a  rough 
dry  wall  of  the  stones  from  a  rock  cut  that  will  have  a  slope  ratio  of  f  :1,  or  it 
may  even  be  steeper. 


FIG.  1 

Width  of  Excavations  and  Embankments. — The  width  required  for  a 
standard-gauge  single-track  roadbed  may  be  estimated  as  follows  (see  Figs.  1 
and  2) :  The  tie  will  be  between  8  and  9  ft.  long,  usually  8  ft.  6  in.,  and  at  the 
ends  the  ballast  will  slope  down  to  subgrade.  The  extra  width  required  for 
this  will  be  about  1  or  2  ft.  at  each  end  of  the  tie.  Usually,  the  embankment 
is  widened  for  about  2  ft.  beyond  the  ballast  on  each  side.  The  absolute 
minimum  for  the  width  of  subgrade  for  a  fill  is,  therefore,  8|ft.+2X(l+2)  ft. 
=  14j  ft.  This  width  would  be  used  only  for  light-traffic,  cheaply  constructed 
roads;  16  to  18  ft.  is  far  more  common,  while  20  ft.  and  even  more  is  frequently 
used,  as  the  danger  of  accident  due  to  a  washing  out  of  the  embankment  is 
materially  reduced  by  widening  the  roadbed. 

In  cuts,  the  proper  width  for  two  ditches  should  be  added.  Unless  the 
soil  is  especially  firm,  the  ditches  should  have  a  side  slope  of  1  J:l.  If  the  ditch 
is  12  in.  wide  at  the  base  and  12  in.  deep,  with  side  slopes  of  1?:1,  each  ditch 
will  require  a  total  width  of  4  ft.  This  will  add  8  ft.  to  the  width  of  the  cut  at 
the  elevation  of  subgrade.  The  usual  distance  between  track  centers  for 
double  track  is  13  ft.  Therefore,  whatever  rate  of  side  slopes  and  width  of 
ditches  is  required  for  single-track  work,,  the  width  for  double-track  work  must 
be  13  ft.  greater.  When  excavation  is  made  through  rock,  the  side  slopes  of 
the  ditches  may  properly  be  made  much  steeper;  the  danger  of  scouring  during 
heavy  rain  storms  being  eliminated,  the  total  required  width  may  be  very 
materially  reduced  from  the  figures  just  given.  The  heavy  expense  of  excavat- 
ing through  solid  rock  requires  that  such  economy  shall  be  used  if  possible. 

Grade  Profile. — For  the  purpose  of  constructing  a  road  as  well  as  for  cal- 
culating the  earthwork,  a  grade  profile  is  prepared  by  setting  stakes  on  the 
center  line  at  every  full  station  and  also  at  all  intermediate  points  at  which  the 
inclination  of  the  natural  surface  of  the  ground  changes  abruptly;  then,  by 
leveling,  the  elevation  of  the  natural  surface  at  each  stake  is  determined  and 
plotted,  as  explained  under  Leveling.  The  established  grade  is  then  drawn  in. 


FIG.  2 


It  consists  of  a  series  of  straight  lines,  the  elevations  of  the  ends  of  which  are 
clearly  indicated.  These  elevatipns  are  those  of  the  subgrade  ac.  Figs.  1  and  2. 
A  short  portion  of  a  profile  is  shown  in  Fig.  3.  The  horizontal  line  XX' 
represents  a  reference  plane,  and  the  broken  line  AGH  shows  the  position  of 
the  established  grade.  The  station  numbers  are  written  along  the  line  XX', 
and  the  elevations  of  the  corresponding  points  of  the  established  grade  are 


SURVEYING 


117 


written  along  the  grade  line.  Thus,  in  Fig.  3,  the  elevation  of  subgrade  at 
Sta.  90,  or  A,  is  100  ft.;  at  Sta.  93,  or  G,  it  is  102.28  ft.;  and  at  Sta.  94,  or  H, 
it  is  101.78  ft.  . 

The  gradient  of  the  established  grade  is  the  per  cent,  of  rise  or  fall  of  grade; 
that  is,  the  number  of  feet  by  which  the  elevation  increases  or  decreases  in 
100  ft.  It  is  usually  marked  on  the  grade  line  in  the  manner  shown  in  Fig.  3. 

The  depth  of  center  stake  is  the  difference  between  the  elevation  of  the 


natural  surface  at  any  stake  and  the  elevation  of  the  subgrade.  The  eleva- 
tion of  the  natural  surface  is  found  in  the  level  notes,  while  the  elevations  of 
the  subgrade  are  computed  from  the  gradients  and  also  entered  in  the  level 
notes.  The  difference  for  each  stake  is  then  figured  and  entered  in  a  column 
headed  Depth  of  Center  Stake,  being  preceded  by  the  letter  C  or  F  to  indi- 
cate cut  or  fill. 

EXAMPLE. — Stakes  are  set  at  the  stations  indicated  in  the  first  column  of  the 
accompanying  field  notes.  The  gradient  is  +.76%  from  Sta.  90  to  Sta.  93, 
and  -.50%  beyond  Sta.  93.  The  elevation  of  the  established  grade  at  Sta.  90 
is  100  ft.;  the  elevation  of  the  natural  surface  at  each  stake  is  given  in  the  third 
column.  Find  the  center  depth  at  each  stake.  (See  Fig.  3.) 


Station 

Subgrade 

Elevation 

Depth  of 
Center  Stake 

94 

101.8 

102.6 

C    .8 

93 

102.3 

103.3 

C  1.0 

92+51 

101.9 

97.3 

F4.6 

92 

101.5 

99.6 

F  1.9 

91+32 

101.0 

104.1 

C3.1 

91 

100.8 

103.2 

C  2.4 

90 

100.0 

100.0 

0 

SOLUTION. — The  elevations  of  the  subgrade  at  the  station  stakes  are  deter- 
mined as  follows: 

Station  Elevation 


91 
91+32 

92 
92+51 

93 

94 


100.00+1. 00  X 
100.00+1. 32  X 
100.00+2.00X 
100.00+2.51  X 
100.00+ 3.00  X 


.76=100.8 
.76  =  101.0 
.76  =  101.5 
.76=101.9 
.76  =  102.3 


102.28+ 1.00 X  -  .50  =  101.8 


The  center  depth  is  the  difference  between  the  corresponding  numbers  in 
the  second  and  third  columns.  This  is  a  fill  if  the  subgrade  is  higher  than 
the  natural  surface;  otherwise,  it  is  a  cut. 

Slope  Stakes. — In  addition  to  center  stakes,  slope  stakes  are  used  to  mark 
the  points  where  the  side  slopes  of  a  cut  or  a  fill  intersect  the  natural  surface 
of  the  ground.  In  Fig.  4,  c  is  the  center  stake  and  m  and  m'  are  the  slope 
stakes.  The  method  of  locating  slope  stakes  is  as  follows,  all  letters  referring 
to  Fig.  4: 

Let  b  be  the  width  IV  of  the  roadbed;  d,  the  depth  ceof  the  center  stake; 
and  5  the  slope  ratio  =  lk  +  mk  =  l'k'  +  m'k'.  For  the  upper  stake  at  m,  let  x 
be  the  distance  mq  from  the  slope  stake  to  the  center  line;  y+d,  the  elevation 
of  m  above  the  subgrade  =  qc+ce  =  mk.  Similarly  for  the  lower  stake  at  m'. 


118 


SURVEYING 


let  xf  be  the  horizontal  distance  m'q'  from  m' to  the  center  line,  and  let  d-y' 
•-m'k',  the  elevation  of  m'  above  the  subgrade. 


Then, 


and 


(1) 
(2) 


If  the  natural  surface  mem'  is  a  level  line,  so  that  q,  c,  and  q'  are  at  the 
same  elevation,  then  y  =  o,  y'  =  o,  and  . 

x  =  x'  =  ca  =  ca'  =  2+sXd        (3) 

Formulas  1  and  2  are  called  slope-stake  equations  and  formula  3  is  called  the 
level-section  equation.  The  last  formula  is  available  when  the  ground  is  nearly 
level.  When  the  ground  is  sloping  or  irregular  formula  1  is  employed,  but 
not  directly  as  the  value  of  y  is  not  known  until  after  the  stake  has  been  located. 
The  distance  x  or  x'  is  determined  by  successive  trials.  Suppose,  for  example, 
that  in  Fig  4  d  =  6.3,  and  let  the  rod  reading  on  the  point  c  be  5.9.  Suppose, 
also,'  that  5=  1.5  :  1  andfe  =  20.  Then,  if  the  ground  is  level,  by  formula  3, 

ac  =  20+ 1.5X6.3  =  19.5  ft. 

To  find  the  location  of  m,  the  rodman  will  hold  the  rod  at  some  point  more 
than  19.5  ft.  from  cr.  Suppose  that  he  holds  it  at  «,  20  ft  from  cr,  and  that  the 

reading  on  the 
rod  in  this  po- 
sition is  2.8. 
Then,  the  height 
of  this  point 
above  c  equals 
the  reading  on  c 

/~n  minus  the  read- 

ing' on  n,  or  5.9 
-  2.8  =  3.1  ft. 
The  computed 
distance  from 
the  rod  to  cr  is, 
by  formula  1, 
¥  +  1.5  X  6.3 
+  1.5  X  3.1 
=  24.2  ft.  As 
the  measured 
distance  (20  ft.) 
is  much  smaller 
than  this,  the 
rod  must  be 
moved  much 
farther  out. 

Suppose  that 
the  rod  is  car- 
ried out  7  ft.  so  that  the  measured  distance  to  cr  is  27  ft.,  and  suppose  that 
the  reading  on  the  rod  in  this  position  is  .8  ft.  The  elevation  of  this  trial  point 
above  c  will  be  5.9  — .8  =  5.1  ft.,  and  by  formula  1,  the  computed  distance  x 
is  ¥+1-5X6.3+1.5X5.1  =  27.2  ft.  This  agrees  so  closely  with  the  measured 
distance  that  the  slope  stake  may  be  driven  at  this  point. 

The  lower  slope  stake  at  m'  is  set  in  the  same  manner  as  the  upper,  except 
that  the  distance  of  each  trial  point  below  c  is  measured,  and  formula  2  is  used 
in  computing  the  corresponding  value  of  *'.  The  distance  of  the  trial  point 
from  cr  will  in  this  case  be  taken  less  than  the  distance  ca'  computed  by  for- 
mula 3.  As  in  the  preceding  case,  if  the  measured  distance  from  cr  to  the  trial 
point  is  less  than  the  computed  distance,  the  point  should  be  moved  out;  if 
greater,  it  should  be  moved  in. 

Form  of  Notes  in  Cross-Section  Work.— When  each  slope  stake  has  been 
set  as  just  explained,  its  distance  from  the  center  line  and  the  elevation  of  the 
stake  above  or  below  subgrade  are  entered  in  the  field  book  in  the  form  of  a 
fraction.  The  numerator  of  this  fraction  is  the  distance  of  the  stake  above 
or  below  subgrade,  and  the  denominator  is  the  distance  of  the  stake  from  the 
center  line.  Thus,  if  the  slope  stakes  in  the  preceding  example  are  set  at 
Sta.  131,  the  complete  entry  in  the  notebook  will  be  as  follows: 


SURVEYING 


119 


Station 

Subgrade 

Elevation 

Center 
Depth 

Left 

Right 

132 
131 
130 

149.80 
148.80 
147.80 

159.7 
155.1 
147.2 

C9.9 
C6.3 
F    .6 

C11.4 

C2.3 

27.2 

13.5 

The  fraction     y'    indicates  that  the  left  slope  stake  at  m.  Fig.  4,  is  27.2  ft. 

from  the  center  line  of  the  roadbed  and  11.4  ft.  above  subgrade.     Similarly,  the 

(~*2  ^ 
fraction  -r~  indicates  that  the  right  slope  stake  m'  is  13.5  ft.  to  the  right  of  the 

center  line  and  2.3  ft.  above  subgrade.     These  expressions  are  called  slope- 
stake  fractions. 

When  the  ground  between  the  slope  stakes  and  the  center  stake  is  irregular, 
the  elevations  and  distances  from  the  center  of  the  intermediate  points  where 
the  ground  changes  abruptly  are  determined  and  also  entered  in  the  notebook 
in  the  form  of  fractions. 

RAILROAD  LOCATION 

The  preliminary  survey  is  made  by  the  methods  given,  a  random  line  being 
run  along  the  proposed  route  and  a  map  of  the  region  made  covering  several 
hundred  feet  on  each  side  of  the  traverse.  The  map  should  show  both  banks  of 
any  streams  and  enough  levels  should  be  taken  to  show  the  contours  within 
the  width  covered  by  the  map.  This  width  will  depend  on  the  nature  of  the 
ground,  being  less  in  hilly  than  in  flat  country.  In  general,  the  map  should 
cover  the  ground  from  the  toe  of  one  side  hill  to  the  toe  of  the  other  and  should 
extend  a  distance  up  each  hill  to  an  elevation  beyond  which  it  would  not  be 
practicable  to  make  a  cut.  After  this  preliminary  line  has  been  mapped,  a 
preliminary  estimate  of  the  cost  of  the  proposed  work  may  be  made. 

Preliminary  Estimate. — When  making  a  preliminary  estimate,  great  accu- 
racy is  not  necessary,  and  no  time  should  be  wasted  in  useless  refinements  of 
calculation.  The  estimate  should  be  high  enough  to  cover  all  probable  cost, 
and  a  liberal  allowance  should  be  made  to  cover  unforeseen  contingencies  that 
may  develop  during  construction.  Most  experienced  engineers  make  it  a  rule 
to  add  10%  to  a  preliminary  estimate  in  order  to  provide  for  contingencies. 

When  estimating  for  earthwork,  the  cross-sections  may  be  considered  as 
level  cuttings;  that  is,  the  cross-section  surface  may  be  considered  as  level, 
unless  its  slope  angle  exceeds  10°,  in  which  case  a  suitable  allowance  must  be 
made  for  the  slope.  The  preliminary  estimate,  which  also  includes  approxi- 
mate figures  for  material  and  labor  required  for  culverts,  bridges,  trestles, 
piers,  and  abutments  is  then  classified  and  summarized.  A  sample  of  a  good 
form  of  a  preliminary  estimate  of  the  cost  of  a  proposed  railroad  follows: 

ESTIMATE  OF  COST — A  &  B  RAILROAD 

Clearing  625  A.  at  $20  per  A $  12,500 

Earth  excavation:  900,000  cu.  yd.  at  17c 153,000 

Loose-rock  excavation:  300,000  cu.  yd.  at  40c 120,000 

Solid-rock  excavation:  200,000  cu.  yd.  at  80c 160,000 


Overhaul  exceeding  600  ft.:  300,000  cu.  yd.  at  lc.. . 

Borrowed  embankment:  80,000  cu.  yd.  at  17c 

Piling:  12,000  lin.  ft.  at  25c 

Framed  trestles:  300,000  ft.  B.  M.  at  $35  per  M.. 

First-class  masonry:  2,800  cu.  yd.  at  $12 

Second-class  masonry:  4,200  cu.  yd.  at  $8 

Box  culvert  masonry:  2,300  cu.  yd.  at  $5 

Dry-rubble  masonry:  2,600  cu.  yd.  at  $4 

Concrete  masonry:  3,000  cu.  yd.  at  $6 

Riprap:  2,000  sq.  yd.  at  $1.50 

Cast-iron  pipe  culverts:  40,000  Ib.  at  3c 

Vitrified  pipe  culverts:  1,800  lin.  ft.  at  $1.50 

Total,  exclusive  of  bridges  and  track 

Add  10  per  cent 


3,000 
13,600 
3,000 
10,500 
33,600 
33.600 
11,500 
10,400 
18,000 
3,000 
1,200 
2,700 
$589,600 
58,960 
Total  cost  for  grading  and  trestles $648,560 


120 


SURVEYING 


Location.— The  location  is  the  operation  of  fitting  the  line  to  the  ground 
in  such  a  manner  as  to  secure  the  best  adjustment  of  the  almement  and  grade, 

consistent  with  an  economical 
cost  of  construction.  It  is  then 
best  projected  on  the  map,  and 
it  is  called  a  paper  location. 

An  example  of  such  location 
is  illustrated  in  Fig.  1.  Here, 
the  line  follows  the  valley  of 
Bear  River,  and  the  gradient 
is  determined  by  the  slope  of 
the  stream.  The  gradient 
adopted  is  .5%,  or  .5  ft.  per 
station.  The  preliminary  line 
is  shown  dotted,  and  the  located 
line  is  drawn  full. 

Let  the  grade  elevation  for 
Sta.  16  be  155  ft.;  the  grade  ele- 
vation for  Sta.  17  will,  there 
fore,  be  155  ft.  +  .5  ft.  =  155.5  ft. 
The  grade  elevation  for  Sta.  18 
will  be  155.5+.5  =  156  ft.  By 
the  same  process,  the  grade 
elevation  is  found  for  each  sta- 
tion shown  in  the  plat;  and  by 
means  of  interpolation  between 
two  contour  curves,  points 
having  the  required  elevation 
are  located  opposite  the  corre- 
sponding stations  of  the  pre- 
liminary survey.  Each  point 
is  marked  by  a  small  dot  en- 
closed in  a  circle.  A  line  join- 


ing the  points  thus  designated 
will  be  the  grade  contour,  or  the 


FIG.  1 


line  where  the  required  gradient 
meets  the  surface  of  the  ground. 
The  tangents  AB  and  CD  are 
then  projected  so  as  to  conform 
as  closely  as  practicable  to  the  grade  contour,  and  a  suitable  curve  is  inserted 
for  the  intersection  angle  EFD.  This  is  most  conveniently  done  by  means  of 
a  curved  protractor,  an  illustration  of  which  is  shown  in  Fig.  2.  This  instru- 
ment, which  is  made  of  transparent  material,  is  shifted  until  there  is  found  a 
curve  that  will  fit  the  topography  and  will  close  the  angle  between  the  tangents, 
as  required. 

Curvature. — There  is  no  fixed  rule  for  limiting  curvature,  but  for  a  per- 
manent track  it  is  desirable  to  have  the  curvature  as  easy  as  possible.     For 
all  ordinary 
traffic  condi- 
tions, it  is  good 
practice  to  use 
such  curves  as 
will    best    C9n- 
form  to  existing 
topographical 
conditions.  Any 
curve  up  to  10° 
will  be  no  ob- 
stacle to  a  speed 
of  35  mi.  per  hr.f 
the    average 
speed  of  passen- 
ger trains.   This 
practice  will  af- 
ford a  range  in  FIG.  2 
curvature  that  will  meet  the  requirements  of  almost  any  locality. 
.     Compensation  for  Curvature.— The  effect  of  curvature  on  a  railroad  line 
18  to  cause  a  resistance  to  the  movement  of  trains.     When  a  curve  occurs  on  a 


SURVEYING 


121 


gradient,  the  effect  of  the  curve  resistance  on  ascending  trains  is  practically 
the  same  as  increasing  the  gradient.  It  is  customary,  when  fixing  the  final 
grades,  to  lighten  the  grade  on  a  curve  by  an  amount  sufficient  to  offset  the  resis- 
tance due  to  the  curvature.  This  operation  is  called  compensating  for  curvature. 
The  usual  rate  of  compensation  for  curvature  is  .03  to  .05  ft.  per  100  ft.  per 
degree  of  curvature.  For  example,  where  the  maximum  gradient  on  tangents 
is  1%,  the  maximum  gradient  on  a  6°  curve,  allowing  a  compensation  of  .03  ft. 

r  degree,  would  be    1- (.03X6)  =  .82%. 
a  compensation  of   .05  ft.   per  degree 
were  made,  the  grade  on  a  6°  curve  would 
be  1- (.05X6)  =  .70%. 

Final  Grade  Lines. — The  establishing 
of  final  grade  lines  is  illustrated  in  Fig.  3, 
where  the  uncompensated  grade  is  1.3%, 
and  the  compensation  for  curvature,  as 
shown  on  the  final  grade  line,  is  .03  ft.  per 
degree.  The  location  notes  for  this  line  are 
as  given  on  page  122. 

The  elevation  of  the  grade  at  Sta.  27  is 
fixed  at  120  ft.,  and  at  Sta.  52,  at  152.5  ft., 
giving  between  these  stations  an  actual  rise 
of  32.5  ft.  and  an  uncompensated  grade  of 
1.3%.  These  grade  points  are  marked  on 
the  profile  with  small  circles.  The  total 
curvature  between  Sta.  27  and  Sta.  52  is 
108|°.  The  resistance  due  to  each  degree 
of  curvature  being  taken  as  equivalent  to 
an  increase  of  .03  ft.  in  grade,  the  total 
resistance  due  to  108.5°  is  equivalent  to 
.03X108.5  =  3.255  ft.  additional  rise  be- 
tween Sta.  27  and  Sta.  52.  Hence,  the 
total  theoretical  grade  between  these  sta- 
tions is  the  sum  of  32.5  ft.,  the  actual 
rise,  and  3.255  ft.  due  to  curvature,  or  40 
35.755  ft.  Dividing  35.755  by  25,  the  num- 
ber of  stations  in  the  given  distance,  there 
results  35.755 -r- 25  =+1.4302  ft.,  as  the 
grade  for  tangents  on  this  line.  The 
starting  point  of  this  grade  is  at  Sta.  27. 
The  P.  C.  of  the  first  curve  is  at  Sta.  29, 
giving  a  tangent  of  200  ft.  which  is  equal  to 
two  stations.  As  the  grade  for  tangents  is 
+  1.4302  ft.  per  station,  the  rise  in  grade 
between  Sta.  27  and  Sta.  29  is  1.4302X2 
=  2.8604  ft.  The  elevation  of  grade  at 
Sta.  27  is  120  ft.,  and  the  elevation  of  grade 
at  Sta.  29  is  120+2.8604  =  122.8604  ft. 
which  is  recorded  on  the  profile  as  shown  in 
the  diagram,  with  the  rate  of  grade,  namely, 
+  1.4302,  written  above  the  grade  line. 
The  first  curve  is  8°,  and,  as  the  compen- 
sation per  degree  is  .03  ft.,  then,  for  8°,  and 
a  full  station,  the  compensation  is  .03X8 
=  .24  ft.  The  grade  on  the  curve  will 
therefore  be  the  tangent  grade  minus  the 
compensation,  or  1.4302  -  .24  =  +1.1902  ft. 
per  station.  The  P.  C.  of  this  curve  is 
at  Sta.  29,  the  P.  T.  at  Sta.  33,  making 
the  total  length  of  the  curve  400  ft.  or 
four  stations.  The  grade  on  this  curve  is 


FIG.  3 


+  1.1902  ft.  per  station  and  the  total  rise  on  the  curve  is  1.1902X4  =  4.7608  ft. 
The  elevation  of  the  grade  at  the  P.  C.  at  Sta.  29  is  122.8604;  hence,  the 
elevation  of  grade  at  the  P.  T.  at  Sta.  33  is  122.8604+4.7608  =  127.6212  ft., 
which  is  recorded  on  the  profile  together  with  the  grade,  namely,  +1.1902, 
written  above  the  grade  line.  The  P.  C.  of  the  next  curve  is  at  Sta.  37+50, 
giving  an  intermediate  tangent  of  450  ft.,  or  four  and  one-half  stations.  The 
grade  for  tangents  is  +1.4302  ft.  per  station;  hence,  the  total  rise  on  the  tan- 
gent is  1.4302X4.5  =  6.4359  ft.  Adding  6.4359  ft.,  to  127.6212  ft.,  the  elevation 


122  SURVEYING 

of  grade  at  Sta.  37+50  is  found  to  be  134.0571  ft.,  which  is  recorded  on  the 
profile,  together  with  the  rate  of  grade  for  tangents. 
LOCATION  NOTES 


52+00 

End  of  Grade 

49  +  75  P.  T. 

44+25  P.  C.  9°  R. 

49°  30' 

42+00  P.  T. 

37+50  P.  C.  6°  L. 

27°  00' 

33+00  P.  T. 

29+00  P.  C.  8°  R. 

32°  00' 

27+00 

Beginning  of  grade 

The  next  curve  is  6°,  and  the  compensation  in  grade  per  station  is  .03  ft. 
X6  =  .18  ft.  The  grade  on  this  curve  will  therefore  be  1.4302  — .18=  1.2502  ft. 
per  station.  The  length  of  the  curve  is  450  ft.,  or  four  and  one-half  stations, 
and  the  total  rise  in  grade  on  this  curve  is  +1.2502  ft.  X 4.5  =  5.6259  ft.  The 
elevation  of  the  grade  at  Sta.  37+50,  the  P.  C.  of  the  curve,  is  134.0571.  The 
elevation  of  the  grade  at  Sta.  42,  the  P.  T.,  is  therefore  134.0571  +  5.6259 
=  139.683  ft.,  which  is  recorded  on  the  profile,  together  with  the  rate  of  grade 
on  the  6°  curve,  namely,  +1.2502.  The  P.  C.  of  the  next  curve  is  at  Sta.  44 
+25,  giving  an  intermediate  tangent  of  225  ft.,  or  two  and  one-fourth  stations, 
The  total  rise  on  the  tangent  is,  therefore,  1.4302X2.25  =  3.21795  ft.  The 
elevation  of  grade  at  the  P.  T.  at  Sta.  42  is  139.683;  therefore,  the  elevation  of 
grade  at  Sta.  44+25  is  139.683+3.21795=  142.90095  ft.,  which  is  recorded  on 
the  profile,  together  with  the  grade  +1.4302. 

The  last  curve  is  9°,  and  the  compensation  in  grade  per  station  is  .03X9 
=  .27  ft.  The  grade  on  this  curve  is  therefore,  1.4302 -.27  =  1.1602  ft.  per 
station.  The  length  of  the  curve  is  550  ft.,  or  five  and  one-half  stations,  and 
the  total  rise  on  the  curve  is  1.1602X5.5  =  6.3811  ft.  The  elevation  of  grade 
at  Sta.  44+25,  the  P.  C.  of  the  9°  curve,  is  142.90095;  hence,  the  elevation  of 
grade  at  the  P.  T.,  at  Sta.  49  +  75,  is  142.90095+6.3811  =  149.28205  ft.,  which  is 
recorded  on  the  profile,  together  with  the  grade,  +1.1602.  The  end  of  the 
line  is  at  Sta.  52,  giving  a  tangent  of  225  ft.,  or  two  and  one-fourth  stations. 
The  rise  on  this  tangent  is  1.4302X2.25  =  3.21795  ft.,  which  is  added  to 
149.28205,  the  elevation  of  the  P.  T.  at  Sta.  49  +  75.  The  sum,  152.5  ft.,  is 
the  elevation  of  grade  at  Sta.  52. 

The  sum  of  the  partial  grades  should  equal  the  total  rise  between  the 
extremities  of  the  grade  line.  The  points  where  the  changes  of  grade  occur 
are  marked  on  the  profile  with  small  circles,  which  are  connected  by  fine  lines 
representing  the  grade  line.  These  points  of  change  are  projected  on  a  hori- 
zontal line  at  the  bottom  of  the  profile.  The  portions  of  this  line  that  represent 
curves  are  dotted,  and  the  portions  that  represent  tangents  are  drawn  full. 
The  P.  C.  and  P.  T.  of  each  curve  are  marked  with  small  circles  on  this 
horizontal  line,  and  are  lettered  as  shown  in  the  diagram. 

Where  the  grades  are  light  and  the  curves  have  large  radii,  there  will  be  no 
need  of  compensation  for  curvature.  Where  the  grades  exceed  .5%  and  the 
curves  5°,  compensation  should  be  made. 

VERTICAL  CURVES 

If  the  grade  of  the  center  line  of  track  changes  at  any  point,  the  two 
grade  lines  that  intersect  at  this  point  form  with  each  other  an  angle  more  or 
less  abrupt.  If  this  angle  points  upwards,  it  is  called  a  spur;  if  it  points  down- 
wards, it  is  called  a  sag.  The  angles  CVD  in  Fig.  1  (a)  and  (b)  are  spurs;  the 
angles  CVD  in  Fig.  2  (a)  and  (b)  are  sags. 

Vertical  Curve  at  a  Spur.— If  AV  and  BV,  Fig.  3,  are  two  grade  lines 
meeting  at  V,  a  vertical  curve  CM D  must  be  introduced  to  join  these  lines. 


SURVEYING 


123 


Between  C  and  D,  the  actual  grade  is  established  along  the  vertical  curve  CM D, 
instead  of  along  CV  and  VD.  The  projections  RT  and  TS  of  the  distances  VC 
and  VD  from  the  vertex  to  the  points  at  which  the  vertical  curve  begins  and 


fb) 

FIG.  2 

ends  are  always  chosen  equal.  If  K  is  the  middle  point  of  the  straight  line  CD, 
the  vertical  curve  is  always  so  chosen  that  it  will  bisect  VK\  that  is,  so  that 
VM^MK. 

Let  E  be  the  elevation  of  C,  Fig.  3,  E'  that  of  D,  and  H  that  of  V,  so  that  E 
-  RC,  E'  =  SD,  and  ff  =  VT.     Then, 


The  distance  FM  is  called  the  correction  in  grade  at  the  point  V. 
Vertical  curves  are  always  made  parabolic.     It  is  a  property  of  the  parabola 
that  the  correction  in  grade  am  at  any  point  a  is  given  by  the  equation. 


The  distance  CV=  VD  is  always  made  a  whole  number  of  stations;  and,  to 
simplify  the  work,  the  grade  stakes  a,  b,  c,  etc.,  are  so  set  that  they  divide  the 
distance  CV  into  a 
number  of  equal 
parts.  The  correc- 
tions in  grade  at 
points  a',  b',  and  c' 
along  DV  are  equal 
to  those  for  the  cor- 
responding points 
along  CV.  That  is, 
if  Ca  =  Da',  then 
am  —  a'm' ;  if  Cb 
*=Dbr,  then  bm 
=  b'm',etc. 

EXAMPLE. — A 
+  .4%  grade  meets 


FIG.  3 


—  .5%  grade  at  Sta.  190,  the  elevation  of  which  is  161.3  ft.  If  a  vertical 
curve  400  ft.  long  is  inserted,  what  is  the  correction  in  grade  and  the  corrected 
grade  elevation  at  each  station  and  half  station? 

SOLUTION.  —  In  this  example,  VC  =  VD  =  200  ft.  The  elevation  of  C  is  161.3 
-2X.  4  =  160.5  ft.,  =  E;  that  of  D  is  161.3  -2X.  5  =  160.3  ft.,  =  E';  that  of  K 
is  *  (E'+E)  =  *X  (160.5  +  160.3)  =  160.4  ft.;  and  that  of  V  is  H  =  161.3  ft. 
Substituting  these  values  in  the  formula  for  VM, 


=  $X  (161.3  -  160.4)  =  .45  ft. 
Since,  for  the  first  stake,  Ca  =  50  ft.  and  CF 


.  200  ft.,  the  formula  for  am 

gives  am  =  (£?a)*X  VM  =  T^X  .45  =  .03  ft.  =  a'm' 

Similarly,  bm=    (M8)2XFM  =  iX.45  =  .ll  =  6'm' 

cm  =  (ifcjj)*  X  VM  =  ft  X  .45  =  .25  =  c'm' 
The  original  and  corrected  grade  elevations  are  as  follows: 


Station 

188 
+  50 

189 
+  50 

190 
+50 

191 
+£0 

192 


Original 
Elevation 
160.50 
160.70 
160.90 
161.10 
161.30 
161.05 
160.80 
160.55 
160.30 


Correction 

.00 
.03 
.11 
.25 
.45 
.25 
.11 
.03 
.00 


Corrected 
Elevation 
160.50 
160.67 
160.79 
160.85 
160.85 
160.80 
160.69 
160.52 
160.30 


124  SURVEYING 


Vertical  Curve  at  a  Sag.— If  two  grade  lines,  AV  and  VB  Fig.  4,  meet  so 
as  to  form  a  sag,  the  vertical  curve  will  evidently  be  wholly  above  both 
grade  lines.  Using  the  same  notation  as  before,  the  correction  m  grade  at  the 

B  point  V  will  be 


The  correction 
in  the  grade  at  any 
point  a  will  be  given 
by  the  preceding 
formula  for  am,  as 

Datum  Plane       ± ^ before.     This  cor- 

„       .  rection,  however,  is 

FlG-  4  now  to  be  added 

to  the  old  elevation  of  the  grade  at  a  to  obtain  the  corrected  elevation. 
EXAMPLE.— The  grade  of  CV,  Fig.  4,  is- 1.2%,  that  of  VD  is  +.6%,  and 
the  elevation  of  V  is'+49.2  ft.     Find  the  corrections  in  grade  and  the  corrected 
elevations  at  stakes  100  ft.  apart,  if  the  length  of  the  vertical  curve  is  600  ft. 
SOLUTION. — The  unconnected  grade  elevations  are  as  follows: 
Along  CV  Along  VD 

At  first  stake. 52.8       At  fifth  stake 49.8 

At  second  stake 51.6       At  sixth  stake 50.4 

At  third  stake 50.4       At  seventh  stake,  D 51.0 

At  fourth  stake,  V 49.2 

Therefore.  i(E+E')  =  *X  (52.8+51.0)  =  51.9; 

and,  by  the  preceding  formula, 

VM  =  |X  (51.9-49.2)  =  1.35  ft. 

The  formula  for  am  may  now  be  applied.     Correction  in  grade  at  second 
stake,  100  ft.  from  C,  is  (i£§)2X  1.35  =  4X1.35=-.  15,  correction  at  sixth  stake. 
Correction  at  third  stake,  (§gg)2X  1.35  =  |X  1.35  =  .60,  correction  at  fifth  stake. 
The  corrected  elevations  will  be 

At  C 52.80+  .00  =  52.80 

At  second  stake 51.60+  .15  =  51.75 

At  third  stake 50.40+  .60  =  51.00 

At  fourth  stake 49.20+1.35  =  50.55 

At  fifth  stake 49.80+   .60  =  50.40 

At  sixth  stake 50.40+   .15  =  50.55 

At  D 51.00+  .00  =  51.00 

CURVED  TRACK 

The  difference  in  length  between  the  inner  and  the  outer  rail  of  a  standard- 
gauge  curve  may  be  found  by  either  of  the  following  rules: 

Rule  I. — Multiply  the  Degree  of  the  curve  by  the  length,  in  stations  of  100  //., 
and  this  product  by  l&;  the  result  will  be  the  difference  in  length  between  the 
inner  and  the  outer  rail,  in  inches. 

Rule  II. — Multiply  the  distance  between  the  center  lines  of  the  rails  by  the 
length  of  the  curve,  in  feet,  and  divide  the  product  by  the  radius  of  the  track  curve; 
the  quotient  will  be  the  required  difference  in  length,  expressed  in  feet. 

For  light  curves  laid  to  exact  gauge,  the  first  rule  is  the  simpler  one,  but  for 
short  curves  where  the  gauge  is  widened,  the  second  rule  should  be  used. 

Curving  Rails. — When  laying  track  on  curves,  in  order  to  have  a  smooth 
line,  the  rails  themselves  must  conform  to  the  curve  of  the  center  line.  To 
accomplish  this,  the  rails  must  be  curved.  The  curving  should  be  done  with 
a  rail  bender  or  with  a  lever,  preferably  with  the  former.  To  guide  those  in 
charge  of  this  work,  a  table  of  middle  and  quarter  ordinates  for  a  30-ft.  rail  for  all 
degrees  of  curve  should  be  prepared.  The  middle  ordinates  in  the  following 
table  are  calculated  by  the  formula 

in  which  m  =  middle  ordinate; 

c  =  length  of  chord,  assumed  to  be  of  same  length  as  rail; 
R  =  radius  of  curve. 

This  formula  is  not  theoretically  correct;  yet  the  error  is  so  small  that  it 
may  be  ignored  in  practical  work. 


SURVEYING 


125 


In  curving  rails,  the  ordinate  is  measured  by  stretching  a  cord  from  end  to 
end  of  the  rail  against  the  gauge  side,  as  shown  in  the  accompanying  illustra- 
tion. Suppose  the  rail  AB  is  30  ft.  in 
length,  and  the  curve  8°,  then  the  mid- 
dle ordinate  at  a  should  be 


To  insure  a  uniform  curve  to  the  rails,  the  ordinates  at  the  quarter  points  b 
and  b'  should  be  tested.  In  all  cases  the  quarter  ordinates  should  be  three- 
quarters  of  the  middle  ordinate.  In  the  illustration,  if  the  rail  has  been  properly 
curved,  the  quarter  ordinates  at  b'  and  b  will  be  f  X  If  in.  =  IJf,  say  If. 

MIDDLE  ORDINATES  FOR  CURVING  RAILS 


Degree  of 
Curve 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 


30 


Length  of  Rail,  in  Feet 


28 


26 


24 


22 


Middle  Ordinates,  in  Inches 


j.   6 

I! 


20 


TURNOUTS 

A  turnout  is  a  contrivance  for  passing  from  one  track  to  another.  The 
principal  parts  are  the  switch,  the  frog,  and  two  guard-rails.  The  switch, 
which  is  the  movable  part  of  the  turnout,  consists  of  two  switch  rails  BA  and 
CD,  Fig.  1.  The  fixed  ends  B  and  C  of  the  switch  rails  are  called  the  heels  of 
the  switch,  and  the  movable  ends  A  and  D,  the  toes  of  the  switch.  The  cross- 
tie  that  supports  the  toes  of  the  switch  is  called  the  head-block,  and  the  tie- 
rod  at  the  toes,  the  head-rod.  The  distance  A  A'  or  DD'  through  which  the 
toes  move  is  called  the  throw  of  the  switch.  A  frog  is  shown  at  K  and  two 
guard-rails  at  R  and  R'. 

Switches. — There  are  two  kinds  of  switches,  which  differ  in  the  arrange- 
ment and  form  of  switch  rails,  namely,  the  stub  switch  and  the  point  switch. 
In  the  stub  switch,  Fig.  1,  a  part  of  each  main-track  rail  is  bent  over  to  connect 
with  the  side  track.  In  the  point  switch,  Fig.  2,  the  outer  rail  DV  of  the  main 
track  is  spiked  rigidly  to  the  ties;  the  opposite  rail  EA'U,  lying  partly  in  the 
main  track  and  partly  in  the  side  track,  is  also  firmly  spiked.  These  two  rails 
are  immovable.  The  two  switch  rails  BA  and  CD  are  planed  to  thin  edges  at  A 
and  D.  The  ends  B  and  C  of  these  rails  are  the  fixed  ends  or  heels;  the  thin 
edges  at  A  and  D  are  the  toes.  The  head-block  is  at  H,  and  the  head-rod  at  g. 


126 


SURVEYING 


The  point  of  the  center  line  at  which  the  turnout  begins  is  called  the  point 
of  switch  In  Figs.  1  and  2,  W  is  the  point  of  switch.  In  stub  switches,  the 
point  of  switch  is  midway  between  the  heels;  in  point  switches, 
it  is  midway  between  the  toes  and 
above  the  head-block. 

Frogs  and  Guard-Rails. — A  frog  is 
a  combination  of  rails  so  arranged  that 
the  broad  tread  of  the  wheel  will 
always  have  a  surface  on  which  to 
roll,  and  that  the  flange  of  the  wheel 
will  have  a  channel  through  which  to 
pass.  A  frog  is  shown  in  position  on 
the  track  at  K,  Fig.  1,  and  a  larger  plan 
of  the  part  at  ab,  Figs.  1  and  2,  is  shown 
in  Fig.  3. 

The  wedge-shaped  part  akb  of  the 
frog  is  called  the  tongue  of  the  frog, 
and  its  point  k  is  called  the  actual 
point  of  frog.  The  actual  point  of  frog 
is  somewhat  shortened  and  rounded. 
The  intersection  c  of  the  outside  edges 
ac  and  be  of  the  tongue  is  called  the 
theoretical  point  of  frog.  When  the 
point  of  frog  is  referred  to,  the  theo- 
retical point  is  usually  meant.  The 
bent  rails  wr  are  called  wing  rails;  the 
narrowest  part  mp  of  the  frog  is  called 
the  throat.  The  throat  of  the  frog 
must  be  wide  enough  to  allow  the 
flanges  of  the  wheels  to  pass  through; 
it  is  usually  made  about  2  in.  wide. 

Frog  Angle  and  Frog  Number. — The 
angle  acb,  Fig.  3,  between  the  outside 


E 

FIG.  1 
edges  of  the  tongue  of  theTrog  is  called  the  frog  angle. 


If 

FIG.  2 
This  is  also  equal  to  the 


angle  dee  between  the  outside  edges  of  the  tongue  produced  beyond  c.'  The  frog 
angle  which  is  represented  by  F  is  also  equal  to  the  angle  between  the  two 
tracks. 

The  distance  ab  between  the  gauge  lines  at  the  end  of  the  tongue  is  called 
the  heel  width;  the  distance  de,  the  mouth  width.  If  sch  is  the  bisector  of  the 
angle  F,  the  distance  ch  is  called  the  length  of  frog. 

The  ratio  of  the  length  to  the  heel  width  is  called  the  frog  number,  and  is 
usually  denoted  by  n;  that  is, 

n  =  ch  -r-  ab 

The  relation  between  n  and  F  is  expressed  by  the  formulas 


and 


cot£F  = 


FIG.  3 

Frogs  are  usually  designated  by  their  numbers;  thus,  a  No.  8  frog  is  one 
in  which  n  =  8. 

If  the  distance  sh  and  the  widths  ab  and  de,  Fig.  3,  are  measured  on  a  frog, 
the  frog  number  n  can  be  determined  by  the  formula 

sh 
n~ab+de 


SURVEYING 


127 


Guard-Rails.  —  Guard-rails,  which  are  usually  from  10  to  15  ft.  long,  are 
placed  opposite  the  frog  on  the  main  track  and  the  switch  track,  as  at  R 
and  R'  in  Figs.  1  and  2.  The  clear 
space  between  the  head  of  the  guard-rail 
and  the  head  of  the  main  or  the  switch 
rail  should  be  about  2  in. 

Radius  and  Lead  of  a  Turnout  for 
Stub  Switches.—  Let  RN,  Fig.  4,  be  the 
main  track  and  QP  the  turnout.  Let 
Q  be  the  point  of  switch  and  K  the  point 
of  frog.  If  a  stub  switch  is  employed, 
the  main-track  rails  will  be  securely 
spiked  along  YB  and  LD\  the  parts  BG 
and  DV  of  these  rails  will  be  movable, 
so  that  they  may  be  bent  outwards  to 
meet  the  turnout  rails  W  and  Z.  Here, 
then,  the  ends  B  and  D  are  the  heels 
of  the  switch,  and  G  and  V  are  the  toes. 
The  head-block  is  underneath  G  and  V. 

In  order  to  lay  out  a  turnout  when 
the  frog  angle  is  given,  it  is  necessary 
to  find  the  radius  r,  in  terms  of  the  frog 
angle,  and  the  distance  KB  from  the 
point  of  frog  to  the  heel  of  switch,  which  distance  is  called  the  lead  and  is  desig- 
nated by  L. 

The  formulas  for  r  and  L  are: 

r=igcot2  JF  =  2gns 
and  L=  g  cot  \F 

In  these  formulas  g  denotes  the  gauge. 
8|  in.  =  4.708  ft. 

The  accompanying  table,  some  parts  of  which  are  calculated  from  the  fore- 
going formulas,  can  be  used  in  laying  out  a  turnout  with  a  stub  switch.     The 


FIG.  4 


R     L 


The  standard  gauge  of  track  is  4  ft. 


DIMENSIONS  OF  STUB-SWITCH  TURNOUTS 


Track  Circular  From  Heel  of  Switch  to  Point  of  Frog.     Throw  =  5f  In. 


Frog 
Num- 
ber 
n 

Frog  Angle  F 

LeadL 

Chord 
(QT) 

Radius 

Degree 
of 
Curve 
d 

Length 
of 
Switch 
Rails 

Dis- 
tance 
Ka, 
Fig.l 

4.0 

14°  15'  00" 

37.67 

37.38 

150.67 

38°  46' 

11.73 

1.50 

4.5 

12    40    59 

42.37 

42.12 

190.69 

30    24 

13.19 

1.69 

5.0 

11     25    16 

47.08 

46.85 

235.42 

24    32 

14.65 

1.87 

5.5 

10     23    20 

51.79 

51.58 

284.85 

20    13 

16.15 

2.06 

6.0 

9    31    38 

56.50 

56.30 

339.00 

16    58 

17.64 

2.25 

6.5 

8    47    51 

61.21 

61.03 

397.85 

14    26 

19.09 

2.44 

7.0 

8     10    16 

65.92 

65.75 

461.42 

12    26 

20.53 

2.62 

7.5 

7    37    41 

70.62 

70.47 

529.69 

10    50 

22.03 

2.81 

8.0 

7      9    10 

75.33 

75.19 

602.67 

9    31 

23.48 

3.00 

8.5 

6    43    59 

80.04 

79.90 

680.36 

8    26 

24.93 

3.19 

9.0 

6    21    35 

84.75 

84.62 

762.75 

7    31 

26.43 

3.37 

9.5 

6       1    32 

89.46 

89.33 

849.85 

6    45 

27.97 

3.56 

10.0 

5    43    29 

94.17 

94.05 

941.67 

6    05 

29.37 

3.75 

10.5 

5    27      9 

98.87 

98.76 

1,038.19 

5    32 

30.85 

3.94 

11.0 

5     12    18 

103.58 

103.47 

1,139.42 

5    02 

32.31 

4.12 

11.5 

4     58    45 

108.29 

108.19 

1,245.36 

4    36 

33.78 

4.31 

12.0 

4     46    19 

113.00 

112.90 

1.356.00 

4    14 

35.17 

4.50 

frog  number,  which  is  usually  given,  is  stated  in  the  first  column;  the  corre- 
sponding frog  angle  in  the  second  column;  and  the  lead,  or  BK,  Fig.  4,  in  the 
third  column.  Then  follow  columns  containing  the  chord  QT,  Fig.  4,  which  is 


128 


SURVEYING 


equal  to  2r  sin  £F;  the  radius  of  the  turnout;  the  corresponding  degree  of  curve 
which  is  equal  to  5iZi9;  the  length  I  of  switch  rails  A  B,  Fig.  1,  obtained  by  the 

formula  1=  V*(2r  — <);  and  the  distance  Ka,  Fig.  1,  or  cw,  Fig.  3,     With  dif- 
ferent forms  of  frogs,  this  distance  varies;  the  engineer  should  therefore  measure 

it  for  the  different  frogs  he  uses,  as  it 
is  necessary  in  determining  the  length 
of  spiked  rail  Aa,  Fig.  1. 

Turnout  Dimensions  for  Point 
Switches.  —  Let  MN,  Fig.  5,  be  the 
center  line  of  the  main  track  and  MJ 
that  of  the  turnout.  Let  BA  and  CD 
be  the  two  switch  rails  whose  fixed 
ends,  or  heels,  are  at  B  and  C,  and 
whose  toes  are  at  A  and  D.  These 
rails  are  usually  of  a  uniform  length 
of  15  ft.,  except  for  the  sharpest 
curves. 

The  center  line  MIJ  will,  when  a 
point  switch  is  used,  have  a  some- 
what different  position  from  that 
which  it  has  when  a  stub  switch  is 
employed.  In  the  stub-switch  turn- 
out, the  rails  A'TU  and  DCK  are 
bent  to  a  uniform  curve  between  M 
and  J;  in  a  point  switch,  the  outer  rail  is  made  up  of  a  straight  part  DC, 
which  is  the  switch  rail,  and  a  curved  part  CE,  which  is  tangent  to  DC 
at  C.  On  this  account,  the  lead  A'K  is  less  with  a  point  switch  than  with  a 

DIMENSIONS  OF  POINT-SWITCH  TURNOUTS 

Turnouts  With  Straight  Point  Rails  and  Straight  Frog  Rails; 
Gauge  4  Ft.  8^. In. 


FIG.  5 


to 

g 

t_. 

^ 

fc 

K) 

^ 

"o-a 

CJ" 

«-t-i  ^ 

O  ctf 

^.S^ 

q 

to 

fee 

& 

1 

]! 

a 

•3 

rt 
M 

11 

1 

o 

|J3 

O5 

!i| 

4.0 

14°  15'  00" 

3°  40' 

32.20 

125.21 

47°  05' 

23.09 

7.5 

1.50 

4.5 

12    40    49 

3     40 

34.29 

159.25 

36    36 

25.03 

7.5 

1.69 

5.0 

11    25    16 

2    45 

41.85 

197.65 

29     22 

29.88 

10.0 

1.87 

5.5 

10    23    20 

2    45 

44.16 

240.44 

24     00 

32.03 

10.0 

2.06 

6.0 

9    31    39 

1     50 

56.00 

288.09 

19     59 

38.66 

15.0 

2.25 

6.5 

8    47    51 

1     50 

58.84 

340.19 

16     54 

41.34 

15.0 

2.44 

7.0 

8     10    16 

1     50 

61.65 

397.65 

14    27 

43.98 

15.0 

2.62 

7.5 

7    37    41 

1     50 

64.36 

460.00 

12     29 

46.50 

15.0 

2.81 

8.0 

7      9    10 

50 

67.04 

527.91 

10     52 

48.99 

15.0 

3.00 

8.5 

6    43    59 

50 

69.60 

600.94 

9    33 

51.38 

15.0 

3.19 

9.0 

6    21    35 

50 

72.20 

681.16 

8    25 

53.80 

15.0 

3.37 

9.5 

6      1    32 

50 

74.70 

767.11 

7     28 

56.11 

15.0 

3.56 

10.0 

5    43    29 

50 

77.04 

858.14 

6    41 

58.28 

15.0 

3.75 

10.5 

5    27      9 

50 

79.51 

959.00 

5     59 

60.57 

15.0 

3.94 

11.0 

5     12    18 

50 

81.82 

1,065.52 

5    23 

62.69 

15.0 

4.12 

11.5 

4    58    45 

1     50 

84.09 

1,180.16 

4    51 

64.78 

15.0 

4.31 

12.0 

4     46    19 

1     50 

86.16 

1,299.93 

4    24 

66.67 

15.0 

4.50 

stub  switch.  As  point  switches  are  used  on  the  main  line  where  very  accurate 
work  is  required,  it  is  necessary  to  take  account  of  the  fact  that  the  short  frog 
rails  are  not  curved,  the  part  EE'  of  the  rail  being  straight. 


SURVEYING 


129 


In  computing  the  dimensions  of  a  point-switch  turnout,  the  usual  data  are 
the  length  AB  =  DC  of  the  switch  rail,  the  angle  CDP  between  the  outer  switch 
rail  and  the  main  rail.  This  angle  is  called  the  switch  angle,  and  will  be  rep- 
resented by  5.  The  frog  number  or  the  frog  angle  must  also  be  known,  as  well 


FlG.  6 


as  the  length  of  the  straight  part  EE'.  It  is  then  required  to  determine  the 
radius  OI  of  the  center  line  of  a  turnout  whose  outer  rail  shall  be  tangent  to 
the  switch  rail  DC  at  C  and  to  the  frog  rail  EE'  at  E,  and  to  find  the  lead  A'K  of 
this  turnout. 

The  formulas  for  computing  these  quantities  are  so  complicated  that,  in 
practice,  tables  giving  the  various  dimensions  of  point  switches  are  always 
employed. 

The  accompanying  table  contains  all  the  dimensions  necessary  for  laying 


__!  =  CD  of  the  switch  rails,  and  the  length  KE  =  Ka  of  the  straight  frog  rail. 
Turnouts  From  the  Outer  Side  of  a  Curved  Track. — A  turnout  from  the 
outer  side  of  a  curved  track  is  shown  in  Fig.  6.  The  radius  DE  =  Rof  the  main 
track,  the  frog  angle  F,  or  frog  number  n,  and  the  gauge  g  are  usually  known; 
from  these  the  lead  BK  =  L,  and  the  radius  Oe  =  roi  the  center  line  of  the  turnout 
must  be  computed.  The  angle  M ,  must  first  be  found  by  the  formula 

a  <        gn 

tan  \M  —  —  cot  jr  =  -^ 

Then,  the  lead  must  be  determined 
by  the  formula 


Finally,  r  is  given  by  the  formula 


When  r  has  been  found,  the  degree 
of  curve  is  given  by  the  formula 
5/730 


If  the  main-track  curve  is  not  very 
sharp,  this  value  of  d  may  be  obtained 
by  subtracting  the  degree  of  curve  of 
the  main  track  from  that  obtained  from  the  sixth  column  of  the  table  for  stub 
switches.     The  lead  L  may  also  be  taken  from  the  table. 

If  the  curvature  of  the  main  track  is  very  sharp,  or  if  the  frog  angle  is  very 
small,  the  turnout  may  curve  in  the  same  direction  as  the  main  track;  in  which 
case,  the  degree  of  curve  taken  from  the  stub-switch  table  will  be  less  than  the 
degree  of  curve  of  the  main  track.  The  difference  between  the  two  degrees 
of  curve  will  still  be  equal  to  the  degree  of  curve  of  the  turnout.  If  the 
degrees  of  curve  are  equal,  the  turnout  rails  will  be  straight. 


FIG.  7 


130 


SURVEYING 


Turnout  from  the  Inner  Side  of  a  Curved  Track. — A  turnout  from  the  inner 
side  of  a  curved  track  is  shown  in  Fig.  7.  The  radius  OR  of  the  turnout  is 
always  less  than  the  radius  DH  of  the  main  track.  The  degree  of  curve  of  the 
center  line  of  the  turnout  and  the  lead  BK  are  found  as  follows: 

Rule  I. — Take  from  the  table  for  a  stub  or  for  a 
point  switch,  the  value  of  the  degree  of  curve  corre- 
sponding to  the  given  frog  number.  Add  this  to  the 
degree  of  curve  of  the  main  track.  The  sum  is  the 
degree  of  curve  of  the  turnout. 

Rule  II. — Take  the  value  of  the  lead  from  the  table 
for  a  stub  or  for  a  point  switch,    corresponding  to 
Y»  the  given  frog  number.     This  will  be  the  value  of  the 
1  desired  lead  BK,  Fig.  7. 

CONNECTING  CURVES 

A  connecting  curve  is  a  curve  introduced  to  con- 
nect a  turnout  with  a  side  track.  Thus,  in  Fig.  8, 
the  two  parallel  straight  tracks  are  connected  by 
the  turnout  ME  and  the  curved  track  ED.  The 
values  of  n  and  g,  and  the  distance  a,  usually 
taken  as  13  ft.,  must  be  known;  then  the  radius  r' 
—  O\D  =  OiE,  and  distance  KT  may  be  computed 
by  the  formulas 

r'  =  2(a-g) 


and 


KT-- 


'XL 


L  is  the  lead  PK  of  the  turnout,  and,  in  such 
cases  as  this,  is  always  to  be  taken  from  the  table  for  a  stub  switch,  even  when 
the  point  switch  is  inserted,  because  in  deriving  the  formula  for  KT,  QK  and 
ME  are  assumed  to  be  circular  arcs. 

CROSS-OVERS 

A  cross-over  is  a  stretch  of  track  that  connects  two  parallel  tracks,  and 
enables  a  train  to  pass  from  one  track  to  the  other.     Thus,  in  Fig.  9,  if  UV 
and  U'V  are  two  parallel  tracks,  the  track  RZR'  is  a  cross-over.    This  cross-over 
consists  of  two  equal  turnouts  Rm 
and  R'm',  whose  frog  angles  at  K  y 

and  K'  are  equal,  and  a  reversed 
curve  mZmf  connecting  the  ends  of 
these  turnouts,  Z  being  the  point  of 
reversal. 

Cross-Over  Between  Two  Paral- 
lel Straight  Tracks. — To  lay  out  the 
cross-over,  it  is  necessary  to  know 
the  radius  r,  the  central  angle  M, 
and  the  distance  BE*=B'E'.  The 
radius  r  may  be  taken  from  the 
table  for  stub  switches.  Then, 


and 

When  the  tracks  are  less  than  30  ft. 

apart,  the    value    of  ~    may  be 

dropped.     The  formulas  for  sin  M 
and  BE  then  become,  respectively. 


sin  M 


and 


$ 


FIG. 


The  preceding  formulas  apply  only  to  stub  switches;  to  apply  them  to  point 
switches,  proceed  as  follows:  Having  located  one  frog  point  K  of  the  point- 
switch  turnout,  measure  back  from  K  the  lead  KB  for  a  stub-switch  turnout 
taken  from  the  table,  and  from  the  point  R  of  the  center  line  opposite  B  run 


SURVEYING 


131 


in  the  curve  RmZ  to  the  point  of  reversal.  Then  measure  off  the  distance 
BE  =  2  ^laT,  and  from  the  point  B'  opposite  to  E  lay  off  the  stub-switch  lead 
B'K'  to  locate  the  second  point  of  frog  K'.  Then  run  in  the  center-line  curve 
R'Z.  The  two  frog  points  and  the  reversed  curve  mZm'  are  thus  located. 
Finally,  measure  back  from  K  and  K'  the  distances  Kb  =  K'b'  equal  to  the  lead 
for  point  switches,  to  locate  the  toes  of  the  point  switches  at  6  and  br,  and  com- 
plete the  location  of  these  switches  as  explained  under  Laying  Out  Turnouts. 

It  is  evident  that  the  whole  length  of  the  cross-over  when  point  switches  are 
employed  is  be  =  b'e'j=BE  —  2XBb  =  2'*Iar  —  2XBb.     Therefore, 

be  =  b'e'  =  2'*Jar  —  2X  (lead  of  stub  switch  — lead  of  point  switch) 

A  stake  is  usually  driven  at  Z,  midway  between  the  inner  rails  and  mid- 
way between  the  points  2V  and  Nf,  and  the  turnout  curves  are  continued  to  this 


point.     This  is  more  accurate  than  to  attempt  to  deterrr 
by  the  use  of  the  central  angle  M  . 
Another  Form  of  Cross-Over  Between 
Two  Parallel  Straight  Tracks.  —  A  second 
form  of  cross-over  is  shown  in  Fig.    10. 
In  this  form,  the  ends  of  the  two  equal  ^ 

line 

V 

i 

i 
k- 

i 

thep 

—  a— 
EB' 

oin 

V 

1 

*1 

Rf 

t  of  reversal 
H' 

KTK'T'.     The  cross-over  with  a  reversed         ^^xj^ 
curve,  Fig.  9,  is  much  shorter  than  this               ^v 
straight-track  cross-over,  and  thus  requires 
less    length    of    track    and    occupies    less 
room.     The   straight-track  form  is,  how- 
ever, to  be  preferred;  it  is  less  wearing  on 
the  rolling  stock  because  it  gives  the  wheel 
trucks  a  better  opportunity  to  adjust  them- 
selves to  the  reversion  of  curvature. 
In  order  to   lay   out  a  straight-track 
cross-over,  it  is  only  necessary  to  compute 
the  distance  BE  =  B'E',  Fig.  10,  in  addi- 
tion to  the  usual  dimensions  of   the  two                 If 
turnouts,  which  may  be  done  by  taking 
the  lead  L  from  the  stubswitch  table  and 
applying  the  formula: 

BE=2L-£-+(a-2g)n 

i 

1 

i 
i 

* 

1 
i 

£ 

'  T  / 
e' 

t 

A 

*' 
*"fc, 

[ 

I 

F 

IG.  10 

i 
V' 

The  turnout  Rm  having  been  put  in  place,  the  distance  BE  is  laid  off  and  the 
heels  B'  and  H'  of  the  second  turnout  are  located  opposite  the  point  E.  This 
turnout  is  then  laid  out  as  far  as  mf,  and  finally  the  straight  rails  KT'  and  K'T 
are  laid  adjoining  the  ends  of  the  two  turnouts. 

The  only  modification  of  the  work  for  a  point  switch  arises  from  the  fact 
that  the  lead  Kb  =  K'b'  of  the  point  switch  is  less  than  that  of  the  stub  switch. 
The  whole  length  of  cross-over  is,  for  a  point  switch, 

be  =  2L'  —  -r~  -f-  (a  —  2g)n 
Here  L'  is  the  lead  taken  from  the  table  for  point  switches. 

LAYING  OUT  TURNOUTS 

To  Lay  Out  a  Stub  Switch. — Having  decided  on  the  position  of  the  end  b, 
Fig.  11,  of  the  frog  rail,  measure  the  total  length  of  the  frog  and  deduct  it  from 
the  length  of  the  rail  to  be  cut,  marking  with  red  chalk  on  the  flange  of  the  rail 
the  point  at  which  the  rail  is  to  be  cut.  From  Fig.  3, 

n  =  — 
ab 
and  ch  =  nX  ab 

To  calculate  the  distance  from  the  heel  to  the  theoretical  point  of  frog, 
the  width  of  the  frog  at  the  heel  is  measured  and  multiplied  by  the  frog  num- 
ber. For  example,  if  the  width  of  the  frog  at  the  heel  is  85  in.,  and  a  No.  8  frog 
is  to  be  used,  the  theoretical  distance  from  the  heel  to  the  point  of  frog  is  8.5X8 
=  68  in.  =  5  ft.  8  in.  Measure  off  this  distance  from  the  point  marking  the  heel 
of  the  frog;  this  will  locate  the  point  of  frog,  which  should  be  distinctly  marked 
with  red  chalk  on  the  flange  of  the  rail.  It  is  a  common  practice  to  make  a 
distinct  mark  on  the  web  of  the  main-track  rail,  directly  opposite  to  the  point 


132  SURVEYING 

of  froe  This  point,  being  under  the  head  of  the  rail,  is  protected  from  wear 
and  the  weather.  The  heel  of  the  turnout  is  then  located  by  measuring  back 
the  lead  from  the  point  of  frog.  Next,  make  a  chalk-mark  on  both  main-track 
rails  on  a  line  marking  the  center  of  the  head-block;  a  more  permanent  mark 
is  made  with  a  center  punch.  Stretch  a  cord  touching  these  marks,  and  drive 
a  stake  on  each  side  of  the  track,  with  a  tack  in  each;  this  line  should  be  at 
right  angles  to  the  center  line  of  the  track,  and  the  stakes  should  be  sufficiently 
far  from  the  tracks  not  to  be  disturbed  when  putting  in  switch  ties.  Next, 
cut  the  switch  ties  to  proper  length;  draw  the  spikes  from  the  track  ties,  three 
or  four  at  a  time,  and  remove  the  ties  from  the  track,  replacing  them  with  switch 
ties  and  tamping  the  latter  securely  in  place.  When  all  the  long  ties  are 
tamped  cut  the  main-track  rail  for  the  frog,  being  careful  that  the  amount  cut 
off  is  just  equal  to  the  length  pf  the  frog.  If,  by  increasing  or  decreasing  the 
length  of  the  lead  5%,  the  cutting  of  a  rail  can  be  avoided,  this  should  be  done, 
especially  for  frogs  above  No.  8. 

Full-length  rails  (30  ft.)  should  be  used  for  moving  or  switch  rails,  and 
care  should  be  taken  to  leave  a  joint  of  proper  width  at  the  head  chair.  The 
head-chairs  should  be  spiked  to  the  head-block  so  that  the  main-track  rails 
will  be  in  perfect  line.  From  8  to  10  ft.  of  the  switch  rails  should  be  spiked 
to  the  ties.  The  tie-rods  are  placed  between  the  switch  ties,  which  should  not 
be  more  than  15  in.  from  center  to  center  of  tie.  The  connection-rod  should 
be  attached  to  the  head-rod  and  switch  stand.  With  these  connections  made 
the  switch  stand  is  easily  placed  to  give  the  proper  throw  of  the  switch. 

It  is  common  practice  to  fasten  the  switch 
stand  to  the  head-block  with  track  spikes,  but  a 

better   fastening    is   made    with 

bolts.    The  stand  is  first  property 

placed,  the  holes  are  marked  and 

bored,  and  the  bolts  passed 

through  from  the  under  side  ,of 

the  head-block.    This  obviates  all 

danger  of  movement  of  the  switch 

stand  in  fastening,  which  is  liable 

to  occur  when  spikes  are  used,   ' 

and  insures  a  perfect  throw. 

The  use  of  track  spikes  is  ad- 
missible when  holes  are  bored  to 

receive  them,   in  which   case  a   - 

i-in.   auger  should   be  used  for 

standard    track    spikes.     The 

switch  stand  should,  when  pos- 
sible, be  placed  facing  the  switch; 

so  as  to  be  seen  from  the  engineer's 

, .,          side  of  the  engine  —  the  right-  •».,,   i  n 

11          hand  side.  riG-  ** 

To  find  the  position  of  the  chord  of  the  arc  of  the  outer  rail  of  the  turnout 
curve,  stretch  a  cord  from  the  heel  a,  Fig.  11,  to  the  point  b,  of  the  frog.  Mark 
the  middle  point  c  and  the  quarter  points  d  and  e,  and  at  these  points  lay  off  the 
offsets  dd',  ccf,  and  eef.  Add  to  these  offsets  the  distance  from  the  gauge  line 
to  the  outside  of  the  rail  flange,  and  mark  the  points  on  the  switch  ties.  Spike 
the  rail  to  these  marks  and  place  the  other  at  easy  track  gauge  from  it.  Spike 
the  rails  of  the  turnout,  as  far  as  the  point  of  frog,  to  exact  gauge,  unless  the 
gauge  has  been  widened  owing  to  the  sharpness  of  the  curve.  Beyond  the 
point  of  frog,  the  curve  may  be  allowed  to  vary  a  little  in  gauge  to  prevent  a 
kink  from  showing  opposite  the  frog.  In  case  the  gauge  is  widened  at  the  frog, 
increase  the  guard-rail  distance  an  equal  amount.  For  a  gauge  4  ft.  8^  in., 
place  the  side  of  the  guard-rail  that  comes  in  contact  with  the  car  wheels  at 
4  ft.  6f  in.  from  the  gauge  line  of  the  frog.  This  gives  a  space  of  1 J  in.  between 
the  mam  rail  and  the  guard-rail.  In  case  the  gauge  is  widened  J  or  ^  in. ,  increase 
the  guard-rail  distance  an  equal  amount. 

When  the  turnout  curve  is  very  sharp,  it  will  be  necessary  to  curve  the 
switch  rails,  to  avoid  an  angle  at  the  head-block.  The  rails  should  be  carefully 
nirved  before  being  laid,  and  great  pains  should  be  taken  to  secure  a  perfect 

To  Lay  Out  a  Point  Switch.— The  frog  point  K,  Fig.  12,  having  been 
located  exactly  as  for  a  stub  switch,  the  lead  KB  is  next  laid  off  from  K  to  the 
toe  of  switch  B,  and  the  positions  of  B  and  D  are  marked  on  the  main-track 
rails.  *rom  D,  the  length  DN  of  the  switch  rail,  which  is  usually  15  ft.,  is  then 


SURVEYING 


133 


measured  forwards  to  2V,  and  the  position  of  2V  is  marked  on  the  web  or  flange 
of  the  rail.  The  heel  M  is  usually  5|  in.  from  the  point  2V.  The  point  /  is 
located  on  a  line  perpendicular  to  MD  and  at  a  distance  %g  from  M.  The  point  / 
is  similarly  located  from  the  point  H.  As  a  check  on  the  work,  the  length  of 
the  clwrd  77  should  have  the  value  given  in  the  table  for  point  switches. 

Switch  ties  of  the  requisite  number  and  length  should  be  prepared  and 
placed  in  the  track  in  proper  order.  As  in  the  case  of  stub  switches,  all  long 
switch  ties  should  be  in  place  before  the  rail  is  cut  for  placing  the  frog;  also,  the 
ends  M  and  L  of  the  rails,  with  which  the  switch  points  connect,  should  be 
exactly  even;  otherwise  the  tie-rods  will  be  skewed,  and  the  switch  will  not 
work  or  fit  well.  The  tie-rods  should  next  be  fastened  in  position,  care  being 
taken  to  place  them  in  their  proper  order,  the  head-rod  being  numbered  1. 
Each  rod  is  marked  with  a  center  punch,  the  number  of  punch  marks  corre- 
sponding to  the  number  of  the  rod. 

The  switch  rails  are  now  coupled  with  the  rails  LK  and  MK,  and  the  sliding 
plates  are  then  placed  in  position  and  securely  spiked  to  the  ties.  The  head- 
rod  is  then  connected  with  the  switch  stand,  and  the  switch  is  closed,  giving  a 
clear  main  track.  The  stand  is  then  adjusted  for  this  position  of  the  switch,  and 
bolted  fast  to  the  head-block.  Next,  rail  BR  is  crowded  against  the  switch 
point  so  as  to  insure  a  close  fit,  and  secured  in  place  with  a  rail  brace  at  each 
tie.  The  laying  of  the  rails  of  the  turnout  is  then  continued. 

The  rail  MH  is  to  be  bent  and  spiked  in  place  by  laying  off  offsets  from  the 
chord  MH  exactly  as  explained  for  stub  switches.  The  rail  between  M  and  H 
usually  consists  of  two  pieces  of 
plain  rail  bent  to  the  proper 
curve.  The  outer  rail  of  the 
main  track  is  not  disturbed. 

Switch  Timbers. — Every 
first-class  railroad  has  its  own 
standards  for  switches,  which 
include  the  necessary  switch 
timbers.  The  number  of  ties 
and  their  lengths  may  be  deter- 
mined by  the  following  rules: 

Rule  I. — To  find  the  number 
of  ties  required  for  any  switch 
lead,  reduce  to  inches  the  distance 
from  the  head-block  to  the  last  long 
tie   behind  the  frog,  and  divide 
this  distance  by  the  number  of    ^~.      ^_ 
inches  from  center  to  center  of  ties;    _'e    A 
the  quotient  will  be  the  number  of 
ties  required. 

Rule  II. — Measure  the  length 
of  the  tie  next  the  head-block  and  the  length  of  the  last  long  tie  behind  the  frog.  Find 
the  difference,  in  inches,  between  them.  Divide  this  difference  by  the  number  of  ties 
in  the  switch  lead;  the  quotient  will  be  the  increase  in  length  per  tie  from  the  head-block 
toward  the  frog  to  have  the  ends  of  the  tie  in  proper  line  on  both  sides  of  the  track. 

Practical  Method  of  Laying  Out  Sharp  Curves  in  a  Mine. — Curves  in  a 
mine  are  usually  so  sharp  that  they  are  designated  as  curves  of  so  many  feet 
radius,  instead  of  as  curves  of  so  many  degrees.  For  example,  suppose  that  it 
is  required  to  connect  the  two  headings  A  and  B,  Fig.  13  (a) ,  which  are  perpen- 
dicular to  each  other,  with  a  curve  of  60  ft.  radius.  Prepare  the  device  shown 
in  (b),  by  taking  three  small  wires  or  inelastic  strings  fg,  gh,  and  gk,  each  10  ft. 
long,  and  connecting  one  end  of  each  to  a  small  ring,  and  the  other  end  of  two  to 
the  ends  of  a  piece  of  wood  If  ft.  long.  Form  a  neat  loop  at  end  /of  string  g/. 

To  use  this  device,  lay  off  on  the  center  line  of  the  heading  B,  cd  ancf  de 
equal  to  60  ft.  and  10  ft.,  respectively.  Place  the  loop  /  of  the  device  described 
over  a  small  wire  peg  driven  in  at  e,  and  the  ring  g  over  a  similar  peg  at  d. 
Take  hold  of  the  stick  hk,  pull  the  strings  gh  and  gk  taut,  and  place  the  center 
mark  on  hk  on  the  center  line  of  the  heading  B.  Drive  a  small  peg  in  at  m, 
located  by  the  point  k,  which  is  on  the  curve.  Move  the  device  forwards, 
place  the  loop  /  over  the  peg  at  d,  the  ring  g  over  the  peg  at  m,  and  take  hold 
of  the  stick  hk  and  pull  until  the  strings  gh  and  gk  are  taut,  and  the  strings  fg 
and  gh  are  in  a  straight  line.  The  point  k  will  fall  on  the  curve  at  n,  which 
mark  by  driving  in  a  peg.  To  locate  other  points,  proceed  exactly  as  in  the 
last  step.  The  distance  cd  in  any  case  is  found  by  the  forniula 


134 

in  which 


SURVEYING 


"T 


jf 


radius  of  curve; 

intersection  angle  of  center  lines  of  headings. 
Fig.  14  shows  a  graphic  method  of  laying  out  curves,  when  it  is  desired  to 
connect  a  main  entry  a  with  a  cross-entry  b  by  a  curve  of  a  given  radius.  Here,  c 
is  the  point  of  curve  on  the  main-entry  center  line  and  d  is  the  point  of  tan- 
gency  on  the  center  line  of  the  cross-entry,  which  is  assumed  to  be  turned  off 
at  right  angles  from  the  main  entry.  From  c  and  d,  arcs  with  a  radius  equal  to 

the  desired  radius  of 
curvature  are  des- 
cribed, thus  locating 
the  center  e  of  the 
curve.  From  this 
point,  with  the  same 
radius,  the  curve  cd, 
which  is  the  center  of 
the  proposed  passage- 
way, is  described.  The 
curves  fg  and  hi  are 
then  drawn,  making 
the  curved  entry  any 
desired  width.  Linejk, 
so  located  that  it 
will  not  cut  either  rib 
of  the  curved  roadway, 
should  then  be  drawn 
and  on  it  points  5  feet 
apart  should  be  laid  off 
to  the  given  scale  and 
the  right  and  left  dis- 
tances to  the  rib  scaled, 
as  shown  in  the  figure. 
If  a  plat  of  this  kind  is 


Cress  Cnfiy 


FIG.  14 


ill 


drawn  on  a  large  enough  scale,  the  angles  and  distances  may  be  scaled  suffici 
ently  accurate  for  the  practical  work  of  the  mine  foreman.  A  blueprint  or  trac- 
ing of  the  plat  is  furnished  to  the  mine  foreman,  and  from  it  he  lays  off  the  right 
and  left  distances  from  the  center  line  of  the  main  entry  and  from  the  line  jk. 
The  line  jk  is  located  by  means  of  two  stations  placed  with  the  transit  at  ft  and  a 
point  either  to  the  right  or  left  of  b,  as  may  be  most  convenient,  and  along  the 
line  bl.  For  the  distances  given  in  the  illustration  and  the  radius  of  curvature 
of  70  ft.,  the  angle  cjk  as  taken  from  the  drawing  is  about  120°  15';  the  angle 
atjld,  about  149°  45';  the  distance  cj,  35  ft.  9  in;  jl,  58  ft.;  and  Id,  11  ft.  6  in. 
These  distances  are  given  as  about  so  much,  to  show  that  they  are  scaled  from 
a  drawing  and  are  not  calculated  by  trigonometry. 


STADIA  SURVEYING 

Stadia  surveying  is  the  process  of  measuring  distances  and  elevations  by 
observing  through  a  telescope  the  distance  intercepted  on  a  rod  between  two 
horizontal  cross-hairs.  These  hairs  are  carried  on  the  same  ring  as  the  regular 
horizontal  cross-hair,  and  are  equidistant  from  it.  The  rod  used  may  be  an 
ordinary  level  rod,  but,  if  much  stadia  work  is  to  be  done,  it  is  advisable  to 
select  some  one  of  the  special  rods  designed  for  the  work;  a  description  of 
these  may  be  found  in  any  instrument  maker's  catalog. 

The  distance  intercepted  on  the  rod  between  the  cross-hairs  of  the  telescope 
bears  a  certain  relation  to  the  distance  of  the  rod  from  the  instrument.  As  the 
transit  is  provided  with  a  vertical  circle  or  arc,  the  angle  of  inclination  between 
the  line  of  sight  and  the  horizon  may  be  determined  in  case  of  inclined  sights. 
The  space  intercepted  between  the  cross-hairs  on  the  rod,  taken  in  connection 
with  the  vertical  angle,  enable  the  distance  and  elevation  of  the  rod  to  be  cal- 
culated. When  the  line  of  sight  is  horizontal,  the  distance  d  of  the  rod  from  the 
instrument  can  be  determined  from  the  formula 


in  which  R  =  stadia  reading  or  distance  intercepted  between  the  stadia  wires  ; 
s  =  stadia  "constant; 
*  =  instrument  constant. 


SURVEYING  135 

The  values  of  the  stadia  and  instrument  constants  are  usually  determined 
by  the  instrument  maker.  The  instrument  constant  varies  from  about  .75  ft. 
to  1.33  ft.  in  different  transits,  according  to  the  size  and  power  of  their  tele- 
scopes. Its  value  is  usually  marked  on  a  card  attached  to  the  inside  of  the 
instrument  box.  It  is  a  general  rule  that  unless  definitely  stated  to  the  con- 
trary, the  stadia  constant  is  made  equal  to  100;  that  is,  in  a  horizontal  line 
of  sight,  the  stadia  wires  will  intercept  a  distance  of  1  ft.  on  a  rod  whose  distance 
from  the  instrument  is  100  ft.  plus  the  instrument  constant.  Thus,  if  the 
stadia  constant  is  100  and  the  instrument  constant  is  1.33  ft.,  if  the  stadia  wires 
intercept  a  distance  of  8.37  ft.  on  the  rod,  the  distance  from  the  rod  to  the 
transit  is  8.37X  100  + 1.33  =  838.33  ft.;  the  line  of  sight  being  horizontal. 

Stadia  wires  are  either  fixed  or  adjustable.  The  former  are  firmly  placed 
by  the  instrument  maker  so  that  the  stadia  constant  is  100.  They  cannot  get 
out  of  adjustment  and  are  much  to  be  preferred  to  the  other  and  older  method 
of  mounting,  in  which  the  distance  between  the  wires  may  be  varied  to  intercept 
any  distance  on  the  rod.  In  the  event  of  the  constants  not  being  known,  they 
may  be  determined  as  follows:  Select  a  piece  of  level  ground  and  set  tacks  in 
stakes  at  exactly  50  ft.  apart  for  a  distance  of  400  to  800  ft.  Let  Rz  and  Ri  be 
two  stadia  readings  taken  at  the  respective  distances  dz  and  di\  then, 

dt-di 
S    R2-Ri 

.     diRz-dzRi 

and  t  =  — = p — 

KZ  —  KI 

Several  pairs  of  readings  and  their  corresponding  distances  are  substituted  in 
these  formulas,  and  the  mean  of  all  the  resulting  values  of  5  and  *  calculated. 

EXAMPLE. — 'Determine  the  stadia  and  the  instrument  constant  from  the 
following  data: 

Distance  Measured  Rod  Reading 

Feet  Feet 

50  .488 

100  .988 

200  1.988 

300  2.991 

400  3.986 

SOLUTION. — Take  50  ft.  for  the  value  of  di  and  100  ft.,  200  ft.,  etc.  suc- 
cessively for  the  values  of  di,  and  apply  the  preceding  formulas  for  s  and  i. 
For  the  first  pair  of  observations: 

100-50 

""m=j&-m 

.     50  X. 988 -.488X100     , 

and  *  = i988^488 =  L2°°  ft< 

The  other  values  are  figured  in  a  similar  manner  and  the  whole  is  tabulated 
as  follows: 

s  i 

100.000  1.200 

1  0  0.0  0  0  1.2  0  0 

9  9.8  8  0  1.2  5  8 

1  0  0.0  5  7  1.172 

4  )  3  9  9.9  3  7  4  )_4.8jJ_0 

means  99.984  =  5  1.208  =  * 

Reduction  of  Inclined  Sights. — For  the  purpose  of  determining  distances 
and  differences  in  elevation  when  the  rod  is  above  or  below  the  level  of  the 
instrument  what  are  known  as  stadia  reduction  tables  have  been  prepared. 
Their  use  is  best  explained  by  an  illustration. 

EXAMPLE. — Using  a  transit  with  fixed  cross-hairs,  the  stadia  constant  being 
100  and  the  instrumental  constant  being  1,  the  distance  intercepted  on  the  rod 
was  4.25  ft.  and  the  vertical  angle  was  18°  23'.  What  was  the  horizontal  and  the 
vertical  distance  from  the  rod  to  the  instrument? 

SOLUTION. — Referring  to  the  table  in  the  column  headed  18°  and  oppo- 
site 22'  in  the  column  headed  M,  for  18°  22'  a  horizontal  distance  of  90.07  is 
found;  and  opposite  24',  for  18°  24',  a  horizontal  distance  of  90.04  is  found. 
For  18°  23',  therefore,  the  horizontal  distance  will  be  the  mean,  or  90.055.  The 
first  column  of  the  three  lowest  lines  of  the  table  contains  the  symbols  c  =  .75, 


136  SURVEYING 

e=  1.00,  and  e  =  1.25.  In  this  c  is  the  instrument  constant,  the  value  of  which 
is  riven  by  the  maker.  In  the  case  in  question  c=1.00.  Following  hori- 
zontally along  the  line  of  c  =  1.00,  the  figures  .95  are  found  in  the  column  headed 
"  18°  Hor.  Dist."  This  .95  is  the  proportion  of  the  instrument  constant  to  be 
added  to  the  reduced  distance  when  the  vertical  angle  is  between  18°  and  19°. 
The  horizontal  distance  is  then, 

Distance  =  rod  reading X  tabular  horizontal  distance+c; 

From  this 

distance  =  4.25X90.055 +  .95  =  382.73 +  .95  =  383.68  ft. 

Referring  again  to  the  table  but  using  the  second  of  the  two  columns 
under  18°  that  headed  Diff.  Elev.  and  by  interpolating  between  the  values 
of  22'  and  24',  the  Diff.  Elev.  for  18°  23'  is  f9und  to  be  29.925.  The  pro- 
portion of  the  instrumental  constant  is  found,  in  the  line  beginning  c=1.00 
in  the  column  headed  18°  but  under  the  subcolumn,  Diff.  Elev.,  to  be  .32  for  all 
values  of  the  vertical  angle  between  18°  and  19°.  The  difference  in  elevation 

Diff.  Elev.  =  rod  reading  X  tabular  Diff.  Elev.  +  c 

From  this 

Diff.  Elev.  =  4.25X29.925 +.32  =127. 18 +.32  =  127.50  ft. 

Use  of  Stadia. — The  stadia  is  not  used  as  much  as  it  should  be  by  the 
mining  engineer,  particularly  in  securing  data  for  making  a  contour  map  of 
the  property  of  which  he  is  in  charge.  In  rolling  and  hilly  country,  some 
.  points  upon  the  surface  may  be  from  500  to  1,500  ft.  higher  than  others  and 
this  difference  in  the  thickness  of  the  rocks,  and  consequent  pressure  upon  the 
coal,  will  have  a  great  bearing  on  the  thickness  of  pillars,  method  of  drawing 
stumps,  etc.,  underground.  If  the  traverse  made  to  determine  the  boundaries 
of  the  property  has  been  made  with  a  400-ft.  tape,  the  elevations  of  the  stations 
are  known  from  the  distances  and  vertical  angles.  By  setting  up  at  the  various 
stations,  stadia  sights  may  be  taken  to  points  at  any  distances  within  which 
the  rod  may  be  read.  This  will  be  1,200  or  1,400  ft.  for  a  12-ft.  or  14-ft.  rod. 
Sights  of  double  this  distance  may  be  taken  if  the  upper  hair  and  the  regular 
horizontal  hair  are  used  instead  of  the  two  stadia  hairs;  that  is,  if  the  two  upper 
hairs  are  used  in  place  of  the  first  and  third.  Distances  so  determined  must 
be  multiplied  by  2,  as  they  are  half  distances.  In  this  case  the  engineer  must 
be  certain  that  the  horizontal  hair  is  exactly  midway  between  the  stadia  hairs. 
This  may  be  ascertained  by  reading  a  distance  with  the  upper  and  middle  hairs 
and  then  with  the  middle  and  lower  hairs.  If  these  distances  are  the  same, 
the  hairs  are  evenly  spaced;  if  the  distances  do  not  agree,  their  mean  must 
be  taken.  x 

Cloudy  days  when  the  air  is  free  from  vibrations  are  best  for  stadia  work. 
An  ordinary  erecting  transit  will  give  excellent  results  up  to  1,200  and  1,800  ft., 
depending  on  its  power,  and  a  high  class  inverting  telescope  with  large  objec- 
tive may  be  used  for  distances  up  to  3,000  ft.  A  good  rodman  is  essential, 
and  if  long  sights  are  being  taken  and  the  slopes  are  regular,  one  observer  can 
keep  two  rodmen  busy.  The  rod  should  be  held  at  all  points  where  there  is 
any  marked  change  in  the  degree  of  slope.  Small  inequalities  in  the  surface 
may  be  neglected,  it  being  apparent  that  an  error  of  20  to  30  ft.  in  determining 
the  thickness  of  the  rocks  overlying  the  seam  is  of  no  importance. 

When  the  sights  are  too  long  to  permit  of  the  rod  being  plainly  read,  the 
rodman  should  drive  a  stake  and  place  a  tack  in  it  to  mark  the  station.  The 
edge  of  the  rod  should  then  be  held  on  the  tack,  the  rodman  running  his  hand 
up  and  down  the  side  of  the  rod  that  is  to  be  sighted  to.  The  transitman 
should  then  move  up  and  take  further  stadia  sights  from  the  station  just 
established.  In  traversing  valleys  or  swales  cutting  across  a  property  or  in 
determining  the  line  of  a  ridge  all  the  work  may  be  done  with  the  stadia  with 
a  degree  of  accuracy  well  within  reasonable  requirements  and  far  more  easily, 
rapidly,  and  cheaply,  than  with  a  transit,  400  ft.  tape,  and  leveling  instrument. 
In  locating  isolated  and  distant  houses,  the  opposite  side  of  a  wide  river  from 
that  on  which  the  traverse  is  being  run,  in  fact  in  all  work  where  an  error 
of  1  :  500  or  1  :  1,000  is  allowable,  the  stadia  is  to  be  preferred  to  the  tape. 


SURVEYING 


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SURVEYING 


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SURVEYING 


BAROMETRIC  LEVELING 

Of  the  two  types  of  barometer  in  general  use,  the  mercurial  barometer  is 
better  adapted  for  work  at  permanent  stations,  and  the  aneroid  barometer, 
shown  in  the  accompanying  figure,  by  reason  of  its  portability,  is  better  suited 
for  use  in  the  field.  In  the  barometer,  the  difference  in  the  pressure  of  the 
air  at  two  different  stations  not  in  the  same  horizontal  plane,  is  made  the  basis 
for  measuring  the  difference  in  their  elevation.  The  aneroid  barometer  con- 
sists of  a  circular  metallic  air-tight  box,  either  of  brass  or  aluminum  (because 
of  its  lightness).  One  side  is  covered  with  a  thin  corrugated  plate  and  only 
enough  air  is  left  within  the  box  to  compensate  for  the  diminished  stiffness 
of  the  cover  at  higher  temperatures.  This  cover  rises  or  falls  as  the  outer 
pressure  changes,  and  this  motion  is  greatly  magnified  by  a  series  of  levers 
and  is  transmitted  to  a  pointer  moving  over  a  scale  on  the  circumference  of 
the  outer  face.  This  scale  is  commonly  doubly  graduated.  The  inner  scale  is 
graduated  by  inches,  tenths,  and  hundredths,  to  correspond  with  the  gradu- 
ations of  a  standard  mercurial  barometer.  The  outer  scale  is  graduated  in 
thousands,  hundreds,  and  tens  of  feet,  indicating  elevations  above  sea  level 
corresponding  to  the  atmospheric  pressures  recorded  by  the  inner  scale.  The 

fineness  of  these  outer  graduations 
varies,  the  ordinary  aneroid  reading 
direct  to  10  ft.  and  by  estimation  to, 
say,  2  ft.,  while  very  large  forms  of  the 
instrument  are  provided  with  a  vernier, 
magnifying  glass,  etc.,  by  which  they 
may  be  read  to  single  feet.  Such  refine- 
ment in  reading  is  unnecessary,  as  in- 
strument and  weather  irregularities 
introduce  much  greater  uncertainties 
than  those  caused  by  too  coarse  gradu- 
ating. 

In  some  aneroids  the  two  sets  of 
graduations  are  fixed,  the  zero  of  the 
altitude  scale  being  opposite  the  31-in. 
mark  of  the  mercurial  scale,  and  this 
relation  cannot  be  changed,  but  in  most 
instruments  of  this  kind  the  zero  may 
be  shifted  either  by  turning  an  arrange- 
ment like  the  stem  of  a  watch  or  by 
turning  the  milled  edge  of  the  aneroid 
itself.  The  zero  of  the  altitude  scale 
may  be  made  to  coincide  with  either 
the  30-  or  31-in.  mark  of  the  mercurial 
scale,  but  whichever  mark  is  decided  on 
by  the  instrument  maker  must  always 
be  used.  That  this  is  the  case  will  be 
obvious  from  the  table  of  Barometric 
Elevations,  which  shows  that  a  difference  of  1  in.  in  the  length  of  the  mercurial 
column  between  29  and  30  inches  corresponds  to  a  difference  of  924  ft.  in 
elevation,  whereas  a  difference  of  1  in.  of  mercury  between  13  and  14  in.  corre- 
sponds to  a  difference  of  2,020  ft.  in  elevation.  Hence,  as  the  length  of  the 
altitude  scale  corresponding  to  a  difference  in  elevation  of  1,000  ft.  is  not 
uniform,  any  shifting  of  the  zeros  of  the  two  scales  will  bring  inharmonious 
graduations  opposite  one  another. 

Aneroids  vary  in  size  from  1|  to  2£  to  3  in.  in  diameter  for  the  standard 
forms  up  to  5  in.  in  diameter  for  the  larger  ones  provided  with  a  vernier,  etc. 
They  are  commonly  graduated  from  31  in.  down  to  27,  25,  21,  19,  17,  and 
14  in.  of  mercury,  corresponding  to  approximate  elevations  of  from  1,000  ft. 
below  sea  level  to  3,000,  5,000,  10,000,  12,000,  16,000,  and  20,000  ft.  above  the 
same.  The  larger  barometers  are  no  more  accurate  than  the  smaller  ones  and 
nothing  is  gained  by  having  them  graduated  to  record  smaller  pressures 
(greater  elevations)  than  those  prevailing  where  the  instrument  is  to  be  used. 
Ihus,  east  of  the  Mississippi  River,  a  2-in.  or  2$-in.  aneroid  graduated  from  27 
to  32  in.  (corresponding  to  elevations  of  3,000  ft.  above  to  2,000  ft.  below  sea 
level),  will  answer  for  all  purposes  of  the  coal-mining  engineer,  except  for 
exploratory  work  in  the  highest  mountains  of  the  Carolinas,  etc.  A  barometer 
reading  to  17  in.  (about  16,000  ft.)  will  answer  for  all  parts  of  the  continental 


SURVEYING  141 

United  States,  as  the  highest  peaks  of  the  Rocky  Mountains  are  but  little  over 
14,000  ft.  high.  It  must  be  remembered  that  the  less  the  pressure  (the  greater 
the  altitude)  the  barometer  will  record,  the  finer  are  the  graduations  on  both 
scales  and,  consequently,  the  more  difficult  is  precise  reading. 

A  small  screw  in  the  center  of  the  back  permits  the  index  pointer  to  be 
accurately  adjusted  to  correspond  with  the  reading  of  a  standard  mercurial 
barometer.  This  adjustment  is  originally  made  by  the  instrument  maker, 
but  the  aneroid  should  be  compared  from  time  to  time  with  a  standard  barom- 
eter at  some  station  of  the  United  States  Weather  Bureau,  9r  elsewhere. 

The  word  compensated  stamped  on  the  face  of  an  aneroid  barometer  does 
not  mean  that  in  determining  elevations  differences  in  temperature  are  not  to 
be  considered,  but  only  that  the  instrument  reads  correctly  at  all  temperatures 
and  that  no  allowance  need  be  made  for  the  effect  of  changes  in  temperature 
upon  the  instrument  itself. 

Too  much  reliance  must  not  be  placed  on  the  accuracy  of  elevations  as 
determined  by  the  aneroid.  All  this  instrument  does  is  to  measure  the  pressure 
of  the  air  at  a  given  place  at  a  certain  time.  As  this  pressure  must  and  does 
vary  at  the  same  place  as  the  weather  changes,  it  must  be  apparent  that  the 
difference  in  elevation  between  two  distant  points  can  be  determined  with  even 
approximate  accuracy  only  when  two  barometers  are  used  and  which  are  read 
simultaneously  at  the  two  points  in  question.  At  sea  level,  1  in.  of  the  mer- 
curial column  corresponds  to  a  difference  in  elevation  of  about  900  ft.  Changes 
of  -fa  in-  frequently  take  place  in  1  hr.,  •&  in.  in  1  da.,  and  in  event  of  storms, 
ranges  of  1  in.  are  not  unusual.  Thus,  as  fa  in.  represents  about  90  ft.  of 
elevation,  a  single  reading  of  the  barometer  may  give  an  elevation  for  a  place 
900  ft.  greater  or  less  than  the  true  one  under  unfavorable  atmospheric  condi- 
tions, and  one  of  as  much  as  100  ft.  under  the  best.  On  the  other  hand,  if  the 
barometer  is  read  two  or  three  times  daily  for  a  period  of  1  yr.  or  more,  the 
temperature  being  noted  at  the  same  time  and  the  proper  corrections  made, 
a  very  fair  idea  may  be  obtained  as  to  the  difference  in  elevation  between  the 
station  in  question  and  that  of  any  other  station  at  which  simultaneous  obser- 
vations have  been  made.  Thus,  the  daily  readings  may  be  made  by  the 
engineer  at  some  isolated  station  and  their  mean  for  a  period  of  time  compared 
with  those  made  at  any  station  of  the  United  States  Weather  Bureau  any 
number  of  miles  distant. 

Barometric  Formulas.* — The  general  formula  for  obtaining  the  difference 
of  elevation  between  two  points  is, 

z  =  60,520[l  +  .001017(/-r-r-64)]  log  ^ 

n 
in  which  z  =  difference  of  elevation  of  the  two  points; 

h  and   *  =  reading  of  barometer  and  thermometer  at  upper  station; 
H  and  T  =  reading  of  barometer  and  thermometer  at  lower  station. 
This  equation  may  be  referred  to  an  approximate  sea  level  (height  of  mer- 
curial barometer  30  in.  instead  of  29.92  in.)  and  to  a  mean  station  temperature 
of  50°  F.,  that  is  t  +  T  is  made  equal  to  100°  F.,  in  which  t  and  T  may  have  any 
values  as  long  as  their  sum  equals  100°  F.     Making  the  substitutions 

on  on 

2  =  62,737  log  ^-62,737  log  ^ 
n  a. 

The  accompanying  table  of  Barometric  Elevations,  from  the  United  States 

30 
Coast  and  Geodetic  Survey,  contains  values  for  62,737  log  -p  for  all  readings 

n 

of  the  aneroid  from  13  to  31  in.  for  use  in  connection  with  the  foregoing  formula, 
no  allowance  being  made  for  the  amount  of  aqueous  vapor  in  the  air.  At 
other  temperatures  and  for  an  assumed  average  humidity  a  correction  obtained 
from  the  table  of  Corrections  for  Temperature  and  Humidity  must  be  applied 
to  the  difference  in  eleyation  as  obtained  from  the  first  table.  Thus,  if  A  is 
the  difference  in  elevation  obtained  from  the  table  of  Barometric  Elevations, 
and  C  the  correction  for  temperature  and  humidity  from  the  second  table, 
z  =  A  (1+Q 

EXAMPLE.— The  means  of  the  readings  of  the  barometer  and  the  thermom- 
eter at  the  summit  and  base  of  a  mountain  were:  Summit,  barometer  17.92  in., 
thermometer  26°  F.;  base,  barometer  24.15,  thermometer  64°  F.  If  the 


*  Adapted  from  The  Theory  and  Practice  of  Surveying,  by  J.  B.  Johnson, 
published  by  John  Wiley  &  Sons,  New  York  City. 


142 


SURVEYING 
BAROMETRIC  ELEVATIONS* 


h 

Inches 

A 
Feet 

Differ- 
ence 
for  .01 

Feet 

h 
Inches 

A 
Feet 

Differ- 
ence 
for  .01 
Feet 

h 
Inches 

A 
Feet 

Differ- 
ence 
for  .01 
Feet 

13.0 
13.1 
13.2 
13.3 
13.4 
13.5 
13.6 
13.7 
13.8 
13.9 
14.0 
14.1 
14.2 
14.3 
14.4 
14.5 
14.6 
14.7 
14.8 
14.9 
15.0 
15.1 
15.2 
15.3 
15.4 
15.5 
15.6 
15.7 
15.8 
15.9 
16.0 
16.1 
16.2 
16.3 
16.4 
16.5 
16.6 
16.7 
16.8 
16.9 
17.0 
17.1 
17.2 
17.3 
17.4 
17.5 
17.6 
17.7 
17.8 
17.9 
18.0 
18.1 
18.2 
18.3 
18.4 

22,785 
22,576 
22,368 
22,162 
21,958 
21,757 
21,557 
21,358 
21,160 
20,962 
20,765 
20,570 
20,377 
20,186 
19,997 
19,809 
19,623 
19,437 
19,252 
19,068 
18,886 
18,705 
18,525 
18,346 
18,168 
17,992 
17,817 
17,643 
17,470 
17,298 
17,127 
16,958 
16,789 
16,621 
16,454 
16,288 
16,124 
15,961 
15,798 
15,636 
15,746 
15,316 
15,157 
14,999 
14,842 
14,686 
14,531 
14,377 
14,223 
14,070 
13,918 
13,767 
13,617 
13,468 
13,319 

-20.9 
20.8 
20.6 
20.4 
20.1 
20.0 
19.9 
19.8 
19.8 
19.7 
19.5 
19.3 
19.1 
18.9 
18.8 
18.6 
18.6 
18.5 
18.4 
18.2 
18.1 
18.0 
17.9 
17.8 
17.6 
17.5 
17.4 
17.3 
17.2 
17.1 
16.9 
16.9 
16.8 
16.7 
16.6 
16.4 
16.3 
16.3 
16.2 
16.0 
16.0 
15.9 
15.8 
15.7 
15.6 
15.5 
15.4 
15.4 
15.3 
15.2 
15.1 
15.0 
14.9 
14.9 

19.0 
19.1 
19.2 
19.3 
19.4 
19.5 
19.6 
19.7 
19.8 
19.9 
20.0 
20.1 
20.2 
20.3 
20.4 
20.5 
20.6 
20.7 
20.8 
20.9 
21.0 
21.1 
21.2 
21.3 
21.4 
21.5 
21.6 
21.7 
21.8 
21.9 
22.0 
22.1 
22.2 
22.3 
22.4 
22.5 
22.6 
22.7 
22.8 
22.9 
23.0 
23.1 
23.2 
23.3 
23.4 
23.5 
23.6 
23.7 
23.8 
23.9 
24.0 
24.1 
24.2 
24.3 
24.4 

12,445 
12,302 
12,160 
12,018 
11,877 
11,737 
11,598 
11,459 
11,321 
11,184 
11,047 
10,911 
10,776 
10,642 
10,508 
10,375 
10,242 
10,110 
9,979 
9,848 
9,718 
9,859 
9,460 
9,332 
9,204 
9,077 
8,951 
8,825 
8,700 
8,575 
8,451 
8,327 
8,204 
8,082 
7,960 
7,838 
7,717 
7,597 
7,477 
7,358 
7,239 
7,121 
7,004 
6,887 
6,770 
6,654 
6,538 
6,423 
6,308 
6,194 
6,080 
5,967 
5,854 
5,741 
5,629 

-14.3 
14.2 
14.2 
14.1 
14.0 
13.9 
13.9 
13.8 
13.8 
13.7 
13.6 
13.5 
13.4 
13.4 
13.3 
13.3 
13.2 
13.1 
13.1 
13.0 
12.9 
12.9 
12.8 
12.8 
12.7 
12.6 
12.6 
12.5 
12.5 
12.4 
12.4 
12.3 
12.2 
12.2 
12.2 
12.1 
12.0 
12.0- 
11.9 
11.9 
11.8 
11.7 
11.7 
11.7 
11.6 
11.6 
11.5 
11.5 
11.4 
11.4 
11.3 
11.3 
11.3 
11.2 

25.0 
25.1 
25.2 
25.3 
25.4 
25.5 
25.6 
25.7 
25.8 
25.9 
26.0 
26.1 
26.2 
26.3 
26.4 
26.5 
26.6 
26.7 
26.8 
26.9 
27.0 
27.1 
27.2 
27.3 
27.4 
27.5 
27.6 
27.7 
27.8 
27.9 
28.0 
28.1 
28.2 
28.3 
28.4 
28.5 
28.6 
28.7 
28.8 
28.9 
29.0 
29.1 
29.2 
29.3 
29.4 
29.5 
29.6 
29.7 
29.8 
29.9 
30.0 
30.1 
30.2 
30.3 
30.4 

4,968 
4,859 
4,751 
4,643 
4,535 
4,428 
4,321 
4.215 
4,109 
4,004 
3,899 
3,794 
3,690 
3,586 
3,483 
3,380 
3,277 
3,175 
3,073 
2,972 
2,871 
2,770 
2,670 
2,570 
2,470 
2,371 
2,272 
2,173 
2,075 
1,977 
1,880 
1,783 
1,686 
1,589 
1,493 
1,397 
1,302 
1,207 
1,112 
1,018 
924 
830 
736 
643 
550 
458 
366 
274 
182 
91 
00 
-  91 
181 
271 
361 

-10.9 
10.8 
10.8 
10.8 
10.7 
10.7 
10.6 
10.6 
10.5 
10.5 
10.5 
1.04 
10.4 
10.3 
10.3 
10.3 
10.2 
10.2 
10.1 
10.1 
10.1 
10.0 
10.0 
10.0 
9.9 
9.9 
9.9 
9.8 
9.8 
9.7 
9.7 
9.7 
9.7 
9.6 
9.6 
9.5 
9.5 
9.5 
9.4 
9.4 
9.4 
9.4 
9.3 
9.3 
9.2 
9.2 
9.2 
9.2 
9.1 
9.1 
9.1 
9.0 
9.0 
9.0 
Q  0 

18.5 

13,172 

24.5 

5,518 

30.5 

•  451 

c  q 

18.6 

13,025 

24.6 

5,407 

30.6 

540 

18.7 
18.8 
18.9 

12,879 
12,733 
12,589 

14.6 
14.4 
-14.4 

24.7 
24.8 
24.9 

5,296 
5,186 
5,077 

11.0 
10.9 
-10.9 

30.7 
30.8 
30.9 

629 
717 
805 

8.8 
8.8 
-  8.8 

"Calculated  for  barometer  at  sea  level  =  30  in.  and  a  mean  temperature  of  50°  F. 


SURVEYING 
CORRECTIONS  FOR  TEMPERATURE  AND  HUMIDITY 


143 


T+t 
F.° 

C 

T  +  t 
F. 

C 

T+t 

F. 

C 

0 

-.1025 

60 

-.0380 

120 

+  .0262 

5 

.0970 

65 

.0326 

125 

.0315 

10 

.0915 

70 

.0273 

130 

.0368 

15 

.0860 

75 

.0220 

135 

.0420 

20 

.0860 

80 

.0166 

140 

.0472 

25 

.0752 

85 

.0112 

145 

.0524 

30 

.0698 

90 

.0058 

150 

.0575 

35 

.0645 

95 

-  .0004 

155 

.0626 

40 

.0592 

100 

+  .0049 

160 

.0677 

45 

.0539 

105 

.0102 

165 

.0728 

50 

.0486 

110 

.0156 

170 

.0779 

55 

.0433 

115 

.0209 

175 

.0829 

60 

-  .0380 

120 

+  .0262 

180 

+.0879 

elevation  of  the  base  was  6,025  ft.  above  sea  level,  what  was  the  elevation  of 
the  summit? 

SOLUTION. — From  the  first  table, 

Height  for  17.92  in.  =  14,039.6  ft. 
Height  for  24. 15  in.  =   5,910.5ft. 

Approx.  difference  in  elevation  =   8,129.1  ft. 
As  r+*  =  90°,  from  the  second  table,  C=  -.0058,  and 

2  =  8,129.1  X(l-. 0058)=   8,082ft. 
Elevation  of  base  =   6,025ft. 


Elevation,  top  of  mountain  =  14,010  ft. 

Use  of  Barometer. — The  mining  engineer  ordinarily  has  but  one  aneroid 
and  this  is  not  commonly  provided  with  a  thermometer.  With  a  single  instru- 
ment reliable  results  are  difficult  to  obtain,  and  depend  as  much  on  good  and 
uniform  weather  conditions  as  on  the  skill  and  carefulness  of  the  engineer. 
In  fact,  the  results  obtained  during  storms,  whether  of  wind  or  rain,  are  not  to 
be  relied  on  at  all.  The  single  aneroid,  then,  should  be  used  only  when  weather 
conditions  are  of  the  best.  In  the  morning,  before  starting  out,  its  reading 
should  be  noted  and  recorded.  If  a  thermometer  is  available,  it,  too,  should 
be  read.  As  the  aneroid  is  usually  employed  in  exploratory  work  in  which 
more  or  less  time  is  required  to  examine  various  coal  openings,  it  should  be  read 
a  few  minutes  after  reaching  an  opening  and  again  on  leaving,  the  times  and 
temperatures  being  noted  as  well.  After  the  examination  of  one  opening  is 
completed,  the  engineer  should  hasten  as  rapidly  as  possible  to  the  next;  that 
is,  he  should  move  rapidly  Trom  place  to  place  but  should  remain  a  sufficient 
time  at  each  to  estimate  the  changes  in  pressure  (and  consequently  in  apparent 
elevation)  that  are  taking  place.  By  taking  two  observations  at  each  opening 
at  intervals  of,  say,  5  hr.,  a  correction  curve  showing  the  changes  in  pressure 
may  be  worked  out  by  means  of  which  an  allowance  may  be  made  for  these 
changes  while  the  barometer  is  being  carried  from  place  to  place.  Thus,  a 
reading  at  Sta.  A  at  9.15  A.  M.,  showed  an  elevation  of  810  ft.,  and  a  reading 
at  Sta.  B  at  9.30  A.  M.  showed  one  of  860  ft.,  and  a  second  at  B  at  10  A.  M. 
indicated  875  ft.  This  last  reading  shows  a  change  in  apparent  elevation  of 
15  ft.  in  30  min.,  or  at  the  rate  of  .5  ft.  per  min.  The  apparent  difference  in 
elevation  between  A  and  B  (first  readings)  is  50  ft.,  but  a  part  of  this  difference 
is  due  to  a  change  in  the  atmospheric  pressure.  The  two  readings  at  Sta.  B 
show  that  the  elevations  are  apparently  increasing  at  the  rate  of  .5  ft.  per  min. ; 
therefore,  as  it  took  15  min.  to  go  from  A  to  B,  the  elevation  of  B  over  A 
apparently  increased  7.5  ft.  Hence,  the  actual  difference  in  elevation  between  A 
and  B  is  not  50  ft.  but  50  —  7.5  =  42.5  ft.  Very  satisfactory  results  may  be 
obtained  in  this  way;  and  if  the  time  between  stations  is  short,  corrections  for 
changes  in  temperature,  etc.,  need  not  be  made,  provided  the  difference  in 


144 


SURVEYING 


elevation  is  not  great.  By  taking  double  readings  at  each  station,  a  con- 
tinuous curve  can  be  worked  out  and  applied  to  correcting  the  day's  observa- 
tions. If  possible,  the  aneroid  should  be  reread  at  the  various  openings  on  the 
way  home,  and  the  mean  of  the  afternoon  and  morning  readings  taken  as  the 
true  reading.  The  instrument  should  be  read  upon  reaching  the  starting  point 
at  night  and  again  when  leaving  the  next  morning. 

When  two  barometers  are  available,  their  readings  are  compared  at  start- 
ing, one  being  carried  into  the  field  and  the  other  retained  at  headquarters 
where  it  is  read  by  an  assistant  throughout  the  day  at  intervals  of  10  or 
15  min.,  a  record  being  kept  of  the  time,  temperature,  and  pressure.  The 
field  man,  then,  need  take  but  one  reading  at  a  station,  preferably  just  before 
leaving,  and  should  likewise  note  the  temperature  and  time.  These  double 
readings,  unless  the  field-man  is  so  far  from  the  base  that  weather  conditions 
are  markedly  different,  afford  a  complete  check  on  fluctuations  in  pressure 
due  to  changed  atmospheric  conditions. 

Care  of  the  Barometer. — The  aneroid  should  not  be  removed  from  its  case; 
should  not  be  subjected  to  violent  jars;  nor  exposed  to  or  read  while  affected 
by  artificial  heat.  It  should  be  read  in  a  horizontal  position  and  on  sunny 
days  should  be  allowed  to  remain  in  the  shade  for,  say,  5  min.  before  being  read, 
that  all  its  parts  may  have  time  to  assume  the  temperature  of  the  air  at  the 
station.  

PRACTICAL  PROBLEMS  IN  SURVEYING 

1.  To  Prolong  a  Straight  Line. — Let  AB,  Fig.  1,  be  a  straight  line  whose 
position  on  the  ground  is  fixed  by  stakes  set  at  A  and  B,  and  let  it  be  required 
A  n  f,  to  prolong  the  line  to  C.  This 

•_ J. can    ke    done   in  two   ways; 

namely,  by  foresight  only,  or 
by  backsight  and  foresight,  the 


FIG.  1 
latter  method  being  commonly  called  backsight. 

By  Foresight.  —  The  transit  is  set  over  the  point  at  A  ,  and  the  line  of  sight 
directed  to  a  flag  held  at  B;  if  the  point  C  is  to  be  set  at  a  given  distance  from  B, 
the  chainmen  measure  the  required  distance,  the  head  chainman  being  kept  in 
line  by  the  transitman.  When  the  required  distance  has  been  measured,  the 
point  C,  which  evidently  lies  in  the  prolongation  of  A  B,  is  marked  by  a  stake 
or  otherwise. 

By  Backsight.  —  The  transit  is  set  over  the  point  at  B  and  a  sight  taken  on 
a  flag  held  at  A.  The  telescope  is  then  plunged  so  that  it  is  directed  along 
the  prolongation  of  A  B.  Any  re- 
quired distance  BC  may  then  be 
measured  from  B  in  the  direction  indi- 
cated by  the  line  of  sight. 

2.  To  Run  a  Line  Over  a  Hill 
When  the  Ends  of  the  Line  Are  Invis- 
ible From  Each  Other.  —  The  points  A 
and  B,  Fig.  2,  are  supposed  to  be  on 
the  opposite  sides  of  a  hill,  and  to  be 

invisible  from  each  other.     It  is  desired  to  run  a  line  between  them,  or  to 
locate  S9me  intermediate  points. 

Having  set  two  poles  at  A  and  B,  two  flagmen  with  poles  station  them- 
selves at  C  and  D,  approximately  in  line  with  A  and  B,  and  in  such  positions 
that  the  poles  at  B  and  D  are  visible  from  C,  and  those 
at  C  and  A  are  visible  from  D.  The  flagman  at  C  lines 
in  the  pole  at  D  between  C  and  B,  and  then  the  flag- 
man at  D  lines  in  that  at  C  between  D  and  A.  Then 
the  flagman  at  C  again  lines  in  that  at  D,  and  so  on 
until  C  is  in  the  line  between  D  and  A  at  the  same  time 
that  D  is  in  line  between  C  and  B.  The  points  C  and 
D  will  then  be  in  line  with  A  and  B. 

3.     To  Erect  a  Perpendicular  to  a  Line  at  a  Given 
5^J'"~"*i*J  lt  be  required  to  erect  a  perpendicular  to 
th,e  lme  AB  at  the  P°int  B>  Fie-  3.     A  triangle  whose 
are  in  the  proportion  of  3,  4,  and  5  is  a  right 
;  for  5'  =  4*+3'.     The  following 


3O  -  J8 

FIG  3 

..    ' 

mptl';    H  =  .          e   oowng 

method  is  based  on  this  principle:     Lay  off  on  BA  a  distance  BC  of  30  ft.  (or 
thl'n-n  t-Ttf  r1^0!^6  Cham  at  one  of  the  extremities  as  C,  and  the  end  of 
link  at  the  other  extremity  B.     Hold  the  end  of  the  fiftieth  link 


th 
the 


SURVEYING 


145 


and  draw  the  chain  until  both  parts  are  taut.  The  point  D  where  the  end  of 
the  fiftieth  link  is  held  will  then  be  a  point  in  the  perpendicular,  and  the  direc- 
tion of  the  latter  will  therefore  be  BD. 

The  distance  BC  may  be  any  other  convenient  multiple  of  3.  In  general, 
if  BC  is  denoted  by  3a,  BD  must  be  4a,  and  CD  must  be  5a.  Thus,  BC  may  be 
made  equal  to  21  (  =  3X7)  li.;  in  which 
case  BD  must  be  4X7  =  28,  and  CD 
must  be  5  X  7  =  35  li.  As  35  +  28  =  63, 
one  end  of  the  chain  must  be  fixed  at 
one  of  the  extremities  of  BC,  the  end 
of  the  sixty-third  link  at  the  other 
extremity,  and  the  chain  pulled  from 
the  end  of  the  thirty-fifth  link  until 
both  parts  are  taut. 

4.  To  Determine  the  Angle  Be- 
tween Two  Lines. — Let  AD  and  AE, 
Fig.  4,  be  two  lines  on  the  ground. 


C 


FIG.  4 

To  determine  the  angle  DAE,  measure  off 

from  A  on  AD  and  AE  equal  distances  AB  and  AC.     Measure  the  distance  BC. 
Then  the  angle  DAE  is  calculated  from  the  relation 


EXAMPLE.—  If  AB  and  AC  are  each  100  ft.  and  BC  is  57.6  ft.,  what  is  the 
value  of  the  angle  DAE? 

SOLUTION.  —  Substituting  the  values  of  BC  and  A  B  in  the  formula, 


44'X2  =  33°  28'. 


~-  =  .  28800; 


whence,  %DAE  =  16°  44'.  nearly;  and,  therefore,  DAE 

5.  To  Find  the  Distance  of  an  Inaccessible  Point.  —  Case  I.  —  Let  it  be 
required  to  determine  the  distance  from  the  point  B  to  an  inaccessible  point  P, 
Fig.  5.  Measure  BC  in  any  convenient  direc- 
tion and  run  a  line  A'D'  parallel  to  BC. 
Measure  AD,  the  distance  between  the  points 
where  the  lines  PB  and  PC  intersect  A'D'. 
Measure  also  AB.  Then, 

ABXBC 
BP=AD-BC 

EXAMPLE.—  If,  in  Fig.  5,  £C=100  ft.,  AB 
=  52.4  ft.,  and  AD  =  124.2  ft.,  what  is  the  dis- 
tance BPJ 

SOLUTION.  —  Substituting  these  values  in 
the  formula, 
52.4X100 


Case  II. — Measure  a  horizontal  base  line  AB,  Fig.  6,  and  take  the  angles 
formed  by  the  lines  BAC  and  ABC,  which  gives 
two  angles  and  the  included  side.  Assuming 
the  angle  A  to  be  60°,  the  angle  B  50°,  and  the 
side  AB  =  50Q  ft.,  angle  C=  180°-(60°+50°) 
=  70°. 

Then,   sin  70°  :  AB  =  sin  A  :  BC,   and  sin 
70°  :  AB  =  sin     B  :  AC:     or,    .939693  :  500 
=  .866025  :  BC.or  460.8+ ,  and  .939693  :  500 
=  .766044  :  AC,  or  407.6  +  . 
By  logarithms: 

Log  500=   2.698970 

Log  sin  60°=   9.937531 

12.636501 

Log  sin  70°=  9.972986 

2.663515  =  log  of  460.8 +  . 


FIG.  6 


Log  500=   2.698970 

Log  sin  50°=   9.884254 

12.583224 

Log  sin  70°=   9.972986 

2.610238  =  log  of  407.6 +. 


146 


SURVEYING 


6.     To  Determine  the  Distance  Between  Two  Points  Invisible  From  Each 
Other  or  Separated  by  an  Impassable  Barrier. — Case  I. — Let  it  be  required 

to  find  the  distance 
between  two  points  A 
and  B,  Fig.  7,  that  are 
invisible  from  each 
other.     First  run  a  ran- 
dom line  AD'  in  such  a 
manner  that  it  will  pass 
TJ^~— ^_     .    as  near  B  as  can  be  es- 
FlG.  7  ^-»      timated.     From  B  drop 

a  perpendicular  BD  on  A  D't  and  compute  the  required  distance  A  B  by  the  formula 


EXAMPLE.— If,  in  Fig.  7,  the  distance  AD  is  206.1  ft.  and  the  distance  BD 
is  35.1  ft.,  what  is  the  distance  from  A  to  Bl 

SOLUTION.— Here  A D  =  206.1   and  BD  =  35.l;   therefore,   substituting   in 
the  formula,  AB=  V  206.12+35.12  =  209.1  ft. 

Case  II. — Select  any  convenient  station,  as  C, 
Fig.  8,  measure  the  lines  CA  and  CB,  and  the  angle 
included  between  these  sides,  so  as  to  obtain  two 
sides  and  the  included  angle.  Assuming  the  angle 
C  to  be  60°,  the  side  CA,  600  ft.,  and  the  side  CB, 
500  ft.,  the  following  formula  is  obtained: 

CA+CB  :  CA-CB  =  tan  4±£  :  tan  ^. 
180° -60° 


Then, 


A+B 


-,  or  60°. 


-;  or,  1,100  :  100  =  1.732050  :  .157459, 


Then,  1,100  :  100  =  tan  60°  :  tan 

a 

or  tangent  of  — = — ,  or  8°  57'. 

Then,  60°+8°  57'  =  68°  57',  or  angle  B, 

and  60°  -  8°  57'  =  51°  03',  or  angle  A , 

Having  found  the  angles,  find  the  third  side  by  the  same  method  as  case  II, 
of  problem  5. 

The  foregoing  formula,  worked  out  by  logarithms,  is  as  follows: 

Log  100=   2.000000 
Log  tan  60°  =  10.238561 


Log  1.100 


12.238561 
3.041393 
9.197168  =  log  tan  of 


-,  or  8°  57'. 


Then, 

60°+8°  57'  =  68°  57',  or  angle  B, 
and         60°  -8°  57'  =  51°  03',  or  angle  A 

NOTE.  —  The  greater  angle  is  always  opposite 
the  greater  side. 

7.  To  Find  the  Distance  Between  Two  Inac- 
cessible Objects  When  Points  Can  Be  Found  From 
Which  Both  Objects  May  Be  Seen.  —  Let  A  B,  Fig. 
9,  be  the  line,  the  ends  A  and  B  of  which  are  inac- 
cessible. Select  two  points  P  and  Q  from  which 
both  ends  of  the  line  can  be  seen,  and  at  a  distance 
from  each  other  of  about  300  or  400  ft.  Measure 
the  line  PQ,  and  the  angles  K,  L,  M,  and  2V. 
Then,  from  triangle  APQ, 


FIG.  9 


in  which  R  =  180°  -(K+L)-M. 
From  triangle  BPQ, 

BP  = 

in  which  5  =  180°-L-(M+ZV). 


;  -  — 


PQsin  (M+N) 
sin  5 


SURVEYING 


147 


Then,  from  triangle  ABP, 


and 


A  R 


(BP-AP)cos 


EXAMPLE.  —  If,  in  Fig.  9,  the  distance  PQ  is  400  ft.,  and  the  angles,  as  meas- 
ured, are  K  =  37°  10',  L  =  36°  30',  M  =  52°  15',  2V  =  32°  55',  what  is  the  dis- 

'anSoLUTiON.—  In  the  triangle  APQ,  R  =  180°-  (37°  10'  +  36°  30'+52°  15') 
=  54°  05',  and  400  sin  52°  15' 

AP     ~iin~54^05'~ 

180°-  (36°  30'+52°  15'  +-32°  55')  =58°  20',  M+N 


In  the  triangle  BPQ,  S=  180° 
=  52°  15'+32°  55'  =  80°  10',  and 


sin  58°  20' 
Also,  A>37°  10',  $  K=18°  35',  and 

i  fv     v\     (468.30-390.53)          ,    0     ., 
tan  1  (X-  F)  =  --  cot  18    35 


whence,  I  (X—  F)  =  15°  04',  and  therefore 

(468.30-390.53)  cos 

sm  15°  04' 

8.  To  Determine  the  Angle  Between  Two  Lines  AB  and  CD,  Whose 
Point  of  Intersection  P  is  Inaccessible,  Also,  the  Distances  BP  and  DP.—  This 
problem  is  of  frequent  occurrence  in 
railroad  work,  the  two  given  lines  being 
the  center  lines  of  two  straight  tracks 
that  are  to  be  connected  by  a  curve 
Measure  the  distance  BD,  Fig.  10,  and 
the  [angles  K  and  L.  Then,  M  =  180° 


A 

and 


BD  sin  K 


9.     Survey  of  a  Closed  Field.—  If 

a  closed  field  is  to  be  surveyed  without 

the  aid  of  an  angle-measuring  instru- 

ment, the  area  may  be  divided  into  "P  r   m 

triangles  by  means  of  diagonals,  which 

are  measured  on  the  ground.     The  area  of  each  triangle  may  then  be  deter- 

mined by  the  formula       A  =  V5(5-fl)"o-6)(5-c) 

in  which  a,  b,  and  c  represent  the  three  sides  and  5  represents  one-half  of  their 

a+b+c 
sum,  or  —  —  —  . 

When  obstacles  make  it  impossible  to 
measure  directly  the  diagonals  of  a  field, 
as,  for  instance,  the  diagonal  BE,  Fig.  11, 
a  tie  line  FG  parallel  to  BE  is  run  and 
measured.  Then,  _GFXAB 
BE~  AF~~ 

To  run  the  line  FG,  produce  BA  and 
select  any  convenient  point  F  and  measure 
AF.     Then  produce  EA  and  locate  G  from 
the  relation 
AFXAE 


FIG.  11 


EXAMPLE.  —  In  Fig.  11,  let  the  lengths  of  the  sides  be  as  follows:  AB 
=  320  ft.,  BC  =  217  ft.,  CD=196  ft.,  DE  =  285  ft.,  and  £A=304  ft.  It  is 
required  to  calculate  the  length  of  the  diagonal  BE  by  means  of  a  tie-line. 

SOLUTION.  —  Let  the  line  BA  be  prolonged  100  ft.  beyond  A  ;  that  is,  make 

AF=100  ft.     Then  AG  must  be  equal  to  A  F  .XgA  E  =  10°21304  =  95  ft.     Let 


.g 
AD 

the  length  of  GF,  as  found  by  measurement,  be  125  ft. 

GFXAB      125X320 
BE—  -——  400  ft 


Then, 


148 


SURVEYING 


FIG.  12 


n 


10.  To  Determine  the  Height  of  a  Vertical  Object  Standing  on  a  Hori- 
zontal Plane.  —  Measure  from  the  foot  of  the  object  any  convenient  horizon- 

tal distance  AB,  Fig.  12;  at  the  point  A,  take  the  angle 
of  elevation  BAC.  Then,  as  B  is  known  to  be  a  right 
angle,  two  angles  and  the  included  side  of  a  triangle  are 
obtained.  Assuming  that  the  line  AB  is  300  ft.  and  the 
angle  BAC  =  4Q°,  the  angle  C=180°-(90°+40°)  =  50°. 
Then,  sin  C  :  AB  =  sin  A  :  BC,  or  .766044  :  300  =  .642788 
:  BC,  or  £C  =  251.73  +  ft.  Or,  by  logarithms: 

Log  300=   2.477121 
Log  sin  40°=   9.808067 
12.285188 
Log  sin  50°=  9.884254 

2.400934  or  log  of  251.73+  ft. 

11.  To  Find  the  Distance  of  a  Vertical  Object  Whose  Height  is  Known. 
At  a  point  A,  Fig.  13,  take  the  angle  of  elevation  to  the  top  of  the  object. 
Knowing  that  the  angle  B  is  a  right  angle,  the  angles  B  and  A  and  the  side 
BC  are  known.     Assuming  that  the  side  BC  =  200  ft.  and 

the  angle  A  =30°,  a  triangle  is  formed  as  follows:     Angle 
A  =  30°,  B  =  90°,  C  =  60°,  and  the  side  BC  =  200  ft.     Then 
sin  A  :  BC  =  s'm  C  :  AB,   or    .5  :  200  =  .866025  :  AB, 
AB  =  346.41  ft.     By  logarithms: 

Log  200=   2.301030 

Log  sin  60°=   9.937531 

12.238561 

Log  sin  30°=   9.698970 

2.539591  or  log  of  346.41  ft. 

12.  To  Find  the  Height  of  a  Vertical  Object  Standing  Upon  an  Inclined 
Plane.  —  Measure  any  convenient  distance  DC,  Fig.  14,  on  a  line  from  the  foot 
of  the  object,  and,  at  the  point  D,  measure  the  angles  of  elevation  EDA  and 

EDB,  and  the  angle  CDB;  also  at  C  measure 

the  angle  BCD.     In  the  triangle  BDC,  the  side 

BD  may  be  calculated  for  the  angles  at  D  and 

C  and  the  side   CD  are  known.     Then,  in  the 

right-angled  triangle  BED  the  sides  BE  and  ED 

may  be  calculated, 

as  the  side  BD  and 

the  angle  at   D   are 

known.      Next,    in 

the  right-angled 

triangle  A  ED,   the 

side    AE    may    be  /        /STVii 

calculated,  for  the  /        /£.     T\- 

Final-  /         /fe;.,|  \ 


FlG    13 


FIG.  14 

side  ED  and  the  angle  at  D  are  known.     

ly,  the  height  of  the  object  may  be  found  by  sub- 
stracting  the  length  AE  from  the  length  BE. 

13.    To  Find  the  ^ 


Height  of  an  Inac-  FIG.  15 

cessible  Object  Above  a  Horizontal  Plane. — First 
Method. —  Measure  any  convenient  horizontal 
line  AB,  Fig.  15,  directly  toward  the  object, 
and  take  the  angles  of  elevation  at  A  and  B. 
In  the  triangle  ABC,  the  side  AC  may  be  calcu- 
lated as  the  angles  at  A  and  B  and  the  side 
AB  are  known.  Then,  in  the  right-angled  tri- 
angle CD  A,  the  side  CD,  which  is  the  height  of 
the  object,  may  be  calculated  as  the  angle  at 
A  and  the  side  AC  are  known. 

Second  Method. — If  it  is  not  convenient  to 
measure  a  horizontal  base  line  toward  the  object, 
measure  any  line  AB,  Fig.  16,  and  also  measure 
the  horizontal  angles  BAD,  ABD,  and  the  angle  of  elevation  DEC.  Then,  by 
means  of  the  two  triangles  ABD  and  CBD,  the  height  CD  can  be  found.  Then, 
with  the  line  A  B  and  the  angles  BAD  and  ABD  known,  the  third  angle  is  readily 
found,  and  the  side  BD  can  be  found.  Then,  in  the  triangle  BDC,  the  angle  B 
is  known,  by  measurement,  D  =  90°,  and  the  side  BD  is  known.  Then,  the 
side  CD,  or  the  vertical  height,  can  be  found  by  preceding  methods. 


FIG.  16 


MECHANICS  149 

MECHANICS 


ELEMENTS  OF  MECHANICS 

GENERAL  LAW 

All  machinery,  however  complicated,  is  merely  a  combination  of  six  ele- 
mentary forms,  viz.:  the  lever,  the  wheel  and  axle,  the  pulley,  the  inclined  plane 
the  wedge,  and  the  screw;  and  these  six  can  be  still  further  reduced  to  the  lever 
and  the  inclined  plane.  They  are  termed  mechanical  powers,  but  they  do  not 
produce  force;  they  are  only  methods  of  applying  and  directing  it.  The  law 
of  all  mechanics  is: 

Law. — The  power  multiplied  by  the  distance  through  which  it  moves  is  equal 
to  the  weight  multiplied  by  the  distance  through  which  it  moves. 

Thus,  20  Ib.  of  power  moving  through  5  ft.  =  100  Ib.  of  weight  moving 
through  1  ft.  In  the  following  discussion  friction  is  not  considered. 

LEVERS 

There  are  three  classes  of  levers:  (1)  power  at  one  end,  weight  at  the  other, 
and  fulcrum  between,  as  shown  in  Fig.  1;  (2)  power  at  one  end,  fulcrum  at 


FIG.  1  FIG.  2  FIG.  3 

the  other,  and  weight  between,  as  shown  in  Fig.  2;  (3)  weight  at  one  end, 
fulcrum  at  the  other,  and  power  between,  as  shown  in  Fig.  3. 

The  handle  of  a  blacksmith's  bellows  is  a  lever  of  the  first  class;  the  hand 
is  the  power  and  the  bellpws  the  weight,  with  the  pivot  between  as  the  fulcrum. 
A  crowbar  used  for  prying  down  top  rock  is  a  lever  of  the  second  class;  the 
hand  is  the  power,  the  rock  to  be  barred  down  the  weight,  and  the  point  in  the 
roof  against  which  the  bar  presses  is  the  fulcrum .  The  treadle  of  a  grindstone 
is  a  lever  of  the  third  class;  the  foot  is  the  power,  the  hinge  at  the  back  of  the 
foot  is  the  fulcrum,  and  the  moving  of  the  machinery  is  the  weight.  A  lever 
is  in  equilibrium  when  the  arms  balance  each  other.  The  distances  through 
which  the  power  and  the  weight  move  depend  on  the  comparative  length  of 
the  arms. 

Let  P  =  power; 

W  =  weight 

L  =  power's  distance  from  fulcrum  C\ 
1  =  weight's  distance  from  fulcrum  C; 
c  =  distance  between  power  and  weight; 
Arranging  these  terms  according  to  the  law  of  mechanics, 
PL  =  Wl,  orP:  W=l  :  L 

p=™       W=*T 

In  levers  of  the  first  class,  a  =  L-\-l\ 

T       Wa 

whence  L  =  W+P 

In  levers  of  the  second  class,  a 

T  W<1 

whence  L=w_p 

In  levers  of  the  third  class,  a  =  l  —  L; 

,        Wa  .       Pa 

whence 


150 


MECHANICS 


In  first-  and  second-class  levers,  as  ordinarily  used,  power  is  gained  and 
time  is  lost;  in  the  third  class,  power  is  lost  and  time  is  gained. 

EXAMPLE. — Having  a  weight  of  2,000  Ib.  to  lift  with  a  lever,  the  short  end 
of  which  is  2  ft.  from  the  fulcrum  and  the  long  end  10  ft.,  how  much  power  will 
be  required? 

SOLUTION.— Applying  the  formula  L  :  1  =  W  :  P,  10  :  2  =  2,000  :  P  :  whence 
P=  (2,000X2)  -f-  10  =  400  Ib. 

The  compound  lever,  Fig.  4,  consists  of  several  levers  so  constructed  that 
the  short  arm  of  the  first  acts  on  the  long  arm  of  the  second,  and  so  on  to  the 
last.  If  the  distance  from  A  to  the  fulcrum  is  four  times  the  distance  from  the 

fulcrum  to  B,  then  a  power  of  5  Ib. 
at  A  will  lift  20  Ib.  at  B.  If  the 
arms  of  the  second  lever  are  of  the 
same  comparative  length,  the  20-lb. 
power  obtained  at  B  will  exert  a 
pressure  of  80  Ib.  on  E;  and  if  the 

„  „  third  lever  has  the  same  compara- 

MG-  4  tive  lengths,  this  80  Ib.  at  E  will 

lift  320  Ib.  at  G.  Thus,  a  power  of  5  Ib.  at  A  will  balance  a  weight  of  320  Ib. 
at  G.  But,  in  order  to  raise  the  weight  1  ft.,  the  power  must  pass  through 
320 -T- 5  =  64  ft.  WHEEL  AND  AXLE 

The  wheel  and  axle,  Fig.  5,  is  a  modification  of  the  lever.  The  ordinary 
windlass  is  a  common  form.  The  power  is  applied  to  the  handle,  the  bucket  is 
the  weight,  and  the  axis  of  the  windlass  is  the  fulcrum. 
The  long  arm  of  the'  lever  is  the  handle,  and  the  short  arm 
is  the  radius  of  the  axle.  Thus,  F  is  the  fulcrum,  Fc  the 
long  arm,  and  Fb  the  short  arm.  The  wheel  and  axle  has 
the  advantage  that  it  is  a  kind  of  perpetual  lever.  It  is  not 
necessary  to  prop  up  the  weight  and  readjust  the  lever,  but 
both  arms  work  continuously. 

By  turning  the  handle  or  wheel  around  once,  the  rope 
will  be  wound  once  around  the  axle,  and  the  weight  will 
be  lifted  that  distance.  Applying  the  law  of  mechanics, 
power X  circumference  of  wheel  =  weight  X  circumference  of 
axle;  9r,  as  the  circumferences  of  circles  are  proportional 
to  their  radii,  P  :  W  =  r  :  R;  whence  PR=  Wr.  Therefore,  FIG.  5 


A  train,  Fig.  6,  consists  of  a  series  of  wheels  and  axles  that  act  on  one  another 
on  the  principle  of  a  compound  lever.  The  driver  is  the  wheel  to  which  power 
is  applied.  The  driven  wheel  or  follower,  is  the  one  that  receives  motion  from 
the  driver.  The  pinion  is  the  small  gear-wheel  on  the  axle. 

If  the  diameter  of  the  wheel  A  is  16  in., 
and  of  the  pinion  B  4  in.,  a  pull  of  1  Ib. 
applied  at  P  will  exert  a  force  of  4  Ib.  on 
the  wheel  C;  if  the  diameter  of  C  is  6  in., 
and  of  D  3  in.,  a  force  of  4  Ib.  on  C  will 
exert  a  force  of  8  Ib.  on 
E.  If  E  is  16  in.  in 
diameter,  and  F  4  in.,  a 
force  of  8  Ib.  on  E  will 
raise  a  weight  of  32  Ib. 
on  F.  In  order,  how- 
ever, to  lift  this  amount, 

,«  according  to  the  prin- 

/<====>>  ciple  already  named, 

I  w  I  the  weight  will  only  pass 

|  _      \  FIG.  6  through  one  thirty-sec-  pIG  7 

ond  of  the  distance  of 

the  power.     Thus,  power  is  gained  and  speed  lost.     To  reverse  this,  power 
may  be  applied  to  the  axle,  and,  with  a  correspondingly  heavy  power,  speed 
gained.     Referring  to  Fig.  7,  applying  the  law  of  mechanics, 
Wrr\"  PRR'R" 

RR'R"  =    rr'r" 


MECHANICS  151 

n  :  n"  =  r'r"  :  RR' 
v.v'  =  rr'r"  iRR'R" 

in  which  «,  »',  n"  =  number  of  revolutions; 

v,  v' —  velocity  or  speed  of  rotation; 
r,  r',  r",  etc.=radii  of  pinions; 
R,  R',  R",  etc.  =  radii  of  wheels. 

INCLINED  PLANE 

In  Fig.  8,  the  power  must  descend  a  distance  equal  to  AC  in  order  to 
elevate  the  weight  to  the  height  BC;  hence,  PX  length  of  inclined   plane 
=  WX height  of  inclined  plane,  or  P  :  W  =  height  of 
inclined  plane  :  length  of  inclined  plane;  or, 

~~    /  h      sin  a 

To  Find  Weight  Required  to  Balance  Any  Weight 
on  Any  Inclined  Plane. — Multiply  the  given  weight  by 
the  sine  of  the  angle  of  inclination.      Thus,  to  find  the  ^ 
weight  required  to  balance  a  loaded  car  weighing  2,000 
Ib.  on  a  plane  pitching  18°,  multiply  2,000  by  the  sine  FIG.  8 

of  18°,  or  2,000 X. 309017  =  618.034  Ib. 

Or,  if  the  length  of  the  plane  and  the  vertical  height  are  given,  multiply 
the  load  by  the  quotient  of  the  vertical  height  divided  by  the  length.  Thus, 
if  a  plane  between  two  levels  is  300  ft.  long  and  rises  92.7  ft.,  and  the  load  is 

92  7 
2,000  Ib.,  the  balancing  weight  'is  found  as  follows:     2.000X -^  =  618  Ib. 

Case  /. — To  find  the  horsepower  required  to  hoist  a  given  load  up  an  inclined 
plane  in  a  given  time,  use  the  formula 

(Load,  in  lb.+ weight  of  hoisting  rope,  in  Ib.)  X  vertical  height  load  is  raised,  in  ft. 
33, 000  X  time  of  hoisting,  in  minutes 

EXAMPLE. — Find  the  horsepower  required  to  raise,  in  3  min.,  a  car  weigh- 
ing 1  T.  and  containing  1  T.  of  material  up  an  inclined  plane  1,000  ft.  long 
and  pitching  30°,  if  the  rope  weighs  1,500  Ib. 

SOLUTION. — The  total  load  equals  car + contents + rope  =  2,000+2,000 
+  1,500  =  5,500  Ib.  The  vertical  height  through  which  the  load  is  hoisted 


equals  1,  000  X  sin  30°  =  1  ,000  X  .5  =  500  ft.;  therefore,  H.  p-  =  "33  000  x  3  =2?.7. 

Case  II.  —  When  the  power  acts  parallel  to  the  base,  use  the  formula 

WX  height  of  inclined  plane  =  P  X  length  of  base. 

These  rules  are  theoretically  correct,  but  in  practice  an  allowance  of  about 
30%  must  be  made  for  friction  and  contingencies. 

SCREW 

The  screw  consists  of  an  inclined  plane  wound  around  a  cylinder.  The 
inclined  plane  forms  the  thread,  and  the  cylinder,  the  body.  It  works  in  a 
nut  that  is  fitted  with  reverse  threads  to  move  on  the  thread  of  the  screw. 
The  nut  may  run  on  the  screw,  or  the  screw  in  the  nut.  The  power  may  be 
applied  to  either,  as  desired,  by  means  of  a  wrench  or  a  lever. 

When  the  power  is  applied  at  the  end  of  a  lever,  it  describes  a  circle  of 
which  the  lever  is  the  radius  r.  The  distance  through  which  the  power  passes 
is  the  circumference  of  the  circle;  and  the  height  to  which  the  weight  is  lifted 
at  each  revolution  of  the  screw  is  the  distance  between  two  of  the  threads, 
called  the  pitch,  p.  Therefore,  P  X  circumference  of  circle  =  WX  pitch;  or 
P  :  W  =  p  :  2*r;  whence,  Wp  ^_2-nrP 

P  =  2^  "~T~ 

The  power  of  the  screw  may  be  increased  by  lengthening  the  lever  or  by 
diminishing  the  distance  between  the  threads. 

EXAMPLE.  —  How  great  a  weight  can  be  raised  by  a  force  of  40  Ib.  applied 
at  the  end  of  a  wrench  14  in.  long,  using  a  screw  with  5  threads  per  in.? 

SOLUTION.—  Substituting  in  the  formula  WX  i  =  40X28X3.1416;  whence 


The  wedge  usually  consists  of  two  inclined  planes  placed  back  to  back,  as 
shown  in  Fig.  9.  In  theory,  the  same  formula  applies  to  the  wedge  as  to  the 
inclined  plane,  Case  II. 

P  :  W  =  thickness  of  wedge  :  length  of  wedge. 


152 


MECHANICS 


Friction,  in  the  other  mechanical  powers,  materially  diminishes  their  efficiency; 

in  this  it  is  essential,  since,  without  it,  after  each  blow  the  wedge  would  fly 
back  and  the  whole  effect  be  lost.  Again,  in  the 
others  the  power  is  applied  as  a  steady  force;  in  this 
it  is  a  sudden  blow,  and  is  equal  to  the  momentum 
of  the  hammer. 


FIG.  9 


The  pulley  is  simply  another  form  of  the  lever 
that  turns  about  a  fixed  axis  or  fulcrum.  With  a 
single  fixed  pulley,  shown  in  Fig.  10,  there  can  be  no 
gain  of  power  or  speed,  as 
the  force  P  must  pull 


down  as  much  as  the  weight  W,  and  both  move 
with  the  same  velocity.  It  is  simply  a  lever  of 
the  first  class  with  equal  arms,  and  is  used  to  change 
the  direction  of  the  force.  If  v  =  velocity  of  W ;  v 
=  velocity  of  P;  then  P=  W  and  v  =  v'. 

A  form  of  the  single  pulley,  where  it  moves 
with  the  weight,  is  shown  in  Fig.  11.  In  this,  one- 
half  of  the  weight  is  sustained  by  the  hook,  and  the 
other  half  by  the  power.  As  the  power  is  only 
one-half  the  weight,  it  must  move  through  twice 
the  space;  in  other  words,  by  taking  twice  the  *IG-  1U  FIG.  11 

time,  twice  as  much  can  be  raised.     Here  power  is  gained  and  time  lost;  there- 
fore, P  =  $W  andv'  =  2». 

Combinations  of  Pulleys. — (1)  In  Fig.  12,  the  weight  W  is  sustained  by 
three  cords,  each  of  which  is  stretched  by  a  tension  equal  to  the  P;  hence, 

8421 


FIG.  12 


FIG.  13 


FIG.  14 


FIG.  15 


FIG.  16 


1  lb.  of  power  will  balance  3  Ib.  of  weight.  (2)  In  Fig.  13,  a  power  of  1  lb. 
will  in  the  same  manner  sustain  a  weight  of  4  lb.,  and  must  descend  4  in.  to  raise 
the  weight  1  in.  (3)  Fig.  14  represents  the  ordinary  tackle  block  used  by 
mechanics,  which  can  be  calculated  by  the  following  general  rule: 

Rule. — In  any  combination  of  pulleys  where  one  continuous  rope  is  used,  a 
load  on  the  free  end  will  balance  a  weight  on  the  movable  block  as  many  times  as 
great  as  the  load  on  the  free  end  as  there  are  parts  of  the  rope  supporting  the  load, 
not  counting  the  free  end. 

(4)  In  the  cord  marked  1,  Fig.  15,  each  part  has  a  tension  equal  to  the 
power  P;  and  in  the  cord  marked  2,  each  part  has  a  tension  equal  to  2  P,  and  so 
on  with  the  other  cords.  The  sum  of  the  tensions  acting  on  the  weight  W  is 
16;  hence,  W=  16  P.  If  n  =  number  of  pulleys, 

P  =  ~  W=2nP 

2  np  K 

Differential  Pulley.— In  the  differential  pulley,  shown  in  Fig.  16,  W-^^ 

In  all  pulley  combinations,  nearly  one-half  the  effective  force  is  lost  by  friction. 


MECHANICS  153 


FALLING  BODIES 

When  the  center  of  gravity  of  a  moving  body  passes  over  equal  distances 
in  equal  intervals  of  time,  the  body  has  a  uniform  motion;  otherwise,  the  motion 
is  variable.  The  velocity  in  a  uniform  motion  is  constant  and  is  equal  to  the 
distance  traversed  by  the  center  of  gravity  of  the  body  in  a  unit  of  time,  as 
feet  per  second,  miles  per  hour,  etc.  When,  in  a  variable  motion,  the  velocity 
increases  or  decreases  uniformly  with  the  time,  the  motion  is  designated,  respec- 
tively, as  uniformly  accelerated  or  uniformly  retarded,  and  the  rate  of  increase 
or  decrease  is  called  acceleration  or  retardation,  being  equal  to  the  amount  that 
the  velocity  increases  or  decreases  in  a  unit  of  time.  A  body  falling  under 
the  action  of  gravity  is  a  case  of  uniformly  accelerated  motion,  the  accelera- 
tion being  equal  to  32.16  ft.  per  sec.  and  being  usually  denoted  by  g. 

Let  t  =  number  of  seconds  that  body  falls; 

v  =  velocity,  in  feet  per  second,  at  end  of  time  t; 
h  =  distance  that  body  falls  during  time  t. 

Then,  »  =  gt  =      =  V2gA  =  8.02  V  h 


WORK 

Work  is  the  overcoming  of  resistance  through  a  distance.  The  unit  of  work 
is  the  foot-pound;  that  is,  it  equals  1  Ib.  raised  vertically  1  ft.  The  amount 
of  work  done  is  equal  to  the  resistance,  in  pounds,  multiplied  by  the  distance, 
in  feet,  through  which  it  is  overcome.  If  a  body  is  lifted,  the  resistance  is  the 
weight,  or  the  overcoming  of  the  attraction  of  gravity,  the  work  done  being  the 
weight  W,  in  pounds,  multiplied  by  the  height  h  of  the  lift,  in  feet,  or  Wh  ft.-lb. 

Power  is  the  amount  of  work  performed  in  a  unit  of  time.  One  horsepower 
is  550  ft.-lb.  of  work  in  1  sec.,  33,000  ft.-lb.  in  1  min.  or  1,980,000  ft.-lb.  in  1  hr. 
In  the  metric  system,  1  H.  P.  is  75  meter-kilograms  per  second,  usually  written 
75  m.  Kg.-sec. 

Kinetic  energy  is  the  capacity  of  a  moving  body  to  perform  work.  If  the 
moving  body  has  a  weight  W  and  a  velocity  v,  the  work  that  it  is  capable  of 

doing  in  being  brought  to  rest  is  -—-.     A  body  falling  through  a  height  of  h  ft. 
acquires  during  its  fall  a"  velocity  of  v=  -\l2gh;  its  kinetic  energy  is  therefore, 


2g 

EXAMPLE  1.  —  What  is  the  horsepower  of  a  stream  of  water  discharging 
12  cu.  ft.  per  sec.  through  a  height  of  125  ft.? 

SOLUTION.—  The  kinetic  energy  per  second,  is  62.5X12X125  ft.-lb.,  62.5 
being  the  weight  of  1  cu.  ft.  of  water.  The  horsepower  is,  therefore, 


EXAMPLE  2.  —  What  is  the  kinetic  energy  per  second  of  a  jet  of  water  whose 
area  of  cross-section  is  .1  sq.  ft.  and  whose  velocity  is  10  ft.  per  sec.? 

SOLUTION.  —  In  this  case,  W=62.5X.  1X10'=  62.5  Ib.     The  kinetic  energy 
is  therefore,  62.5X10^6^50 

2g 


COMPOSITION  AND  RESOLUTION  OF  FORCES 

The  resultant  of  two  or  several  forces  acting  on  a  body  is  the  single  force 
that,  if  acting  alone,  would  produce  the  same  effect  as  the  several  forces  com- 
bined. The  latter  forces  are  called  components  with  respect  to  the  resultant. 

Composition  of  forces  is  the  process  of  finding  the  resultant  when  the  com- 
ponents are  known,  and  the  converse  process  of  finding  the  components  when 
the  resultant  is  given,  is  called  resolution  offerees. 


154  MECHANICS 

Parallelogram  of  Forces. — If  two  forces,  as  Fi  and  Ft,  Fig.  1,  are  repre- 
sented in  magnitude  and  direction  by  two  lines,  as  OA  and  OB,  their  resultant  R 
0  will  be  represented  in  magnitude  and  direction 
-?  by  the  diagonal  OC  of  the  parallelogram  OACB 
which  is  constructed  by  drawing  BC  and  AC 
parallel  to  OA  and  OB,  respectively,  and  join- 
ing the  intersection  C  with  O. 

The  resultant  R  can  also  be  determined  an- 
alytically:   its    magnitude    by    the    formula 
R  =  VFi2+F22— 2FiF2  cos  L,    and   the   angles 
Mi  and  M2  that  R  makes  with  Fi  and  Ft,  re- 
FiG.  1  spectively,  may  be  found  by  the  formulas, 

F2  sin  L 
sin  Mi  = 


and  sin  M2  = 


R 

Fi  sin  L 


R 

For  rectangular  components,  L  =  90°.     The  formulas  then  become: 


Resolution  of  Forces. — A  given  force 
may  have   an   innumerable   number  of 
combinations  of  components.     The  prob-        / 
lem  is,  however,  determinate  when  the    &/. 
directions  of  the  components  are  given,    a.  wo 

Let  OC,  Fig.  2,  represent  in  magnitude      '  r  G< 

and  direction  the  force  R  acting  at  O,  and  let  it  be  required  to  find  its 
components  in  the  directions  OX2  and  OX\.  Draw  from  C,  lines  parallel  to 
these  directions  meeting  OXi  at  A  and  OXz  at  5.  Then,  OA  and  OB  are  the 
required  components  Fi  and  F2.  They  may  also  be  determined  analytically 
by  the  formulas,  =  R  sin  Ms 

1- 

and  F 

sin  (Mi+M2) 

When  Fi  and  F2  are  perpendicular  to  each  other, 
and  F 


MOMENTS  OF  FORCES 

The  moment  of  a  force  about  a  point  is  the  product 
obtained  by  multiplying  the  magnitude  of  the  force  by  the 
perpendicular  distance  from  the  point  to  the  line  of  action 
/  of  the  force.     In  the  accompanying  figure,  the  moment  of 

I    .  F  about  the  point  C  is  Fp;  and  about  the  point  Ci  it  is  Fpi. 

The  point  to  which  a  moment  is  referred,  or  about  which 
a  moment  is  taken  is  called  the  center  of  moments,  or  origin 
of  moments.  The  perpendicular  p  or  p\  from  the  origin  of 
moments  on  the  line  of  action  of  the  force  is  called  the  lever 
arm  or  simply  the  arm,  of  the  force  with  respect  to  the  origin. 
A  moment  is  expressed  in  foot-pounds,  inch-tons,  etc., 
according  to  the  units  to  which  the  force  and  its  arm  are 
referred. 

The  moment  is  either  positive  or  negative,  depending 
on  the  direction  in  which  the  force  tends  to  cause  rota- 
tion.    It  is  positive  for  clockwise  motion,  and  negative 
for  counter-clockwise  motion.     Thus,  the  moment  of  F 
^  about  C  is  positive  and  the  moment  about  Ci  is  negative, 
because,  if  the  arms  p  and  pi  were  bars,  the  force  would  tend  to  rotate  p  in  a 
clockwise  direction,  and  pi  in  a  counter-clockwise  direction. 


MECHANICS  155 


CENTER  OF  GRAVITY 

The  center  of  gravity  of  a  figure  or  a  body  is  that  point  upon  which  the 
figure  or  the  body  will  balance  no  matter  in  what  position  it  may  be  placed, 
provided  it  is  acted  upon  by  no  other  force  than  gravity. 

If  a  plane  figure  is  alike,  or  symmetrical,  on  both  sides  of  a  center  line, 
the  latter  line  is  termed  an  axis  of  symmetry,  and  the  center  of  gravity  lies  in 
this  line.  If  the  figure  is  symmetrical  about  any  other  axis,  the  intersection 
of  the  two  axes  will  be  'the  center  of  gravity  of  the  section;  thus,  the  center  of 
gravity  of  a  parallelogram  is  at  the  intersection  of  the  diagonals  and  that  of  a 
circle  or  an  ellipse  is  at  the  geome- 
trical center  of  the  figure.  The  cen- 
ter of  gravity  of  a  triangle  lies  on  a 
line  drawn  from  a  vertex  to  the  mid- 
dle point  of  the  opposite  side,  and  at 
a  distance  from  that  side  equal  to 
one-third  the  length  of  the  line;  or  it 
is  at  the  intersection  of  lines  drawn 
from  the  vertexes  to  the  middle 
points  of  the  opposite  sides. 

To  find  the  center  of  gravity  of  a  „ 

trapezoid,  Fig.  1,  lay  off  BF  =  DC  and 

DE  =  AB;  the  center  of  gravity  is  at  the  intersection  of  EF  with  Mi  Mi,  the  line 
joining  the  middle  points  of  the  parallel  sides.  GMi  can  also  be  determined 
by  the  formula  „,,  _m(bi+2bz) 

\J  lyL  1  —       rt/t         i     T    \ 

3(61+62) 

The  center  of  gravity  of  any  quadrilateral  may  be  determined  as  follows: 
First  divide  it,  with  a  diagonal,  into  two  triangles,  and  join  with  a  straight 
line  the  centers  of  gravity  of  the  two  triangles;  then,  with  the  second  diagonal, 
divide  the  figure  into  two  other  triangles  and  join  the  centers  of  gravity  of  these 
triangles  with  a  straight  line.  The  center  of  gravity  of  the  quadrilateral  is  at 
the  intersection  of  the  lines  joining  the  centers  of  gravity  of  the  two  sets  of 
triangles. 

For  an  arc  of  a  circle,  the  center  of  gravity  lies  on  the  radius  drawn  to  the 
middle  point  of  the  arc  (an  axis  of  symmetry)  and  at  a  distance  from  the 
center  equal  to  the  length  of  the  chord  multiplied  by  the  radius  and  divided 
by  the  length  of  the  arc.  2r 

For  a  semicircle,  the  distance  from  the  center  =  —  =  .6366  r,  when  r  =  radius. 

For  the  area  included  in  a  half  circle,  the  distance  of  the  center  of  gravity 
from  the  center  is  4r 

3ir 

For  a  circular  sector,  the  distance  of  the  center  of  gravity  from  the  center 
equals  two-thirds  of  the  length  of  the  chord  multiplied  by  the  radius  and 
divided  by  the  length  of  the  arc. 

For  a  circular  segment,  let  A  be  its  area  and  C  the  length  of  its  chord;  then 

C3 
the  distance  of  the  center  of  gravity  from  the  center  of  the  circle  is  equal  to  j^-- 

The  center  of  gravity  of  any  irregular  plane  figure  can  be  determined  by 
applying  the  following  principle:  The  static  moment  of  any  plane  figure  with 
regard  to  a  line  in  its  plane  —  that  is,  the  product  of  its  area  A  by  the  distance 
D  of  its  center  of  gravity  from  that  line—  is  equal  to  the  algebraic  sum  of  the 
static  moments  of  the  separate  parts  into  which  the  figure  may  be  divided,  with 
regard  to  the  same  axis,  or 

AD  =  aidi  -\-azdz,  etc., 


in  which,  fli,  02,  etc.,  denote  the  areas  of  the  subdivided  parts  of  the  figure,  and 
d\,  di,  etc.  are  the  distances  of  their  respective  centers  of  gravity  from  the 
reference  line.     Solving  this  equation  for  the  value  of  D, 
=  aidi  +  azdz  +  etc. 

A 

The  figure  whose  center  of  gravity  is  required  is  divided  into  separate  parts 
whose  centers  of  gravity  are  easily  ascertained,  usually  into  rectangles  or 
triangles.  A  suitable  axis  is  then  assumed  with  reference  to  which  the  expres- 
sions a\di,  a-id<i,  etc.  are  found,  and  their  sum  is  divided  by  A  =ai+a2+etc.,  the 
quotient  giving  D.  The  center  of  gravity  of  the  whole  figure  lies,  therefore,  on 
a  line  parallel  to  the  assumed  axis  and  distant  D  from  it.  In  a  similar  manner, 


156 


MECHANICS 


another  line  containing  the  center  of  gravity  is  obtained,  the  intersection  of  the 
two  lines  giving  its  exact  position.  *.-*...«_ 

EXAMPLE  1. — Find  the  center  of  gravity  of  the  cross-section  of  the  dam 

shown  in  Fig.  2. 

A\~~2o'-^-n  SOLUTION. — Divide  the  section  into 

^^  the  rectangles  ABC'l  and  HEFG  and 

the  triangle  CDC',  and  assume  the  lines 
X-X  and  Y-Y  as  reference  lines. 
Then, 


and 


01*1  +02*2  +03*3 


«%r* 


01  +  02  +  03 

From  the  illustration,  01 
=  2,000,    yi  =  70, 

=  1,587,  y2  =  43,  *2  =  45.33; 
=  1,720,  ys  =  10,  and  xa  =  ' 
ting  these  values, 

_  2,000X70+1.587X43  +  1.720X10 
2.000+1.587  +  1,720 

=  42.48 

_  2,000X20 +1.587X45.33 +  1.720X43 

F.c.2  "135.03 

EXAMPLE  2. — Find  the  center  of  gravity  of  the  bridge  chord  section  shown 

SOLUTION. — The  center  of  gravity  is  on  the  line  YY,  which  is  an  axis  of 
symmetry.  To  find  the  distance  y,  divide  the  section  into  angles  and  plates 
and  take  moments  about  XX.  The  areas  and  centers  of  gravity  of  the  angles 
might  be  located  by  the  preceding  principles  or  taken  from  a  manufacturer's 
handbook.  They  are:  For  the  4""X4"X*"  angle,  area  =  3.75  sq.  in.  and 
distance  from  center  of  gravity  to  back  of  angle  =  1 . 18  in. ;  for  the  3  \"  X  3 \"  X  \" 
angle,  area  =  3.25  sq.  in.  and  distance  from  center  of  gravity  to  back  of  angle 
=  1.06  in.  Hence,  the  moment  of  the  bottom  angles  is  2X3.75X1.18  =  8.85 
and  that  of  the  top  angles  is  2X3.25X  (15—1.06)  =90.61.  The  moment  of  the 
two  web-plates  is  2X15X^X7.5=  112.5,  and  that 
of  the  cover-plate,  24  X I  X  15.25  =  183.00.  The 
sum  of  the  moments  is,  8.85+90.61  +  112.5+183.00 
=  394.96.  The  sum  of  the  areas  is  2X3.25+2X3.75 
+24X^+2X15X^  =  41  sq.  in.  Then,  y  =  394 .96 -f- 41 
=  9.63  in. 

Center  of  Gravity  of  Solids. — For  a  solid  having 
three  axes  of  symmetry,  all  perpendicular  to  each 
other,  like  a  sphere,  cube,  right  parallelepiped,  etc., 
the  point  of  intersection  of  these  axes  is  the  center 
of  gravity. 

For  a  cone  or  pyramid,  draw  a  line  from  the 
apex   to   the   center   of   gravity   of  the  base;    the 
required  center  of  gravity  is  one-fourth  the  length  of  this  line  from  the  base, 
measured  on  the  line. 

For  two  bodies,  the  larger  weighing  W  lb.,  and  the  smaller  P  lb.,  the  center 
of  gravity  will  lie  on  the  line  joining  the  centers  of  gravity  of  the  two  bodies  and 

at  a  distance  from  the  larger  body  equal  to         Mr,  where  o  is  the  distance 

between  the  centers  of  gravity  of  the  two  bodies. 

For  any  number  of  bodies,  first  find  the  center  of  gravity  of  two  of  them, 
and  consider  them  as  one  weight  whose  center  of  gravity  is  at  the  point  just 
found.  Find  the  center  of  gravity  of  this  combined  weight  and  a  third  body. 
So  continue  for  the  rest  of  the  bodies,  and  the  last  center  of  gravity  will  be  the 
center  of  gravity  of  the  whole  system  of  bodies. 

To  find  the  center  of  gravity  mechanically,  suspend  the  object  from  a  point 
near  its  edge  and  mark  on  it  the  direction  of  a  plumb-line  from  that  point;  then 
suspend  it  from  another  point  and  again  mark  the  direction  of  a  plumb-line. 
The  intersection  of  these  two  lines  will  be  directly  over  the  center  of  gravity. 


MECHANICS 


157 


MOMENT  OF  INERTIA 

The  moment  of  inertia  of  a  plane  surface  about  a  given  axis  is  the  sum  of  the 
products  obtained  by  multiplying  each  of  the  elementary  areas,  into  which 
the  surface  may  be  conceived  to  be  divided,  by  the  square  of  its  distance  from 
the  axis. 

MOMENTS  OF  INERTIA,  ETC. 


Name  of  Section 

/ 

7 

c 

r* 

Solid  circular 
Hollow  circular        | 
Solid  square 
Hollow  square 

• 

e 

ird* 
64 

ir(d«-di«) 

*d3 
32 

*•(<*«-<*,«) 

d« 
16 

d2  +  dl«         • 

64 

d« 
12 

d*-di* 

32d 

d3 

6 
d*-dS 

16 

rf2 

12 

dz+di* 

B 

12 

12 

6d3 

12 

bd*-bidi* 

64 

bd* 
6 

6rf"-6idi« 

12 

62 

12 

W-fcl'dl 

i 

L 

I- 

U 

i 

3 

Solid  rectangular     ' 

*. 

Hollow 
rectangular 

12 

bd* 
36 

rid* 
64 

M 

6d« 
24 

TT&d2          . 

32 

ir(b&-bidi*) 

12(W-Mi) 

rfz 
18 

6« 
16 

&3d-6i'di 

A 

Solid  triangular 
Solid  elliptic             * 

Hollow  elliptic         *  iS 

r—  ±~ 

pl|pi 

I"bCam 
t—  ->— 
Cross  with  equal    |T     g 
arms  (approxi-    ^^^M 
mate)                   OF 

Angle  with  equal     | 
arms  (approxi-    *  || 
mate)                    U 

(.oo*1     Oiai0; 
bffi-bidS 

32d 
bdz-bidf 

16(6d-6irfi) 
b*d-fa*di 

12 

6d 

12(bd-bidi) 

d* 
22.5 

d2 
25 

The  moment  of  inertia  is  usually  designated  by  the  letter  /.  The  value  of 
the  moment  of  inertia  used  in  calculating  the  strength  of  beams  and  columns  is 
usually  taken  about  the  neutral  axis  of  the  figure,  which,  with  the  exception  of 
reinforced-concrete  sections,  passes  through  the  center  of  gravity  of  the  figure. 

Formulas  for  the  values  of  /  about  an  axis  passing  through  the  center 
of  gravity  of  the  section  are  given  for  various  forms  of  sections  in  the 


158 


MECHANICS 


accompanying  table.     For  any  other  section,  it  can  be  computed  by  means 
of  the  following  principles: 

Principle  I. — The  moment  of  inertia  of  a  section  about  any  axis  is  equal  to  the 
algebraic  sum  of  the  moments  of  inertia  about  the  same  axis,  of  the  separate  parts  of 
•which  the  figure  may  be  conceived  to  consist. 

Principle    II. — The  moment  of  „   _ 

inertia  of  any  figure  about  an  axis 
not   passing  through  the  center  of 
gravity,  is  equal  to  the  moment  of 
inertia  about  a  parallel  axis  through 
nf     ,.    ,       the  center  of  gravity,  plus  the  product 
^   |       of  the  entire  area  of  the  section  by 
f  1        c|  the  square  of  the  distance  between 

the  two  axes. 

EXAMPLE  1. — Find  the  moment 
of  inertia  about  the  neutral  axis 


--I--  — -4JC 


FIG.  2 


XX  of  the  Bethlehem  I  column  section  having  dimensions  as  shown  in  Fig.  1. 
SOLUTION. — Conceive  the  section  to  consist  of  the  square  A  BCD  minus 
twice  the  rectangle  abed.     Then,  by  applying  principle  I  and  the  formulas  of 
the  table  for  moments  of  inertia. 

12*     2X5.75X10.53 


-* 

—    -«  r» 


:  618.6 


12  12 

NOTE. — This  result  can  be  obtained  directly  by  the  I-beam  formula,  given 
in  the  same  table. 

EXAMPLE  2. — Find  the  moment  of  inertia  of  the  section  shown  in  Fig.  2 
about  the  neutral  axis  parallel  to  the  cover-plate. 

SOLUTION. — The  neutral  axis  passes  through  the  center  of  gravity,  which  has 
been  found  to  be. 9. 63  in.  from  the  back  of  the  bottom  angles.  The  distances 
of  the  centers  of  gravity  of  the  subdivisions  of  this  section  from  the  axis  XX, 
Fig.  2,  are: 

For  the  cover-plate  15.25-9.63 =  5.62 

For  the  web-plates  9.63  —  7.50 =2.13 

For  the  3£"X3£"X  J"  L's,  15.00-1.06-  9.63 =4.31 

For  the  4"X4"xr  L's,  9.63-1.18 =8.45 

The  moments  of  inertia  of  the  respective  parts  about  their  own  neutral  axes 
parallel  to  XX  are:  04. y  i i\s 

For  the  cover-plate 12      =       '25 

For  the  web-plates 2X  **— -281.25 

From  a  steel  manufacturer's  handbook,  the  value  of  /  for  a  3|"X35"X  \"  L 
is  found  to  be  3.64;  and  for  a  4"X4"X*"  L  it  is  5.56.  Applying  principle 
II,  the  moment  of  inertia  of  the  entire  section  is,  /  =  .25+24  X  |  X  5.622+281.25 

+2X15X|X2.132+2X3.64  +  2X3.25X4.312+2X5.56+2X3.75X8.452 
=  1,403.22. 


RADIUS  OF  GYRATION 

Let  /denote  the  moment  of  inertia  of  any  section  and  a  its  area;  then,  the 
relation  between  /  and  a  is  expressed  in  the  formula,  /  =  ar2,  in  which  r  is  a  con- 
y  stant  depending  on  the  shape  of  the  section  and  is 

-"  H       called  the  radius  of  gyration  of  the  section  referred  to 
the  same  axis  as  /.     Then, 


EXAMPLE  1. — What  is  the  radius  of  gyration  of  the 
"•*  section  shown  in  Fig.  1  about  the  axis  XX? 

SOLUTION. — The  moment  of  inertia  of  this  section 
has  been  found  to  be  618.6  and  its  area  is  2X12X1 
+  10.5X  5  =  23.25  sq.  in.  Substituting  in  the  formula, 

18^6     . 


EXAMPLE  2. — Determine  the  distance  b  in  the  strut 
made  up  of  two  latticed  channels,  as  shown  in  Fig.  3, 
so  that  the  radii  of  gyration  about  the  axes  XX   and    YY   will  be   equal. 


FIG.  3 


MECHANICS  159 

SOLUTION.  —  Let  Ix,  rx,  Iy,  ry  be,  respectively,  the  moments  of  inertia  and 
radii  of  gyration  of  a  single  C  about  the  axes  XX  and  YY;  a  its  area  and  CG,  its 
center  of  gravity,  then,  from  the  figure,  b  =  d  —  c,  and  Ix  =  arx'i\  also,  Iy  =  ary* 
-{-ad2.  Hence,  by  the  condition  of  the  problem,  arx^  =  ary2-}-  ad"*,  or  rxt  =  ryz 
+  d*.  Whence,  d  -  ^rx2  -  ry*.  The  values  of  rx,  r"y  and  c  for  any  C  may  be  taken 
from  a  steel  manufacturer's  handbook.  For  instance,  for  a  15-in.  E  of  33  Ib. 


rx  =  5.62,  r~  =  £12,  and  c  =  .794;  hence,  d=  \5.622-.9122  =  5.546,  and  b  =  d-c 
=  5.546  -.794  =  4.752. 

A  practical  rule  giving  good  approximate  results  for  a  channel  column  or 
strut  is  to  subtract  ry  from  rx;  the  result  is  6.  Applying  this  rule  to  the  15-in. 
C  of  33  Ib.  column  or  strut,  b  =  5.62  -  .912  =  4.708. 


SECTION  MODULUS  AND  MOMENT  OF  RESISTANCE 

The  expression  -,  in  which  /  is  the  moment  of  inertia  and  c  the  distance  of 

the  outermost  fiber  of  the  section  from  the  neutral  axis,  is  called  the  section 
modulus.  For  a  given  material,  this  quantity  is  a  measure  of  the  capacity  of 
the  section  to  resist  bending.  Multiplied  by  the  unit  stress  to  which  the  outer- 
most fibers  are  subjected  under  given  loads,  the  product  gives  the  amount  of 
bending  moment  the  section  is  resisting,  and  is  called  moment  of  resistance. 
If  /  is  the  unit  stress  that  certain  loads  develop  in  the  outermost  fibers  of  the 
section,  the  moment  of  resistance  is  T 

K,-\f 

EXAMPLE  1. — What  is  the  section  modulus  of  a  20-in.  I  beam  of  75  Ib.  whose 
moment  of  inertia  is  1,268.9? 

SOLUTION. — As  the  neutral  axis  passes  through  the  center  of  the  section,  the 
distance  c  is  in  this  case  equal  to  one-half  the  depth;  that  is  20 -j- 2  =  10.  The 
section  modulus  is  therefore  I  _  1,268.9  _ 

---^--126.9 

EXAMPLE  2. — When  subjected  to  loads  perpendicular  to  the  cover-plates  the 
outermost  fibers  of  the  section  shown  in  Fig.  2,  are  stressed  to  16,000  Ib.  per 
sq.  in.  What  is  the  resisting  moment  of  the  section? 

SOLUTION. — The  moment  of  inertia  of  the  section  has  been  found  to  be 
1,403.22,  and  the  outermost  fibers  are  9.63  in.  from  the  neutral  axis;  hence,  the 
section  modulus  is  equal  to  1,403.22 -=-9.63  =  145.7;  this  multiplied  by  16,000 
gives  2,331,200  in.-lb. 

Formulas  for  obtaining  directly  the  section  moduli  of  sections  frequently 
used  are  given  in  the  table  of  Moments  of  Inertia,  etc. 


FRICTION 

Friction  is  the  resistance  that  a  body  meets  from  the  surface  on  which  it 
moves.  It  depends  on  the  degree  of  roughness  of  the  surfaces  in  contact,  and 
is  directly  proportional  to  the  perpendicular  pressure  between  the  surfaces.  It 
is  independent  of  the  extent  of  the  surfaces  in  contact  as  long  as  the  normal 
pressure  remains  the  same.  It  is  generally  greater  between  surfaces  of  the  same 
material  than  between  those  of  different  materials,  and  greater  between  soft 
bodies  than  hard  ones. 

Coefficient  of  Friction. — The  ratio  between  the  resistance  to  the  motion 
of  a  body  due  to  friction  and  the  perpendicular  pressure  between  the  surfaces  is 
called  the  coefficient  of  friction.  When  the  coefficient  of  friction  between  two 
surfaces  is  known,  the  frictional  resistance  is  obtained  by  multiplying  the 
normal  pressure  by  the  coefficient. 

EXAMPLE  1. — What  is  the  resistance  per  linear  foot  of  a  retaining  wall  against 
sliding  when  the  normal  pressure  on  the  foundation  is  10,000  Ib.  per  lin.  ft.  of 
wall  and  the  coefficient  of  friction  of  the  masonry  on  the  foundation  is  .65? 

SOLUTION.— The  frictional  resistance  is  10,000  X  .65  =  6,500  Ib. 

The  coefficient  of  friction  of  the  wheels  of  suddenly  stopping  engines  and 
cars  on  the  rails  is  usually  assumed  at  .20.  The  rails  on  bridges  or  trestles  will 
transfer  to  the  bridge  or  trestle  tower  the  frictional  forces  produced  by  the  brakes 
in  order  to  stop  the  cars,  causing  stresses  that  must  be  provided  for. 


160 


MECHANICS 


EXAMPLE  2. — What  is  the  longitudinal  force  on  a  bridge  caused  by  the 
sudden  stopping  of  a  car  weighing  60,000  Ib? 

SOLUTION.— The  longitudinal  force  will  be  60,000 X. 20=  12,000  Ib. 

Angle  of  Friction. — When  a  body,  as  B  in  the  accompanying  illustration, 

weighing  W  Ib.  is  placed  on  an  inclined  plane  making  an  angle  a  with  the 

horizontal,  the  normal  pressure  is  N  =  W  cos  a;  and,  if  the  coefficient  of  friction 

is  denoted  by  /,  the  frictional  resistance  against  sliding  down  of  the  body  is 

F  =fN=fW  cos  a.  This  force  acts  in 
a  direction  opposite  to  that  of  the  force 
P=Wsina.  When  the  angle  a  is  such 
that  F  just  balances,  or  is  equal  to  P,  so 
that  the  slightest  force  will  cause  the 
body  to  slide,  the  angle  is  then  called 
the  angle  of  friction.  The  tangent  of 
that  angle  is  equal  to  the  coefficient  of 
friction,  or/=tan  a. 

Angle  of  Repose. — On  a  sloping 
bank  of  loose  material,  such  as  sand, 
earth,  etc.,  when  the  angle  of  slope  is 
such  that  the  particles  are  on  the  point 
of  moving,  the  angle  is  called  the  angle  of  repose.  It  is  the  same  as  the  angle 
of  friction  of  the  material  on  itself.  The  slope  is  then  called  the  slope  of 
repose,  or  the  natural  slope  of  the  material,  for  it  is  the  slope  that  the  material 
will  assume  when  subject  to  gravity  only. 

EXAMPLE. — The  coefficient  of  friction  of  dry  sand  on  itself  is  .65;  what  is 
its  angle  of  repose? 

SOLUTION. — The  angle  of  repose  is  the  same  as  the  angle  of  friction,  whose 
tangent  equals  the  coefficient  of  friction;  consequently,  .65  =  tan  a,  and  from  a 
table  of  natural  tangents  a  =  33°. 

The  accompanying  tables  give  coefficients  of  friction  and  angles  of  repose  of  a 
number  of  materials. 

COEFFICIENTS  OF  FRICTION  AND  ANGLES  OF  REPOSE  FOR 
MASONRY  MATERIALS 


Material 

Coefficient 
of 
Friction 

Angle  of 
Repose 
Degrees 

Fine-cut  granite,  on  same,  dry  

.60 
.65 
.70 
.75 
.65 
.60 
.65 
.65 
.60 
.75 
.70 
.65 
.50 
.50 
.50  to  .60 
.35  to  .45 
.50 
.35 

31 
33 
35 
37 
33 
31 
33 
33 
31 
37 
35 
33 
27 
27 
27  to  31 
19  to  24 
27 
19 

Fine-cut  granite,  on  rough-pointed  granite,  dry  
Rough-pointed  granite,  on  same,  dry 

Well-dressed  soft  limestone,  on  same,  dry  

Concrete  blocks,  on  same,  dry  

Concrete  blocks,  on  fine-cut  granite  dry 

Common  brick,  on  same,  dry  

Common  brick,  on  well-dressed  soft  limestone,  dry  .  . 
Common  brick,  on  well-dressed  hard  limestone,  dry 
Common  brick,  on  same,  with  slightly  damp  mortar 
Hard  brick,  on  same,  with  slightly  damp  mortar  .... 
Hard  limestone,  on  same,  with  slightly  damp  mortar 
Common  brick,  on  same,  with  fresh  mortar 

Well-dressed  granite,  on  same,  with  fresh  mortar.  .  .  . 
Granite,  roughly  worked,  on  dry  sand  and  gravel  
Granite,  roughly  worked,  on  wet  sand.  .  .  . 

Granite,  roughly  worked,  on  dry  clay 

Granite,  roughly  worked,  on  moist  clay  . 

Rolling  Friction. — The  friction  between  the  circumference  of  a  rolling  body 
and  the  surface  upon  which  it  rolls  is  known  as  rolling  friction.  It  is  due  to  the 
compressibility  of  substances,  the  weight  of  the  rolling  body  causing  a  small 
depression  in  the  supporting  surface  and  a  flattening  of  the  roller.  Its  magni- 
tude depends  on  the  materials  of  the  roller  and  the  supporting  surface,  and  is 
proportional  to  the  normal  pressure  exercised  by  the  roller  on  the  rolling  sur- 
face. It  depends  also  on  the  diameter  of  the  roller,  being  less  for  large  rollers 


MECHANICS 


161 


than  for  small  ones.  On  highways  with  soft  compressible  surfaces,  the  resis- 
tance is  also  affected  by  the  width  of  the  wheel  tires,  being  greater  for  narrow 
tires  than  for  wide  ones. 

COEFFICIENTS  OF  FRICTION,  ANGLES  OF  REPOSE,  AND  WEIGHTS 
OF  EARTHS 


Material 


Coefficient 
of  Friction 


Angle  of 
Repose 
Degrees 


Weight 
Pounds  per 
Cubic  Foot 


Mixed  earth,  dry.  .  .  . 
Mixed  earth,  damp. . 
Mixed  earth,  wet. .  .  . 

Sand,  dry 

Sand,  wet 

Loam,  dry 

Loam,  wet 

Clay,  dry 

Clay,  wet 


.70 
.80 
.40 
.65 
.05 
.70 
.50. 
1.00 
.30 


35 
39 
22 
33 
3 

35 
27 
45 
17 


95 

115 

115 

110 

125 

75  to  100 
90  to  120 

100 

125 


COEFFICIENTS  AND  ANGLES  OF  FRICTION  FOR  MISCEL- 
LANEOUS MATERIALS 


Materials 


Coefficient 
of  Friction 


Angle 
of  Friction 


Cast  iron  on  cast  iron .15 

Cast  iron  on  brass .15 

Cast  iron  on  oak .49 

Wrought  iron  on  wrought  iron .14 

Wrought  iron  on  cast  iron .  .19 

Wrought  iron  on  brass .17 

Wrought  iron  on  mahogany .18 

Wrought  iron  on  oak .62 

Steel  on  cast  iron .20 

Steel  on  brass .15 

Steel  on  ice .014 

Yellow  copper  on  cast  iron .19 

Yellow  copper  on  oak .62 

Brass  on  cast  iron .22 

Brass  on  brass .20 

Brass  on  wrought  iron .16 

Bronze  on  cast  iron .21 

Bronze  on  wrought  iron .16 

Bronze  on  bronze .20 

Oak  on  oak .48 

Oak  on  elm .25 

Oak  on  cast  iron .37 

Leather  on  oak .33 

Leather  belt  on  oak  drum .27 

Leather  belt  on  cast  iron .56 

Leather  packing .56 


Deg.  Min. 

8  32 

8  32 
26  6 

7  58 
10  46 

9  39 

10  12 
31  47 

11  19 

8  32 
0  48 

10  46 
31  48 

12  25 

11  19 

9  6 
11  52 

9  5 

11  19 

25  38 

14  3 
20  19 
18  16 

15  7 


The  first  table  on  page  162  gives  the  maximum,  minimum,  and  mean  values 
of  the  coefficient  of  rolling  friction  for  different  roadway  surfaces.  They  are 
expressed  in  pounds  required  to  overcome  the  resistance  on  a  level  road  of  a 
gross  ton  (2,240  lb.).  The  mean  value  is  also  expressed  as  a  ratio  between 
the  frictionaj  resistance  and  the  load. 

The  friction  of  liquids  moving  in  contact  with  solid  bodies  is  independent 
of  the  pressure,  because  the  forcing  of  the  particles  of  the  fluid  over  the 


IQ2  MECHANICS 

oroiections  on  the  surface  of  the  solid  body  is  aided  by  the  pressure  of  the  sur- 
rounding particles  of  the  liquid,  which  tend  to  occupy  the  places  of  those 

ROLLING  FRICTION  FOR  DIFFERENT  ROADWAY  SURFACES 


Character  of  Roadway 
Surface 

Rolling  Friction 

In  Pounds  per  Gross  Ton 

Mean 
In  Terms 
of  Load 

Maximum 

Minimum 

Mean 

Earth,  ordinary  
Earth,  dry  and  hard  
Gravel,  common  
Gravel,  hard  rolled  
Macadam  ordinary  

300 
125 
147 

140 
80 
64 

80 
40 

50 
56 

40 
39 

125 
75 
140 

60 
41 
30 

45 
25 

26 
32 

20 
15 

200 
100 
143 
75 
90 
60 
50 
140 
75 
90 
56 
34 
56 
38 
44 

30 
22 

| 

'    t 
*% 

* 

lizr 

Macadam,  good  
Macadam,  best  

Cobblestone,  ordinary  .... 
Cobblestone,  good.  .'.  

Granite  block,  good  

Granite  block,  best  
Belgian  block,  ordinary  
Belgian  block,  good  

Plank                             

Wooden  block,  in  good  condi- 

Asphalt                         

forced  over.  Therefore,  the  coefficients  of  friction  of  liquids  over  solids  do 
not  correspond  with  those  of  solids  over  solids.  The  resistance  is  directly  as 
the  area  of  surface  or  contact. 

COEFFICIENTS  OF  FRICTION  IN  AXLES 


Axle 

Bearing 

Ordinary 
Lubrication 

Lubricated 
Continuously 

Bell  metal  

Bell  metal  .  . 

.097 

Cast  iron  

Bell  metal 

.07 

.049 

Wrought  iron  
Wrought  iron  

Bell  metal  
Cast  iron  

.07 
.07 

.05 
.05 

Cast  iron  
Cast  iron  
Wrought  iron  

Cast  iron  
Lignum  vitae  
Lignum  vitae  

.07 
.10 
.12 

.05 

Friction  naturally  varies  with  the  character  of  the  surfaces,  lubrication, 
and  the  nature  of  the  lubricant.     The  best  lubricants  for  the  purposes  should 
always  be  used,  and  the  supply  should  be  regular.     When  machinery  is  well 
lubricated,  the  lubricant  keeps  the  surfaces  apart,  and  the  frictional  resistance 
becomes  very  small,  or  about  the  same  as  the  friction  of  liquids. 
Frictional  Resistance  of  Shafting. — 
Let     K  —  coefficient  of  friction; 

PF=work  absorbed,  in  foot-pounds; 

P  =  weight  of  shafting  and  pulleys -{-resultant  stress  of  belts; 

H  =  horsepower  absorbed; 

D  —  diameter  of  journal,  in  inches; 

R  =  number  of  revolutions  per  minute. 


MECHANICS  163 

Then,          ORDINARY  OILING  CONTINUOUS  OILING 

W=.0182PD  .0112PD 

H  =  .000000556PDK  .000000339PDK 

K  =  .066  .044 

As  a  rough  approximation,  100  ft.  of  shafting,  3  in.  diameter,  making  120 
rev.  per  min.,  requires  1  H.P. 

For  friction  of  air  in  mines,  see  Coefficient  of  Friction,  under  Ventilation. 

Friction  of  Mine  Cars. — The  friction  of  mine  cars  varies  so  much  that  it  is 
impossible  to  give  a  formula  for  calculating  it  in  every  case.  No  two  mine 
cars  will  show  the  same  frictional  resistance,  when  tested  with  a  dynamome- 
ter, and,  therefore,  nothing  but  an  average  friction  can  be  dealt  with.  The 
construction  of  the  car,  the  condition  of  the  track,  and  the  lubrication  are 
important  factors  in  determining  the  amount  of  friction. 

Some  of  the  requisites  of  good  oil  box  and  journal  bearings  may  be  stated. 
Tightness  is  a  prerequisite,  and,  in  dry  mines  where  the  dust  is  very  penetrating, 
this  is  especially  important;  the  bearings  should  be  sufficiently  broad;  the  oil 
box  large  enough  to  hold  sufficient  oil  to  run  1  mo.  without  renewal,  and  so 
constructed  that,  while  it  may  be  quickly  and  easily  opened,  it  will  not  open 
by  jarring  or  by  being  accidentally  struck  by  a  sprag  or  a  lump  of  coal. 

There  are  a  number  of  patented  self-oiling  wheels  that  are  improvements 
on  the  old-style  plain  wheels,  and  each  of  these  has  undoubtedly  some  point  of 
superiority  over  the  old  style. 

Among  the  most  extensively  used  of  these  patented  wheels  are  those  with 
annular  oil  chambers,  and  those  with  patent  bushings.  Their  superiority  con- 
sists in  the  fact  that,  if  properly  attended  to,  a  well-lubricated  bearing  is  secured 
with  greater  regularity  and  less  work  than  when  the  old-style  wheel  is  used. 

With  a  view  of  adopting  a  standard  wheel,  the  Susquehanna  Coal  Co.,  of 
Wilkes-Barre,  Pa.,  experimented  for  a  number  of  years  with  different  styles 
of  self -lubricating  wheels. 

Mr.  R.  Van  A.  Norris,  E.  M.,  assistant  engineer,  made  a  series  of  989  tests 
with  old-style  wheels,  some  of  which  had  patent  removable  bushings,  and 
others  annular  oil  chambers,  and  the  self- oiling  wheel.  The  old  wheels  were 
found  to  be  practically  alike  in  regard  to  friction.  All  the  wheels  were  of 
the  loose  outside  type,  16  in  in  diameter,  mounted  on  2|  in.  steel  axles,  with 
journals  5J  in.  long.  The  axles  passed  loosely  through  solid  cast  boxes,  bolted 
to  the  bottom  sills  of  the  cars,  and  were  not  expected  to  revolve. 

The  table  of  friction  tests  shows  the  results  obtained  with  both  old-  and 
new-style  wheels,  and  is  of  interest  to  all  colliery  managers,  inasmuch  as 
the  figures  given  for  the  old-style  wheels  alone  are  the  most  complete  in  existence 
and,  as  stated  before,  they  are  good  averages. 

Tests  were  made  on  the  starting  and  running  riction  of  each  style  of 
wheel,  under  the  conditions  of  empty  and  loaded  cars  level  and  grade  track, 
curves,  and  tangents.  The  instruments  used  were  a  Pennsylvania  Railroad 
spring  dynamometer,  graduated  to  3,000  lb.,  with  a  sliding  recorder,  a  hydraulic 
gauge  (not  recprding)  reading  to  10,000  lb.,  graduated  to  25  lb  ,  and  a  spring 
balance,  capacity  300  lb.,  graduated  to  3  lb.  All  these  were  tested  and  found 
correct  previous  to  the  experiments. 

Most  of  the  observations  on  single  cars  were  made  with  the  300-lb.  balance. 
The  two  types  of  old-style  wheels  have  been  classed  together  in  the  table.  Each 
car  was  carefully  oiled  before  testing,  and  several  of  each  type  were  used,  the 
results  being  averages  from  the  number  of  trials  shown  in  the  table. 

In  the  experiments  on  the  slow  start  and  motion,  the  cars  were  started 
very  slowly  by  a  block  and  tackle,  and  the  reading  was  taken  at  the  moment 
of  starting.  They  were  then  kept  just  moving  along  the  track  for  a  considerable 
distance,  and  the  average  tractive  force  was  noted,  the  whole  constituting  one 
experiment. 

The  track  selected  for  these  experiments  was  a  perfectly  straight  and 
level  piece  of  42  in.  gauge,  about  200  ft.  long,  in  rather  better  condition  than 
the  average  mine  track.  The  cars  were  41|  in.  gauge,  31  ft.  wheel  base,  10  ft. 
long,  capacity  about  85  cu.  ft.,  with  6-in.  topping. 

To  ascertain  the  tractive  force  required  at  higher  speeds,  trips  of  one,  four 
and  twenty  cars,  both  empty  and  loaded,  were  attached  to  a  mine  locomotive 
and  run  about  1  mi.  for  each  test,  the  resistance  at  various  points  on  the 
track,  where  its  curve  and  grade  were  known,  being  noted,  care  also  being 
taken  to  run  at  a  constant  speed.  Unfortunately,  only  four  of  the  new-style 
cars  were  available  on  the  tracks  where  these  trials  were  made. 

The  remarkably  low  results  for  the  twenty-car  trips  are  attributed  to 
variations  in  the  condition  of  the  track,  and  the  fact  that  the  whole  train 


164 


MECHANICS 


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166 


MECHANICS 


was  seldom  pulling  directly  on  the  locomotive,  the  cars  moving  by  jerks,  so 
that  correct  observations  were  impracticable.  The  hydraulic  gauge  was  used 
for  these  twenty-car  tests,  and  the  needle  showed  vibrations  from  1  to  4  1 .  and 
back  The  mean  was  taken  as  nearly  as  possible.  The  gauge  was  rather  too 
quickly  sensitive  for  the  work,  and  the  Pennsylvania  Railroad  dynamometer 
was  not  strong  enough  to  stand  the  starting  jerks  and  the  strain  of  accelerating 

>P6<The  tests  jerked  ROpe  Haul  were  made  on  an  empty-car  haulage  system, 
about  500  ft.  long,  with  overhead  endless  rope  running  continuously  at  a  speed 
of  180  ft  per  min.,  the  cars  being  attached  to  the  moving  rope  by  a  chain, 
a  ring  at  the  end  of  which  was  slipped  over  a  pin  on  the  side  of  the  car.  The 
increase  of  friction  on  the  heavier  grades  was  due  to  the  rope  pulling  at  a 
greater  angle  across  the  car.  Correction  was  not  made  for  this  angularity  at 
the  time,  and  the  rope  has  since  been  rearranged,  so  that  the  correction  cannot 
now  be  made.  There  were  not  enough  curve  experiments  to  permit  the 
deduction  of  any  general  formula  for  the  resistance  of  these  cars  on  curves. 

The  experiments  on  grade  agree  fairly  well  with  those  on  a  level,  the  rather 
higher  values  obtained  being  probably  due  more  to  the  greater  effort  required 
in  moving  them,  and  the  consequent  jerkiness  of  the  motion,  than  to  any  real 
increase  in  resistance.  As  the  experiments  on  all  styles  of  wheels  were  made  in 
an  exactly  similar  manner,  the  comparative  value  of  the  results  is  believed  to 
be  nearly  correct,  the  probable  error  in  each  set  of  experiments,  as  computed  by 
the  method  of  least  squares,  varying  from  about  4%  for  slow  start  and  motion  to 
12%  for  the  rapid  motion  and  twenty-car  trips. 

Ball  and  Roller  Bearings. — Some  of  the  leading  manufacturers  now  provide 
mine-car  wheels  with  either  ball  or  roller  bearings.  In  the  former  type,  a  series 
of  steel  balls  placed  within  the  hub  bear  upon  the  axle;  and  in  the  latter  type, 
a  series  of  steel  rollers.  In  other  features,  however,  such  as  the  method  of 
lubrication,  etc.,  the  improved  wheels  are  essentially  the  same  as  the  old.  Only 
a  limited  number  of  tests  have  thus  far  been  published  upon  the  savings  effected 
by  the  use  of  these  improved  bearings  in  power-transmission  shafting,  mine- 
car  wheels,  etc.,  but  these  indicate  a  diminution  of  from  15  to  75%  in  the  fric- 
tion over  the  old  type  of  bearings.  In  the  case  of  mine  cars,  those  equipped 
with  the  new  type  of  bearing  require  about  one-half  the  drawbar  pull  formerly 
demanded  either  to  start  them  from  rest  or  to  continue  them  in  motion. 

Quoting  from  one  of  the  leading  manufacturers  of  spiral  roller  bearings: 
"The  saving  in  power  varies  to  a  certain  extent  with  conditions.  In  some  cases 
it  has  run  as  high  as  60%;  in  others,  it  has  been  as  low  as  30%;  a  safe  average 
saving  is  40%  to  50%.  The  following  series  of  tests  was  made  in  November, 
1912.  The  twenty-five  cars  used  in  the  test  had  been  in  constant  use  for  about 
6  mo.;  the  wheels  were  16  in.  and  the  axles  21  in.  in  diameter. 


« 

Average 
Starting 
Pull 
Pounds 

Average 
Constant 
Pull 
Pounds 

Gross 
Weight 
Pounds 

Up-Grade 
Per  Cent. 

Constant 
Tractive 
Effort 
Per  Ton 
Pounds 

Tractive 
Effort 
Per  Ton, 
Corrected 
For  Level 

Pounds 

Plain 

297 

120 

5,800 

.25 

41.3 

26.8 

Spiral  \ 
Roller/ 

104 

80 

5,800 

.25 

27.5 

13.0 

Lubrication. — There  is  probably  no  factor  that  has  a  more  direct  bearing 
on  the  cost  of  production  per  ton  of  coal  and  ores  than  the  lubrication  of  mine 
machinery,  and  yet  it  is  doubtful  if  there  is  another  item  connected  with  the 
operation  of  a  mine  less  understood  by  owners,  their  managers,  and  engineers  in 
charge. 

Steam  plants  are  equipped  with  boilers  of  the  highest  known  efficiency; 
heaters  are  used  that,  by  utilizing  waste  steam,  will  heat  the  feedwater  for 
boilers  to  the  highest  point.  Modern  engines  that  will  develop  a  horsepower 
with  the  least  amount  of  steam  are  installed;  bends,  instead  of  elbows,  are 
placed  in  steam  and  exhaust  pipes,  so  that  the  friction  and  back  pressure 
may  be  reduced  to  a  minimum.  In  a  word,  everything  is  done  in  the  equip- 
ment of  a  plant  to  secure  economy  in  its  operation.  After  all  this  is  done, 


MECHANICS  167 

frequently  a  long  step  is  taken  in  the  opposite  direction  by  the  use  of  an  oil 
unsuited  to  the  existing  conditions,  and  those  in  charge  of  the  plant  are  led 
to  believe  that  the  lubrication  is  all  that  could  be  desired,  simply  because 
the  engines  and  machinery  run  quietly  and  the  temperature  of  the  bearings 
does  not  become  alarmingly  high.  The  office  of  a  lubricant  is  not  merely  to 
secure  this  result,  but,  primarily,  to  reduce  friction  and  wear  to  a  minimum; 
and  an  oil  that  will  do  this  is  the  best  oil  to  use,  no  matter  what  the  price  per 
gallon  may  be. 

Few  realize  the  great  loss  in  power  due  to  the  friction  of  wearing  parts. 
One  of  the  greatest  living  authorities  on  lubrication  writes: 

"It  may  probably  be  fairly  estimated  that  one-half  the  power  expended 
in  the  average  case,  whether  in  mill,  mine,  or  workshop,  is  wasted  on  lost  work, 
being  consumed  in  overcoming  the  friction  of  poorly  lubricated  surfaces." 

He  adds  that  a  reduction  of  50%  in  the  work  lost  by  friction  has  often  been 
secured  by  a  change  of  lubricants. 

As  one  of  many  instances  showing  the  loss  that  will  occur  by  the  use  of 
inferior  lubricants,  attention  is  called  to  two  flour  mills  located  in  one  of  the 
Middle  States.  One  of  the  plants  was  equipped  with  a  condensing  engine 
capable  of  developing  1  H.  P.  on  24  Ib.  of  water  per  hr.;  the  other  plant  had 
a  simple  engine,  taking  30  Ib.  of  water  per  hr.  The  plant  containing  the  con- 
densing engine  was  purchased  by  the  owner  of  the  plant  containing  the  simple 
engine.  The  new  owner  of  the  plant  was  surprised  to  learn  that  the  cost  of 
operation  per  barrel  of  flour  manufactured  was  equally  as  great  in  the  new  plant 
as  in  the  old  one.  The  engines  were  indicated,  and  valves  found  to  be  properly 
adjusted  and  the  engine  working  within  the  economical  range,  so  far  as  load  was 
concerned.  The  loss  was  then  attributed  to  the  boilers,  but  an  evaporative  test 
proved  that  there  was  no  practical  difference  here,  as  the  boilers,  in  both  instan- 
ces, were  evaporating  a  fraction  over  8  Ib.  of  water  per  Ib.  of  coal.  At  this  point, 
the  question  of  lubrication  was  taken  up,  and,  on  the  advice  of  an  expert  sent 
by  a  prominent  manufacturer  of  lubricants  to  look  over  the  plant,  an  entire 
change  was  made  in  the  lubricants  used,  and,  as  a  result,  a  money  saving  of 
over  $2.25  per  da.  (practically  $700  per  annum  —  this  in  a  plant  of  less  than 
250  H.  P.)  was  effected,  notwithstanding  the  fact  that  the  new  lubricants 
used  cost  considerably  more  per  gallon  than  those  formerly  \|sed.  This  sim- 
ply indicates  that  the  price  of  an  oil  is  of  little  importance  in  comparison  with 
its  friction-reducing  power.  Friction  costs  money,  because  it  means  greater 
cost  of  operation  per  unit  of  output. 

Among  the  expenses  chargeable  to  waste  power,  due  to  inferior  lubrica- 
tion, may  be  included:  (1)  The  cost  of  power  produced  in  excess  of  that 
really  required  to  operate  the  mine  per  ton  of  output.  In  this  calculation 
should  be  included  the  proper  proportion  of  salaries  of  engineers,  and  all  other 
items  that  contribute  to  the  cost  of  the  motive  department,  as  well  as  the  cost 
of  mining  the  fuel  consumed  in  producing  this  excess  power.  (2)  Wear  and 
tear  of  machinery,  which  is  constantly  doing  more  work  per  ton  of  coal  mined 
than  should  be  required  of  it. 

There  is  also  an  element  of  danger  that  ought  to  receive  serious  consid- 
eration, as,  while  it  is  true  that  cylinder  and  bearing  lubricants  of  indifferent 
merit  will,  under  ordinary  conditions,  keep  the  cylinders  from  groaning  and 
the  bearings  from  becoming  hot,  experiments  have  proved  that,  in  accom- 
plishing such  results,  the  oils  in  use  were  being  taxed  to  their  utmost;  and 
there  is  record  of  many  instances  where,  as  a  result  of  using  oils  of  such  lim- 
ited endurance,  accidents  of  a  serious  nature  have  occurred,  necessarily 
causing  shut-downs  just  at  the  time  when  the  operation  of  the  plant  to  its 
fullest  capacity  was  imperative.  It  is  most  difficult  to  do  much  more  than 
point  out  the  danger  due  to  the  use  of  inferior  lubricants,  leaving  it  to  the 
purchaser  himself  to  determine  as  to  the  intrinsic  worth  of  the  lubricants 
offered  to  him.  In  making  his  selection  he  would  do  well  to  consult  with 
and  heed  the  advice  of  some  highly  responsible  manufacturer  of  lubricants 
who  has  given  to  the  question,  in  all  its  phases,  the  most  careful  study,  and 
who  would  most  probably  have  the  benefit  of  a  wide  experience  in  the  applica- 
tion as  well  as  the  manufacture  of  lubricants.  Some  buyers  have,  to  their 
ultimate  regret,  adopted,  as  a  method  of  determining  the  merits  of  lubri- 
cants, a  schedule  of  laboratory  tests.  Such  a  method  is  not  only  useless,  but 
it  is  misleading  to  any  one  other  than  a  manufacturer  of  lubricants,  who  makes 
use  of  it  merely  as  a  means  of  insuring  uniformity  in  his  manufactured  products, 
and  not  as  a  measure  whereby  to  judge  their  practical  value.  Indeed,  many 
oils  can  be  very  properly  described  by  practically  the  same  schedule  of  tests, 
and  yet  are  widely  apart  when  their  utility  for  a  given  service  is  considered. 


168  MECHANICS 

As  a  general  guide  in  purchasing  cylinder  oil  for  mine  lubrication,  it  might 
be  said  that  a  dark-colored  oil  is  of  greater  value,  as  a  rule,  than  one  that  has 
been  filtered  to  a  red  or  light  amber  color,  as  the  process  of  filtration  neces- 
sarily takes  from  the  oil  a  considerable  percentage  of  its  lubricating  value, 
and  at  the  same  time  the  process  is  an  expensive  one.  In  short,  if  a  light- 
colored  oil  is  insisted  upon,  a  high  price  must  be  paid  for  an  inferior  lubricant. 
As  a  word  of  caution,  however,  it  would  be  well  to  add  right  here  that  irre- 
sponsible manufacturers  frequently  take  advantage  of  the  fact  that  the  most 
efficient  and  best  known  cylinder  oils  are  dark-colored,  and  endeavor,  with 
more  or  less  success,  to  market  as  "cylinder  oil"  products  absolutely  unsuited 
to  the  lubrication  of  steam  cylinders,  and  that  would  consequently  be  expen- 
sive could  they  be  procured  without  cost. 

For  the  lubrication  of  engine  bearings,  where  modern  appliances  for 
feeding  are  used,  an  engine  oil  of  a  free  running  nature  is  best,  as  it  more  quickly 
reaches  the  parts  requiring  lubrication  than  an  oil  of  a  more  sluggish  nature. 
It,  of  course,  must  not  be  an  oil  susceptible  to  temperature  changes,  but  must 
be  capable  of  performing  the  service  required  of  it  under  the  most  severe  con- 
ditions, where  an  oil  of  less  backbone  would  fail.  Such  an  oil  would  also  be 
suitable  for  the  lubrication  of  dynamos,  and  should  also  give  satisfaction  where 
used  in  lubricating  the  cylinders  of  air  compressors.  Where  the  machinery  is 
of  an  old  type  and  loose-jointed,  or  when  the  bearings  are  open  and  the  oil  is 
applied  directly  to  them  by  means  of  an  oiler,  an  engine  oil  of  a  more  sluggish, 
or  viscid,  nature  is  best. 

Perhaps  of  equal  importance  to  the  lubrication  of  power  machinery  must 
be  considered  the  lubrication  of  the  axles  of  mine  cars.  This  is  important, 
first,  because  of  the  fact  that  perhaps  three-fourths  of  the  oil  used  about  a  coal 
mine  is  used  for  this  purpose,  and,  secondly,  because  there  is  really  a  marked 
difference  in  the  quality  and,  therefore,  in  the  efficiency  of  lubricants  used  for 
this  purpose.  Fully  nine-tenths  of  the  prominent  railroads  of  this  country  are 
today  using  car-axle  oil,  costing  perhaps  as  much  per  gallon  as  much  of  the  so- 
calledi  cylinder  oil  that  is  used  in  coal  mines,  they  having  discovered,  by  exhaust- 
ive experiments,  that  the  increased  efficiency  gained  by  using  an  oil  of  such 
quality  many  times  offsets  the  difference  in  the  cost  per  gallon  and  enables 
them  to  secure  A  greater  mileage  without  any  increase  in  their  power  or  other 
fixed  charges.  This  will  apply  just  as  forcibly  to  the  lubrication  of  coal  cars, 
no  matter  whether  the  power  is  derived  from  mules  or  electric  motors;  there- 
fore, this  feature  of  lubrication  of  mine  equipment  should  receive  more  careful 
attention  than  it  does  receive,  as  a  rule. 

There  is  considerable  waste  in  the  lubrication  of  mine  cars.  This  waste  is 
hard  to  avoid,  and,  naturally,  makes  the  buyer  hesitate  before  adopting  the  use 
of  a  car  oil  that  costs  very  much  per  gallon;  but  even  in  the  face  of  this  waste 
the  increased  efficiency  secured  by  the  use  of  a  high-grade  car  oil  will  warrant 
its  use.  Such  waste  is  pretty  hard  to  correct  in  mines  where  the  old-fashioned 
style  of  car  axle  is  still  in  use,  and  where  the  oil  is  applied  through  an  ordinary 
spout  oil  can  into  the  axle  box,  and  allowed  to  drip  off  the  axles  and  on  to  the 
ground.  When  axles  are  equipped  in  the  same  manner  as  those  of  freight  cars, 
or  where  cars  are  equipped  with  one  of  the  several  different  styles  of  patent 
car  wheels  and  axles  that  are  coming  into  use  quite  extensively,  it  is  possible 
to  regulate  the  feeding  of  the  oil  to  the  axles,  so  as  to  reduce  the  waste  to  a 
minimum.  One  of  these  patent  car  wheels,  which  is  perhaps  better  known  than 
any  other,  is  constructed  with  a  hollow  hub  that  acts  as  a  reservoir  for  the  oil, 
the  oil  passing  from  this  reservoir  through  small  holes  on  to  a  felt  washer, 
which  it  must  saturate,  and  by  which  it  is  applied  to  the  axles.  Such  wheels 
require  a  limpid  oil,  as  a  heavy,  sluggish  oil  will  not  so  readily  saturate  the  felt 
washer  referred  to.  A  tight  cap  is  adjusted  to  the  end  of  the  axle,  to  prevent 
waste  of  oil.  These  wheels  will  run  quite  a  length  of  time  without  reoiling 
after  the  reservoir  is  once  filled.  While  it  costs  something  to  equip  mine  cars 
with  these  patent  axles,  such  an  outlay  will  result  in  more  economical  oper- 
ation, particularly  if  at  the  same  time  the  very  best  quality  of  car  oil  obtainable 
is  used. 

Lubricant  Tests. — There  are  certain  simple  tests  that  may  readily  be  made 
to  determine  the  suitability  of  certain  oils  for  certain  grades  of  work.  When 
testing  oils  for  use  in  connection  with  engines  running  under  constant  load 
and  speed,  Mr.  W.  W.  Davis,  of  Boston,  recommends  that  a  thermometer  be 
placed  in  the  bearing  so  that  the  bulb  rests  on  the  shaft,  a  constant  feed  of  oil 
being  maintained.  Another  thermometer  is  hung  in  the  engine  room  near 
the  bearing  and  away  from  drafts  of  air,  so  as  to  show  the  temperature  of 
the  room.  Commence  the  test  when  the  engine  is  started,  note  the  rise  of 


STRENGTH  OF  MATERIALS  169 

temperature  at  frequent  intervals,  also  that  of  the  room;  continue  the  test 
until  the  temperature  of  the  bearing  ceases  to  rise.  Every  hearing  will  in  the 
course  of  a  few  hours  reach  a  point  where  heat  is  radiated  as  fast  as  generated. 
Deducting  the  temperature  of  the  room  from  that  of  the  bearing  will  give  the 
rise  in  temperature  due  to  friction.  If  the  engine  runs  during  the  day  only, 
the  bearing  will  cool  off  over  night  and  after  cleaning  thoroughly  with  gasoline, 
will  be  in  condition  to  test  another  oil  the  next  day. 

While  it  is  true  that  the  coefficient  of  friction  often  decreases  with  the  rise 
in  temperature,  in  everyday  practice  it  is  safe  to  assume  that  of  two  oils  the  one 
that  will  keep  the  bearing  the  cooler  is  the  best  lubricant,  so  in  tests  of  this  kind 
the  oil  showing  the  least  rise  in  temperature  will  be  the  better  lubricant.  Such 
tests  can  also  be  made  in  ring-oiled  bearings  of  motors,  dynamos,  or  shafting. 

When  testing  the  value  of  two  or  more  cylinder  oils,  Mr.  Ward  recommends 
that  one  oil  be  fed  in  at  a  given  rate  for  a  few  days,  the  cylinder  head  then 
removed,  and  the  inner  surface  wiped  over  with  a  piece  of  soft  white  paper. 
If  there  is  no  stain  of  oil  and  a  liberal  amount  has  been  used,  either  the  steam 
is  very  wet  or  not  enough  fatty  oil  has  been  used  in  compounding  the  lubricant. 
A  separator  will  remove  the  excess  moisture  from  the  steam,  when  further 
tests  will  indicate  if  there  is  enough  fatty  91!  present. 

The  same  tests  can  be  used  to  determine  the  least  amount  necessary  to 
maintain  good  lubrication.  By  gradually  reducing  the  amount  of  oil  fed 
and  examining  the  surfaces  from  time  to  time  the  proper  amount  necessary 
to  maintain  good  lubrication  can  be  determined.  Where  tests  of  this  kind  are 
to  be  made  some  means  must  be  provided  for  the  easy  removal  of  the  cylin- 
der heads. 

BEST  LUBRICANTS  FOR  DIFFERENT  PURPOSES  (THURSTON) 

LObytecXp?eS'a1?inrOCkdriUSdriVen}Light  mineral  lubricatine  oils- 
VeJgreYpressures  and  slow  speed . '. '. '. '. . {  ^g^**00*-  and  °ther  S°Ud 

Heavy  pressures  and  slow  speed {^^SSlS 

Heavy  pressures  and  high  speed {  ^raL^  ^  **' 

Light  pressures  and  high  speed {**££  ^^rol^m.    °liv6' 

|  Lard  oil,  tallow  oil,  heavy  mineral 
Ordinary  machinery <      oils,  and  the  heavier  vegetable 

I     oils. 
Steam  cylinders Heavy  mineral  oils,  lard,  tallow. 

( Clarified  sperm,  neat's  foot,   por- 
Watches  and  other  delicate  mechanism.  <      poise,   olive,    and    light   mineral 

L     lubricating  oils. 

For  mixture  with  mineral  oils,  sperm  is  best;  lard  is  much  used;  olive  and 
cottonseed  are  good. 

STRENGTH  OF  MATERIALS 


DEFINITIONS 

Stress  is  the  cohesive  force  by  which  the  particles  of  a  body  resist  the  exter- 
nal load  that  tends  to  produce  an  alteration  in  the  form  of  the  body.  It  is 
always  equal  to  the  effective  external  force  acting  upon  the  body;  thus,  a  bar 
subjected  to  a  direct  pulling  force  of  1,000  Ib.  endures  a  stress  of  1,000  Ib. 

Unit  stress  is  the  stress  or  load  per  unit  of  area,  usually  taken  per  square  inch 
of  section.  For  instance,  if  the  bar  just  mentioned  is  1  in.  X  2  in.  in  section,  the 
unit  stress  of  the  bar  will  be  1,000^-2  (sectional  area)  =  500  Ib. 

Tensile  stress  is  produced  when  the  external  forces  tend  to  stretch  a  body, 
or  pull  the  particles  away  from  one  another.  A  rope  by  which  a  weight  is 
suspended  is  an  example  of  a  body  subjected  to  tensile  stress. 

Compressive  stress  is  produced  when  the  forces  tend  to  compress  the  body, 
9r  push  the  particles  closer  together.  A  post  or  column  of  a  building  is  sub- 
jected to  compresive  stress. 


170  STRENGTH  OF  MATERIALS 

AVERAGE  ULTIMATE  STRENGTHS  OF  METALS,  IN  POUNDS  PER 
SQUARE  INCH 


Kind  of  Metal 

Com- 
pression 

Ten- 
sion 

Elastic 
Limit 

Shear- 
ing 

Modu- 
lus of 
Rup- 
ture 

Modulus 
of 
Elasticity 

Aluminum: 
Aluminum,  commercia 
Aluminum,  nickel  
Brass,   Bronze,  and   Cop 
per: 

12,000 
30,000) 

15,000 
40,000 

24000 

6,500 
22,000 

6,000 

12,000 
36,000 

20,000 

11,000,000 
9  000  000 

Brass    wire,    annealed 
(softened  by  reheat- 
ing)   
Brass  wire,  unannealed 
Bronze,  aluminum  
Bronze,  gun  metal  
Bronze,  manganese.  .  .  . 
Bronze,  phosphor  

120,000 
(20,000) 
120,000 

50,000 
80,000 
75.000 
32,000 
60,000 
50,000 
66000 

16,000 

10,000 
30,000 
24,000 
40000 

53,000 

14,000,000 
10,000,000 

14,000,000 
4  500  000 

Copper,  bolts  

30,000 

30,000 

Copper,  cast  
Copper  wire,  annealed 
(softened  by  reheat- 
ing) 

(40,000) 

24,000 
36000 

6.000 

30,000 

22,000 

10,000,000 
15  000  000 

Copper     wire,     unan- 
nealed    
Cast  and  Wrought  Iron: 
Iron,  cast  

80,000 

60,000 
15000 

10,000 
6000 

18000 

30000 

18,000,000 
12  000  000 

Iron  chains  
Iron,  corrugated  
Iron     wire,      annealed 
(softened  by  reheat- 
ing)   

35,000 
60000 

40,000 

15  000  000 

Iron  wire,  unannealed. 
Iron,  wrought,  shapes.  . 
Iron,  wrought,  rerolled 
bars  .... 

46,000 
48000 

80,000 
48,000 

50  000 

27,000 
26,000 

27  000 

40,000 
40  000 

44,000 
48  000 

25,000,000 
27,000,000 

26  000  000 

Lead: 
Lead,  cast  

2  000 

1  000 

1  000  000 

Lead  pipe. 

1  600 

Cast  and  Structural  Steel: 
Steel,  castings  
Steel,  structural,  soft  .  . 
Steel,    structural,    me- 
dium   

70,000 
56,000 

64  000 

70,000 
56,000 

64  000 

40.000 
30,000 

3  000 

60,000 
48,000 

50  000 

70.000 
54.000 

60  000 

30,000,000 
29,000,000 

20  000  OOO 

Steel     wire,     annealed 
(softened  by  reheat- 
ing)   

80  000 

0  000 

on  nnn  nnn 

Steel  wire,  unannealed 
Steel  wire,  crucible  
Steel  wire,  for  suspen- 
sion bridges  
Steel  wire,  special  tem- 
pered   
Tin  and  Zinc: 
Tin,  cast  . 

(6  000) 

20,000 
80,000 

200,000 
300,000 

q  zfto 

60,000 
0,000 

0,000 

30,000,000 
30,000,000 

30,000,000 

Zinc,  cast  

(20*000) 

5  000 

4  000 

7  OOfi 

ino7 --Compression  values  enclosed  in  parentheses  indicate  loads  producing 
10%  reduction  in  original  lengths. 


STRENGTH  OF  MATERIALS 


171 


Shearing  stress  is  produced  when  the  forces  tend  to  cause  the  particles  in 
one  section  of  a  body  to  slide  over  those  of  the  adjacent  section.  A  steel  plate 
acted  on  by  the  knives  of  a  shear,  and  a  beam  carrying  a  load,  are  subjected 
to  shearing  stress. 

Tension,  compression,  and  shear  are  called  simple  or  direct  stresses,  to  dis- 
tinguish them  from  bending  and  torsion. 

The  amount  of  alteration  in  form  of  a  body  produced  by  a  stress  is  called 
deformation,  or  strain.     It  may  be  tensile  deformation,  compressiye  deforma- 
tion, or  shearing  deformation,  according  as  the  stress  producing  it  is  tensile, 
compressive,  or  shearing.     The  rate  of  deformation,  also  called  unit  deformation, 
is  the  deformation  of  a  body,  subjected  to  tension  or  compression,  per  unit  of 
AVERAGE  ULTIMATE  STRENGTHS  OF  WOODS,  IN  POUNDS 
PER  SQUARE  INCH 


Tension 

Compression 

Transverse 

Shearing 

With  Grain 

Kind 

d 

.s 

G 

en        >> 

.s 

.3 

of 
Timber 

1 

G 

G 

c 

*2g 

1 

iji 

3  -.€ 

G 

2 
G 

1 

1 

||| 

1 

|s| 

H 

I 

I 

1 

"o  !uQ 

W 

O-o 

White  oak  

12,000 

2,000 

7,000 

5.000 

2,000 

7.000 

1,500,000 

800 

4.000 

White  pine  

7.000 

500 

5,500 

3,500 

700 

4,000 

1,000,000 

400 

2,000 

Southern    long- 

leaf  or  Georgia 

pine  
Douglas  fir  

12,000 
8,000 

600 

7,000 
5,700 

5,000 
4,500 

1,400 
800 

7,000 
5,000 

1,500,000 
1,400,000 

600 
500 

5,000 

Short-leaf     yel- 

low pine  

9,000 

500 

6,000 

4,500 

1,000 

6,000 

1,200,000 

400 

4,000 

Red  pine  (Nor- 

way pine)  

8,000 

500 

5,000 

4,000 

800 

5,000 

1,130,000 

Spruce    and 

Eastern  fir  

8,000 

500 

6,000 

4,000 

700 

4,000 

1,200.000 

400 

3,000 

Hemlock  

6,000 

4,000 

600 

3,500 

900,000 

350 

2,500 

Cypress  

6,000 

5,000 

4,000 

700 

5,000 

900,000 

Cedar  

7,000 

5,500 

3,500 

700 

4,000 

700,000 

400 

1,500 

Chestnut  

8,500 

4,000 

900 

5,000 

1,000,000 

600 

2,000 

California    red- 

wood   

7,000 

4,000 

600 

4,500 

700,000 

400 

California 

spruce  

4,000 

5,000 

1,200,000 

Factor  of  safety 

10 

10 

5 

5 

4 

6 

2 

4 

4 

length.  If  an  iron  bar  6  ft.  long  is  subjected  to  a  force  that  elongates  it  1  in., 
the  rate  of  deformation  will  be  1  in.  -5-  72  (length  of  the  bar,  in  inches)  =  .0139  in. 
The  modulus  or  coefficient  of  elasticity  is  the  ratio  between  the  stresses  and 
corresponding  deformations  for  a  given  material,  which  may  have  a  somewhat 
different  modulus  of  elasticity  for  tension,  compression,  and  shear.  If  /  is  the 
increase  per  unit  9f  length  of  a  material  subjected  to  tensile  stress,  and  p  the 
unit  stress  producing  this  elongation,  the  modulus  of  elasticity 


For  example,  a  wrought-iron  bar,  80  in.  long,  subjected  to  a  unit  tensile  stress 
p  of  10,000  lb.,  stretched  .029  in.  The  unit  strain  I,  or  stretch  per  inch  of 
length,  is  .029  in.T-80  in.  =  .0003625  in.  Then, 


172 


STRENGTH  OF  MATERIALS 


The  relation  E  =  p  -5-  Us  true  only  when  equal  additions  of  stress  cause  equal 
increases  of  strain.  Previous  to  rupture,  this  condition  ceases  to  exist,  and  the 
material  is  said  to  be  strained  beyond  the  elastic  limit,  which,  therefore,  is  that 
degree  of  stress  within  which  the  modulus  of  elasticity  is  nearly  constant  and 
equal  to  the  unit  stress  divided  by  the  unit  strain. 

The  ultimate  strength  of  a  given  material  in  tension,  compression,  or  shear 
is  that  unit  stress  which  is  just  sufficient  to  break  it,  and  is  equal  to  the  maxi- 
mum stress  causing  rupture  divided  by  the  original  area  of  the  cross-section. 
The  accompanying  tables  show  the  average  ultimate  strengths,  in  pounds  per 
square  inch,  of  both  metals  and  woods. 

Working  stress  is  the  maximum  unit  stress  to  which  the  parts  of  a  structure 
are  to  be  subjected. 

Factor  of  safety  is  the  ratio  of  ultimate  strength  to  working  stress.  The 
factor  of  safety  required  for  a  structure  depends  on  the  material  and  on  the 
character  of  the  loads  applied  —  that  is,  whether  the  loads  are  quiescent  or  such 
that  cause  impact  and  vibrations.  For  stone  and  brick,  a  factor  of  safety  of 
from  10  to  30  is  used;  for  timber,  from  8  to  15;  for  cast  iron,  from  6  to  20;  for 
reinforced  concrete,  from  4  to  6;  and  for  structural  steel,  from  3  to  6. 

It  is  obvious  that  structures  subjected  to  loads  causing  impact  should  be 
designed  for  a  higher  factor  of  safety  than  those  having  to  carry  static  loads. 
When  a  structure,  as  a  bridge,  carries  both  dead  load  and  live  loads,  the  modern 
practice  favors  the  specifying  of  one  working  unit  stress  for  both  kinds  of  loads, 
and  providing  for  the  effect  of  vibration  by  increasing  the  live-load  stress  or 
bending  moment  by  an  amount  /  determined  from  a  so-called  impact  formula. 
The  formula  most  in  use  for  railroad  bridges  is 

300 
' 


in  which  5  =  maximum  live-load  stress  or  bending  moment  in  member, 

L  =  length,  in  feet,  of  single  track  that  must  be  loaded  in  order  to 
obtain  value  5. 


SIMPLE,  OR  DIRECT,  STRESS 

Formula  for  Simple  Stress. — If  P  is  an  external  force  producing  tension, 
compression,  or  shear  uniformly  distributed  over  an  area  A,  and  s  is  the  unit 
working  stress,  the  fundamental  formula  for  designing   parts  of   structures 
subjected  to  a  simple,  or  direct,  stress  is 
P  =  sA 

When  designing  members  that  are  in  tension,  A  must  be  taken  as  the  net 
area  of  the  section.  This  is  determined  by  deducting  from  the  gross  section 
the  greatest  number  of  pin,  bolt,  or  rivet  holes  that  can  be  cut  by  a  plane  at 
right  angles  to  the  section.  Rivet  holes  are  usually  taken  f  in.  larger  than 
the  diameter  of  the  rivet. 

Important  Applications  of  Formulas  for  Direct  Stress. — 1.  ^Tension  mem- 
bers aiid  short  compression  members  of  roof  or  bridge  trusses  are  examples  of 
simple  stress,  and  their  sections  are  determined  by  the  preceding  formula. 

EXAMPLE. — A  tension  member  of  a  roof  truss  is  made  of  two  3|"X3£"X  \" 
angles  connected  by  one  line  of  rivets  J  in.  in  diameter.  What  stress  will  it 
carry  at  16,000  Ib.  per  sq.  in.? 


FIG. 


FIG.  2 


SOLUTION.— The  gross  sectional  area  of  a  3i"X3£"X  J"  angle  is  3.25  sq.  in. 
The  deduction  for  one  rivet  hole  is  (|  +  i)X|  =  .5.  The  net  area  is  3.25 -.5 
•=  2  J5-  A  he  carrying  capacity  of  the  angle  is  therefore  2.75X  16,000  =  44,000  Ib. 
•  TJ?-'  i  I?  •  J°"}ts  als?  are  examples  of  simple  stress.  In  the  joint  shown 

Fig.  1,  the  rivet  is  in  single  shear,  because  there  is  only  one  section  e  of  the 
rivet  subjected  to  a  shearing  stress.  The  amount  R  that  one  rivet  will  carry 
being  equal  to  the  area  of  the  cross-section  of  the  rivet  multiplied  by  the  unit 


STRENGTH  OF  MATERIALS 

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174  STRENGTH  OF  MATERIALS 

shearing  stress,  or  R  =  sA,  the  number  n  of  rivets  required  to  transfer  a  stress 
T  by  single  shear  is  ,_^_JL 

.     n~R~As 

In  Fig.  2,  the  rivet  is  subjected  to  shear  on  two  sections,  d  and  e,  and  it  is 
said  to  be  in  double  shear.  The  amount  of  stress  that  one  rivet  can  carry  in 
double  shear  is  twice  that  of  one  in  single  shear,  and,  using  the  preceding  nota- 
tion, _  T 

H~2R 

The  bearing  value  of  a  rivet  is  the  compressive  stress  induced  by  the  rivet 
in  bearing  on  the  plate,  and  is  also  calculated  by  the  simple-stress  formula 

P  =  sA 
in  which  P  =  value  of  rivet  in  bearing; 

5  =  unit  working  stress  in  bearing; 
A  =  bearing  area. 

It  is  customary  to  assume  that  the  bearing  area  A  is  the  thickness  of  the 
plate  multiplied  by  the  diameter  of  the  rivet.  In  calculating  the  required 
number  of  rivets,  both  the  shearing  and  the  bearing  value  of  one  rivet  are 
determined  and  the  critical  value  (the  smaller)  used. 

The  accompanying  table  gives  the  shearing  and  bearing  values  of  rivets,  in 
pounds,  for  different  values  of  the  working  stress. 

3.     Strength  of  Cylindrical    Shells  and  Pipes  With  Thin  Walls.  —  When  a 
cylinder  is  subjected  t9  internal  pressure,  the  tensile  stress  developed  in  the 
walls  or  shell  of  the  cylinder  is  called  circumferential  stress,  or  hoop  tension. 
Let         s  =  intensity  of  this  stress; 

d  =  internal  diameter  of  cylinder; 

p  =  intensity  of  pressure  on  inner  surface  of  the  cylinder; 

t  =  thickness  of  shell. 

pd  pd 

l~2s  2t 

The  first  formula  serves  to  compute  the  thickness  when  p,  d,  and  s  (working 
stress)  are  given;  and  the  second  one  is  used  to  compute  the  intensity  of  stress 
when  the  intensity  of  pressure  p  and  the  dimensions  of  the  cylinder  are  given. 

EXAMPLE.  —  What  should  be  the  thickness  of  walls  of  a  cast-iron  water  pipe, 
inside  diameter  24  in.,  to  resist  a  water  pressure  of  200  Ib.  per  sq.  in.,  using  a 
unit  working  stress  of  2,000  Ib.? 

SOLUTION.—  Here,  d  =  24,  p  =  200,  and  s  =  2,000.  Substituting  in  the  formula 
for*,  M  200X24 


4.  Temperature  Stresses.  —  If  a  bar  subjected  to  change  of  temperature  is 
constrained  so  that  it  can  neither  expand  nor  contract,  the  constraint  exerts  on 
it  a  force  sufficient  to  prevent  the  deformation.  This  causes  in  the  bar  a 
corresponding  stress  called  temperature  stress.  It  is  compressive  when  the 
change  of  temperature  is  a  rise,  and  tensile  when  a  fall. 

Let  T  be  the  stress  induced  in  a  bar,  whose  area  is  a,  by  a  rise  or  fall  of  <°; 
also  let  c  be  the  coefficient  of  expansion  and  E  the  modulus  of  elasticity  of  the 
material.  Then,  T  =  ctaE 

The  coefficient  of  expansion  for  a  number  of  substances  is  given  in  the 
section  on  Heat,  Fuels,  Etc. 

EXAMPLE.  —  A  wrought-iron  bar  1.5  in.  square  has  its  ends  fastened  to  firm 
supports.  What  is  the  stress  produced  in  it  by  a  change  of  50°  in  its  tempera- 
ture? 

SOLUTION.—  Here,  £  =  25,000,000;  0  =  1.5X1.5  =  2.25  sq.  in.,  and  <  =  50; 
and,  c  =  .  00000686.  Substituting  in  the  formula,  T=,  00000686X50X2.25 
X  25,000,000  =  19,294  Ib. 


BEAMS 

A  beam  is  a  body  resting  upon  supports  and  liable  to  transverse  stress. 
Beams  are  designated  by  the  number  and  location  of  the  supports,  and  may 
be  simple,  cantilever,  fixed,  or  continuous, 

A  simple  beam  is  one  that  is  supported  at  each  end,  the  distance  between  its 
supports  being  the  span. 

A  cantilever  is  a  beam  that  has  one  or  both  ends  overhanging  the  support; 
or  a  beam  that  has  one  end  firmly  fixed  and  the  other  end  free. 

A  fixed  beam  is  one  that  has  both  ends  firmly  secured. 

A  continuous  beam  is  one  which  rests  upon  more  than  two  supports. 


STRENGTH  OF  MATERIALS 


175 


Reactions.  —  The  loads  acting  on  a  beam  are  balanced  by  the  reactions  or 
supporting  forces;  their  sum  must  therefore  be  equal  to  the  sum  of  the  loads. 
To  find  any  reaction,  as  #2,  at  B,  Fig.  1,  take  moments  of  all  the  external  forces 
about  the  other  support  A  and  divide  their  sum  by  the  span.  With  reference  to 
Fig.  1, 


The  reaction  R\  can  be  found  in  a  similar  manner  by  taking  moments  about 
the  support  B.     Their  sum  Ri+Ri  must  be  equal  to  the  sum  of  loads 


EXAMPLE.  —  Find  the  reactions  of  a  cantilever  bridge  loaded  as  shown  in 
Fig.  2. 

SOLUTION.  —  Substituting  given  values  in  the  formula  and  noting  that  the 
moment  of  Pi  about  B  is  of  opposite  sign  to  the  moments  of  the  other  loads, 

10.000X120+8.000X90  +  15.000X40-20.000X30 
Ri  =  -  —  jgQ  -  =  12,800  Ib. 

and 


_ 

loO 

The  sum  of  the  loads  is  10,000  +  8,000+15,000+20,000  =  53,000.     The  sum  of 
the  reactions  is  40.200+12,800  =  53,000. 

External  Shear  and  Bending  Moment.  —  The  forces  acting  on  a  beam  tend, 
on  the  one  hand,  to  shear  its  fibers  vertically  and,  on  the  other  hand,  to  bend 
it,  producing  compressional  stresses  in  the  fibers  on  one  side  of  the  neutral  axis 
and  tensional  on  the  other  side.  The  tendency  to  shear  the  fibers  vertically  is 
determined  by  the  external  shear,  and  that  of  bending  by  the  bending  moment. 
For  brevity,  external  shear  is  often  called  simply  shear,  but  it  must  not  be  con- 
fused with  shearing  stress  at  the  section. 

Forces  acting  upwards  are  considered  positive,  and  those  acting  downwards, 
negative.  The  external  shear  at  any  section  of  a  beam  is  the  algebraic  sum  of 
all  the  external  forces  (loads  and  reactions)  on  one  side  of  the  section.  It 
is  equal  to  either  reaction  minus  the  sum  of  the  loads  between  that  reaction 
and  the  section  considered.  The  maximum  shear  is  always  equal  to  the 
greater  reaction.  For  a  simple  beam  with  a  uniformly  distributed  load,  the 
maximum  shear  is  at  the  supports,  and  is  equal  to  one-half  the  load,  or  to  the 
reaction;  the  shear  changes  at  every  point  of  the  loaded  length,  the  minimum 
shear  being  zero  at  the  center  of  the  span.  The  maximum  shear  in  a  simple 
beam  having  a  single  load  concentrated  at  the  center  is  equal  to  one-half  the 
load,  and  is  uniform  throughout  the  beam.  Where  a  beam  supports  several 
concentrated  loads,  changes  in  the  amount  of  shear  occur  only  at  the  points 
where  the  loads  are  applied. 

The  external  shear  is  resisted  by  the  internal  shear,  or  shearing  stress,  of  the 
beam,  which  is  numerically  equal  to  the  external  shear.  If  the  external  shear  is 
denoted  by  V,  and  the  area  of  the  cross-section  by  A  ,  the  average  intensity  of 

Y 
shearing  stress  in  the  section  is  —  .     This  shearing  stress  is   not  uniformly 

A 
distributed,  and  in  beams  of  rectangular  cross-section,  the  maximum  intensity 

of  shearing  stress  is  —  .     Hence,  a  rectangular  beam  must  be  so  designed  that 

this  value  will  not  exceed  the  working  shearing  strength  of  the  material. 

In  metallic  beams  with  thin  webs  (plate  girders),  the  shearing  stress  may  be 
considered  as  uniformly  distributed  over  the  cross-section  of  the  web.  There 
is,  also,  at  every  horizontal  or  longitudinal  section  of  the  beam,  a  horizontal 
shearing  stress  the  intensity  of  which  at  any  point  is  equal  to  the  intensity  of  the 
vertical  shearing  stress  at  that  point. 


176  STRENGTH  OF  MATERIALS 

Although  the  maximum  intensity  of  shearing  stress,  both  horizontal  and 
vertical,  in  wooden  beams  is  usually  small,  the  shearing  strength  of  wood  along 
the  grain  is  also  small.  As  the  horizontal  external  shear  usually  acts  along  the 
grain,  the  safe  load  for  a  wooden  beam  may  depend  on  its  shearing  strength  and 
not  on  its  bending  strength.  For  instance,  the  safe  load  for  a  beam  4  in.  X 12  in. 
and  4  ft.  long  is  16,000  lb.,  uniformly  distributed,  when  based  on  a  fiber  strength 
of  1,000  lb.  per  sq.  in.  Such  a  load  will  produce  a  shearing  stress  per  unit 

of  area  equal  to     ^    '  —  =250  lb.  per  sq.  in.,  which  exceeds  the  working 

2,  /x  4o 
shearing  stress  for  the  wood  along  the  grain  by  about  100  lb.  per  sq.  in. 

The  bending  moment  at  any  section  of  a  loaded  beam  is  equal  to  the  algebraic 
sum  of  the  moments  of  all  the  external  forces  (loads  and  reactions)  to  the  right  or 
left  of  the  section  about  that  section.  For  example, 
the  bending  moments  at  several  points  on  the 
beam  shown  in  Fig.  3  are  as  follows:  At  Wi 
=  /?io;  at  W2  —  Ri(a+b)  —  Wib;  at  W3  =  Ri(a-\-b-\-c) 
—  [Wzc+Wi(b  +  c)],  or  Rid. 

The  bending  moment  varies,  depending  on  the 
shear,  and  attains  a  maximum  value  at  the  point 
Fir  ^  8*    wnere  the  shear  changes  sign.     If  the  loads  are  con- 

centrated at  several  points,  the  maximum  bending 
moment  will  be  under  the  load  at  which  the  sum  of  all  the  loads  between  one 
support  up  to  and  including  the  load  in  question  first  becomes  equal  to,  or 
greater  than,  the  reaction  at  the  support.  Hence,  to  find  the  maximum  bend- 
ing moment  in  any  simple  beam: 

Rule. — Compute  the  reactions  and  determine  the  point  where  the  shear  changes 
sign.  Calculate  the  moment  about  this  point  of  either  reaction,  and  of  each  load 
between  the  reaction  and  the  point,  and 
subtract  the  sum  of  the  latter  moments 
from  the  former. 

EXAMPLE. — What  is  the  maximum 
bending  moment  of  the  beam  loaded  as 
shown  in  Fig.  4? 

SOLUTION. — The  reactions  due  to 
the  uniform  load  are  equal  to  one-half 
of  the  load;  those  due  to  the  concen- 
trated loads  are  computed  by  the  prin- 
ciple given  under  Reactions.  Both 

added    give    /?i  =  18,170     lb.    and    R2  ^  R.  •&  ' 

=  14,330  lb.     Beginning  at  Ri  and  sub-  FlG'  4 

tracting  the  loads  in  succession,  it  is  found  that  the  shear  just  to  the  left  of 
the  load  d  is  18,170  —  16,500;  and  just  to  right  of  the  load  d  it  becomes  nega- 
tive. Hence,  the  shear  changes  sign  under  the  load  d  and  the  bending  moment 
is  maximum  at  that  point.  It  is  equal  to 


18,170  X 13  - 10,000  X  7  - =  123,960  ft.-lb. 

Formulas  for  the  maximum  bending  moments  and  shears  for  beams  loaded 
and  supported  in  different  ways  are  given  in  the  following  table. 

For  a  beam  supporting  moving  loads,  the  maximum  bending  moment  occurs: 

1.  For  a  single  load,  when  the  load  is  at  the  middle  of  the  span. 

2.  For  two  equal  loads,  under  either  load,  when  the  two  loads  are  on 
opposite  sides  of  the  center,  and  one  of  the  loads  is  at  a  distance  from  the  center 
equal  to  one-fourth  the  distance  between  the  loads. 

3.  For  two  unequal  loads,  under  the  heavier  load,  when  that  load  and  the 
center  of  gravity  of  the  two  loads  are  equidistant  from  the  center  of  gravity 
of  the  beam. 

EXAMPLE. — A  beam  24  ft.  long  supports  two  moving  loads  6  ft.  apart.  The 
left-hand  load  is  8,000  lb.,  and  the  right-hand  load  is  4,000  lb.  Find  the  maxi- 
mum bending  moment. 

SOLUTION. — The  center  of  gravity  of  the  loads  is  2  ft.  from  the  left-hand 
load.  The  maximum  bending  moment  occurs  under  the  heavy  load,  and 
obtains  when  the  latter  is  1  ft.  to  the  left  of  the  center  of  the  beam.  The  left 

reaction  is,  then,  — — — =5,500  lb.,  and  the  maximum  bending  moment  is 

5,500X11  =  60,500  ft.-lb. 

Designing  of  Beams.— In  every  section  of  a  carrying  beam  there  is  induced 
an  internal  moment  called  the  moment  of  resistance,  which  is  equal  to  the  bending 


STRENGTH  OF  MATERIALS 


177 


S« 


H 

|a^ 


Is 


r 


5       K 


l 


Slw' 


1=1 


•h 


178  STRENGTH  OF  MATERIALS 

moment  at  that  section.  As  previously  explained,  the  resisting  moment  is 
equal  to  -/;  and,  if  the  maximum  bending  moment  is  denoted  by  M,  M  =  -f; 

whence, 

M  =  7 

/      c 

which  is  the  fundamental  formula  for  the  designing  of  beams;  /  is  the  working 
stress  in  flexure,  which  is  the  modulus  of  rupture  divided  by  a  suitable  factor 
of  safety. 

The  modulus  of  rupture,  also  called  the  ultimate  strength  of  flexure,  is  the 
extreme  fiber  stress  that  a  material  subjected  to  bending  can  withstand.  Its 
value  is  intermediate  between  the  ultimate  strength  in  compression  and  tension. 
The  accompanying  tables  give  the  average  values  of  the  modulus  of  rupture  for 
a  number  of  materials. 

When  a  beam  is  to  be  designed  to  carry  certain  loads,  the  maximum  bending 
moment  is  determined  and  divided  by  /.  The  latter  is  usually  given  or  is  found 
by  dividing  the  modulus  of  rupture  of  the  material  by  a  suitable  factor  of  safety. 
The  problem  then  reduces  itself  to  the  finding  of  a  section  that  has  a  value  of 

-,  the  section  modulus,  equal  to  -7.     For  rolled-  steel  sections,  the  value  of  -  can 

j  c 

be  taken  from  a  manufacturer's  handbook.     For  a  rectangular  section, 

7  =  M2 

c      6 

b  being  the  breadth  and  d  the  depth  of  the  secti9n.  As  the  expression  contains 
two  unknown  quantities  b  and  d,  a  value  for  either  one  may  be  assumed  and 
substituted,  and  the  formula  solved  for  the  other.  If  a  built-up  beam  is  used 
the  section  has  to  be  found  by  trial;  a  suitable  section  is  first  assumed  and  its 
section  modulus  is  computed  by  the  principles  given  under  the  heading  Moment 

of  Inertia;  if  necessary,  it  is  modified  until  it  is  equal  to  -7. 

EXAMPLE.  —  Design  both  a  rolled-steel  I  beam  and  a  solid  wooden  beam  TO  ft 
long,  each  to  carry  a  uniform  load  of  250  Ib.  per  ft.  in  addition  to  a  central  load 
of  2,000  Ib.,  assuming  for  wood  a  working  stress  of  1,000  Ib.  per  sq.  in.  and  for 
steel  15,000  Ib.  per  sq.  in. 

SOLUTION.  —  The  maximum  bending  moment  occurs  at  the  middle  of  the 
beam  and  is  equal  to  the  sum  of  the  moments  due  to  the  uniform  load  and  the 
central  load;  therefore, 


For  a  steel  beam,  —  =  J^QQQ  =  6.5.     From  a  manufacturer's  handbook,  a 
6-in.  I  beam  of  12.25  lb.  has  a  section  modulus  of  7.3  and  can  therefore  be  used. 


For  a  wooden  beam,  —  =  y  =  97.5  =  p  assuming  that  b  =  6  in.,  d  =  V97T5 
=  10  in.  nearly. 

Stiffness.  —  When  designing  a  beam,  it  is  sometimes  necessary  to  ascer- 
tain the  amount  that  it  will  deflect  under  given  loads.  This,  for  instance,  is  the 
case  when  designing  supports  for  machinery  parts  or  joists  for  plastered  ceilings, 
in  which  latter  case  the  deflections  should  not  exceed  3^  of  the  span.  The 
following  table  gives  deflection  formulas  for  the  most  usual  cases.  In  these 
formulas  I  is  the  span,  in  inches;  W,  the  total  load  acting  on  the  beam;  /, 
the  moment  of  inertia  of  the  cross-section  of  the  beam;  and  E,  the  modulus  of 
elasticity  of  the  material. 

EXAMPLE  1.  —  A  simple  timber  beam  10  ft.  long,  and  having  a  width  of  4  in. 
and  a  depth  of  12  in.,  carries  a  uniform  load  of  400  lb.  per  ft.  What  is  the 
deflection? 

SOLUTiON.yAccording  to  the  table,  the  deflection  for  a  uniformly  distributed 

In   this   case>   *=1°X12  =  120;     W=  400X10  =  4,000;     E 


=  1,500,000;  and  I  =  ~~~  =  576.     Substituting  in  the  formula, 


STRENGTH  OF  MATERIALS 


179 


£  ^ 

S  co 


&ftj 

tS  10 


LL 


Hg) 


180 


STRENGTH  OF  MATERIALS 


COLUMNS 

The  strength  of  a  compression  member  depends  on  the  ratio  of  its  length 
to  its  least  lateral  dimension,  or,  what  is  the  same  thing,  on  the  ratio  of  slender- 
ness;  that  is,  the  ratio  of  its  length  to  its  radius  of  gyration. 

For  compression  members  whose  ratio  of  slenderness  does  not  exceed  30, 

r> 

the  formula  S  =  ~T.  f°r  simple  stress,  may  be  used. 

When  this  ratio  exceeds  30,  but  is  not  more  than  150,  s  should  be  deduced 
from  Rankine's  formula,  su 


in  which 


»*? 

ultimate  strength  in  compression; 


1  =  length; 
r  =  radius 


ius  of  gyration. 
coefficient  from  table. 
The  ultimate  strength  in  compression  s,t  should  be  divided  by  a  suitable 
factor  of  safety.     Both  /  and  r  are  expressed  in  the  same  unit.     The  values  of  ki, 
which  depend  on  the  material  of  the  column  and  the  condition  of  its  ends  — 
that  is  whether  fixed  or  round  —  are  given  in  the  following  table: 

VALUES  OF  fei  (RANKINE'S  FORMULA) 


Material 

Both  Ends 
Flat  or  Fixed 

One  End 
Round 

Both  Ends 
Round 

Cast  iron  
Wrought  iron. 
Steel  
Wood 

1 

1.78 

4 

5,000 
1 

5,000 
1.78 

5,000 
4 

36,000 
1 
25,000 
1 

36,000 
1.78 

36,000 
4 

25,000 

1.78 

25,000 
4 

3,000 

3,000 

3,000 

When  the  value  of  -  exceeds  150,  Euler's  formula,  which  is  given  later, 

should  be  used. 

The  straight  line  formula  is  more  convenient  for  determining  the  value  of  s, 
and  is  now  in  extensive  use.  It  is  only  approximate,  giving  values  of  s  that 
differ  somewhat  from  those  obtained  by  Rankine's  formula;  but  the  difference 
is  on  the  side  of  safety.  For  the  same  notation  as  before,  the  straight-line 

formula  is  s  =  su—  k  - 

CONSTANTS   FOR  THE  STRAIGHT-LINE  AND  EULER'S  FORMULAS 


1      •  .  - 

Medium  Steel 

Wrought  Iron 

Cast 
Iron 

Flat 
Ends 

Pin 
Ends 

Flat 
Ends 

Pin 

Ends 

Flat 
Ends 

Su 

52,500 
179 

lt>5 
666m 

52,500 
220 

159 

444  m 

42,000 
128 

218 
666m 

42,000 
157 

178 
444  m 

80,000 
438 

122 
395  m 

k.  :::::\  

limit  of  -  
nE*t  

STRENGTH  OF  MATERIALS 


181 


The  values  of  su  and  k  are  given  in  the  accompanying  table,  in  which  will 
also  be  found  the  limit  of  -  within  which  the  formula  may  be  used.  When  - 

exceeds  this  limit,  Euler's  formula,  which  follows,  should  be  used. 

EXAMPLE. — What  is  the  ultimate  strength  per  square  inch  of  a  medium- 
steel  column  25  ft.  long  both  ends  of  which  are  fixed  and  the  radius  of  gyration 
of  which  is  2.5? 

SAFE  LOADS  FOR  HOLLOW,  CYLINDRICAL,  CAST-IRON   COLUMNS 

(The  Carnegie  Steel  Co.,  Limited) 


1 

1 

o> 

Length  of  Columns  in  Feet 

^ 

c  5 

side  Diai 
Inches 

Jl 

8 

10 

12 

14 

16 

18 

20 

22 

24 

-4 

0  C 

tP 

US! 

i§* 

s 

JE: 

Safe  Load,  in  Tons  of  2,000  Lb. 

& 

11' 

6 

26.2 

23.0 

20.1 

17.5 

15.2 

13.2 

11.5 

8.6 

26.95 

6 

37.5 

33.0 

28.8 

25.0 

21.7 

18.9 

16.5 

12.4 

38.59 

6 

42.7 

37.6 

32.8 

28.5 

24.7 

21.5 

18.8 

14.1 

43.96 

6 

1 

47.6 

41.9 

36.5 

31.8 

27.6 

24.0 

21.0 

15.7 

49.01 

6 

H 

52.2 

46.0 

40.1 

34.8 

30.2 

26.3 

23.0 

17.2 

53.76 

7 

1 

47.7 

43.1 

38.5 

34.3 

30.4 

26.9 

23.9 

21.2 

18.9 

14.7 

45.96 

7 

1* 

61.1 

55.2 

49.3 

43.8 

38.9 

34.4 

30.6 

27.1 

24.2 

18.9 

58.90 

7 

H 

67.2 

60.8 

54.3 

48.3 

42.8 

37.9 

33.7 

29.9 

26.7 

20.8 

64.77 

8 

f 

57.9 

53.3 

48.6 

44.1 

39.7 

35.8 

32.2 

28.9 

26.1 

17.1 

53.29 

8 

1* 

74.6 

68.7 

62.5 

56.7 

51.1 

46.0 

41.4 

37.3 

33.6 

22.0 

68.64 

8 

u 

89.9 

82.8 

75.5 

68.4 

61.7 

55.5 

49.9 

44.9 

40.5 

26.5 

82.71 

9 

1 

68.1 

63.6 

58.9 

54.2 

49.6 

45.2 

41.2 

37.5 

34.1 

19.4 

60.65 

9 

1 

88.0 

82.3 

76.2 

70.0 

64.1 

58.4 

53.2 

48.4 

44.1 

25.1 

78.40 

9 

11 

106.6 

99.6 

92.2 

84.8 

77.6 

70.8 

64.4 

58.7 

53.4 

30.4 

94.94 

9 

123.8 

115.7 

107.1 

98.5 

90.1 

82.2 

74.8 

68.1 

62.0 

35.3 

110.26 

9 

ll 

139.6 

130.5 

120.8 

111.1 

101.6 

92.7 

84.4 

76.8 

69.9 

39.9 

124.36 

10 

1 

101.4 

95.9 

89.8 

83.6 

77.4 

71.5 

65.8 

60.5 

55.5 

28.3 

88.23 

10 

li 

123.3 

116.5 

109.1 

101.6 

94.1 

86.8 

79.9 

73.4 

67.5 

34.4 

107.23 

10 

if 

143.7 

135.8 

127.3 

118.5 

109.7 

101.2 

93.2 

85.6 

78.7 

40.1 

124.99 

10 

ll 

162.7 

153.8 

144.1 

134.1 

124.2 

114.6 

105.5 

97.0 

89.1 

45.4 

141.65 

11 

1 

114.8 

109.4 

103.5 

97.3 

91.0 

84.8 

80.2 

73.1 

67.7 

31.4 

98.03 

11 

139.9 

133.3 

126.1 

118.6 

110.9 

103.3 

97.8 

89.4 

82.5 

38.3 

119.46 

11 

if 

163.5 

155.9 

147.5 

138.6 

128.7 

120.8 

114.3 

104.1 

96.4 

44.8 

139.68 

11 

If 

185.7 

177.1 

167.5 

157.5 

147.3 

137.2 

129.8 

118.3 

109.5 

50.9 

158.68 

11 

2 

206.6 

196.9 

186.3 

175.1 

163.8 

152.6 

144.4 

131.5 

121.8 

56.6 

176.44 

12 

1 

128.0 

122.9 

117.2 

111.0 

104.7 

98.4 

92.2 

86.1 

80.4 

34.6 

107.51 

12 

156.4 

150.1 

143.1 

135.7 

127.9 

120.2 

112.6 

105.2 

98.2 

42.2 

131.41 

12 

ji 

183.3 

175.9 

167.7 

159.0 

149.9 

140.9 

132.0 

123.3 

115.1 

49.5 

154.10 

12 

If 

208.7 

200.4 

191.0 

181.1 

170.7 

160.4 

150.3 

140.5 

131.1 

56.4 

175.53 

12 

2 

232.7 

223.4 

213.0 

201.9 

190.4 

178.9 

167.6 

156.6 

146.1 

62.8 

195.75 

13 

1 

141.2 

136.3 

130.7 

124.7 

118.5 

112.1 

105.8 

99.5 

93.5 

37.7 

117.53 

13 

11 

172.8 

166.8 

160.0 

152.7 

145.0 

137.2 

129.4 

121.8 

114.4 

46.1 

143.86 

13 

H 

203.0 

195.9 

187.9 

179.3 

170.3 

161.1 

152.0 

143.1 

134.3 

54.2 

168.98 

13 

If 

231.6 

223.6 

214.5 

204.7 

194.4 

183.9 

173.5 

163.3 

153.3 

61.9 

192.88 

13 

2 

258.9 

249.9 

239.7 

228.7 

217.3 

205.5 

193.9 

182.5 

171.3 

69.1 

215.56 

14 

1 

154.3 

149.6 

144.3 

138.5 

132.3 

125.9 

119.5 

113.1 

106.8 

40.8 

127.60 

14 

u 

189.2 

183.4 

176.9 

169.7 

162.2 

154.4 

146.5 

138.6 

131.0 

50.1 

156.31 

14 

H 

222.6 

215.8 

208.1 

199.7 

190.8 

181.7 

172.3 

163.1 

154.1 

58.9 

183.67 

14 

If 

254.4 

246.7 

237.9 

228.3 

218.1 

207.6 

197.0 

186.5 

176.2 

67.4 

210.00 

14 

2 

284.8 

276.2 

266.4 

255.6 

244.2 

232.4 

220.6 

208.8 

197.2 

75.4 

235.12 

15 

1 

167.4 

162.9 

157.8 

152.1 

146.0 

139.7 

133.3 

126.8 

120.4 

44.0 

137.28 

15 

205.5 

200.0 

193.7 

186.7 

179.3 

171.5 

163.6 

155.7 

147.9 

54.0 

168.48 

15 

U 

242.1 

235.7 

228.2 

220.0 

211.2 

202.1 

192.8 

183.5 

174.2 

63.6 

198.74 

15 

If 

277.2 

269.8 

261.3 

251.9 

241.9 

231.4 

220.7 

210.1 

199.5 

72.9 

227.45 

15 

2 

310.8 

302.5 

293.0 

282.5 

271.2 

259.5 

247.5 

235.5 

223.6 

81.7 

254.90 

182  STRENGTH  OF  MATERIALS 

SOLUTION.  —  By  the  straight-line  formula, 

QC  vv  1  O 

5  =  60,000-  179  Xf^~  =  38,520  Ib.  per  sq.  in. 


Using  Rankine's  formula, 


38.070tb.pers,.  in. 


+25,OOOX2.52 

Euler's  Formula.  —  Structural   members    in   compression   whose   ratio   of 
slenderness  exceeds  150  should  preferably  not  be  used.     Sometimes,  however, 

long  columns  cannot  be  avoided,  and  when  -  exceeds  the  limits  for  which  the 

preceding  formulas  may  be  applied,  Euler's  formula   should  be  used.     This 
formula  is  as  follows: 


in  which  E  =  modulus  of  elasticity  of  material; 

»  =  constant. 

The  value  of  the  constant  n  depends  on  the  end  condition;  it  has  the 
value  of  1  for  columns  with  both  ends  pivoted  and  4  for  columns  with  both  ends 
fixed.  The  table  of  constants  on  page  180  gives  the  values  of  nv2E,  expressed 
in  millions  of  pounds. 

Formula  for  Wooden  Columns.  —  The  formula  for  determining  the  strength 
of  wooden  columns  having  flat  or  square  ends  was  deduced  from  exhaustive 
tests  of  full-size  specimens,  made  at  the  Watertown  Arsenal,  Mass.,  and  may  be 
expressed  as  follows: 


in  which  5  =  ultimate  strength  of  column,  per  square  inch  of  section; 

U  =  ultimate  compressive  strength  of  material,  per  square  inch; 
/  =  length  of  column,  in  inches; 
d  =  dimension  of  least  side  of  column,  in  inches. 

This  formula  may  be  applied  to  all  wooden  columns,  the  length  or  height 
of  which  is  not  under  10  times  nor  over  45  times  the  dimension  of  the  least  side. 

In  other  words,  -y  should  not  be  less  than  10  nor  more  than  45.     If  the  length 

a 

is  less  than  10  times  the  least  side,  the  direct  compressive  strength  of  the 
material  per  square  inch,  multiplied  by  the  sectional  area  of  the  column  in 
square  inches,  will  give  the  strength  of  the  column.  If  the  length  is  over  45 
times  the  least  side,  Rankine's  formula  should  be  used. 


COMBINED  STRESSES 

Bending  Combined  With  Compression  or  Tension.  —  Assume  that  P  is  the 
axial  force  acting  on  the  beam;  M  ,  the  maximum  bending  moment  to  which  the 
beam  is  subjected;  A,  the  cross-sectional  area  of  the  beam;  7,  its  moment  of 
inertia;  and  c,  the  distance  from  the  neutral  axis  of  the  most  distant  fiber, 
having  the  same  kind  of  stress  (tension  or  compression)  as  that  caused  by  P. 
Then,  the  working  stress  should  not  exceed 

P  ,  Me 

5=A+-F 

In  case  of  compression,  5  should,  in  addition,  be  deduced  from  one  of  the 
compression  formulas  previously  given. 

The  preceding  formula  for  5  is  the  one  commonly  used  in  practice,  but  it  is 
only  approximate.  When  more  accurate  results  are  required,  the  following 
formula  should  be  used, 

P  ,       Me 


Here,  I  is  the  span;   E,  the  modulus  of  elasticity,  and  k',  a  constant  having 
the  following  values: 


STRENGTH  OF  MATERIALS 


183 


Value  of  k 
For  a  cantilever  loaded  at  end  .............................  % 

For  a  cantilever  loaded  uniformly  ..........................  \ 

For  a  beam  supported  at  both  ends  and  loaded  at  center  .....  ^ 

For  a  beam  supported  at  both  ends  and  loaded  uniformly  ......  ^ 

For  a  beam  fixed  at  both  ends  and  loaded  at  center  ..........  ^ 

For  a  fixed  beam  uniformly  loaded  .........................  -fa 

The  minus  sign  before  k  is  for  the  case  when  the  direct  stress  is  compressive, 
and  the  plus  sign,  when  it  is  tensile. 

STRENGTH  OF  HEMP  AND  MANILA  ROPES  AND  OF  CHAINS 

Ropes.  —  If  C  is  the  circumference  of  a  rope,  in  inches,  and  P  the  working  load, 
in  pounds,  then,  for  hemp  and  manila  rope, 
P  =  10C2 

This  formula  gives  a  factor  of  safety  of  from  7^  for  manila  or  tarred  hemp 
rope  to  about  11  for  the  best  three-strand  hemp  rope. 

For  iron-wire  rope  of  seven  strands,  nineteen  wires  to  a  strand, 


and  for  the  best  steel-wire  rope  of  seven  strands,  nineteen  wires  to  the  strand, 
P  =  1,OOOC2 

The  last  two  formulas  are  based  on  a  factor  of  safety  of  6. 

Chains.  —  If  P  is  the  safe  load,  in  pounds,  and  d  the  diameter  of  link,  in 
inches,  then,  for  open-link  chains  made  from  a  good  quality  of  wrought  iron, 

and  for  stud->link  chains,  P  =  IS.'oOOd* 

Chain  Cables.  —  The  strength  of  a  chain  link  is  less  than  twice  that  of  a 
straight  bar  of  a  sectional  area  equal  to  that  of  one  side  of  the  link.  A  weld 
exists  at  one  end  and  a  bend  at  the  other,  each  requiring  at  least  one  heat, 
which  produces  a  decrease  in  the  strength.  The  report  of  the  committee  of 
the  U.  S.  Testing  Board,  on  tests  of  wrought-iron  and  chain  cables,  contains 
the  following  conclusions: 

"That,  beyond  doubt,  when  made  of  American  bar  iron,  with  cast-iron  studs, 
the  studded  link  is  inferior  in  strength  to  the  unstudded  one. 

"That  when  proper  care  is  exercised  in  the  selection  of  material,  the  strength 
of  chain  cables  will  vary  by  about  5%  to  17%  of  the  resistance  of  the  strongest. 
Without  this  care  the  variation  may  rise  to  25%. 

"That  with  proper  material  and  construction  the  ultimate  resistance  of  the 
chain  may  be  expected  to  vary  from  155%  to  170%  of  that  of  the  bar  used  in 
making  the  links,  and  show  an  average  of  about  163%. 

"That  the  proof  test  of  a  chain  cable  should  be  about  50%  of  the  ultimate 
resistance  of  the  weakest  link." 

From  a  great  number  of  tests  of  bars  and  unfinished  cables,  the  com- 
mittee considered  that  the  average  ultimate  resistance  and  proof  tests  of  chain 
cables  made  of  the  bars,  whose  diameters  are  given,  should  be  such  as  are  shown 
in  the  accompanying  table. 

ULTIMATE  RESISTANCE  AND  PROOF  TESTS  OF  CHAIN 
CABLES 


Diam- 
eter of 
Bar 

Average 
Resistance 
=  163%  of 

Proof 
Test 

Diam- 
eter of 
Bar 

Average 
Resistance 
=  163%  o/ 

Proof 
Test 

Inches 

Bar 

Pounds 

Pounds 

Inches 

Bar 

Pounds 

Pounds 

1 

71,172 

33,840 

1* 

162,283 

77,159 

1A 

79,544 

37,820 

ir 

174,475 

82,956 

|I 

88,445 
97,731 

42,053 
46,468 

it 

187.075 
200,074 

88,947 
95,128 

107,440 

51,084 

I'M 

213,475 

101,499 

1& 

117,577 

55,903 

if 

227,271 

108,058 

If 

128,129 

60,920 

Jii 

241,463 

114,806 

139,103 

66,138 

2 

256,040 

121,737 

H 

150,485 

71,550 

184 


STRENGTH  OF  MATERIALS 


PRACTICAL  PROBLEMS  IN  THE  STRENGTH  OF 
BEAMS  AND  PROPS 

To  Find  the  Quiescent  Breaking  Load  of  a  Horizontal  Square  or  Rectangular 
Beam  Supported  at  Both  Ends  and  Loaded  at  the  Middle.— Multiply  the 
breadth,  in  inches,  by  the  square  of  depth,  in  inches;  divide  the  product  by 
distance  in  feet,  between  supports,  and  multiply  the  quotient  by  the  con- 
stant given  in  the  Table  of  Constants  for  Seasoned  Timber.  Take  as  the  safe 
working  load  one-third  of  the  breaking  load. 

To  Find  the  Quiescent  Breaking  Load  of  a  Horizontal  Cylindrical  Beam. 
Divide  the  cube  of  the  diameter,  in  inches,  by  the  distance  between  the  sup- 
ports in  feet,  and  multiply  the  quotient  by  the  constant. 

When  the  load  is  uniformly  distributed  on  the  beam,  the  results  obtained 
by  the  foregoing  rules  should  be  doubled. 

EXAMPLE  1. — Find  the  quiescent  breaking  load  and  safe  working  load  of 
a  yellow-pine  collar  8  in.  square,  12  ft.  between  legs. 


SOLUTION. — Breaking    load  = 
10,666  Ib.  for  green  timber. 


8X82 
12 


X  500  =  21,333    Ib.    for    seasoned,    and 


Safe  working  load  =  7,111  Ib.  for  seasoned,  and  3,556  Ib.  for  green  timber. 
EXAMPLE  2. — Find  the  quiescent  breaking  load,   and  the  safe  working 
load  of  a  hemlock  collar  10  in.  diameter,  7  ft,  between  legs. 

1  f)3 

SOLUTION.— Breaking  load  =  — X  236  =  33, 7 14  Ib.  for  seasoned,  timber,  and 

33  714-^2  =  16,857  Ib.  for  green  timber. 

Safe  working  load  =  33, 7 14 -r-3  =  11,238  Ib.  for  seasoned,  and  33,714-1-6  or 
11  238-4-2  =  5,619  Ib.  for  green  timber. 

To  Find  the  Load  a  Rectangular  Collar  Will  Support  When  Its  Depth  Is 
Increased. — When  the  length  and  width  remain  constant,  the  load  varies  as 
the  square  of  the  depth. 

EXAMPLE. — A  rectangular  collar  10  in.  deep  supports  15,000  Ib.  What  will 
it  support  if  its  depth  is  increased  to  12  in.? 

SOLUTION. — Applying  the  rule  just  given  102  :  12*  =  15,000  :  21,600. 

Having  the  Length  and  Diameter  of  a  Collar,  to  Find  the  Diameter  of  a 
Longer  Collar  to  Support  the  Same  Weight. — For  the  same  load,  the  strength 
of  collars  varies  as  the  cubes  of  their  diameters,  and  inversely  as  their  lengths. 

EXAMPLE. — If  a  collar  6  ft,  long  and  8  in.  diameter  supports  a  certain 
weight,  what  must  be  the  diameter  of  a  collar  12  ft.  long  to  support  the  same 
weight? 

TABLE  OF  CONSTANTS  FOR  SEASONED  TIMBER 


Woods 

Constant 

Woods 

Constant 

Square  or 
Rectan- 
gular 

Round 

Square  or 
Rectan- 
gular 

Round 

Ash,  white  
Ash,  swamp  
Ash,  black  
Balsam,  Canada  .  .  . 
Beech  white  . 

650 
400 
300 
350 
450 
550 
450 
450 
250 
450 
350 
600 
400 
650 
600 

383 
236 
177 
206 
265 
324 
265 
266 
147 
265 
206 
353 
236 
383 
353 

Locust  
Lignum  vitae.  .  .  . 
Larch  
Maple  
Oak,  red  or  b  ack 
Oak,  white  
Oak,  live.....  ... 
Pine,  white/  
Pine,  yellow  

600 
650 
400 
550 
550 
600 
600 
450 
500 
550 
550 
450 
500 
350 

353  . 

383 
236 
324 
324 
353 
353 
265 
295 
324 
324 
265 
295 
206 

Beech,  red  

Birch,  black  
Birch,  yellow  
Cedar,  white  
Chestnut  

Elm 

Poplar 

Elm,  rock  
Hemlock  

Spruce 

Hickory  

Willow 

Ironwood  ....;... 

STRENGTH  OF  MATERIALS 


185 


SOLUTION.  —  Applying  the  rule  just  given  \12:>/6 
Having  the  Loads 


8  in.  :  6.35  in. 

s  of  Two  Beams  of  Equal  Length  and  the  Diameter  of  One. 
to  Find  the  Diameter  of  the  Other.  —  When  the  lengths  are  equal,  the  diameters 
vary  as  the  cube  roots  of  the  loads,  or  the  cubes  of  the  diameters  vary  as  the 
loads. 

EXAMPLE  1.  —  A  beam  11  in.  in  diameter  supports  a  load  of  32,160  Ib.  What 
will  be  the  diameter  of  another  beam  the  same  length,  to  support  a  load  of 
19,440  Ib.? 

SOLUTION.  —  Applying  the  rule  just  given 

-^32,160  :  ^19,440  =  11  :  9.3. 

EXAMPLE  2.  —  A  beam  8  in.  in  diameter  will  support  a  load  of  10,240  Ib. 
What  load  will  a  beam  the  same  length  and  7  in.  in  diameter  support? 

SOLUTION.  —  Applying  the  rule  just  given  83  :  7s  =  10,240  :  6,860. 

The  preceding  Table  of  Constants  has  been  calculated  for  seasoned  timber; 
for  green  timber,  take  one-half  of  these  constants.  The  safe  working  load  is 
one-third  of  the  breaking  load. 

To  Find  the  Diameter  of  a  Collar  When  the  Weight  Increases  in  Proportion 
to  the  Length.  —  Find  the  required  diameter  to  support  the  same  weight  as  the 
short  collar.  Then  the  length  of  the  short  collar  is  to  the  length  of  the  long 
one  as  the  diameter  found  to  support  the  original  weight  is  to  the  required 
diameter. 

EXAMPLE.  —  If  a  collar  6  ft.  long,  8  in.  in  diameter,  supports  a  certain  weight, 
what  must  be  the  diameter  of  a  collar  12  ft.  long  to  support  twice  the  weight? 

03       (        )3 

SOLUTION.—  From  the  rule  just  given,  1:2  =  -:  ~-  ,  or  1  :  2  =  2X  83  :  (     )3, 


12.7. 


To  Find  the  Breaking  Load  of  Either  Square  or  Rectangular  Wooden  Pil- 
lars or  Props.  —  Call  one  side  of  the  square  or  the  least  side  of  the  rectangle  the 
breadth.  Divide  the  square  of  the  length,  in  inches,  by  the  square  of  the 
breadth,  in  inches,  multiply  the  quotient  by  .004,  add  1  to  the  product  and 
divide  the  crushing  load  by  the  result.  Then  multiply  this  quotient  by  the 
number  of  square  inches  in  the  end  of  the  prop 


Or,  breaking  load  in  Ib. ; 


Crushing  load        , 


in  which 


1  =  length,  in  inches; 
b  =  breadth,  in  inches, 
d  =  depth,  in  inches 


CRUSHING  LOADS  OF  WELL-SEASONED  AMERICAN  WOODS 


Wood 

Crushing 
Load 
Pounds 
per  Square 
Inch 

Wood 

Crushing 
Load 
Pounds 
per  Square 
Inch 

Ash 

6,800 

Maple,  sugar,  black  .  .  . 

8,000 

Beech  
Birch                            .... 

7,000 
8,000 

Maple,  white,  red  
Oak,  white,  red,  bla  k.  . 

6,800 
7,000 

Cedar  red 

6,000 

Oak,  scrub,  basket.    .  .  . 

6,000 

Cedar,  white  

4,400 
5  300 

Oak,  chestnut,  live.    .  .  . 
Oak   pin  

7,500 
6,500 

Hemlock 

5  300 

Pine,  white  

5,400 

8  000 

5000 

Linden  

5,000 
9  800 

Pine,  Georgia  

8,500 
5,000 

7  000 

Spruce,  black  

5,700 

Maple,    broad-leafed, 

5  300 

Spruce,  white  
Willow  

4,500 
4,400 

g 

For  green  timber,  take  one-half  of  the  crushing  strength  given  in  the 
foregoing  table.     The  safe  working  load  equals  one-third  of  crushing  load. 


186 


STRENGTH  OF  MATERIALS 


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CONCRETE  '  187 

EXAMPLE.  —  What  is  the  breaking  load  of  a  well-seasoned  hemlock  post 
10  in.XS  in.  and  12  ft.  long? 

SOLUTION.—  Applying    the    rule    just    given,    5,300  -^  [l+  (^~X.004)] 

=  2,308.4  Ib.  per  sq.  in.  of  area.     2,308.4X80=  184,672  Ib.     Ans. 

To  Find  the  Breaking  Load  of  a  Cylindrical  Wooden  Prop.  —  Find  the  break- 
ing load  of  a  square  prop  whose  ends  are  equal  in  area  to  those  of  the  cylin- 
drical one,  and  proceed  according  to  foregoing  rule. 

EXAMPLE.  —  What  is  the  safe  working  load  for  a  hemlock  mine  prop  10  in. 
diameter,  10  ft.  long? 

SOLUTION.  —  The  area  of  the  end  of  the  prop  =  78.54  sq.  in.  A  square  of  equal 
area  will  have  sides  equal  to  V78.54  =  8.86+in.  Then, 

5,300  -f-  [l+  (jff^X.  004)]  =3,058.3  Ib.  per  each  sq.  in.  of  area. 


And  3,058.3  X  78.54  =  240,  198  Ib.  This  is  the  crushing  strength  of  a  similar 
prop  of  seasoned  timber,  but,  as  mine  timber  is  used  in  its  green  state,  take 
one-half  of  240,198  Ib.,  or  120,099  Ib.,  as  the  crushing  load  of  the  prop  in  ques- 
tion. Then,  the  safe  working  load  is  one-third  of  this,  or  40,033  Ib. 

The  strength  of  similar  props  varies  as  the  cubes  of  their  diameters,  and 
inversely  as  their  lengths. 

IRON  AND  STEEL  BEAMS 

Constants  for  use  in  calculating  the  strength  of  iron  and  steel  beams  are: 
Cast  iron,  2,000;  wrought  iron,  2,200;  steel,  5,000.  Hard  steel  will  break  the 
same  as  cast  iron;  soft  steel  will  bend  like  wrought  iron.  The  elastic  limit 
of  wrought  iron  is  reached  at  about  2,200  Ib.  As  it  does  not  break,  the  limit  of 
elasticity  should  be  used. 

To  Find  the  Quiescent  Breaking  Load  of  a  Horizontal  Square  or  Rectangular 
Iron  or  Steel  Beam  Supported  at  Both  Ends  and  Loaded  at  the  Middle.  —  Mul- 
tiply the  square  of  its  depth,  in  inches,  by  its  breadth,  in  inches;  multiply  this 
result  by  the  constant  for  the  material  used,  and  divide  by  the  length,  in  feet, 
between  the  supports.  For  the  net  load,  subtract  one-half  the  weight  of  the 
beam. 

To  Find  the  Quiescent  Breaking  Load  of  a  Cylindrical  Iron  or  Steel  Beam. 
Find  the  breaking  load  of  a  square  beam  the  sides  of  which  are  equal  to  the 
diameter  of  the  round  one,  and  multiply  by  .6. 

The  safe  working  load  in  each  of  the  preceding  cases  is  one-third  of  the 
breaking  load.  If  the  load  is  equally  distributed  over  the  beam,  it  will  be  twice 
as  great. 

CONCRETE 


CEMENTING  MATERIALS 

DEFINITIONS 

Any  substance  that  becomes  plastic  under  certain  treatment  and  subse- 
quently reverts  to  a  tenacious  and  inelastic  condition  may,  in  a  broad  sense,  be 
termed  a  cement.  However,  nearly  all  the  cementing  materials  employed  in 
building  construction  are  obtained  by  the  heating,  or  calcination,  as  it  is  called, 
of  minerals  composed  wholly  or  in  part  of  lime.  The  different  composition  of 
these  minerals,  as  well  as  the  properties  of  the  calcined  products,  enables  the 
various  resulting  substances  to  be  classified  as  limes,  hydraulic  cements,  plasters, 
and  miscellaneous  cements.  Although  all  these  materials  have  cementing 
properties,  the  term  cement  is  commonly  used  to  apply  only  to  the  group  made 
up  of  hydraulic  cements,  hydraulic  meaning  that  these  substances  possess  the 
ability  to  set,  or  become  hard,  under  water. 

Limes  and  hydraulic  cements  (commonly  called  simply  cements)  are  com- 
posed essentially  of  oxide  of  calcium,  or  lime,  generally  called  quicklime,  with 
which  may  be  combined  certain  argillaceous,  or  clayey,  elements,  notably 
silica  and  alumina,  it  being  to  these  elements  that  the  hydraulic  properties  of 
certain  of  these  materials  are  due.  The  quantity  of  silica  and  alumina  present 
in  these  substances  enables  them  to  be  classified  as  common  limes,  hydraulic 
limes,  and  cements. 


188  CONCRETE 

The  ratio  of  the  quantity  of  silica  and  alumina  present  in  these  materials 
to  the  quantity  of  lime  is  called  the  hydraulic  index.  In  common  limes,  this 
index  is  less  than  ,>&;  in  hydraulic  limes,  it  lies  between  ^  and  /<&;  and  in 
cements,  it  exceeds  i$y.  These  limes  merge  into  9ne  another  so  gradually, 
however,  that  it  is  often  difficult  to  distinguish  the  dividing  line  between  them. 

LIMES 

The  commercial  varieties  of  lime  may  be  classified  as  common,  hydrated, 
and  hydraulic.  The  common  limes,  also  called  quicklimes,  may  be  subdivided 
into  rich,  or  fat,  lime,  and  meager,  or  poor,  lime. 

Common  Limes. — The  grade  of  common  lime  known  as  fat,  or  rich,  lime 
is  almost  pure  oxide  of  calcium,  CaO,  and  contains  only  about  5%  of  impurities. 
It  has  a  specific  gravity  of  about  2.3  and  a  great  affinity  for  water,  of  which  it 
absorbs  about  one-quarter  of  its  weight.  This  absorption  is  accompanied  by 
a  great  rise  in  temperature,  by  the  lime  bursting,  and  by  the  giving  off  of  vapor. 
The  lime  finally  crumbles  into  a  powder.  This  powder  occupies  from  two  and 
one-half  to  three  and  one-half  times  as  much  volume  as  the  original  lime,  the 
exact  amount  depending  on  its  initial  purity.  When  the  lime  is  in  this  plastic 
state,  it  is  said  to  be  slaked.  It  is  then  unctuous  and  soft  to  the  touch,  and 
from  this  peculiarity  it  derives  the  name  of  fat  or  rich. 

Meager,  or  poor,  lime  consists  of  from  60  to  90%  of  pure  lime,  the  remainder 
being  impurities,  such  as  sand  or  other  foreign  matter.  These  impurities  have 
no  chemical  action  on  the  lime,  but  simply  act  as  adulterants.  Compared  with 
fat  lime,  poor  lime  slakes  more  slowly  and  evolves  less  heat.  The  resulting 
paste  is  also  thinner  and  not  so  smooth,  greatly  resembling  fat  slaked  lime 
mixed  with  sand.  Poor  lime  is  not  so  good  for  building  purposes  as  fat  lime, 
nor  has  it  such  extensive  use. 

Hydrated  Lime. — The  class  of  lime  called  hydrated  lime  (calcium  hydrate) 
is  merely  thoroughly  slaked  fat  lime  dried  in  the  form  of  a  fine  powder,  Ca(OH)t. 
It  is  used  extensively  in  conjunction  with  cement  for  making  mortar,  and  also 
in  the  sand-lime  brick  industry. 

Hydraulic  Limes. — Limes  that  contain  enough  quicklime  to  slake  when 
water  is  added,  and  enough  clay  or  sand  to  form  a  chemical  combination 
when  wet,  thus  giving  them  the  property  of  setting  under  water,  are  called 
hydraulic  limes.  The  slaking  qualities  vary,  the  time  of  setting  under  water 
also  varies,  but  these  limes  usually  become  as  hard  as  stone  in  3  or  4  da.  The 
use  of  hydraulic  lime  has  rapidly  decreased  in  this  country.  Large  quantities 
were  formerly  imported  from  Europe. 

CEMENTS 

Cement  may  be  divided  into  four  general  classes:  Portland,  natural, 
puzzolan  (also  called  pozzuolana),  and  mixed.  The  relative  importance  of 
each  cement  is  indicated  by  the  order  in  which  it  is  named. 

Portland  cement  may  be  defined  as  the  product  resulting  from  the  process 
of  grinding  an  intimate  mixture  of  calcareous  (containing  lime)  and  argillaceous 
(containing  clay)  materials,  calcining  (heating)  the  mixture  until  it  starts  to 
fuse,  or  melt,  and  grinding  the  resulting  clinker  to  a  fine  powder.  It  must 
contain  not  less  than  1.7  times  as  much  lime  by  weight  as  it  does  of  those 
materials  that  give  the  lime  its  hydraulic  properties,  and  must  contain  no 
materials  added  after  calcination,  except  small  quantities  of  certain  substances 
used  to  regulate  the  activity  or  the  time  of  setting. 

Natural  cement  is  the  product  resulting  from  the  burning  and  subsequent 
pulverization  of  an  argillaceous  limestone  or  other  suitable  rock  in  its  natural 
condition,  the  heat  of  burning  being  insufficient  to  cause  the  material  to  start 
to  melt. 

Puzzolan  cement  is  a  material  resulting  from  grinding  together,  without 
subsequent  calcination,  an  intimate  mixture  of  slaked  lime  and  a  puzzolanic 
substance,  such  as  blast-furnace  slag  or  volcanic  scoria.  That  made  from  slag  is 
know  as  slag  cement. 

Mixed  cements  cover  a  wide  range  of  products  obtained  by  mixing,  or 
blending,  the  foregoing  cements  with  one  another  or  with  other  inert  sub- 
stances. Sand  cements,  improved  cements,  and  many  second-grade  cements 
belong  to  this  class.  Mixed  cements,  however,  are  of  comparatively  little 
importance. 

Properties  of  Cements. — The  hydraulic  cements  differ  from  the  limes  in 
that  they  do  not  slake  after  calcination  and  that  they  set,  or  harden,  under 
water.  They  can  be  formed  into  a  paste  with  water  without  any  sensible 
increase  in  volume  and  with  little,  if  any,  disengagement  of  heat.  They  do 


CONCRETE 


189 


not  shrink  appreciably  in  hardening,  so  that  the  sand  and  broken  stone  with 
which  they  are  mixed  are  employed  merely  through  motives  of  economy  and 
not,  as  with  limes,  of  necessity. 

The  color  of  the  different  grades  of  cement  is  variable,  but  in  certain  cases 
it  is  distinctive.  Portland  cement  is  a  dark  bluish  or  greenish  gray;  if  it  is  a 
light  yellow,  it  may  indicate  underburning.  Natural  cement  ranges  in  color 
from  a  light  straw,  through  the  grays,  to  a  chocolate  brown.  Slag  cement  is 
gray  with  usually  a  tinge  of  lilac.  In  general,  however,  the  color  of  cement  is 
no  criterion  of  its  quality. 

Cement  is  packed  either  in  wooden  barrels  or  in  cloth  or  paper  bags,  the 
latter  being  the  form  of  package  most  commonly  employed.  A  barrel  of 
Portland  or  of  slag  cement  contains  the  equivalent  of  4  bags,  while  but  3  bags 
of  natural  cement  equal  a  barrel.  The  average  weights  of  the  various  cements 
are  given  in  the  accompanying  table. 

In  proportioning  mortar  or  concrete  by  volume,  a  common  assumption  is 
that  a  bag  of  Portland  cement  occupies  .9  cu.  ft.  This  practice,  however,  is, 
not  entirely  uniform. 

AVERAGE  WEIGHTS  OF  HYDRAULIC  CEMENTS 


Kind  of  Cement 

Net  Weight 
of  Bag 
Pounds 

Net  Weight 
of  Barrel 
Pounds 

Weight  per  Cubic  Foot 
Pounds 

Packed 

Loose 

Portland  

94 
94 

82  £ 

376 

282 
330 

100  to  120 
75  to    95 
80  to  100 

70  to  90 
45  to  65 
55  to  75 

Natural 

Slag  

Portland  cement  may  be  distinguished  by  its  dark  color,  heavy  weight, 
slow  rate  of  setting,  and  greater  strength.  Natural  cement  is  characterized  by 
lighter  color,  lighter  weight,  quicker  set,  and  lower  strength.  Slag  cement  is 
somewhat  similar  to  Portland,  but  may  be  distinguished  from  it  by  its  lilac- 
bluish  color,  by  its  lighter  weight,  and  by  the  greater  fineness  to  which  it  is 
ground. 

Portland  cement  is  adaptable  to  any  class  of  mortar  or  concrete  construc- 
tion, and  is  unquestionably  the  best  material  for  all  such  purposes.  Natural 
and  slag  cements,  however,  are  cheaper,  and,  under  certain  conditions,  may  be 
substituted  for  the  more  expensive  Portland  cement.  All  heavy  construction, 
especially  if  exposed,  all  reinforced-concrete  work,  sidewalks,  concrete  blocks, 
foundations  of  buildings,  piers,  walls,  abutments,  etc.  should  be  made  with 
Portland  cement.  In  second-class  work,  as  in  rubble  masonry,  brick  sewers, 
unimportant  work  in  damp  or  wet  situations,  or  in  heavy  work  in  which  the 
working  loads  will  not  be  applied  until  long  after  completion,  natural  cement 
may  be  employed  to  advantage.  Slag  cement  is  best  adapted  to  heavy  founda- 
tion work  that  is  immersed  in  water  or  is  at  least  continually  damp.  This  kind 
of  cement  should  never  be  exposed  directly  to  dry  air,  nor  should  it  be  subjected 
either  to  attrition  or  impact. 

SAND  AND  ITS  MIXTURES 

Sand  is  an  aggregation  of  loose  gr&ins  of  crystalline  structure,  derived  from 
the  disintegration  of  rocks.  It  is  called  silicious,  argillaceous,  or  calcareous, 
according  to  the  character  of  the  rock  from  which  it  is  derived.  Sand  is 
obtained  from  the  seashore,  from  the  banks  and  beds  of  rivers,  and  from  land 
deposits. 

The  first  class,  called  sea  sand,  contains  alkaline  salts  that  attract  and 
retain  moisture  and  cause  efflorescence  in  brick  masonry.  This  efflorescence 
is  not  at  first  apparent  but  becomes  more  marked  as  time  goes  on.  It  can  be 
removed  temporarily,  at  least,  by  washing  the  stonework  in  very  dilute  hydro- 
chloric acid. 

The  second,  termed  river  sand,  is  generally  composed  of  rounded  particles, 
and  may  or  may  not  contain  clay  or  other  impurities. 

The  third,  called  pit  sand,  is  usually  composed  of  grains  that  are  more 
angular;  it  often  contains  clay  and  organic  matter.  When  washed  and  screened 
it  is  a  good  sand  for  general  purposes. 


19o  CONCRETE 

Sand  is  used  in  making  mortar  because  it  prevents  excessive  shrinkage  and 
reduces  the  quantity  of  lime  or  cement  required.  Lime  adheres  better  to  the 
particles  of  sand  than  it  does  to  its  own  particles;  hence,  it  is  considered  that 
sand  adds  strength  to  lime  mortar.  On  cement  mortar,  on  the  contrary,  sand 
has  a  weakening  effect. 

Properties  of  Sand.  —  The  weight  of  sand  is  determined  by  merely  filling 
a  cubic-foot  measure  with  dried  sand  and  obtaining  its  weight.  Dry  sand 
weighs  from  80  to  120  Ib.  per  cu.  ft.;  moist  sand,  however,  occupies  more  space 
and  weighs  less  per  cubic  foot.  The  weight  of  sand  is  more  or  less  dependent 
on  its  specific  gravity  and  on  the  size  and  shape  of  the  sand  grains,  but,  other 
things  being  equal,  the  heaviest  sand  makes  the  best  mortar. 

The  specific  gravity  of  sand  ranges  from  2.55  to  2.80.  For  all  practical 
purposes  the  specific  gravity  may  be  assumed  to  be  2.65  with  little  danger  of 

By  percentage  of  voids  is  meant  the  amount  of  air  space  in  the  sand.  Struc- 
turally, it  is  one  of  the  most  important  properties  of  sand.  The  greater  these 
voids,  the  more  cement  paste  will  be  required  to  fill  them  in  order  to  give  a 
dense  mortar.  The  percentage  of  voids  may  be  determined  by  observing  the 
quantity  of  water  that  can  be  introduced  into  a  vessel  filled  with  sand,  but 
it  is  best  computed  as  follows: 

r      -j       ,™     100  X  weight  per  cubic  foot 
percentage  of  voids  =  100  --  62.5X  specific  gravity 

EXAMPLE.  —  What  is  the  percentage  of  voids  in  a  sand  having  a  specific 
gravity  of  2.65  and  weighing  105  Ib.  per  cu.  ft.? 

SOLUTION.  —  Substituting  in  the  formula,  the  percentage  of  voids  is 


The  percentage  of  voids  depends  principally  on  the  size  and  shape  of  the 
sand  grains  and  the  gradation  of  its  fineness,  and  hence  will  vary  from  25 
to  50%.  Sand  containing  over  45%  of  voids  should  not  be  used  to  make 
mortars. 

The  shape  of  the  grains  of  sand  is  of  chief  importance  in  the  influence  that  the 
sand  exerts  on  the  percentage  of  voids.  Obviously,  a  sand  with  rounded  grains 
will  compact  into  a  more  dense  mass  than  one  whose  grains  are  angular  or  flat 
like  particles  of  mica.  Therefore,  the  more  nearly  the  grains  approach  the 
spherical  in  shape,  the  more  dense  and  strong  will  be  the  mortar  for  the  same 
amount  of  cement.  This  fact  is  contrary  to  the  common  opinion  on  the 
subject. 

The  fineness  of  sand  is  determined  by  passing  a  dried  sample  through  a 
series  of  sieves  having  10,  20,  30,  40,  50,  74,  100,  and  200  meshes,  respectively, 
to  the  linear  inch.  The  result  of  this  test,  expressed  in  the  amount  of  sand 
passing  each  sieve,  is  known  as  the  granulometric  composition  of  the  sand. 
Material  that  does  not  pass  a  J-in.  screen  is  not  considered  to  be  sand,  and 
should  be  separated  by  screening.  Sand  that  is  practically  all  retained  on  a 
No.  30  sieye  is  called  coarse,  while  80  or  90%  of  sand  known  as  fine  will  pass 
through  this  sieve.  Fine  sand  produces  a  weaker  mortar  than  coarse  sand,  but  a 
mixture  of  fine  and  coarse  sand  will  surpass  either  one  in  those  cases,  at  least, 
where  there  is  not  enough  cement  to  fill  voids  using  either  sand. 

The  purity,  or  cleanness,  of  -sand  may  be  roughly  ascertained  by  rubbing 
it  between  the  fingers  and  observing  how  much  dirt  remains.  To  determine 
the  percentage  of  the  impurities  more  accurately,  a  small  dried  and  weighed 
sample  is  placed  in  a  vessel  and  stirred  up  with  water.  The  sand  is  allowed  to 
settle,  the  dirty  water  poured  off,  and  the  process  repeated  until  the  water  pours 
off  clear.  The  sand  is  then  dried  and  weighed.  The  loss  in  weight  gives  the 
quantity  of  impurities  contained  in  the  sand.  The  presence  of  dirt,  organic 
loam,  mica,  etc.  is  decidedly  injurious  and  tends  to  weaken  the  resulting 
mortar.  Clay  or  fine  mineral  matter  in  small  proportions  may  actually  result 
in  increased  strength,  but  excessive  quantities  of  these  materials  may  be  a 
possible  source  of  weakness.  The  best  modern  practice  limits  the  quantity  of 
impurities  found  by  this  washing  test  to  5%. 

Attention  is  called  to  the  fact  that  the  sand  found  and  used  around  many 
collieries  is  inferior.  It  is  apt  to  be  dirty  and  to  consist  of  fine  uniform  grains. 
Such  sand  is  sometimes  suitable  for  building  brattices  or  small  foundations 
where  a  certain  amount  of  air-tightness  or  weight,  but  not  strength,  is  required. 
In  all  important  work  or  in  reinforced  concrete,  however,  good,  carefully  selected 
sand  should  be  used.  The  sand  should  always  be  tested  to  see  whether  it  will 
make  a  mortar  or  a  concrete  of  the  desired  qualities. 


CONCRETE  191 

Preparation  of  Sand. — Sand  is  prepared  for  use  by  (1)  screening  to  remove 
the  pebbles  and  coarser  grains,  the  fineness  of  the  meshes  of  the  screen  depend- 
ing on  the  kind  of  work  in  which  the  sand  is  to  be  used;  (2)  washing,  to  remove 
salt,  clay,  and  other  foreign  matter;  and  (3)  drying  if  necessary.  When  dry 
sand  is  required,  it  is  obtained  by  evaporating  the  moisture  either  in  a  machine, 
called  a  sand  dryer,  or  in  large,  shallow,  iron  pans  supported  on  stones,  with  a 
wood  fire  placed  underneath. 

LIME  AND  CEMENT  MORTARS 

Mortars  are  composed  of  lime  or  cement  and  sand  mixed  to  the  proper 
consistency  with  water.  The  proportions  of  the  ingredients  depend  on  the 
character  of  the  work  in  which  the  mortar  is  to  be  used. 

In  proportioning  mortar,  the  quantities  of  the  separate  ingredients  are 
usually  designated  by  a  ratio,  such  as  1-1,  1-2,  1-3,  etc.  Thus,  1-2  signifies 
that  1  part  of  lime  or  cement  is  used  to  2  parts  of  sand,  etc.  For  great  accuracy 
these  measurements  should  be  made  by  weight,  but  they  are  usually  specified 
to  be  measured  by  volume. 

Lime  Mortars. — In  lime  mortar,  besides  effecting  an  economy,  the  presence 
of  sand  is  necessary  to  prevent  the  shrinkage  that  would  otherwise  occur  during 
the  hardening  of  the  paste. 

When  a  mortar  is  made  of  lime  and  sand,  enough  lime  should  be  present 
to  just  cover  completely  each  grain  of  sand.  An  excess  of  lime  over  this 
quantity  will  cause  the  mortar  to  shrink  excessively  on  drying,  while  a  deficiency 
of  lime  will  produce  a  weak  and  crumbly  mortar.  The  correct  quantity  of 
lime  depends  on  the  character  of  the  ingredients,  the  method  of  treatment 
and,  to  some  extent  on  the  judgment  of  the  builder.  The  mixtures  employed 
vary  from  1-2^  to  1-5.  Building  laws  in  many  municipalities  require  the  use  of 
a  1-3  mixture,  and  for  most  materials  this  proportion  will  be  found  satisfactory, 
although  for  rich,  fat  limes  a  l-3£  or  a  1-4  mixture  is  sometimes  preferable. 

In  mixing  lime  mortar,  a  bed  of  sand  is  made  in  a  mortar  box,  and  the 
lime  distributed  as  evenly  as  possible  over  it,  first  measuring  both  the  lime  and 
the  sand  in  order  that  the  proportions  specified  may  be  obtained.  The  lime  is 
then  slaked  by  pouring  on  water,  after  which  it  should  be  covered  with  a  layer 
of  sand,  or,  preferably,  a  tarpaulin,  to  retain  the  vapor  given  off  while  the  lime 
is  undergoing  the  chemical  reaction  of  slaking.  Additional  sand  is  then  used, 
if  necessary,  until  the  mortar  attains  the  proper  proportions. 

Care  should  be  taken  to  add  just  the  proper  quantity  of  water  to  slake  the 
lime  completely  to  a  paste.  If  too  much  water  is  used,  the  mortar  will  never 
attain  its  proper  strength,  while  if  too  little  is  used  at  first,  and  more  is  added 
during  the  process  of  slaking,  the  lime  will  have  a  tendency  to  chill,  thereby 
injuring  its  setting  and  hardening  properties.  Rather  than  make  up  small 
batches,  it  is  considered  better  practice  to  make  lime  mortar  in  large  quantities 
and  to  keep  it  standing  in  bulk  so  that  it  can  be  used  as  needed. 

Lime  mortar  is  employed  chiefly  for  brickwork  of  the  second  class,  and  its 
use  is  continually  decreasing  as  that  of  cement  increases.  It  is  absolutely 
unsuitable  for  any  important  construction,  because  it  possesses  neither  strength 
nor  the  property  of  resisting  water.  It  cannot  be  used  in  damp  or  wet  situ- 
ations, nor  should  it  ever  be  laid  in  cold  weather,  as  it  is  very  susceptible  to 
the  action  of  frost,  being  much  injured  thereby.  Moreover,  since  it  hardens 
by  the  action  of  dry  air,  only  the  exterior  of  lime  mortar  ever  becomes  fully 
hardened,  so  that  anything  like  a  concrete  with  lime  as  a  matrix  is  impossible. 
However,  for  second-class  brickwork,  such  as  is  commonly  used  in  the  walls  of 
smaller  buildings,  lime  mortars  are  economical  and  sufficiently  good. 

The  strength  of  lime  mortars  is  extremely  variable,  depending  on  the 
ingredients  themselves  and  on  their  treatment,  environment,  etc.  It  is  unsafe 
to  figure  a  lime-mortar  joint  as  possessing  much  strength,  since  only  a  part 
of  the  joint  is  hardened  and  capable  of  developing  any  strength  at  all.  The 
tensile  strength  of  thoroughly  hardened  1-3  lime  mortars  averages  from  40  to 
70  Ib.  per  sq.  in.,  and  the  compressive  strength  from  150  to  300  Ib. 

Cement  Mortars. — The  sand  for  all  mortars  should  be  clean,  of  suitable 
size  and  granulometric  composition.  For  structures  designed  to  withstand  • 
heavy  unit  stresses,  or  for  those  intended  to  resist  either  the  penetration  of 
moisture  or  the  actual  pressure  of  water,  the  selection  of  the  sand  should 
be  most  carefully  made.  A  simple  method  of  determining  the  best  sand  for 
cement  mortar  is  to  prepare  mixtures  of  the  cement,  sand,  and  water,  using 
the  same  quantities  in  each  case,  and  then  to  place  each  mixture  in  a  measure; 
that  mixture  giving  the  least  volume  of  mortar  may  be  considered  to  contain 
the  most  desirable  sand  for  use. 


192 


CONCRETE 


Limestone  screenings,  brick  dust,  crushed  cinders,  etc.,  are  sometimes 
substituted  for  sand  in  making  mortars,  and,  if  care  is  taken  in  their  selection, 
they  may  prove  economical  and  entirely  suitable  for  certain  purposes. 

The  theory  of  the  composition  of  a  correctly  proportioned  mortar  is  that  the 
cement  paste  will  just  a  little  more  than  fill  all  the  voids  between  the  particles 
of  sand,  thus  giving  an  absolutely  dense  mortar  at  the  least  expense.  The 
correct  proportion  of  cement  to  sand,  therefore,  is  more  or  less  variable,  depend- 
ing on  the  granulometric  composition  of  the  sand.  Since,  however,  Portland- 
cement  paste  that  has  set  weighs  nearly  as  much  as  sand,  and  since  the  average 
sand  contains  about  30  to  40%  of  voids,  it  is  evident  that  1-3  mixtures  most 
nearly  approach  the  best  and  most  economical  proportion. 

Mortars,  however,  are  made  in  proportions  varying  from  1-1  to  1-8.  The 
richer  mixtures  are  used  for  facing,  pointing,  waterproofing,  granolithic  mix- 
tures, etc.,  the  1-2  mixture  being  usually  made  for  such  purposes.  The 
leaner  mixtures  are  used  for.rough  work,  filling,  backing,  etc.,  but  should  never 
be  employed  where  either  much  strength  or  much  density  is  desired.  Natural- 
cement  mortars  are  commonly  made  1  part  of  sand  less  than  Portland-cement 
mortars  intended  for  the  same  purpose;  that  is,  where  a  1-3  Portland-cement 
mortar  would  be  used,  a  1-2  natural  mortar  would  be  required,  although 
natural-cement  mortars  should  be  decreased  by  about  2  parts  of  sand  to  equal 
the  strength  of  Portland.  In  other  words,  a  1-4  Portland  mortar  closely  equals 
the  strength  of  a  1-2  natural  mortar.  Puzzolan  cements  are  usually  propor- 
tioned the  same  as  Portlands. 

Cements  are  commonly  proportioned  by  volume,  the  unit  volume  of  the 
cement  barrel  being  assumed.  If  a  1-3  mortar  is  desired,  a  box  having  a 
capacity  of  10.8  cu.  ft.  is  filled  with  sand  and  mixed  with  4  bags  or  1  bbl.  of 
cement.  A  box  3  ft.  3^  in.  square  and  1  ft.  deep  will  have  a  capacity  of  very 
nearly  10.8  cu.  ft.  and,  besides,  makes  a  convenient  size  of  box  for  actual  work. 

For  general  purposes,  the  mortar  should  be  of  a  plastic  consistency — firm 
enough  to  stand  at  a  considerable  angle  yet  soft  enough  to  work  easily.  Wet 
mortars  are  easiest  to  work  and  are  the  strongest.  However,  they  are  subject 
to  greater  shrinkage,  are  slower  setting,  and  are  more  easily  attacked  by  frost. 
Dry  mortars,  on  the  other  hand,  are  often  friable  and  porous. 

In  the  accompanying  table  are  given  the  quantities  of  materials  required 
to  produce  1  cu.  yd.  of  compacted  mortar.  The  proportions  are  by  volume, 
a  cement  barrel  being  assumed  to  contain  3.6  cu.  ft.  Of  course,  the  exact  values 
vary  with  the  variety  of  sand,  etc.,  but  the  table  will  serve  as  an  approximation. 

MATERIALS  REQUIRED  PER  CUBIC  YARD  OF  MORTAR 


Kind  of  Mixture 

Portland  Cement 
Barrels 

Loose  Sand 
Cubic  Yards 

1-1 

4  95 

65 

1-2  

3  28 

88 

1-3. 

2  42 

1  01 

1-1  

1  99 

1  06 

1-5  

1  62 

1  11 

1-6... 

1  34 

1  15 

1-7  

1  18 

1  17 

1-8  

1  05 

1  18 

EXAMPLE.— How  much  cement  and  sand  will  be  required  to  obtain  8.5  cu. 
yd.  or  l-«i  Portland-cement  mortar? 

SOLUTION.— According  to  the  table,  1  cu.  yd,  of  a  1-3  Portland-cement 
mortar  requires  2.42  bbl.  of  cement;  therefore,  8.5  cu.  yd.  will  require  8.5 
X 2.42  =  20.57  bbl.  of  cement.  Also,  since  1  cu.  yd.  of  a  mixture  of  this  kind 
requires  1.01  cu.  yd.  of  sand,  the  quantity  of  sand  required  will  be  8.5X1.01 
=  8.59  cu.  yd. 

Mortar  that  is  to  be  mixed  by  hand  is  prepared  on  a  platform  or  in  a  mortar 
box.  The  sand  is  first  measured  by  means  of  a  bottomless  box  with  handles 
on  the  sides.  After  filling  the  box,  the  sand  is  struck  off  level,  the  box  lifted 
up,  and  the  sand  spread  in  a  low,  flat  pile.  The  required  number  of  bags  of 
cement  are  then  emptied  on  the  sand  and  spread  evenly  over  it.  The  pile  is 
then  mixed  with  shovels,  working  through  it  not  less  than  four  times.  After 


CONCRETE 


193 


this  operation,  the  dry  mixture  is  formed  into  a  ring,  or  crater,  and  the  water 
intended  to  be  used  is  poured  into  the  center.  The  material  from  the  sides  of 
the  basin  is  then  shoveled  into  the  center  until  the  water  is  entirely  absorbed, 
after  which  the  pile  is  worked  again  with  shovels  and  hoes  until  the  mixture  is 
uniform  and  in  a  plastic  condition. 

Another  method  of  mixing,  where  a  mortar  box  is  used,  is  to  gather  the 
mixed  dry  materials  at  one  end  of  the  box  and  pour  in  the  water  at  the  other 
end,  drawing  the  mixture  into  the  water  with  a  hoe,  a  little  at  a  time,  and 
hoeing  until  a  plastic  consistency  is  obtained. 

Properties  and  Uses  of  Ceirent  Mortars. — The  strength  of  a  mortar  is 
measured  by  its  resistance  to  tensile,  compressive,  cross-breaking,  and  shearing 
stresses,  and  also  by  determinations  of  its  adhesion  to  inert  surfaces,  its  resist- 
ance to  impact,  abrasion,  etc.  There  is  no  definitely  fixed  ratio  between  the 
strength  of  mortar  subjected  to  these  different  stresses,  but  there  is  nevertheless, 
a  close  relation  between  them,  so  that,  practically,  it  may  be  assumed  that  if  a 
mortar  shows  either  abnormally  high  or  low  values  in  any  one  test,  the  same 
relation  will  develop  when  tested  under  other  stresses.  In  practice,  therefore, 
the  strength  of  mortar  is  commonly  determined  through  its  resistance  to  tensile 
stresses,  and  its  resistance  to  other  forms  of  stress  is  computed  from  these 
results. 

TENSILE  STRENGTH  OF  CEMENT  MORTARS 


Proportions 

Age  of  Mortar 

7  da. 

28  da. 

3  mo. 

7  da. 

28  da. 

3  mo. 

Cement 
Parts 

Sand 
Parts 

Tensile  Strength,  in  Pounds  per  Square  Inch 

Portland  Cement 

Natural  Cement 

1 
1 

1 
1 
1 
1 
1 
1 

1 
2 
3 
4 
5 
6 
7 
8 

450 
280 
170 
125 
80 
50 
30 
20 

600 
380 
245 
180 
140 
115 
95 
70 

610 
395 
280 
220 
175 
145 
120 
100 

160 
115 
85 
60 
40 
25 
15 
10 

245 
175 
130 
100 
75 
60 
50 
45 

280 
215 
165 
'135 
110 
90 
75 
65 

The  tensile  strength  of  mortar  has  been  shown  to  vary  with  the  character 
of  its  ingredients,  with  its  consistency,  its  age,  and  with  many  other  factors. 
In  the  above  table  is  given  a  fair  average  of  the  tensile  strength  that  may  be 
expected  from  mortars  of  Portland  and  natural  cements  that  are  made  in  the 
field  and  with  a  sand  of  fair  quality  but  not  especially  prepared. 

The  strength  of  Portland-cement  mortar  increases  up  to  about  3  mo.; 
after  that  period,  it  remains  practically  constant  for  an  indefinite  time. 
Natural-cement  mortar,  on  the  other  hand,  continues  to  increase  in  strength 
for  2  or  3  yr.,  its  ultimate  strength  being  about  25%  in  excess  of  that  attained 
in  3  mo.  The  strength  of  slag-cement  mortar  averages  about  three-quarters 
of  that  of  Portland-cement  mortar. 

The  compressive  strength  of  cement  mortars  is  usually  given  in  textbooks 
as  being  from  eight  to  ten  times  the  tensile  strength.  This  value  is  rather 
high  for  the  average  mortar,  a  ratio  of  from  6  to  8  being  one  more  nearly 
realized  in  practice.  The  ratio  increases  with  the  age  and  richness  of  the 
mortar,  and  varies  considerably  with  the  quality  of  the  sand.  Portland- 
cement  mortars  of  1-3  mixture  that  are  3  mo.  old  develop,  on  an  average,  a 
compressive  strength  of  about  1,800  Ib.  per  sq,  in.,  while  1-2  natural-cement 
mortars  average  about  1,600  Ib. 

The  strength  of  mortars  in  cross-breaking  and  shear  may  be  taken  at  about 
'one  and  one-half  to  two  times  the  tensile  strength,  with  a  fair  amount  of  accu- 
racy. 


194  CONCRETE 

The  adhesion  of  mortars  to  inert  materials  varies  both  with  the  character 
of  the  mortar  and  with  the  roughness  and  porosity  of  the  surfaces  with  which 
they  are  in  contact.  The  adhesion  of  1-2  Portland-cement  mortar,  28  da.  old, 
to  sandstone  averages  about  100  Ib.  per  sq.  in.  ;  to  limestone,  75  Ib.  ;  to  brick, 
60  Ib.;  to  glass,  50  Ib.;  and  to  iron  or  steel,  75  to  125  Ib.  Natural-cement  mor- 
tars have  nearly  the  same  adhesive  strength  as  those  made  of  Portland  cement. 

In  bricklaying  and  in  other  places  in  which  mortar  is  employed  it  is  fre- 
quently desired  to  use  a  material  that  is  more  plastic  or  smooth  than  pure 
cement  mortar.  This  quality  is  usually  obtained  by  adding  from  10  to  25% 
of  lime  to  the  mortar.  This  addition  of  lime  not  only  renders  the  mortar  more 
plastic,  and  hence  easier  to  work,  but  also  increases  both  its  adhesive  strength 
and  its  density,  which  assists  in  making  the  mortar  waterproof.  Hydrated 
lime  is  to  be  preferred  for  use  in  cement  mortar,  because  its  complete  slaking  is 
assured.  Hydrated  lime  may  also  be  readily  handled  and  measured  on  the 
work. 

Occasionally,  small  quantities  of  cement  are  added  to  lime  mortars  so  as 
to  make  them  set  quicker  and  to  increase  their  strength.  Such  mixtures,  how- 
ever, are  not  especially  economical  nor  are  they  convenient  in  practice. 

Retempering  of  Mortar.  —  Mortar  composed  of  cement,  sand,  and  water 
soon  begins  to  set  and  finally  becomes  hard.  When  it  is  desired  to  use  this 
material,  more  water  has  to  be  added  and  the  mixture  worked  until  it  again 
becomes  plastic.  This  process  is  called  retempering.  Laboratory  tests  gen- 
erally show  that  retempering  slightly  increases  the  strength  of  mortar,  but  the 
reworking  is  more  thorough  as  a  rule  in  the  laboratory  than  would  be  the  case 
in  actual  work.  Any  part  of  the  hardened  mortar  that  is  not  retempered  is  a 
source  of  weakness  when  incorporated  in  the  building.  The  adhesive  strength 
of  cement,  moreover,  is  greatly  diminished  by  this  process.  For  these  reasons, 
it  is  generally  inadvisable  to  permit  the  use  of  retempered  mortars;  but  if  they 
are  allowed,  great  care  should  be  taken  to  see  that  the  second  working  is  thor- 
ough and  complete. 

Laying  Mortar  in  Freezing  Weather.  —  Frost,  or  even  cold,  has  a  tendency 
to  retard  greatly  the  set  of  cement  mortars.  When  the  temperature,  moreover, 
is  so  low  that  the  water  with  which  the  mortar  is  mixed  freezes  before  it  com- 
bines with  the  cement,  it  may,  if  care  is  not  exercised,  result  in  complete  destruc- 
tion of  the  work.  A  single  freezing  is  not  particularly  harmful,  because  when 
thawing  occurs,  the  arrested  chemical  action  continues.  A  succession  of  alter- 
nate freezings  and  thawings,  however,  is  extremely  injurious.  Nevertheless, 
Portland-cement  mortars  may  be  laid  even  under  the  worst  conditions  if  cer- 
tain precautions  are  observed,  but  mortars  of  natural  cement  should  never  be 
used  in  extremely  cold  weather,  as  they  are  generally  completely  ruined  by 
freezing. 

The  bad  results  that  arise  during  mild  frosts  may  be  successfully  guarded 
against  by  heating  the  sand  and  water  and  by  using  a  quick-setting  cement 
mixed  rich  and  as  dry  as  possible.  In  extremely  cold  weather,  salt  must  be 
added  to  the  water,  so  as  to  convert  it  into  a  brine  that  requires  a  temperature 
lower  than  32°  F.  to  freeze  it.  The  common  rule  for  adding  salt  is  to  use  a 
quantity  equal  to  1%  of  the  weight  of  the  water  for  each  degree  of  temperature 
that  is  expected  below  33°  F.  Thus,  at  32°  F.,  a  1%  solution  would  be  used, 
while  at  25°,  an  8%  solution  would  be  required.  Solutions  greater  than  12% 
should  not  be  employed,  and  if  a  temperature  below  20°  F.  is  expected,  heat 
must  be  used  in  addition  to  the  salt.  The  finished  work  should  also  be  pro- 
tected with  canvas  or  straw.  Manure  should  not  be  used  for  this  purpose, 
because  the  acids  it  contains  tend  to  rot  the  cement.  Unless  the  conditions  are 
such  as  to  make  it  imperative,  it  is  not  advisable  to  lay  mortars  during  freezing 
weather. 

Shrinkage  of  Mortars.—  Cement  mixtures  exposed  to  the  air  shrink  during 
the  process  of  hardening,  while  those  immersed  in  water  tend  to  expand.  The 
shrinkage  of  ordinary  cement  mortars  is  slight,  and  when  they  are  used  as  a 
bonding  material  it  need  not  be  considered.  When  used  as  a  monolith,  as  in 
sidewalks,  shrinkage  is  guarded  against  by  keeping  the  mortar  wet  during  set- 
ting. This  can  be  done  by  covering  with  moist  straw  or  by  sprinkling  the 
mixture  with  water. 


•  -  —  By  grouting  is  meant  the  process  of  filling  spaces  in  masonry 

with  a  thin,  semifluid  mixture  known  as  grout.  This  mixture  consists  of  cement, 
1  or  2  parts  of  sand,  and  an  excess  of  water.  Grout  can  be  used  for  filling  the 
voids  in  walls  of  rubble  masonry  for  backing  arches  and  tunnels,  for  filling  the 
joints  between  paving  brick,  and  in  all  places  where  mortar  cannot  be  laid  in 
the  ordinary  manner.  When  hardened,  grout  is  weak,  friable,  and  porous. 


CONCRETE  195 


CEMENT  TESTING 

FIELD  INSPECTION  AND  SAMPLING 

When  cement  is  mentioned  anywhere  in  the  following  pages,  Portland  cement, 
is  meant,  as  this  is  by  far  the  most  important  cement. 

In  order  to  determine  correctly  the  structural  value  of  a  shipment  of  cement, 
an  examination  in  the  field  is  very  necessary.  A  number  of  packages  of  cement 
should  be  weighed  at  intervals,  and  the  average  weight  should  never  be  per- 
mitted to  fall  below  94  Ib.  per  bag,  as  mortar  and  concrete  are  usually  propor- 
tioned on  the  assumption  of  this  weight.  Each  package  should  also  be  plainly 
marked  with  the  brand  and  name  of  the  manufacturer;  those  not  branded 
should  be  discarded,  and,  if  possible,  a  mixture  of  different  brands  should  be 
avoided. 

A  possible  indication  of  inferiority  is  the  presence  of  lumps  throughout  the 
bulk  of  the  material.  On  standing,  cement  gradually  absorbs  moisture  from  the 
air.  At  first  this  moisture  is  present  in  merely  a  minute  and  harmless  state, 
but  eventually  it  combines  chemically  with  the  cement;  that  is,  in  the  same 
manner  as  when  cement  and  water  are  actually  mixed  together  in  practice. 
In  the  first  condition,  lumps  usually  appear,  but  they  are  so  soft  that  they  may 
be  readily  crushed  with  the  fingers,  and  of  course  would  be  entirely  broken  up 
when  mixed  into  mortar.  When,  however,  the  cement  contains  lumps  that  are 
hard  and  pebble-like  and  that  can  be  crushed  only  with  considerable  effort,  it 
indicates  that  chemical  action  has  begun.  Cement  containing  any  appreciable 
amount  of  these  hardened  lumps  is  generally  of  decidedly  inferior  quality,  and 
it  should  never  be  permitted  to  enter  any  important  part  of  a  structure. 

Storing  cement  too  long  will  tend  to  weaken  it.  Cement  from  2  to  6  mo.  old 
is  usually  the  safest  and  will  produce  the  best  results. 

The  color  of  Portland  cement,  ranging  from  bluish  to  yellowish  gray,  affords 
no  indication  of  quality  except  in  cases  where  different  shipments  or  different 
parts  of  the  same  shipment  show  a  variation  in  color,  thus  pointing  to  a  lack  of 
uniformity. 

Sampling. — When  securing  a  sample  for  testing,  the  essential  point  is  to  get 
one  that  will  fairly  represent  the  entire  shipment  whose  qualities  are  to  be 
determined.  The  common  practice  is  to  take  a  small  portion  of  material  from 
every  tenth  barrel  or,  what  is  the  same  thing,  from  every  fortieth  bag.  When 
tests  are  to  be  made,  however,  on  a  shipment  of  only  a  few  barrels,  more 
packages  than  one  in  ten  should  be  opened;  and  when  the  shipment  is  large, 
say  over  150  bbl.,  it  should  be  subdivided  and  each  portion  tested  separately. 
The  bags  selected  should  be  taken  at  random  and  from  different  layers  and  not 
all  from  one  part  of  the  pile. 

The  cement,  moreover,  should  be  taken  not  only  from  the  top  of  the  pack- 
ages, but  from  the  center  and  sides  as  well.  When  the  cement  is  contained  in 
barrels,  a  sampling  auger  is  used  to  extract  the  sample,  a  hole  being  bored  in  the 
staves  midway  between  the  heads.  After  the  samples  of  cement  have  been 
taken  from  the  packages  they  are  thoroughly  mixed  in  a  can  or  basin,  and  this 
mixed  sample  is  used  for  the  various  tests.  To  make  a  complete  series  of  tests, 
the  sample  should  contain  from  6  to  8  Ib.  The  cement,  after  sampling  and 
before  testing,  must  be  well  protected,  as  exposure  to  heat,  cold,  dampness, 
or  any  other  abnormal  condition  may  seriously  affect  the  results. 

Purpose  and  Classification  of  Tests. — In  order  that  a  mortar  or  a  con- 
crete made  with  cement  shall  give  good  results  in  actual  construction,  it  must 
possess  two  important  properties,  namely,  strength  and  durability.  The  primary 
purpose  of  cement  testing,  therefore,  is  to  determine  whether  any  particular 
shipment  of  cement  possesses  sufficient  strength  and  durability  to  admit  of  its 
use  in  construction. 

A  determination  of  the  quality  of  cement  necessitates  the  employment  of 
several  tests,  which  may  be  classified  as  primary  tests  and  secondary  tests.  The 
former  tests,  which  include  tests  for  soundness  and  tensile  strength,  are  made  to 
give  directly  a  measure  of  the  essential  qualities  of  strength  and  durability. 
Unfortunately,  neither  of  these  tests  is  capable  of  being  made  with  precision. 
Therefore,  the  secondary  tests,  which  include  tests  to  determine  the  time  of 
setting,  the  fineness,  the  specific  gravity,  and  the  chemical  analysis,  are  made 
to  obtain  additional  information  in  regard  to  the  character  of  the  material. 
However,  with  the  possible  exception  of  the  test  of  time  of  setting,  the  secondary 
tests  have  but  little  importance  and  only  indicate  by  their  results  indirectly  the 
properties  of  the  material. 


196 


CONCRETE 


PRIMARY  TESTS 

Tests  for  Soundness. — The  property  of  cement  that  tends  to  withstand 
any  forces  that  may  operate  to  destroy  or  disintegrate  it  is  known  as  soundness. 
This  property,  which  is  sometimes  called  constancy  of  volume,  is  the  most  impor- 
tant requisite  of  a  good  cement. 

The  most  common  cause  of  unsoundness  in  Portland  cement  is  an  excess 
of  free  or  uncombined  lime,  which  crystallizes  with  great  increase  of  volume, 


and  thus  breaks  and  destroys  the  bond  of  the  cement.  This  excess  of  lime 
may  be  due  to  incorrect  proportioning  or  to  insufficient  grinding  of  the  raw 
materials,  to  underburning,  or  to  lack  of  sufficient  storing  before  use,  called 
seasoning.  A  certain  amount  of  seasoning  is  usually  necessary,  because  almost 
every  cement,  no  matter  how  well  proportioned  or  burned  it  may  be,  will  con- 
tain a  small  amount  of  this  excess  of  lime,  which,  on  standing,  will  absorb  mois- 
ture from  the  air,  slake,  and  become  inert. 

Excess  of  magnesia  or  the  alkalies  may  also  cause  unsoundness,  but  the 
ordinary  cement  rarely  contains  a  sufficient  amount  of  these  ingredients  to  be 
harmful.  Sulphate  of  lime  is  occasionally  responsi- 
ble for  unsoundness,  but  this  ingredient  usually  acts 
in  the  opposite  direction,  tending  to  make  sound 
a  cement  that  otherwise  might  disintegrate. 

The  property  of  soundness  is  determined  in  one 
or  more  of  three  ways:  by  measurements  of  expan- 
sion, by  normal  tests,  and  by  accelerated  tests. 

Measurements  of  expansion  are  made  by  form- 
ing specimens  of  cement,  usually  in  the  shape  of 
prisms,  and  measuring  the  change  in  volume  by 
means  of  a  micrometer  screw.  At  the  present  time, 
however,  it  is  believed  that  expansion  is  not  a  sure 
index  of  unsoundness,  so  that  this  test  is  seldom 
/«»  employed. 

„       „  Normal  tests  consist  in  making  specimens   of 

•^IG-  *  cement  mixed  with  water,  preserving  them  in  air 

or  in  water  under  normal  conditions,  and  observing  their  behavior.  The  com- 
mon practice  is  to  make  on  glass  plates  about  4  in.  square,  from  a  paste  of  neat 
or  pure  cement,  two  circular  pats  about  3  in.  in  diameter,  |  in.  thick  at  the 
center,  and  tapering  to  a  thin  edge.  These  pats  are  kept  in  moist  air  for  24  hr. ; 
then  one  of  them  is  placed  in  fresh  water  of  ordinary  temperature  and  the  other 


CONCRETE 


197 


is  preserved  in  air.     The  condition  of  the  pats  is  observed  7  da.  and  28  da. 
from  the  date  of  making,  and  thereafter  at  such  times  as  may  be  desired. 

The  most  characteristic  forms  of  failure  are  illustrated  in  Figs.  1  and  2. 
Fig.  1  (a)  shows  a  pat  in  good  condition.  View  (b)  illustrates  shrinkage  cracks 
that  are  due,  not  to  inferior  cement,  but  to  the  fact  that  the  pat  has  been 
allowed  to  dry  out  too  quickly  after  being  made.  Pats  must  be  kept  in  a  moist 
atmosphere  while  hardening,  or  these  cracks,  indicative  merely  of  careless 
manipulation,  will  develop.  View  (c)  shows  cracks  that  are  due  to  the  expan- 
sion of  the  cement;  this  condition  is  common  in  the  air  pats,  and  is  not  indi- 
cative of  injurious  properties.  Pats  kept  in  water,  however,  should  not  show 
these  cracks.  View  (d)  shows  cracking  of  the  glass  plate  to  which  the  pat  is 
attached;  this  cracking  is  caused  by  expansion  or  contraction  of  the  cement, 
combined  with  strong  adhesion  to  the  glass;  it  rarely  indicates  injurious  prop- 
erties. View  (e)  illustrates  blotching  of  the  i»ts,  the  cause  of  which  should 
always  be  investigated  by  chemical  analysis  or  otherwise,  which  may  or  may  not 
warrant  the  rejection  of  the  material.  Slag  cements  or  cements  adulterated 
with  slag  invariably  show  this  blotching.  View  (/)  shows  the  radial  cracks 
that  mark  the  first  stages  of  disintegration;  such  cracks  should  never  occur 
with  good  material.  They  are  signs  of  real  failure,  and  cement  showing  them 
should  never  be  used. 

Fig.  2  shows  three  pats  that,  for  different  reasons,  have  left  the  glass  plate 
on  which  they  were  made.  The  disk  shown  in  (a)  left  the  plate  because  of  lack 
of  adhesion;  the  one  in  (6),  through  contraction;  and  the  one 
in  (c),  through  expansion.  The  condition  illustrated  in  (a)  is 
never  dangerous  in  either  air  or  water;  that  in  (c)  is  only  dan- 
gerous when  existing  in  a  marked  degree;  and  that  in  (b)  hardly 
ever  occurs  in  water,  but  in  air  it  often  indicates  dangerous 
properties.  Air  pats  that  develop  the  curvature  shown  in  (b) 
generally  disintegrate  later.  A  curvature  of  about  f  in.  in  a 
3-in.  pat  can  be  considered  to  be  about  the  limit  of  safety. 

The  normal  pat  tests  are  the  only  absolutely  fair  and  ac- 
curate methods  of  testing  cements  for  soundness,  but  the 
serious  objection  to  them  lies  in  the  fact  that  frequently  several 
months  or  even  years  elapse  before  failure  in  the  cement  so 
tested  becomes  apparent.     To  overcome  this  difficulty  the 
accelerated  tests  have  been  de- 
vised.   These  tests  are  intended 
to  produce  in  a  few  hours  results 
that  require  months  in  the  nor- 
mal tests. 

Many  forms  of  accelerated 
tests   have   been   devised.     At 
present,  however,  the  only  tests 
employed  commercially  are  the 
boiling  test  and  the  steam  test. 
The  boiling  test  is  made  by 
forming    specimens     of     neat- 
cement  paste  into  pats,  such  as  are  employed  for  the  normal  tests,  or  prefer- 
ably into  balls  about  1?  in.  in  diameter.     The  specimens  are  allowed  to  remain 
in  moist  air  for  24  hr.  and  are  then  tested. 

The  form  of  the  apparatus  used  for  the  boiling  test  is  shown  in  Fig.  3.  It 
consists  of  a  copper  tank  that  is  heated  by  a  Bunsen  burner  and  is  filled  with 
water.  The  water  in  the  tank  is  kept  at  a  uniform  height  by  means  of  a  con- 
stant-level bottle.  A  wire  screen  placed  an  inch  from  the  bottom  of  the  tank 
prevents  the  specimens  from  coming  into  contact  with  the  heated  bottom.  The 
test  pieces,  which  are  24  hr.  old,  are  placed  in  the  apparatus,  which  is  filled  with 
water  of  a  normal  temperature,  and  heat  is  applied  at  a  rate  such  that  the  water 
will  come  to  boiling  in  about  i  hr.  Quiet  boiling  is  continued  for  3  hr.,  after 
which  the  specimens  are  removed  and  examined.  Care  must  be  taken  that  the 
water  employed  is  clean  and  fresh,  because  impure  water  may  seriously  affect 
the  results.  The  same  water,  also,  should  never  be  used  for  more  than  one  test. 
A  good  cement  will  not  be  affected  by  this  treatment,  and  the  ball  will  remain 
firm  and  hard.  Inferior  cement  will  fail  by  checking,  cracking,  or  entirely 
disintegrating. 

The  steam  test  is  made  in  the  same  way  as  the  boiling  test,  except  that 
instead  of  immersing  the  specimens  in  water,  they  are  kept  in  the  steam  above 
the  water.  The  apparatus  employed  is  the  same  as  that  used  for  the  boiling 


198  CONCRETE 

test.  The  wire  screen,  however,  is  raised  so  that  it  is  an  inch  above  the  sur- 
face of  the  water;  also,  there  must  be  provided  a  cover  that  is  close  enough  to 
retain  the  steam  without  creating  pressure.  The  steam  test  is  less  severe  than 
the  boiling  test  and  is  somewhat  less  accurate. 

The  result  of  the  normal  tests,  if  properly  made  and  interpreted,  may  be 
considered  reliable  guides  to  the  soundness  of  the  material,  and  cement  failing 
in  these  tests  should  always  be  rejected.  The  accelerated  tests,  on  the  other 
hand,  merely  furnish  indications,  and  are  by  no  means  infallible.  A  cement 
passing  the  boiling  test  can  generally  be  assumed  sound  and  safe  for  use,  but, 
if  failure  occurs,  it  simply  means  that  other  tests  should  be  performed  with 
greater  care  and  watchfulness.  It  often  is  advisable  to  hold  for  a  few  weeks 
cement  that  fails  in  boiling,  so  that  the  expansive  elements  may  have  an  oppor- 
tunity to  hydrate  and  become  inert;  but  if  the  material  fulfils  all  the  conditions 
except  the  boiling  test,  and  is  sound  in  the  normal  tests  up  to  28  da.,  it  is  gen- 
erally safe  f9r  use.  All  things  being  equal,  however,  a  cement  that  will  pass  the 
boiling  test  is  to  be  preferred. 

Tests  for  Tensile  Strength. — The  tensile-strength  test  is  for  the  purpose 
of  ascertaining  a  measure  of  the  ability  of  the  material  to  withstand  the  loads 
that  the  structure  must  carry.  This  test  is  made  by  forming  specimens,  called 
briquets,  of  cement  and  cement  mortar,  and  determining  the  force  necessary  to 
rupture  them  in  tension  at  the  expiration  of  fixed  intervals  of  time.  Cement 
constructions  are  rarely  called  on  to  withstand  tensile  stresses,  but  if  the  tensile 
strength  is  known,  the  resistance  to  other  forms  of  stress  may  be  computed  with 
a  fair  degree  of  accuracy.  The  tensile-strength  test  is  the  most  convenient  for 
laboratory  determinations,  on  account  of  the  small  size  of  the  specimens  and  the 
comparatively  low  stress  required  to  cause  rupture. 

Cement  is  tested  both  neat  or  pure  and  in  a  mortar  commonly  composed  of 
1  part  of  cement  and  3  parts  of  sand.  The  periods  at  which  the  briquets  are 
broken  have  been  fixed  by  usage  at  7  da.  and  28  da.  after  making,  although 
tests  covering  much  longer  periods  of  time  are  necessary  in  research  or  in  inves- 
tigative work. 

The  strength  of  cement  and  cement  mortars  varies  considerably  with  the 
amount  of  water  employed  in  making  the  briquets.  Dry  mixtures  ordinarily 
give  the  higher  results  for  short-time  tests,  and  wet  mixtures  show  stronger  with 
a  greater  lapse  of  time.  For  testing  purposes,  therefore,  it  is  essential  that 
all  cements  be  mixed,  not  with  the  same  amount  of  water,  but  with  the 
amount  that  will  bring  all  the  cements  to  the  same  physical  condition,  or  to 
what  is  called  normal  consistency.  Different  cements  require  different  per- 
centages of  water  because  of  their  varying  chemical  composition,  degree  of 
burning,  age,  fineness,  etc, 

The  normal  consistency  of  neat-cement  pastes  may  be  determined  by  either 
of  the  methods  that  follow.  In  these  tests,  the  quantities  are  given  in  grams. 

The  first  method  is  taken  from  that  part  of  the  final  report  of  the  Special 
Committee  on  Uniform  Tests  of  Cement  of  the  American  Society  of  Civil 
Engineers  which  may  be  found  on  pp.  679  to  684,  inclusive,  of  Vol.  LXXV,  Dec., 
1912,  of  the  Transactions  of  that  Society.  In  this  method  that  quantity  of 
cement  that  it  is  proposed  to  use  subsequently  in  each  batch  for  making  test 
pieces  should  be  weighed,  but  in  no  case  should  less  than  500  grams  be  taken. 
The  amount  is  placed  on  a  non-absorbent  mixing  slab  in  the  form  of  a  crater, 
and  a  definite  amount  of  water  poured  into  the  center.  The  cement  is  turned 
over  from  the  sides  into  the  center  with  a  trowel  until  the  water  is  absorbed. 
It  is  then  kneaded  vigorously  for  1  min.  and  quickly  formed  into  a  ball  and 
tossed  six  times  from  one  hand  to  the  other  maintained  6  in.  apart.  During  the 
operation  of  kneading  and  making  the  ball  the  hands  should  be  protected  by 
rubber  gloves.  The  ball  of  cement  on  the  palm  of  the  hand  is  then  pressed  into 
the  large  end  of  the  hard-rubber  ring  of  the  Vicat  apparatus  in  such  a  way  that 
the  ring  is  completely  filled  with  paste.  A  Vicat  apparatus  working  on  the 
same  principle  as  the  one  illustrated  in  the  Society's  report  and  with  the  same 
weight  of  movable  rod  and  the  same  principal  dimensions  is  described  in  connec- 
tion with  Tests  for  Times  of  Setting.  The  excess  paste  at  the  large  end  of  the 
ring  is  removed  with  one  movement  of  the  palm  of  the  hand,  the  ring  is  placed 
large  end  down  on  the  plate  under  the  movable  rod,  and  the  excess  paste  on  the 
top  is  sliced  off  with  a  trowel  held  at  an  angle.  The  paste  must  not  be  com- 
pressed. The  plunger  is  brought  into  contact  with  the  surface  of  the  material, 
quickly  released,  and  its  penetration  noted.  The  penetration  should  be 
exactly  10  millimeters  in  $  min.;  if  the  test  shows  a  greater  or  less  amount, 
other  trials  must  be  made,  using  more  or  less  water,  until  the  correct  consist- 
ency is  obtained. 


CONCRETE 


199 


The  other  method  is  to  form  of  the  paste  a  ball  about  2  in.  in  diameter  and 
to  drop  this  ball  on  a  table  from  a  height  of  about  2  ft.  If  the  cement  is  of  the 
correct  consistency,  the  ball  will  not  crack  nor  will  it  flatten  to  less  than  one- 
half  its  original  thickness.  The  percentage  of  water  required  will  vary  from 
16  to  25,  depending  on  the  characteristics  of  the  material,  the  average  cement 
taking  about  20%. 

The  consistency  of  sand  mortars,  however,  cannot  be  obtained  by  either  of 
the  foregoing  methods,  because  the  sand  grains  do  not  permit  of  the  measure- 
ment of  the  consistency  by  penetration,  and  the  mixture  is  too  incoherent  for 
use  of  the  ball  method. 

The  accompanying  table  gives  the  amount  of  water  required  to  make  mor- 
tar of  normal  consistency  and  is  given  in  the  report  of  the  committee  just 
referred  to  above.  It  is  for  a  mortar  consisting  of  1  part  of  cement  and 
3  parts  of  Standard  Ottawa  Sand.  The  amount  of  water  is  given  as  a  percent- 
age of  the  combined  weight  of  the  cement  and  sand.  Each  percentage  corre- 
sponds with  the  water  required  for  a  normal  consistency  with  the  neat  cement 
formed  by  the  method  recommended  by  the  Committee. 

PERCENTAGE  OF  WATER  FOR  STANDARD  SAND  MORTAR 


Water  in 

Water  in 

Water  in 

Water  in 

Water  in 

Water  in 

Neat 

Standard 

Neat 

Standard 

Neat 

Standard 

Cement 

Mortar 

Cement 

Mortar 

Cement 

Mortar 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

15 

8.0 

23 

9.3 

31 

10.7 

16 

8.2 

24 

9.5 

32 

10.8 

17 

8.3 

25 

9.7 

33 

11.0 

18 

8.5 

26 

9.8 

34 

11.2 

19 

8.7 

27 

10.0 

35 

11.3 

20 

8.8 

28 

10.2 

36 

11.5 

21 

9.0 

29 

10.3 

37 

11.7 

22 

9.2 

30 

10.5 

38 

11.8 

The  following  formula  has  been  devised  to  give  the  normal  consistency  to 
any  mortar  with  any  sand.  It  will  be  noted  that  the  values  derived  by  the 
formula  differ  somewhat  from  those  given  in  the  table. 

Let   x  =  per  cent,  of  water  required  for  sand  mixture; 

2V  =  per  cent,  of  water  required  to  bring  neat  cement  to  normal  con- 
sistency; 

n  =  parts  of  sand  to  one  of  cement; 
S  =  constant  depending  on  character  of  sand. 

_.  3JV+5n+l 

Then'  *  =  ^(^+Tr 

For  crushed-quartz  sand,  the  constant  5  is  30;  for  Ottawa  sand,  it  becomes 
25;  and  for  the  bar  and  bank  sands  used  in  construction,  it  varies  from  25  to  35, 
and  must  be  determined  for  each  particular  sand. 

EXAMPLE. — How  much  water  is  required  in  a  mixture  of  1  part  of  cement 
and  3  parts  of  crushed-quartz  sand?  The  neat  cement  requires  19%  of  water 
to  give  normal  consistency. 

SOLUTION. — Here,  N  =  19,  5  =  30,  and  «  =  3.  Substituting  these  values  in 
the  formula,  _ 3X19+30X3  +  1  _ 0  ~~ 

4XC3  +  1) 

Sand  for  Mortar  Tests. — The  size,  gradation,  and  shape  of  the  particles  of 
sand  with  which  cement  mortars  are  made  have  great  influence  on  the  resulting 
strength.  There  are  two  varieties  of  standard  sand  for  cement  testing,  one  an 
artificial  sand  of  crushed  quartz,  the  particles  of  which  are  angular  in  shape, 
and  the  other  a  natural  sand  from  Ottawa,  Illinois,  the  particles  of  which  are 
almost  spherical.  Both  sands  are  sifted  to  a  size  that  will  pass  a  sieve  of  20 
meshes  to  the  inch  and  be  retained  on  a  sieve  of  30  meshes,  the  diameters  of 
the  sieve  wires  being  .0165  and  .0112  in.,  respectively.  The  Ottawa  sand  will 
develop  strengths  in  1-3  mortars  about  20  to  30%  greater  than  those  obtained 
with  crushed  quartz,  and  it  is  theoretically  the  better  sand  for  testing.  On 
most  important  works,  tests  for  purposes  of  comparison  are  also  made  of  the 
actual  sand  entering  the  construction. 


200 


CONCRETE 


Briquets. — The  form  of  tensile  briquet,  adopted  as  standard  in  the  United 
States,  is  shown  in  the  accompanying  figure;  its  cross-section  is  exactly  1  sq.  in. 
These  briquets  are  made  in  molds  that  come  either  single  or  in  gangs  of  three, 
four,  or  five.  The  gang  molds  are  preferable,  as  they  tend  to  produce  greater 
uniformity  in  the  results.  Molds  should  be  made  of  brass  or  of  some  other 
non-corrodible  material;  those  made  of  cast  iron  soon  rust  and  become  unfit 
for  use. 

When  making  the  briquets,  1,000  g.  of  cement  is  carefully  weighed  and 
placed  on  the  mixing  table  in  the  form  of  a  crater,  and  into  the  center  of  this 
is  poured  the  amount  of  water  that  is  necessary 
to  give  the  correct  normal  consistency.  Cement 
from  the  sides  of  the  crater  is  then  turned  into 
the  center,  by  means  of  a  trowel,  until  all  the 
water  is  absorbed,  after  which  the  mass  is  vigor- 
ously worked  with  the  hands,  as  dough  is  kneaded, 
for  1$  min.  When  sand  mixtures  are  being 
tested,  250  g.  of  cement  and  750  g.  of  sand  are 
first  weighed  and  thoroughly  mixed  dry  until  the 
color  of  the  pile  is  uniform;  then  the  water  is 

r~i 1— — — i ; —   added  and  the  operation  is  completed  by  vigorous 
/                     V          *»       kneading. 
/                      \  After  kneading,  the  material  is  immediately 

placed  into  the  molds,  which  should  have  been 
wiped  with  oil  to  prevent  the  cement  from  stick- 
ing to  them.  The  entire  mold  is  filled  with  ma- 
terial at  once  —  not  compacted  in  layers — and 
pressed  in  firmly  with  the  fingers  without  any 
ramming  or  pounding.  An  excess  of  material  is 
then  placed  on  the  mold  and  a  trowel  drawn  over 
it  under  moderate  pressure,  at  each  stroke  cut- 
ting off  more  and  more  of  the  excess  material,  until  the  surface  of  the  briquets 
is  smooth  and  even.  The  mold  is  then  turned  over,  and  more  material  placed 
in  it  and  smoothed,  as  before.  The  mixing  and  molding  should  be  performed 
on  a  surface  of  slate,  glass,  or  some  other  smooth,  non-absorbent  material. 
During  the  mixing  the  operator  should  wear  rubber  gloves,  so  as  to  protect 
his  hands  from  the  action  of  the  lime  in  the  cement. 

For  24  hr.  after  making,  the  briquets  are  stored  in  a  damp  closet  so  that 
the  cement  can  harden  in  a  moist  atmosphere.  The  damp  closet  is  simply  a 
tight  box  of  soapstone  with  doors  of  wood  lined  with  zinc,  or  some  similar 
arrangement,  with  a  receptacle  for  water  at  the  bottom  and  racks  for  holding 
the  briquets.  The  briquets  remain  in  the  molds  while  in  the  damp  closet, 
but  at  the  expiration  of  24  h,  they  are  removed,  marked,  and  placed  in  clean 
water  near  70°  F.  until  broken. 

Testing  Machines. — There  are  many  styles  of  testing  machines  on  the 
market;  that  shown  is  called  a  shot  machine  and  is  made  by  the  Fairbanks 
Company.  It  is  constructed  on  the  cast-iron  frame  a,  and  is  operated  as 
follows:  The  cup  /  is  hung  on  the  end  of  the  beam  d,  the  poise  r  placed  at 
the  zero  mark,  and  the  beam  balanced  by  turning  the  weight  /.  The  hopper  b 
is  then  filled  with  fine  shot,  and  the  briquet  to  be  tested  is  placed  in  the 
clips  h.  The  hand-wheel  p  is  now  tightened  sufficiently  to  cause  the  gradu- 
ated beam  d  to  rise  until  the  indicators  at  k  are  in  line.  In  the  case  is  a  ten- 
sion arrangement  containing  a  worm  and  worm-gear  that  is  connected  to  an 
axis  that  is  threaded  and  passes  up  through  the  hand  wheel  p  and  into  a  block 
connected  to  the  lower  clip.  A  knob  in  the  case  engages  this  gear  when  it  is 
required.  After  the  hand-wheel  p  has  been  tightened  until  the  indicators  are 
in  line,  the  worm  is  engaged  and  the  automatic  valve  j  is  opened  so  as  to 
allow  the  shot  to  run  into  the  cup  /.  The  flow  of  the  shot  can  be  regulated  by 
means  of  a  small  valve  located  where  the  spout  joins  the  reservoir.  As  the 
briquet  stretches,  the  beam  is  kept  stationary  by  applying  tension  to  the 
briquet  by  means  of  the  hand  wheel  5.  When  the  briquet  breaks,  the  beam  d 
drops  and  by  means  of  the  lever  i  automatically  closes  the  valve  j.  After 
the  specimen  has  broken,  the  cup  with  its  contents  is  removed,  and  the 
counterpoise  g  is  hung  in  its  place.  The  cup  /  is  then  hung  on  the  hook 
under  the  large  ball  e,  and  the  shot  weighed.  The  weighing  is  done  by  using 
the  poise  r  on  the  graduated  beam  d  and  the  weights  n  on  the  counterpoise  g. 
The  result  will  show  the  number  of  pounds  required  to  break  the  specimen. 
A  mold  for  a  single  briquet  is  shown  at  c. 


CONCRETE 


201 


The  load  should  be  applied  in  all  tests  at  the  uniform  rate  of  600  Ib.  per 
min.  The  briquets  should  be  broken  as  soon  as  they  are  removed  from  the 
storage  tanks  and  while 
they  are  still  wet,  because 
drying  out  tends  to  lower 
their  strength.  The  aver- 
age of  from  three  to  five 
briquets  should  be  taken 
as  the  result  of  a  test. 

Results  of  Tensile- 
Strength  Tests.— The  ten- 
sile strength  of  briquets 
tested  in  the  preceding  man- 
ner should  increase  with  age 
up  to  about  3  mo.,  and 
should  then  remain  practi- 
cally stationary  for  longer 
periods.  The  average  re- 
sults of  tests  of  Portland 
cement  made  in  the  Phila- 
delphia laboratories,  cover- 
ing aperiod  of  several 
years  and  based  on  over 
200,000  briquets,  are  given 
in  the  accompanying  table. 
Specifications  for  strength 
commonly  stipulate  mini- 
mum values  for  the  7-  and 
28-da.  tests,  the  customary 
requirements  for  Portland 
cement  being  500  Ib.  at  7 
da.  and  600  Ib.  at  28  da., 
when  tested  neat,  and  170 
Ib.  at  7  da.  and  240  Ib.  at 
28  da.,  when  tested  in  a 
mortar  consisting  of  1  part 
of  cement  and  3  parts  of 
crushed-quartz  sand.  When 
Ottawa  sand  is  used,  the 
requirements  for  mortar 
should  be  raised  to  200  and 
280  Ib.,  respectively.  Re- 
trogression in  strength  in 
the  periods  specified  is  not  often  allowed.  Although  this  retrogression  in  neat 
briquets  between  7  and  28  da.  is  not  necessarily  indicative  of  undesirable 

TENSILE  STRENGTH  OF  CEMENT  BRIQUETS 


J 

1 

| 

| 

ntS  8 

fcjS  S 

w,  £    u 

.jj+j  8 

«<fe  3 

*^>    3 

<J>   3 

<>    3 

Mixture 

•S.Sw 

•s^ 

•SficH* 

•Scc^ 

E£    Q, 

Q  as  a 

°P      M 

Qg  P. 

"*1 

"«1 
o 

"Sl 

"sl 

£ 

Neat 

420 

710 

770 

775 

1  cement, 
1  cement, 

1  crushed-quartz  sand  
2  crushed-quartz  sand  

360 
210 
105 

590 
370 
210 

695 
455 
300 

700 
465 
310 

1  cement, 

4  crushed-quartz  sand  

60 
35 

130 
80 

210 
155 

230 
195 

202 


CONCRETE 


properties  according  to  some  authorities,  yet  if  the  mortar  briquets  show 
retrogression,  the  cement  should  be  condemned.  Abnormally  high  strength 
in  the  7-da.  test  of  neat  cement,  say  over  900  lb.,  may  generally  be  taken  as  an 
indication  of  weakness  rather  than  of  superiority,  because  such  a  condition 
is  usually  created  by  an  excess  of  lime  or  of  sulphates,  either  of  which  may  be 
injurious.  Neat  cement  testing  from  600  to  800  lb.,  at  7  da.  is  generally  the 
most  desirable. 

SECONDARY  TESTS 

Tests  for  Time  of  Setting. — The  time-of-setting  test  is  made  to  determine 
whether  or  not  the  cement  will  become  hard  at  the  time  most  desirable  in  actual 
construction.  If  it  begins  to  set  too  soon,  the  crystallization  of  the  particles 
will  have  begun  before  the  mortar  or  concrete  is  thoroughly  tamped  into  place. 
If,  on  the  other  hand,  the  cement  sets  too  slowly  the  material  is  more  likely  to 
suffer  from  exposure  to  heat,  cold,  dampness,  and  frost;  also,  the  progress  of 
the  work  will  be  much  delayed  on  account  of  the  greater  interval  required 
between  different  sections,  and  the  longer  time  the  forms  must  be  left  up. 

In  the  setting  of  cements,  two  stages  are  recognized:  When  the  paste  begins 
to  harden  or  to  offer  resistance  to  change  of  form,  called  initial  set;  and  when 
the  setting  is  complete,  or  when  the  mass  cannot  be  appreciably  distorted 
without  rupture,  called  hard  set.  The  time-of-setting  test  consists,  therefore, 
in  determining  the  time  required  for  the  cement  to  reach  these  two  critical 
points. 

The  test  is  made  by  mixing  cement  with  the  amount  of  water  required  to 
produce  normal  consistency,  in  the  same  manner  as  for  neat  tensile  briquets, 
forming  specimens,  placing  them  under  one  of 
the  forms  of  apparatus,  and  observing  the  time 
that  elapses  between  the  moment  the  mixing 
water  is  added  and  the  moments  when  the  paste 
acquires  initial  set  and  hard  set. 

The  Vicat  needle,  shown  in  Fig.  1,  consists 
of  a  frame  k,  holding  a  movable  rod  /,  which 
carries  a  cap  d  at  the  upper  end  and  a  needle  h 
at  the  lower.  A  screw  /  holds  the  rod  in  any 
desired  place.  The  position  of  the  needle  is 
shown  by  a  pointer  moving  over  a  graduated 
scale.  The  rod  with  needle  and  cap  weighs 
exactly  300  g.  and  the  needle  is  1  mm.  in 
diameter  with  the  end  cut  off  square.  When 
making  tests  of  normal  consistency,  the  plunger 
b,  which  is  1  cm,  in  diameter,  is  substituted  for 
the  needle  h,  and  the  cap  a  for  the  cap  d,  the 
difference  in  weight  between  the  needle  and 
plunger  being  compensated  by  the  difference  in 
the  weight  of  the  caps.  The  mold  i  for  hold- 
ing the  cement  paste  is  in  the  form  of  a  trun- 
cated cone.  It  has  an  upper  diameter  of  6  cm., 
a  lower  diameter  of  7  cm.,  and  a  height  of  4  cm., 
and  rests  on  a  4"X4"X  i"  glass  plate  j. 

After  the  cement  paste  is  mixed,  the  mold 
is  filled  by  forcing  the  cement  through  the 
large  end;  then,  after  turning  it  over  and  smoothing  the  top,  it  is  placed 
on  the  glass  plate  under  the  needle.  The  needle  is  lowered  until  it  is 
exactly  in  contact  with  the  surface  of  the  paste,  then  quickly  released  and  the 
depth  to  which  it  penetrates  is  read  from  the  graduated  scale.  Initial  set  is 
said  to  have  taken  place  when  the  needle  ceases  to  penetrate  to  within  5  mm.  of 
the  bottom  of  the  specimen;  and  hard  set  takes  place  when  the  same  needle 
ceases  to  make  an  impression  on  the  surface.  Trials  of  penetration  are  made 
every  5  or  10  min.  until  these  points  are  reached. 

Time  of  setting  varies  considerably  with  the  amount  of  mixing  water 
employed,  so  that  it  is  essential  that  every  sample  tested  be  brought  exactly  to 
normal  consistency;  otherwise,  the  results  may  be  in  decided  error.  Variations 
in  temperature  in  both  environment  and  in  the  mixing  water,  also  influence  the 
results.  Standard  practice  requires  that  both  the  materials  and  the  room  in 
which  the  tests  are  made  be  at  a  temperature  of  as  nearly  70°  P.  as  practicable. 
When  specifying  results  to  be  obtained  in  testing  the  time  of  setting,  it  is 
obvious  that  a  minimum  value  should  be  stipulated  for  initial  set  and  a 
maximum,  as  well  as  a  minimum,  for  hard  set.  It  must  also  be  remembered 
that  a  cement  mixed  with  an  aggregate  and  with  an  excess  of  water  in  the 


CONCRETE  203 

field,  will  require  from  two  to  four  times  as  long  to  set  as  the  neat-cement 
paste  mixed  with  little  water  in  the  laboratory.  Cement,  therefore,  showing 
an  initial  set  at  the  expiration  of  20  min.  with  the  Vicat  needle,  will  rarely 
begin  to  set  on  the  actual  work  in  less  than  f  hr.,  which  gives  ample  time  for 
mixing  and  placing  the  materials,  and  cement  setting  in  less  than  10  hr./will 
usually  have  hardened  completely  in  the  work  in  24  or  at  least  in  36  hr. 
Specifications  usually  stipulate  that  Portland  cement  shall  show  initial  set  in 
not  less  than  20  minutes  and  shall  develop  hard  set  in  not  less  than  1  hr.  nor 
more  than  10  hr.  Cement  reaching  initial  set  in  less  than  12  or  15  min.  should 
never  be  used  for  any  work. 

Tests  for  Fineness. — The  fineness  of  cement  is  important,  because  it  affects 
both  the  strength  and  the  soundness  of  the  product.  The  fineness  of  cement 
is  determined  by  passing  it  through  a  series  of  sieves  of  different  mesh  and  then 
measuring  the  amount  retained  on  each.  Three  sieves  are  commonly  employed, 
namely,  those  having  50,  100,  and  200  wires  to  the  linear  inch.  Sieves  for 
cement  testing  should  never  be  used  until  they  have  been  carefully  examined 
and  found  to  conform  to  the  following  standard  specifications: 

1.  Cloth  for  cement  sieves  shall  be  of  woven  brass  wire  of  the  following 
diameters:     No.  50,  .0090  in.;   No.  100,  .0045  in.;  and  No.  200,  .00235  in. 

2.  Mesh  to  count  on  any  part  of  the  sieve  as  follows:  No.  50,  not  less  than 
48  nor  more  than  50  per  lin.  in. ;   No.  100,  not  less  than  96  nor  more  than  100 
per  lin.  in.;  and  No.  200,  not  less  than  188  nor  more  than  200  per  lin.  in. 

3.  Cloth  to  be  mounted  squarely  and  to  show  no  irregularities  of  spacing. 
The  method  of  using  the  sieves  in  the  fineness  test  is  to  weigh  out  50  g.  of 

cement  on  a  scale  sensible  at  least  to  fa  g.  and  to  place  it  on  the  No.  200  sieve,  on 
which  it  is  shaken  until  not  more  than  ^j  g.  passes  the  sieve  at  the  end  of  1  min. 
of  shaking.  The  arrival  of  this  stage  of  completion  can  be  watched  either  by 
using  a  pan  under  the  sieve  or  by  shaking  over  a  piece  of  paper.  The  residue 
remaining  on  the  sieve  is  weighed,  placed  on  the  No.  100  sieve  and  the  operation 
repeated,  again  weighing  the  residue.  The  amount  remaining  on  the  No.  50 
sieve  is  then  determined  similarly.  The  process  of  sifting  can  be  accelerated 
by  placing  a  small  quantity  of  coarse  shot  or  pebbles  on  the  sieves  with  the 
cement  during  the  shaking.  These  may  be  separated  from  the  cement  by 
passing  the  residue  with  the  shot  through  a  coarse  sieve,  such  as  the  No.  20. 

Portland  cement  should  be  ground  to  such  a  fineness  that  it  will  leave  a 
residue  of  not  more  than  25%,  by  weight,  on  the  No.  200  sieve,  and  not 
more  than  8%  on  the  No.  100  sieve.  Of  these  two  requirements,  the  first 
is  the  more  important,  because  it  is  only  that  part  of  the  cement  passing  the 
finest  sieve  that  is  active  in  the  setting  and  hardening  of  the  material.  The 
amount  remaining  on  the  No.  100  sieve  is  also  important,  because  this  part  is 
most  liable  to  cause  unsoundness  in  the  cement,  and  although  specifications 
do  not  call  for  tests  with  the  No.  50  sieve,  it  is  usually  employed  for  the  same 
reason  as  the  No.  100  sieve.  Any  appreciable  residue  on  this  sieve  indicates 
that  the  material  is  much  more  liable  to  unsoundness.  Any  cement  failing  to 
pass  the  fineness!  test  should  be  watched  more  carefully  in  the  soundness  and 
strength  tests,  but  if  these  tests  show  good  results  up  to  28  da.,  the  cement 
can,  as  a  rule,  be  used  safely.  It  must  be  remembered,  however,  that  only 
that  part  passing  the  No.  200  sieve  is  really  cement,  so  that  a  coarsely  ground 
shipment  is  practically  equivalent  to  one  adulterated  with  weak  and  unsound 
material. 

Tests  for  Specific  Gravity. — The  object  of  the  specific  gravity  test  is  to 
furnish  indications  of  the  degree  of  burning,  the  presence  or  absence  of  adultera- 
tion, and  the  amount  of  seasoning  that  the  cement  has  received.  When  Port- 
land cement  is  burned,  the  separate  ingredients  are  in  close  contact  and  grad- 
ually combine  by  a  process  of  diffusion.  The  greater  the  amount  of  this 
burning  the  more  thoroughly  are  the  elements  combined.  Thus,  by  their 
contraction  they  give,  in  volume,  a  higher  density  or  specific  gravity.  Since, 
to  secure  good  cement  the  burning  must  have  been  made  within  definite  limits, 
it  follows  that  the  specific  gravity  must  also  lie  within  fixed  limits  if  the  cement 
has  been  properly  manufactured. 

The  common  adulterants  of  Portland  cement,  namely,  limestone,  natural 
cement,  sand,  slag,  cinder,  etc.,  all  have  specific  gravities  ranging  from  2.6  to 
2.75,  while  the  specific  gravity  of  Portland  cement  averages  about  3.15.  An 
appreciable  amount  of  adulteration,  therefore,  is  at  once  indicated  in  the 
results  of  the  test. 

Seasoning  is  indicated  because  the  cement  on  standing  gradually  absorbs 
water  and  carbonic  acid  from  the  air.  These  ultimately  combine  with  it  and 
thus  lower  the  specific  gravity. 


204  CONCRETE 

Of  the  many  forms  of  apparatus  employed  for  the  specific-gravity  test,  the 
Le  Chatelier  flask,  shown  in  Fig.  2,  is  the  one  most  commonly  used.  It  is  also 
the  one  adopted  by  the  technical  societies  as  standard.  It  consists  of  a  glass 
flask  about  30  cm.  high.  The  lower  part  up  to  mark  a  contains  120  cc.,  and 
the  bulb  between  the  marks  a  and  b  contains  exactly  20  cc.  The  neck  of  the 
flask  above  the  mark  b  is  graduated  into  j*ff  cc.  The  funnel  c  inserted  in  the 
neck  is  to  facilitate  the  introduction  of  the  cement. 

The  method  of  conducting  the  specific-gravity  test  is  as 
follows:  64  g.  of  cement  is  carefully  weighed  on  scales  that 
should  have  a  sensibility  of  at  least  .005  g.  The  flask  is 
filled  to  the  lower  mark  a  with  benzine  or  kerosene,  which 
has  no  action  on  the  cement,  and  is  carefully  adjusted 

Precisely  to  the  mark  by  adding  the  liquid  a  drop  at  a  time, 
he  funnel  is  then  placed  in  the  neck  of  the  flask  and  the 
weighed  cement  introduced  slowly  through  it,  the  last  traces 
of  the  cement  being  brushed  through  with  a  camel's-hair 
brush.  The  funnel  is  then  renwved  and  the  height  of  the 
benzine  read  from  the  graduations,  estimating  to  .01  cc. 
The  displaced  volume  is  then  20  plus  the  reading,  in  cubic 
centimeters,  and  the  specific  gravity  of  the  cement  is  64 
divided  by  that  quantity.  For  example,  suppose  that  the 
reading  on  the  flask  is  .54,  then  the  displaced  volume  will 
be  20 +.54  =  20.54  and  the  specific  gravity  will  be  64 
-7-20.54  =  3.116. 

The  apparatus  must  be  protected  from  changes  in  tem- 
perature while  in  use;  even  touching  the  flask  with  the 
fingers  will  change  the  volume  of  the  liquid  noticeably. 
The  flask  is  sometimes  immersed  in  water  during  the  tests 
to  prevent  these  changes  of  temperature,  but  this  precau- 
tion is  unncessary  if  proper  care  is  exercised. 

The  specific  gravity  of  well-burned  Portland  cement 
averages  about  3.15  and  should  not  fall  below  3.1.  If  it 
falls  below  3.1,  tests  should  also  be  made  on  dried  and  on 
ignited  samples  to  ascertain  whether  or  not  this  condition 
has  been  produced  by  reason  of  excessive  seasoning.  As  a 
rule,  low  specific  gravity  merely  indicates  well-seasoned 
cement,  and  if  sound  and  sufficiently  strong,  such  cement 
is  the  best  sort  of  material  for  use,  as  its  durability  is 
scarcely  open  to  question. 

Tests  of  Natural  and  Slag  Cements.— The  methods  of 
conducting  tests  of  natural  and  slag  cements  are,  in  all  important  particulars, 
identical  with  those  employed  for  Portland  cement,  although  the  results  ob- 
tained and  the  interpretation  to  be  put  on  them  are  often  radically  different. 
In  the  testing,  the  only  essential  difference  is  in  the  amount  of  water  required 
by  these  cements  to  produce  normal  consistency;  natural  cement  requires  from 
23  to  35%  and  slag  cement  takes  about  18%,  or  an  average  of  2  or  3%  less 
than  Portland.  Tests  of  natural  cement  for  tensile  strength  are  also  fre- 
quently made  on  1-1  and  1-2  mortars,  but  recent  practice  is  to  test  mortars 
of  all  kinds  of  cement  in  1-3  mixtures.  For  these  cements,  moreover,  the 
specific-gravity  test  has  practically  no  significance,  except  in  determining  the 
uniformity  with  which  the  different  brands  are  made. 


FIG.  2 


CEMENT  SPECIFICATIONS 

A  good  example  of  a  complete  modern  specification  for  Portland  cement  is 
here  given. 

SPECIFICATIONS  FOR  PORTLAND  CEMENT 

Kind.— All  cement  shall  be  Portland  of  the  best  quality,  dry  and  free  from 
lumps.  By  Portland  cement  is  meant  the  finely  pulverized  product  resulting 
from  the  calcination  to  incipient  fusion  of  an  intimate  mixture  of  properly  pro- 
portioned argillaceous  and  calcareous  materials  to  which  no  addition  greater 
than  3%  has  been  made  subsequent  to  calcination. 

Packages. — •Cement  shall  be  packed  in  strong  cloth  or  canvas  bags,  or  in 
sound  barrels  lined  with  paper,  which  shall  be  plainly  marked  with  the  brand 


CONCRETE 


205 


and  the  name  of  the  manufacturer.     Bags  shall  contain  94  Ib.  net  and  barrels 
shall  contain  376  Ib.  net. 

Inspection. — All  cement  must  be  inspected,  and  may  be  reinspected  at  any 
time.  The  contractor  must  submit  the  cement,  and  afford  every  facility  for 
inspection  and  testing,  at  least  12  da.  before  desiring  to  use  it.  The  chief 
engineer  shall  be  notified  at  once  on  receipt  of  each  shipment  at  the  work.  No 
cement  will  be  inspected  or  allowed  to  be  used  unless  delivered  in  suitable 
packages  properly  branded.  Rejected  cement  must  be  immediately  removed 
from  the  work. 

Protection. — The  cement  must  be  protected  in  a  suitable  building  having 
a  wooden  floor  raised  from  the  ground,  or  on  a  wooden  platform  properly  pro- 
tected with  canvas.  It  shall  be  stored  so  that  each  shipment  will  be  separate, 
and  each  lot  shall  be  tagged  with  identifying  number  and  date  of  receipt. 

Quality. — The  acceptance  or  rejection  of  a  cement  to  be  used  will  be  based 
on  the  following  requirements: 

Specific  gravity:     Not  less  than  3.1. 

Ultimate  tensile  strength  per  square  inch:  POUNDS 

7  da.  (1  da.  in  air,  6  da.  in  water) 500 

28  da.  (1  da.  in  air,  27  da.  in  water) 600 

7  da.  (1  da.  in  air,  6  da.  in  water),  1  part  cement  to  3  parts  of 

standard  quartz  sand 170 

28  da.  (1  da.  in  air,  27  da.  in  water),  1  part  of  cement  to  3  parts  of 

standard  quartz  sand 240 

Fineness:  Residue  on  No.  100  sieve  not  over  8%,  by  weight;  residue  on  No. 
200  sieve  not  over  25%,  by  weight. 

Set:  It  shall  require  at  least  20  min.  to  develop  initial  set,  and  shall  develop 
hard  set  in  not  less  than  1  hr.  nor  more  than  10  hr.  These  requirements  may 
be  modified  where  the  conditions  of  use  make  it  desirable. 

Constancy  of  Volume:  Pats  of  cement  3  in.  in  diameter,  |  in.  thick  at  center, 
tapering  to  thin  edge,  immersed  in  water  after  24  hr.  in  moist  air,  shall  show 
no  signs  of  cracking,  distortion,  or  disintegration.  Similar  pats  in  air  shall  also 
remain  sound  and  hard.  The  cement  shall  pass  such  accelerated  tests  as  the 
chief  engineer  may  determine. 

Analysis:  Sulphuric  anhydride,  SOz,  not  more  than  1.75%;  magnesia, 
MgO,  not  more  than  4%. 

The  common  requirements  for  high-grade  Portland,  natural,  and  slag 
cements  are  given  in  the  following  table. 

REQUIREMENTS  FOR  HIGH-GRADE  CEMENTS 


Requirements 

Portland 
Cement 

Natural 
Cement 

•Slag 
Cement 

Specific  gravity: 
Not  less  than  

3.1 

2.8 

2.7 

Fineness: 
Residue  on  No.  100  sieve,  not  over  
Residue  on  No.  200  sieve,  not  over  
Time  of  Setting: 
Initial   not  less  than  

8% 
25% 

20  min. 

10% 
30% 

10  min. 

3% 
10% 

20  min. 

Ihr. 

30  min. 

1  hr. 

Hard,  not  more  than  
Tensile  strength  per  sq.  in. 
7  da.,  neat,  not  less  than  
28  da.   neat  not  less  than          

10  hr. 

500  Ib. 
600  Ib. 

3  hr. 

125  Ib. 
225  Ib. 

10  hr. 

350  Ib. 
450  Ib. 

7  da.,  1—3  quartz,  not  less  than  

170  Ib. 

50  Ib. 

125  Ib. 

28  da.,  1-3  quartz,  not  less  than  
Soundness: 
Normal  pats  in  air  and  water  for  28  da.  / 
to  be                     I 

240  Ib. 

sound  and 
hard 

110-lb. 

sound  and 
hard 

200  Ib. 

sound  and 
hard 

Boiling  test  to  be  { 

sound  and 

sound  and 

Analysis: 

4% 

4% 

Anhydrous  sulphuric  acid,  SOa,  not  over 
Sulphur   5  not  over 

1.75% 

1  3% 

206  CONCRETE 


PLAIN  CONCRETE 

DEFINITIONS  AND  TERMS 

Concrete  is  usually  made  of  cement,  sand,  and  broken  stone.  The  cement 
in  a  plastic  state,  either  by  itself  or  with  the  sand  that  is  generally  mixed  with 
it,  is  called  the  matrix,  and  the  broken  stone,  gravel,  or  other  material  used  as  a 
filler  is  called  the  aggregate.  The  sand  is  correctly  classed  as  a  part  of  the  aggre- 
gate, although  some  engineers  include  it  with  the  matrix.  The  aggregate  is  used 
to  cheapen  concrete.  Pure,  or  neat,  cement,  when  wet  with  water,  would  in 
a  way  fulfil  all  the  physical  requirements  of  concrete,  but  it  would  be  too 
expensive. 

In  the  concrete  of  today,  hydraulic  cement  is  used  almost  exclusively.  For 
this  reason,  the  term  concrete,  as  commonly  used,  refers  only  to  that  variety. 
In  specifying  any  other  kind  of  concrete,  the  usual  custom  is  to  mention  it 
by  its  full  name,  as  bituminous  concrete,  lime  concrete,  etc.  Such  varieties,  how- 
ever, are  of  comparatively  little  importance.  . 

The  term  concrete,  besides  being  restricted  to  hydraulic-cement  concrete, 
has  another  restriction:  the  aggregate  must  not  be  sand  alone,  although  it  may 
be  partly  sand.  A  mixture  of  hydraulic  cement,  sand,  and  water  is  called  by  the 
special  name  of  mortar. 

Concrete  is  usually  named  from  the  kind  of  aggregate  used.  For  example, 
stone  concrete  embodies  the  use  of  broken  stone  or  coarse  pebbles,  while  in  cinder 
concrete,  the  aggregate  consists  of  cinders  or  broken  slag. 

The  proportion  of  cement  and  sand  to  the  broken  stone  depends  on  the 
spaces  between  the  stones,  which  are  known  as  voids.  In  all  instances,  there 
must  be  sufficient  mortar  to  fill  the  voids  entirely  and  to  cover  all  surfaces  of  the 
separate  stones. 

AGGREGATES  OTHER  THAN  SAND 

The  aggregates  or  broken  stone  used  in  concrete  work  should  possess  three 
qualities:  (1)  They  should  be  hard  and  strong,  so  as  to  resist  crushing  and 
shearing  or  transverse  stresses;  (2)  they  should  have  surface  texture  that  will 
permit  the  cement  mortar  to  adhere  to  their  surfaces;  and  (3)  where  the  con- 
crete is  to  be  used  for  building  construction,  such  as  in  reinforced-concrete  work, 
and  for  fireproofing,  they  should  possess  refractory,  or  fire-resisting,  qualities. 
Usually,  aggregates  that  break  in  such  a  way  as  to  allow  the  smallest  spaces,  or 
interstices,  between  the  particles,  will  make  the  strongest  concrete  for  con- 
struction purposes  because  the  voids  can  be  most  economically  filled  with 
cement  mortar. 

Size  of  Aggregates. — When  measuring  broken  stone,  the  size  of  the  stone 
is  determined  by  the  size  of  the  ring  through  which  it  will  pass.  For  instance,  a 
2-in.  stone  is  one  that  will  pass  through  a  ring,  or  hole,  that  is  2  in.  in  diameter. 

The  broken  stone  used  in  concrete  work  varies  in  size  with  the  nature  of  the 
work.  For  foundation  and  mass  construction,  it  is  the  custom  to  use  broken 
stone  of  a  size  that  will  pass  through  a  2-  or  2^-in.  ring.  For  filling  the 
spandrels  of  bridges  or  the  spaces  between  walls,  where  mere  bulk  is  desired, 
broken  stone  of  a  much  larger  size  is  used. 

In  reinforced-concrete  work,  the  broken  stone  must  be  small,  owing  to  the 
narrow  spaces  in  the  forms.  For  columns  and  wall  work,  stone  that  will  pass 
through  a  1-  or  f-in.  ring  is  suitable,  while  for  filling  beam  and  girder  forms, 
where  numerous  reinforcing  rods  occur,  the  broken  stone  is  sometimes  so  small 
as  to  pass  through  a  ^-in.  ring. 

The  latest  practice  in  making  concrete  is  to  use  stone  as  it  comes  from  the 
crusher,  without  screening  it.  While  such  stone,  termed  the  run  of  crusher, 
contains  broken  stone  of  a  size  specified,  it  also  has  smaller  particles  of  stone 
and  such  stone  dust  as  is  carried  along  with  the  broken  stone  from  the  crusher. 
Where  the  run  of  crusher  is  used,  the  proportion  of  the  cement  and  sand  must 
be  changed,  because  the  stone  dust  takes  the  place  of  some  of  the  sand.  In 
using  run  of  crusher  the  very  finest  dust  should  be  washed  or  screened  out  as  it 
tends  to  coat  the  large  pieces  and  to  prevent  the  cement  from  adhering  to  them. 

The  size  of  the  aggregates  has  much  to  do  with  the  quality  and  strength  of 
the  concrete.  It  can,  however,  be  stated  as  a  general  proposition,  that  the 
larger  the  stones  the  stronger  will  be  the  concrete.  This  fact  was  well  proved 
in  a  series  of  tests  made  at  the  Watertown  Arsenal  in  1898.  These  tests  also 
showed  that  the  concrete  becomes  heavier  per  cubic  foot,  or,  in  other  words, 


CONCRETE  207 

more  dense,  the  larger  the  stone  used.  All  these  tests  were  made  with  con- 
crete manufactured  in  the  proportion  of  1  part  of  cement,  1  part  of  sand, 
and  3  parts  of  broken  stones,  or  a  1-1-3  (1  to  1  to  3)  mixture,  as  it  is  usually 
expressed.  The  figures  on  cinder  concrete  in  the  table  are  added  simply  to 
give  a  comparison  of  weights,  for  it  will  be  noted  that  the  cinder  concrete  is 
older  than  the  other  concretes,  and  therefore  stronger  in  proportion. 

Aggregates  that  consist  of  stone  of  varying  sizes  are  best  for  making  con- 
crete, owing  to  the  fact  that  they  pack  closer.  It  is  well,  however,  to  screen 
all  the  fine  particles,  such  as  i-in.  sizes,  and  use  them  with  the  sand,  as  other- 
wise they  will  not  mix  properly  with  the  cement. 

Selection  of  Aggregates. — Usually  the  character  of  the  aggregates  used  in 
mixing  concrete  depends  on  the  availability  of  the  supply.  Where  there  is 
much  choice  in  the  selection  of  the  aggregates  those  that  are  hardest  and  break 
with  a  cubical  fracture  will  make  the  best  concrete,  although  rounded  pebbles 
are  considered  by  some  engineers  to  P9ssess  great  advantages. 

Some  years  ago  the  American  Society  of  Civil  Engineers,  American  Society 
for  Testing  Materials,  American  Railway  Engineering  and  Maintenance  of  Way 
Association,  and  the  Association  of  American  Portland  Cement  Manufacturers 
appointed  committees  to  obtain  information  concerning  the  practice  in  and 
properties  of  concrete  and  reinforced  concrete  and  recommend  formulas  for 
design,  etc.  This  general  committee  is  commonly  known  as  the  Joint  Com- 
mittee and  references  will  be  made  to  its  report  in  the  following  pages.  These 
references  are  taken  from  the  Proceedings  of  the  American  Society  of  Civil 
Engineers,  Vol.  XXXIX,  No.  2,  pp.  117  to  168,  where  the  Progress  Report  of 
the  Special  Committee  of  that  Society  on  concrete  and  reinforced  concrete  will 
be  found.  It  was  presented  to  that  society  by  its  committee  on  Jan.  15,  1913. 

The  relative  merit  of  various  aggregates  for  concrete  cannot  of  course  be 
defined  accurately,  because  in  any  one  aggregate  the  quality  may  vary  con- 
siderably. The  working  stresses  for  concrete  have  been  discussed  by  the 
Joint  Committee.  This  committee  recommends  in  its  report  certain  tests  for 
the  ultimate  strength  of  concrete.  In  the  absence  of  such  tests  there  are  given 
certain  values  for  the  strength  of  concrete  that  should  be  obtained  under 
certain  conditions.  The  values  given  vary  among  other  things  with  the  kind 
of  aggregate  used.  The  aggregates  are  arranged  into  four  groups  in  so  far  as 
they  govern  the  strength  of  the  concrete.  These  groups  are  as  follows: 

First  group,  granite,  trap  rock. 

Second  group,  gravel,  hard  limestone,  and  hard  sandstone. 

Third  group,  soft  limestone  and  sandstone. 

Fourth  group,  cinders. 

The  difference  in  quality  between  any  two  adjacent  groups  is  not  constant. 

Elsewhere  in  the  report  it  is  stated:  "Cinder  concrete  should  not  be  used 
for  reinforced-concrete  structures.  It  may  be  allowable  in  mass  for  very 
light  loads  or  for  fire-protection  purposes.  The  cinders  should  be  composed 
of  hard,  clean,  vitreous  clinker,  free  from  sulphides,  unburned  coal,  or  ashes." 

PROPORTIONING  OF  INGREDIENTS 

Effect  on  Strength  and  Imperviousness.— The  strength  of  concrete  depends 
on  the  strength  of  the  cement  and  the  thoroughness  with  which  the  cement 
binds  together  the  various  pieces  of  aggregate.  The  more  completely  the 
voids  are  filled,  the  more  completely  will  the  aggregate  be  held  together. 
Therefore,  the  more  solid  and  condensed  the  concrete  is,  the  less  voids  it  will 
have,  and  the  stronger  it  will  be.  The  same  is  true  with  regard  to  making  con- 
crete water-proof;  the  more  dense  the  concrete  is,  the  more  nearly  water-proof 
it  is. 

A  mixture  of  1  part  of  cement,  \\  parts  of  sand,  and  3  parts  of  stone,  which 
would  be  considered  extravagantly  rich  for  a  dry  place,  is  probably  as  dense 
a  concrete,  and  as  good  for  waterproofing  qualities,  as  can  be  made. 

When  a  concrete  is  made  of  cement,  sand,  and  stone,  and  the  stone  is  of  such 
a  size  that  it  will  pass  through  a  3-in.  ring,  but  will  not  pass  through  a  22-in. 
ring,  the  concrete  is  weaker  and  requires  more  cement  than  one  made  with 
graded  stone  from  3-in.  down.  .  When  the  stone  is  graded  in  size,  the  stones 
of  smaller  size  fill  the  voids  between  the  larger  stones  and  thus  reduce  the 
quantity  of  cement  and  sand  required. 

Proportioning  by  Weights. — The  ingredients  for  a  sample  batch  of  concrete 
are  weighed  out  in  known  proportions  and  mixed  to  the  desired  consistency  on  a 
sheet  of  steel.  They  are  then  tamped  in  a  piece  of  10-in.  pipe  capped  at  one 
end.  The  pipe  thus  partly  filled  is  weighed,  and  subtracting  the  weight  of  the 
receptacle  a  check  is  obtained.  The  height  of  the  concrete  in  the  pipe  is  then 


208 


CONCRETE 


g  3"g  cT  COMPRESSIVE  STRENGTH  OF  CONCRETE  MADE  OF  DIFFERENT-SIZED  STONES 

0, 

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measured   and    the 
mixture  dumped  out 
before   it    hardens. 
After   all  the   appar- 
atus is  cleaned  another 
batch   of  concrete   is 
mixed,  using  the  same 
weight  of   water,  ce- 
ment ,  and  total  weight 
of  sand  and  stone  as 
before,  but  a  different 
ratio  of   weight   of 
sand     to    weight    of 
stone.     The  height  of 
this   concrete   in   the 
pipe    is   measured. 
This  operation  is  re- 
peated.   The  concrete 
occupying    the    least 
volume  is  the  densest 
and  strongest  that  can 
be    made    with    that 
particular    sand    and 
stone  as  they  are  and 
with  the   given   pro- 
portion of  cement. 
The    volumes    corre- 
sponding    to     the 
weights  can  be  found 
by    trial    measure- 
ments. 
Usual  Proportions 
of  Materials.  —  It  is 
not  always  necessary 
to   use  the  strongest 
concrete,  as  the  con- 
crete may  be  required 
to  withstand  only 
slight  stresses  and  be 
simply    used   for    its 
weight.     The  strong- 
est concrete  would 
then  be  unnecessarily 
expensive.    Often  the 
foregoing     method 
of  proportioning  con- 
crete is  not  employed 
and  the   engineer 
specifies     a     mixture 
from  his  own  experi- 
ence without  testing 
the  aggregates  in  any 
way,    except    to    see 
that  the  stone  is  un- 
der the  specified  maxi- 
mum size  and  properly 
graded,  and  that  the 
sand  is  in  large  grains, 
graded  down,  and  free 
from  dirt   and  loam. 
A  common  proportion 
for  unimportant  work 
is    1-3-6.     This   pro- 
portion may  be  used 
oundations  for  asphalt 
e  1-2-4  is  used  in  piers, 
in  other  places  where 

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ts 

foundations  below  groun 
Cements,  and  for  similar  i 
dams,  in  important  rein 
at  strength  is  desired. 

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d,  in  engine  bases,  in  the  : 
>urposes.     A  richer  mixtui 
'orced-concrete  work,  anc 

CONCRETE  209 

In  regard  to  the  proportioning  of  ingredients  the  Joint  Committee  states 
as  follows: 

"  Quality  and  Proportions. — The  materials  to  be  used  in  concrete  should  be 
carefully  selected,  of  uniform  quality,  and  proportioned  with  a  view  to  secur- 
ing as  nearly  as  possible  a  maximum  density. 

"  Unit  of  Measure. — The  unit  of  measure  should  be  the  cubic  foot.  A  bag 
of  cement,  containing  94  Ib.  net  should  be  considered  the  equivalent  of  1  cu.  ft. 

"The  measurement  of  the  fine  and  coarse  aggregates  should  be  by  loose 
volume. 

"Relation  of  Fine  and  Coarse  Aggregates. — The  fine  and  coarse  aggregates 
should  be  used  in  such  relative  proportions  as  will  insure  maximum  density. 
In  unimportant  work,  it  is  sufficient  to  do  this  by  individual  judgment,  using 
correspondingly  higher  proportions  of  cement;  for  important  work  these 
proportions  should  be  carefully  determined  by  density  experiments,  and  the 
sizing  of  the  fine  and  coarse  aggregates  should  be  uniformly  maintained  or  the 
proportions  changed  to  meet  the  varying  sizes. 

"Relation  of  Cement  and  Aggregates. — For  reinforced-concrete  construction, 
1  part  of  cement  to  a  total  of  6  parts  of  fine  and  coarse  aggregates  measured 
separately  should  generally  be  used.  For  columns,  richer  mixtures  are  gen- 
erally preferable;  and  in  massive  masonry  or  rubble  concrete,  a  mixture  of  1-9 
or  even  1-12  may  be  used. 

"These  proportions  should  be  determined  by  the  strength  or  the  wearing 
qualities  required  in  the  construction  at  the  critical  period  of  its  use.  Experi- 
enced judgment  based  on  individual  observation  and  tests  of  similar  conditions 
in  similar  localities  is  an  excellent  guide  as  to  the  proper  proportions  for  any 
particular  case. 

"For  all  important  construction,  advance  tests  should  be  made  of  concrete 
composed  of  the  materials  in  the  proportions,  and  of  the  consistency  to  be 
used  in  the  work.  These  tests  should  be  made  under  laboratory  conditions 
to  obtain  uniformity  in  mixing,  proportioning,  and  storage,  and  in  case  the 
results  do  not  conform  to  the  requirements  of  the  work,  aggregates  of  a  better 
quality  should  be  chosen  or  richer  proportions  used  to  obtain  the  desired 
results." 

Water  for  Concrete. — The  wetter  the  concrete  is,  the  easier  it  will  be  put 
in  place,  but  mixtures  that  are  too  wet  are  not  so  strong  as  medium  mixtures. 
The  amount  of  water  that  will  make  the  best  mixture  is  such  that  after  the 
concrete  has  been  put  in  place  and  rammed  it  will  quake  like  jelly  when  struck 
with  a  spade,  and  water  will  come  to  the  surface.  If  the  concrete  is  wetter  than 
this,  the  water  will  have  a  slight  chemical  effect  on  the  cement,  and,  moreover, 
the  sand  and  cement  will  tend  to  separate  from  the  broken  stone. 

In  cinder  concrete,  owing  to  the  porosity  of  the  cinders,  it  is  necessary  to 
use  a  little  more  water,  so  that  the  cement  will  be  liquid  enough  to  fill  the  little 
cavities  in  each  cinder.  This  precaution  is  indispensable  when  the  concrete  is 
to  be  used  with  steel,  as  otherwise  the  steel  will  be  rapidly  corroded  by  the 
action  of  air  reaching  it  through  the  pores  in  the  cinders. 

DESTRUCTIVE  AGENCIES 

Various  causes  may  affect  the  strength  and  durability  of  concrete.  The 
principal  causes  have  been  discussed  by  the  Joint  Committee  already  referred 
to,  and  as  the  various  effects  are  often  more  or  less  complex  it  is  probably  best 
to  quote  directly  from  the  Joint  Committee. 

"Corrosion  of  Metal  Reinforcement. — Tests  and  experience  indicate  that 
steel  sufficiently  embedded  in  good  concrete  is  well  protected  against  corrosion, 
no  matter  whether  located  above  or  below  water  level.  It  is  recommended 
that  such  protection  be  not  less  than  1  in.  in  thickness.  If  the  concrete  is 
porous,  so  as  to  be  readily  permeable  by  water,  as  when  the  concrete  is  laid 
with  a  very  dry  consistency,  the  metal  may  corrode  on  account  of  the  presence 
of  moisture  and  air. 

"Electrolysis. — The  most  recent  experimental  data  available  on  this  subject 
seem  to  show  that  while  reinforced-concrete  structures  may,  under  certain  con- 
ditions, be  injured  by  the  flow  of  electric  current  in  either  direction  between 
the  reinforcing  material  and  the  concrete,  such  injury  is  generally  to  be  expected 
only  where  voltages  are  considerably  higher  than  those  that  usually  occur  in 
concrete  structures  in  practice.  If  the  iron  is  positive,  trouble  may  manifest 
itself  by  corrosion  of  the  iron  accompanied  by  cracking  of  the  concrete;  if  the 
iron  is  negative,  there  may  be  softening  of  the  concrete  near  the  surface  of  the 
iron,  resulting  in  a  destruction  of  the  bond.  The  former,  or  anode  effect, 
decreases  much  more  rapidly  than  the  voltage,  and  almost,  if  not  quite, 


210  CONCRETE 

disappears  at  voltages  that  are  most  likely  to  be  encountered  in  practice.  The 
cathode  effect,  on  the  other  hand,  takes  place  even  at  very  low  voltages,  and 
is,  therefore,  more  important  from  a  practical  standpoint  than  that  of  the  anode. 

"Structures  containing  salt  or  calcium  chloride,  even  in  very  small  quanti- 
ties, are  very  much  more  susceptible  to  the  effects  of  electric  currents  than 
normal  concrete,  both  the  anode  and  cathode  effects  progressing  much  more 
rapidly  in  the  presence  of  chlorine. 

"There  is  great  weight  of  evidence  to  show  that  normal  reinforced-concrete 
structures  free  from  salt  are  in  very  little  danger  under  most  practical  condi- 
tions, while  non-reinforced-concrete  structures  are  practically  immune  from 
electrolysis  troubles.  The  results  of  experiments  now  in  progress  may  yield 
more  conclusive  information  on  this  subject. 

"Sea- Water. —The  data  available  concerning  the  effect  of  sea-water  on 
concrete  or  reinforced  concrete  are  limited  and  inconclusive.  Sea  walls  out 
of  the  range  of  frost  action  have  been  standing  for  many  years  without  apparent 
injury;  in  many  harbors  where  the  water  is  brakish,  through  rivers  discharging 
into  them,  serious  disintegration  has  taken  place.  This  has  occurred  chiefly 
between  low-  and  high-tide  levels,  and  is  due,  evidently,  in  part  to  frost. 
Chemical  action  also  appears  to  be  indicated  by  the  softening  of  the  mortar. 
T9  effect  the  best  resistance  to  sea- water,  the  concrete  must  be  proportioned, 
mixed,  and  placed  so  as  to  prevent  the  penetration  of  sea-water  into  the  mass 
or  through  the  joints.  The  cement  should  be  of  such  chemical  composition 
as  will  best  resist  the  action  of  sea-water;  the  aggregates  should  be  carefully 
selected,  graded,  and  proportioned  with  the  cement  so  as  to  secure  the  maxi- 
mum possible  density;  the  concrete  should  be  thoroughly  mixed;  the  joints 
between  old  and  new  work  should  be  made  water-tight;  and  the  concrete  should 
be  kept  from  exposure  to  sea-water  until  it  is  thoroughly  hard  and  impervious. 

"Acids. — Concrete  of  first-class  quality,  thoroughly  hardened,  is  affected 
appreciably  only  by  strong  acids  that  seriously  injure  other  materials.  A 
substance  like  manure  is  injurious  to  green  concrete,  but  after  the  concrete  has 
hardened  thoroughly  it  satisfactorily  resists  the  action  of  such  acid. 

"Oils. — When  concrete  is  properly  made  and  the  surface  is  carefully  finished 
and  hardened,  it  resists  the  action  of  such  mineral  oils  as  petroleum  and  ordinary 
engine  oils.  Oils  that  contain  fatty  acids  produce  injurious  effects,  forming 
compounds  with  the  lime  that  result  in  a  disintegration  of  the  concrete  in 
contact  with  them. 

"Alkalies. — The  action  of  alkalies  on  concrete  is  problematic.  In  the 
reclamation  of  arid  land,  where  the  soil  is  heavily  charged  with  alkaline  salts, 
it  has  been  found  that  concrete,  stone,  brick,  iron,  and  other  materials  are 
injured  under  certain  conditions.  It  would  seem  that  at  the  level  of  the 
ground  water,  in  an  extremely  dry  atmosphere,  such  structures  are  disin- 
tegrated through  the  rapid  crystallization  of  the  alkaline  salts,  resulting  from 
the  alternate  wetting  and  drying  of  the  surface.  Such  destructive  action  can 
be  prevented  by  the  use  of  a  protective  coating,  and  is  minimized  by  securing 
a  dense  concrete." 

Effect  of  Fire  on  Concrete. — Concrete  is  essentially  a  fire-proof  material. 
All  the  ingredients  of  which  it  is  composed  are  of  a  highly  refractory  nature, 
the  aggregates  being  the  elements  of  the  mixture  that  are  most  quickly  affected 
by  intense  heat.  This  is  especially  true  of  granite  and  limestone  aggregates, 
the  former  being  likely  to  crack  or  burst  when  heated,  and  the  latter  to  calcine. 
After  cement  has  set,  the  chemical  union  of  its  particles  is  liable  to  destruction 
by  fire,  because  intense  heat  robs  the  cement  of  the  water  of  crystallization, 
or  dehydrates  the  cement,  thus  softening  the  material  and  making  it  crumbly. 
If  concrete  in  a  mass  is  subjected  to  intense  heat,  this  action  of  dehydration 
extends  into  the  concrete  for  a  depth  of  only  |  to  5  in.,  and  is  not  likely  to 
penetrate  farther. 

Effect  of  Mine  Water  on  Concrete. — The  water  from  coal  mines  contains 
sulphuric  acid,  ammonium  compounds,  and  other  chemicals  decidedly  injurious 
to  concrete.  The  use  of  concrete  about  the  mines  has  assumed  large  propor- 
tions only  in  the  last  few  years,  and  as  yet  no  cheap  method  that  is  always 
effective  has  been  uniformly  adopted  to  protect  the  concrete  from  this  water. 
Since  the  mine  water  will  not  attack  silica,  sand  containing  at  least  92%  silica 
should  be  used.  The  stone  employed  should  also  be  acid-resisting  and  at  least 
90%  insoluble  in  dilute  hydrochloric  acid.  The  cement  should  be  properly 
burned  and  should  be  the  best  obtainable  for  such  work.  Some  of  the  coal 
companies  have  special  specifications  for  cement.  Although  the  foregoing 
precautions  will  not  make  concrete  entirely  permanent  in  some  conditions, 
they  will  increase  its  life. 


CONCRETE  211 

Expansion  and  Contraction.  —  Considere,  a  French  concrete  expert,  has 
found  by  experiment  that  a  1-3  mortar  will  shrink  from  about  .05  to  .15% 
when  setting  in  air,  and  that  the  shrinkage  will  be  two  to  three  times  as 
great  with  neat  cement.  The  shrinkage  in  concrete  will  be  much  less  than 
with  neat  cement  or  cement  mortar. 

The  shrinkage  of  concrete  is  lessened  by  embedding  in  it  steel  rods  or  bars, 
as  these,  by  their  tensile  resistance,  prevent  the  shrinkage  of  the  material  when 
setting.  By  the  experiments  of  Considere,  it  is  found  that  with  1-3  mortar 
reinforced  with  steel  the  shrinkage  when  setting  is  about  one-fifth  that  of  the 
same  mortar  without  the  steel  reinforcement. 

Effect  of  Thermal  Changes  on  Concrete.  —  Nearly  all  materials  expand 
slightly  as  they  become  heated.  Concrete  and  steel  also  follow  this  law.  The 
contraction  or  the  expansion  of  concrete  due  to  changes  in  temperature  is 
about  the  same  as  that  of  steel.  The  average  coefficient  of  expansion  of  a 
1-2-4  concrete  for  each  Fahrenheit  degree  in  change  of  temperature  is  .0000055. 
Experiments  made  on  1-3-6  concrete  give  a  coefficient  of  expansion  of  .0000065, 
which  is  practically  the  same  as  the  coefficient  of  steel. 

Effect  of  Vibration  on  Concrete.  —  The  effect  of  constant  vibration  on 
concrete  structures  has  not  been  definitely  determined.  Many  buildings  and 
bridges  constructed  of  concrete  reinforced  with  steel  rods  and  bars  have  with- 
stood heavy  and  constant  vibration,  both  continuous  and  intermittent,  for  an 
extended  period  of  years  with  no  apparent  deterioration  in  strength.  Fresh 
concrete  is  always,  however,  subject  to  deterioration  by  vibration,  and  the 
strength  of  concrete  subjected  to  jar  or  shock  when  setting  is  materially  re- 
duced, because  the  process  of  crystallization  between  the  particles,  and  the 
consequent  cohesion  of  the  mass,  seems  to  be  partly  destroyed. 

WORKING  STRESSES  AND  STRENGTH  VALUES  OF  CONCRETE 

The  ultimate  strength  of  concrete  varies  so  with  the  proportion  of  the 
mixture,  manner  of  working,  character  of  ingredients,  and  age  of  material, 
that  it  is  necessary  to  assume  low  unit  working  stresses  for  it. 

There  can  be  no  unit  stresses  recommended  for  use  for  all  conditions.  It 
takes  experience  to  make  good  concrete.  Moreover,  complete  and  detailed 
instructions  and  directions  must  be  followed;  more  complete  and  detailed  than 
there  is  room  for  here.  The  Joint  Committee's  report  recommends  for  allow- 
able stresses  for  concrete,  certain  percentages  of  the  crushing  strength  of 
cylinders  of  the  concrete,  of  certain  size,  and  tested  under  certain  conditions. 
In  the  absence  of  tests  to  learn  this  crushing  strength,  this  report  states  that 
for  cylinders  of  certain  size,  age,  and  method  of  manufacture,  if  made  of  1-2-4, 
according  to  the  directions  laid  down,  of  gravel,  hard  limestone,  or  hard  sand- 
stone, the  crushing  strength  should  be  2,000  pounds  per  square  inch.  The 
allowable  stresses  for  such  a  concrete,  when  made  of  Portland  cement,  with 
static  loads  are: 


Axial  compression,  columns  under  12  diameters  ...........  450 

Compression  in  extreme  fiber  of  beam,  due  to  bending  .....  650 

Shear  in  beams,  without  web  reinforcement  ..............  40 

Shear,  pounding  shear  .................................  120 

Bond,  plain  bars  ......................................  80 

Bond,  drawn  wire  .....................................  40 

The  strength  of  concrete  varies,  of  course,  with  the  age  and  richness  of  the 
mixture.  To  show  this  variation,  the  ultimate  compressive  strength  of  con- 
crete of  various  ages  and  mixtures  made  from  Portland  cement,  sand,  and 
crushed  stone,  is  given  in  the  accompanying  table.  These  results  represent 
the  product  of  some  six  hundred  tests  made  by  W.  Purves  Taylor,  engineer- 
in-charge  of  the  municipal  testing  laboratory  of  Philadelphia.  Of  course,  to 
obtain  similar  figures,  the  concrete  must  be  made  and  tested  as  it  was  in  this 
experiment.  The  table,  however,  shows  the  increase  of  strength  with  age 
and  richness  of  mixture. 

CONCRETE  MIXTURES 

Methods  of  Measuring  Ingredients.  —  After  deciding  what  proportions  of 
ingredients  will  be  used  for  the  concrete,  the  engineer  must  be  able  to  calculate 
the  quantity  of  each  material  that  he  must  order.  An  ordinary  box  car  holds 
from  400  to  600  bags  of  cement.  The  purchaser  is  charged  for  the  bags  by  the 
manufacturer,  unless  they  are  of  paper,  but  he  gets  a  rebate  for  those  that 
are  returned. 


212  CONCRETE 

AVERAGE  ULTIMATE  CRUSHING  STRENGTH  OF  CONCRETE 


Proportion  of 

Ultimate  Crushing  Strength 

Ingredients 

Pounds  per  Square  Inch 

Cement 

Sand 

Stone 

7  da. 

1  mo. 

3  mo. 

6  mo. 

1 

20 

4 

1,600 

2,150 

2,400 

2,500 

1 

2.5 

5 

1,430 

1,950 

2,250 

2,350 

3.0 

6 

1,250 

1,800 

2,100 

2,200 

3.5 

7 

1,100 

1,660 

1,960 

2,080 

4.0 

8 

980 

1,520 

1,820 

1,950 

4.5 

9 

850 

1,400 

1,690 

1,840 

5.0 

10 

750 

1,260 

1,550 

1,720 

1 

5.5 

11 

650 

1,120 

1,420 

1,600 

1 

6.0 

12 

600 

1,000 

1,300 

1,500 

Cement  is  usually  measured  by  the  barrel  just  as  it  comes  from  the  manu- 
facturer, or  as  4  bags  to  the  barrel,  while  broken  stone  and  sand  are  measured 
loose  in  a  barrel.  Portland  cement,  after  it  is  taken  out  of  its  original  package 
and  stirred  up,  fills  a  larger  volume  than  when  packed.  It  is  therefore  necessary 
to  state  just  how  the  cement  is  to  be  measured;  and,  as  said  before,  the  custom 
is  to  measure  it  by  the  barrel,  compact.  A  cement  barrel  contains  about 
3.8  cu.  ft. 

Fuller's  Rule  for  Quantities. — A  practical  rule  has  been  devised  by  W.  B. 
Fuller  whereby,  after  the  proportions  of    ingredients   have  been    fixed,  the 
quantity  of  material  for  a  certain  work  may  be  obtained  with  reasonable 
closeness.     It  is  called  Fuller's  rule  for  quantities,  and  may  be  expressed  in 
mathematical  symbols  as  follows: 
Let  c  =  number  of  parts  of  cement; 
5  =  number  of  parts  of  sand ; 
g  =  number  of  parts  of  gravel  or  broken  stone; 
C  =  number  of  barrels  of  Portland  cement  required  for  1  cu.  yd.  of 

concrete; 

5  =  number  of  cubic  yards  of  sand  required  for  1  cu.  yd.  of  concrete; 
G  =  number  o£  cubic  yards  of  stone  or  gravel  required  for  1  cu.  yd.  of 
concrete. 


Then 


3-8  r         Ar 

Cs' and  G  = 


in  the  second  formula,  S  =  -^=- 


If  the  broken  stone  is.  of  uniformly  large  size,  with  no  smaller  stone  in  it, 
the  voids  will  be  greater  than  if  the  stone  were  graded.  Therefore,  5%  must 
be  added  to  each  value  found  by  the  preceding  formulas. 

EXAMPLE. — If  a  1-2-4  mixture  is  considered,  what  will  be:  (a)  the  number 
of  barrels  of  cement?  (&)  the  number  of  cubic  yards  of  sand?  and  (c)  the  number 
of  cubic  yards  of  stone  required  for  1  cu.  yd.  of  concrete? 

SOLUTION. — (a)  Here  c  =  l,  s  =  2,  and  g  =  4.     Substituting  these  values  in 

the  first  formula,  C  =  — ^—  =  1.57. 
1+2+4 

(b)  Substituting  the  values  of  C  and 
X  1.57X2  =  .44. 

(c)  Substituting  the  values  of  C  and  g  in  the  third  formula,  C  =  |f  X  1.57 
X4  =  .88. 

WORKING  OF  CONCRETE 

Mixing  of  Concrete. — Concrete  may  be  mixed  either  by  hand  or  by  machine- 
£or  small  work,  the  concrete  is  mixed  by  hand  in  small  batches,  such  as  would 
be  made  up  from  1  or  2  bags  of  cement.  When  mixing,  hand  work  should  be 
performed  on  a  flat,  water-tight  platform.  The  sand,  after  it  has  been  meas- 
ured, is  spread  over  the  platform  in  an  even  layer.  Upon  the  sand  is  placed 
the  cement,  and  these  two  materials  are  turned  over  with  shovels  at  least  three 


CONCRETE  213 

times,  or  until  the  uniform  color  of  the  mixture  indicates  that  they  are  thor- 
oughly incorporated.  The  stones,  or  aggregates,  having  previously  been  well 
wetted,  are  then  placed  on  the  top  of  the  mixture  of  sand  and  cement,  and 
these  materials  are  also  turned  at  least  three  times,  water  being  added  after 
the  first  turning.  The  water  should  always  be  added  in  small  quantities.  If 
a  hose  is  used  for  this  purpose,  it  should  be  fitted  with  a  sprinkling  nozzle,  as 
otherwise  much  of  the  cement  is  liable  to  be  washed  out  of  the  mixture.  The 
concrete,  when  ready  for  placing,  should  be  of  uniform  consistency,  either 
mealy  for  a  dry  mix  or  mushy  for  a  wet  mix.  In  large  work,  the  mixing  should 
be  done  by  machine. 

Retempering  of  Concrete. — If  the  cement  of  the  concrete  has  attained  its 
initial  set  before  being  placed — that  is,  if  the  concrete  has  commenced  to 
harden — remixing  with  water,  or  retempering  the  concrete,  as  it  is  called,  should 
not  be  allowed;  and  if  concrete  treated  in  this  manner  has  been  deposited  in 
the  forms,  it  should  be  taken  out  and  removed  from  the  site  of  the  operation, 
because  concrete  cannot  be  retempered  properly,  except  in  small  quantities 
for  laboratory  tests. 

Concreting  at  High  Temperatures. — If  the  weather  is  extremely  warm,  the 
stone  and  sand  are  liable  to  become  heated  to  a  high  temperature.  In  such 
cases,  when  the  materials  are  being  mixed,  the  water  necessary  for  the  crystal- 
lization of  the  cement  is  rapidly  absorbed  by  the  stone  and  the  sand,  or  else 
is  rapidly  evaporated  by  contact  with  them.  Besides,  the  extreme  heat  will 
hasten  the  setting  of  the  cement,  which  gives  it  a  tendency  to  cake  in  the  mixing 
machine,  producing  lumpy  and  inferior  concrete.  In  order  to  overcome  such 
difficulties,  the  stone  should  be  thoroughly  wetted  with  a  hose,  and  the  sand  and 
stone  should  be  kept  under  cover,  away  from  the  direct  rays  of  the  sun.  Like- 
wise, the  mixing  platform  or  machine  should  be  roofed  over.  It  is  well,  also, 
to  wet  down  the  finished  concrete  work  with  a  hose  several  times  a  day  in 
extremely  hot  weather,  and  less  frequently  in  moderate  temperatures. 


and  placed  even  at  this  temperature,  if  there  is  a  possibility  that  the  temper- 
ature will  fall.  If  concrete  is  frozen,  its  setting  is  retarded  and  it  is  liable 
to  become  worthless,  never  properly  setting  and  obtaining  the  requisite  hard- 
ness and  strength.  There  is,  however,  no  certainty  of  the  action  of  frost  on 
concrete,  as  frozen  concrete  will  frequently  thaw  out  and  set,  with  apparently 
little  loss  of  strength. 

To  prevent  the  freezing  of  concrete  when  the  temperature  has  fallen  below 
32°  F.,  salt  is  sometimes  used  in  the  mixture. 

One  rule  is  1%  of  salt  to  the  water  for  each  degree  below  32°  F.,  as  already 
stated  in  the  case  for  mortar.  More  than  12%  salt  should  never  be  used.  The 
addition  of  salt,  however,  is  never  advisable  if  a  surface  finish  is  required,  as 
the  salt  is  liable  to  cause  efflorescence,  or  a  white  deposit,  on  the  surface  causing 
the  work  to  become  very  unsightly. 

Aggregates  that  are  coated  with  ice  or  that  have  been  exposed  to  severe 
weather  for  a  long  time  should  be  heated  or  thawed  out  before  being  used. 
Concrete  that  is  exposed  to  freezing  after  it  is  set  should  always  be  protected 
by  placing  over  it  a  layer  of  boards  and  straw,  or  salt  hay,  or  cement  bags; 
or,  where  the  work  is  in  the  nature  of  a  reinforced-concrete  floor  system,  by 
heating  the  interior  of  the  structure  by  means  of  salamanders  or  fires. 

Joining  of  Old  Concrete  With  New. — New  and  old  concrete  can  be  joined 
only  with  difficulty,  and  the  strength  of  such  a  connection  is  always  uncertain. 
The  joining  of  old  and  new  concrete  work  is  best  done  by  thoroughly  chipping, 
or  cutting  away,  the  old  surface,  saturating  it  with  water,  and  working  into  it 
thin  coats  of  a  1-1  Portland-cement  mortar,  and,  then,  while  the  coating  is 
still  fresh,  placing  against  it  the  new  concrete. 

There  are  some  high-grade,  imported  cements  that,  in  the  form  of  cement 
mortar,  more  readily  adhere  to  old  concrete  work  than  the  usual  Portland 
cements.  These  cements  are  frequently  used  for  patching  arid  piecing  out  work 
already  in  place. 


214  CONCRETE 

ELEMENTS  OF  STEEL  REINFORCEMENT 

PRINCIPLES  OF  CONSTRUCTION 

When  a  beam  is  subjected  to  tranverse  stress,  due  to  loads,  the  portion 
of  the  beam  section  above  the  neutral  axis,  or  axis  along  which  there  is  no 
stress,  is  in  compression,  while  in  that  portipn  below  the  neutral  axis,  tensile 
stresses  are  created.  Ordinarily,  concrete  is  about  ten  times  as  strong  in 
compression  as  it  is  in  tension.  Thus,  it  can  readily  be  seen  that  a  beam  of 
plain  concrete  without  steel  reinforcement  will  fail  primarily  from  lack  of 


tensile  resistance,  without  realizing  its  full  compressive  strength.  In  order, 
therefore,  to  make  concrete  an  economical  material  to  use  in  construction,  its 
deficiency  in  tensile  resistance  must  be  made  up  by  embedding  steel  rods, 
bars,  or  some  other  form  of  metallic  reinforcement  in  that  portion  of  the  beam 
section  subjected  to  tensile  stress. 

In  order  to  explain  more  fully  this  primary  principle  of  reinforced,  concrete, 
reference  is  made  to  the  reinforced,  rectangular  concrete  beam  here  shown. 
The  neutral  line  of  the  section  is  shown  at  y\  y\  in  the  side  view  (a) ,  while  the 
neutral  axis  is  represented  by  y  y  in  the  end  view  (b).  When  the  concrete  beam 
is  under  tranverse  stress,  there  is  neither  tensile  nor  compressive  stress  at  the 
neutral  axis.  Therefore,  the  point  a  in  the  beam  which  is  on  the  neutral  axis,  is 
subjected  to  zero  stress. 

Should  the  concrete  be  cut  away  below  the  neutral  plane,  leaving  the  steel 
reinforcing  rods,  or  bars,  exposed  as  at  b,  the  strength  of  the  beam  will  not  be 
greatly  affected,  as  the  necessary  tension  below  the  neutral  axis  is  supplied  by 
the  reinforcing  rods  of  steel,  while  the  necessary  compression  above  it  is  fur- 
nished by  the  concrete,  as  at  c.  The  amount  of  compression  in  each  square 
inch  of  concrete  above  the  neutral  axis  varies  from  zero  at  the  axis  to  a  maxi- 
mum at  the  extreme  upper  surface  of  the  beam.  The  concrete  below  the 
neutral  axis  yy  is  usually  so  filled  with  very  fine  cracks  that  all  the  tension 
must  be  carried  by  the  steel  alone. 

In  ordinary  reinforced-concrete  column  construction,  merely  vertical  rods 
are  employed.  They  are  tied  together,  however,  at  intervals  with  wire  or 
other  ties. 

The  principle  ot  hooped  columns  is  best  explained  as  follows:  It  is  well 
known  that  a  column  of  sand  will  not  resist  compression,  because  it  will  spread, 
while  a  cylinder  of  very  thin  metal  will  sustain  only  a  small  load.  However, 
if  the  cylinder  is  filled  with  sand,  the  tensile  strength  of  the  cylinder  combined 
with  the  compressive  resistance  of  the  sand,  will  produce  a  column  capable  of 
resisting  considerable  compression.  This  principle  is  applied  to  the  reinforce- 
ment of  concrete  columns  by  binding,  or  tying,  together  the  concrete  with 
cylindrical  hoops,  or  helical,  or  spiral,  windings  of  steel  a  few  inches  below 
the  surface. 

PARTS  OF  STEEL  REINFORCEMENT 

In  the  accompanying  illustration  is  shown  a  perspective  view  (a)  of  a 
complete  bay  of  a  reinforced-concrete  floor  system,  and  a  diagrammatic  repre- 
sentation (b)  of  a  typical  system  of  reinforcement  for  a  concrete  girder  and 
column.  In  (a),  the  heavy  members  A  running  between  columns  are  com- 
monly known  as  girders,  and  the  lighter  members  B  running  between  girders, 
as  beams.  In  both  (a)  and  (&),  the  rods,  or  bars,  a  are  the  main  reinforcing 
bars,  or  rods,  of  the  girders.  The  beams,  of  course,  have  similar  main  rein- 
forcing bars.  Of  these  main  reinforcing  bars,  several  are  bent  up,  as  at  b,  to 
form  trussed  bars.  The  web  reinforcement  of  the  girders  is  shown  at  c,  and 
consists  of  U-shaped  pieces  of  iron  or  steel,  called  stirrups.  The  rods  that 


CONCRETE 


215 


reinforce  the  slab  of  the  reinforced-concrete  floor  system,  called  slab  rods,  are 
shown  at  d.     This  slab  reinforcement  may  consist  of  straight  rods,  expanded 


metal,  woven-wire  lath,  or  any  other  metallic  reinforcement.  The  stirrups 
are  bent  over  at  the  upper  ends  or  fastened  to  the  slab  rods  so  that  they  will 
not  pull  put.  The  rods  of  the  columns  e  are  called  longitudinal  column  rods, 
and  the  ties  /,  column  ties. 

Any  rod,  or  bar,  used  to  resist  shearing  stresses  is  designated  as  a  shear  bar. 
A  rod,  or  bar,  used  to  resist  the  shrinkage  of  the  concrete  in  setting,  or  to 
provide  against  cracks  due  to  thermal  changes,  is  called  a  shrinkage  rod.  Shrink- 
age rods  are  shown  at  g  in  view  (a).  Sometimes  all  the  slab  rods  run  one  way 
and  an  occasional  shrinkage  bar  is  used  at  right  angles  to  them  as  shown,  to  pre- 
vent shrinkage  cracks.  A  rod  used  to  connect  abutting  beams  or  girders  is 
called  a  tension  bar  or  a  tie  bar.  The  short  rods  used  at  the  splice  when  longi- 
tudinal column  rods  are  butted  are  called  splice  rods,  or  bars. 

Members  to  Resist  Lines  of  Failure. — In  the  accompanying  figure  are 
illustrated  a  typical  beam  having  the  usual  type  of  steel  reinforcement  and 


the  several  methods  of  failure  that  might  occur.  At  a  are  shown  cracks,  or 
lines  of  failure,  that  would  be  caused  by  lack  of  tensile  resistance  in  the  main 
reinforcing  rods  b.  These  cracks,  are  usually  invisible,  and  generally  extend 


216 


CONCRETE 


from  the  bottom  surface  to  the  neutral  axis.  They  are  nearly  always  present 
in  concrete,  but,  of  course,  so  long  as  the  steel  holds,  the  beam  will  not  fail. 

If  the  main  reinforcing  rods  do  not  extend  to  the  bearings,  failure  by  vertical 
shear  may  occur  near  the  abutments,  along  the  line  x  x.  Failures  of  this  kind 
seldom  happen,  because  the  main  rods  usually  extend  across  all  such  lines 
of  vertical  shear,  and  add  greatly  to  the  shearing  resistance  of  the  beam. 

If  the  slab  concrete  is  not  placed  at  the  same  time  that  the  concrete  of  the 
beam  section  is  poured,  failure  by  shearing  usually  occurs  at  the  junction  of  the 
beam  with  the  slab,  as  shown  at  c.  The  shearing  resistance  at  this  junction 
should  be  increased,  however,  by  extending  stirrups  d  into  the  slab.  If  the 
crack  c  opens,  it  usually  joins  with  a  crack,  like  e,  at  each  end  of  the  beam,  as 
suggested  in  the  preceding  paragraph. 

The  lines  of  failure  indicated  at  e  are  those  that  usually  occur  from  diagonal 
tension  stresses  that  cross  these  lines  of  failure  at  right  angles.  A  beam  is 
held  against  failure  in  this  manner  by  placing  stirrups  in  the  concrete  either 
vertically  or  obliquely.  The  bending  up  of  the  main  reinforcing  rods  to  form 
the  trussed  bar,  as  shown  at  ff,  will  also  assist  in  resisting  such  stresses,  and, 
besides,  will  provide  against  negative  bending  moment  where  tension  instead 
of  compression  is  created  at  gg.  The  line  of  fracture  shown  at  ee  is  typical  of 
nearly  all  reinforced-concrete  failures. 

AREAS  AND  WEIGHTS  OF  SQUARE  AND  ROUND  BARS 


c:rp 

Square 

• 

Round 

• 

olZG 

Inches 

Area 
Inches 

Weight 
per  Foot 
Pounds 

Area 
Inches 

Weight 
per  Foot 
Pounds 

T6 

.0039 

.013 

.0031 

.010 

i 

.0156 

.053 

.0123 

.042 

A 

.0352 

.120 

.0276 

.094 

i 

.0625 

.213 

.0491 

.167 

JL 

.0977 

.332 

.0767 

.261 

1 

.1406 

.478 

.1104 

.376 

iV 

.1914 

.651 

.1503 

.511 

I 

.2500 

.850 

.1963 

.668 

& 

.3164 

1.076 

.2485 

.845 

| 

.3906 

1.328 

.3068 

1.043 

'fi 

.4727 

1.607 

.3712 

1.262 

A 

.5625 

1.913 

.4418 

1.502 

if 

.6602 

2.245 

.5185 

1.763 

i 

.7656 

2.603 

.6013 

2.044 

16 

.8789 

2.989 

.6903 

2.347 

1 

1.0000 

3.400 

.7854 

2.670 

1ft 

1.1289 

3.838 

.8866 

3.014 

H 

1.2656 

4.303 

.9940 

3.379 

A 

1.4102 

4.795 

1.1075 

3.766 

j 

1.5625 

5.312 

1.2272 

4.173 

1*5 

1.7227 

5.857 

1.3530 

4.600 

8 

1.890G 

6.428 

1.4849 

5.049 

'IS 

2.0664 

7.026 

1.6230 

5.518 

% 

2.2500 

7.650 

1.7671 

6.008 

& 

2.4414 

8.301 

1.9175 

6.520 

f 

2.6406 

8.978 

2.0739 

7.051 

li 

2.8477 

9.682 

2.2365 

7.604 

| 

3.0625 

10.413 

2.4053 

8.178 

it 

3.2852 

11.170 

2.5802 

8.773 

1 

3.5156 

11.953 

2.7612 

9.388 

It 

3.7539 

12.763 

2.9483 

10.024 

2 

4.0000 

13.600 

3.1416 

10.681 

CONCRETE 


217 


REINFORCING  MATERIALS 

The  reinforcement  for  concrete  is  almost  uniformly  steel,  but  the  grade  to 
be  used  should  be  determined  by  one  who  has  made  a  careful  study  of  this 
matter.  He  should  both  write  the  specifications  and  inspect  the  steel  after- 
wards to  make  sure  that  the  steel  specified  has  been  furnished.  Steel  used  for 
reinforcement  should  be 
free  from  rust  and  scale 
or  any  coating  that  will 
tend  to  weaken  the  bond 
between  the  metal  and 
the  concrete. 

Plain  Bar  Iron. 
The  cheapest  form  of 
metallic  reinforcement 
for  concrete  is  the  plain, 
round,  rolled  bar.  This 
bar  can  be  obtained  in 
any  part  of  the  United 
States  and  as  its  price 
per  pound  is  lower  than 
that  of  any  other  form  of  rolled  steel,  it  is  the  cheapest  and  most  available 
material.  For  slabs,  f-  to  ^-in.  round  bars  are  used,  while  for  beam,  girder, 
and  column  reinforcement,  from  f-  to  H-in.  bars  are  ordinarily  employed. 

The  principal  objection  to  the  use  of  plain,  round  bars  in  reinforced-concrete 
work  is  that  they  are  not  gripped,  or  held,  well  by  the  concrete.  Plain  square 
and  flat  bars  are  sometimes  used  for  the  reinforcement  of  concrete,  though, 
generally,  both  of  these  sections,  when  so  used,  are  deformed  by  twisting. 


FIG.  1 


In  the  nomenclature  of  reinforced  concrete,  round,  rolled  sections  are 
designated  as  rods;  square  sections  as  bars;  and  rectangular  sections  as  flats, 
or  flat  bars. 

In  the  preceding  table  are  given  the  areas  and  weights  of  square  and  round 
bars  from  ^-  to  2-in.  sizes. 

Bars  of  Special  Construction. — Some  early  forms  of  bars  used  in  reinforce- 
ment of  concrete  are  shown  in  Fig.  1.  That  shown  in  (a)  is  known  as  the 
Hyatt  bar.  In 
(fe)  is  shown  the 
Staff  bar;  this 
consists  of  a 
flat  bar,  through  I 

which    a    coun-  ,ff\ 

tersunk     punch 

has  been  partly  driven,  thus  forcing  the  metal  out  on 
the  opposite  side  so  as  to  form  projections.  The  De  Mann 
bar  is  shown  in  (c). 

There  are  numerous  bars  on  the  market  having  special 
mechanical  bonds.  The  complete  descriptions  of  such 
bars  can  be  obtained  from  their  manufacturers.  Only 
a  few  will  be  mentioned  here  as  examples. 

Square-Twisted  Bars. — The  square-twisted  bar  con-     ,. 
sists  of  a  square  bar  that  is  twisted  by  being  given  a  cer-  $xZ%t 
tain  number  of  turns  around  its  axis,  either  while  it  is  hot  foof-Xreff=o.795f.t. 
or  while  it  is  cold;  this  bar  is  often  known  as  the  Ran-  ^ 

some  bar.     By  twisting  the  bar  to  the  screw  shape,  as  T?       Q 

shown  in  Fig.  2  (a),  a  form  is  obtained  that  has  great  re-  ^IG*  " 

sistance  to  pulling  from  a  mass  of  concrete.  If  the  square  bars  are  twisted 
cold,  their  elastic  limit  and  ultimate  strength  are  increased  from  8  to  25%.  The 
square-twisted  bar  can  be  obtained  in  various  sizes  for  various  purposes. 

Corrugated  Bar. — In  Fig.  2  (fc)  is  shown  a  corrugated  bar  known  as  the 
Johnson  bar,  after  its  inventor,  A.  L.  Johnson.  The  corrugations  on  the 
sides,  of  course,  increase  greatly  over  smooth  bars  the  grip  on  the  concrete. 


218 


CONCRETE 


Kahn  Trussed  Bar. — Fig.  3  (a)  shows  the  Kahn  Trussed  Bar.  The  sec- 
tion of  one  of  these  bars  is  shown  in  (fe).  The  fins  are  partly  sheared  across 

and  also  in  a  direction  parallel  with 
the  axis  of  the  bar,  and  are  bent 
up,  as  shown  in  (a),  so  as  to  form  a 
grip  with  the  concrete  and  to  pro- 
vide the  stirrups,  or  web  members, 
necessary  to  resist  diagonal  stresses. 
The  Kahn  bar  is  made  in  various 
sections. 

Expanded  Metal. — One  form  of 
metallic  reinforcement  for  concrete 
is  the  distorted  steel  plate  known 
as  expanded  metal,  a  familiar  illus- 
tration of  which  is  shown  in  Fig.  4 
(a).  This  form  of  reinforcement  is 
manufactured  by  partly  shearing  a 
sheet  of  steel  in  parallel  rows,  as 
shown  in  (b),  and  then  pulling  the 
material  sidewise,  thus  forming  a 
diamond  mesh.  In  this  way,  the 
area  of  a  sheet  is  increased  about 
eight  times,  with  a  corresponding 
decrease  in  weight  per  unit  area  and  without  any  waste  of  material.  The 
material  is  made  in  various  sizes.  Various  forms  of  metal  lath  are  to  be  had. 
Woven  Wire. — Various  forms  of  wire  cloth,  or  woven  wire,  are  also  on  the 
market.  Among  them  is  Clinton  wire  cloth.  It  is  a  fabric  that  is  secured  at  the 
intersections  by  a  perfect,  electric  weld,  and  it  has  at  intervals  a  double  wire 
that  twines  in  and  out,  as  shown  at  a,  Fig.  5. 

Floor  Systems. — A  complete  floor  system  constructed  of  loose  rods  is  shown 
in  Fig.  6.  The  beam  reinforcement  consists  of  three  reinforcing  rods.  Two  of 
these  rods  a  run  straight  through  the  entire  length  of  the  beam,  while  the  third  b 
is  bent  upwards  at  the  ends.  This  bent  member  provides  tensile  resistance 
at  the  top  of  the  beams  and  thus  takes  care  of  the  negative  bending  moment, 
which  occurs  in  all  beams  fixed  at  the  end.  The  bend  in  such  rods  is  usually 
made  at  an  angle  of  about  30°  with  the  horizontal.  The  rods  should  be  straight 
at  the  center  of  the  span  for  at  least  one- third  the  distance  between  the  supports. 
A  tie-rod  c,  that  is  4  or  5  ft.  in  length,  and  sometimes  bent  down  at  the 
ends,  should  be  placed  over  the  top  of  the  beam  juncture. 

The  girder  reinforcement  consists  of  five  rods,  two  of  them  c  being  bent  up 
to  provide  against  negative  bending  moment. 

In  the  best  work,  two  short  rods  /  are  located  transversely  through  the 
column.  These  rods  tie  the  adjoining  girders  together  and  provide  additional 
rigidity  at  the  junction  of  the  girders  with  the  column. 

The  slab  rods  h  are  generally  spaced  at  about  6  in.  from  center  to  center. 
They  should  bond  with  the  stirrups,  or  web  reinforcement,  of  the  beams,  and 
may  be  threaded  through,  interlocked,  or 
wired  to  them.  It  is  customary  to  provide  ' 
shrinkage  rods  that  extend  at  right  angles 
to  the  regular  slab  reinforcement,  in  order  ' 
to  prevent  shrinkage  cracks  in  the  con- 
crete. For  this  purpose,  J-in.  round  or  ' 
square  rods  j  are  generally  spaced  about 
2  ft.  from  center  to  center.  In  order  to  ' 
bond  the  concrete  over  the  main  girders 
securely,  it  is  also  good  practice  to  pro- 
vide over  these  important  members  rods 
d  of  about  the  same  size  as  the  slab  rods. 
These  rods  should  run  through  holes 
punched  in  the  top  of  the  stirrup,  as 
illustrated  at  g,  and  should  extend  at 
right  angles  to  the  axis  of  the  girder. 
Sometimes,  similar  rods  are  used  in  the 
slab  over  beams,  as  shown  at  k. 

The  longitudinal  reinforcement  of  the 
concrete  columns  consists   of   four  round 


FIG.  5 


rods  /.     It  is  customary  to  project  them  above  the  concrete  of  each  story 
about  a  foot  and  to  splice  them  by  lapping  and  wiring  or  by  using  pipe 


CONCRETE 


219 


220 


CONCRETE 


sockets  m,  as  illustrated.  Frequently,  it  is  not  possible  to  lay  out  beforehand 
the  electric-light  or  power  wiring,  but  if  this  installation  is  to  be  adopted 
IJ-in.  pipes  to  serve  as  a  passageway  should  be  embedded  near  the  center  of 
the  span  of  all  beams  and  girders  close  to  the  under  side  of  the  slab  con- 
struction, as  at  n.  

FORM  WORK 

CONSTRUCTION  AND  FINISH  OF  FORM  WORK 

In  the  erection  of  reinforced-concrete  work,  nothing  requires  more  careful 
consideration  than  the  construction  of  the  form  work,  or  molds,  necessary  to 
shape  and  support  the  concrete  until  it  has  thoroughly  set  and  hardened. 
Throughout  the  practice  of  reinforced-concrete  construction  various  methods 
of  form  constructions  are  in  use. 

The  greatest  economy  is  gained  by  constructing  the  forms  so  that  they  can 
be  used  over  and  over  again  in  the  structure.  Economy  in  construction  can 


FIG.  1 

also  be  gained  by  fastening  the  form  work  together  with  a  minimum  amount  of 

nailing.     Every  nail  that  is  driven  gives  trouble  when  the  forms  are  taken  down 

to  be  replaced  for  the  upper  floors.     In  many  constructions,  wedges  and  clamps 

are  used  instead  of  nails  or  screws  if  the  forms  are  to  be  reused. 

In  some  instances,  both  wooden  and  metal  forms  are  coated  on  the  side  next 

to  the  concrete  in  order  that  the  forms  may  be  detached  more  readily.     Coating 

the  forms  also  serves  to  prevent  the  marking  of  the  grain  of  the  wooden  forms 

on  the  finished  concrete  work. 

Dead  oil,  or  crude  petroleum,  has  been  used  with  success  for  this  purpose. 

It  is  not  unusual  to  soap  wooden  forms,  and  in  some  cases  tallow  and  bacon  fat 

have  been  employed.    The  latter  is  especially  recommended 

for  coating  metal  forms,  as  it  seems  to  give  the  best  results 

with  forms  of  this  material.     In  some  instances,  wooden 

forms  have  been  covered  on  the  inside  with  paper,  and  even 

canvas  has  been  used,  although  it  is  usually  found  that  the 
paper  adheres  to  the 
concrete  work  and  is  de- 
tached only  with  diffi- 
culty. It  is  not  cus- 
tomary, however,  to  oil 
or  coat  the  forms  unless 
they  are  to  be  used  for 
fine  exterior  work. 

FORMS  FOR  FLOOR 

SYSTEMS 

,,  „  Common   Types   of 

FlG-  2  Form  Work.— In  Fig.  1 

is  shown  a  type  of  form  work  extensively  used  for  the  construction  of  rein- 
forced-concrete  floor  systems,  and  in  Fig.  2  is  shown  a  perspective  of  the  forms 
at  the  intersection  of  a  beam  and  girder.  This  form  work  is  designed  so  that 
light  g-in.  dressed  tongued-and-grooved  material  may  be  used  extensively  in  its 


CONCRETE 


221 


construction.     It  is  so  arranged  that  the  sides  of  the  beams  and  girders,  to- 
gether with  the  slab  form  boards,  may  be  removed  without  the  necessity  of 


PIG.  4 


removing  the  supports  directly  underneath  the  beams  and  girders.     The  form 
for  columns  in  this  type  of  construction  is  shown  in  Fig.  3. 


FIG.  5 


FIG.  6 


Forms  Constructed  of  Plank. — A  superior  type  of  form  for  a  reinforced- 
concrete  floor  system  is  shown  in  Fig.  4.  The  wooden  forms  are  supported 
by  3"X4"  studs.  As  it  is  important  to  bring 
the  forms  to  a  true  level,  a  double  adjustment 
wedge  is  provided  at  the  bottom  of  the  studs. 
The  forms  for  the  columns  are  made  of  \%-  or 
2-in.  material.  In  the  construction  of  the  beam 
and  girder  forms  2-in.  planks  are  generally 
used  for  the  sides.  In  order  to  form  a  cham- 
fer on  the  lower  edges  of  the  beams  and  girders, 
triangular  fillet  pieces  are  nailed  in  the  forms. 
It  is  customary  in  this  type  of  construction  to 
make  the  forms  for  the  slabs  of  |-in.  plain 
boards,  frequently  using  tongued-and-grooved  material  for  the  purpose. 

Wall  Forms  With  Wire  Ties. — A  type  of-  wall-form  construction  that  is 
frequently  used  is  illustrated  in  Fig.  5.     In  order  to  prevent  the  sides  of  the 


FIG.  7 


222  CONCRETE 

forms  from  spreading  when  the  concrete  is  tamped  in  place,  a  wire  tie  c  is  used. 
This  tie  is  made  taut  by  twisting  with  a  bar,  or  stick  d.  To  keep  the 
form  boards  the  proper  distance  apart  for  the  thickness  of  the  wall,  a  block 
or  stick  e,  of  wood  is  sometimes  inserted. 

Wall-Form  Construction  With   Clamp  Bolts. — A  wall-form  construction 
similar  to  that  shown  in  Fig.  5  is  illustrated  in  Fig.  6  (a).     In  this  form,  how- 


FIG. 


ever,  a  clamp  bolt  a,  instead  of  a  wire  tie,  is  used  to  prevent  spreading.  If  a 
bolt  of  this  character  is  used,  it  must  be  knocked  out  before  the  concrete  has 
finally  set  and  when  the  form  boards  are  to  be  raised  to  form  the  next  course 
of  concrete.  The  bolt  is  preferable  to  the  wire  tie,  because  it  is  removed  from 
the  concrete.  Wire  ties  are  usually  cut  off  close  to  the  concrete  work  after  the 
form  boards  have  been  removed,,  and  as  the  ends  frequently  project,  they  rust 
and  thus  stain  the  wall. 


CONCRETE  223 

In  (b)  is  shown  the  construction  of  a  wall  f of  m  in  which  a  pipe  separator  a 
is  used  with  the  clamp  bolt.  The  pipes  may  be  driven  out  of  the  concrete  after 
it  has  obtained  its  initial  set,  or  .they  may  be  left  in  place. 

Clamping  Devices  and  Plank  Holders  for  Wall  Forms. — Many  devices  that 
aid  in  the  construction  of  concrete  walls  have  been  invented.  One  of  the  most 
useful  of  these  devices  is  the  Sullivan  pressed-steel  plank  holder,  various  forms 
of  which  are  shown  in  Fig.  7.  These  holders  are  formed  from  an  iron  plate  by 
shearing  and  bending  it  so  as  to  form  clips.  The  application  of  this  type  of 
plank  holder  is  illustrated  in  Fig.  8. 

Braces  for  Wall  Forms. — If  a  wall  is  to  be  constructed  in  a  place  where 
there  is  no  embankment,  a  double  set  of  forms  braced  as  shown  in  Fig.  9  (a) 
must  be  used.  If  the  soil  of  an  embankment  against  which  a  concrete  wall  is  to 
be  built  is  unstable,  it  is  necessary  to  sheath  and  brace  it.  This  may  be  accom- 
plished in  the  manner  shown  in  (b)  or  (c). 


CONCRETE  MIXERS 

In  the  construction  of  a  reinforced-concrete  structure,  the  quantity  of  con- 
crete to  be  placed  decides  the  amount  of  equipment  and  the  character  of  the 
machinery  that  is  to  be  employed.  The  character  of  the  work  also  influences 
these  two  factors.  In  all  instances,  the  concrete  plant  should  be  equipped 
with  machinery  suitable  for  the  size  of  the  work  and  the  number  of  men  that 
will  be  available  in  the  construction  operation.  On  small  work,  the  concrete  is 
frequently  mixed  by  hand;  it  is,  however,  unusual  for  the  concrete  in  large  9per- 
ations  to  be  so  mixed.  The  successful  contractor  will  employ  the  mixing 
machine  that  is  found  most  efficient  and  will  give  careful  attention  to  its  erec- 
tion in  the  field. 

There  are  many  kinds  of  concrete  mixers  in  commercial  use.  These  mixers 
are  classified  according  to  the  principles  upon  which  they  operate,  and  are 
known  as  batch  mixers  and  continuous  mixers. 

Frequently,  the  selection  of  the  mixer,  especially  in  work  where  new  equip- 
ment is  to  be  used,  is  left  to  the  superintendent.  In  making  the  selection,  the 
superintendent  should  bear  in  mind  the  character  of  the  work;  that  is,  whether 
it  is  of  more  importance  to  turn  out  great  quantities  of  concrete  than  it  is  to 
have  a  uniform  mixture,  or  whether,  as  in  a  reinforced-concrete  building,  the 
most  important  consideration  is  to  have  concrete  delivered  from  the  mixer  of 
uniform  consistency.  Usually,  for  heavy  mass  work  the  continuous  mixer  is 
advantageous,  but  the  batch  mixer  is  now  more  used  for  work  such  as  that 
included  in  ordinary  reinforced-concrete  buildings. 

The  batch  mixer  often  consists  of  a  metal  box  in  the  shape  of  a  cube,  a 
cylinder,  etc.  The  materials  are  put  in  this  box  and  are  mixed  by  revolving 
the  box  on  a  horizpntal  axis.  There  are  often  deflectors  on  the  inside  of  the 
box  to  help  in  mixing.  The  machines  are  sometimes  discharged  by  tipping 
them  until  the  contents  slide  out  of  an  opening  or  by  other  suitable  means. 

The  continuous  mixer  often  consists  of  a  trough  or  cylinder  or  long  box 
square  in  section.  The  materials  enter  continuously  at  one  end  and  are  dis- 
charged mixed  at  the  other.  They  are  usually  mixed,  in  their  passage  through 
the  machine,  by  paddles  or  deflectors,  or  by  revolving  the  cylinder  or  box. 
The  ingredients  are  often  moved  from  the  receiving  to  the  discharging  end  of  the 
machine  either  by  the  trough  or  cylinder  being  tilted  or  by  paddles  that  grad- 
ually force  the  mass  in  one  direction. 


CONCRETE  STRUCTURES 

It  is  proposed  to  mention  briefly  a  few  of  the  uses  in  engineering  to  which 
concrete  can  be  put.  Complete  examples  of  work  with  all  details  cannot  be 
given  in  such  a  short  space,  but  the  few  words  and  illustrations  may  suggest  to 
the  designer  ideas  that  may  be  elaborated  and  changed  to  suit  various  condi- 
tions. The  calculations  of  stresses  and  proportioning  of  parts  is  beypnd  the 
scope  of  this  work.  They  should  be  left  to  a  competent  designing  engineer. 

Tank  Tower  of  Reinforced  Concrete. — The  tower  shown  in  Fig.  1  was 
designed  to  carry  a  200,000-gal.  steel  tank.  The  tower  consists  of  eight  con- 
crete columns  spaced  on  centers  around  the  circumference  of  a  26|-ft.  circle 
and  surrounding  a  hollow  concrete  cylinder  with  an  inside  diameter  of  8  ft. 
The  columns  and  cylinders  are  held  together  by  two  intermediate  platforms 


224 


CONCRETE 


and  a  heavy  platform .  or  slab,  at  the  top.  The  footing  is  spread  over  the  entire 
base  of  the  tower,  and  is  in  the  form  of  a  sixteen-sided  polygon  being  6  ft  m 
thickness  and  38  ft.  in  diameter  at  the  bottom.  The  central  shaft,  in  addi- 
tion to  carrying  some  of  the  load  of  the  tank,  acts  as  a  cylinder  around  which 
the  reinforced-concrete  stairs  are  run  and  likewise  forms  a  shaft  for  the  pipes 
leading  to  and  from  the  tank.  The  columns  of  the  lower  tier  are  3  ft.  6  in. 
square;  those  of  the  second  tier  3  ft.  square;  and  those  of  the  top  tier,  2  ft.  6  m. 
square.  The  offset  is  made  at  the  outside  of  the  column,  as  shown  in  Fig.  2. 

The  details  of  construction  and  the  method  of  reinforcing  the  columns, 
cylinder,  and  balcony  floor  construction  are  illustrated  m  Fig.  3,  a  halt  plan  ot 

the  structure  being  shown  m  (a),  and  a 
section  through  the  column  construc- 
tion, balcony,  and  cylinder,  in  (b).  As 
will  be  9bserved,  the  thickness  of  the 
cylinder  is  dropped  off  3  in.  at  each  tier; 
thus,  the  walls  of  the  cylinder  at  the 
bottom  are  18  in.  in  thickness,  and  at 
the  second  and  the  third  tier  they  are 
15  in.  and  12  in.,  respectively.  The 
reinforcing  rods  are  likewise  reduced  in 
size  in  both  the  columns  and  the  cylin- 
der from  the  first  tier  upwards.  In  the 
lower  tiers,  the  columns  have  four  IJ-in. 
round  rods;  in  the  second  tier,  four 
If -in.  rods;  and  in  the  upper  tier,  four 
If-in.  rods.  The  vertical  reinforcing  rods 
are  placed  near  the  corners  of  the  col- 
umns and  are  tied  in  with  J-in.  wire  ties 
placed  12  in.  from  center  to  center. 
These  rods  were  figured  in  estimating 
the  compressive  strength  of  the  columns. 
Their  ends  are  neatly  fitted  and  are 
surrounded  with  a  pipe  sleeve.  The 
bottom  rods  project  into  the  reinforced- 
concrete  footing  and  are  slipped  into  pipe 


FIG.  1 


_    y'__ 


— J-g- 


r, 


FIG.  2 


sleeves  provided  with  a  12-in.  circular  cast-iron  base.  In  this  way,  the  bearing 
strength  of  the  bars  was  well  realized.  The  cylinder  is  reinforced  with  vertical 
rods  placed  about  12  in.  from  center  to  center,  and  horizontal  reinforcement, 
consisting  of  1-in.  hoop  rods,  is  also  provided  in  it.  The  balcony  floors  are 
reinforced  with  rods  that  radiate  from  the  cylinder  and  bear  upon  the  concrete 
lintels  spanning  the  space  between  the  columns,  each  of  these  lintels  being  rein- 
forced with  four  corrugated  bars.  The  floor  of  the  third  balcony,  which  carries 
the  tank,  is  about  36J  ft.  in  diameter  and  16  in.  in  thickness.  It  is  heavily 
reinforced  with  radiating  1-in.  rods,  and  is  cantilevered  about  4  ft.  beyond  the 


CONCRETE 


225 


column.  At  each  balcony  is  provided  a  monolithic  railing,  or  balustrade.  This 
railing  is  about  3  ft.  high  and  6  in.  in  thickness  and  is  reinforced.  In  the  con- 
struction of  this  work,  a  1-3-5  mixture  was  used  for  the  foundation  and  a 
1-2-4  mixture,  placed  very  wet,  was  employed  for  the  rest  of  the  construc- 
tion. The  aggregates  used  throughout  the  construction  were  sand  and  good, 


clean  gravel,  which,  being  very  coarse,  took  the  place  of  broken  stone.  No 
effort  was  made  to  finish  the  structure  after  erection,  but  in  placing  the  con- 
crete a  very  wet  mixture  was  used.  It  was  thoroughly  spaded  along  the  sides 
of  the  forms,  so  as  to  force  the  gravel  away  from  the  surface  and  allow  the 
neat  cement  to  mold  smooth  against  the  form  boards.  The  work  that  resulted 
was  smooth  and  presentable. 


226 


CONCRETE 


Reinforced-Concrete  Retaining  Walls. — Fig.  4  shows  a  retaining  wall  of 
moderate  height.  The  base  is  spread  out  at  A  B  so  as  to  make  the  wall  less 
easily  tipped.  The  earth  behind  the  wall  resting  on  the  part  B  has  to  be  lifted 
if  the  wall  tips,  so  this  earth  also  assists  in  preventing  the  wall  from  turning 
over.  The  part  A,  called  the  toe,  extends  out  in  front  of  the  wall,  and  by 
increasing  the  lever  arm  of  the  loads  also  tends  to  prevent  tipping.  The  load 
of  earth  on  the  part  B  tends  to  prevent  sliding.  If  the  wall  still  has  a  tendency 
to  slide,  a  projection,  as  at  c,  is  put  on.  Weepers  d  prevent  the  collection  of 
water,  which  would  endanger  its  stability.  A  wall  such  as  shown  must  be 
thoroughly  and  scientifically  reinforced.  One  method  of  so  doing  is  shown. 

High  Retaining  Walls. — If  retaining  walls  are  to  be  over  12  ft.  in  height, 
they  are  often  designed  with  a  buttress  every  10  or  12  ft.  A  design  suitable 
for  a  high  retaining  wall  is  shown  in  Fig.  5.  In  order  to  stiffen  the  wall  and  to 
cause  it  to  act  merely  as  a  slab  subjected  to  transverse  stress  between  supports, 
the  buttresses  shown  at  a  are  provided.  As  the  resultant  pressure  of  the  earth 
is  in  the  direction  shown  by  the  arrow  b,  the  buttresses  are  subjected  to  trans- 


!  I  I  I  !  !  !  I  '  I  I  I  I  '  ' 

M  M 

j 


MI  rr»"t~n"ni 

el  i  I  i  M 

"^rUn  I  n  HI 

• 


verse  stress  as  a  cantilever.  The  tension  at  the  inside  edge  of  the  buttress  is 
provided  for  by  Kahn  bars  c. 

The  wall  spans  from  buttress  to  buttress  are  reinforced  in  the  same  manner 
as  a  reinforced  floor  slab  span  between  beams  or  girders.  The  wall  is  rein- 
forced with  horizontal  Kahn  bars  d  and  as  the  thrust  of  the  earth  per  square 
foot  on  the  back  of  the  wall  increases  with  the  depth,  these  bars  are  placed 
closer  together  at  the  bottom,  the  spacing  being  increased  toward  the  top. 

To  prevent  its  failure,  the  footing  is  reinforced  along  the  inside  edge  with 
the  beam  e.  This  beam  is  monolithic  with  the  buttress,  so  that  the  footing  is 
logically  reinforced  with  transverse  bars  /.  In  order  that  the  entire  design  may 
be  stiffened  and  strengthened,  gussets  or  fillets  are  inserted  in  the  junctions 
between  the  buttresses  and  the  footing.  To  reinforce  the  footing  further, 
longitudinal  bars  g  are  provided.  Additional  reinforcement  h  running  in  a  ver- 
tical direction  is  provided  in  the  wall. 

Conduits. — Reinforced  concrete  is  used  for  such  constructions  as  water 
conduits,  sewers,  aqueducts,  etc.  A  type  of  conduit  for  carrying  water  is 


CONCRETE 


227 


shown  in  Fig.  6.     As  will  be  observed,  it  is  reinforced  with  expanded  metal. 
In  nearly  all  instances,  such  conduits  are  constructed  with  collapsible  centering 


1 

1                1   . 

1              1 

1 

inside,  and  with  forms  and  lagging  for  the  outside  work.     The  work  is  always 
carried  along  in  sections. 

Coal  Breakers  in  Reinforced  Concrete. — The  Taylor  coal  breaker  was  the 
first  all  reinforced-concrete  breaker  constructed  in  the  anthracite  fields, 
although  the  Pine  Hill  breaker,  at  Minersville,  Pa.,  was  built  in  1906,  of  rein- 
forced concrete  from  the  foundations  to  the 
main  breaker  floor,  including  the  coal  pockets, 
slate  pockets,  and  shaker  and  jig  supports. 

Under  favorable  conditions,  the  average 
wooden  anthracite  breaker  has  a  life  of  about 
20  yr.,  but  mostly  conditions  are  unfavorable 
to  such  longevity,  and  this,  coupled  with  the 
rapidly  advancing  price  of  timber  suitable 
for  such  structures,  has  caused  engineers  to 
consider  the  more  durable  iron  and  rein- 
forced concrete  as  building  materials. 
Wherever  anthracite  is  prepared  wet,  the 
decay  of  the  timbers  is  hastened. 

The  rear  of  the  breaker  in  the  course  of 
construction  is  shpwn  in  Fig.  7.  The  first 
two  rows  of  posts  in  the  rear  of  the  breaker 
are  about  2  ft.  square  and  up  to  the  second 
or  pocket  floor  have  a  length  of  65  ft.  Di- 


FiG.  6 


rectly  under  and  between  the  pockets,  where  the  most  weight  will  come,  the 
2-ft.-square  posts  are  supplemented  with  36-in.-square  posts.     As  the  posts  are 


CONCRETE 


FIG.  8 


CONCRETE 


229 


carried  upwards  this  size  is  decreased  until  at  the  top  floors  they  are  but  12  in. 
square. 

In  Fig.  8  the  breaker  is  shown  practically  finished  with  the  top  forms  still 
in  place,  and  as  it  looks  today  from  the  outside,  could  be  taken  for  an  office 
building.  It  will  be  noted  that  the  architect  has  furnished  windows  for  day- 
light; also  each  post  is  supplied  with  tubes  for  wiring  for  electric  lights,  thus 
making  this  breaker  an  exceptional  one  for  light  and  comfort  of  the  employes. 
In  the  construction  of  the  posts  and  beams,  corrugated  rods  If  in.  in  diameter 
were  placed  at  each  corner,,  then  bound  with  hoop  bands  and  wire  so  as  to  form 
a  rectangular  cage.  They  were  reinforced  by  smaller  corrugated  iron  rods 
from  f-in.  diameter  up  to  l^-in.,  as  the  occasion  demanded.  Inside  this  cage 
pipes  for  the  electric  wiring  were  placed  and  then  wooden  forms  were  con- 
structed around  these  skeleton  post  frames.  Concrete  was  poured  in  a  little 
at  a  time  from  the  top  of  the  forms  and  tamped  with  iron  rods  about  the  pipes 
and  rods.  In  this  way  the  posts  were  built  up  to  the  height  of  a  floor,  where 
the  rods  for  the  beams  were  tied  with  those  of  the  posts.  The  beams  were 
made  the  same  as  the  posts. 


FIG.  9 

It  will  be  noted  that  the  coal  pockets  are  large  and  provided  with  two 
chutes  so  that  two  cars  can  be  loaded  from  the  same  pocket  at  the  same  time. 
There  are  fourteen  chutes  for  each  track,  or  twenty-eight  for  both  tracks.  To 
the  rear  of  Fig.  8  is  seen  the  old  Taylor  breaker,  constructed  of  wood. 

It  may  be  of  interest  to  know  that  while  the  Taylor  breaker  is  concrete, 
500,000  ft.  of  lumber  will  be  needed  inside  for  machinery  bed-plates  and  other 
fittings.  However,  very  little  if  any  of  this  lumber  is  large  sized  and  there  are 
no  sticks  such  as  breaker  framing  demands. 

Concrete  Coal  Pockets. — The  Pennsylyania  Coal  Co.  has  erected  a  new 
breaker  at  Throop,  Pa.  In  the  construction  of  this  breaker  both  reinforced 
concrete  and  steel  are  used;  reinforced  concrete  for  the  coal  and  rock  pockets, 
and  part  of  the  washery,  and  steel  for  the  main  part  of  the  building,  which  will 
contain  the  washery. 

The  capacity  of  the  coal  pockets  is  3,500  T.  The  coal  cars  are  to  be  loaded 
directly  beneath  the  pockets,  while  box  cars  are  to  pass  on  the  outside  of  the 
building  and  are  to  be  loaded  from  a  chute  leading  from  the  center  of  the  bottom 
slab  of  the  pocket.  The  slope  on  the  bottom  of  the  coal  pockets  is  9  in  12  and 
on  the  rock  pockets  6  in  12.  The  width  of  these  pockets  varies  from  10  ft.  8  in. 
to  16  ft.  Where  the  pocket  is  not  over  12  ft.  wide,  the  floor  slab  is  designed  so 


230 


CONCRETE 


as  to  carry  the  load  without  any  beam  for  support.  But  for  the  ppckets  16  ft. 
wide  a  beam  is  placed  beneath  the  floor  slab.  Fig.  9  shows  a  view  through 
the  coal  pockets  of  this  breaker  during  construction.  The  forms,  it  will  be 

Concrete  Shaft  Lining. — Concrete  is  now  being  used  to  line  shafts  in  mines. 
As  yet  there  is  no  uniform  method  of  doing  this  work  and  the  designs  are 
changed  to  suit  various  conditions  to  be  met.  The  shaft  with  concrete  lining 
about  to  be  described  is  the  main  shaft  of  the  Filbert  mine  of  the  H.  C.  Fnck 
Coke  Co.;  it  is  located  in  Fayette  County,  Pa. 

The  shaft,  elliptical  in  plan,  measures  13  ft.  X  28  ft.  in  the  clear  on  the  center 
lines  of  the  axes,  and  has  a  depth  of  550  ft.  below  the  top  of  the  coping  to  the 


Section  A- A. 


FIG.  10 


bottom  of  the  9-ft.  coal  bed,  and  is  provided  with  a  sump  15  ft.  below  the  coal. 
This  shaft  is  divided  into  four  compartments,  containing  two  cageways,  a  stair- 
way, and  pipe  way. 

The  plan  of  the  shaft  is  shown  in  Fig.  10.  At  a  is  shown  the  concrete  lining; 
at  b,  the  8"X10"  yellow-pine  buntons;  at  c,  the  6"X10"  buntons;  at  d,  the 
4"X8"  yellow-pine  nailing  strips;  and  at  e,  the  yellow-pine  cage  guides.  The 
compartment  reserved  for  the  various  pipes  that  go  up  the  shaft  is  shown  at  /. 
The  two  hoisting  cages  are  shown  at  g.  At  A  is  a  compartment  for  foot  travel- 
ing fitted  with  steps  and  landings.  The  hoisting  part  proper  is  largely  lined 
with  1-in.,  yellow  pine,  tongued-and-grooved  sheathing. 

The  circumference  of  the  inside  of  the  concrete  lining  is  69  ft.,  with  a  clear- 
opening  area  of  310  sq.  ft.,  comprising  195  sq.  ft.  for  the  two  cageways,  80  sq.  ft. 


CONCRETE 


231 


for  the  stairway,  and  35  sq.  ft.  for  the  pipeway.  The  ends  of  the  shaft  conform 
to  a  radius  of  5  ft.  8  in.  and  the  curvature  of  the  sides  to  a  45-ft.  radius.  From 
the  top  of  the  coping  to  solid  rock,  a  distance  of  19  ft.,  the  structure  is  of  heavy 
concrete  construction  forming  a  solid  foundation  for  the  structural  steel  head- 
frame  of  135  ft.  superimposed  thereon.  Fig.  11  shows  the  irregular-shaped 
plan  and  elevation  of  this  portion  of  the  work.  This  shaft  has  two  water  rings 
constructed  therein;  one  at  78  ft.,  and  the  other  at  494  ft.  below  the  top  of  the 
coping. 

All  concrete  for  lining  the  shafts  is  composed  of  1  part  Portland  cement; 
2  parts  clean,  sharp,  river  sand,  and  5  parts  of  stone  crushed  to  pass  through 
H-in.  ring.  About  50%  of  the  stone  used  for  concrete  was  obtained  from  the 


FIG.  11 

materials  excavated  from  the  shafts.  About  30%  was  shipped  in,  crushed 
ready  for  use,  while  about  20%  was  obtained  from  a  quarry  on  the  grounds. 
In  sinking  this  shaft,  an  excavation  was  first  made  to  a  depth  of  65  ft. 
All  excavating  was  done  to  the  full  measurements  of  the  outside  perimeter  of 
the  concrete  lining,  being  kept  to  a  correct  line  by  plumb-bobs  suspended  from 
a  template  placed  above  the  opening.  Derricks  were  used  to  handle  the  mate- 
rial excavated.  At  the  depth  mentioned,  the  concreting  was  begun.  Forms 
were  put  in  near  the  bottom  to  the  height  of  5  ft.  and  filled.  Then  5  ft.  more  of 
forms  were  put  on  top  of  the  first  forms  and  again  filled.  Then  another  sec- 
tion was  built  and  filled  and  so  on  until  the  surface  was  reached.  The  shaft  was 
then  sunk  about  50  ft.  deeper  and  concreted  up  from  the  bottom  in  the  same 
way.  Then  another  section  of  the  shaft  was  sunk,  and  so  on  until  the  job  was 
completed. 


232  CONCRETE 

The  dividing  struts  for  the  compartments  of  the  shafts  are  8"X10"  bun- 
tons,  spaced  vertically  5  ft.  center  to  center.  The  buntons  support  the  guide 
rails  for  the  cages — these  are  8  in.X  10  in.,  surfaced  on  four  sides  and  fastened 
to  the  dividing  struts  or  buntons  as  shown  in  Fig.  12.  The  buntons  are  set  in 
the  concrete  shaft  lining  to  a  depth  of  6  in.  on  each  end,  allowing  from  6  in.  up 
of  concrete  beyond  their  ends,  thus  insuring  a  water-tight  wall.  The  minimum 
thickness  of  the  concrete  lining  wall  is  12  in.  In  soft  strata,  the  concrete  is  as 
much  as  33  in.  in  thickness,  as  no  voids  were  left  between  the  rock  and  lining, 
all  such  being  carefully  filled  with  concrete.  Bolts  for  the  guides  have  a  1-in. 
stud  nut  and  two  wrought-iron  washers  $  in.  thick. 

Throughout  a  portion  of  the  shaft,  wedge-shaped  blocks  with  a  base 
6  in.X 8  in.  and  4  ft.  long,  tapering  to  a  point,  were  placed  on  the  buntons  just 
at  the  face  of  the  concrete  lining,  making  pockets  for  the  removal  of  the  bun- 
tons,  when  necessary  to  replace  them. 

To  take  care  of  the  water  during  the  construction  of  the  shaft  above  the 
water  rings,  two  methods  were  successfully  used.  During  the  concreting, 
when  any  flow  of  water  was  encountered,  sheet-iron  plates  were  used  to  turn 
the  water  away  from  the  concrete  until  it  had  set  sufficiently  so  as  not  to  be 
damaged  by  water  flowing  over  it.  Then  the  sheets  were  deflected  so  as  to 
cause  the  water  to  run  down  the  face  of  the  rock  wall  of  the  shaft,  where,  at 

intervals  around  the  cir- 
cumference of  the  shaft, 
were  placed  3-in.  tile 

pipe  set  in  loose  broken 

t  stone  and  extending 
>  down  behind  the,  shaft 
lining  to  the  water  ring. 
The  tile  pipe,  set  with 
open  joints,  takes  care 
of  the  water,  conducting 
it  to  the  water  ring. 
To  hold  the  tile  pipes 
to  their  proper  place 
and  to  insure  their  non- 
stoppage  from  concrete 
packing  in  around  them, 
sheet-iron  strips  of  No. 
22  gauge  were  bent  into 
semicircular  form  and 
placed  around  the  tile 
pipe  with  the  open  side 
toward  and  against  the 
rock  face;  then  broken 
stone  was  placed  around 
the  pipe  within  this  pro- 
tection. In  this  way  an 


L 


FIG.  12 


opening  was  kept  between  the  rock  face  and  the  tile  pipe,  allowing  the  water 
to  reach  the  drain  and  thus  flow  into  the  water  rings.  This  also  eliminated 
the  danger  of  water  gathering  behind  the  lining  wall  and  exerting  undue  pres- 
sure thereon. 

Another  method  successfully  used  was  to  locate  the  fissure  or  opening 
where  larger  streams  entered  the  excavation,  and  to  enlarge  them  so  as  to  form 
a  reservoir  of  several  cubic  feet  capacity;  then  to  tightly  close  the  openings 
of  this  reservoir  with  concrete  and  sheet  iron,  having  placed  a  wrought-iron 
pipe  of  sufficient  capacity  to  handle  the  water  gathered  therein.  This  pipe 
conducts  the  water  to  a  pipe  set  vertically  in  the  lining-wall  concrete  and 
leading  to  the  water  rings.  This  latter  method  was  used  only  where  a  large 
flow  of  water  was  encountered. 

The  water  rings  in  the  shaft  were  constructed  behind  the  shaft-lining  wall, 
where  a  niche  was  blasted  out  of  the  rock  to  form  an  opening  2  ft.  wide  and  4  ft. 
high  throughout  the  entire  perimeter  of  the  shaft.  The  bottom  of  this  niche 
was  concrete  in  gutter  shape,  with  a  drop  of  3  in.  from  its  highest  to  its  lowest 
point,  located  at  the  pipe-compartment  end  of  the  shaft.  At  the  lowest  point 
a  wrought-iron  pipe,  2$  in.  in  diameter,  set  through  the  lining  wall  on  an  angle 
of  45°  and  protected  by  strainer  plates,  connected  with  a  line  in  the  pipe  com- 
partment and  led  the  water  to  a  permanent  disposal  pump.  In  the  shaft-lining 
wall,  on  its  inner  face  and  throughout  the  entire  perimeter  of  the  wall,  and  at  a 
point  near  the  top  of  the  water  ring,  a  groove  4$  in.  deep  and  5  in.  from  the  face 


CONCRETE 


233 


of  the  groove  to  the  edge  of  the  lip  extending  1£  in.  beyond  the  inner  face  of 
the  wall  was  constructed  to  catch  any  seepage  or  water  from  the  surface  of  the 
lining.  This  groove  and  lip  has  a  fall  of  3  in.  from  its  highest  to  its  lowest 
point,  where  a  2-in.  wrought-iron  pipe  passes  through  the  lining  wall  on  an 
angle  of  45°  leading  all  water  caught  in  the  groove  to  the  water  ring.  Thus,  all 
the  water  both  behind  the  lining  wall  and  all  water  on  the  inner  surface  is  col- 
lected in  the  water  rings  and  thence  led  to  the  pumps  and  expelled  from  the 
shaft. 

In  the  shaft,  the  approaches  leading  to  the  shaft  bottom  from  both  the 
loaded  and' empty  sides  are  of  concrete.  These  are  of  18-ft.  span  having  a 
minimum  thickness  of  24  in.  for  side  walls  and  crowns.  Each  arch  extends 


Lining 


Section  on  (£  Arch 


Section  thipujh  Arch 


FIG.  13 


13  ft.  from  the  face,  of  the  shaft  lining.  Arches  of  9-ft.  span  having  a  minimum 
thickness  of  18  in.  extend  a  distance  of  11  ft.  6  in.  from  both  ends  of  the  face 
of  the  shaft  lining.  These  arches  connect  with  the  cross-entries  and  man- 
way  around  the  shaft  bottom.  An  archway  of  4-ft.  span  was  placed  in  the  side 
walls  for  entrance  to  the  run-around.  At  the  intersection  of  all  arches  with  the 
shaft-lining  wall,  steel  bars  were  placed  for  reinforcement.  The  method  of  this 
reinforcement  is  shown  in  Pig.  13.  All  centering  was  built  of  2-in.  oak  plank, 
spaced  2?  ft.  center  to  center,  covered  with  2-in.  tongued-and-grooved  oak 
lagging.  Concreting  for  the  four  arches  was  brought  up  at  one  time  and  also 
at  the  same  time  as  the  shaft-lining  wall  was  placed. 


234 


MASONRY 


MASONRY 


MATERIALS  OF  CONSTRUCTION 

STONE 

The  materials  employed  in  the  construction  of  masonry  are  stone,  brick, 
terra  cotta,  and  the  cementing  materials  used  in  the  manufacture  of  mortars; 
namely,  lime,  cement,  and  sand. 

Strength  of  Stone. — In  ordinary  buildings  and  engineering  structures, 
stones  are  generally  under  compression.  Occasionally,  they  are  subjected  to 
cross-stresses,  as  in  lintels  over  wide  openings.  They  are  never  subjected  to 
direct  tension.  As  a  general  rule,  a  stone  should  not  be  subjected  to  a  greater 
compressive  stress  than  one-tenth  of  the  ultimate  crushing  strength,  as  found 
by  experiment. 

The  resistance  to  crushing  varies  within  wide  limits,  owing  to  the  great 
variety  in  the  structure  of  the  stones;  the  method  of  preparing  and  finishing 
the  test  pieces  also  affects  the  results;  hence,  the  great  variations  found  in  the 
values  given  by  different  experiments.  The  accompanying  table  shows  the 
average  resistance  of  the  principal  building  stones  to  crushing  and  to  rupture 
when  used  as  beams. 

CRUSHING  STRENGTH  AND  MODULUS  OF  RUPTURE  OF 
BUILDING  STONE 


Stone 

Crushing  Strength 
Pounds  per  Square 
Inch 

Modulus  of  Rupture 
Pounds  per  Square 
Inch 

Granite  
Sandstone  

15,000 
10,000 

1,800 
1,200 

Limestone  
Marble 

13,000 
14  000 

1,500 
2  160 

MINIMUM  SAFE-BEARING  VALUES  OF  MASONRY 
MATERIALS 


Materials 


Granite,  capstone 

Squared  masonry 

Sandstone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar 

Limestone,  capstone 

Squared  masonry 

Rubble,  laid  in  lime  mortar 

Rubble,  laid  in  cement  mortar 

Bricks,  hard,  laid  in  lime  mortar 

Hard,  laid  in  Portland  cement  mortar 

Hard,  laid  in  Rosendale  cement  mortar 
Concrete,  1  Portland,  2  sand,  5  broken  stone. 


Safe-Bearing 

Value 

Tons  per 

Square  Foot 


50 
25 
25 
12 

5 
10 
36 
18 

5 
10 

7 
14 
10 
10 


MASONRY 


235 


ULTIMATE  UNIT  CRUSHING  STRENGTH  OF  VARIOUS  STONES  AND 
STONE  MASONRY  PIERS 


Material 

Compressive 
Strength 
Pounds  per 
Square  Inch 

Material 

Compressive 
Strength 
Pounds  per 
Square  Inch 

Granite,  Colo  

15,000 
14  000 

Limestone,      Marquette, 
Mich. 

8000 

Granite,  Mass  
Granite   Me 

16,000 
15000 

Limestone,  Conshohock- 
en,  Pa. 

15,000 

Granite,  Minn  
Granite,  N.  Y  
Granite,  N.  H  

25,000 
16,000 
12,000 
15000 

Marble,        Montgomery 
Co.,  Pa  
Marble    (dolomite),  Lee, 
Mass  

11,000 
22,800 

Sandstone,  Middletown, 
Conn  

7,000 

Marble     (dolomite), 
Pleasantville,  N.  Y.  ... 

22,000 

Marble  Italian 

12  000 

Mass 

10000 

Marble,  Vt  

10,000 

Slate 

10,000 

River,  N.  Y  

12,000 

Piers,  ashlar,  bluestone.  . 

2.100 

Sandstone  (brown),  Little 
Falls  N  Y 

10000 

Piers,  ashlar,  granite  
Piers,  ashlar,  limestone  .  . 

2,100 
1,500 

Sandstone,  Ohio  

8,000 

Piers,     ashlar,     common 

1,050 

Hummelstown,  Pa.  .  . 

12,000 

Piers,     rubble,     cement 

900 

N.  Y....  ..!n.gS.°.n>. 

12,000 

Piers,  rubble,  lime  mor- 

tar 

480 

Station,  N.  Y  
Limestone  (oolitic),  Bed- 
ford, Ind  

18,000 
8,000 

ULTIMATE  CRUSHING  STRENGTH  OF  BRICK  MASONRY  PIERS 

(Average  Age  of  Brickwork,  6  Mo.) 


Material 

Composition  of  Mortar 

Compressive 
Strength 
Pounds  per 
Square  Inch 

Wire-cut  brick                                  .... 

1  cement,  5  sand 

3,000 

Dry-pressed  brick  
Dry-pressed  brick.  

1  cement,  5  sand 
1  cement,  1  lime,  3  sand 
1  cement,  5  sand 

3,400 
2,300 
1,700 

Light-hard,  sand-struck  brick  

1  cement,  5  sand 

1,900 

Light-hard,  sand-struck  brick  
Hard,  sand-struck  brick  
Hard,  sand-struck  brick  
Hard,  sand-struck  brick  
Sand-lime  brick  

1  cement,  7  sand 
1  cement,  1  sand 
1  cement,  1  lime,  3  sand 
1  cement,  5  sand 
1  cement,  3  sand 

853 
2,100 
1,500 
1,200 
1,100 

Sand-lime  brick  

1  lime,  3  sand 

450 

Sand-lime  brick       '                 

Neat  cement 

1,400 

1  cement,  3  sand 

2,000 

236 


MASONRY 


Absorptive  Power  of  Stone. — The  absorptive  power  9!  a  stone  is  a  very 
important  property,  a  low  absorption  generally  indicating  a  good  quality. 
The  accompanying  table  gives  the  average  percentage  of  water  absorbed  by 
stones. 

ABSORPTIVE  POWER  OF  STONE  Durability  of  Stone.— The  fol- 

lowing rough  estimate,  based  on 
observations  made  in  the  city  of 
New  York,  indicates  the  number  of 
years  a  sound  stone  may  be  expected 
to  last  without  being  discolored  or 
disintegrated  to  such  an  extent  as 
to  require  repairs: 

Life  of  Stone 
Name  of  Stone  Years 

Coarse  brownstone 5  to    15 

Compact  brownstone.  .100  to  200 

Limestone 20  to    40 

Granite 75  to  200 

Marble 40  to  200 

BRICK 

Size  and  Weight. — The  dimensions  of  bricks  vary  considerably.  The 
standard  adopted  by  the  National  Brickmakers'  Association  is,  for  common  clay 
brick,  8J  in.X4  in.X2J  in.,  and  for  face  or  pressed  brick  (clay)  85  in.X4J  in. 
X2i  in.  The  weight  of  a  common  clay  brick  is  about  4£  lb.;  that  of  a  pressed- 
clay,  enameled  brick,  about  7  lb.  Enameled  and  glazed  bricks  are  made  in  two 
sizes:  English  size,  9  in.XS  in.X4£in.;  American  size,  8 1  in.X2J  in.X4|  in. 
The  usual  dimensions  for  firebricks  are  9  in.X4£  in.X2J  in.;  various  sizes  and 
forms  are  made  to  suit  the  required  work.  The  dimensions  of  the  lime-sand 
bricks  are  8|  in.  X  4|  in.  X 2jf  in.  The  weight  varies  between  5  and  6  lb.  The 
accompanying  table  gives  the  approximate  weight  and  resistance  to  crushing 
of  brick. 

WEIGHT  AND  STRENGTH  OF  BRICK 


Stone 

Absorptive  Capacity 
Per  Cent. 

Granites  

.066  to    .155 
.410  to  5.480 

Limestones  

.200  to  5.000 

Marbles  
Trap  

.080  to    .160 
.000  to    .019 

•--; 
Kind  of  Brick 

Weight 
Pounds  per 
Cubic  Foot 

Crushing 
Strength 
Pounds  per 
Square  Inch 

Best  pressed-clay  

150 

5,000  to  15,000 

Common  hard-clay 

125 

5,000  to    8  000 

Soft-clay 

100 

450  to       600 

Lime-sand  .... 

120 

3,600  to    7,600 

Firebrick  . 

120 

1  000  to    1  500 

Requisites  for  Good  Brick. — Bricks  of  good  quality  should  be  of  regular 
shape,  with  parallel  surfaces,  plane  faces,  and  sharp  square  edges.  They 
should  be  of  uniform  texture;  burnt  hard;  and  thoroughly  sound,  free  from 
cracks  and  flaws.  They  should  emit  a  clear  ringing  sound  when  struck  a  sharp 
blow.  A  hard  well-burned  brick  should  not  absorb  more  than  one-tenth  of  its 
weight  of  water;  it  should  have  a  specific  gravity  of  2  or  more.  The  crushing 
strength  of  a  brick  laid  flat  should  be  at  least  6,000  lb.  per  sq.  in.  The  modulus 
of  rupture  should  be  at  least  1,000  lb.  per  sq.  in. 


WIRE  ROPES  237 


WIRE  ROPES* 


GENERAL  DESCRIPTION 

WIRE-ROPE  MATERIALS 

Wire  ropes  are  used  about  mines  chiefly  for  hoisting  from  shafts,  for  haulage 
and  the  transmission  of  power,  for  the  cables  of  aerial  tramways,  for  the  guy 
ropes  of  derricks  and  smokestacks,  etc.,  and,  rarely,  for  the  cables  of  small, 
short-span,  suspension  bridges,  as  where  the  town  or  settlement  is  situated  on 
the  opposite  side  of  a  narrow  stream  from  the  mine.  While  wire  ropes  are  now 
almost  universally  made  of  steel,  manufacturers  still  make  and  list  iron  ropes, 
which  have  a  limited  field  of  usefulness. 

Swedish,  Swedes,  or  charcoal-iron  ropes  are  made  of  a  very  pure  wrought 
or  puddled  iron  having  a  tensile  strength  of  from  50,000  to  100,000  Ib.  per  sq.  in. 
These  ropes  are  soft,  tough,  and  pliable,  and  are  adapted  especially  for  passenger 
elevators,  small  hoists,  steering  gear  of  vessels,  etc.,  where  the  loads  are  inter- 
mittently applied  and  are  not  too  great,  or  where  the  speed  is  high  and  the  bend- 
ing stresses  great.  It  will  be  noted  from  tables  given  later  that  the  ultimate 
breaking  strength  of  a  6X 19  Swedish  iron  hoisting  rope  1  in.  in  diameter,  is  but 
14.5  T.,  whereas,  the  breaking  strength  of  a  steel  rope  of  the  same  kind  and 
size  is  from  30  to  45  T.  For  general  mine  use,  iron  ropes  have  been  almost 
entirely  superseded  by  steel  ropes  because  of  their  greater  strength  and 
elasticity. 

Steel  ropes  are  generally  made  of  open-hearth  steel  having  a  tensile  strength 
of  from  150,000  to  275,000  Ib.  per  sq.  in.  and  in  some  cases  even  more,  the 
tensile  strength  depending  on  the  composition  of  the  metal  and  the  method  of  its 
treatment.  Steel  ropes  are  in  almost  every  way  superior  to  iron  ropes.  The 
principal  advantage  is  that  they  have  more  than  double  the  strength  of  iron 
ropes  of  the  same  size;  consequently,  for  equal  strains,  they  can  be  made  of 
much  less  diameter  than  iron  ropes  and  can,  therefore,  be  used  in  connection 
with  much  smaller  and  lighter  drums,  sheaves,  or  pulleys.  Iron-wire  ropes  are 
not  so  elastic  as  ropes  made  of  steel  wire,  hence  a  larger  sheave  is  required  for 
iron  than  for  steel  ropes  of  the  same  diameter.  Iron  ropes,  however,  are 
usually  more  flexible  than  steel  ropes,  are  less  brittle  though  not  so  strong, 
and  better  resist  the  acid  in  mine  water.  A  1-in.  Swedish  iron  rope  has  about 
the  same  strength  as  a  f-in.  ordinary  cast-steel  rope;  weighs  1.58  Ib.  per  ft.  as 
opposed  to  .62  Ib.;  costs  (list  price)  26c.  per  ft.  as  opposed  to  16.5c.;  and 
requires  a  sheave  or  drum  6  ft.  in  diameter  as  against  one  2.5  ft.  for  a  cast-steel 
rope. 

Cast-steel,  crucible-steel,  and  crucible  cast-steel  ropes  are  the  trade  names 
given  to  the  ordinary  grades  of  ropes  made  from  wire  having  an  ultimate  tensile 
strength  of  160,000  to  210,000  Ib.  per  sq.  in.  _  The  breaking  strength  of  a 
6X  19  standard  hoisting  rope  of  this  grade  and  1  in.  in  diameter  is  given,  in  the 
manufacturers'  tables,  as  30  T.,  more  than  twice  the  strength  of  a  similar  iron 
rope.  Ropes  of  this  material  are  those  commonly  used  in  and  around  mines 
for  haulage  and  hoisting  purposes. 

Extra  strong  cast-steel,  extra  strong  crucible-steel,  special  steel,  and  patent  steel 
ropes  are  the  trade  names  for  the  next  stronger  grades  of  ropes,  intermediate  in 
strength  between  cast-steel  and  plow-steel  ropes  in  strength.  The  wire  from 
which  they  are  made  has  an  ultimate  tensile  strength  of  from  190,000  to 
230,000  Ib.  per  sq.  in.  The  breaking  strength  of  a  6X  19  hoisting  rope  of  this 
grade  and  1  in.  in  diameter  is  given  as  34  T,  11.33%  more  than  that  of  an 
ordinary  cast-steel  rope  of  the  same  dimensions.  These  ropes  are  also  standard 
and  are  in  general  use  where  it  is  desirable  to  increase  the  factor  of  safety  while 
retaining  the  same  diameter  of  rope. 

*  Acknowledgement  for  the  use  of  data  and  tables  in  this  section  is  made 
to  the  Broderick  &  Bascom  Rope  Co.,  Hazard  Manufacturing  Co.,  A.  Leschen 
&  Sons  Rope  Co.,  John  A.  Roebling's  Sons  Co.,  The  Trenton  Iron  Co.,  The 
Waterbury;  Co.,  and  the  Link  Belt  Co.  As  in  most  instances,  the  manufacturers 
have  identically  the  same  tables,  etc.,  credit  is  given  generally  in  this  manner, 
rather  than  specifically  for  each  item. 


238  WIRE  ROPES 

Plow-,  or  plough-steel  ropes  are  made  of  wires  having  an  ultimate  tensile 
strength  of  220,000  to  250,000  Ib.  per  sq.  in.  The  breaking  strength  of  a  6X  19 
hoisting  rope  of  this  grade  and  1  in.  in  diameter  is  given  as  38  T.,  or  11.18% 
more  than  that  of  an  extra  strong  cast-steel  rope  of  the  same  dimensions.  Ropes 
of  this  grade  are  not  generally  recommended,  except  where  it  is  necessary  to 
have  the  maximum  of  tensile  strength  with  the  least  weight  of  rope,  or  where 
it  is  necessary  to  employ  a  rope  of  much  greater  strength  but  of  the  same 
diameter.  The  first  necessity  will  arise  when  hoisting  through  extremely  deep 
shafts;  the  second,  where  by  reason  of  increased  loads  it  becomes  essential  to 
have  a  stronger  rope,  but  at  the  same  time  the  diameter  of  the  rope  is  fixed  by 
the  size  of  existing  drums,  sheaves,  etc.  Plow-steel  ropes  are  extensively 
employed  for  logging  lines,  dredge  and  wrecking  ropes,  ballast  unloading  ropes, 
quarry  ropes,  etc. 

Extra,  special,  or  improved  plow-steel  ropes  are  made  of  wires  having  an 
ultimate  tensile  strength  of  from  240,000  to  300,000  Ib.  per  sq.  in.  A  rope  of 
this  grade  of  the  size  cited  before  has  a  breaking  strength  of  45  T.,  or  about 
11.84%  more  than  an  ordinary  plow-steel  rope  of  the  same  dimensions.  The 
comments  upon  standard  plow  steel  ropes  apply  as  well  to  ropes  of  this  grade 

CONSTRUCTION  OF  WIRE  ROPES 

Wire  ropes  consist  of  a  number  of  strands,  each  composed  of  the  same 
number  of  single  wires  twisted  around  a  hemp  or  wire  core  or  center  to  form  a 
single  rope.  The  hemp  core  adds  practically  nothing  to  the  strength  of  the 
rope  but,  being  saturated  with  lubricant,  tends  to  prevent  rusting  of  the  wires 
and,  being  soft,  acts  as  a  cushion  for  the  individual  strands,  thus  reducing 
internal  friction  and  wear.  A  wire  core  adds  largely  to  the  internal  friction 
and  consequent  wear  of  rope  as  the  strands  rub  upon  the  wire  center;  increases 
the  weight;  and,  while  adding  about  10%  to  the  strength,  reduces  the  flexibility 
in  a  marked  degree,  at  the  same  time  adding  10%  to  the  cost.  Manufacturers, 
whose  judgment  should  be  final,  recommend  ropes  with  wire  cores  only  for 
standing  lines,  such  as  the  guy  ropes  of  derricks,  etc.,  because  they  lack  the 
flexibility  demanded  of  running  ropes  (those  used  for  hoisting,  haulage,  etc.), 
and  because  of  their  much  greater  internal  wear  in  bending  around  drums, 

sheaves,  and  the  like. 

Lay  of  Ropes. — The  lay  of  a  rope 
is  the  direction  of  the  twist  of  the 
strands  composing  it.  Ropes  are 
either  right  or  left  lay,  the  former 
being  the  ordinary  construction  as 
shown  in  Fig.  1  where  the  strands  are 
bent  to  the  right.  The  left-lay  con- 
struction is  shown  in  Fig.  2. 
The  term  lay  is  also  used  to  describe  the  direction  of  twist  of  the  individual 
wires  composing  the  strands  in  a  rope.  Thus,  in  Fig.  1,  while  the  rope  is  right 
lay  (strands  twisted  to  the  right),  the  strands  are  left  lay,  the  single  wires  being 
twisted  to  the  left.  Similarly,  in  Fig.  2,  while  the  rope  is  left  lay,  the  strands 
are  right  lay. 

Finally,  the  term  lay  is  used  to  designate  the  pitch  of  the  rope;  that  is,  the 
rate  at  which  the  strands  twist  or,  what  is  the  same  thing,  the  ratio  that  the 
length  of  strand  required  for  one  complete  turn  bears  to  the  diameter  of  the  rope. 
In  ordinary  rope  making,  the  lay  or 
(better)  pitch  of  the  wires  varies  from 
2.5  to  3.5  times  the  diameter  of  the 
rope,  and  that  of  the  strands  from  6.5 
to  9  times  the  diameter  of  the  rope. 
The  lay  exerts  an  important  influence 

upon  the  life  of  a  rope.     For  the  same    . 

kind  and  size  of  rope,  the  shorter  the  FlG.  2 

lay  or  pitch,  the  greater  the  flexibility 
and  elasticity,  but  the  less  the  strength.  This  falling  off  in  the  strength,  due  to 
the  shortening  of  the  pitch,  is  brought  about  by  the  nicking,  or  cutting,  of  one 
wire  by  another,  which  is  naturally  less  when  the  ropes  cross  one  another  at 
a  long  angle  (long  pitch)  than  when  they  cross  at  a  sharp  angle  (short  pitch). 
In  practice,  ropes  are  commonly  classified  as  ordinary-lay  or  regular-lay 
ropes,  and  as  Lang  lay  or  universal-lay  ropes.  In  the  ordinary  lay  ropes,  which 
are  shown  in  Fig.  1  and  Fig.  2,  the  wires  in  the  strands  are  twisted  in  the 
opposite  direction  from  that  of  the  strands  in  the  rope,  while  in  Lang  lay  ropes, 
shown  in  .big.  3,  the  single  wires  and  the  strands  are  twisted  in  the  same 


WIRE  ROPES 


239 


direction.     Lang  lay  ropes  may  be  either  right  or  left  twist,  and  their  price  is 
the  same  as  that  of  ordinary-lay  ropes. 

The  principal  advantages  of  the  Lang  lay  are  that,  the  wires  and  strands 
being  twisted  in  the  same  direction,  the  surface  of  the  rope  is  smoother,  the 
outside  wires  do  not  so  soon  become  worries  a  much  longer  surface  of  each  wire 
is  exposed  to  wear,  and,  the  wires  being  straighter,  these  ropes  are  somewhat 
more  flexible.  The  disadvantages  of 
Lang  lay  ropes  are  a  tendency  to  un- 
twist, rendering  them  unsuited  for 
hoisting  except  where  guides  are  used; 
they  can  be  spliced  to  ropes  of  ordin- 
ary-lay only  with  difficulty;  and  when 
the  wires  break,  the  loose  ends  are 
very  troublesome,  because  a  much 
greater  length  of  each  wire  is  exposed 
than  in  ordinary-lay  ropes.  Under  careful  inspection,  a  regular-lay  haulage 
rope  may  be  used  for  some  time  after  a  few  of  its  wires  are  (broken  here 
and  there  throughout  its  length,  except  when  a  dangerous  risk  would  be  incurred 
by  so  doing.  The  Lang  lay  ropes  are  commonly  used  tor  haulage,  particularly 
where  grips  are  used  to  attach  the  cars  to  the  ropes,  and  are  sometimes  used  for 
hoisting,  but  only  where  the  cage  works  in  guides. 


FIG.  3 


HOISTING  ROPES 

ROUND  ROPES 

6X 19  Ropes. — Ropes  used  for  hoisting  through  shafts  are  round  or  flat 
and  in  either  case  may  be  of  uniform  or  tapering  section.  Round  ropes  of 
uniform  section,  are  practically  the  only  ones  used  in  American  mines.  The 

standard  American 
hoisting  rope,  shown  in 
Fig.  1,  is  composed  of 
6  strands  of  19  wires 
each  (114  wires)  wrap- 
ped around  a  hemp 
center.  It  is  frequently 
spoken  of  as  a  6X19 
FIG.  1  rope.  These  ropes  are 

commonly  made  of  cast- 
steel  or,  where  greater  strength  is  required,  extra  strong  cast-steel.  The 
diameter  of  sheave  recommended  for  use  with  a  1-in.  rope  of  this  type  is 
variously  given  at  4  to  4.5  ft. 

8X19  Ropes. — Where  extreme  flexibility  is  required,  ropes  composed  of 
8  strands  of    19   wires 
each  (152  wires)  may  be 
employed.      From    the 
tables    given    later,    it 
will  be  noted  that  the 
maximum   diameter   of 
rope  of  this  section  com- 
monly carried  in  stock  FIG.  2 
is  1?  in.  as  against  2| 

in.  for  the  6X19.  Fig.  2  shows  that  the  core  is  much  larger  in  proportion 
to  the  area  of  metal  than  in  a  6X19  rope  of  the  same  size  and  quality. 
Consequently,  this  rope  is  not  so  strong  as  a  6X19  rope  of  the  same  diameter 

(24  T,  as  against  30  T. 
for  1-in.  cast-steel  rope) 
and  is  more  liable  to 
flatten  out  under  heavy 
pressure.  The  diameter 
of  sheave  suggested  for 
use  with  a  1-in.  rope  of 
FIG.  3  this  type  is  variously 

given  as  2. 5  to  3.25  ft.; 

materially  less  than  that  required  for  a  6X19  rope.  Ropes  of  this  class  are 
recommended  for  derricks  and  similar  work  where  small  sheaves  must  be  em- 
ployed, but  it  should  be  noted  that,  so  far  as  the  working  life  of  this  type  is 


240 


WIRE  ROPES 


concerned,  the  increased  flexibility  in  a  very  considerable  measure  offsets  its 
decreased  strength. 

6X37  Ropes. — A  form  of  very  flexible  rope  that  is  not  infrequently  used 
in  preference  to  the  8X19,  is  shown  in  Fig.  3;  in  this,  the  rope  is  composed 
of  6  strands  of  37  wires  each.  As  ^ere  is  a  much  greater  area  of  metal  m 
proportion  to  the  hemp  core  than  in  an  8  X 19,  the  breaking  strength  of  a  1-in. 

cast-steel  rope  of  this 
type  is  given  as  29  T., 
only  1  T.  less  than  that 
of  the  standard  6X19 
rope  and  3  T.  more  than 
the  8X19.  The  diam- 
eter of  sheave  suggested 
FIG.  4  for  this  rope  is  the  same 

as  that  for  the  8X19; 

viz.,  2.5  to  3.25  ft.  As  the  wires  in  this  rope  are,  of  necessity,  smaller  than 
those  in  a  6X19  rope  of  the  same  diameter,  it  is  apparent  that  this  type  of 
rope  is  not  so  well  adapted  to  withstand  abrasion  as  those  containing  larger 
wires.  This  rope  is  employed  where  the  bending  strains  are  very  great,  as  in 
logging  operations,  for  use  with  electric  cranes,  etc.  When  galvanized,  this 
rope  is  largely  used  for  hawsers  in  towing,  etc. 

Non-Spinning  Ropes. — Non-spinning  hoisting  rope,  made  by  one  of  the 
leading  manufacturers,  is  shown  in  Fig.  4,  It  is  composed  of  18  strands  of  7 
wires  each  (126  wires),  12  of  the  strands  being  laid  m  a  reversed  direction 
about  6  which,  in  turn,  are  laid  about  a  hemp  core.  Because  of  the  reversed 
directions  in  which  the  inner  and  outer  sets  of  strands  are  laid,  there  is  no 
tendency  to  twist  and  the  rope  is,  thence,  adapted  to  hoisting  where  the  load 
is  not  raised  between  guides  but 
hangs  freely  as  a  bucket  in  shaft- 
sinking.  The  rope  is  slightly  more 
flexible  than  the  standard  6X 19  rope 
and  slightly  stronger.  However,  it 
cannot  be  spliced. 

Flattened-Strand  Ropes. — In 
order  to  present  a  larger  and  smoother 
wearing  surface,  and  thus  to  increase 
the  life  of  the  rope,  flattened-strand 
wire  ropes  have  been  devised.  In 
these  ropes  the  strands  have  an  ellip- 
tic, or  triangular,  cross-section,  de- 
pending on  the  shape  of  the  metal 
center  of  the  strand,  and  the  rope  has  either  a  hemp  or  a  wire  core.  They  are 
made  either  5X28  (5  strands  of  28  wires  each,  or  140  wires)  as  shown  in  Fig.  5 
(a),  or  6X25  (6  strands  of  25  wires  each,  or  150  wires)  as  shown  in  (b).  These 
ropes  are  made  of  Swedes  iron,  and  of  cast-steel,  extra  strong  cast-steel,  and 
extra  plow-steel.  The  breaking  strength  of  a  cast-steel  rope  of  this  make, 
5X28,  and  1  in.  in  diameter  is  given  as  30  T.,  the  same  as  that  of  the  same 
size  and  kind  round,  6X19  standard  rope.  A  6X25  cast-steel  rope  of  this 
type  1  in.  in  diameter  is  given  as  33  T.,  which  is  greater  than  that  of  the 
corresponding  6X 19  round  rope  and  nearly  as  great  as  that  of  an  extra  strong 
cast-steel  rope.  There  is  claimed  for  this  rope  greater  flexibility,  less 
liability  of  the  wires  becoming  brittle,  and  freedom  from  all  tendency  to  spin  or 
kink;  also  that  they  maintain  their  form  better  than  round  ropes. 

Scale  Ropes. — A 
form  of  rope  made  by 
some  manufacturers  and 
used  for  hoisting,  but 
possibly  better  adapted 
to  haulage  purposes,  is 
shown  in  Fig.  6,  as  it  is 
FIG.  6  oi  the  6X19  type  used 

in  standard  hoisting 

ropes.  This  is  known  as  Seale  rope  or  Scale  lay  rope,  and  consists  of  6  strands 
of  19  wires  each,  in  which  9  large  wires  are  twisted  around  9  small  ones,  which 
in  turn  surround  one  of  the  larger  size.  This  rope  is  intermediate  in  flexibility 
and  ability  to  stand  abrasion  between  the  standard  ropes  of  7-wire  (haulage)  and 
19-wire  (hoisting)  strands.  This  type  of  rope,  on  account  of  the  large  outside 
wires,  will  withstand  heavy  f  rictional  wear  and  is  used  on  slopes,  planes,  and  cable 


FIG.  5 


(ft) 


WIRE  ROPES 


241 


roads  where  the  rope  commonly  drags,  provided ,  however,  that  there  are  no  bends 
of  sharp  angle  to  overstrain  the  outer  wires.  While  there  is  more  metal  in 
the  outer  wires  than  in  those  of  the  standard  rope,  there  is  correspondingly 
less  in  the  inner  wires,  and  closer  inspection  of  the  outer  wires  is,  therefore, 
necessary  to  prevent  the  rope  being  used  too  long.  The  price  of  these  ropes 
is  the  same  as  the  standard  6X 19  hoisting  rope  of  the  same  grade. 

FLAT  ROPES 

Flat  ropes,  Fig.  7,  are  composed  of  a  number  of  loosely  twisted  ropes  of  four 
wires  each  and  without  hemp  centers.  The  ropes,  of  alternately  right  and 
left  lay,  are  placed  side  by  side  and  are  then  sewed  together  with  soft  iron  or 
annealed  steel  wire  to  form  a  single  rope.  The  sewing  wires,  which  vary  in 
number  from  8  to  12  pass  through  the  centers  of  the  individual  ropes  from 
side  to  side  and  often  have  to  be  renewed,  as  they  naturally  wear  faster  than 
the  wires  composing  the  rope 
proper. 

Flat  ropes  may  be  made  to 
order  of  any  width  to  give  any 
desired  strength,  but  the  width 
must,  of  necessity,  be  some 
multiple  of  the  diameter  of  a 
single  strand.  They  are  made 
of  the  same  grades  of  steel  as 
round  ropes  and,  under  certain 
conditions  present  material  ad- 
vantages over  the  ordinary  FlG.  7 
type.  In  very  deep  shafts 

round  ropes  have  a  tendency  to  twist  and  untwist,  or  to  spin,  something 
that  flat  ropes  do  not  do.  The  width  of  the  reel  upon  which  a  flat  rope 
winds  is  very  much  less  than  that  of  the  drum  used  for  round  ropes,  and 
as  the  rope  coils  upon  itself  like  a  ribbon,  it  tends  to  equalize  the  load  upon  the 
engine,  the  effect  being  approximately  the  same  as  that  produced  by  conical 
drums.  Likewise,  in  hoisting,  the  rope  is  always  in  the  same  vertical  plane, 
thus  avoiding  the  weaj  that  round  ropes  are  subject  to  when  wound  on  a  drum. 
Flat  ropes  are  not  used  in  coal  mines  in  the  United  States,  owing  to  the  com- 
paratively shallow  depths  of  the  shafts,  but  are  quite  extensively  used  in  the 
metal-mining  districts,  where  vertical  lifts  of  2,000  ft.  and  over  are  common. 

TAPER  ROPES 

Taper  ropes,  both  round  and  flat,  have  been  used  in  deep  hoisting.  Such 
a  rope  has  its  diameter  or  width  reduced  uniformly  throughout  its  length  by 
dropping  a  single  wire  at  a  time,  or  by  decreasing  the  size  of  the  wire  used  at 
regular  intervals,  so  as  to  reduce  the  sectional  area  of  the  rope  in  proportion 
to  the  weight  to  be  supported.  The  reason  for  using  taper  rope  is  as  follows: 
When  the  load  is  at  the  bottom  of  the  shaft,  the  upper  part  of  the  rope 
sustains  both  the  load  to  be  hoisted  and  the  weight  of  the  rope  itself.  As  the 
rope  is  wound  up,  the  load  on  the  rope  at  the  drum  gradually  decreases  and, 
therefore,  the  size  of  the  rope  may  be  proportionately  decreased.  Owing  to 
the  difficulties  of  manufacture,  taper  ropes  cannot  be  made  as  perfect  as  straight 
ropes  and  their  cost  is  greater;  furthermore,  they  cannot  "be  used  for  haulage 
and  other  purposes  when  partly  worn,  as  is  the  case  with  straight  ropes. 


HAULAGE  ROPES 

6X7  Ropes. — For  underground  haulage  and  for  the  transmission  of  power, 
a  rope  of  the  section  shown  in  Fig.  1,  and  either  ordinary  or  Lang  lay,  is  in 

general  use  in  American 
mines,  to  the  practical 
exclusion  of  any  other 
type.  It  is  composed 
of  6  strands  of  7  wires 
each  (6X7)  twisted 


FIG. 


around  a  hemp  center. 

It  is  decidedly  stiffer 
than  a  6X 19  standard  hoisting  rope  and  requires  larger  sheaves,  as  will  appear 
from  the  tables.  Owing  to  the  small  number  of  wires  (there  are  but  42  as 
against  114,  152,  and  222,  in  the  6X19,  8X19,  and  6X37  hoisting  ropes)  this 


242 


WIRE  ROPES 


rope  should  be  used  with  a  higher  factor  of  safety  than  is  employed  with  hoist- 
ing ropes,  as  the  breaking  of  one  or  two  wires  materially  reduces  the  strength 
of  the  rope.  These  ropes  are  made  of  Swedes  iron  and  of  the  four  grades  or 
strengths  of  steel  previously  mentioned.  As  in  the  case  of  hoisting  ropes, 
haulage  ropes  of  iron  require  the  use  of  deecidedly  larger  sheaves  than  do 
those  of  steel.  Manufacturers  recommend  a  sheave  from  10.5  to  11  ft.  in 
diameter  for  a  1-in.  iron  rope  of  this  type  as  against  a  sheave  7  to  8  ft.  in 

diameter  for  a  corresponding  steel  rope. 
Flattened-Strand  Ropes. — Flat- 
tened-strand rope,  similar  in  general 
construction  to  the  rope  of  the  same 
name  used  for  hoisting,  is  also  em- 
ployed for  haulage.  Ropes  of  this  type 
are  shown  in  Fig.  2  (a)  and  (&).  The 
former  shows  the  5X9  (45  wires)  rope 
very  similar  to  the  5X28  hoisting  rope 
of  the  same  type.  View  (b)  shows  the 
6X8  haulage  rope,  which  is  not  un- 
like the  6X25  hoisting  rope.  The  ulti- 
mate breaking  strength  of  a  1-in.,  cast- 
steel,  ordinary,  haulage  rope  is  given 
as  31  T.,  and  those  of  the  5X9,  and  6X8,  flattened-strand  rope  of  the  same 
diameter  and  material  are  31  and  34  T.,  respectively.  The  diameter  of  sheave 
suggested  for  the  standard  6X7  1-in.  haulage  rope  is  7,  and  5.75  ft.  for  either 
type  of  the  flattened-strand  rope.  Tne  comments  made  upon  hoisting  ropes 
of  this  type  apply  here. 

Scale  Ropes. — Seale  lay  ropes  are  used  to  a  certain  extent  for  haulage  and 
those  of  the  Lang  lay  type  are  very  commonly  employed  for  the  same  purpose, 
as  explained  before. 


FIG.  2 


ROPES  FOR  MISCELLANEOUS  PURPOSES 

Ropes  for  Cableways.— Many  of  the  ropes  described,  and  particularly  the 
6X7  Lang  lay,  are  used  for  the  track  or  supporting  cable  of  what  are  variously 
known  as  cable-ways, 
•wire-rope  tramways, 
aerial  tramways,  and  the 
like.  In  this  system  of 
transportation,  the  ma- 
terials to  be  moved  are 
carried  in  buckets  sus- 
pended from  wheeled  TJT_ 
trucks,  which  are  hauled  *IG< 
by  a  lighter  rope  upon  a  fixed  rope  known  as  the  cable,  or  track  cable.  Such 
cables  are  subject  to  extreme  wear  and  to  produce  a  rope  having  the  maxi- 
mum of  wearing  surface,  what  are  known  as  locked-wire  cables  and  locked-coil 
cables  have  been  devised. 

The  locked-wire  construction  is  shown  in  Fig.  1.  The  outside  wires  are 
drawn  of  such  a  shape  as  to  interlock  one  with  the  other,  making  a  smooth 
cylindrical  surface  for  the  carrier  wheels  to  run  up9n.  Ropes  of  this  type  have 
wire  cores  and  are,  consequently,  stiffer  than  ordinary  ropes  of  the  same  size; 

but  as  they  are  proportionally 
stronger  for  equal  strengths  there 
is  probably  not  much  difference  in 
the  stiffness  of  the  two  forms  of 
construction.  The  advantages 
claimed  for  this  rope  are  lessened 
wear,  both  on  the  part  of  the  rope 
and  on  that  of  the  wheels  of  the 
traveling  carriage;  absence  of  any 
tendency  to  twist  and  turn;  and 
FlG.  2  freedom  from  unraveling  should  any 

of  the  wires  break. 

The  locked-coil  construction  is  illustrated  in  Fig.  2.  It  differs  from  the 
preceding  only  in  the  smaller  number  and  larger  size  of  the  wires,  which  makes 
it  stiffer. 


WIRE  ROPES 


243 


Another  and  cheaper,  but  very  satisfactory,  construction  for  track  cables, 
shown  in  Fig.  3,  is  known  as  the  tramway  strand,  or  smooth-coil.  It  is  merely 
a  heavy  strand  of  very  large  wires  resembling  a  spirally  fluted  cylinder  in  appear- 
ance. The  large  wires  give  increased  durability  over  smaller  wires,  owing  to 
the  greater  surface  exposed  to  wear. 

A  disadvantage  of  the  track 
cables  here  illustrated  is  that  they 
cannot  be  spliced.  In  order  to 
connect  them  the  coupling  shown 
in  Fig.  4  must  be  employed.  This 
consists  of  two,  narrow,  tapered 

sockets,  joined  at  the  middle  by  a  pIG   •-. 

plug  with  right-  and  left-hand  screw 

threads.  The  ends  of  the  wires  are  spread  apart  in  the  funnel-shaped  apertures, 
and  the  space  between  them  rilled  with  conical  thimbles  and  narrow  wedges 
made  approximately  to  the  shape  of  the  interstices.  The  sockets  are  attached 
to  the  ends  of  the  cables  by  a  special  form  of  press,  after  which  they  are  brought 
nearly  together  and  in  line  and  the  proper  end  of  the  plug  inserted  in  each. 
The  plug  is  then  turned  until  the  sockets  are  brought  together. 

Ropes  for  Suspension  Bridges. — Small  suspension  bridges  at  mines  are 
frequently  built  of  old  and  partly  worn  hoisting  or  haulage  ropes,  but  a 
special  form  of  rope,  shown  in  Fig.  5,  is  not  infrequently  used  for  this  pur- 
pose, particularly  if  the  span  is  considerable.  This  is  the  familiar  6X7  haulage 
rope,  but  with  a  wire  instead  of  a  hemp  center,  which  gives  increased  strength 
but  with  lessened  flexibility,  the  latter  quality  not  being  of  prime  importance 
in  bridge  construction. 

There  are  many  other  purposes  for  which  ropes  are  used  in  and  around 
mines,  such  as  in  running  ropes  for  derricks,  aerial  tramways,  and  steam 


FIG.  4 

shovels,  as  guy  ropes  for  derricks  and  smokestacks,  as  rigging,  hawsers,  and 
mooring  ropes  for  vessels  engaged  in  the  transportation  of  coal,  etc.  The 
forms  of  some  of  these  ropes  are  in  Figs.  5,  6,  7,  and  8. 

Derrick  Ropes. — -Guys  for  derricks  and  stacks,  shrouds  and  stays  aboard 
ship,  etc.,  are  commonly  made  of  ordinary  6X7  rope  with  a  hemp  center; 
though  where  greater  flexibility  is  required  of  a  6  strand  rope  with  12  instead 
of  7  wires  to  the  strand,  that  is  a  6X  12  rope,  is  used.  The  wires  are  commonly 
single  or  double  galvanized;  that  is,  they  receive  a  single  or  double  coating 
of  zinc  to  prevent  rusting. 

Hawsers. — Steel  hawsers,  mooring  lines,  and  running  rigging  for  vessels, 
which  must  be  more  flexible  than  ropes  used  for  guys,  standing  rigging,  etc., 
are  very  commonly  made  of  the  6X37  ropes.  Special  rope  for  these  purposes 
is  made  of  tne  section  shown  in  Fig.  6,  in  which  6  strands  (each  with  a  hemp 


FIG.  5 


FIG.  6 


FIG.  7 


FIG. 


center)  of  12  wires  each  are  wrapped  around  a  common  hemp  core.  Such 
ropes  are  very  much  stronger  than  those  of  Manila  hemp  of  the  same  size  and 
are  fully  as  flexible. 

Another  form  of  rope  used  for  the  same  purposes  is  shown  in  Fig.  7.  In 
this  case,  6  strands  of  24  wires  each  with  a  hemp  center  are  wrapped  around 
a  common  hemp  core.  This  is  more  flexible  than  the  form  shown  in  Fig.  6  and 


244 


WIRE  ROPES 


is  consequently  well  adapted  for  mooring  lines,  which  muse  be  wound  upon 
capstans,  piles,  etc.  of  comparatively  small  diameter.  The  strands  vary  in 
their  make-up ;.  with  some  manufacturers,  the  24  wires  are  all  of  the  same 
size,  while  with  others,  the  12  inner  wires  are  considerably  smaller  than  the 
outer  ones,  as  in  Scale  lay  ropes. 

Tiller  rope  is  made  of  six  small  6X7  ropes  laid  around  a  hemp  center  as 
shown  in  Fig.  8.  Containing  252  wires,  this  is  the  most  flexible  wire-rope  made. 
It  is  used  mostly  for  steering  or  tiller  ropes  on  steamers,  for  hand-lines  on  pas- 
senger elevators,  and  in  any  place  where  a  smooth  and  very  flexible  rope  is 
required.  The  ultimate  strengths  of  tiller  ropes  are  about  one-third  less  than 
those  of  standard  6X19  wire  ropes  of  the  same  size  and  grade.  The  minimum 
diameter  of  sheaves  recommended  for  usual  loads  are:  for  iron,  30  times  the 
rope  diameter;  for  steel,  25  times  the  rope  diameter.  Owing  to  the  small  size 
of  the  wires,  tiller  rope  should  be  subject  to  as  little  abrasion  as  possible. 

With  the  exception  of  tiller  rope,  and  that  only  when  used  for  passenger 
elevators,  the  ropes  that  have  been  described  are  but  rarely  made  of  Swedes 
iron,  steel  giving  much  better  results.  These  ropes  are  almost  always  gal- 
vanized, at  a  cost  of  about  10%  above  that  of  untreated  ropes. 

For  use  in  and  around  oil  wells,  ropes  of  6X  7,  6X 12,  and  6X 19  construction 
are  commonly  employed.  The  6X7  rope  is  used  for  sand  lines  and,  when 
left-lay,  for  cleaning  out  or  redrilling  wet  holes.  Casing  lines  and  drilling  lines 
for  new  holes,  the  latter  left-lay,  are  made  of  6 X  19  rope. 


ROPE  DRUMS  AND  FASTENINGS 

Fastening  Rope  to  Drum. — A  common  method  of  fastening  a  rope  to  a 
drum  is  shown  in  Fig.  1  (c),  where  the  rope  is  passed  through  a  hole  in  the  drum 
shell  and  then  around  the  shaft,  clamping 
the  end  to  the  rope  between  the  shaft  and 
the  shell,  as  shown.  Care  should  be  taken 
to  make  the  radius  of  curvature  of  the  hole 
at  a  as  large  as  possible,  so  that  the  rope 
will  not  be  bent  any  sharper  than  is  neces- 
sary. 

When  an  iron  drum  is  used,  the  thick- 
ness of  the  rim  does  not  afford  enough 
depth  in  which  to  bend  the  rope,  so  it  is 
necessary  to  build  in  a  pocket  for  the  pur- 
pose, as  shown  in  (b).  In  no  case  should 
the  rope  be  bent  sharply  at  right  angles 
where  it  passes  through  the  drum  shell. 

The  securing  of  the  rope  to  the  drum 
or  the  drum  shaft  by  several  coils  around 
each  is  unnecessary.  With  one  coil  around 
either  the  drum  or  the  shaft,  a  pull  of  1  Ib. 
will  resist  a  weight  of  9  Ib.;  if  two  coils,  a 
pull  of  1  Ib.  will  resist  9X9  =  811b.;  if  three 
coils,  9X9X9  =  729  Ib.;  and  so  on,  multi- 
plying the  former  result  by  9 'for  each  ad- 
ditional coil. 

Rope  Sockets. —  The  common  method 
of  attaching  the  socket  shown  in  Fig.  2  to  a  rope  is  as  follows:  The  rope  is 
pushed  through  from  the  small  end  and  is  allowed  to  project  any  convenient 
distance.  It  is  then  firmly  wrapped  with  wire  at  a  point  a  little  more  than 
twice  the  depth  of  the  socket  from  the  end.  The  end  of  each  strand  is  un- 
twisted, a  few  of  the  wires  cut  away,  and  the  others  bent  back  upon  themselves. 
This  makes  the  end  of  the  rope  conical,  in 
which  condition  it  is  drawn  back  into  the 
socket,  and  a  conical  wedge  is  rammed 
into  the  center  of  the  hemp  core  to  spread 
the  wires  against  the  side  of  the  socket. 
The  socket  and  a  small  length  of  the  rope 
next  thereto  are  covered  with  a  layer  of 
moist  fireclay,  and  melted  Babbitt  metal  is 


FIG.  2 


run  into  the  socket,  until  it  fills  the  space  completely  and  thus  cements  the 
whole  into  a  solid  mass.  This  entire  operation  must  be  carefully  performed, 
otherwise  all^of  the  wires  will  not  be  engaged,  and  thus  an  undue  strain  will 


WIRE  ROPES 


245 


be  thrown  upon  other  wires  or  strands,  possibly  resulting  in  the  failure  of  the 
rope  at  some  distance  from  the  socket. 

The  following  method  of  attaching  the  socket  is  employed  by  John  A.  Roeb- 
ling's  Sons  Company.  As  before,  the  rope  is  fitted  through  the  socket  and 
allowed  to  project.  Wires  are  then  securely  served  around  the  rope,  the 
strands  opened  for  a  distance  equal  to  the  length  of  the  basket  of  the  socket,  and 
the  hemp  center  cut  off  the  length  of  the  opening.  The  wires  are  then  well 
cleaned  with  kerosene  and  wiped  dry.  After  the  strands  are  separated  into 
wires,  which  may  be  conveniently  done  with  a  small  piece  of  pipe,  the  wires  are 
placed  into  a  solution  of  equal  parts  of  water  and  hydrochloric  acid  or  muriatic 
acid,  HCl,  for  5  min.,  and  then  are  cleaned  off.  They  are  then  redipped  into 
the  solution,  which  has  been  made  weaker  by  the  addition  of  1  part  of  water 
(now  2  parts  of  water  to  1  part  of  acid).  The  wires  are  then  bunched  and 
bound  together  by  wire  about  1  in.  from  the  top.  When  the  socket  has  been 
pushed  over  the  wires  until  their  ends  are  even  with  the  top  of  the  basket, 
fireclay  is  placed  around  the  rope  at  the  bottom  of  the  socket,  to  serve  as  a 
shield,  and  melted  zinc  is  poured  into  the 
basket  of  the  socket.  It  will  be  noted 
that  in  this  method  of  fastening  none  of  the 
wires  are  cut  out  and  none  are  bent  back 
upon  themselves;  the  rope  is  rrerely  opened 
up,  untwisted,  and  the  ends  of  the  wires 
bunched  together. 

Instead  of  using  a  socket,  the  end  of  the 
rope  may  be  bent  around  a  thimble  and  the 
end  fastened  by  clamping  the  parts  of  the 
rope  with  devices,  as  shown  in  Fig.  3  (a) : 
or  with  iron  bands  that  are  sometimes  held 
in  place  by  nails,  inserted  between  the 
strands,  as  in  (6) ,  though  this  practice  is  not 
recommended;  or  by  wrapping  the  rope  with 
wire,  as  in  (c).  In  the  last  method,  the  end 
of  the  rope  is  frayed,  and  the  loosened 
wires  are  arranged  evenly  around  the  main 
portion  of  the  rope  before  wrapping  is 
commenced. 

WIRE-ROPE  TABLES 

The  accompanying  tables  (eleven  in  number)  giving  the  ultimate  strengths 
of  wire  ropes,  proper  size  of  sheaves  to  be  used  therewith,  etc.  are  taken  from 
the  latest  practice  of  the  leading  American  manufacturers  of  wire  rope.  The 
strengths  given  are  ultimate  strengths,  the  working  strains  to  which  the  rope 
is  actually  subjected  being  usually  one-fifth  of  these;  that  is,  a  factor  of  safety 
of  5  is  commonly  employed,  although  one  of  6  is  not  unusual,  and  even  10  is 
used,  particularly  in  elevator  work  where  passengers  are  carried.  The  use  of 
these  tables  when  selecting  a  hoisting  rope  for  any  particular  service  is  best 
illustrated  by  means  of  an  example. 

EXAMPLE. — A  total  load  of  8  T.  is  to  be  hoisted  from  a  shaft  300  ft.  deep. 
What  size  rope  should  be  employed,  allowing  a  factor  of  safety  of  5? 

SOLUTION. — Since  the  factor  of  safety  is  5,  the  rope  selected  must  have 
an  ultimate  strength  of  5X8  =  40T.  Standard  hoisting  ropes  are  6 X  19  and 
commonly  of  cast  steel.  The  first  table  shows  that  a  If-in.  rope  of  this  kind 
has  a  breaking  strength  of  38  T.,  and  one  \\  in.  in  diameter,  a  breaking 
strength  of  56  T.  The  weight  of  the  smaller  rope  is  2  Ib.  per  ft.,  and  of  the 
larger  2.45  Ib.  In  the  one  case  the  weight  of  the  rope  will  be  300  X  2  =  600  Ib. 
=  .3  T.,  and  in  the  other  300X2.45  =  735  lb.  =  .36  T.  If  a  H-in.  rope  is 
used,  the  rope  is  called  upon  to  sustain  a  load  of  40.3  T.;  if  a  IJ-in.  rope  is 
used,  the  strain  is  40.36  T.  Therefore,  the  smaller  rope  is  not  quite  strong 
enough  and  the  larger  rope  is  considerably  over  strength.  Probably  the 
ly-in.  rope  with  a  factor  of  safety  a  little  less  than  5  would  answer,  but  bet- 
ter practice  demands  the  selection  of  the  larger  rope;  the  factor  of  safety  being 
nearly  6.  The  table  also  shows  that  the  minimum  diameter  of  sheave  or 
drum  for  the  l|-in.  rope  is  5  ft.,  and  for  the  IJ-in.  rope,  6  ft. 


246 


WIRE  ROPES 


»O^OCOOi 
t  CO  W  (N  y>  O 


Minimum  Diameter 
of  Sheave  or  Drum 
Feet 


* 
-S 


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WIRE  ROPES 


247 


saqouj 


te 
r 
ron 
pe 


Appro 
Weig 
Foot 
or  Ste 
Po 


SO'CiOi 
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s  of  25  Wires 
Each 


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fOOO-^C^O 


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Ow 


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248  WIRE  ROPES 

SIZES  AND  STRENGTHS  OF  FLAT  HOISTING  ROPES 


Width 
and 
Thick- 
ness 
Inches 

Weight 
per  Foot 
Pounds 

Approximate 
Strength,  in  Tons 
of  2.000  Ib. 

Width 
and 
Thick- 
ness 
Inches 

Weight 
per  Foot 
Pounds 

Approximate 
Strength,  in  Tons 
of  2,000  Lb. 

Cast 
Steel 

Plow 
Steel 

Cast 
Steel 

Plow 
Steel 

r*K*  HIM 

t~soic>OT}<T}teoco 
XXXXXXXX 

5.90 
5.20 
4.82 
4.27 
4.00 
3.30 
2.97 
2.38 

129 
113 
105 
97 
89 
81 
72 
56 

158 
138 
128 
118 
108 
99 
89 
69 

1X5* 
1X5 
iX4| 

1X4 
1X3* 
1X3 
1  X2i 
1X2 

3.90 
3.40 
3.12 
2.70 
2.30 
2.00 
1.75 
1.30 

76 
72 
63 
58 
49 
45 
36 
27 

99 
93 
81 
76 
64 
58 
46 
35 

SIZES  AND  STRENGTHS  OF  STANDARD  6X?  HAULAGE  ROPES 


Minimum 

1 

&  * 

Approximate  Strength,  in  Tons  of 
of  2,000  Ib. 

Diameter  of 
Sheave  or 
Drum 

I 

*o   « 

Feet 

o.  *c 

ll 

4»      0 

5 

Swedish 
Iron 

Cast 
Steel 

Extra 
Cast 
Steel 

Plow 
Steel 

Extra 
Plow 
Steel 

Iron 

Steel 

1 

u 

32.0 

63.0 

73.00 

82.0 

90.00 

16* 

13* 

3.55 

i 

28.0 

53.0 

63.00 

72.0 

79.00 

15 

III 

3.00 

i 

23.0 

46.0 

54.00 

60.0 

67.00 

13f 

10) 

2.45 

i 

19.0 

37.0 

43.00 

47.0 

52.00 

w 

91 

2.00 

i 

15.0 

31.0 

35.00 

38.0 

42.00 

11 

8 

1.58 

j 

12.0 

24.0 

28.00 

31.0 

33.00 

9f 

1.20 

i 

8.8 

18.6 

21.00 

23.0 

25.00 

81 

5 

.89 

u 

7.3 

15.4 

16.70 

18.0 

20.00 

7* 

5 

.75 

I 

6.0 

13.0 

14.50 

16.0 

17.50 

7 

4 

.62 

A 

4.8 

10.0 

11.00 

12.0 

13.00 

61 

4 

.50 

I 

3.7 

7.7 

8.85 

10.0 

11.00 

5i 

3 

.39 

A 

2.6 

5.5 

6.25 

7.0 

7.75 

4| 

3 

.30 

1 

2.2 

4.6 

5.25 

5.9 

6.50 

4^ 

2 

.22 

JL. 

1.7 

3.5 

3.95 

4.4 

2 

.15 

A 

1.2 

2.5 

2.95 

3.4 

3* 

2 

.125 

L           1 

GALVANIZED  STEEL  CABLES  FOR  SUSPENSION  BRIDGES 


Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength 
in  Tons  of 
2,000  Lb. 

Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength 
in  Tons  of 
2,000  Lb. 

2! 
2f 
2i 
2f 
21 

12.70 
11.60 
10.50 
9.50 
8.52 
7.60 
6.73 

310 
283 
256 
232 
208 
185 
164 

1 

1 

1 

5.90 
5.10 
4.34 
3.70 
3.10 
2.57 

144 
124 
106 
90 
75 
62 

WIRE  ROPES 


249 


SIZES    AND    STRENGTHS    OF    PATENT,    FLATTENED-STRAND 
HAULAGE  ROPES 


1 

0 

•8 

oj 
P 

1 

1 
1 

1 
1 

I 

_g 

Approximate  Total  Strength  of 
Rope,  in  Tons  of  2,000  Lb. 

Minimum 
Diameter  of 
Sheave  or 
Drum  for 
Either  Section 
of  Rope 
Feet 

Approx- 
imate 
Weight 
per  Foot 
of  Iron 
or  Steel 
Rope 
Pounds 

o 
"o 

1 

S 

5  Strands  of 
9  Wires  Each 

6  Strands  of 
8  Wires  Each 

3  . 

•3  § 

CO 

Oco 

1 

0-3 

£co 

H 

M 

& 
^o 

M 

w 

31 

4* 

f 

I1 

fi 

CO 

Jl 

£ 

5X9 

6X8 

! 

23.0 
19.0 
15.0 
12.0 
8.8 
6.0 
3.7 
2.2 

63.0 
53.0 
46.0 
37.0 
31.0 
24.0 
18.6 
13.0 
7.7 
4.6 

73.00 
63.00 
54.00 
43.00 
35.00 
28.00 
21.00 
14.50 
8.85 
5.25 

67.0 
52.0 
42.0 
33.0 
25.0 
17.5 
11.0 
6.5 

68.0 
57.0 
50.0 
40.0 
34.0 
26.0 
20.0 
14.0 
8.3 
5.0 

79.0 
68.0 
58.0 
46.0 
38.0 
30.0 
22.7 
15.7 
9.6 
5.7 

73.0 
56.0 
46.0 
36.0 
27.0 
19.0 
11.9 
7.0 

sf 

7| 

6 
4f 

34 

1! 

61 

5 

44 
34 
24 
2 

8 

!' 

3 

2f 

3.65 
3.10 
2.55 
2.05 
1.65 
1.24 
.92 
.64 
.40 
.23 

4.00 
3.45 
2.80 
2.30 
1.80 
1.38 
1.00 
.72 
.45 
.25 

j| 

CAST  STEEL  LOCKED-WIRE  CABLE 


Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength, 
in  Tons  of 
2,000  Lb. 

Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength 
in  Tons  of 
2,000  Lb. 

24     - 
21 
2 
1} 
If 

H 

if 
U 

15.60 
12.50 
10.00 
7.65 
6.60 
5.70 
4.75 
3.80 

275 
220 
170 
129 
114 
95 
80 
67 

H 

I 

3.15 
2.50 
1.88 
1.30 
.90 
.72 
.57 

55.00 
43.00 
36.00 
27.00 
19.00 
13.25 
11.50 

TRAMWAY  OR  SMOOTH-COIL  CABLE 


Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength, 
in  Tons  of 
2,000  Lb. 

Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength, 
in  Tons  of 
2,000  Lb. 

Cast 
Steel 

Plow 
Steel 

Cast 
Steel 

Plow 
Steel 

24 

I 

if 
if 
14 

13.10 
10.36 
9.35 
8.40 

7.28 
6.59 
5.63 

4.88 

285.0 
233.0 
204.0 
185.0 
161.0 
145.8 
124.0 
108.4 

335.0 
266.0 
240.0 
218.0 
189.0 
171.0 
146.0 
127.5 

H 

4.01 
3.23 
2.70 
2.20 
1.69 
1.24 
.86 

88.8 
71.8 
60.0 
49.2 
37.6 
27.6 
19.2 

105.0 
84.6 
70.7 
58.0 
44.4 
32.5 
22.3 

250  WIRE  ROPES 

GALVANIZED  IRON  AND  STEEL  RUNNING  ROPE 


Ultimate 

Ultimate 

Diameter 
of 
Rope 

Weight 
Foot 

Strength 
in  Tons  of 
2,000  Lb. 

Diame- 
ter of 
Rope 

Weight 
per 
Foot 

Strength 
in  Tons  of 
2,000  Lb. 

Inches 

Pounds 

Inches 

Pounds 

Iron 

Cast 
Steel 

Iron 

Cast 
Steel 

1& 

1.18 

10.1 

22.5 

& 

.33 

2.80 

6.50 

1 

1.05 

8.7 

19.5 

I 

.26 

2.20 

5.00 

I 

.80 

6.9 

15.5 

iV 

.20 

1.70 

3.90 

f 

.68 
.59 

6.0 
5.1 

13.5 
11.5 

A 

.14 
.10 

1.30 
.82 

2.85 
1.98 

I 

.42 

3.6 

8.0 

GALVANIZED  STEEL  HAWSERS 


2L 

8. 

Diameter  of  Rope 
Inches 

Approximate 
Circumference 
Inches 

Weight  per  Foot 
Pounds 

Ultimate  Strength, 
in  Tons  of 
2,000  Lb. 

of  New  Manila  Ro 
of  Same  Strength 
Inches 

Diameter  of  Rope 
Inches 

Approximate 
Circumference 
Inches 

Weight  per  Foot 
Pounds 

Ultimate  Strength, 
in  Tons  of 
2,000  Lb. 

of  New  Manila  Ro 
of  Same  Strength 
Inches 

1 

1 

w 

2A 

6* 

4.43 

83 

11 

41 

2.36 

45 

12.00 

2 

61 

4.20 

77 

1& 

4} 

2.16 

41 

11.50 

JL| 

6 

3.89 

71 

It 

41 

2.00 

38 

11.00 

H 

5| 

3.42 

66 

11 

4 

1.63 

31 

10.00 

^ 

5* 

3.23 

61 

13.5 

1& 

3} 

1.47 

28 

9.25 

XI 

51 

2.94 

57 

13.0 

H 

3* 

1.33 

26 

8.75 

1 

5 

2.76 

53 

12.5 

GALVANIZED  STEEL  MOORING  LINES 


Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength, 
in  Tons  of 
2,000  Lb. 

Diameter 
of  Rope 
Inches 

Weight 
per  Foot 
Pounds 

Ultimate 
Strength, 
in  Tons  of 
2,000  Lb. 

2& 

5.81 

113 

1| 

2.62 

50 

2 

5.51 

106 

2.15 

42 

5.09 

98 

in 

1.93 

38 

4.48 

88 

i-i6 

1.75 

34 

4.24 

82 

1_L 

1.54 

27 

3.86 

76 

f? 

1.38 

25 

3.63 

74 

1.05 

20 

3.10 

63 

H 

.90 

17 

2.92 

55 

1 

.78 

14 

WIRE  ROPES  251 


WIRE-ROPE  CALCULATIONS 

The  working  load,  also  called  the  proper  working  load,  is  the  maximum 
load  that  a  rope  should  be  permitted  to  support  under  working  conditions. 
The  stress  on  a  rope  to  which  a  load  is  attached,  and  which  bends  over  a  sheave, 
is  made  up  of  the  load  on  the  rope,  known  as  the  load  stress,  and  the  bending 
of  the  rope  about  a  sheave  or  drum,  known  as  the  bending  stress.     That  is,  if 
5  =  total  safe  stress; 
5*  =  bending  stress; 
5/  =  load  stress; 
S  =  Sd+Si  and  5/=5-5*. 

The  total  stress  must  not  equal  the  elastic  limit  of  the  material  composing 
the  rope  and  is  usually  taken  as  from  one-third  to  one-fourth  the  approx- 
imate breaking  stress.  It  is  only  quite  recently  that  account  has  been  taken  of 
this  second  stress  and  it  is  not  by  any  means  universal  practice  to  consider  it 
when  calculating  the  size  of  rope  needed  for  a  given  purpose. 

If  a  given  weight  is  to  be  hoisted  with  a  wire  rope,  the  proper  size  of  rope 
to  use  may  be  taken  directly  from  the  tables,  but  these  do  not  take  account  of 
the  bending  stress,  except  by  allowing  for  it  in  the  factor  of  safety  assumed. 

A  second  method  calculates  the  bending  stress.  The  following  formulas 
and  the  diagram  based  on  them  are  given  by  Mr.  E.  T.  Sederholm,  former 
chief  engineer  for  Fraser  &  Chalmers,  and  will  be  found  in  the  hoisting-engine 
catalog  of  the  Allis-Chalmers  Co.  The  general  formula  for  the  bending  stress  is 

£  a  A 
St  --  p-, 

in  which  Sf>  =  bending  stress; 

E  =  modulus  of  elasticity; 
a  =  diameter  of  each  wire; 
D  =  diameter  of  drum  or  sheave,  in  inches; 
A  =  total  area  of  wire  cross-section,  in  inches. 
For  a  rope  of  19  wires  to  the  strand  the  diameter  of  each  wire  is  about  one- 

fifteenth  (exactly         2>  of  the  diameter  of  the  rope.     That  is,  if  d=  diameter 
of  rope,  a  =  Tr^;  and  by  substituting  'this  in  the  formula,  St=  ?-^jL  . 


The  modulus  of  elasticity  for  the  different  kinds  of  wire  is  given  different 
values  by  different  authorities.  Mr.  Sederholm  uses  29,400,000  in  his  formula 
and  diagram,  and  Mr.  Hewitt  28,500,000,  the  same  modulus  being  used  for 
the  different  materials  of  which  ropes  are  made. 

The  cross-section  of  metal  A  in  a  wire  rope  is  approximately  Ad2,  or  it  may 
be  more  accurately  calculated  by  multiplying  the  cross-section  of  each  wire, 
as  given  by  a  wire  table,  by  the  number  of  wires  in  the  rop.e. 

EXAMPLE.  —  'Find  the  bending  stress  in  a  19-wire,  cast-steel  hoisting  rope 

2  in.  in  diameter,  winding  on  an  8-ft.  drum,  if  A  =  Ad2,  and  £  =  29,400,000. 

SOLUTION.  —  Applying    the   formula   just  given,   the  bending  moment  is 

29  ,400.000  X  23  X.  4 
**~  10X  15.52X96X2,000~dl<51  L' 
The  approximate  breaking  stress  for  such  a  rope  is  106  T.,  and  if  a  factor  of 

3  is  assumed  106-^3  =  35+  T.  for  the  safe  working  stress,  and  35-32  =  3  T., 
for  the  safe  lifting  load  under  the  given  conditions. 

Mr.  Wm.  Hewitt,  of  the  Trenton  Iron  Co.,  has  given  a  similar  but  more 
complicated  formula  for  the  bending  stress,  which  is  supposed  to  give  some- 
what more  accurate  results,  as  he  has  introduced  terms  that  allow  for  the 
actual  radius  of  the  bend  at  the  outside  fiber  of  the  rope,  while  the  Sederholm 
formula  assumes  the  radius  of  the  bend  to  be  the  radius  of  the  sheave. 

Mr.  Hewitt's  formula  is  as  follows: 


2.06     +C 

in  which   Sb  =  bending  stress,  in  pounds; 

£  =  modulus  of  elasticity  (28,500,000); 

A  =  aggregate  area  of  wires,  in  square  inches; 

R  =  radius  of  drum  or  sheave,  in  inches; 

d  =  diameter  of  individual  wires,  in  inches; 

C  =  a  constant  depending  on  number  of  wires  in  strands. 


252 


WIRE  ROPES 


The  values  of  d  and  C  are: 

7 -Wire  Rope  19-Wire  Rope 

d  =  %  diameter  of  rope  a  =  A  diameter  of  rope 

C=9.27  .  C-  15.45 

For  12-wire  and  16-wire  ropes  the  values  are  intermediate  in  proportion  to 
the  number  of  wires.  In  the  case  of  ropes  having  strands  composed  of  dif- 
ferent sizes  of  wires,  take  the  larger  of  the  outer  layer  for  the  value  of  d. 

(By  permission  of  E.  T.  Sederholm,  Chief  Engr.,  Fraser  &»  Chalmers,  Chicago.) 


6OOOO 


550OO 


3OOOO 


45000 


ZOOOO 


SOOO 


WIRE  ROPES 


253 


Mr.  Hewitt  assumes  one-third  of  the  approximate  breaking  stress  as  the 
maximum  safe  stress  and  uses  28,500,000  for  the  modulus  of  elasticity. 

If  the  problem  given  under  the  Sederholm  formula  is  worked  out  by  the 
Hewitt  formula  the  safe  working  load  will  be  11?  T.,  while  the  table  gives 
106-^5  =  21.2  T. 

The  Sederholm  diagram  gives  for  a  load  of  21.2  T.  a  sheave  between  13  and 
14  ft.  in  diameter,  the  formula  gives  a  sheave  of  11£  ft.  in  diameter,  while  the 
table  gives  9|  ft.  It  is  evident  that  there  is  a  wide  difference  of  opinion 
among  the  wire-rope  authorities  and  a  good  opportunity  for  experimental 
work  along  this  line. 

In  using  the  Sederholm  or  Hewitt  formulas,  there  are  two  unknown  quan- 
tities, the  diameter  of  the  ropa  d  and  the  diameter  D  o'r  radius  R  of  the  drum. 
d  varies  inversely  as  D,  that  is,  for  a  given  load,  the  smaller  d  is  taken  the 
larger  D  must  be  to  give  the  same  conditions  of  safety. 

If  a  certain  ratio  between  Sb  and  Si  could  be  assumed  in  the  formula 
S  =  Sb+  Si  the  problem  could  be  easily  solved,  but  an  examination  of  this 
ratio  in  a  number  of  cases  where  good  .results  have  been  obtained  from 

hoisting  ropes  shows  it  to  vary  from  ^r  =  1  to  ^  =  s.     In  the  transmission  of 

»jd  o£      O 

power  by  wire  ropes,  Mr.  Hewitt  assumes  -^r  =  «»  kut  ^s  relation  will  scarcely 

o£      & 

hold  in  a  hoisting  problem,  and  the  foregoing  problem  must  be  solved  by  the 
cut-and-try  method. 

Proper  Working  Load.  —  For  steel  hoisting  ropes,  made  with  19  wires  to 
the  strand,  when  used  on  drums  of  different  diameters,  the  proper  working 
load  may  be  found  from  the  following  formula,  in  which  the  total  strain  on 
the  rope,  including  bending  strain  and  the  strain  due  to  load  is  assumed  at' 
50,000  Ib.  per  sq.  in.  of  actual  steel  section. 

Let  d  =  diameter  of  rope,  in  inches; 

D  =  diameter  of  drum,  in  inches; 
S  =  strain  per  square  inch  due  to  bending; 
L  =  proper  working  load,  in  pounds. 

S=  1,894,000  X^ 

L  =  20,000^  -  757,600  X 


STARTING  STRESS  ON  ROPE 


Dynamometer  Tests 

Starting  Stress 

Tons 

Cwt. 

First  Test 
Empty  cage  lifted  gently  

1 
2 
4 
5 

2 
3 
5 
5 

7 

5 
5 
5 
8 
8 
10 
11 
12 
11 

16 
10 
0 
10 

17 
0 
0 
10 
0 

1 
1 
3 
10 
10 
10 
10 
10 
10 

Empty  cage  with    2  5  in  slack  chain 

Empty  cage  with    6    in.  slack  chain  

Empty  cage  with  12    in.  slack  chain  

Second  Test 
Cage  and  four  empty  cars  weighed  by  machine  

Cage  and  four  empty  cars  with    6  in.  slack  chain  

Cage  and  four  empty  cars  with  12  in   slack  chain 

Third  Test 
Cage  and  full  cars  weighed  by  machine  

No    1   lifted  gently                                                                 .    ... 

No  2  lifted  gently 

No    1   with  3  in.  slack  chain                               

No.  1   with  6  in.  slack  chain  /  

No   2   with  6  in   slack  chain                        

254 


WIRE  ROPES 


Starting  Stress  on  Hoisting  Rope. — When  selecting  a  hoisting  rope,  due 
allowance  must  be  made  for  the  shock  and  extra  stress  imposed  on  the  rope 
when  the  load  is  started  from  rest.  Experiments  made  by  placing  a  dyna- 
mometer between  the  rope  and  the  cage  have,  shown  that  the  starting  stress 
may  be  from  two  to  three  times  the  actual  load.  The  experiments  referred 
to  were  made  in  England  and  are  here  given;  the  tons  are  those  of  2,240  lb., 
and  the  hundredweights  (.cwt.),  112  lb. 

STRESS  OF  ROPE  ON  PLANES 


Rise  per 
100  Ft. 
Horizontal 
Feet 

Angle 
of 
Inclination 

Stress 
per  Ton  of 
2,000  Lb. 
Pounds 

Rise  per 
100  Ft. 
Horizontal 
Feet 

Angle 
of 
Inclination 

Stress 
per  Ton  of 
2,000  Lb. 
Pounds 

5 

2°  52' 

140 

105 

46°  24' 

1,484 

10 

5°  43' 

240 

110 

47°  44' 

1,516 

15 

8°  32' 

336 

115 

49°  00' 

1^535 

20 

11°  10' 

432 

120 

50°  12' 

1,573 

25 

14°  03' 

527 

125 

51°  21' 

1,597 

30 

16°  42' 

613 

130 

52°  26' 

1,620 

35 

19°  18' 

700 

135 

53°  29' 

1,642 

40 

21°  49' 

782 

140 

54°  28'- 

1,663 

45 

24°  14' 

860 

145 

55°  25' 

1,682 

50 

26°  34' 

933 

150 

56°  19' 

1,699 

55 

28°  49' 

1.003 

155 

57°  11' 

1.715 

60 

30°  58' 

1,067 

160 

58°  00' 

1,730 

65 

33°  02' 

1,128 

165 

58°  47' 

1,744 

70 

35°  00' 

1,185 

170 

59°  33' 

1,758 

75 

36°  53' 

1,238 

175 

60°  16' 

1,771 

80 

38°  40' 

1,287 

180 

60°  57' 

1,782 

85 

40°  22' 

1,332 

185 

61°  37' 

1,794 

90 

42°  00'     . 

1,375 

190 

62°  15' 

1,804 

95 

43°  32' 

1,415 

195 

62°  52' 

1,813 

100 

45°  00' 

1,450 

200 

63°  27' 

1,822 

Stress  in  Hoisting  Ropes  on  Inclined  Planes  of  Various  Degrees. — The 

preceding  table  is  based  on  an  allowance  of  40  lb.  per  T.  for  rolling  fric- 
tion, but  there  will  be  an  additional  stress  due  to  that  portion  of  the  weight 
of  the  rope  which  acts  vertically. 

Relative  Effect  of  Various  Sized  Sheaves  or  Drums  on  Life  of  Wire  Ropes. 
Mine  officials  and  other  users  of  wire  ropes  have  often  felt  the  want  of  a  table 
or  set  of  tables  that  would  enable  them  to  determine  at  a  glance  what  effect 
the  use  of  various  sized  sheaves  would  have  on  various  sized  ropes.  The 
following  tables  have  been  specially  prepared  for  the  Coal  and  Metal  Miner's 
Pocketbook  by  Mr.  Thomas  E.  Hughes,  of  Pittsburg,  Pennsylvania.  The 
cast-steel  ropes  for  inclines  are  made  of  6  strands  of  7  wires  each,  laid 
around  a  hemp  core,  the  cast-steel  hoisting  ropes  are  made  of  6  strands  of 
19  wires  each,  laid  a  hemp  core;  and  the  iron  hoisting  ropes,  of  6  strands 
of  19  wires  each,  laid  around  a  hemp  core. 

CAST-STEEL  ROPES  FOR  INCLINES 


Diameter 
-      of 
Rope. 
Inches 

Percentages  of  Life  for  Various  Diameters 

100 

90        |        80 

75        |     60      |      50 

25 

Diameters  of  Sheaves  or  Drums  in  Feet 

1* 
If 
1J 
l| 
1 

16.00 
14.00 
12.00 
10.00 
8.50 
7.75 
7.00 
6.00 
5.00 

14.00 
12.00 
10.00 
8.50 
7.75 
7.00 
6.25 
5.25 
4.50 

12.00 
10.00 
8.00 
7.75 
6.75 
6.25 
5.50 
4.50 
4.00 

11.00 
8.50 
7.25 
7.00 
6.00 
5.75 
5.00 
4.00 
3.50 

9.00 
7.00 
6.00 
6.00 
5.00 
4.50 
4.25 
3.25 
2.75 

7.00 
6.00 
5.50 
5.00 
4.50 
3.75 
3.50 
3.00 
2.25 

4.75 
4.50 
4.25 
4.00 
3.75 
3.25 
2.75 
2.50 
1.75 

WIRE  ROPES 
CAST-STEEL  HOISTING  ROPES 


255 


Diameter 

Percentages  of  Life  for  Various  Diameters 

of 
Rope. 

100       |        90 

80                75 

60     |      50            25 

Inches 

Diameters  of  Sheaves  or  Drums  in  Feet 

14 

14.00 

12.00 

10.00 

8.50 

7.00        6.00 

4.50 

1 

12.00 

10.00 

8.00 

7.00 

6.00 

5.25 

4.25 

1 

10.00 

8.50 

7.50 

6.75 

5.50 

5.00 

4.00 

1 

9.00 

7.50 

6.50 

5.50 

5.00 

4.50 

3.75 

1 

8.00 

7.00 

6.00 

5.50 

4.50 

4.00 

3.50 

7.50 

6.75 

5.75 

5.00 

4.25 

3.50 

3.00 

5.50 

4.50 

4.00 

3.75 

3.25 

3.00 

2.25 

4.50    • 

4.00 

3.75 

3.25 

3.00 

2.50 

2.00 

4.00 

3.00 

3.00 

2.75 

2.25 

2.00 

1.50 

3.00 

2.00 

1.50 

IRON  HOISTING  ROPES 


Diameter 

Percentages  01  Lite  tor  Various  JLJiameters 

of 
Rope. 

100 

90 

80 

75 

60 

5Q 

25 

Inches 

Diameters  of  Sheaves  or  Drums  in  Feet 

li 

12.00 

11.00 

9.00 

7.50 

6.00 

5.00 

4.25 

H 

10.00 

9.00 

7.50 

7.00 

5.25 

4.75 

4.00 

H 

9.00 

7.75 

6.50 

5.75 

4.50 

4.00 

3.50 

if 

8.00 

6.75 

5.50 

5.00 

4.25 

3.50 

3.00 

1 

6.75 

6.00 

5.00 

4.75 

4.00 

3.25 

2.75 

6.75 

6.00 

5.00 

4.50 

4.00 

3.00 

2.50 

5.00 

4.75 

4.00 

3.75 

3.00 

2.75 

2.00 

4.50 

3.75 

3.25 

3.00 

2.75 

2.25 

1.75 

3.50 

3.25 

3.00 

2.75 

2.00 

1.50 

1.00 

3.00 

2.00 

1.25 

1.00 

CARE  OF  WIRE  ROPES 

Ordinary  Method  of  Splicing  Wire  Rope. — The  tools  required  for  splicing 
wire  ropes  by  the  ordinary  method  are  a  pair  of  iron  nippers  for  cutting  off 
strands;  two  marline  spikes,  one  round  and  one  9val,  for  opening  strands; 
one  knife  to  cut  hemp  center;  two  clamps  to  untwist  rope  to  insert  ends  of 
strands  or,  in  place  of  them,  two  short  hemp-rope  slings,  with  a  stick  for  each 
as  a  lever;  a  wooden  mallet  and  some  rope  twine.  Also,  a  bench  and  vise  are 
handy. 

The  length  of  the  splice  depends  on  the  size  of  the  rope.  The  larger  ropes 
require  the  longer  splices.  The  splice  of  ropes  from  |  in.  to  f  in.  in  diameter 
should  not  be  less  than  20  ft.;  from  f  in.  to  1|  in.,  30  ft.;  and  from  H  in. 
up,  40  ft. 

To  splice  a  rope,  tie  each  end  with  a  piece  of  cord  at  a  distance  equal  to 
one-half  the  length  of  the  splice,  or  10  ft.  back  from  the  end  for  a  f-in.  rope,  after 
which  unlay  each  end  as  far  as  the  cord.  Then  cut  out  the  hemp  center, 
and  bring  the  two  ends  together  as  close  as  possible,  placing  the  strands  of 
the  one  end  between  those  of  the  other,  as  shown  in  Fig.  1  (a).  Now  remove 
the  cord  k  from  the  end  M  of  the  rope,  and  unlay  any  strand,  as  a,  and  follow  it 
up  with  the  strand  of  the  other  end  M'  ot  the  rope  that  corresponds  to  it,  as 
a'.  About  6  in.  of  a  is  left  out,  and  a'  is  cut  off  about  6  in.  from  the  rope, 
thus  leaving  two  short  ends,  as  shown  at  P  in  (&),  which  must  be  tied  for  the 
present  by  cords  as  shown.  Wind  the  cord  k  again  around  the  end  M  of  the 
rope,  to  prevent  the  unraveling  of  the  strands;  after  which  remove  the  cord  k' 
on  the  other  or  M'  end  of  the  rope,  and  unlay  the  strand  &;  follow  it  up,  as 
4>efore,  with  the  strand  &',  leaving  the  ends  out,  and  tying  them  down  for  the 
present,  as  described  in  the  case  of  strands  a  and  a',  see  Q\  also,  replace  the 
cord  k'.  Again  remove  the  cord  k  and  unlay  the  next  strand,  as  c,  and  follow 
it  up  with  c',  stopping,  however,  this  time  within  4  ft.  of  the  first  set.  Con- 


256 


WIRE  ROPES 


tinue  this  operation  with  the  remaining  six  strands,  stopping  4  ft,  short  of  the 
preceding  set  each  time.  The  strands  are  now  in  their  proper  places,  with  the 
ends  passing  each  other  at  intervals  of  4  ft.,  as  shown  in  (c).  To  dispose  of 
the  loose  ends,  clamp  the  rope  in  a  vise  at  the  left  of  the  strands  a  and  a'. 


6 


FIG.  1 


view  (c),  and  fasten  a  clamp  to  the  rope  at  the  right  of  these  strands;  then 
remove  the  cords  tied  around  the  rope  that  hold  these  two  strands  down; 
after  which  turn  the  clamp  in  the  opposite  direction  to  which  the  rope  is 
twisted,  thereby  untwisting  the  rope,  as  shown  in  (d).  The  rope  should  be 
untwisted  enough  to  allow  its  hemp  core  to  be  pulled  out  with  a  pair  of 
nippers.  Cut  off  24  in.  of  the  hemp  cores,  12  in.  at  each  side  from  the  point 
of  intersection  of  the  strands  a  and  a',  and  push  the  ends  of  the  strands  in 
their  place  as  shown  in  (d).  Then  allow  the  rope  to  twist  up  to  its  natural 
shape,  and  remove  the  clamps.  After  the  rope  has  been  allowed  to  twist  up, 
the  strands  tucked  in  generally  bulge  out  somewhat.  This  bulging  may  be 
reduced  by  lightly  tapping  the  bulged  part  of  the  strands  with  a  wooden 


rr^>     ^T^  ^^=TTv     ^^~? 
k     c         G.          ^~*  ^^a 


(C) 

FIG.  2 

mallet,  which  will  force  their  ends  farther  into  the  rope.     Proceed  in  the  same 
manner  to  tuck  in  the  other  ends  of  the  strands. 

Rapid   Method  of   Splicing   Wire   Rope. — The  only  tools  needed  in  the 
rapid  method  of  splicing  wire  ropes  are  a  cold  chisel  and  hammer  for  cutting 


WIRE  ROPES  257 

and  trimming  the  strands,  and  two  needles  12  in.  long,  made  of  good  steel  and 
tapered  ovally  to  a  point.  Cut  off  the  ends  of  the  ropes  to  be  spliced  and 
unlay  three  adjacent  strands  of  each  back  15  ft.;  cut  out  the  hemp  center  to 
this  point  and  relay  the  strands  for  7  ft.  and  cut  them  off.  Pull  the  ropes  by 
each  other  until  they  have  the  position  shown  in  Fig.  2,  (a),  cut  off  a  and  d',  b 
and  c',  view  (&),  making  their  lengths  approximately  10  and  12 £  ft.,  respectively, 
measured  from  the  point  where  the  hemp  centers  were  cut.  Place  the  ropes 
together,  unlay  e,  d,  c,  Fig.  2,  view  (a),  keeping  the  strands  together,  and  follow 
with  e',  d',  c',  (b).  Similarly,  unlay  /',  a',  b',  and  follow  with  /,  a,  b,  until  the 
rope  appears  as  in  (c).  Next  run  the  strands  into  the  middle  of  the  rope.  To 
do  this,  cut  off  the  end  of  the  strand  e',  so  that  when  it  is  put  in  place  it  will 
just  reach  to  the  end  x  of  the  hemp  core,  and  then  push  the  needle  A,  through 
the  rope  from  the  under  side,  leaving  two  strands  at  the  front  of  the  needle, 
as  shown.  Push  the  needle  B  through  from  the  upper  side  and  as  close  to  the 
needle  A  as  possible,  leaving  the  strands  e  and  e'  between  them;  place  the 
needle  A  on  the  knee  and  turn  the  needle  B  around  with  the  coil  of  the  rope, 
and  force  the  strand  e'  into  the  center  of  the  rope.  Repeat  this  operation 
with  the  other  ends  and  cut  them  off  so  that  the  ends  coming  together  in  the 
center  of  the  rope  will  butt  against  each  other  as  nearly  as  possible. 

Wear  of  Wire  Ropes. — The  deterioration  of  wire  ropes  may  be  either 
external  or  internal,  and  may  be  due  (1)  to  abrasion,  due  to  the  rubbing  of 
the  outside  surface  of  the  rope  against  other  objects,  or  to  the  internal  chafing 
of  the  wires  composing  the  strands  against  one  another;  (2)  to  injury  from 
overloading,  to  shock  due  to  sudden  starting  of  the  load,  or  to  repeated  bend- 
ings  about  too  sharp  angles  or  over  sheaves  or  rollers  of  too  small  a  diameter 
for  the  size  of  the  rope;  (3)  to  rust  or  corrosion  of  the  wiie  from  acid  waters,  or 
to  decay  of  the  hemp  cores. 

As  a  result  of  abrasion,  the  wires  in  a  rope  are  either  flattened  or  torn  apart. 
With  properly  designed  drums  and  head-frame  and  properly  placed  sheaves, 
a  hoisting  rope  is  but  slightly  abraded,  and  the  wear  is  due  chiefly  to  bending 
or  to  overloading.  A  haulage  rope  is  subjected  to  constant  abrasion  in  passing 
over  rollers  and  sheaves  and  from  dragging  along  the  bottom  and  sides  of  the 
haulage  ways  and  from  the  grips.  It  is  also  often  subject  to  severe  shocks  and 
abrasion  from  the  lashing  or  vibration  when  the  winding  engine  starts. 

The  wear  and  tear  on  a  rope  increases  as  its  velocity  is  increased;  hence, 
conditions  permitting,  it  is  better  to  increase  the  output  by  increasing  the 
load  within  allowable  limits  rather  than  by  increasing  the  velocity  of  the  rope. 

Inspection  of  Ropes. — The  life  of  a  hoisting  rope  depends  not  only  on  its 
quality,  but  also  on  the  conditions  under  which  it  is  used  and  on  the  care- 
fulness of  the  engineer  in  handling  the  load.  A  rope  should  be  inspected  often 
and  at  regular  intervals;  at  some  mines,  the  hoisting  ropes  are  inspected  every 
morning  before  lowering  the  men.  The  cage  is  slowly  lowered  and  then  raised, 
each  rope  being  carefully  examirTed  by  an  inspector  to  detect  any  broken  wires. 
Particular  attention  should  be  given  to  the  part  of  the  rope  where  it  is  attached 
to  the  socket  at  the  cage,  as  this  part  is  more  subject  to  corrosion  and  sharp 
bending  than  any  other.  When  the  core  fails  at  any  point  the  rope  should  be 
discarded  at  once  as  the  wires  are  likely  to  kink  and  break  internally  as  the 
rope  passes  over  the  sheave.  At  some  mines,  hoisting  ropes  are  discarded  at 
regular  intervals,  whether  they  show  wear  or  not.  Haulage  ropes  do  not 
require  as  frequent  examination  and  are  not  discarded  as  quickly  as  hoisting 
ropes,  as  much  less  in  the  way  of  life  and  property  is  dependent  on  them.  If 
a  new  piece  of  loose  hemp  rope  is  given  one  turn  around  the  haulage  rope  and 
each  end  held  firmly  while  the  rope  is  run  the  presence  of  loose  wire  ends  will 
be  shown. 

Lubrication  of  Wire  Ropes. — Mine  water  has  a  very  corrosive  action  on 
wire  ropes,  and  a  rope  will  soon  be  destroyed  unless  the  water  is  prevented 
from  coming  in  contact  with  the  metal.  For  this  reason,  black  oil  or  some 
lubricating  preparation  is  applied  to  the  rope,  but  any  lubricant  used  must 
be  free  from  acids  or  other  substances  that  will  corrode  the  wire. 

For  hoisting  ropes,  1  bu.  of  freshly  slaked  lime  to  1  bbl.  of  pine  or  coal 
tar  makes  a  good  lubricant;  with  pine  tar,  which  contains  no  acid,  tallow  may 
be  used  instead  of  lime.  Another  mixture  contains  tar,  summer  oil,  axle 
grease,  and  a  little  pulverized  mica,  mixed  to  such  a  consistency  that  it  will 
penetrate  thoroughly  between  the  wires  and  will  not  dry  or  strip  off.  The 
lubricant  should  not  be  thick  enough  to  render  difficult  the  thorough  inspection 
of  the  rope,  and  all  lubricants  of  this  nature  should  be  used  sparingly  after  the 
first  application,  as  the  rope  should  be  kept  clean  and  free  from  grit.  Graphite, 
is  also  used  for  the  purpose. 


258  WIRE  ROPES 

Lubricants  may  be  applied  by  running  the  engine  slowly  and  allowing  the 
rope  to  pass  through  a  bunch  of  waste  saturated  with  lubricant;  by  rubbing 
the  lubricant  into  the  rope  by  means  of  a  brush;  or  by  pouring  the  oil  into  the 
groove  of  the  sheave  as  the  rope  is  run  slowly  back  and  forth.  A  new  hoisting 
rope  should  be  passed  through  a  bath  of  hot  lubricant  and  thus  be  thoroughly. 

Haulage  ropes  are  not  usually  lubricated  as  thoroughly  as  hoisting  ropes 
on  account  of  the  grease  causing  slipping  of  grips  and  gathering  of  dirt  and 
dust,  but  they  can  be  treated  with  raw  linseed  oil  thickened  with  lamp-black 
boiled  with  an  equal  portion  of  pine  tar,  and  the  mixture  applied  while  hot. 
Ordinary  black  oil,  such  as  is  used  to  oil  mine  cars  and  hoisting  ropes,  can  be 
used  on  haulage  ropes  where  no  friction  grips  are  employed.  These  mixtures, 
if  fluid,  can  be  poured  on  the  rope  as  it  is  run  over  the  sheave,  or  applied 
from  a  leather  lined  box  filled  with  oil.  Patent  lubricants  known  as  cable 
shields  or  rope  fillers,  which  fill  the  interstices  between  the  strands,  are  often 
used  on  tail  and  main  ropes. 

General  Precautions. — Wire  rope  is  as  pliable  as  new  hemp  rope  of  the 
same  strength;  the  former  will  therefore  run  on  the  same  sized  sheaves  and 
pulleys  as  the  latter.  But  the  greater  the  diameter  of  the  sheaves,  pulleys, 
and  drums,  the  longer  wire  rope  will  last.  In  the  construction  of  machinery 
for  wire  rope,  it  will  be  found  good  economy  to  make  the  drums  and  sheaves 
as  large  as  possible. 

The  tables  of  wire-rope  manufacturers  give  proper  diameters  of  drum  or 
sheave  at  from  50  to  65  times  the  rope  diameter;  but  the  expression  should 
more  properly  be  the  minimum  admissible  diameter.  For  ordinary  ser- 
vice, by  using  sheaves  and  drums  from  75  to  100  times  the  diameter  of  the 
rope,  the  average  life  of  hoisting  ropes  will  be  materially  lengthened.  For 
rapid  hoisting,  during  which  abnormal  strains  are  most  likely  to  occur,  or 
where  a  low  factor  of  safety  is  employed,  a  sheave  diameter  of  150  times  that 
of  the  rope  is  to  be  recommended. 

Experience  has  demonstrated  that  the  wear  increases  with  the  speed;  it  is 
therefore  better  to  increase  the  load  than  the  speed.  Wire  rope  is  manufactured 
either  with  a  wire  or  a  hemp  center;  the  latter  is  more  pliable  than  the  former, 
and  will  wear  better  where  there  is  short  bending. 

Wire  rope  must  not  be  coiled  or  uncoiled  like  hemp  rope.  When  mounted  on 
a  reel,  the  reel  should  be  mounted  on  a  spindle  or  flat  turntable  to  pay  off 
the  rope.  When  shipped  in  a  small  coil,  without  reel,  the  coil  should  be  rolled 
over  the  ground  like  a  wheel,  and  the  rope  run  off  in  that  way.  All  untwisting  or 
kinking  must  be  avoided. 

A  rope  should  not  be  changed  from  a  large  drum  to  a  small  one,  for  it 
will  not  work  so  well,  neither  will  it  last  as  long.  This  is  also  true,  but  in  a 
lesser  degree,  of  ropes  changed  from  a  small  drum  to  a  large  one.  After  having 
been  used  for  some  time  on  a  drum,  the  rope  adapts  itself  to  that  diameter  and 
resents  a  change.  Rope  sheaves  should  be  made  to  fit  the  rope,  and  should 
be  filled  in  with  well-seasoned  blocks  of  oak  or  other  hardwood,  set  on  end; 
this  will  save  the  rope  and  increase  adhesion. 


CABLEWAYS  AND  TRAMWAYS 

Cableways. — A  suspension  cableway  is  a  hoisting  and  conveying  device 
using  a  suspended  cable  for  a  trackway.  There  are  two  types:  the  inclined,  or 
semi-gravity,  Fig.  1,  and  the  horizontal,  Fig.  2. 

The  inclined  cableway  consists  of  a  cable  inclined  20°  to  22°  to  the  horizontal, 
and  passing  over  a  cast-iron  saddle  B  on  top  of  a  tower  or  frame  A.  It  is 
anchored  by  logs  D  buried  about  5  ft.  underground,  or  from  iron  plugs  secured 
in  the  rock,  when  the  rock  is  near  the  surface.  The  trolley  carriage  G  runs  down 
the  incline  of  the  cableway  by  gravity  until  it  reaches  a  stop.  A  hoisting  rope 
E  operated  by  a  winding  drum  F  leads  over  a  sheave  pulley  e,  thence  to  a  pulley 
in  the  carriage  G,  thence  to  a  fall  block  M ,  upwards  again  to  a  second  pulley  in 
the  carriage,  and  downwards  again  to  the  fall  block.  Winding  in  the  rope 
hoists  the  fall  block  to  the  carriage,  the  carriage  remaining  at  the  lower  stop. 
When  the  fall  block  collides  with  the  carriage,  both  the  carriage  and  the  fall 
block  are  pulled  up  the  incline  cable,  and  when  the  carriage  arrives  at  the 
head-tower,  a  gate,  or  hook,  O  is  lowered  to  hold  it  in  place.  The  fall  block  is 
then  lowered  and  the  load  discharged.  The  engine  F  has  usually  a  10" X 12" 
double  cylinder  and  a  single  friction  drum  37  in.  in  diameter. 


WIRE  ROPES 


259 


260 


WIRE  ROPES 


An  endless  rope  H  takes  several  turns  around  the  sheave  J  to  prevent  it  from 
slipping,  and  both  ends  are  passed  over  sheaves  at  the  top  of  the  derrick,  one 
end  being  secured  to  the  front  of  the  carriage,  while  the  other  end  is  taken 
through  the  carriage  and  around  the  return  sheave  /  and  fastened  to  tne  rear 
end  of  the  carriage  G.  The  endless-rope  wheel  J  is  provided  with  a  band  brake, 
which,  when  applied,  holds  the  carriage  securely  at  any  point  on  the  cable. 

All  ropes  pass  through  the  supporting  trolleys  K,  which  are  connected  by  a 
chain  L.  These  trolleys  follow  the  carriage  by  gravity,  and  the  chain  may  or 
may  not  be  fast  to  the  carriage. 

Instead  of  chain-connected  trolleys,  patent  button-stop,  fall-rope  carriers, 
which  are  lighter,  may  be  used.  These  are  spaced  along  an  auxiliary  rope  on 
which  buttons  are  screwed.  The  carriers  are  picked  up  by  a  horn  on  the  front 
of  the  carriage.  These  are  said  to  be  cheaper  for  operation  than  the  chain 
trolleys. 

The  length  of  the  span  for  inclined  cableways  varies  from  200  to  1,200  ft. 
The  main  rope  is  from  1^  to  2  J  in.  in  diameter,  the  hoisting  rope  from  f  to  f  in., 
and  the  endless  rope  &  and  £  in.  The  rope  mostly  used  is  6  strands,  19  wires  to 
the  strand,  crucible  cast  steel.  The  hoisting  rope  lasts  from  1  to  2  yr.,  and  the 
main  cable  from  5  to  10  yr.  These  cableways  are  widely  used  about  the  slate 
quarries  in  Eastern  Pennsylvania,  where  the  operating  expense  for  each  cable, 
where  two  or  more  are  connected  with  one  boiler,  is  about  $5  per  da.  of  10  hr. ; 
this  includes  the  engineer,  steam,  and  maintenance  of  the  cableway. 

The  horizontal  cableway  requires  a  double  friction  drum  and  reversible 
link-motion  engine.  It  may  be  operated  at  any  inclination  of  the  carrying 
cable  and  either  from  the  high  or  low  point  of  the  support,  though,  if  possi- 
ble, it  should  be  from  the  higher  end.  The  endless,  or  traction,  rope,  is  attached 
to  one  of  the  drums  of  the  engine  so  that  the  engineer  has  complete  control  of 
the  carriage;  hence,  because  of  its  greater  applicability,  this  system  is  supplant- 
ing the  inclined,  although  the  inclined  costs  one-fourth  less  for  installation. 
The  method  of  operation  is  similar  to  the  inclined.  The  amount  of  rope 
required  is  the  same  in  each  system.  A  horizontal  cableway  of  the  Hamilton 
Coal  Co.,  near  Tarentum,  Pennsylvania,  has  a  span  of  2,200  ft.  The  stationary 
rope  is  2,500  ft.  long  and  2  J  in.  in  diameter.  The  hoisting  rope  is  4,500  ft.  long 
and  f  in.  in  diameter.  The  head-tower  is  80  ft.  high,  the  tail-tower  is  100  ft. 
and  the  rope  deflects  80  ft.  The  skip  used  holds  3  T.  of  coal  and  makes  10  trips 
per  hour.  Five  men  operate  the  plant  and  it  takes  2  T.  of  coal  for  the  engine. 
Based  on  a  capacity  of  100  T.  per  da.,  the  cost  of  carrying  the  coal  is  13c.  per  T. 
For  a  cableway  of  average  length,  1,000-1,500  ft.,  the  cost  of  operation  should 
not  be  one-haft  the  above  cost.  A  cableway,  2,140  ft.  long  was  used  in  con- 
structing the  dam  at  the  power  plant  at  Glens  Falls,  New  York. 

One  or  both  towers  of  a  cableway  may  be  mounted  on  wheels  capable  of 
moving  on  a  track  at  right  angles  to  the  cable  and  the  cableway  then  made 
to  cover  a  wide  territory. 


WIRE-ROPE  TRAMWAYS 

Single  Tramways. — A  tramway,  in  America,  is  a  cableway  of  the  horizontal 
type  consisting  of  a  number  of  spans.  In  England,  the  term  cableway  includes 
tramways. 


FIG.  1 

Single  wire-rope  tramways  have  a  single  moving  rope,  which  serves  ti 
support  and  advance  the  load  at  one  and  the  same  time,  Fig.  1.  This  rop 
passes  over  suitable  sheaves  at  the  intermediate  supports,  and  the  load  i 
carried  in  buckets  suspended  from  it  by  gooseneck  or  straight  hangers.  Th 
hangers  are  usually  attached  to  the  cable  by  means  of  a  clip,  which  is  eithe 


WIRE  ROPES 


261 


inserted  in  the  center  of  the  cable  or  strapped  to  it.  The  carriers  are  often 
loaded  and  unloaded  while  in  motion,  the  loading  being  accomplished  by 
a  traveling  mechanical  hopper  and  the  unloading  by  a  drop  bottom  to  the 
bucket.  If  the  line  is  level,  or  the  grade  light,  the  hangers  are  provided 
with  box  heads  filled  with  wood  or  leather  and  rubber,  which  rest  on  the 
rope;  the  rubber  or  wood  providing  sufficient  friction  to  prevent  the  hangers' 
slipping.  With  this  system,  long  spans  are  evidently  out  of  the  question, 
because  with  a  long  span  the  angle  of  the  rope  in  the  vertical  plane,  at  the 
supports,  becomes  so  great  that  the  friction  will  not  hold  the  box  head.  For  all 
practical  purposes,  grades  exceeding  1  :  4  are  to  be  avoided;  and  for  steeper 
grades,  to  prevent  slipping,  a  clamp  or  a  clip  inserted  in  the  rope  is  used  to 
fasten  the  hanger  to  the  rope. 

The  single-moving  rope  tramways  carry  loads  not  exceeding  200  Ib.  The 
speed  of  the  rope  for  the  variety  in  which  the  hangers  are  fastened  to  the  rope 
may  be  as  high  as  450  ft.  per  min.,  and  for  one  in  which  the  hanger  is  loose, 
200  ft.  per  min.  The  single  moving-rope  tramway  has  a  capacity  up  to  200  T. 
per  da.,  and  may  be  built,  say,  H  to  2  mi.  long. 

Double  Tramways. — The  more  satisfactory  and  substantial  kind  of  wire- 
rope  tramway  has  one  or  more  fixed  ropes,  which  constitute  the  permanent 
way,  and  an  endless  traction  rope.  The  loaded  carrier  travels  outwards  on 
one  fixed  cable  and  returns  by  a  parallel  one  suspended  from  the  opposite 
side  of  the  same  supports.  The  terminals  have  suitable  appliances  for  load- 
ing and  unloading  the  buckets,  either  by  hand  or  automatically. 

The  intermediate  supports  are  built  of  wood  or  steel  framing,  with  sad- 
.dles  of  cast  iron  a,  Fig.  2  in  which  the  fixed  cables  b  rest.  The  traction  rope  c 
is  supported  (in  the  absence  of  a  bucket)  by  the  rollers  d,  set  conveniently  on  the 
supports.  The  load  is  carried  in  buckets  e,  or  other  contrivances  suitable  for 
the  purpose,  which  are  suspended  from  a  trolly  /,  which  runs  on  the  fixed 
cables,  the  wheels  of  which  are  large  enough  to  pass  over  the  rope  couplings,  and 


also  to  clear  the  saddles.  Grips  g  attach  the  carriers  to  the  traction  rope. 
These  grips  may  be  operated  by  hand  or  automatically. 

This  kind  of  tramway  is  capable  of  carrying  individual  loads  up  to  1,400 
or  1,500  Ib.,  not  including  the  weights  of  the  bucket  and  hanger  itself.  The 
speed  of  traction  rope  may  be  from  150  to  350  ft.  per  min.  The  capacity  is 
from  200  to  1,000  T.  per  da.  of  10  hr.  These  figures  represent  good,  safe, 
practice,  but  they  are  not,  of  course,  inflexible. 

The  maximum  length  of  line  that  may  be  built  in  one  section  varies  largely 
with  conditions  of  load,  spacing  of  supports,  contour  of  ground,  etc.  Wire-rope 
tramways  work  under  great  difficulties,  and  probably  2?  to  4  mi.  is  the  econom- 
ical limit.  This  has  been  exceeded,  but  for  a  much  greater  distance  the  friction 
becomes  too  great  for  economical  working  of  the  traction  rope.  This  does  not, 
however,  limit  the  length  of  tramway  which  may  be  built,  as  the  power  station 
may  be  located  at  a  convenient  intermediate  point,  dividing  the  line  into  sec- 
tions. Several  intermediate  power  stations  may  be  used,  and  the  length  of  the 
line  greatly  increased  above  the  limit  given.  A  tramway  at  Grand  Encamp- 
ment, Wyoming,  is  16  mi.  long  and  carries  40  T.  of  ore  each  hour. 


262  GLOSSARY  OF  ROPE  TERMS 


GLOSSARY  OF  ROPE  TERMS 

Annealed  Wire  Rope.— -A.  wire  rope  made  from  wires  that  have  been  softened 
by  annealing  and  the  tensile  strength  thereby  lowered. 

Bending  Stress— The  stress  produced  in  the  outer  fibers  of  a  rope  by  bend- 
ing over  a  sheave  or  drum. 

Breaking  Strain,  Breaking  Strength,  Breaking  Stress. — The  least  load  that 
will  break  a  rope.  These  terms  are  used  indiscriminately  to  mean  the  load 
that  will  break  a  rope.  The  stress  on  a  rope  at  the  moment  of  breaking  is 
the  breaking  stress,  and  the  strain  or  deformation  produced  in  the  material  by 
this  stress  is  the  breaking  strain. 

Bright  Rope. — 'Rope  of  any  construction,  whose  wires  have  not  been  gal- 
vanized, tinned,  or  otherwise  coated. 

Cable-Laid  Rope. — 'Wire  cables  made  of  several  ropes  twisted  t9gether,  each 
rope  being  composed  of  strands  twisted  together  without  limitation  as  to  the 
number  of  strands  or  direction  of  twist.  A  fiber  cable-laid  rope  is  a  rope  having 
three  strands  of  hawser-laid  rope,  twisted  right-handed. 

Cable.— Same  as  cable-laid  rope;  a  fiber  cable  consists  of  three  hawsers  laid 
up  left-handed. 

Cast  Steel. — Steel  that  has  been  melted,  cast  into  ingots,  and  rolled  out  into 
bars. 

Clamp. — A  device  for  holding  two  pieces  or  parts  of  rope  together  by  pressure. 

Clip. — A  device  similar  to  a  clamp  but  smaller  and  for  the  same  purpose. 

Coir. — Cocoanut-husk  fiber. 

Compound. — A  lubricant  applied  to  the  inside  and  outside  of  ropes  pre- 
venting corrosion  and  lessening  abrasion  of  the  rope  when  in  contact  with  hard 
surfaces. 

Core. — The  central  part  of  a  rope  forming  a  cushion  for  the  strands.  In 
wire  ropes  it  is  sometimes  made  of  wire,  but  usually  it  is  of  hemp,  jute,  or  some 
like  material. 

Coupling. — A  device  for  joining  two  rope  ends  without  splicing. 

Crucible  Steel. — A  fine  quality  of  steel  made  by  the  crucible  process. 

Drum. — The  part  of  a  hoisting  engine  on  which  the  rope  is  wound. 

Elastic  Limit. — That  point  at  which  the  deformations  in  the  material  cease 
to  be  proportional  to  the  stresses. 

Elevator  Rope. — A  rope  use  to  operate  an  elevator. 

Endless  Rope. — A  rope  that  moves  in  one  direction,  one  part  of  which 
carries  loaded  cars  from  a  mine  at  the  same  time  that  another  part  brings  the 
empties  into  the  mine. 

Fiber. — A  single  thread-like  filament. 

Flat  Rope. — A  rope  in  which  the  strands  are  woven  or  sewed  together  to 
form  a  flat,  braid-like  rope. 

Flattened-Strand  Rope. — A  wire  rope  whose  strands  are  flattened  or  oval, 
and  therefore  presents  an  increased  wearing  surface  over  that  of  the  ordinary 
round-strand  rope. 

Flattened-Strand  Triangular  Rope. — A  wire  rope  of  the  flattened-strand  con- 
struction in  which  the  strands  are  triangular  in  shape. 

Fleet. — Movement  of  a  rope  sidewise  when  winding  on  a  drum. 

Fleet  Wheel. — A  grooved  wheel  or  sheave  that  serves  as  a  drum  and  about 
which  one  or  more  coils  of  a  haulage  rope  pass. 

Galvanized  Rope. — Rope  made  of  wires  that  have  been  galvanized  or  coated 
with  zinc  to  protect  them  from  cprrosion. 

Grip  Wheel. — A  wheel,  the  periphery  of  which  is  fitted  with  a  series  of  toggle- 
jointed,  cast-steel  jaws  that  grip  the  rope  automatically. 

Guy. — A  strand  or  rope  used  to  support  a  pole,  structure,  derrick,  or  chim- 
ney, etc. 

Haulage  Rope. — A  rope  used  for  haulage  purposes. 

Hawser. — 'Any  wire  rope  used  for  towing  on  lake  or  sea.  A  fiber  hawser 
consists  of  three  strands  laid  up  right-handed. 

Hawser-Laid  Rope  has  three  strands  of  yarn  twisted  left-handed,  the  yarns 
being  laid  up  right-handed.  Synonymous  with  cable-laid  rope  as  applied  to 
wire  ropes. 

Hawser  Wire  Rope. — Galvanized  rope  of  iron  or  steel,  usually  composed  of 
6  strands,  12  wires  each,  principally  used  in  marine  work  for  towing  purposes. 

Hemp. — A  tough,  strong  fiber  obtained  from  the  hemp  plant. 


GLOSSARY  OF  ROPE  TERMS  263 

Hoisting  Rope. — A  rope  composed  of  a  sufficient  number  of  wires  and 
strands  to  insure  flexibility.  Such  ropes  are  used  in  shafts,  elevators,  quarries, 
etc. 

Idler. — A  sheave  or  pulley  running  19086  on  a  shaft  to  guide  or  support  a  rope. 

Jute. — A  fiber  obtained  from  the  inner  bark  of  two  Asiatic  herbs:  Cor- 
chorus  capsularis  and  C.  olitorius. 

Lang  Lay  Rope. — A  rope  in  which  the  wires  in  each  strand  are  twisted  in 
the  same  direction  as  the  strands  in  the  rope. 

Lay. — The  direction,  or  length,  of  twist  of  the  wires  and  strands  in  a  rope. 

Live  Load. — A  load  that  is  variable  in  distinction  from  a  constant  load. 

Load  Stress. — The  stress  produced  by  the  load. 

Locked-Wire  Rope. — A  rope  with  a  smooth  cylindrical  surface,  the  outer 
wires  of  which  are  drawn  to  such  shape  that  each  one  interlocks  with  the 
other  and  the  wires  are  disposed  in  concentric  layers  about  a  wire  core  instead 
of  in  strands.  Particularly  adapted  for  haulage  and  rope-transmission  purposes. 

Manila. — The  fiber  of  Musa  textilis;  Manila  hemp. 

Modulus  of  Elasticity. — The  ratio  between  the  amount  of  extension  or 
compression  of  a  material  and  the  load  producing  this  same  extension 
or  compression. 

Plow  Steel. — A  select  grade  of  steel  of  high  tensile  strength;  first  used  in 
rope  for  plowing  fields. 

Proper  Working  Load. — -The  maximum  load  that  a  rope  should  be  permitted 
to  support  under  working  conditions.  (See  working  load.) 

Regular-Lay  Rope. — A  rope  in  which  the  wires  in  each  strand  are  twisted  in 
opposite  direction  to  the  strands  in  the  rope. 

Round-Strand  Rope. — A  rope  made  of  round  twisted  strands. 

Running  Rope. — A  flexible  rope  that  will  pass  through  blocks  and  used  for 
hoisting  on  shipboard.  The  term  is  also  often  used  for  any  moving  rope. 

Sheave. — A  wheel  or  pulley  around  or  over  which  a  rope  passes. 

Shroud  Laid,  or  Four-Strand,  Rope  has  four  strands  laid  around  a  core. 

Sisal. — A  nemp;  the  fiber  of  the  Agave  Sisalona. 

Socket. — A  device  fastened  to  the  end  of  a  rope  by  means  of  which  the  rope 
may  be  attached  to  its  load;  the  socket  may  be  opened  or  closed. 

Splice. — 'The  joining  of  two  ends  of  rope  by  interweaving  the  strands. 

Step  Socket. — A  special  form  of  socket  for  use  on  locked-wire  rope. 

Stirrup. — An  adjustable  bale  of  a  socket. 

Stone  Wire. — -Wire  smaller  than  No.  14  put  up  in  12-lb.  coils,  which  are 
about  8  in.  inside  diameter. 

Strand. — A  varying  number  of  wires  or  fibers  twisted  together;  the  strands 
in  turn  are  twisted  together,  forming  a  rope. 

Stress. — A  force  or  combination  of  forces  tending  to  change  the  shape  of  a 
body. 

Strain. — A  change  of  shape  produced  in  a  body.  (Stress  and  strain  are 
often  used  incorrectly  as  synonymous  terms.) 

Surging. — The  flapping  of  a  moving  rope. 

Swedish  Iron. — A  soft  and  comparatively  pure  iron. 

Switch  Rope. — A  short  length  of  rope  fitted  with  a  hook  on  one  end  and  a 
link  on  the  other,  used  for  the  switching  of  freight  cars. 

Tail-Rope. — (1)  The  rope  that  is  used  to  draw  the  empties  back  into  a 
mine  in  a  tail-rope  haulage  system.  (2)  A  rope  attached  beneath  the  cage 
when  the  cages  are  hoisted  in  balance. 

Taper  Rope. — A  rope  that  has  a  gradually  diminishing  diameter  from  the 
upper  to  the  lower  end.  The  diameter  of  the  rope  is  decreased  by  dropping 
one  wire  at  a  time  at  regular  intervals.  Both  round  and  flat  ropes  may  be 
made  tapered,  and  such  ropes  are  intended  for  deep-shaft  hoisting  with  a  view 
to  proportioning  the  diameter  of  the  rope  to  the  load  to  be  sustained  at  different 
depths. 

Tensile  Strength. — The  stress  required  to  break  a  rope  by  pulling  it  in  two. 

Thimble. — An  oval  iron  ring  around  wnich  a  rope  end  is  bent  and  fastened 
to  form  an  eye. 

Titter  Rope. — A  very  flexible  wire  rope  composed  of  six  small  ropes,  usually 
of  seven-wire  strands  laid  about  a  hemp  core. 

Tinned  Rope. — Rope  made  of  wires  that  have  been  coated  with  tin  to  protect 
them  from  corrosion. 

Torsion. — The  process  of  twisting  a  wire,  thereby  showing  its  ductility. 

Traction  Rope. — A  rope  used  for  transmitting  the  power  in  a  wire-rope 
tramway  and  to  which  the  buckets  are  attached. 

Transmission  Rope. — A  rope  used  for  transmitting  power. 


264  POWER  TRANSMISSION 

Traveler. — A  truck  rolling  along  a  suspended  rope  for  supporting  a  load  to 
be  transported. 

Turnbuckle. — A  form  of  coupling  so  threaded  or  swiveled  that  by  turning  it 
the  tension  of  a  rope  or  rod  may  be  regulated. 

Ultimate  Tensile  Strength. — Same  as  tensile  strength. 

Universal  Lay. — Another  term  for  lang  lay. 

Whipping.— The  flopping  of  a  moving  rope. 

Wire  Gauge. — Standard  sizes  or  diameters  for  wire. 

Wire  Rope. — A  rope  whose  strands  are  made  of  wires,  twisted  or  woven 
together. 

Working  Load. — The  maximum  load  that  a  rope  can  carry  under  the  con- 
ditions of  working  without  danger  of  straining.  (Same  as  proper  working  load.) 

Wrought  Iron.— A  comparatively  pure  and  malleable  iron. 

Farw.— Twisted  fiber  of  which  rope  strands  are  made. 

POWER  TRANSMISSION 


TRANSMISSION  BY  WIRE  ROPES 

The  term  transmission,  as  here  used,  applies  simply  to  the  modification  of  belt 
driving,  using  grooved  wheels  or  sheaves  at  each  end  of  the  line.  The  power 
is  applied  to  one  sheave  and  taken  off  from  the  other.  The  friction  between 
rope  and  sheaves  depends  directly  on  the  weight  and  tension  of  the  rope  and 
on  the  nature  of  the  surfaces  in  contact.  This  pressure  is  better  obtained  by 
using  a  large,  heavy  rope  at  a  low  tension  than  by  using  a  smaller  rope  at  a  high 
tension.  The  deflection,  or  sag,  of  the  rope,  between  the  sheaves,  is  the  same 
for  both  upper  and  lower  parts  of  the  rope  when  the  transmission  is  not  run- 
ning and  should  be,  according  to  John  A.  Roebling's  Sons  Co.-,  equal  to  about 
3*5  of  the  span.  The  deflection  may  be  calculated  by  the  formula  from  the 
Trenton  Iron  Co.:  .  wsz 

h=~8T' 
in  which  h  =  deflection,  in  feet ; 

w  =  weight  of  rope  per  foot,  in  pounds; 
s  =  span,  in  feet; 
t  —  tension,  in  pounds. 

When  driving  from  the  under  side,  this  part  of  the  rope  will  be  tightened 
and  its  deflection  decreased,  while  the  upper  part  of  the  rope  becomes  slackened 
and  its  deflection  increased.  Under  proper  conditions,  the  deflection  of  the 
lower  rope  should  be  about  ^,  and  that  of  the  upper  about  ^  of  the  span. 
The  difference  in  the  tensions  of  the  two  parts  of  the  rope  is  the  effective  pull 
of  the  driving  sheaves,  enabling  power  to  be  transmitted. 

Transmission  ropes  are  subject  to  three  stresses:  (1)  The  direct  tension, 
due  to  the  power  transmitted,  plus  the  friction  and  weight  of  the  rope;  (2)  the 
bending  stress,  due  to  the  bending  of  the  rope  around  the  sheaves;  (3)  the 
centrifugal  tension,  due  to  the  centrifugal  force  in  the  rapidly  running  rope. 
The  following  data  on  stresses  in  transmission  ropes  are  given  by  Mr.  Wm. 
Hewitt,  of  the  Trenton  Iron  Co.:  When  transmitting  power  by  wire  rope, 
working  tension  should  not  exceed  the  difference  between  the  maximum  safe 
stress  and  the  bending  stress.  It  may  be  greater;  therefore,  as  the  bending 
stress  is  less,  but  to  avoid  slipping,  a  certain  ratio  must  exist  between  the 
tensions  in  taut  and  slack  portions  of  the  rope  when  running,  which  is 
determined  by  the  formula  T  =  Se^w; 

in  which  T  =  tension  in  taut  porti9n  of  rope; 
5  =  tension  in  slack  portion; 

e  =  base  of  Naperian  systen  of  logarithms  =  2.7182818; 
n  =  number  of  half  laps  of  rope  about  sheaves  or  drums  at  either  end 

of  line; 
*  =  3.1416; 
/= coefficient  of  friction  depending  on  kind  of  filling  in  grooves  of 

sheaves,  or  character  of  material  on  which  rope  tracks. 
The  useful  effort  of  transmitting  force  is  the  difference  between  the  tension 
of  the  taut  and  slack  portions  of  the  rope,  T  —  S  =  Se(f»v—  1),  and  to  obtain 
this,  the  initial  tension,  or  tension  when  the  rope  is  at  rest,  must  be  one-half 
the  sum  of  the  two  tensions. 


POWER  TRANSMISSION 


265 


The  following  are  some  of  the  values. of  /: 

Dry  rope  on  a  grooved  iron  drum 120 

Wet  rope  on  a  grooved  iron  drum 085 

Greasy  rope  on  a  grooved  iron  drum 070 

Dry  rope  on  wood-filled  sheaves 235 

Wet  rope  on  wood-filled  sheaves 170 

Greasy  rope  on  wood-filled  sheaves 140 

Dry  rope  on  rubber  and  leather  filling 495 

Wet  rope  on  rubber  and  leather  filling 400 

Greasy  rope  on  rubber  and  leather  filling 205 

The  values  of  the  coefficients  corresponding  to  the  foregoing  values  of  /, 
for  one  up  to  six  half  laps  of  the  rope,  are  given  in  the  accompanying  table. 

VALUE  OF  COEFFICIENTS 


n  =  Number  of  Half  Laps  About  Sheaves  or  Drums  at  Either 
End  of  Line 


/= 

1 

2 

3 

4 

5 

6 

Values  of  «/»' 

.070 

1.246 

1.552 

1.934 

2.410 

3.003 

3.741 

.085 

1.306 

1.706 

2.228 

2.910 

3.801 

4.964 

.100 

1.369 

1.875 

2.566 

3.514 

4.810 

6.586 

.120 

1.458 

2.125 

3.099 

4.518 

6.586 

9.602 

.130 

1.504 

2.263 

3.405 

5.122 

7.706 

11.593 

.140 

1.552 

2.410 

3.741 

5.808 

9.017 

13.998 

.150 

1.602 

2.566 

4.111 

6.586 

10.551 

16.902 

.170 

1.706 

2.910 

4.964 

8.467 

14.445 

24.641 

.200 

1.875 

3.514 

6.586 

12.346 

23.140 

43.376 

.205 

1.904 

3.626 

6.904 

13.146 

25.031 

47.663 

.235 

2.092 

4.378 

9.160 

19.166 

40.100 

83.902 

.250 

2.193 

4.810 

10.551 

23.140 

50.637 

.111.318 

.265 

2.299 

5.286 

12.153 

27.941 

64.239 

147.693 

.300 

2.566 

6.586 

16.902 

43.376 

111.318 

285.680 

.350 

3.001 

9.017 

27.077 

81.307 

244.152 

733.145 

.400 

3.514 

12.346 

43.376 

152.405 

535.488 

1,849.140 

.410 

3.626 

13.146 

47.663 

172.814 

626.577 

2,271.775 

.450 

4.111 

16.902 

69.487 

285.680 

1,174.480 

4,828.510 

.495 

4.716 

22.425 

106.194 

502.881 

2,381.400 

.500 

4.810 

23.140 

111.318 

535.488 

2,575.940 

.  Values  of 


.070 

9.130 

4.623 

3.141 

2.418 

1.999 

1.729 

.085 

7.536 

3.833 

2.629 

2.047 

1.714 

1.505 

.100 

6.420 

3.287 

2.280 

1.795 

1.525 

1.358 

.120 

5.345 

2.777 

1.953 

1.570 

1.358 

1.232 

.130 

4.968 

2.584 

1.832 

1.485 

1.298 

1.189 

.140 

4.623 

2.418 

1.729 

1.416 

1.249 

1.154 

.150 

4.322 

2.280 

1.643 

1.358 

1.209 

1.126 

.170 

3.833 

2.047 

1.505 

1.268 

1.149 

1.085 

.200 

3.287 

1.795 

1.358 

1.176 

1.090 

1.047 

.205 

3.212 

1.762 

1.338 

1.165 

1.083 

1.043 

.235 

2.831 

1.592 

1.245 

1.110 

1.051 

1.024 

.250 

2.676 

1.525 

1.209 

1.090 

1.040 

1.018 

.265 

2.539 

1.467 

1.179 

1.072 

1.032 

1.014 

.300 

2.280 

1.358 

1.126 

1.047 

1.018 

1.007 

.350 

2.000 

1.249 

1.077 

1.025 

1.008 

1.003 

.400 

1.795 

1.176 

1.047 

1.013 

1.004 

1.001 

.410 

1.765 

1.164 

1.043 

1.012 

1.003 

1.001 

.450 

1.643 

1.126 

1.029 

1.007 

1.002 

1.000 

.495 

1.538 

1.093 

1.019 

1.004 

1.001 

1.000 

.500 

1.525 

1.090 

1.018 

1.004 

1.001 

1.000 

266 


POWER  TRANSMISSION 


For  a  given  diameter  of  sheave,  and  a  variable  diameter  of  wire,  a  ratio 
exists  between  these  diameters  corresponding  to  a  maximum  working  tension. 
This  ratio  results,  approximately,  in  a  working  tension  of  one-third  and  a 
bending  stress  of  two-thirds  of  the  maximum  safe  tension,  which  is  from  one- 
third  to  two-fifths  of  the  ultimate  stress,  and  practically  determines  the  mini- 
mum diameter  of  sheave  for  any  rope.  The  ratio  for  any  size  of  wire  varies 
slightly,  according  to  the  number  of  wires  composing  the  rope,  and  in  terms 
of  rope  diameter  is,  Steel  Iron 

For    7-wire  rope 79.6  160.5 

For  12-wire  rope 59.3  120.0 

For  19-wire  rope 47.2  95.8 

from  which  the  following  table  is  derived. 

MINIMUM  DIAMETERS  OF  SHEAVES 


Steel  Rope 

Iron  Rope 

Diameter 
of  Rope 

7-Wire 

12-Wire 

19-Wire 

7-Wire 

12-Wire 

19-Wire 

Inch 

Diameter  of  Sheaves,  in  Inches 

! 

20 

15 

12 

40 

30 

24 

JL 

25 

19 

15 

50 

38 

30 

I 

30 

22 

18 

60 

45 

36 

A 

35 

26 

21 

70 

53 

42 

i 

40 

30 

24 

80 

60 

48 

45 

33 

27 

90 

68 

54 

50 

37 

30 

100 

75 

60 

55 

41 

32 

110 

83 

66 

60 

44 

35 

120 

90 

72 

;  : 

70 

52 

41 

140 

105 

84 

1 

80 

59 

47 

160 

120 

96 

Sheaves.  —  To  decrease  the  bending  stresses,  the  sheaves  for  wire-rope 
transmissions  are  generally  of  as  large  diameter  as  is  practicable  to  give  the 
required  speed  to  the  rope.  Large  sheaves  are  also  advantageous  because 
with  them  the  rope  is  run  at  a  high  velocity  allowing  of  a  lower  tension,  and 
permitting  a  rope  of  smaller  diameter  to  be  used  than  would  be  possible  with 
smaller  sheaves,  provided,  of  course,  that  the  span  is  of  sufficient  length  to 
give  the  necessary  weight. 

Sheaves  are  generally  made  of  cast  iron  when  not  exceeding  12  ft.  in  diam- 
eter; when  larger  than  this,  they  are  usually  built  up  with  wrought-iron  arms. 
Sheaves,  upon  which  the  rope  is  to  make  but  a  single  half-turn,  are  made 
with  V-shaped  grooves  in  their  circumference.  The  bottom  part  of  the  groove 
is  widened  to  receive  the  filling,  which  consists  of  some  substance  to  give  a 
bed  for  the  rope  to  run  on  and  protect  it  from  wear,  and  to  increase  the  friction 
so  that  the  rope  will  not  slip.  This  filling  is  made  of  blocks  of  wood,  rubber, 
leather,  or  other  material.  Rubber  and  leather  have  been  used  separately,  but 
blocks  of  rubber  separated  by  pieces  of  leather  have  been  found  to  give  the 
best  results. 

Power  Transmitted.—  The  horsepower  transmitted  is  equal  to  the  resistance 
overcome  (the  effective  pull),  in  pounds,  multiplied  by  the  speed  of  the  rope, 
in  feet  per  minute,  and  divided  by  33,000  that  is  (formula  from  John  A.  Roeb- 
ling  s  Sons  Co.),  TV 


in  which  H^hprsepower  transmitted; 

T  =  difference  in  tension  between  driving  and  driven  sides  of  rope; 

V  =  speed  of  rope,  in  feet  per  minute. 

When  applying  this  formula,  V  is  either  given  or  assumed.  T  is  equal  to 
the  weight  of  the  rope  suspended  between  the  sheaves  multiplied  by  3  (for  the 
proportion  of  deflection  stated). 


POWER  TRANSMISSION 


267 


To  transmit  a  given  horsepower,  the  speed  of  the  rope  may  be  increased 
and  the  tension  (effective  pull)  correspondingly  decreased,  and  a  smaller  rope 
may  be  used  provided  other  considerations  will  allow  it. 

For  determining  the  horsepower  that  can  be  transmitted  over  a  given 
transmission,  the  following  formula  is  given  by  the  Trenton  Iron  Co.: 

H  =  (cd*-. 000006  (W+g'+g")]s 
in  which  H  =  horsepower  that  can  be  transmitted; 

c  =  constant,  depending  on  material  of  rope,  falling  in  grooves  of 
sheaves,  and  number  of  half  laps  about  sheaves  or  drums  at 
either  end  of  line; 
d  =  diameter  of  rope,  in  inches; 
W  =  weight  of  rope,  in  pounds; 
g'  =  weight  of  terminal  sheaves  and  shafts; 
g"  =  weight  of  intermediate  sheaves  and  shafts. 
The  accompanying  table  gives  the  value  of  c  for  ropes  on  different  materials. 

TABLE  OF  CONSTANTS  FOR  ROPES  ON  DIFFERENT  MATERIALS 


c  =  for 
Steel  Rope  on 

Number  of  Half  Laps  About  Sheaves  or  Drums  at 
Either  End  of  Line 

1 

2 

3 

4 

5 

6 

Value  of  c 

Iron 

5.61 

6.70 
9.29 

8.81 
9.93 
11.95 

10.62 
11.51 
12.70 

11.65 
12.26 
12.91 

12.16 
12.66 
12.97 

12.56 
12.83 
13.00 

Wood  

Rubber  and  leather 

The  values  of  c  for  iron  rope  are  one-half  of  those  given.  It  is  evident  from 
these  figures  that  when  more  than  three  laps  are  made  it  is  immaterial  what 
the  surface  is  on  which  the  rope  tracks,  as  far  as  frictional  adhesion  is  concerned. 

From  the  foregoing  formula,  assuming  the  sheaves  to  be  of  equal  diameter, 
and  of  a  size  not  less  than  the  minimum  diameter  given  in  the  table,  it  is  pos- 
sible to  find  the  horsepower  that  may  be  transmitted  by  a  steel  rope,  as  is  shown 
in  the  accompanying  table. 

HORSEPOWER  THAT  MAY  BE  TRANSMITTED  BY  A  STEEL  ROPE 
MAKING  A  SINGLE  LAP  ON  WOOD-FILLED  SHEAVES 


Velocity  of  Rope,  in  Feet  per  Second 


Diameter 

of  Rope 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

Inch 

Horsepower  That  May  Be  Transmitted 

1 

4 
7 
10 

8 
13 
19 

13 
20 

28 

17 
26 
38 

21 
33 

47 

25 

40 
56 

28 
44 
64 

32 
51 
73 

37 
57 
80 

40 
62 
89 

A 

13 

26 

38 

51 

63 

75 

88 

99 

109 

121 

|- 

17 

34 

51 

67 

83 

99 

115 

130 

144 

159 

22 

43 

65 

86 

106 

128 

147 

167 

184 

203 

? 

27 

53 

79 

104 

130 

155 

179 

203 

225 

247 

If 

32 

63 

95 

126 

157 

186 

217 

245 

a. 

38 

76 

103 

150 

186 

223 

I 

52 

104 

156 

206 

1 

68 

135 

202 

268  POWER  TRANSMISSION 

The  horsepower  that  may  be  transmitted  by  iron  ropes  is  one-half  of  the 
above. 

The  table  gives  the  maximum  amount  of  power  capable  of  being  trans- 
mitted under  the  conditions  stated,  so  that  when  using  wood-lined  sheaves, 
it  is  well  to  make  some  allowance  for  the  stretching  of  the  rope,  and  to  advocate 
somewhat  heavier  equipments  than  the  table  would  give;  that  is,  if  it  is 
desired  to  transmit  20  H.  P.,  for  instance,  to  put  in  a  plant  that  would  transmit 
25  to  30  H.P.,  thus  avoiding  the  necessity  of  having  to  take  up  a  comparatively 
small  amount  of  stretch;  On  rubber  and  leather  filling,  however,  the  amount 
of  power  capable  of  being  transmitted  is  considerably  greater  than  on  wood,  so 
that  this  filling  is  generally  used;  and  in  this  case  no  allowance  need  be  made 
for  stretch,  as  such  sheaves  will  likely  transmit  the  power  given  by  the  table, 
under  all  possible  deflections  of  the  rope. 

The  transmission  of  more  than  250  H.  P.  is  impracticable  with  filled  sheaves, 
because  the  tension  is  so  great  that  the  filling  will  quickly  cut  out,  and  the 
frictional  adhesion  on  a  metallic  surface  is  insufficient  where  the  rope  makes  but 
a  single  lap,  or  a  half  lap  at  either  end  of  the  line. 


TRANSMISSION  BY  HEMP  ROPE 

There  is  a  growing  tendency  toward  the  substitution  of  hemp  and  cotton 
ropes  for  belting  and  line  shafting  as  a  means  of  transmitting  power  in  large 
factories  and  shops.  The  advantages  claimed  for  the  rope-driving  system  are: 
(1)  Economy;  for  a  rope  system  is  cheaper  to  install  than  either  leather 
belting  or  shafting.  (2)  In  the  rope  system,  there  is  less  loss  of  power  by 
slipping.  (3)  Flexibility;  that  is,  the  ease  with  which  the  power  is  trans- 
mitted to  any  distance  and  in  any  direction. 

In  the  United  States,  a  single  rope  is  carried  round  the  pulley  as  many 
times  as  is  necessary  to  produce  the  required  power,  and  the  necessary  tension 
is  obtained  by  passing  the  rope  round  a  tension  pulley  weighted  to  give  the 
desired  tension.  The  ropes  used  in  rope  transmission  are  either  of  hemp, 
manila,  or  cotton;  manila  ropes  are  mostly  used  in  the  United  States.  They 
are  of  three  strands,  hawser  laid,  and  may  be  from  \  in.  to  2  in.  in  diameter. 

The  weight  of  ordinary  manila  or  cotton  rope  is  about  .3  Dz  Ib.  per  ft.  of 
length,  where  D  =  diameter  of  rope,  in  inches.  Letting  w  =  weight  per  foot  of 
length,  w  =  .3  D2.  The  breaking  strength  of  the  rope  varies  from  7,000  to 
12,000  Ib.  per  sq.  in.  of  cross-section.  The  average  value  may  be  taken  as 
7,000  D2,  when  D  is  the  diameter  of  rope. 

For  a  continuous  transmission,  it  has  been  determined  by  experiment  that 
the  best  results  are  obtained  when  the  tension  in  the  driving  side  of  the  rope  is 
about  &  of  the  breaking  strength.  That  is, 


Ti  =  tension  in  tight  side  =       __     =  200  D« 

oO 

The  ropes  run  in  V-shaped  grooves,  and  the  coefficient  of  friction  is,  of  course, 
greater  than  on  a  smooth  surface.  The  coefficient  for  grooves  with  sides  at  an 
angle  of  45°  may  be  taken  at  from  .25  to  .33. 

The  horsepower  that  can  be  transmitted  by  a  single  rope  running  under 
favorable  conditions  is  given  by  the  formula 


in  which 


H  =  horsepower  transmitted  ; 
D  =  diameter  of  rope,  in  inches  ; 


v  =  velocity  of  rope,  in  feet  per  second. 

The  maximum  power  is  obtained  at  a  speed  of  about  84  ft.  per  sec.  For 
higher  velocities,  the  centrifugal  force  becomes  so  great  that  the  power  is 
decreased,  and  when  the  speed  reaches  145  ft.  per  sec.  the  centrifugal  force  just 
balances  the  tension,  so  that  no  power  at  all  is  transmitted.  Consequently, 
a  rope  should  not  run  faster  than  about  5,000  ft.  per  min.,  and  it  is  preferable  on 
the  score  of  durability  to  limit  the  velocity  to  3,500  ft.  per  min. 

EXAMPLE.  —  A  rope  flywheel  is  26  ft.  in  diameter,  and  makes  55  rev.  per  min. 
The  wheel  is  grooved  for  35  turns  of  1|  in.  rope.  What  horsepower  may  be 
transmitted? 

SOLUTION.—  Velocity,  in  feet  per  second  is 


POWER  TRANSMISSION 


269 


Applying  the  formula  H  =  ~~(20Q — fnw7»)»  the  horsepower  transmitted 
by  one  rope  or  turn  is 

74.9X(1*)2S 

825 

Then,  30.16X35  =  1,055.6  H.  P.  transmitted  by  the  35  ropes. 
EXAMPLE. — How  many  times  should  a   1-in.  rope  be  wrapped  around  a 
grooved  wheel  in  order  to  transmit  200  H.  P.,  the  speed  being  3,500  ft.  per  min.? 
SOLUTION.— 3,500  ft.  per  min.  =  3,500  H-  60  =  58i  ft.  per  sec.     Applying  the 
formula,  the  horsepower  transmitted  with  one  turn  is, 


Hence,  200-^-11.9  =  16.8,  say  17  turns. 

Rope  pulleys  differ  from  belt  pulleys  only  in  their  rims.  The  inclination  of 
the  sides  of  the  grooves  may  vary  from  30°  to  60°.  The  more  acute  the  angle, 
the  greater  the  coefficient  and,  consequently,  the  wear  on  the  rope. 

The  long  radius  R  is  determined  by  drawing  a  line  through  the  center  of  the 
rope  at  an  angle  of  22*,°  with  the  horizontal,  and  producing  it  until  it  intersects 
a  line  drawn  through  the  tops  of  the  ribs  dividing  the  grooves,  then,  with  this 
point  of  intersection  as  a  center,  drawing  the  curve  forming  the  side  of  the 
groove  tangent  to  the  circumference  of  the  rope.  The  advantage  claimed  for 
this  groove  is  that  the  rope  will  turn  more  freely  in  it,  thus  presenting  new 
sets  of  fibers  to  the  sides  of  the  grooves  and  increasing  the  life  of  the  rope. 

The  diameter  of  a  rope  pulley  should  be  at  least  30  times  the  diameter  of  the 
rope.  Good  results  are  obtained  when  the  diameters  of  pulleys  and  idlers  on  the 
driving  side  are  40  times,  and  those  on  the  driven  side  30  times,  the  rope 
diameter.  Idlers  used  simply  to  support  a  long  span  may  have  diameters 
as  small  as  18  rope  diameters,  without  injuring  the  rope. 

When  possible,  the  lower  side  of  the  rope  should  be  the  driving  side,  for  in 
that  case  the  rope  embraces  a  greater  portion  of  the  circumference  of  the  pulley, 
and  increases  the  arc  of  contact. 

When  the  continuous  system  of  rope  transmission  is  used,  the  tension 
pulley  should  act  on  as  large  an  amount  of  rope  as  possible.  It  is  good  practice 
to  use  a  tension  pulley  and  carriage  for  every  1 ,200  ft.  of  rope,  and  have  at  least 
10%  of  the  rope  subjected  directly  to  the  tension. 

Aside  from  the  grooved  rim,  rope  pulleys  are  constructed  the  same  as  other 
pulleys.  They  may  be  cast  solid,  in  halves,  or  in  sections.  The  pulley  grooves 
must  be  turned  to  exactly  the  same  diameter;  otherwise,  the  rope  will 
be  severely  strained. 


HORSEPOWER  OF  MANILA  ROPES 

(Link-Belt  Engineering  Co.) 


am.  of  Rope 
Inches 

ill 

* 

Breaking 
Strain 
Pounds 

Working 
Strain 
Pounds 

1,000  Ft. 
per  Min. 

2,000  Ft. 
per  Min. 

3,  000  Ft. 

per  Min. 

4,000  Ft. 

per  Min. 

5,000  Ft. 
per  Min. 

CM 

%f 

CM 

%f 

CM 

%f 

ri 

3^ 

CM 

%^ 

& 

a 

£> 

8 

£> 

a 

&> 

a 

£> 

a 

H> 

. 

.15 

4,000 

121 

2* 

90 

4* 

90 

. 

80 

7* 

80 

8* 

70 

1 

.18 

5,000 

151 

al 

110 

5* 

110 

71 

100 

9? 

100 

10? 

90 

1 

.27 

7,500 

227 

4* 

170 

8* 

170 

11? 

160 

14* 

150 

16 

130 

1 

.33 

9,000 

272 

5 

200 

10 

200 

14 

180 

17* 

170 

19 

150 

T 

.45 

12,250 

371 

7 

280 

13* 

270 

19 

250 

23* 

230 

26 

210 

1 

.50 

14,000 

424 

8 

320 

15* 

310 

22 

290 

27 

270 

29 

240 

1 

.65 

18,062 

547 

10* 

410 

20 

400 

28* 

370 

34? 

350 

38 

310 

.73 

20,250 

613 

11* 

460 

22 

440 

314 

420 

39 

390 

43 

350 

1 

.82 

25,000 

760 

570 

27? 

550 

39* 

520 

49 

490 

55 

448 

1 

1.08 

30,250 

916 

17 

680 

33* 

660 

47* 

630 

58* 

580 

64 

520 

2 

1.27 

36,000 

1,000 

20| 

810 

40 

790 

740 

69* 

670 

77 

620 

1      1 

I 

270 


POWER  TRANSMISSION 


LINE  SHAFTING 

Shafting  is  usually  made  cylindrically  true,  either  by  a  special  rolling 
process,  when  it  is  known  as  cold-rolled  shafting,  or  it  is  turned  up  in  a  machine 
called  a  lathe.  In  the  latter  case,  it  is  called  bright  shafting.  What  is  known  as 
black  shafting  is  simply  bar  iron  rolled  by  the  ordinary  process  and  turned  where 
it  receives  the  couplings,  pulleys,  bearings,  etc. 

Bright  turned  shafting  varies  in  diameter  by  £  in.  up  to  about  3$  in.;  above 
this  the  diameter  of  the  shafting  varies  by  £  in.  The  actual  diameter  of 
a  bright  shaft  is  in. 


less  than    the    com- 
mercial  diameter,   it 
being  designated  from 
the  diameter  of    the 
ordinary  round  bar 
iron  from  which  it  is 
turned.     Thus,  a 
length    of     what    is 
called     3-in.     bright 
shafting   is   only  2}f 
in.  in  diameter.  Cold- 
rolled  shafting  is  de- 
signated by  its  com- 
mercial   diameter; 
thus,    a    length    of 

CONSTANTS  FOR  LINE  SHAFTING 

Material  of  Shaft 

No 
Pulleys 
Between 
Bearings 

With 
Pulleys 
Between 
Bearings 

Steel  or  cold-rolled  iron. 
Wrought  iron  

65 
70 
90 

85 
95 
120 

Cold-rolled  iron  is  considerably  stronger  than  ordinary  turned  wrought 
iron,  the  increased  strength  being  due  to  the  process  of  rolling,  which  seems 
to  compress  the  metal  and  so  make  it  denser — not  merely  skin  deep,  but 
practically  throughout  the  whole  diameter. 
Let  D  =  diameter  of  shaft ; 

R  =  revolutions  per  minute; 
H  =  horsepower  transmitted; 
C  =  constant  given  in  table. 

In  the   above   table   the   bearings   are   supposed  to  be  spaced  so   as  to 
relieve  the_shaft  of  excessive  bending;  also,  in  the  third  vertical  column, 

an  average  number  and  weight 

MAXIMUM  DISTANCE  BETWEEN        of  pulleys  and  power  given  off  is 
BEARINGS  assumed. 

When  determining  these  con- 
stants   allowance   was  made    to 
insure    the    stiffness   as  well   as 
strength  of  the  shaft. 
,     D3R 


Distance   Between   Bearings 


Shafts  are  subject  to  forces 
that  produce  stresses  of  two 
kinds — transverse  and  torsiqnal. 
When  the  machines  to  be  driven 
are  below  the  shaft,  there  is  a 
transverse  stress  on  the  shaft, 
due  to  the  weight  of  the  shaft 
itself,  of  the  pulley  and  the  ten- 
sion of  the  belt.  Sometimes,  the 
power  is  taken  off  horizontally  on 
one  side,  in  which  case  the  tension 
of  the  belt  produces  a  horizontal 
transverse  stress,  while  the  weight 
of  the  pulley  acts  with  the  weight 
of  the  shaft  to  produce  a  vertical  transverse  stress.  When  the  machinery  to  be 
driven  is  placed  on  the  floor  above  the  shaft,  the  tension  of  the  belt  produces 
a  transverse  stress  in  an  opposite  direction  to  that  due  to  the  weight  of  the 
shaft  and  pulley. 

The  torsional  strength  of  shafts,  or  their  resistance  to  breaking  by  twisting, 
is  proportional  to  the  cube  of  their  diameter.  Their  stiffness  or  resistance  to 
bending  is  proportional  to  the  fourth  power  of  their  diameters,  and  inversely 


Diameter 

Jbeet 

of  Shaft 

Inches 

Wrought-Iron 
Shaft 

Steel  Shaft 

2 

11 

11.50 

3 

13 

13.75 

4 

15 

15.75 

5 

17 

18.25 

6 

19 

20.00 

7 

21 

22.25 

8 

23 

24.00 

9 

25 

26.00 

POWER  TRANSMISSION 


271 


proportional  to  the  cube  of  the  lengths  of  their  spans.  No  simple  general 
formula  can  be  given  that  will  safely  apply  to  engine  and  other  shafting  that 
is  subjected  to  the  bending  stresses  produced  by  overhung  cranks,  the  weight 
of  heavy  flywheels,  the  pull  of  large  belts,  or  to  severe  shocks  produced  by  the 
intermittent  action  of  the  power  or  load.  The  calculations  for  such  shafts 
should  always  be  based  on  the  special  conditions  involved. 

In  the  preceding  table  are  given  the  maximum  distances  between  the  bear- 
ings of  some  continuous  shafts  that  are  used  for  the  transmission  of  power. 
Pulleys  from  which  considerable  power  is  to  be  taken  should  always  be  placed 
as  close  to  a  bearing  as  possible. 

The  diameters  of  the  different  lengths  of  shafts  composing  a  line  of  shaft- 
ing may  be  proportional  to  the  quantity  of  power  delivered  by  each  respective 
length.  In  this  connection,  the  positions  of  the  various  pulleys  depend  on 
the  distance  between  the  pulley  and  the  bearing,  and  on  the  amount  of  power 
given  off  by  the  pulleys.  Suppose,  for  example,  that  a  piece  of  shaft- 
ing delivers  a  certain  amount  of  power;  then,  the  shaft  will  deflect  or  bend 
less  if  the  pulley  transmitting  that  power  is  placed  close  to  a  hanger  or  bear- 
ing, than  if  it  is  placed  midway  between  the  two  hangers  or  bearings.  It  is 
impossible  to  give  any  rule  for  the  proper  distance  of  bearings  that  could  be 
used  universally,  as  in  some  cases  the  requirements  demand  that  the  bear- 
ings be  nearer  together  than  in  others.  If  the  work  done  by  a  line  of  shafting 
is  distributed  quite  equally  along  its  entire  length,  and  the  power  can  be 
applied  near  the  middle,  the  strength  of  the  shaft  need  be  only  one-half  as  great 
as  when  the  power  is  applied  at  one  end  of  the  shaft. 

HORSEPOWER  SHAFTING  WILL  TRANSMIT 


Revolutions  per  Minute 

Diame- 

ter 

of 

100 

125 

150 

175 

200 

225 

250 

300 

350 

400 

Shaft 

Inches 

Horsepower  Transmitted 

1.2 

1.4 

1.7 

2.1 

2.4 

2.6 

3.1 

3.6 

4.3 

5.0 

1-? 

2.4 

3.1 

3.7 

4.3 

4.9 

5.5 

6.1 

7.3 

8.5 

9.7 

1 

4.3 

5.3 

6.4 

7.4 

8.5 

9.5 

10.5 

12.7 

14.8 

16.9 

iS 

6.7 

8.4 

10.1 

11.7 

13.4 

15.1 

16.7 

20.1 

23.4 

26.8 

1 

10.0 

12.5 

15.0 

17.5 

20.0 

22.5 

25.0 

30.0 

35.0 

40.0 

2? 

14.3 

17.8 

21.4 

24.9 

28.5 

32.1 

35.6 

42.7 

49.8 

57.0 

2 

19.5 

24.4 

29.3 

34.1 

39.0 

44.1 

48.7 

58.5 

68.2 

78.0 

2^* 

26.0 

32.5 

39.0 

43.5 

52.0 

58.5 

65.0 

78.0 

87.0 

104.0 

015 

33.8 

42.2 

50.6 

59.1 

67.5 

75.9 

84.4 

101.3 

118.2 

135.0 

3-*- 

43.0 

53.6 

64.4 

75.1 

85.8 

95.6 

107.3 

128.7 

150.3 

171.6 

3" 

53.6 

67.0 

79.4 

93.8 

107.2 

120.1 

134.0 

158.8 

187.6 

214.4 

3H 

65.9 

82.4 

97.9 

115.4 

121.8 

148.3 

164.8 

195.7 

230.7 

243.6 

015 

80.0 

100.0 

120.0 

140.0 

160.0 

180.0 

200.0 

240.0 

280.0 

320.0 

4-4 

113.9 

142.4 

170.8 

199.3 

227.8 

256.2 

284.7 

341.7 

398.6 

455.6 

4M 

156.3 

195.3 

234.4 

273.4 

312.5 

351.5 

390.6 

468.7 

546.8 

625.0 

BELT  PULLEYS 

Solid  and  Split  Pulleys. — Besides  being  used  with  ropes  or  chains  for  the 
hoisting  of  loads,  pulleys  are  extensively  employed  with  belts  for  transmitting 
power.  Belt  pulleys  may  be  divided  into  two  classes,  namely,  solid  pulleys  and 
split  pulleys.  A  solid  pulley  is  one  in  which  the  arms,  hub,  and  rim  are  cast  m 
one  solid  piece.  A  split  pulley  is  one  that  is  cast  in  halves  that  are  afterwards 
bolted  together;  the  latter  style  of  pulley  is  more  readily  placed  on  or  removed 
from  a  shaft  than  is  the  solid  pulley.  Pulleys  are  generally  cast  in  halves  or 
parts  when  they  are  more  than  6  ft.  in  diameter.  This  is  done  on  account  of 
the  shrinkage  strains  in  large  pulley  castings,  which  render  the  pulleys  liable 
to  crack  as  a  result  of  unequal  cooling  of  the  metal. 


272  POWER  TRANSMISSION 

Wooden  Pulleys.  —  Although  most  belt  pulleys  are  made  of  cast  iron, 
wrought  iron,  and  steel,  wooden  pulleys  have  come  into  extensive  use.  These 
are  built  of  segments  of  wood,  usually  maple,  securely  glued  together.  It  is 
possible  to  procure  wooden  split  pulleys  that  are  fitted  with  removable  bushings, 
thus  allowing  the  same  pulley  to  be  adapted  readily  to  shafting  of  different 
diameters.  Wooden  pulleys  are  somewhat  lighter  than  cast-iron  pulleys  for 
the  same  service. 

Driving  and  Driven  Pulleys.  —  The  pulley  that  imparts  motion  to  the  belt 
is  called  the  driving  pulley,  or  the  driver,  and  the  one  that  receives  motion 
from  the  belt  is  called  the  driven  pulley,  or  simply  the  driven.  When  two 
pulleys  are  connected  by  a  belt,  the  speeds  at  which  the  pulleys  run  are 
inversely  proportional  to  their  diameters.  Thus,  if  two  pulleys  have  diameters 
of  12  in.  and  24  in.,  the  speed  of  the  smaller  is  to  the  speed  of  the  larger  as  24  to 
12,  or  as  2  to  1.  The  speed  of  a  pulley  or  of  a  shaft  is  usually  stated  in  revo- 
lutions per  minute,  abbreviated  rev.  per  min.  or  R.  P.  M. 

Diameter  and  Speed  of  Driver.  —  It  often  becomes  necessary  to  calculate 
the  size  or  the  speed  of  a  pulley  that  drives  or  is  being  driven  by  a  machine. 

Let  D  =  diameter  of  driving  pulley,  in  inches; 

d  =  diameter  of  driven  pulley,  in  inches; 
N  =  number  of  rev.  per  min.  of  driving  pulley; 
n  =  number  of  rev.  per  min.  of  driven  pulley. 

Then,  if  the  diameter  of  the  driven  and  the  required  speeds  of  both  pulleys 
are  given,  the  diameter  of  the  driver  may  be  found  by  the  formula 


If  the  speed  of  the  driver  is  to  be  found,  it  is  necessary  to  use  the  formula 

»-5        (2> 

EXAMPLE.  —  A  12-in.  pulley  on  a  certain  machine  is  to  run  at  160  rev.  per 
min.  and  is  to  be  driven  by  belt  from  a  pulley  on  the  shaft  of  an  engine  that 
make  96  rev.  per  min.  What  must  be  the  diameter  of  the  pulley  on  the  engine 
shaft? 

SOLUTION.  —  Substituting  in  formula  1, 


Diameter  and  Speed  of  Driven.  —  If  the  diameter  of  the  driving  pulley 
and  the  desired  speeds  of  both  pulleys  are  known,  the  required  diameter  of  the 
driven  pulley  may  be  found  by  the  formula  , 


,  I  . 

If  the  speed  of  the  driven  pulley  is  to  be  found,  it  is  necessary  to  use  the 
formula 

»=T     <*> 

EXAMPLE  1.  —  A  30-in.  pulley  on  a  line  shaft  running  at  120  rev.  per  min. 
is  to  drive  a  pulley  on  a  machine  at  300  rev.  per  min.  What  must  be  the 
diameter  of  the  pulley  on  the  machine? 

SOLUTION.  —  Substituting  in  formula  1, 


EXAMPLE  2.  —  A  driving  pulley  48  in.  in  diameter  makes  175  rev.  per  min. 
andjs  connected  by  belt  to  a  driven  pulley  14  in.  in  diameter.  What  is  the 
speed  of  the  driven  pulley? 

SOLUTION.—  Substituting  in  formula  2, 
n  =  48)075 


BELTING 

A  belt  is  a  flexible  band  by  which  motion  is  transmitted  from  one  pulley  to 
another.  The  materials  most  commonly  used  for  belts  are  leather,  cotton,  and 
rubber,  although  thin,  flat  bands  of  steel  are  coming  into  use.  Leather  belts 
are  usually  made  either  single  or  double.  A  single  belt  is  one  composed  of  a 
single  thickness  of  leather,  and  a  double  belt  is  one  composed  of  two  thicknesses 


POWER  TRANSMISSION  273 

of  leather  cemented  and  riveted  together  throughout  the  whole  length  of  the 
belt.  Still  heavier  belts,  consisting  of  three  or  four  thicknesses  of  leather,  and 
known  as  triple  or  quadruple  belts,  are  sometimes  made  for  heavy  drives.  Cotton 
belts  are  made  up  of  a  number  of  layers,  or  plies,  sewed  together  and  treated 
with  a  water-proofing  substance.  They  are  termed  two-ply,  three-ply,  etc., 
according  to  the  number  of  plies  they  contain.  Four-ply  cotton  belting  is 
usually  considered  equal  to  single  leather  belting.  Rubber  belts  are  par- 
ticularly adapted  for  use  in  damp  or  wet  places.  They  withstand  changes  of 
temperature  without  injury,  are  durable,  and  are  said  to  be  less  liable  to  slip 
than  are  leather  belts. 

Sag  of  Belts.  —  The  distance  between  pulley  centers  depends  on  the  size  of 
the  pulleys  and  of  the  belt;  it  should  be  great  enough  so  that  the  belt  will  run 
with  a  slight  sag  and  a  gently  undulating  motion,  but  not  great  enough  to  cause 
excessive  sag  and  an  unsteady  flapping  motion  of  the  belt.  In  general,  the 
centers  of  small  pulleys  carrying  light  narrow  belts  should  be  about  15  ft.  apart 
and  the  belt  sag  1^  to  2  in.;  for  large  pulleys  and  heavy  belts  the  distance 
should  be  20  to  30  ft.  and  the  sag  2£  to  5  in.  Loose-running  belts  will  last 
much  longer  than  tight  ones,  and  will  be  less  likely  to  cause  heating  and  wear 
of  bearings. 

Speed  of  Belts.  —  The  higher  the  speed  of  a  belt,  the  less  may  be  its  width 
to  transmit  a  given  horsepower;  consequently,  a  belt  should  be  run  at  as  high 
a  speed  as  conditions  will  permit.  The  greatest  allowable  speed  for  a  belt 
joined  by  lacing  is  about  3,500  ft.,  per  min.  for  ordinary  single  and  double 
leather  belts.  For  belts  joined  by  cementing,  when  the  joint  has  about  the 
same  strength  as  the  solid  belt,  the  velocity  may  be  as  high  as  5,000  ft.  per 
min.  Higher  speeds  than  these  have  been  used,  but  there  is  little  to  be  gained 
by  exceeding  about  4,800  ft.  per  min.  In  choosing  a  proper  belt  speed,  due 
regard  must  be  paid  to  commercial  conditions.  Although  a  high  speed  of  the 
belt  means  a  narrow  and  cheaper  belt,  the  increased  cost  of  the  larger  pulleys 
that  may  be  required  may  offset  the  gain  due  to  the  high  speed  of  the  belt, 
at  least  so  far  as  the  first  cost  is  concerned.  The  speed  of  a  belt,  in  feet  per 
minute,  may  be  found  by  multiplying  the  number  of  revolutions  per  minute 
of  the  pulley  by  3.1416  times  the  diameter  of  the  pulley,  in  inches,  and 
dividing  the  product  by  12. 

Horsepower  of  Belts.  —  The  pull  on  a  belt  is  greatest  on  the  tight,  or  driving, 
side,  and  least  on  the  slack  side.  The  difference  between  the  tensions,  or  pulls, 
in  these  two  sides  is  called  the  effective  pull.  The  effective  pull  that  may  be 
allowed  per  inch  of  width  for  single  leather  belts  with  different  arcs  of  contact 
is  given  in  the  accompanying  table.  The  arc  of  contact  is  the  portion  of  the  cir- 
cumference of  the  smaller  pulley  that  is  covered  by  the  belt.  The  horsepower 
that  can  be  transmitted  by  a  single  leather  belt  may  be  found  by  the  formula 


in  which  H  =  horsepower  of  belt; 

C  —  effective  pull,  taken  from  table; 

W  =  width  of  belt,  in  inches; 

V  =  speed  of  belt,  in  feet  per  minute. 

If  it  is  desired  to  find  the  width  of  single  belt  required  to  transmit  a  given 
horsepower,  the  formula  becomes 

W-SMgS         (2) 

EXAMPLE  1.  —  What  horsepower  can  be  transmitted  by  a  single  leather  belt 
4  in.  wide  running  at  a  speed  of  2,500  ft.  per  min.,  if  the  belt  covers  one-third  of 
the  circumference  of  the  small  pulley? 

SOLUTION.  —  The  fraction  of  the  circumference  covered  by  the  belt  is  £  =  .333. 
From  the  table,  the  allowable  effective  pull  corresponding  to  this  value  is  28.8. 
Substituting  in  formula  1, 

28.8X4X2,500 

—33.000  ---  8'7H-P- 

EXAMPLE  2.  —  A  single  leather  belt  is  to  run  at  a  speed  of  3,000  ft.,  per  min. 
and  is  to  transmit  18  H.  P.  Find  the  width  of  the  belt,  if  the  arc  of  contact  is 
150°. 

SOLUTION.  —  The  effective  pull  corresponding  to  an  arc  of  contact  of  150°, 
from  the  table,  is  33.8.  Substituting  in  formula  2, 

,      33,000X18 
Ty  =  3 
A  6-in.  belt  would  be  used. 


274 


POWER  TRANSMISSION 
ALLOWABLE  EFFECTIVE  PULL 


Arc  of  Contact 

Allowable 
Effective  Pull 
Pounds  per 
Inch  of  Width 

Degrees 

Fraction  of 
Circumference 

90 

112* 

120 
135 
150 
157| 
180  or  over 

.250 
.312 
.333 
.375 
.417 
.437 
.500  or  over 

23.0 
27.4 
28.8 
31.3 
33.8 
34.9 
38.1 

The  horsepower  of  a  double  leather  belt  may  be  taken  as  If  times  that  of  a 
single  leather  belt  of  the  same  width  running  under  the  same  conditions. 
Accordingly,  the  width  of  a  double  leather  belt  required  for  any  service  is  only 
&  that  of  a  single  belt  for  the  same  service. 

Lacing  of  Belts. — A  very  satisfactory  way  of  lacing  belts  less  than  3  in. 
wide  is  shown  in  Fig.  1,  in  which  A  is  the  outside  of  the  belt  and  B  is  the  side 
that  runs  against  the  face  of  the  pulley.  The  ends  of 
the  belt  are  first  cut  square,  and  then  holes  are  punched 
in  the  ends,  in  corresponding  positions  opposite  one 
another.  The  number  of  holes  in  each  row  should 
always  be  odd,  in  the  style  of  lacing  shown,  using  three 
holes  in  belts  up  to  2  in.  wide  and  five  holes  in  belts 
between  2  and  3  in.  wide.  The  lacing  is  first  drawn 
through  one  of  the  middle  holes  from  the  under  side, 
or  pulley  side,  as  at  1.  Then  it  is  drawn  across  the 
upper  side  and  is  passed  down  through  2,  across  under 
the  belt  to  3,  up  through  S,  across  and  down  again  FIG.  1 

through  2,  back  under  the  belt  and  up  through  3  again, 

then  across  and  down  through  4  and  finally  up  through  6,  where  a  barb  is 
cut  in  the  edge  of  the  lacing  to  prevent  it  from  pulling  out.  This  completes  the 
lacing  of  one  half.  The  other  end  of  the  lacing  is  then  carried  through  the 
holes  in  the  other  half,  in  the  same  order. 

For  belts  wider  than  3  in.,  the  lacing  shown  in  Fig.  2  may  be  used.  In 
this  case,  there  are  two  rows  of  holes  in  each  end  of  the  belt  to  be  joined. 
The  row  nearer  the  end  of  the  belt  should  have  one  more  hole  than  the  row  far- 
ther away.  For  belts  up  to  4  4-  in.  wide  use  three  holes  in  the  first  row  and  two 
holes  in  the  second  row.  For  belts  up  to  6  in.  wide,  use  four  and  three  holes, 
respectively.  For  wider  belts,  make  the  total  number  of  holes  in  both  rows 
either  one  or  two  more  than  the  number  of  inches  of 
width  of  the  belt,  the  object  being  to  get  an  odd  total 
number  of  holes.  For  example,  a  10-in.  belt  should 
have  eleven  holes,  and  a  13-in.  belt  should  have  fifteen 
holes.  The  outside  holes  of  the  first  row  should  not 
be  nearer  the  side  edges  of  the  belt  than  f  in.  and  not 
nearer  the  joint  edge  than  |  in.  The  second  row  should 
be  at  least  If  in.  from  the  joint  edge.  In  Fig.  2,  A  is 
the  outside  face  and  B  the  face  next  the  pulley.  The 
lacing  is  first  drawn  up  through  1  from  the  pulley  side, 
and  then  is  carried  through  2,  3,  4,  5,  6,  7,  6,  7,  4,  5,  2, 
S,  8,  and  out  at  9  to  be  fastened.  The  other  end  of  the 
lacing  is  used  on  the  other  half  of  the  belt  in  the  same 
way. 

Care  and  Use  of  Belts. — It  is  a  much  disputed  question  as  to  which  side  of  a 
leather  belt  should  be  run  next  to  the  pulley.  The  more  common  practice,  it 
is  believed,  is  to  run  the  belt  with  the  hair,  or  grain,  side  nearest  the  pulley. 
This  side  is  harder  and  more  liable  to  crack  than  the  flesh  side;  by  running  it 
on  the  inside,  the  tendency  is  to  cramp  or  compress  it  as  it  passes  over  the 
pulley,  while,  if  it  ran  on  the  outside,  the  tendency  would  be  for  it  to  stretch 


PROPERTIES  OF  MATERIALS  275 

and  crack.  The  flesh  side  is  the  tougher  side,  but  for  the  reason  just  given  the 
life  of  the  belt  will  be  longer  if  the  wear  comes  on  the  grain  side.  The  lower 
side  of  the  belt  should  be  the  driving  side,  the  slack  side  running  from  the 
top  of  the  driving  pulley.  The  sag  of  the  belt  will  then  cause  it  to  encompass 
a  greater  length  of  the  circumference.  Long  belts,  running  in  any  other  direc- 
tion than  vertical,  work  better  than  short  ones,  as  their  weight  holds  them  more 
firmly  to  their  work. 

It  is  bad  practice  to  use  rosin  to  prevent  slipping.  Rosin  gums  the  belt, 
causes  it  to  crack,  and  prevents  slipping  for  only  a  short  time.  If  a  belt  in  good 
condition  persists  in  slipping,  a  wider  belt  should  be  used.  Sometimes,  larger 
pulleys  on  the  driving  and  driven  shafts  are  of  advantage,  as  they  increase  the 
belt  speed  and  reduce  the  stress  on  the  belt.  Belts  may  be  kept  soft  and 
pliable  by  being  oiled  once  a  month  with  castor  oil  or  neat's-foot  oil. 

When  rubber  belts  are  used,  animal  oils  or  animal  grease  should  never  be 
used  on  them.  If  the  belt  should  slip,  it  may  be  lightly  moistened  on  the  side 
nearest  the  pulley  with  boiled  linseed  oil. 

Flapping  of  Belts. — One  of  the  most  annoying  troubles  experienced  with 
belting  of  all  kinds  is  the  violent  napping  of  the  slack  side.  Flapping  may  be 
due  to  one  or  both  of  the  pulleys  running  out  of  true,  causing  the  belt  to  be 
alternately  stretched  and  released.  This  will  usually  cause  a  belt  to  flap 
when  running  at  a  high  speed.  If  the  belt  is  rather  slack,  tightening  it  may 
lessen  or  stop  the  flapping.  Another  frequent  cause  of  the  flapping  of  a  belt  is 
the  want  of  alinement  of  the  pulleys.  To  remedy  this,  the  pulleys  should  be 
brought  in  line;  should  this  fail,  the  belt  should  be  tightened  if  it  is  rather 
loose.  If  no  improvement  is  noticed  and  it  is  not  possible  to  turn  the  pulleys, 
the  belt  speed  should  be  reduced  a  little,  either  by  the  substitution  of  smaller 
pulleys  or  by  changing  the  speed  of  the  driving  shaft,  according  to  circum- 
stances. 

With  belts  running  at  speeds  above  4,000  ft.  per  min.,  flapping  may  occur 
when  the  pulleys  are  perfectly  true  and  in  line  with  each  other,  even  when  the 
belt  has  the  proper  tension.  This  is  believed  to  be  due  to  air  becoming 
entrapped  between  the  face  of  the  p  ulley  and  the  belt;  in  this  case  the  trouble 
may  be  prevented  by  perforating  the  belt  with  a  series  of  small  holes. 
Perforated  belts  may  now  be  bought  in  the  market. 

Another  cause  of  flapping  is  that  the  distance  between  the  pulleys  may  be 
too  great.  In  general,  the  distance  between  the  pulleys  should  not  exceed 
15  ft.  for  belts  up  to  4  in.  wide;  20  ft.  for  belts  from  4  to  12  in.;  25  ft.,  from 
12  to  18  in.;  and  30  ft.,  f9r  wider  belts.  A  belt  that  is  not  joined  square  will 
flap,  especially  when  running  at  a  rather  high  speed. 

SPECIFIC  GRAVITY,  WEIGHT,  AND  OTHER 
PROPERTIES  OF  MATERIALS 


DEFINITIONS 

The  specific  gravity  of  a  body  is  the  ratio  of  its  weight  to  the  weight  of 
an  equal  bulk  of  pure  water,  at  a  standard  temperature  (62°  F.  =  16.670°  C.). 
Some  experimenters  have  used  60°  F.  as  the  standard  temperature,  others 
32°  and  still  others,  39.1°.  To  reduce  a  specific  gravity,  referred  to  water 
at  39.1°  F.,  to  the  standard  of  water  at  62°  F.,  multiply  by  1.00112. 

Rule  I. — Given  the  specific  gravity  referred  to  water  at  62°  F.,  multiply  by 
62.355  to  find  the  weight  of  1  cu.  ft.  of  the  substance. 

Rule  II. — Given  weight  per  cubic  foot,  to  find  specific  gravity,  multiply  by 
.016037. 

Rule  III. — Given  specific  gravity,  to  find  the  weight  per  cubic  inch,  multiply  by 
.036085. 

To  Find  the  Specific  Gravity  of  a  Solid  Heavier  Than  Water.— Weigh  the 
body  both  in  air  and  in  water,  and  divide  the  weight  in  air  by  the  difference  of 
the  weights  in  air  and  water. 

EXAMPLE. — If  a  piece  of  coal  weighs  480  gr.  in  air  and  weighs  82  gr.  in 
water,  what  is  its  specific  gravity? 

SOLUTION. — As  480  —  82  =  398,  or  loss  of  weight  in  water.  Then  480 -i- 
398  =  1.206,  the  specific  gravity  of  coal. 


276 


PROPERTIES  OF  MATERIALS 


To  Find  the  Specific  Gravity  of  a  Solid  Lighter  Than  Water.— Attach  to  it 
another  body  heavy  enough  to  sink  it;  weigh  severally  the  compound  mass 
and  the  heavier  body  in  water,  divide  the  weight  of  the  body  in  air  by  the 
weight  of  the  body  in  air  plus  the  weight  of  the  sinker  in  water  minus  the 
combined  weight  of  the  sinker  and  body  in  water. 

To  Find  the  Specific  Gravity  of  a  Fluid. — Weigh  both  in  and  out  of  the  fluid 
a  solid  (insoluble)  of  known  specific  gravity,  and  divide  the  product  of  the 
weight  lost  in  the  fluid  and  the  specific  gravity  of  the  solid  by  the  weight  of 
the  solid. 

The  weight  of  1  cu.  ft.  of  water  at  a  temperature  of  62°  is  about  1,000 
oz.  avoir.,  and  the  specific  gravity  of  a  body,  multiplied  by  1,000,  shows  the 
weight  of  1  cu.  ft.  of  that  body  in  ounces  avoirdupois.  Then,  if  the  magnitude 
of  the  body  is  known,  its  weight  can  be  computed;  or,  if  its  weight  is  known, 
its  magnitude  can  be  calculated,  provided  its  specific  gravity  is  known;  or,  of  the 
magnitude,  weight,  and  specific  gravity,  any  two  being  known,  the  third  may 
be  found. 

To  Find  the  Weight  of  a  Body,  in  Ounces,  From  Its  Magnitude. — Multiply 
the  magnitude  of  the  body  in  cu.  ft.,  by  the  specific  gravity  of  the  substance 
multiplied  by  1,000. 

To  Find  the  Magnitude  of  a  Body,  in  Cubic  Feet,  From  Its  Weight.— Divide 
the  weight  of  the  body  in  ounces  by  1,000  times  the  specific  gravity  of  the  body. 

NOTE. — The  specific  gravity  of  any  substance  is  equal  to  its  weight  in 
grams  per  cubic  centimeter. 


SPECIFIC  GRAVITY  OF  COMMON  SUBSTANCES 

SPECIFIC  GRAVITY  OF  MINERALS  AND  EARTHS 


Material 

Specific 
Gravity 

Material 

Specific 
Gravity 

Alabaster  gypseous    . 

2.31 

Lime,  quick  

1.50 

Alabaster,  calcareous  .  . 

2.76 

Limestone  

2.70 

1.72 

Magnetic  iron  ore   .  .  . 

5.09 

Amethyst  

3.92 

Malachite  

4.01 

Asbestos,  starry  
Asphaltum  

3.07 
1.40 

Marble,  African  
Marble,  common.  .  .  !;,K 

2.71 
2.67 

Barytes  (heavy  spar)  .  . 
Bluestone  

3.05  to  3.38 
2.45  to  3.00 

Marble,  Egyptian...;..7 
Marble,  Parian.  .......  . 

.  2.67 
2.84 

Borax     

1.71 

Marble,  Italian,  white. 

2.71 

3  50 

Marl  

1.60  to  2  34 

Brick     . 

2.00 

Mica  

2.80 

Chalk 

2  78 

Niter     

1  90 

Clay  

1.90 

Opal  

2.09 

Coral  red 

2  70 

Phosphorus.  .            .    . 

1.77 

Diamond  

3.50  to  3.53 

Plaster  of  Paris  

1.87  to  2.47 

Earth  loose 

1  36 

Potash  

2.10 

Emerald  

3.95 

Quartz  

2.66 

Emerald,  aquamarine.  . 

2.73 
4  00 

Rotten  stone  
Ruby 

1.98 
395 

Feldspar  
Flint  black 

.      2.60 
2  58 

Salt,  common  
Saltpeter 

2.13 
209 

Flint,  white  

2.59 

Sand  

2.65 

Garnet  

3.60  to  4  20 

2.08  to  2  52 

Glass,  bottle  

2.73 

Sapphire  

3.98 

Glass,  flint  

3  50 

Serpentine 

2.81 

Glass  green 

2  64 

Shale 

2  60 

Glass,  white  

2.90 

Slate  . 

2.80 

Granite,  Patapsco  

2.64 

Soil,  common  

1.98 

Granite,  Quincy  
Granite,  Scotch   

2.65 
2  62 

Specular  iron  ore  ...... 

5.25 
248 

Granite,  Susquehanna. 
Graphite  

2.70 
2  20 

Sulphur,  native  
Talc 

2.03 
2.90 

Grindstone   .  . 

2  14 

Topaz 

3  50 

Gypsum,  opaque  

2.17 

Tourmaline 

2.07 

Jasper  

2.65 

Turquoise  

2.84 

Lapis  lazuli  

2.96 

Zircon  

4.50 

PROPERTIES  OF  MATERIALS 
SPECIFIC  GRAVITY  OF  METALS 


277 


Metal 

Specific 
Gravity 

Metal 

Specific 
Gravity 

Aluminum,  wrought  

2.660 
6.712 

Magnesium  
Manganese 

1.740 
8  000 

Bismuth  
Brass,  common  
Brass,  wire  
Bronze,  bell-metal  

9.746 
8.500 
8.548 
8.060 
8.500 

Mercury,  solid,  at  —40°  F.. 
Mercury,  liquid,  at  32°  F.  .  . 
Mercury,  liquid,  at  60°  F.  .  . 
Mercury,  liquid,  at  212°  F.  . 
Molybdenum  

15.632 
13.619 
13.580 
13.375 
8.620 

1.580 

Nickel,  cast 

8  280 

Chromium  

6.000 

Platinum,  hammered.  ...... 

20.337 

Cobalt 

8.500 

Platinum  rolled 

21  042 

Copper,  cast  

8.700 

Platinum,  wire  

22.009 

8.788 

Potassium  .  . 

.860 

Copper,  wire  and  rolled  .... 

8.878 
19.361 

Silver,  pure  
Sodium  ... 

10.474 
970 

19.258 

Steel,  cast  

7.919 

Gold'  22  carat  fine 

17.486 

Steel,  common   soft 

7.833 

18.680 

Steel,  hard  and  tempered  .  . 

7.818 

Iron,  cast  

7.207 

Tin,  Bohemian  

7.312 

7.780 

Tin,  English  

7.201 

7.768 

Titanium  .  .          ... 

5.300 

iron,  pure.  ...  .  . 

7  780 

17  600 

Lead,  hammered  

11.388 
11  330 

Zinc,  cast  
Zinc   rolled 

6.860 
7  101 

SPECIFIC  GRAVITY  OF  LIQUIDS 


Liquid 

Specific 
Gravity 

Liquid 

Specific 
Gravity 

Acid,  acetic  
Acid,  hydrochloric  
Acid,  nitric  
Acid,  phosphoric  
Acid,  sulphuric.  
Alcohol,  commercial  
Alcohol,  proof  -spirit  
Alcohol,  pure  
Alcohol,  wood  
Beer,  lager  
Bordeaux,  wine  
Bromine  

1.062 
1.200 
1.217 
1.558 
1.841 
.833 
.925 
.792 
.800 
1.034 
.992 
2.996 
.997 
1.530 

Cider.    .            .            .    . 

1.018 
1.090 
.739 
1.450 
1.054 
1.032 
.940 
.915 
.870 
.932 
.878 
1.000 
1.030 
.992 

Egg  

Ether,  sulphuric  
Honey  

Human  blood  
Milk  

Oil,  linseed  
Oil,  olive  

Oil,  turpentine  
Oil  whale 

Petroleum  
Water  distilled 

Water,  sea  
Wine  

Chloroform  

SPECIFIC  GRAVITY  OF  GASES  AND  VAPORS 


Gas  or  Vapor 

Specific 
Gravity 

Gas  or  Vapor 

Specific 
Gravity 

Air,  32°  F.   and   1  atmos.. 
Alcohol,  vapor  
Ammonia  
Bromine  vapor  
Carbon  dioxide  

1.000 
1.589 
.589 
4.540 
1.520 
.967 
2.450 
5.300 
.069 
6.974 

.553 
.917 
.967 
1.106 
.102 
.900 
.488 
1.1912 
4.700 
.623 

Nitrogen  
Olefiant  gas  
Oxygen  
Smoke,  bituminous  coal  .... 
Smoke,  wood  
Steam  at  212°  F  
Sulphureted  hydrogen  
Turpentine  vapor  

Carbon  monoxide  
Chlorine  

Chloroform   vapor  

Mercury  vapor  (ideal)  

278 


PROPERTIES  OF  MATERIALS 
SPECIFIC  GRAVITY  OF  DRY  WOODS 


Wood 

Specific 
Gravity 

Wood 

Specific 
Gravity 

Alder 

.80 

Hazel  

.60 

Annie 

.89 

Lemon  

.70 

Ash 

.86 

Lignum  vitae  

1.33 

Bay                                   .... 

.82 

Linden  

.60 

Beech 

.85 

Logwood  

.91 

.96 

Mahogany,  Honduras  

.56 

1  33 

Maple 

.79 

Box,  Brazilian,  red  

PprJar    wild 

1.03 
60 

Mulberry  
Oak 

.90 
.95 

Cedar,  Palestine  

.61 
56 

Orange  
Pear 

.71 

.66 

.67 

Pine,  southern  

.72 

Cork 

.25 

Pine,  white  

.40 

Ebony  American  

1.22 

Poplar  

.38 

Elder                               

.70 

Poplar,  white  Spanish  

.53 

Elm                

.56 

Sassafras  

.48 

Filbert 

60 

.50 

Fir  male  

.55 

Spruce,  old  

.46 

50 

Walnut 

.61 

SPECIFIC  GRAVITY  OF  MISCELLANEOUS  SUBSTANCES 


Substance 

Specific 
Gravity 

Substance 

Specific 
Gravity 

Amber         

1.085 

India  rubber  

.935 

Air 

.0012 

Ivory. 

1.822 

Beeswax  . 

.965 

Lard  

.947 

Bone 

1.8  to  2.0 

Pearl,  oriental 

2.650 

Butter  

.942 

Spermaceti  

.943 

Cotton 

1.950 

Sugar  ...                    

1.605 

Fat 

.923 

Tallow  sheep  and  ox 

.923 

Gunpowder,  loose  
Gunpowder,  shaken  .  .  . 

.900 
1.000 

Tallow,  calf... 
Tar.  .  . 

.934 
1.000 

Gum  Arabic  

1.452 

Wool  

1.610 

AVERAGE  WEIGHT  OF  VARIOUS  SUBSTANCES 

WEIGHT  OF  1  CU.  FT.  OF  VARIOUS  METALS 


Metal 

Weight 
Pounds 

Metal 

Weight 
Pounds 

Aluminum 

167 

109 

Antimony  

418 

Manganese                 

499 

Bismuth  
Brass,  cast 

613 
504 

Mercury,  at  32°  F  
Mercury  at  60°  F 

849 
846 

Brass,  rolled  
Bronze 

524 
546 

Mercury,  at  212°  F  

836 
538 

Chromium  

456 

Nickel 

548 

Cobalt 

560 

1  270 

Copper,  cast  

552 

Platinum  rolled         .        .  . 

1,313 

Copper,  rolled 

555 

1  372 

Gold,  cast,  24  carat  
Gold,  pure,  hammered 

1,204 
1  217 

Silver,  hammered  

657 
653 

Gun-metal  bronze  

529 

Sulphur  

125 

Indium  

1,400 

Steel 

490 

Iron,  cast  

450 

Tin  

458 

Iron,  wrought  

480 

Tungsten                           .... 

1,097 

Lead,  commercial,  cast  

712 

Zinc  

437 

PROPERTIES  OF  MATERIALS  279 

WEIGHT  OF  1  CU.  FT.  OF  VARIOUS  WOODS,  WHEN  DRY* 


Wood 

Weight 
Pounds 

Wood 

Weight 
Pounds 

Alder  

42 

Cypress,  Spanish  

29 
40 

Apple 

47 

Dagame.  .  . 

56 

Arbor  vitae  

19 

Dogwood  

50 

Ash,  black  
Ash  blue 

39 
34 

Ebony  
Elder  tree 

76 
43 

Ash,  green  .  .     .        

39 

Elm,  cork  

45 

Ash   Oregon 

35 

Elm,  slippery 

43 

Ash,  red  
Ash,  white 

38 
39 

Elm,  white  
Elm,  wing.    . 

34 
46 

Aspen  

27 

Filbert  tree  

38 

Bamboo 

22 

Fir,  balsam  

23 

28 

Fir,  great  silver 

22 

Bay  tree  ... 

51 

Fir,  red,  or  California  

29 

Beech 

42 

Fir,  red,  or  noble 

28 

Bethabara  

76 

Fir,  white  

22 

Birch  paper  or  white 

37 

Greenheart.                  

72 

Birch,  red  

35 

Gum,  cotton  

32 

Birch   sweet 

47 

Gum,  sour  

39 

40 

Gum,  sweet 

37 

Blue  beech  (iron  wood)  .  . 

45 
43  to  69 

Hackmatack    (American 
larch) 

38 

Box  elder  

26 

Hawthorn  .  .  . 

57 

Boxwood  Brazilian  red 

64 

Hazel  . 

38 

Boxwood,  Dutch  

83 

Hemlock  

26 

Boxwood   French 

57 

Hemlock,  western 

28 

Buckeye,  Ohio  

28 

Hickory,  mocker  nut  

53 

Buckeye  sweet 

27 

Hickory,  pecan  . 

49 

Bullet  tree  

65 

Hickory,  pignut  

56 

Butternut 

25 

Hickory,  shagbark,  or  shell- 

35 

bark 

51 

Cabacalli  .  . 

56 

Holly  

36 

27 

Hornbeam 

47 

Catalpa,  hardy  .  .  . 

25 

Ironwood,  or  blue  beech  .... 

45 

Cedar,  California,  white.  .  .  . 
Cedar,  canoe  

25 
23 

Ironwood,  or  hop  hornbeam 
Jasmine,  Spanish  

51 

48 

Cedar  incense 

25 

Joshua  tree.  .  . 

23 

Cedar,  Indian  

82 

Juneberry  .  .  . 

54 

Cedar,  juniper 

35 

Karri  

63 

Cedar  Palestine 

38 

Kauri 

37 

Cedar,  Port  Oxford 

28 

Laburnum  

57 

Cedar  red 

30 

Lancewood 

53 

Cedar,  white,  or  post  .  . 

23 

Larch  

38 

Cedar,  white  (arbor  vitae)  .  . 
Cedar,  wild  

19 
37 

Larch,  tamarack  
Laurel,  California  

46 
40 

Cedar,  yellow 

29 

Laurel,  Madrona  

43 

36 

Lemon 

45 

Chestnut  

28 

Lignum  vitae  

83 

36 

Linden  

38 

Citron  
Cocoa  wood. 

45 
65 

Locust,  black,  or  yellow.  .  .  . 
Locust,  honey  

45 

42 

Cocobolo  

55 

Logwood  

58 

24 

Madrona 

43 

Cottonwood  black 

23 

Mahoe  

41 

29 

Mahogany     .  .    .        

45 

*  The  weight  of  wood  depends  largely  on  the  amount  of  moisture  it  con- 
tains. The  weights  in  this  and  the  following  tables  are  for  very  dry  wood  and 
not  for  green  wood.  Separate  tables  are  given  for  Philippine,  Indian, 
and  Australian  woods.  The  weight  of  moisture  contained  in  the  wood  must 
be  added  to  the  values  given  in  these  tables. 


280 


PROPERTIES  OF  MATERIALS 


TABLE — (Continued) 


Wood 

Weight 
Pounds 

Wood 

Weight 
Pounds 

Mahogany,  Mexican  
Mahogany,  Spanish  

32 
53 

Pine,  white,  (Pacific  States 
and  British  Columbia)  .  .  . 

24 

Mahogany,  white  
Maple  Oregon 

33 
30 

Pine,  white,  (Rocky  Moun- 
tains)   

27 

Maple,  red  

38 

Pingow  

47 

Maple  silver  or  soft 

32 

Plum  tree  

49 

Maple,  sugar,  or  hard  

43 

Pockwood  

81 

Mastic  tree 

53 

Pomegranate  tree 

85 

Medlar 

59 

Poon 

36 

Mesquit.   .   . 

47 

Poplar,  or  large-tooth  aspen 

28 

Missel  tree  
Mora  . 

59 
57 

Poplar,  yellow,  or  tulip  tree 
Quebracho  

26 
82 

36 

44 

Oak,  black. 

45 

Redwood  

26 

Oak,  burr  

46 

Roller  wood  

52 

Oak,  chestnut  . 

46    " 

Rosewood     .    . 

68 

Oak,  cow  

46 

Sal  

60 

Oak,  English... 

51 

Sassafras  ...    . 

31 

Oak,  live,  California  .... 

51 

Shadblow  

54 

Oak,  live,  Southern  United 

Shadbush  . 

54 

States 

59 

28 

Oak,  pin  

43 

Spruce   Douglas 

32 

Oak,  post 

50 

29 

Oak,  red  

45 

Spruce,  single  (balsam  fir) 

23 

Oak,  Spanish 

43 

Spruce  Sitka 

26 

Oak,    white   (North-central 
and    Eastern    United 

Spruce,     white,    (Northern 
United  States)  

25 

States)  

50 

Spruce  white  (RockyMoun- 

Oak,   white,  (Pacific  Coast 
from  British  Columbia  to 

tains    and     British    Col- 
umbia) 

21 

California) 

46 

35 

Orange,  osage  

48 

Sycamore,  California 

30 

Orange  tree 

44 

Tamarack 

38 

Paddlewood  

52 

Teak        

50 

Palm,  Washington  

32 

Tonka  

64 

Palmetto,  cabbage.  .  . 

27 

Tooart  

67 

Pear  

41 

Tulip  tree 

26 

Persimmon  .  .  . 

49 

Tulip  wood       

61 

Pine,  bull  

29 

83 

Pine,  Cuban  . 

39 

Walnut  black 

38 

Pine,  Kauri  

60 

35 

Pine,  loblolly  

33 

Walnut,  English  

36 

Pine,  long-leaf,  or  Georgia 

38 

Walnut   Italian 

42 

Pine,  northern  .    . 

34 

Walnut   Persian 

36 

Pine,  Norway  

31 

Walnut  white 

25 

Pine,  Oregon  

32 

Wasahba 

76 

Pine,  pitch  

32 

Whitewood 

26 

Pine,  short-leaf,  or  Carolina 

32 

Willow,  black  

27 

Pine,  sugar  

22 

52 

Pine,  white,  (North-Central 

Yew   Dutch 

4P 

and  Northeastern  States)  . 

24 

Yew  Spanish  

50 

Yucca,  or  Joshua  tree  

23 

PROPERTIES  OF  MATERIALS  281 

WEIGHT  OF  1  CU.  FT.  OF  PHILIPPINE  WOODS,  WHEN  DRY 


Wood 


Weight 
Pounds 


Wood 


Weight 
Pounds 


Acle.. 

Amuguis 

Apitong 

Aranga 

Balacat 

Balacbacan 

Bansalaguin.  .  .  . 

Banuyo 

Batitinan v. 

Betis 

Calantas 

Dungon 

Guijo 

IP" 

Lauan 


Liusin 

Lumbayao 

Macaasin 

Malasantol 

Malugay 

Mayapis 

Molave 

Narra 

Palo  Maria 

Sacat 

Sasalit ' 

Supa 

Tanguile 

Tindalo 

Yacal... 


44 
35 
44 
40 
40 
25 
49 
30 
39 
37 
55 
45 
30 
48 
52 


WEIGHT  OF  1  CU.  FT.  OF  AUSTRALIAN  WOODS,  WHEN  DRY* 


Wood 


Weight 
Pounds 


Acacia  dealbata  (silver  wattle) 57 

Acacia  decurrens  (common  wattle) 47 

Acacia  implexa 44 

Acacia  melanoxylon  (blackwood;   lightwood) 47 

Acacia  mollissima  (silver  wattle) 50 

Acacia  pycnantha  (golden  wattle) 52 

Acacia  salicina 48 

Araucaria  cunninghamii  (pine) 45 

Aster  argophyllus  (musk  tree) 40 

Banksia  integrifolia  (coast  honeysuckle  tree) 

Banksia  marginata  (common  honeysuckle  tree) 38 

Banksia  serrata  (heath  honeysuckle  tree) 50 

Callitris  verrucosa  (dessert  sandarac  pine,  or  cypress) 43 

Castanaspermum  australe  (black  bean) 57 

Casuarina  torulusa  (forest  oak) 66 

Casuarina  quadravalvis  (drooping  she  oak) 61 

Cedrela  australis  (cedar) 28 

Ceratopetalum  apetalum  (coach wood) 

Dacrydium  cupressinum  (rimu) 38 

Dissiliaria  baloghioides  (teak) 60 

Dysoxylon  muelleri  (red  bean) 46 

Eucalyptus  amygdalina  regnans  (mountain  ash  or  peppermint  tree)  60 
Eucalyptus  botryoides  (blue  gum,  Gippsland  mahogany,  or  bastard 

mahogany) ' 60 

Eucalyptus  corymbosa  (bloodwood) 

Eucalyptus  corynocalyx  (sugar  gum) 69 

Eucalyptus  diversicolor  (karri) 61 

Eucalyptus  globulus  (blue  gum) 57 

Eucalyptus  gomphocephala  (tuart) 66 

Eucalyptus  goniocalyx  (bastard  box,  spotted  gum) 

Eucalyptus  haewastowa  (spotted  gum) 69 

Eucalyptus  hemiphloia  (canary  wood,  white  box,  or  gray  box) 48 


*  On  account  of  the  unsettled  nomenclature  of  Australian  woods,  this 
table  gives  botanical  names,  with  common  names,  so  far  as  possible,  in  paren- 
thesis after  the  botanical  name.  Also  see  note  at  foot  of  table,  Weight  of 
Various  Woods,  page  279. 


PROPERTIES  OF  MATERIALS 
TABLE — (Continued) 


Wood 


Eucalyptus  largiflorens  (slaty  gum) 

Eucalyptus  leucoxylon   (iron  bark,  red  flowering,  or  black  iron 

bark) 

Eucalyptus  longifolia  (wollybutt  tree) 

Eucalyptus  maculata  (spotted  gum) 

Eucalyptus  marginata  (jarrah) 

Eucalyptus  melliodora  (yellow  box) 

Eucalyptus  microcorys  (tallow  wood) 

Eucalyptus  obliqua  (messmate,  stringy  bark) 

Eucalyptus  pilularis  (blackbutt,  or  flintwood) 

Eucalyptus  piperita  (blackbutt,  white  stringy  bark  tree) 

Eucalyptus  resinifera  (mahogany) 

Eucalyptus  robusta  (swamp  mahogany) 

Eucalyptus  rostrata  (red  gum  tree) 

Eucalyptus  saligna  (gray  gum) 

Eucalyptus  siderophloia  (iron  bark) 

Eucalyptus  sieberiana  (iron  bark,  gumtop  stringy  bark,  mountain 

ashes) 

Eucalyptus  tereticarnis  (flooded  gum) 

Eucalyptus  viminalis  (manna  gum  tree,  drooping  gum,  or  white 

gum  tree) 

Eugenia  smithii  (myrtle) 

Exocarpus  cupressiformis  (native  cherry  tree) 

Fagus  cunninghamii  (evergreen  beech  or  native  myrtle) 

Hakea  leucoptera  (water  tree) 

Heterodendron  oleif olium 

Lomatia  f  raseri 

Melalenca  decussata 

Melalenca  parviflora 

Mypqrum  insulare 

Myrsine  variabilis 

Panax  murrayi  (palm  panax) 

Pimelea  microcephala 

Pittosporum  bicolor  (white  wood) 

Pomaderris  apetala  (hazel) 

Prostanthera  lasianthas  (mint  tree) 

Santalum  acuminatum  (native  peach  or  quandong) 

Santalum  persicarium  (native  sandalwood) 

Senecio  bedf ordii  (native  dogwood) 

Syncarpia  laurifolia  (turpentine) 

Tristania  conf erta  (brush  or  white  box) 

Tristania  nerifolia  (water  gum) 

Viminaria  denudata. . . 


WEIGHT  OF  1  CU.  FT.  OF  INDIAN  WOODS 

(Berkley-Clark) 


Wood 

Weight 
Pounds 

Wood 

Weight 
Pounds 

Bibla  

56 

Poon 

39 

Blackwood  
Erroul  
Hedoo  

56 
63 
39 

Red   eyne  
Teak,  Jungle  
Teak   Northern 

68 
41 
55 

Khair  »  
Kullum  .    . 

73 

41 

Teak,  Southern  

48 

PROPERTIES  OF  MATERIALS 
WEIGHT  OF  AMERICAN  TIMBERS 


Wood 

Specific 
Gravity 

Weight 

Cubic 
Foot 
Pounds 

Weight 
per  Foot 
Board 

Measure 
Pounds 

Remarks 

California  redwood  . 
California  spruce  
Cedar  
Chestnut  

.39 
.40 
.37 
.66 

24.16 
24.97 
23.10 
41.20 

2.01 
2.08 
1.93 
3.43 

The  weights  given 
are  the  averages  of  a 
large  number  of  de- 

Cypress  
Douglas  fir  

.46 
.51 

28.72 
31.84 

2.39 
2.65 

commercially  dry 

Hemlock  
Red  pine  (Norway  pine)] 
Short-leaf  yellow  pine.  .  . 
Southern,    long-leaf,    or 
Georgia  yellow  pine.... 
Spruce  and  eastern  fir  .  . 
White  oak  

.40 
.50 
.51 

.61 
.40 

.80 

24.97 
31.31 
31.84 

38.08 
24.97 
49.94 

2.08 
2.60 
2.65 

3.17 
2.08 
4.16 

less  than  15%  of 
moisture.  The 
weights  of  unsea- 
soned green  lumber 
will  be  from  20  to 
40  %  greater.  Green 

White  pine  

.38 

23.72 

1.98 

taken  to  weigh  5 
Ib.  per  running  foot 
board  measure. 

WEIGHT  OF  1  SQ.  FT.  OF  BUILDING  MATERIALS 


Name  of  Material 

Average 
Weight 
Pounds 

Name  of  Material 

Average 
Weight 
Pounds 

Corrugated    (2£ 
-in.)   galvanized 
iron 

Corrugated  galvar 
No.  20,  average 
side  lap,  unboar 
Copper       roofing, 
standing  seam  .  . 
Felt     and     pitch, 

No.  16.. 
No.  18.. 
No.  20.  . 
No.  22.. 
No.  24.. 
No.  26.. 
No.  27.. 
No.  28.  . 
lized  iron, 
amount  of 
ded  
16-oz., 

without 

2.91 
2.36 
1.82 
1.54 
1.27 
.99 
.93 
.86 

2.25 
1.25 

3.00 
1.75 

2.00 
6  to  8 

6  to  8 
10.00 

.50 
2.00 

2.00 
4  to  10 

Slate,  single  , 
thickness. 

Slag  roof,  foui 
Steel  roofing, 
Tiles,  Spanish 
in.,  1\  in.  tc 
Tiles,  plain,  1 
Xf  in.,  5ii 
White-pine  sh 
thick 

\  in.  thick.  .  . 
•fe  in.  thick  .  . 
Jin.  thick.  .  . 
|  in.  thick.  .  . 
£in.  thick.  .  . 
fin.  thick.  .  . 
f  in.  thick  .  .  . 

-ply  
standing  seam 
,  14iin.X10£ 
weather  
0s  in.X  61  in. 
n.  to  weather, 
eathing,   1  in. 

1.81 
2.71 
3.62 
5.43 
7.25 
9.06 
10.87 
4.00 
1.00 

8.50 
18.00 
2.00 

3.00 
5.50 
6.00 

6  to  10 
2.00 
4.00 

5.00 
3.00 
6.50 

Glass,  |  in.  thick. 
Hemlock    sheathii 
thick 

Yellow-pine  sheathing,  1  in. 
thick         ...    .  '.  

ig,     1    in. 

Gravel  roof  and  four-ply  felt 
Gravel  roof  and  five-ply  felt 
Roofing,      three-ply     ready 
(asphalt,  rubberoid,  etc.) 
Purlins,  wooden,  with  12-  to 
16-ft.  span  
Chestnut  or  maple  sheath- 
ing, 1  in.  thick  
Ash,  hickory,  or  oak  sheath- 
ing, 1  in.  thick  
Sheet  iron,  -&  in.  thick  
Thatch  

Lead,  about  |  in.  thick  
Lath-and-plaster     ceiling 

Mackite,    1  in.   thick,   with 
plaster  
Neponset  roofing  felt,   two 
layers  

Spruce  sheathing,  1  in.  thick 
Shingles,  common,  6  in.X  18 
in.,  5  in.  to  weather  
Skylight  of  glass,  A  to  1  in., 
including  frame  

284  PROPERTIES  OF  MATERIALS 

WEIGHT  OF  1  CU.  FT.  OF  BUILDING  MATERIALS 


Material 

Weight 
Pounds 

Material 

Weight 
Pounds 

Asphalt-pavement  corn- 

130 

Earth,      soft,      flowing 

108 

160 

Earth,  dense  mud  

125 

150 

150 

Granite  

165  to  170 

hard 

125 

Gravel  

117  to  125 

150 

Iron,  cast*  

450 

Brick!  soft,  inferior  .... 

100 

Iron,  wroughtf  

480 
146  to  168 

Brickwork,  in  lime  m 

120 

Marble  

168 

Brickwork,    in    cement 
mortar,  average  
Brickwork,     pressed 
brick,  thin  joints  .... 
Cement,    Portland, 
packed  
Cement,    Portland, 

130 
140 
100  to  120 
70  to  90 

Masonry,  squared  gran- 
ite or  limestone  
Masonry,     granite     or 
limestone  rubble  
Masonry,     granite     or 
limestone  dry  rubble 
Masonry,  sandstone.  .  . 
Mineral  wool  

165 
150 

138 
145 
12 

Cement,        natural 
packed  
Cement,   natural,  loose 
Cement,  slag,  packed.. 
Cement,  slag,  loose  

75  to  95 
45  to  65 
80  to  100 
55  to  75 
105 

Mortar,  hardened  
Quicklime,   ground, 
loose,  or  small  lumps 
Quicklime,   ground, 
thoroughly  shaken... 
Sand,  pure  quartz,  dry  . 

90  to  100 
53 

75 
90  to  106 

140 

Sandstone,        building, 

135 

dry 

130  to  151 

140 

Slate..  

160  to  180 

Concrete,       reinforced, 

150 

Snow,  fresh  fallen  
Steel,  structural  J  

5  to  12 

489.6 

Terra  cotta     

110 

loose..         

72  to  80 

Terra  -  cotta  masonry 

82  to  92 

work  

112 

Tile 

110  to  120 

ly  rammed 

90  to  100 

WEIGHT  OF  1  CU.  FT.  OF  MISCELLANEOUS  MATERIALS 


Material 

Weight 
Pounds 

Material 

.  Weight 
Pounds 

Acid,  acetic  .  . 

66 

40 

Acid,  fluoric  
Acid,  hydrochloric.  .  .  . 

94 
75 

Asphalt,  pure  
Borax 

80 
107 

Acid,  nitric. 

76 

Bran 

16 

Acid,  phosphoric  

97 

Chalk  

156 

Acid,  sulphuric  
Alabaster,  white  
Alabaster,  yellow  
Alcohol,  commercial 

115 
171 
169 
52 

Charcoal,  birch  
Charcoal,  fir  
Charcoal,  oak  

34 

28 
21 
18 

Alcohol,  grain  
Alcohol,  wood  

49.6 
49.9 

Chrome  ore  dust,  well 

160 

Ammonia,  28%  

56 

Clay,  ordinary  

120  to  150 

Antimony  

418 

119 

Apples  . 

38 

Clinker 

85 

Asbestos,  starry  

192 

Coal,      anthracite, 
broken  

54 

*Weight  per  cubic  inch,  .260  Ib. 
JWeight  per  cubic  inch,  .283  Ib. 


tWeight    per    cubic    inch,    .277    Ib. 


PROPERTIES  OF  MATERIALS 
TA  BLE — (Continued) 


Material 

Weight 
Pounds 

Material 

Weight 
Pounds 

Coal,      anthracite, 
moderately     shaken 

58 

Magnesite,  calcined...  . 
Mica     

110 

183 

Coal       anthracite 

155 

solid*            

93 

Naphtha  

53 

Coal,  bituminous,  bro- 

Niter   

119 

ken,  loose  

50 

Oats     .            .... 

26 

Coal,        bituminous, 

Oil,  linseed...  

59 

slacked  

52 

Oil  olive 

57 

Coal,        bituminous, 

Oil,  turpentine  ?  .  . 

54 

solidt  

84 

Oil  whale. 

58 

Coal,  cannel,  solid  
Coke,  loosej  

79 
23  to  32 

Ore,  iron,  magnetite  .  .  . 
Ore  iron   hematite 

312 
306 

Coral,  red  

169 

Paper,  calendered  book 

50 

Cork        

15 

Paper   leather-board  .    . 

59 

56 

37 

Corn  on  cob    unhusked 

.  58 

Paper,  news       

38 

Corn   shelled 

45 

33 

Corn  meal,  bolted  
Corn  meal,  unbolted.  .  . 

37 
38 

Paper,  supercalendered 
book  

69 

Corundum  .  .  ~  

244 

Paper,  wrapping  

10 

Cotton  yarn,  skeins  

11 
134  to  157 

Paper,  writing  

64 
150 

250 

Pearl    oriental 

165 

Ether   

45 

Peat,  dry,  compressed 

20  to  30 

Feldspar          

166 

55 

Flint  

162 

Pitch   . 

72 

Glass,  common  
Glass  flint  

156  to  172 
180  to  196 

Plaster  of  Paris,  cast  .  . 
Plumbago 

80 
140 

168 

41 

Gneiss  in  loose  piles  .  .  . 

96 

Potatoes,  white  .  . 

48 

134 

57 

Gun-metal  

528 
56 

Quartz,  common,  pure. 
Rosin 

165 
69 

Gunpowder,  shaken.  .  .  . 

63 

Rope,  manila  

42 

Gunpowder   solid 

105 

Rottenstone 

124 

Gutta  percha  

61 
143 

Salt,  coarse  
Salt   West-Indies   well- 

45 

Hay,  alfalfa,  baled  .  . 

12.5  to  14.3 

dried  

74 

Hay      alfalfa      double 

Saltpeter 

131 

compressed  bales.  .  .  . 

25.53 

Shales  

162 

Hay     alfalfa     cylindri- 

Soil common 

124 

cal,      double      com- 

Soapstone   

170 

pressed  bales 

36.36 

Spelter  (zinc) 

437 

Hay,  clover,  baled  

14 

Straw  

19 

Hay        clover        corn- 

Sugar  

100 

24  ^ 

125 

Hay,  clover,  in  mow  .  .  . 
Hematite  iron  ore  

4.6 
306 

Talc,  block  
Tallow,  sheep  or  ox  .... 

181 
58 

Ice     

57 

Tar  

63 

58 

Trap  rock 

170 

Ivory  

114 

Turf,  or  peat  

20  to  30 

Land  plaster 

80 

Turnips       .        

•    44 

17 

68 

Macnesia.  carbonate.  .  . 

150 

Wheat.. 

48 

*Anthracite  increases  about  75%  in  bulk  when  broken  to  any  market 
size:  1  T.  loose,  averages  from  38  to  46  cu.  ft. 

|A  heaped  bushel,  loose,  weighs  about  74  lb.,  and  1  T.  occupies  from  43 
to  48  cu.  ft.  Bituminous  coal,  when  broken,  occupies  75%  more  space  than 
in  the  solid. 

JA  heaped  bushel,  loose,  weighs  from  35  to  42  lb.;  1  T.  occupies 
80  to  97  cu.  ft. 


286 


PROPERTIES  OF  MATERIALS 


PROPERTIES  OF  COAL 

SPECIFIC  GRAVITY  OF  AMERICAN  COALS 

(17.  5.  Bureau  of  Mines) 


Specific 

Gravity 

State 

County 

Locality 

Seam 

"S  59 

« 

.     -.. 

|| 

!l 

Alabama 

Walker 

Carbon  Hill 

Jagger 

1.32 

1.37 

Alabama 

Bibb 

Garnsey 

Underwood 

1.30 

1.38 

Alabama 

Bibb 

Belle  Ellen 

Youngblood 

1.28 

1.32 

Arkansas 

Sebastian 

Midland 

Hartshorne 

1.32 

1.44 

Illinois 

Williamson 

Bush 

No.  6 

1.31 

1.33 

Illinois 

Madison 

Donkville 

No.  6 

1.22 

1.26 

Illinois 

Logan 

Lincoln 

No.  5 

1.22 

1.31 

Illinois 

Sangamon 

Auburn 

No.  6 

1.24 

1.28 

Indiana 

Sullivan 

Hymera 

No.  5 

1.28 

1.42 

Indiana 

Sullivan 

Hymera 

No.  4 

1.25 

1.39 

Indiana 

Pike 

Littles 

No.  5 

1.27 

1.40 

Indiana 

Vigo 

Terre  Haute 

No.  7 

1.29 

1.30 

Indiana 

Vigo 

Macksville 

No.  7 

1.25 

1.36 

Indiana 

Park 

Rosedale 

No.  6 

1.24 

1.29 

Indiana 

Sullivan 

Dugger 

No.  4 

1.26 

1.30 

Indiana 

Pike 

Hartwell 

No.  5 

1.26 

1.32 

Kansas 
Kentucky 
Kentucky 
Kentucky 

Linn 
Bell 

Johnson 

Jewett 
Straight  Creek 
Big  Black  Mt. 
Paintsville 

Weir-Pittsburg 
Straight  Creek 
High  Splint 
No.  1 

1.23 
1.27 
1.29 
1.27 

1.34 
1.40 
1.30 
1.28 

Kentucky 

Muhlenburg 

Central  City 

No.  9 

1.31 

1.44 

Maryland 
Missouri 

Garrett 
Randolph 

Westernport 
Huntsville 

Lw.  Kittanning 

1.36 
1.21 

1.41 
1.36 

New  Mexico 

Colfax 

Van  Houten 

Raton 

1.29 

1.37 

New  Mexico 

Colfax 

Brilliant 

Raton 

1.30 

1.39 

New  Mexico 
North  Dakota 

Colfax 
Stark 

Blossburg 
Lehigh 

Raton 
Lignite 

1.31 
1.25 

1.35 

1.44 

North  Dakota 

McLean 

Wilton 

Lignite 

1.22 

1.23 

Ohio 

Jackson 

.      Wellston 

No.  4 

1.29 

1.35 

Ohio 

Jackson 

Wellston 

No.  5 

1.31 

1.36 

Ohio 

Perry 

Shawnee 

No.  6 

1.30 

1.33 

Ohio 

Jefferson 

Bradley 

No.  8 

1.30 

1.39 

Ohio 

Jefferson 

Rush  Run 

No.  8 

1.29 

1.33 

Ohio 

Guernsey 

Danford 

No.  7 

1.30 

1.34 

Ohio 

Perry 

Dixie 

No.  6  Hocking 

1.30 

1.42 

Ohio 

Vinton 

Clarion 

No.  4 

1.30 

1.36 

Pennsylvania 
Pennsylvania 
Pennsylvania 
Pennsylvania 
Pennsylvania 
Pennsylvania 
Pennsylvania 
Pennsylvania 
Tennessee 

Westmoreland 
Washington 
Washington 
Westmoreland 
Westmoreland 
Cambria 
Somerset 
Allegheny 
Campbell 

Greensburg 
Ellsworth 
Ellsworth 
East  Millsboro 
Ligonier 
Ehrenfeld 
Kimmelton 
Bruce 
Gatliff 

Pittsburg 
Pittsburg 
Pittsburg 
Pittsburg 
Pittsburg 
Lw.  Kittanning 
Lw.  Kittanning 
Pittsburg 
Log  Mountain 

1.30 
1.30 
1.28 
1.30 
1.33 
1.31 
1.35 
1.30 
1.28 

1.35 
1.31 
1.33 
1.33 
1.41 
1.36 
1.39 
1.36 
1.33 

Tennessee 
Tennessee 
Tennessee 

Campbell 
Roane 
Cumberland 

Gatliff 
Oliver  Springs 
Waldensia 

Regal  Block 
Wind  Rock 
Lower  Sewanee 

1.29 
1.29 
1.29 

1.32 
1.37 
1.31 

Tennessee 

Fentress 

Wilder 

Wilder 

1.34 

1.39 

PROPERTIES  OF  MATERIALS 
TABLE— (Continued) 


287 


Specific 

Gravity 

.    State 

County 

Locality 

Seam 

•Sg 

8>a 

It 

s  1* 

z| 

JH 

Tennessee 

White 

Clifty 

1st.  Abv.  Sewanee 

1.34 

1.37 

Tennessee 

Marion 

Orme 

Battle  Creek 

1.35 

Texas 

Milan 

Olsen 

Lignite 

1.25 

Texas 

Wood 

Hoyte 

Lignite 

1.26 

Virginia 

Lee 

Crab  Orchard 

Wilson 

.27 

1.32 

Virginia 

Lee 

Crab  Orchard 

McConnell 

.28 

1.37 

Virginia 

Wise 

Tom's  Creek 

Upper  Banner 

.27 

1.28 

Virginia 

Lee 

Darby 

Darby 

.28 

1.28 

Washington 

King 

Renton 

Black  Lignite 

.28 

.33 

Washington 
West  Virginia 
West  Virginia 

Kittitas 
Preston 
Fayette 

Roslyn 
Bretz 
Page 

Upper  Freeport 
Ansted 

.32 
.31 

.27 

.39 
.35 
.30 

West  Virginia 
West  Virginia 

Fayette 
Harrison 

Page 
Clarksburgh 

Eagle 
Pittsburg 

.27 

1.28 

1.28 
1.31 

West  Virginia 
West  Virginia 

Marion 
Preston 

Monongah 
Bretz 

Pittsburg 
Bakerstown 

1.29 
1.28 

1.35 
1.41 

West  Virginia 
West  Virginia 

Mingo 
Fayette 

Glen  Alum 
McDonald 

Glen  Alum 
Sewell 

1.30 
1.26 

1.34 
1.38 

West  Virginia 

Kanawha 

Acme 

Keystone 

1.27 

1.34 

West  Virginia 

Kanawha 

Winifrede 

Winifrede 

1.28 

1.34 

Wyoming 

Weston 

Cambria 

Cambria  Fuel  Co. 

1.31 

1.37 

Wyoming 

Crook 

Aladdin 

Stillwell  Coal  Co. 

1.28 

1.40 

Wyoming 

Carbon 

Hanna 

1.33 

1.35 

Wyoming 

Sweetwater 

Rock  Springs 

1.26 

1.30 

Wyoming 

Uinta 

Kemmerer 

1.28 

Average  of  70  American  Coals 

1.286 

1.348 

WEIGHTS  AND  MEASUREMENTS  OF  COAL 

(Coxe  Bros.  &=  Co.,  Chicago,  III.) 


Coal 

Weight  per 
Cubic  Foot 
Pounds 

He* 

fo  OH} 
yH0 

|fe§ 

6ftN 

Coal 

Weight  per 
Cubic  Foot 
Pounds 

$«3 

fe  Of-} 

ja 

Lehigh  lump  
Lehigh  cupola  
Lehigh  broken 

55.26 
55.52 
56.85 

36.19 
36.02 
35.18 

Free-burning  egg  — 
Free-burning  stove.  . 
Free-burning  nut  .  .  . 

56.07 
56.33 
56.88 

35.67 
35.50 
35.16 

Lehigh  egg  
Lehigh  stove  

57.74 
58.15 
58.26 

34.63 
34.39 
34.32 

Pittsburg  
Illinois  
Connellsville  coke.  .  . 

46.48 
47.22 
26.30 

43.03 
42.35 
76.04 

53  18 

37  60 

Hocking 

49.30 

40.56 

Lehigh  buckwheat 

54.04 

37.01 

Indiana  block  

43.85 

45.61 

Lehigh  dust  

57.25 

34.93 

Erie  
Ohio  cannel  

48.07 
49.18 

41.61 
40.66 

288  PROPERTIES  OF  MATERIALS 

AVERAGE  WEIGHT  AND  BULK  OF  AMERICAN  COALS 

(W.  R.  Johnson) 


Coal 

Specific 
Gravity 

Weight  of 
1  Cu.  Ft. 
Solid 
Pounds 

Weight  of 
1  Cu.  Ft. 
Heaped 
Pounds 

Bulk  of 
1  T.( 
Heaped 
Cubic  Feet 

1.  Anthracites  
2.  Bituminous,  free-burning.  . 
3.  Bituminous,  coking  
Average  of  1,  2,  and  3  . 
Foreign  and  Western  
Cokes                     

.500 
.358 
.342 
.400 
.318 

93.78 
84.93 
83.90 
87.54 
82.39 

53.05 
52.84 
49.28 
51.72 
49.31 
32.13 

42.35 
42.42 
45.71 
43.49 
45.51 
69.76 

SPECIFIC  GRAVITIES  OF  VARIOUS  COALS 


Name  of  Coal 

Specific 
Gravity 

Weight  of 
1  Cu.  Ft. 
Pounds 

Weight  of 
1  Cu.  Yd. 
Tons 

Newcastle  Hartley,  England  
Wigan  4  ft    England 

1.29 

.20 

80.6 
75.0 

.972 
.914 

Portland,  England  
Anthracite,  Wales  :  .  .  . 

.30 
.39 

81.2 
86.9 

.978 
1.047 

Eglington,  Scotland  ;.  .  .  . 

.25 
.59 

78.1 
99.4 

.941 
1.193 

Anthracite,  Pennsylvania  
Bituminous  Pennsylvania 

.55 

.40 

96.9 
87.5 

1.167 
1.054 

Block  coal,  Indiana  

.27 

79.4 

.956 

To  Mr.  Irving  A.  Stearns,  mining  engineer  and  former  general  superinten- 
dent of  the  Pennsylvania  Railroad  Co.'s  Coal  Department,  we  are  indebted 
for  the  following  summary  of  tests  made  by  the  mining  engineers  of  this  com- 
pany. Although  these  tests  were  made  25  yr.  ago,  they  are  still  of  value  as 

WEIGHT  OF  SUSQUEHANNA  COAL  CO.'S  WHITE  ASH  ANTHRACITE 


Size 

Size  of  Mesh, 
in  Inches 

Weight  per 
Cubic  Foot 

Cubic  Feet 
From  1 
Cubic  Foot 

Pounds 

of  Solid 

Over 

Through 

Lump  

4*  to  9 

57 

1.614 

Broken  

2|  to  2J 

3|  to  4 

53 

1.755 

Egg  

If  to2J 

2|  to  2 

52 

1.769 

Large  stove  
Small  stove. 

li  to  1 
1    to  1J 

If  to  2 
1  1  to  1 

5H 
51i 

1.787 
1  795 

Chestnut... 

1  to    - 

1    to  1 

51 

1.804 

Pea  

I  to    { 

f  to 

50f 

1.813 

No.  1  buckwheat  

&  to    ], 

ito 

50| 

1.813 

No.  2  buckwheat.  

A  to    f 

50| 

1.813 

giving  the  weight  of  anthracite,  but  the  sizes  corresponding  to  the  different 
grades  are  not  now  in  use.  Sizes  of  anthracite  should  be  taken  from  the 
table  Sizes  of  Prepared  Anthracite.  These  determina^ns  showed  an  average 
value  for  the  specific  gravity  of  the  coal  from  the  various  seams  upon  this 


PROPERTIES  OF  MATERIALS  289 

company's  property  of  1.4784,  together  with  an  average  weight  per  cubic  foot 
of  coal  in  the  solid  of  92.5  Ib. 

CONTENTS  OF  HORIZONTAL  COAL  SEAMS* 


Thickness  of  Seam 

Lignitef 
Tons  per  Acre 

Bituminoust 
Tons  per  Acre 

Anthracitef 
Tons  per  Acre 

Feet 

Inches 

1 

141.32 

152.62 

151.41 

2 

282.63 

305.24 

302.82 

3 

423.95 

457.87 

454.23 

4 

565.27 

610.49 

605.64 

5 

706.58 

763.11 

757.06 

6 

847.90 

915.73 

908.47 

7 

989.22 

1,068.35 

1,059.88 

8 

1,130.54 

1,220.98 

1,211.29 

9 

1,271.85 

1,373.60 

1,362.70 

10 

1,413.17 

1,526.22 

1,514.11 

11 

1,554.49 

1,678.84 

1,665.63 

1 

0 

1.695.80 

1,831.47 

1,816.93 

2 

0 

3,391.61 

3,662.93 

3,633.86 

3 

0 

5,087.41 

5,494.40 

5,450.79 

4 

0 

6,783.21 

7.325.87 

7,267.73 

5 

0 

8,479.01 

9,157.34 

9.084.66 

6 

0 

10,174.82 

10,988.80 

10,901.59 

7 

0 

11,870.62 

12,820.27 

12,718.52 

8 

0 

13,566.42 

14,651.74 

14,535.45 

9 

0 

15,262.23 

16,483.20 

16,352.38 

10 

0 

16,958.03 

18,314.67 

18,169.32- 

Mr.  Robert  A.  Quin,  Manager  Susquehanna  Coal  Co.,  has  very  kindly 
furnished  the  two  following  tables.  The  first  shows  the  present  (1914)  sizes  of 
anthracite,  and  the  second  shows  the  number  of  cubic  feet  per  ton  occupied  by 
each  of  these  sizes,  according  to  the  region  in  which  it  is  mined. 

SIZES  OF  PREPARED  ANTHRACITE 


Size 

Through 

Over 

Square 
Inches 

Round 
Inches 

Square 
Inches 

Roi 
Inc 

I 

3J 

2 

1; 

ii 

and 

hes 

• 
r 

51 

\> 

1| 
i 

6 
4 
3 
2 
1 

i 

. 

y 

i5 
I1 
'i 

Steamboat  

Broken  
Egg  

Stove         

Chestnut               

Pea 

No.  1  Buckwheat  
No.  2  Buckwheat  
No.  3  Buckwheat  

*  This  table  is  based  on  the  average  specific  gravity  of  American  coals. 
t  The  contents  of  the  bituminous  coal  and  lignite  is  given  in  tons  of  2,000 
Ib.;  the  contents  of  anthracite  seams,  in  tons  of  2,240  Ib. 


290  PROPERTIES  OF  MATERIALS 

CUBIC  FT.  IN  1  T.  OF  ANTHRACITE  BROKEN  IN  TRADE  SIZES 


Size 

Wyoming 
Region 
Cubic  Feet 

Shamokin 
Region 
Cubic  Feet 

Schuylkill 
Region 
Cubic  Feet 

Lykens 
Region 
Cubic  Feet 

37.713 

Steamboat  

38.55 

38.00 

39.03 

40.138 

38.60 

43.00 

Egg     

38.66 

42.499 

39.40 

43.41 

Stove                

37.72 

41.559 

40.30 

43.92 

Nut                                    

40.43 

42.308 

41.00 

44.78 

Pea                

41.63 

42.692 

41.70 

45.16 

No.  1  Buckwheat  
No.  2  Buckwheat  
No.  3  Buckwheat  

41.96 
42.65 
43.36 

45.373 
43.282 
43.686 

42.30 
43.10 
43.90 

45.71 
46.09 

WEIGHTS  OF  ENGLISH  AND  FRENCH  COALS 
[Delabeche  &•  Playfair  (D.  K.  Clark)  ] 


Name  of  Coal 

Specific 
Gravity 

Weight  of 
1  Cu.  Ft. 

Cubic 
Feet 
in  1  T. 
Heaped 

Solid 

Heaped 

Wales.     Anthracite                   

1.370 
1.390 
1.280 
1.315 
.310 
.250 
.256 
.296 
.280 
.270 
.285 
.292 

.350 
.230 
.273 
.290 
.200 
1.259 
1.590 

85.4 
86.7 
80.3 
82.3 
81.8 
78.0 
78.3 
80.8 
79.8 
79.8 
79.6 
79.6 

84.1 
76.8 
79.4 
80.5 
74.8 
78.6 
99.6 

58.3 
53.3 
53.1 
53.1 
52.0 
49.1 
49.8 
47.2 
47.4 
49.9 
45.9 
45.9 

52.6 
48.3 
49.7 
54.3 
54.6 
50.0 
62.8 
55.0 
54.3 
53.7 
53.1 
52.5 
51.8 
50.0 
49.3 
52.5 
56.2 

38.4 
42.0 
42.0 
42.7 
43.1 
45.6 
45.3 
47.4 
47.3 
44.9 
48.8 
47.4 

42.6 
46.4 
45.2 
40.1 
41.0 
42.0 
35.7 
40.8 
41.2 
41.7 
42.2 
42.7 
43.2 
44.8 
45.4 
42.75 
40.0 

Port  Mawr  (highest) 

Llynvi  (one  of  the  lowest)  
Average  of  37  samples  

Newcastle.     Hedley's  Hartley  (highest) 
Original  Hartley  (one  of  the  lowest)  . 
Average  of  18  samples  
Derbyshire  and  Yorkshire.     Elsecar.  .    . 
Butterley  

Stavely  

Loscoe  soft 

Average  of  7  samples  
Lancashire.       Laffack      Bushy      Park 
(highest)  

Cannel,  Wigan  (lowest)  
Average  of  28  samples  
Scotland.     Grangemouth  (highest)  
Wallsend,  Elgin 

Average  of  8  samples  
Ireland.     Slievardagh,  Anthracite  
France.     Labarthe  
Auvergne  and  Blanzy  .  . 

Combelle  .   . 

Lataupe 

Saint  Etienne  

Decise.  . 

Mons  

Creusot 

Average  of  French  bituminous  coals  . 
Anthracite  

WIRE  AND  SHEET-METAL  GAUGES 

TABLE  OF  WIRE  AND  SHEET-METAL  GAUGES 


Number 
of 
Gauge 

U.S. 
Standard 
Gauge  for 
Sheet  and 
Plate  Iron 
and  Steel. 
Inch* 

British 
Imperial 
Standard 
Wire  Gauge. 
Millim.t 

Bir- 
ming- 
ham 
Gauge 
Inch 

Ameri- 
can or 
Brown 
& 
Sharpe 
Gauge 
Inch 

Roeb- 
ling's 
Gauge 
Inch 

Tren- 
ton 
Iron 
Co.  'a 
Wire 
Gauge 
Inch 

English 
Legal 
Stan- 
dard 

Inch 

0000000 

.5 

12.7 

.49 

.500 

000000 

.469 

11.78 

.46 

.464 

00000 

.438 

10.97 

.43 

.45 

.432 

0000 

.406 

10.16 

.454 

.46 

.393 

.40 

.4 

000 

.375 

9.45 

.425 

.40964 

.362 

.36 

.372 

00 

.344 

8.84 

.38 

.3648 

.331 

.33 

.348 

0 

.313 

8.23 

.34 

.32486 

.307 

.305 

.324 

1 

.281 

7.62 

.3 

.2893 

.283 

.285 

.3 

2 

.266 

7.01 

.284 

.25763 

.263 

.265 

.276 

3 

.25 

6.4 

.259 

.22942 

.244 

.245 

.252 

4 

.234 

5.89 

-.238 

.20431 

.225 

.225 

.232 

5 

.219 

5.38 

.22 

.18194 

.207 

.205 

.212 

6 

.203 

4.88 

.203 

.16202 

.192 

.19 

.192 

7 

.188 

4.47 

.18 

.14428 

.177 

.175 

.176 

8 

.172 

4.06 

.165 

.12849 

.162 

.16 

.16 

9 

.156 

3.66 

.148 

.11443 

.148 

.145 

.144 

10 

.141 

3.26 

.134 

.10189 

.135 

.13 

.128 

11 

.125 

2.95 

.12 

.09074 

.12 

.1175 

.116 

12 

.109 

2.64 

.109 

.08081 

.105 

.105 

.104 

13 

.094 

2.34 

.095 

.07196 

.092 

.0925 

.092 

14 

.078 

2.03 

.083 

.06408 

.08 

.08 

.08 

15 

.07 

1.83 

.072 

.05707 

.072 

.07 

.072 

16 

.0625 

1.63 

.065 

.05082 

.063 

.061 

.064 

17 

.0563 

1.42 

.058 

.04526 

.054 

.0525 

.056 

18 

.05 

1.22 

.049 

.0403 

.047 

.045 

.048 

19 

.0438 

1.01 

.042 

.03589 

.041 

.04 

.04 

20 

.0375 

.91 

.035 

.03196 

.035 

.035 

.036 

-  21 

.0344 

.81 

.032 

.02846 

.032 

.031 

.032 

22 

.0313 

.71 

.028 

.02535 

.028 

.028 

.028 

23 

.0281 

.61 

.025 

.02257 

.025 

.025 

.024 

24 

.025 

.56 

.022 

.0201 

.023 

.0225 

.022 

25 

.0219 

.51 

.02 

.0179 

.02 

.02 

.02 

26 

.0188 

.45 

.018 

.01594 

.018 

.018 

.018 

27 

.0172 

.42 

.016 

.01419 

.017 

.017 

.0164 

28 

.0156 

.38 

.014 

.01264 

.016 

.016 

.0148 

29 

.0141 

.35 

.013 

.01126 

.015 

.015 

.0136 

30 

.0125 

.31 

.012 

.01002 

.014 

.014 

.0124 

31 

.0109 

.29 

.01 

.00893 

.0135 

.013 

.0116 

32 

.0101 

.27 

.009 

.00795 

.013 

.012 

.0108 

33 

.0094 

.25 

.008 

.00708 

.011 

.011 

.01 

34 

.0086 

.23 

.007 

.0063 

.01 

.01 

.0092 

35 

.0078 

.21 

.005 

.00561 

.0095 

.0095 

.0084 

36 

.007 

.19 

.004 

.005 

.009 

.009 

.0076 

37 

.0066 

.17 

.00445 

.0085 

.0085 

.0068 

38 

.0063 

.15 

.00396 

.008 

.008 

.006 

39 

.13 

.00353 

.0075 

.0075 

.0052 

40 

.12 

.00314 

.007 

.007 

.0048 

41 

.11 

.0044 

42 

.10 

.004 

43 

.09 

.0036 

44 

.08 

.0032 

45 

.07 

.0028 

46 

.06 

.0024 

47 

.05 

.002 

48 

.04 

.0016 

49 

.03 

.0012 

50 

.025 

.001 

291 


*  Legal  standard 


t  Legal  standard  in  Great  Britain 


292 


PROPERTIES  OF  MATERIALS 
STANDARD  DECIMAL  GAUGE* 


Thickness 

Weight  of 
Square  Foot, 

Thickness 

Weight  of 
Square  Foot, 

in  Pounds 

in  Pounds 

Deci- 
mal 
Inch 

Frac- 
tion 
Inch 

Milli- 
meters 

Iron 

Steel 

Deci- 
mal 
Inch 

Frac- 
tion 

Inch 

Milli- 
meters 

Iron 

Stejel 

.002 

.0508 

.08 

.082 

.060 

ft 

1.5240 

2.40 

2.448 

.004 
.006 

*fe 

.1016 
.1524 

.16 
.24 

.163 
.245 

.065 
.070 

1 

1.6510 
1.7780 

2.60 
2.80 

2.652 
2.856 

.008 

nv 

.2032 

.32 

.326 

.075 

1.9050 

3.00 

3.060 

.010 

TI 

.2540 

.40 

.408 

.080 

5\ 

2.0320 

3.20 

3.264 

012 

Tffff 

.3048 

.48 

.490 

.085 

17 

2.1590 

3.40 

3.468 

!014 
.016 

yjff 

.3556 
.4064 

.56 
.64 

.571 
.653 

.090 
.095 

t 

2.2860 
2.4130 

3.60 
3.80 

3.672 
3.876 

.018 

9 

.4572 

.72 

.734 

.100 

2.5400 

4.00 

4.080 

.020 

1 

.5080 

.80 

.816 

.110 

2.7940 

4.40 

4.488 

.022 

I? 

.5588 

.88 

,898 

.125 

3.1750 

5.00 

5.100 

.025 
.028 

i 

.6350 
.7112 

1.00 
1.12 

1.020 
1.142 

.135 
.150 

* 

3.4290 
3.8100 

5.40 
6.00 

5.508 
6.120 

.032 

.8128 

1.28 

1.306 

.165 

fijtg 

4.1910 

6.60 

6.732 

.036 

fl.' 

.9144 

1.44 

1.469 

.180 

& 

4.5720 

-7.20 

7.344 

.040 

'.i  i 

1.0160 

1.60 

1.632 

.200 

i 

5.0800 

8.00 

8.160 

.045 

a 

1.1430 

1.80 

1.836 

.220 

il 

5.5880 

8.80 

8.976 

.050 

15 

1.2700 

2.00 

2.040 

.240 

6.0960 

9.60 

9.792 

.055 

ft 

1.3970 

2.20 

2.244 

.250 

6.3500 

10.00 

10.200 

*  The  weights  per  square  foot  of  sheet  metal  given  in  this  table  are  based  on 
a  weight  of  480  Ib.  per  cu.  ft.,  for  iron  and  one  of  489.6  Ib.  per  cu.  ft.  for  steel. 


MISCELLANEOUS  TABLES 

WEIGHT  OF  WROUGHT-IRON  BOLTHEADS,  NUTS,  AND 
WASHERS 


Diameter  of 
Bolt 
Inches 

Hexagon  Heads 
and  Nuts 
Per  Pair 

Square  Heads 
and  Nuts 
Per  Pair 

Round  Washers 
Per  Pair 

20    to  1  Ib. 

16    to  lib. 

20  to  1  Ib. 

10    to  1  Ib. 

81  to  1  Ib. 

10  to  1  Ib. 

5    to  1  Ib. 

4|  to  1  Ib. 

5  to  1  Ib. 

2f  to  1  Ib. 

2i  to  1  Ib. 

3  to  1  Ib. 

2    to  1  Ib. 

.56  Ib. 

.63  Ib. 

.77  Ib. 

.88  Ib. 

.77  Ib. 

1 

1.25  Ib. 

1.31  Ib. 

1.25  Ib. 

1 

\ 

1.75  Ib. 

2.10  Ib. 

1.75  Ib. 

1 

2.13  Ib. 

2.56  Ib. 

2.25  Ib. 

1 

3.00  Ib. 

3.60  Ib. 

3.25  Ib. 

1 

3.75  Ib. 

4.42  Ib. 

4.25  Ib. 

1 

\ 

4.75  Ib. 

5.70  Ib. 

5.25  Ib. 

1 

i 

5.75  Ib. 

7.00  Ib. 

6.50  Ib. 

ll 

7.27  Ib. 

8.72  Ib. 

8.00  Ib. 

2 

8.75  Ib. 

10.50  Ib. 

9.60  Ib. 

PROPERTIES  OF  MATERIALS 


293 


WEIGHTS  OF  SHEETS  AND  PLATES  OF  STEEL,  WROUGHT  IRON, 
COPPER,  AND  BRASS 

(Cambria  Steel  Co) 


American, 
or  Brown 
&  Sharpe, 
Gauge 
Number 

Thickness 
Inch 

Weight  Per  Square  Foot,  in  Pounds 

Steel 

Iron 

Copper 

Brass 

0000 

.460000 

18.7680 

18.4000 

20.8380 

19,6880 

000 

.409642 

16.7134 

16.3857 

18.5568 

17.5327 

00 

.364796 

14.8837 

14.5918 

16.5253 

15.6133 

0 

.324861 

13.2543 

12.9944 

14.7162 

13.9041 

1 

.289297 

11.8033 

11.5719 

13.1052 

12.3819 

2 

.257627 

10.5112 

10.3051 

11.6705 

11.0264 

3 

.229423 

9.3605 

9.1769 

10.3929 

9.8193 

4 

.204307 

8.3357 

8.1723 

9.2551 

8.7443 

5 

.181940 

7.4232 

7.2776 

8.2419 

7.7870 

6 

.162023 

6.6105 

6.4809 

7.3396 

6.9346 

7 

.144285 

5.8868 

5.7714 

6.5361 

6.1754 

8 

.128490 

5.2424 

5.1396 

5.8206 

5.4994 

9 

.114423 

4.6685 

4.5769 

5.1834 

4.8973 

10 

.101897 

4.1574 

4.0759 

4.6159 

4.3612  / 

11 

.090742 

3.7023 

3.6297 

4.1106 

3.8838 

12 

.080808 

3.2970 

3.2323 

3.6606 

3.4586 

13 

.071962 

2.9360 

2.8785 

3.2599 

3.0800 

14 

.064084 

2.6146 

2.5634 

2.9030 

2.7428 

15 

.057068 

2.3284 

2.2827 

2.5852 

2.4425 

16 

.050821 

2.0735 

2.0328  - 

2.3022 

2.1751 

17 

.045257 

1.8465 

1.8103 

2.0501 

1.9370 

18 

.040303 

1.6444 

1.6121 

1.8257 

1.7250 

19 

.035890 

1.4643 

1.4356 

1.6258 

1.5361 

20 

.031961 

1.3040 

1.2784 

1.4478 

1.3679 

21 

.028462 

1.1612 

1.1385 

1.2893 

1.2182 

22 

.025346 

1.0341 

1.0138 

1.1482 

1.0848 

23 

.022572 

.92094 

.90288 

1.0225 

.96608 

24 

.020101 

.82012 

.80404 

.91058 

.86032 

25 

.017900 

.73032 

.71600 

.81087 

.76612 

26 

.015941 

.65039 

.63764 

.72213 

.68227 

27 

.014195 

.57916 

.56780 

.64303 

.60755 

28 

.012641 

.51575 

.50564 

.57264 

.54103 

29 

.011257 

.45929 

.45028 

.50994 

.48180 

30 

.010025 

.40902 

.40100 

.45413 

.42907 

31 

.008928 

.36426 

.35712 

.40444 

.38212 

32 

.007950 

.32436 

.31800 

.36014 

.34026 

33 

.007080 

.28886 

.28320 

.32072 

.30302 

34 

.006305 

.25724 

.25220 

.28562 

.26985 

35 

.005615 

.22909 

.22460 

.25436 

.24032 

36 

.005000 

.20400 

.20000 

.22650 

.21400 

37 

.004453 

.18168 

.17812 

.20172 

.19059 

38 

.003965 

.16177 

.15860 

.17961 

.16970 

39 

.003531 

.14406 

.14124 

.15995 

.15113 

40 

.003144 

.12828 

.12576 

.14242 

.13456 

204 


PROPERTIES  OF  MATERIALS 


WEIGHT  OF  CAST-IRON  PIPE  PER  FT.,  IN  POUNDS* 


DiaTYi 

Thickness  of  Pipe,  in  Inches 

-L/icirn- 
eter  of 
Pipe 

TnrVif><; 

1 

t 

i 

I 

! 

* 

1 

It 

U 

H 

H  H 

2 

incnes 

Weight  of  Pipe,  in  Pounds 

1 

3.07 

5.07 

7.38 

11 

3.69 

6.00 

8.61 

if 

4.30 

6.92 

9.84 

if 

4.92 

7.84 

11.10 

2 

5.53 

8.76 

12.30 

16.2 

2i 

6.15 

9.69 

13.50 

17.7 

2i 

6.76 

10.60 

14.80 

19.2 

24.0 

2f 

7.37 

11.50 

16.00 

20.8 

25.9 

3 

7.98 

12.50 

17.20 

22.3 

27.7 

33.4 

31 

9.21 

14.30 

19.70 

25.4 

31.4 

37.7 

4 

10.30 

16.10 

22.20 

28.5 

35.1 

42.0 

41 

11.70 

18.00 

24.60 

31.5 

38.8 

46.3 

- 

5 

12.90 

19.80 

27.10 

34.6 

42.5 

50.6 

5* 

14.20 

21.70 

29.50 

37.7 

46.1 

54.9 

»   6 

15.40 

23.50 

32.00 

40.8 

49.8 

59.2 

68.9 

6i 

16.60 

25.40 

34.50 

43.8 

53.5 

63.5 

73.8 

84.4 

7 

17.80 

27.20 

36.90 

46.9 

57.2 

67.8 

78.7 

89.4 

7i 

19.10 

29.10 

39.40 

50.0 

60.9 

72.1 

83.7 

95.5 

108 

8 

20.30 

30.90 

41.80 

53.1 

64.6 

76.4 

88.6 

101.0 

114 

127 

8| 

21.50 

32.80 

44.30 

56.1 

68.3 

80.7 

93.5 

107.0 

120 

134 

148 

9 

22.80 

34.60 

46.80 

59.2 

72.0 

85.1 

98.4 

112.0 

126 

140 

155 

9* 

24.00 

36.40 

49.20 

62.3 

75.7 

89.3 

103.0 

118.0 

132 

147 

163 

10 

25.10 

38.30 

51.70 

65.3 

79.4 

93.6 

108.0 

123.0 

138 

164 

170 

202 

11 

27.60 

42.00 

56.60 

71.5 

86.7 

102.0 

118.0 

134.0 

151 

168 

185 

220 

12 

30.00 

45.70 

61.50 

77.7 

94.1 

111.0 

128.0 

145.0 

163 

181 

199 

237 

275 

13 

32.50 

49.40 

66.40 

83.8 

102.0 

120.0 

138.0 

156.0 

175 

195 

214 

254 

294 

14 

35.00 

53.10 

71.40 

89.4 

109.0 

128.0 

148.0 

168.0 

188 

208 

229 

271 

314 

15 

37.40 

56.70 

76.30 

96.1 

116.0 

137.0 

158.0 

179.0 

200 

222 

244 

289 

334 

16 

39.10 

60.40 

81.20 

102.0 

124.0 

145.0 

167.0 

190.0 

212 

235 

258 

306 

353 

17 

42.30 

64.10 

86.10 

108.0 

131.0 

154.0 

177.0 

201.0 

225 

249 

273 

323 

373 

18 

44.80 

67.80 

91.00 

115.0 

139.0 

163.0 

187.0 

212.0 

237 

262 

288 

340 

393 

19 

47.30 

71.50 

96.00 

121.0 

146.0 

171.0 

197.0 

223.0 

249 

276 

303 

357 

412 

20 

49.70 

75.20 

101.00 

127.0 

153.0 

180.0 

207.0 

234.0 

261 

289 

317 

375 

432 

21 

52.20 

78.90 

106.00 

133.0 

161.0 

188.0 

217.0 

245.0 

274 

303 

332 

392 

452 

22 

54.60 

82.60 

111.00 

139.0 

168.0 

196.0 

227.0 

256.0 

286 

316 

347 

409 

471 

23 

57.10 

86.30 

116.00 

145.0 

175.0 

206.0 

236.0 

267.0 

298 

330 

362 

426 

491 

24 

59.60 

89.90 

121.00 

152.0 

183.0 

214.0 

246.0 

278.0 

311 

343 

375 

444 

511 

25 

62.00 

93.60 

126.00 

158.0 

190.0 

223.0 

256.0 

289.0 

323 

357 

391 

461 

531 

26 

64.50 

97.30 

131.00 

164.0 

198.0 

231.0 

266.0 

300.0 

335 

370 

406 

478 

550 

27 

66.90 

101.00 

135.00 

170.0 

205.0 

240.0 

276.0 

311.0 

348 

384 

421 

495 

570 

28 

69.40 

105.00 

140.00 

176.0 

212.0 

249.0 

286.0 

323.0 

360 

397 

436 

512 

590 

29 

71.80 

109.00 

145.00 

182.0 

220.0 

257.0 

295.0 

334.0 

372 

411 

450 

530 

609 

30 

74.20 

112.00 

150.00 

188.0 

227.0 

266.0 

305.0 

345.0 

384 

424 

465 

547 

629 

*  These  weights  are  for  plain  pipe.  For  hautboy  pipe,  add  8  in.  in  length 
for  each  joint.  For  copper,  add  |;  for  lead,  f;  for  welded  iron,  ^. 

PROPERTIES  OF  MATERIALS  295 

CONTENTS  OF  CYLINDERS  OR  PIPES  FOR  1  FT.  IN  LENGTH* 

DIAMETERS  IN  INCHES 


$ 

fj| 

^    --d 

"o.c.S  % 

| 

*1l 

i*i 

•8S.sf 

ff  -S 

Jdw^ 

iUrf'S 

1  1 

g'Sfe 

g.^W'd 

£  4>  «>  J 

1    G 

§Q     «5 

wi  & 

•sfS'S's 

S   « 

rtQ  rt 

|^a5§ 

•§cJ  C'g 

Q~ 

s.s° 

Oc3iD 

**!*! 

s  w 

p.s° 

°^5 

e^l£ 

j 

.0208 
.0417 

.0025 
.0102 

.02122 
.08488 

5 

5i 

.4167 
.4583 

1.020 
1.234 

8.488 
10.270 

1 

.0625 

.0230 

.19098 

6 

.5000 

1.469 

12.223 

I* 

.0833 

.0408 

.33952 

6* 

.5417 

1.724 

14.345 

H 

.1042 

.0638 

.53050 

r 

.5833 

1.999 

16.636 

H 

.1250 

.0918 

.76392 

.6250 

2.295 

19.098 

11 

.1458 

.1249 

1.0398 

82 

.6667 

2.611 

21.729 

2* 

.1667 

.1632 

1.3581 

8i 

.7083 

2.948 

24.530 

.1875 

.2066 

1.7188 

9 

.7500 

3.305 

27.501 

2| 

.2083 

.2550 

2.1220 

9i 

.7917 

3.682 

30.641 

21 

.2292 

.3085 

2.5676 

10 

.8333 

4.080 

33.952 

3 

.2500 

.3672 

3.0557 

101 

.8750 

4.498 

37.432 

.2917 

.4998 

4.1591 

11 

.9167 

4.937 

41.082 

4* 

.3333 

.6528 

5.4323 

1H 

.9583 

5.396 

44.901 

.3750 

.8263 

6.8750 

12 

1.0000 

5.875 

48.891 

DIAMETERS  IN  FEET 


H 

1.25 

9.18 

76.392 

10 

10.00 

587.6 

4,889.12 

li 

1.50 

13.22 

110.00 

10| 

10.50 

647.7 

5,404.24 

li 

1.75 

'17.99 

149.73 

11 

11.00 

710.9 

5,915.84 

2 

2.00 

23.50 

195.56 

HI 

11.50 

777.0 

6,485.72 

2i 

2.25 

29.74 

247.51 

12 

846.1 

7,040.00 

2$ 

2.50 

36.72 

305.57 

13 

992.8 

8,710.00 

2f 

2.75 

44.43 

369.74 

14 

1,152.0 

10,096.00 

3 

3.00 

52.88 

440.00 

15 

1,322.0 

11,000.50 

3J 

3.25 

65.28 

544.37 

16 

1,504.0 

12,516.00 

3i 

3.50 

71.97 

631.00 

17 

1,698.0 

14,166.00 

3| 

3.75 

82.62 

687.53 

18 

1,904.0 

15,841.00 

4 

4.00 

94.0 

782.24 

19 

2,121.0 

17,691.00 

4i 

4.25 

106.1 

885.40 

20 

2,350.0 

19,556.50 

4i 

4.50 

119.0 

990.04 

21 

2,591.0 

21,617.00 

4| 

4.75 

132.5 

,105.71 

22 

2,844.0 

23,663.00 

5 

5.00 

146.9 

,222.28 

23 

3,108.0 

25,943.00 

5J 

5.25 

161.9 

,351.06 

24 

3,384.0 

28,160,00 

5| 

5.50 

177.7 

,478.96 

25 

3,672.0 

30,557.00 

5f 

5.75 

194.3 

,621.43 

26 

3,971.0 

34,840.00 

6 

6.00 

211.5 

,760.00 

27 

4,283.0 

35,641.00 

6i 

6.25 

229.5 

1,915.18 

28 

4,606.0 

40,384.00 

6i 

6.50 

248.2 

2,177.48 

29 

4,941.0 

41,117.00 

6f 

6.75 

267.7 

2,233.96 

30 

5,288.0 

44,002.00 

7 

7.00 

287.9 

2,524.00 

31 

5,646.0 

46,984.00 

7i 

7.50 

330.5 

2,750.12 

32 

6,017.0 

50,064.00 

8 

SAM) 

376.0 

3.128.96 

33 

6,398.0 

53,242.00 

8i 

8.50 

424.5 

3,541.60 

34 

6,792.0 

56,664.00 

9 

9.00 

475.9 

3,960.16 

35 

7,197.0 

59,891.50 

9i 

9.50 

530.2 

4,422.84 

36 

7,614.0 

63,364.00 

*  The  contents  of  pipes  or  cylinders  in  gallons  or  pounds  are  to  each  other 
as  the  squares  of  their  diameters.  Thus,  a  pipe  9  ft.  in  diameter  will  contain 
9  times  as  much  as  a  3-ft.  pipe,  or  4  times  as  much  as  a  4^-ft.  pipe. 


296  PROPERTIES  OF  MATERIALS 

STANDARD    DIMENSIONS    OF    WROUGHT-IRON    WELDED    PIPES 


u 

u 

ll 

^£ 

M 

1 

1 

1 

1 

1 

!3.g 

§.s 

ctf 

S& 

J 

8 

Sg 

g 

a 

w 

P 

c 

#8 

w  8 

g 

.s 

£ 

&£ 

2J| 

rt   w 

S| 

ll 
HM 

JZ 

sl 

13  £ 
a 

ll 
U£ 

11 

0  £ 
13 

^•2 
.1*3 

^ 
0,3 

<UCO 

<z 
11 

fi 

£ 

c 

6-3 

a§ 

f<2 

££! 

li 

1 

w 

1 

c 

"x 
W 

£j  g 

M1-1 

21 

"c 

"bo'S 

in 

13 

& 

!* 

3° 

<u*o 

0 

i 

.40 

.068 

.27 

.85 

1.27 

14.15 

9.440 

.057 

2,513.0 

.002 

.24 

27 

.54 

.088 

.36 

1.14 

1.70 

10.50 

7.075 

.104 

1,383.3 

.002 

.42 

18 

1 

.67 

.091 

.49 

1.55 

2.12 

7.67 

5.657 

.192 

751.2 

.005 

.56 

18 

£ 

.84 

.109 

.62 

1.96 

2.65 

6.13 

4.502 

.305 

472.4 

.010 

.84 

14 

3 

1.05 

.113 

.82 

2.59 

3.30 

4.64 

3.637 

.533 

270.0 

.023 

1.13 

14 

1 

1.31 

.134 

1.05 

3.29 

4.13 

3.66 

2.903 

.863 

166.9 

.040 

1.67 

114 

1.66 

.140 

1.38 

4.33 

5.21 

2.77 

2.301 

1.496 

96.25 

.063 

2.26 

111 

14 

1.90 

.145 

1.61 

5.06 

5.97 

2.37 

2.010 

2.038 

70.66 

.091 

2.69 

114 

2 

2.37 

.154 

2.07 

6.49 

7.46 

1.85 

1.611 

•3.355 

42.91 

.163 

3.67 

114 

24 

2.87 

.204 

2.47 

7.75 

9.03 

1.55 

1.328 

4.783 

30.10 

.255 

5.77 

8 

3 

3.50 

.217 

3.07 

9.64 

11.00 

1.24 

1.091 

7.388 

19.50 

.367 

7.55 

8 

34 

4.00 

.226 

3.55 

11.15 

12.57 

1.08 

0.955 

9.887 

14.57 

.500 

9.05 

8 

4 

4.50 

.237 

4.03 

12.65 

14.14 

.95 

0.849 

12.730 

11.31 

.652 

10.73 

8 

5.00 

.247 

4.51 

14.15 

15.71 

.85 

0.765 

15.939 

9.02 

.826 

12.49 

8 

53 

5.56 

.259 

5.04 

15.85 

17.47 

.78 

0.629 

19.990 

7.20 

1.02 

14.56 

8 

6 

6.62 

.280 

6.06 

19.05 

20.81 

.63 

0.577 

28.889 

4.98 

1.46 

18.77 

8 

7 

7.62 

.301 

7.02 

22.06 

23.95 

.54 

0.505 

38.737 

3.T2 

2.00 

23.41 

8 

8 

8.62 

.322 

7.98 

25.08 

27.10 

.48 

0.444 

50.039 

2.88 

2.61 

28.35 

8 

9 

9.69 

.344 

9.00 

28.28 

30.43 

.42 

0.394 

63.633 

2.29 

3.30 

34.08 

8 

10 

10.75 

.366 

10.02 

31.47 

33.77 

.38 

0.355 

78.838 

1.82 

4.08 

40.64 

8 

STRENGTH  OF  METALS  PER  SQUARE  INCH 


Material 

Ulti- 
mate 
Tensile 
Pounds 

Ulti- 
mate 
Com- 
pression 
Pounds 

Ulti- 
mate 
Shear- 
ing 
Pounds 

Modu- 
lus of 
Rupture 
Pounds 

Modu- 
lus of 
Elas- 
ticity 
Millions 

Wrought  iron  
Shape  iron  . 

50,000 
48  000 

44,000 

44,000 

48,000 

27 
2fi 

Structural  steel  | 

60,000 

Cast  iron 

65,000 
18  000 

52,000 
81  000 

52,000 
2^  nnn 

60,000 
A~  f)(\o 

29 

Steel,  castings.  .  . 

70  000 

70  000 

60  000 

70  000 

30 

Brass,  cast 

24  000 

*30  000 

on  ooo 

on  nnn 

Bronze,  phosphor.  .  . 

50  000 

14 

Bronze,  aluminum  
Aluminum,  commercial  

75,000 
15,000 

120,000 
12,000 

12,000 

11 

*Unit  stress  producing  10%  reduction  in  original  length. 


PROPERTIES  OF  MATERIALS 
STANDARD  AND  EXTRA-GAUGE  STEEL  BOILER  TUBES 


297 


Out- 

Standard 
Thickness 

Nominal  Weight  per  Foot,  in 
Pounds 

side 

Diam- 

Nearest 

Stand- 

One 

Two 

Three 

Four 

eter 

Birm. 

ard 

Extra 

Extra 

Extra 

Extra 

Inches 

Wire 

Inch 

Thick- 

Wire 

Wire 

Wire 

Wire 

Gauge 

ness 

Gauge 

Gauges 

Gauges 

Gauges 

1 

13 

.095 

.90 

1.04 

1.13 

1.24 

1.35 

H 

13 

.095 

1.15 

1.33 

1.45 

1.60 

1.74 

H 

13 

.095 

1.40 

1.62 

1.77 

1.96 

2.14 

1J 

13 

.095 

1.66 

1.91 

.    2.09 

2.31 

2.53 

^ 

13 

.095 

1.91 

2.20 

2.41 

2.67 

2.93 

2J 

13 

.095 

2.16 

2.49 

2.73 

3.03 

3.32 

2£ 

12 

.109 

2.75 

3.05 

3.39 

3.72 

4.12 

2f 

12 

.109 

3.04 

3.37 

3.74 

4.11 

4.56 

3 

12 

.109 

3.33 

3.69 

4.10 

4.51 

5.00 

3i 

11 

.120 

3.96 

4.46 

4.90 

5.44 

5.90 

3J 

11 

.120 

4.28 

4.82 

5.30 

5.88 

6.38 

31 

11 

.120 

4.60 

5.18 

5.69 

'     6.32 

6.86 

4 

10 

.134 

5.47 

6.09 

6.76 

7.34 

8.23 

4| 

10 

.134 

6.17 

6.88 

7.64 

8.31 

9.32 

5 

9 

.148 

7.58 

8.52 

9.27 

10.40 

11.23 

6 

8 

.165 

10.16 

11.19 

12.57 

13.58 

14.65 

7 

8 

.165 

11.90 

13.11 

14.74 

15.93 

17.19 

8 

8 

.165 

13.65 

15.04 

16.91 

18.28 

19.73 

9 

7 

.180 

16.76 

19.07 

20.63 

22.27 

24.18 

10 

6 

.203 

21.00 

22.98 

24.82 

26.95 

29.47 

11 

5 

.220 

25.00 

27.36 

29.71 

32.51 

34.29 

12 

4£ 

.229 

28.50 

31.19 

34.01 

36.52 

39.92 

13 

4 

.238 

32.06 

35.25 

38.57 

40.70 

45.98 

STANDARD  LAP-WELDED  CHARCOAL-IRON  BOILER  TUBES 


Length  of 

Diameter 
Inches 

Thick- 

Circumference 
Inches 

Transverse  Area 
Square  Inches 

Tube  in  Feet 
per  Square 
Foot  of 

Weight 
per 

ness 

Surface 

Foot 

Inch 

P         H 

Out- 

In- 

Out- 

In- 

Out- 

In- 

Out- 

In- 

oun s 

side 

side 

side 

side 

side 

side 

side 

side 

1 

.810 

.095 

3.142 

2.545 

.785 

.515 

3.820 

4.479 

.90 

u 

1.060 

.095 

3.927 

3.330 

1.227 

.882 

3.056 

3.604 

1.15 

H 

1.310 

.095 

4.712 

4.115 

1.767 

1.348 

2.547 

2.916 

1.40 

if 

1.560 

.095 

5.498 

4.901 

2.405 

1.911 

2.183 

2.448 

1.65 

2 

1.810 

.095 

6.283 

5.686 

3.142 

2.573 

1.910 

2.110 

1.91 

2i 

2.060 

.095 

7.069 

6.472 

3.976 

3.333 

1.698 

1.854 

2.16 

2h 

2.282 

.109 

7.854 

7.169 

4.909 

4.090 

1.528 

1.674 

2.75 

2| 

2.532 

.109 

8.639 

7.955 

5.940 

5.035 

1.389 

1.508 

3.04 

3 

2.782 

.109 

9.425 

8.740 

7.069 

6.079 

1.273 

1.373 

3.33 

3i 

3.010 

.120 

10.210 

9.456 

8.296 

7.116 

1.175 

1.269 

3.96 

3* 

3.260 

.120 

10.996 

10.242 

9.621 

8.347 

1.091 

1.172 

4.28 

3f 

3.510 

.120 

11.781 

11.027 

11.045 

9.676 

1.019 

1.088 

4.60 

4 

3.732 

.134 

12.566 

11.724 

12.566 

10.939 

.955 

1.024 

5.47 

4* 

4.232 

.134 

14.137 

13.295 

15.904 

14.066 

.849 

.903 

6.17 

5 

4.704 

.148 

15.708 

14.778 

19.635 

17.379 

.764 

.812 

7.58 

6 

5.670 

.165 

18.850 

17.813 

28.274 

25.250 

.637 

.674 

10.16 

7 

6.670 

.165 

21.991 

20.954 

38.485 

34.942 

.546 

.573 

11.90 

8 

7.670 

.165 

25.133 

24.096 

50.266 

46.204 

.477 

.498 

13.65 

9 

8.640 

.180 

28.274 

27.143 

63.617 

58.630 

.424 

.442 

16.76 

10 

9.594 

.205 

31.416 

30.141 

78.540 

72.292 

.382 

.398 

21.00 

298 


PROPERTIES  OF  MATERIALS 
WEIGHT  OF  WROUGHT  IRON* 


Thick- 
ness or 
Diam- 
eter 
Inches 

Weight 
of 
1  Sq.  Ft. 
Pounds 

Weight 
of 
Square 
Bar  1  Ft. 
Long 
Pounds 

Weight 
of 
Round 
Bar  1  Ft. 
Long 
Pounds 

Thick- 
ness or 
Diam- 
eter 
Inches 

Weight 
of 
1  Sq.  Ft. 
Pounds 

Weight 
of 
Square 
Bar  1  Ft. 
Long 
Pounds 

Weight 
of 
Round 
Bar  1  Ft. 
Long 
Pounds 

5.052 

.0526 

.0414 

4 

176.8 

64.47 

50.63 

10.10 

.2105 

.1653 

4 

181.9 

68.20 

53.57 

15.16 

.4736 

.3720 

4 

186.9 

72.05 

56.59 

20.21 

.8420 

.6613 

4 

192.0 

75.99 

59.69 

25.26 

1.316 

1.033 

4 

197.0 

80.05 

62.87 

30.31 

1.895 

1.488 

5 

202.1 

84.20 

66.13 

35.37 

2.579 

2.025 

5 

212.2 

92.83 

72.91 

1 

40.42 

3.368 

2.645 

5 

222.3 

101.9 

80.02 

1 

45.47 

4.263 

3.348 

5 

232.4 

111.4 

87.46 

50.52 

5.263 

4.133 

6 

242.5 

121.3 

95.23 

55.57 

6.368 

5.001 

6 

252.6 

131.6 

103.3 

60.63 

7.578 

5.952 

6 

262.7 

142.3 

111.8 

65.68 

8.893 

6.985 

6 

272.8 

153.5 

120.5 

70.73 

10.31 

8.101 

7 

282.9 

165.0 

129.6 

75.78 

11.84 

9.300 

71 

293.0 

177.0 

139.0 

2 

80.83 

13.47 

10.58 

7* 

303.1 

189.5 

148.8 

2i 

85.89 

15.21 

11.95 

7i 

313.2 

202.3 

158.9 

2 

90.94 

17.05 

13.39 

8 

323.3 

215.6 

169.3 

2 

95.99 

19.00 

14.92 

8 

333.4 

229.3 

180.1 

2 

101.0 

21.05 

16.53 

g 

343.5 

243.4 

191.1 

2 

106.1 

23.21 

18.23 

8 

353.6 

247.9 

202.5 

2 

111.2 

25.47 

20.01 

9 

363.8 

272.8 

214.3 

2 

116.2 

27.84  • 

21.87 

9J 

373.9 

288.2 

226.3 

3 

121.3 

30.31 

23.81 

9£ 

384.0 

304.0 

238.7 

3* 

126.3 

32.89 

25.83 

9f 

394.1 

320.2 

251.5 

3 

131.4 

35.57 

27.94 

10 

404.2 

336.8 

264.5 

3 

136.4 

38.37 

30.13 

10* 

414.3 

353.9 

277.9 

3 

141.5 

41.26 

32.41 

10* 

424.4 

371.3 

291.6 

3 

146.5 

44.26 

34.76 

10f 

434.5 

389.2 

305.7 

3 

151.6 

47.37 

37.20 

11 

444.6 

407.5 

320.1 

3 

156.6 

50.57 

39.72 

11 

. 

454.7 

426.3 

334.8 

4 

161.7 

53.89 

42.33 

11 

""*'• 

464.8 

445.4 

349.8 

4 

166.7 

57.31 

45.01 

11 

474.9 

465.0 

365.2 

4 

;''!; 

171.8 

60.84 

47.78 

12 

485.0 

485.0 

380.9 

*This  table  is  for  wrought  iron.     Multiply  by  .95  for  weight  of  cast  iron ; 
by  1.02  for  steel;  by  1.16  for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 

DIAMETER  AND  NUMBER  OF  WOOD  SCREWS 


Formulas  for  Wood 
Screws 

No. 

Diameter 

No. 

Diameter 

No. 

Diameter 

N  =  number 
D  =  diameter 
D  =  (N  X.  01325)  +  .056 
D-.056 

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

.056 
.069 
.082 
.096 
.109 
.122 
.135 
.149 
.162 
.175 
.188 

11 

12 
13 
14 
15 
16 
17 
18 
19 
20 
21 

.201 
.215 
.228 
.241 
.255 
.268 
.281 
.293 
.308 
.321 
.334 

22 
23 
24 
25 
26 
27 
28 
29 
30 

.347 
.361 
.374 
.387 
.401 
.414 
.427 
.440 
.453 

.01325 

SPIKES  AND  NAILS 


Standard  Steel-Wire  Nails 

Common  Iron 

Steel-Wire 

I 

Common 

Finishing 

Nails 

Spikes 

1 

1,1 
ft 

1$ 

|| 

{4 

|| 

• 

.|8 

2$ 

S3 

L 

|| 

CO 

V    £ 

§   % 

3" 

|£ 

3 

8(2 

CO 

§1 

If 

I'l 

li 

e£ 

2d 

1 

.0524 

1,060 

.0453 

1,558 

2d 

1 

800 

3 

.1620 

41 

3d 

u 

.0588 

640 

.0508 

913 

3d 

u 

400 

3* 

.1819 

30 

4d 

If 

.0720 

380 

.0508 

761 

4d 

If 

300 

4 

.2043 

23 

5d 

11 

.0764 

275 

.0571 

500 

5d 

if 

200 

.2294 

17 

6d 

2 

.0808 

210 

.0641 

350 

6d 

2 

150 

53 

.2576 

13 

7d 

2i 

.0858 

160 

.0641 

315 

7d 

21 

120 

51 

.2893 

11 

8d 

2i 

.0935 

115 

.0720 

214 

8d 

2* 

85 

6 

.2893 

10 

9d 

2f 

.0963 

93 

.0720 

195 

9d 

21 

75 

6* 

.2249 

7f 

lOd 

3 

.1082 

77 

.0808 

137 

lOd 

3 

60 

7 

.2249 

7 

12d 

3* 

.1144 

60 

.0808 

127 

12d 

31 

50 

8 

.3648 

5 

16d 

3i 

.1285 

48 

.0907 

90 

16d 

3* 

40 

9 

.3648 

4J 

20d 

4 

.1620 

31 

.1019 

62 

20d 

4 

20 

30d 

4i 

.1819 

22 

30d 

41 

16 

40d 

5 

.2043 

17 

40d 

6 

14 

50d 

5i 

.2294 

13 

50d 

11 

60d 

6 

.2576 

11 

60d 

6* 

8 

WEIGHT  OF  100  BOLTS  WITH  SQUARE  HEADS  AND  NUTS 

(The  Carnegie  Steel  Co.,  Limited) 


Length 

Diameter  of  Bolts 

TTnHpr 

under 
Head  to 

"D/-vi-nf 

Un. 

A  In. 

fin. 

A  In. 

fin. 

Un. 

fin. 

Jin. 

1  In. 

JrOint 
Inches 

Weight,  in  Pounds 

li 

4.0 

7.0 

10.5 

15.2 

22.5 

39.5 

63.0 

H 

4.4 

7.5 

11.3 

16.3 

23.8 

41.6 

66.0 

2 

4.8 

8.0 

12.0 

17.4 

25.2 

43.8 

69.0 

109.0 

163 

21 

5.2 

8.5 

12.8 

18.5 

26.5 

45.8 

72.0 

113.3 

169 

2i 

5.5 

9.0 

13.5 

19.6 

27.8 

48.0 

75.0 

117.5 

174 

2i 

5.8 

9.5 

14.3 

20.7 

29.1 

50.1 

78.0 

121.8 

180 

3 

6.3 

10.0 

15.0 

21.8 

30.5 

52.3 

81.0 

126.0 

185 

3i 

7.0 

11.0 

16.5 

24.0 

33.1 

56.5 

87.0 

134.3 

196 

4 

7.8 

12.0 

18.0 

26.2 

35.8 

60.8 

93.1 

142.5 

207 

«f 

8.5 

13.0 

19.5 

28.4 

38.4 

65.0 

99.1 

151.0 

218 

5 

9.3 

14.0 

21.0 

30.6 

41.1 

69.3 

105.2 

159.6 

229 

5i 

10.0 

15.0 

22.5 

32.8 

43.7 

73.5 

111.3 

168.0 

240 

6 

10.8 

16.0 

24.0 

35.0 

46.4 

77.8 

117.3 

176.6 

251 

6i 

25.5 

37.2 

49.0 

82.0 

123.4 

185.0 

262 

7 

27.0 

39.4 

51.7 

86.3 

129.4 

193.7 

273 

7| 

28.5 

41.6 

54.3 

90.5 

135.0 

202.0 

284 

8 

30.0 

43.8 

59.6 

94.8 

141.5 

210.7 

295 

9 

46.0 

64.9 

103.3 

153.6 

227.8 

317 

10 

48.2 

70.2 

111.8 

165.7 

224.8 

339 

11 

50.4 

75.5 

120.3 

177.8 

261.9 

360 

12 

52.6 

80.8 

128.8 

1-89.9 

278.9 

382 

13 

86.1 

137.3 

202:0 

296.0 

404 

14 

91.4 

145.8 

214.1 

313.0 

426 

15 

96.7 

154.3 

226.2 

330.1 

448 

16 

102.0 

162.8 

238.3 

347.1 

470 

17 

107.3 

171.0 

250.4 

364.2 

492 

18 

112.6 

179.5 

262.6 

381.2 

514 

19 

117.9 

188.0 

274.7 

398.3 

536 

20     ' 

123.2 

206.5 

286.8 

415.3 

558 

Per  Inch 

1.4 

2.1 

3.1 

4.2 

5.5 

8.5 

12.3 

16.7 

21.8 

Additional 

1 

299 


300 


PROPERTIES  OF  MATERIALS 


PROPORTIONS  OF  THE  UNITED  STATES  STANDARD  SCREW 
THREADS,  NUTS,  AND  BOLT  HEADS 


Diam. 

of 

Screw 
Inches 


Threads 
per 
nch 


20 

18 

16 

14 

13 

12 

11 

10 

9 

8 

7 

7 


Diam. 

of 

Core 
Inch 


Width 

of 

Flat 
Inch 


.185 

.240 

.294 

.344 

.400 

.454 

.507 

.620 

.731 

.837 

.940 

1.065 

1.160 

1.284 

1.389 

1.490 

1.615 

1.712 

1.962 

2.175 

2.425 

2.628 

2.878 

3.100 

3.317 

3.566 

3.798 

4.027 

4.255 

4.480 

4.730 

4.953 

5.203 

5.423 


.0062 
.0070 
.0078 
.0089 
.0096 
.0104 
.0113 
.0125 
.0140 
.0156 
.0180 
.0180 
.0210 
.0210 
.0227 
.0250 
.0250 
.0280 
.0280 
.0310 
.0310 
.0357 
.0357 
.0384 
.0410 
.0410 
.0435 
.0460 
.0480 
.0500 
.0500 
.0526 
.0526 
.0555 


Inside 
Diam. 
Inch 


Outside 
Diam. 
Inch 


Diagonal 
Inch 


Height 

of 

Head 
Inches 


The  threads  have  an  angle  of  60°,  with  flat  tops  and  bottoms,  and  are  of  the 
following  proportions: 

Notation  of  Letters,  All  Dimensions  in  Inches 


D  =  outside  diameter  of  screw; 

d  =  diameter  of  root  of  thread,  or  of 

hole  in  nut; 
p  =  pitch  of  screw; 
t  =  number  of  threads  per  inch; 
/=flat  top  and  bottom; 
o  =  outside  diameter  of  hexagon  nut 

or  bolt  head; 


P  = 


Vl6D  + 10  -2.909 


=  D- 


1.299 


16.64 


3D  ,  1 


=  inside  diameter  of  hexagon,   or 
side  of  square  nut  or  bolt  head ; 
5  =  diagonal  of  square  nut  or  bolt 

head; 
h  =  height  of  rough  or  unfinished  bolt 

head. 

The  height  of  a  finished  nut  or  bolt 
head  is  made  equal  to  the  diameter  D 
of  the  screw. 


o=1.155* 


PROPERTIES  OF  MATERIALS 
WEIGHT  OF  1  LIN.  FT.  OF  FLAT  WROUGHT  IRON* 


301 


Size 
Inches 

Weight 
Pounds 

Size 
Inches 

Weight 
Pounds 

Size 

Inches 

Weight 
Pounds 

1   Xi 

.85 

5iXf 

6.65 

4   X 

8.45 

HXi 

1.06 

six! 

6.97 

8.98 

Hxi 

1.27 

SfXf 

7.29 

ix 

9.51 

HXi 

1.48 

6  X| 

7.60 

X 

10.03 

2^i 

1.69 

5  X 

10.56 

1.90 

1   X 

1.69 

ix 

11.09 

2|Xi 

2.11 

HX 

2.11 

x 

11.62 

2fXi 

2.32 

HX 

2.53 

X 

12.15 

3   Xi 

2.53 

HX 

2.96 

6  XI 

12.67 

2.75 

2   X 

3.38 

ix  *• 

2.96 

3.80 

1   X 

2.53 

Xi 

3.17 

!x 

4.22 

HX 

3.17 

4   Xi 

3.38 

X 

4.65 

HX 

3.80 

4iXi 

3.59 

31XI 

5.07 

4.44 

3.80 

5.49 

2*X 

5.07 

4aX  i 

4.01 

3|X 

5.92 

!x 

5.70 

5   Xi 

4.22 

3fX 

6.33 

x 

6.33 

4.44 

4   X 

6.76 

X  j 

6.97 

s|xi 

4.65 

7.18 

3   X 

7.60 

slxf 

4.86 

!x 

7.60    - 

3  jX  • 

8.24 

6  Xi 

5.07 

X 

8.03 

slxj 

8.87 

5   X 

8.45 

3|X- 

9.51 

1   X 

1.27 

six 

8.87 

10.14 

HX 

1.58 

six 

9.30 

4iX  ; 

10.77 

HX 

1.90 

six 

9.72 

4iX  i 

11.41 

ifx 

2.22 

6  X 

10.14 

4f  X  '- 

12.04 

2  X 

2.53 

5   Xi 

12.67 

2.85 

1   X 

2.11 

5iXi 

13.31 

2|X 

3.17 

HX 

2.64 

5JX  i 

13.94 

2|X 

3.49 

HX 

3.17 

5fx! 

14.57 

3   X 

3.80 

ifx 

3.70 

6   Xi 

15.21 

4.12 

2   X 

4.22 

3|X 

4.44 

4.75 

HXI 

5.07 

3fX 

4.75 

2AX 

5.28 

2   XI 

6.76 

4   X 

5.07 

2|X 

5.81 

3   XI 

10.14 

5.39 

3   X 

6.33 

4   XI 

13.52 

4  *  V 

5.70 

3iX 

6.87 

5  XI 

16.90 

4|X 

6.02 

six 

7.39 

6   XI 

20.28 

5   X 

6.33 

3fX 

7.92 

7   XI 

23.66 

TIMBER  AND  BOARD  MEASURE 

TIMBER  MEASURE 

Volume  of  Round  Timber.— The  cubic  contents  of  a  round  log  are  those 
of  a  cylinder  of  the  same  dimensions.  As  logs  usually  taper  throughout  their 
length,  the  diameter  taken  is  the  mean  of  the  two  end  diameters.  The  cubic 
contents  of  a  cylinder  are  expressed  by  the  formula,  -^-l  =  ~^dl.  From  this 

it  is  possible  to  deduce,  for  field  use,  the  following: 

Rule. — The  number  of  cubic  feet  in  a  round  log  is  equal  to  one-quarter  of  the 

mean  girth  (circumference  or  y)  multiplied  by  the  mean  diameter  multiplied  by 
the  length.  If,  as  is  usually  the  case,  the  girth  and  diameter  are  given  in  inches, 
the  result  obtained  must  be  divided  by  144- 


*Multiply  by  .95  lor  weight  of  cast  iron;  by  1.02  for  weight  of  steel;  by  1.16 
for  copper;  by  1.09  for  brass;  by  1.48  for  lead. 


302 


PROPERTIES  OF  MATERIALS 


When  the  accompanying  table  of  quarter  girths  is  used,  it  is  only  necessary 
to  measure  the  circumference  of  each  end  of  the  log  and  divide  the  sum  by  2, 
for  the  mean  girth.  Opposite  one-quarter  of  this  mean  girth,  find  the  area  in 
feet  This  multiplied  by  the  length  of  the  log,  gives  the  cubic  contents  in  feet. 

EXAMPLE.— The  circumferences  of  a  20-ft.  log  are  48  and  60  in.,  respect- 
ively. What  is  the  cubic  contents  of  the  log? 

SOLUTION.—  ( 48 + 60  )  -h 2  =  54  -  mean  girth.  54-7-4  =  13*  =  one-quarter 
girth.  The  area  corresponding  to  a  quarter  girth  of  13*  in.  is  1.26  sq.  ft.  Hence, 
1.26X20  =  25.20,  number  of  cubic  feet  in  the  log. 

TABLE  OF  QUARTER  GIRTHS 


Quarter 
Girths 
Inches 

Area 
Feet 

Quarter 
Girths 
Inches 

Area 
Feet 

Quarter 
Girths 
Inches 

Area 
Feet 

6 

.250 

121 

1.04 

19 

2.50 

61 

.272 

12* 

1.08 

19* 

2.64 

el 

.294 

12f 

1.12 

20 

2.77 

61 

.317 

13 

1.17 

20* 

2.91 

7 

.340 

131 

1.21 

21 

3.06 

71 

.364 

13* 

1.26 

21* 

3.20 

7* 

.390 

131 

1.31 

22 

3.36 

7f 

.417 

14 

1.36 

22* 

3.51 

8 

.444 

141 

1.41 

23 

3.67 

81 

8* 

.472 
.501 

14* 
141 

1.46 
1.51 

23* 
24 

3.83 
4.00 

81 

.531 

15 

1.56 

24* 

4.16 

9 

.562 

151 

1.61 

25 

4.34 

91 

.594 

15* 

1.66 

25* 

4.51 

8* 

.626 

151 

1.72 

26 

4.69 

91 

.659 

16 

1.77 

26* 

4.87 

10 

.694 

161 

1.83 

27 

5.06 

101 

.730 

16* 

1.89 

27* 

5.25 

10* 

.766 

161 

1.94 

28 

5.44 

101 

.803 

17 

2.00 

28* 

5.64 

11 
Hi 

m 

.840 
.878 
.918 

171 
17* 
171 

2.09 
2.12 
2.18 

29 
29* 
30 

5.84 
6.04 
6.25 

111 

.959 

18 

2.25 

12 

1.000 

18* 

2.37 

BOARD  MEASURE 

The  unit  of  board  measure  (B.  M.)  is  the  board  foot,  which  is  the  contents 
of  a  board  1  ft.  square  and  1  in.  thick.  When  calculating  board  feet  all  thick- 
nesses under  1  in.  are  counted  as  if  1  in.,  while  all  over  1  in.  are  counted  at  their 
exact  value.  Thus,  a  1-in.  plank  is  counted  as  a  1-in.  plank,  and  a  li-in. 
plank  as  11  in.  When  estimating  the  number  of  board  feet  that  should  be  cut 
from  a  log,  numerous  rules  have  been  devised,  but  the  one  in  most  general  use 
is  known  as  Doyle's,  Connecticut  River,  or  Scribner's  rule;  it  is  as  follows: 

Rule. — The  diameter  of  the  small  end  of  the  log,  inside  the  bark,  is  first  mea- 
sured. From  this  diameter,  4  in.  are  deducted  for  slabbing  and  squaring  up.  The 
square  of  one-fourth  of  this  remainder,  multiplied  by  the  length,  in  feet,  will  give 
the  resultant  board  feet. 

Table  of  Board  Feet. — The  number  of  feet  board  measure  for  1  ft.  in  length 
of  planks  of  all  thicknesses,  increasing  by  single  inches,  up  to  12  in.,  and  thence, 
by  each  2  in.  up  to  24  in.,  are  given  in  the  accompanying  table.  In  the  rare 
cases  where  the  thickness  is  not  an  even  inch,  the  value  for  the  board  feet  may 
be  found  by  interpolation.  For  timbers  larger  than  12X24,  it  is  necessary 
to  take  the  board  feet  of  two  pieces  each  one-half  the  size  of  the  stick  under 
consideration.  Thus,  the  number  of  board  feet  in  one  piece  16X24  is  twice 
the  number  of  board  feet  in  a  piece  8X24  or  in  one  16  X 12, 

To  economize  space,  the  values  have  been  carried  to  the  first  repeating 
decimal  only,  which  is  marked  with  a  (*).  Unless  the  extension  indicated  is 


HYDROSTATICS 


303 


made,  the  final  figure  should  be  made  1  greater  than  in  the  table;  thus,  if  the 
figures  in  the  table  are  1.6*,  this  should  be  used  as  1.7;  or,  better,  as  1.67,  or  If, 
because  the  correct  value  is  1.66666,  repeating  indefinitely. 


TABLE  OF  BOARD  FEET 


D 

Width  of  Plank,  in  Inches 

o 

£ 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 

Size  of  Plank,  in  Board  Feet 

1 

.083* 

.16* 

.25 

.3* 

.416* 

.5 

.583* 

.6* 

.75 

.83* 

.916* 

1 

2 

.166* 

.33* 

.50 

.6* 

.833* 

1.0 

1.166* 

1.3* 

1.50 

1.66* 

1.833* 

2 

3 

.250 

.50 

.75 

1.0 

1.250 

1.5 

1.750 

2.0 

2.25 

2.50 

2.750 

3 

4 

.333* 

.66* 

1.00 

1.3* 

1.666* 

2.0 

2.333* 

2.6* 

3.00 

3.33* 

3.666* 

4 

5 

.416* 

.83* 

1.25 

1.6* 

2.083* 

2.5 

2.916* 

3.3* 

3.75 

4.16* 

4.583* 

5 

6 

.500 

1.00 

1.50 

2.0 

2.500 

3.0 

3.500 

4.0 

4.50 

5.00 

5.500 

6 

7 

.583* 

1.16* 

1.75 

2.3* 

2.916* 

3.5 

4.083* 

4.6* 

5.25 

5.83* 

6.416* 

7 

8 

.666* 

1.33* 

2.00 

2.6* 

3.333* 

4.0 

4.666* 

5.3* 

6.00 

6.66* 

7.333* 

8 

9 

.750 

1.50 

2.25 

3.0 

3.750 

4.5 

5.250 

6.0 

6.75 

7.50 

8.250 

9 

10 

.833* 

1.66* 

2.50 

3.3* 

4.166* 

5.0 

5.833* 

6.6* 

7.50 

8.33* 

9.166* 

10 

11 

.916* 

1.83* 

2.75 

3.6* 

4.583* 

5.5 

6.416* 

7.3* 

8.25 

9.16* 

10.833* 

11 

12 

1.000 

2.00 

3.00 

4.0 

5.000 

6.0 

7.000 

8.0 

9.00 

10.00 

11.000 

12 

14 

1.166* 

2.33* 

3.50 

4.6* 

5.833* 

7.0 

8.166* 

9.3* 

10.50 

11.66* 

12.833* 

14 

16 

1.333* 

2.66* 

4.00 

5.3* 

6.666* 

8.0 

9.333* 

10.6* 

12.00 

13.33* 

14.666* 

16 

18 

1.500 

3.00 

4.50 

6.0 

7.500 

9.0 

10.500 

12.0 

13.50 

15.00 

16.500 

18 

20 

1.666* 

3.33* 

5.00 

6.6* 

8.333* 

10.0 

11.666* 

13.3* 

15.00 

16.66* 

18.333* 

20 

22 

1.833* 

3.66* 

5.50 

7.3* 

9.166* 

11.0 

12.833* 

14.6* 

16.50 

18.33* 

20.166* 

22 

24 

2.000 

4.00 

6.00 

8.0 

10.000 

12.0 

14.000 

16.0 

18.00 

20.00 

22.000 

24 

HYDROSTATICS 

Hydrostatics  treats  of  the  equilibrium  of  liquids  and  of  their  pressures  on 
the  walls  of  vessels  containing  them;  the  science  depends  on  the  way  in  which 
the  molecules  of  a  liquid  form  a  mass  under  the  action  of  gravity  and  molecular 
attraction,  the  latter  of  which  is  so  modified  in  liquids  as  to  give  them  their 
state  of  liquidity.  While  the  particles  of  a  liquid  cohere,  they  are  free  to  slide 
upon  one  another  without  the  least  apparent  friction;  and  it  is  this  perfect 
mobility  that  gives  them  the  mechanical  properties  considered  in  hydrostatics. 

The  fundamental  property  of  hydrostatics  is  a  physical  axiom,  and  on  it 
are  based  nearly  all  the  principles  of  hydrostatics;  it  is  as  follows: 

When  a  pressure  is  exerted  on  any  part  of  the  surface  of  a  liquid,  that  pressure 
is  transmitted  undiminished  to  all  parts  of  the  mass,  and  in  all  directions. 

Equilibrium  of  Liquids. — The  equilibrium  of  liquids  is  a  property  that  can 
be  easily  demonstrated,  and  examples  are  frequently  seen.  Thus,  if  two  bar- 
rels are  connected  at  the  bottom  with  a  pipe,  and  water  is  poured  in  one  until 
it  reaches  within  1  ft.  of  the  top,  the  water  in  the  other  will  be  found  to  have 
attained  the  same  height. 

Pressure  of  Liquids  on  Surfaces. — The  general  law  governing  the  pressure 
of  liquids  on  surfaces  is  as  follows: 

Law. — The  pressure  of  a  liquid  on  any  surface  immersed  in  it  is  equal  to  the 
weight  of  a  column  of  the  liquid  whose  base  is  the  surface  pressed,  and  whose  height 
is  the  perpendicular  depth  of  the  center  of  gravity  of  the  surface  below  the  surface 
of  the  liquid. 

The  pressure  exerted  by  liquids  is  independent  of  the  shape  or  size  of  the  ves- 
sel or  cavity  containing  the  liquid.  The  pressure  of  a  liquid  against  any  point 
of  any  surface,  either  curved  or  plane,  is  always  perpendicular  to  the  surface 
at  that  point.  At  any  given  depth,  the  pressure  of  a  liquid  is  equal  in  every 
direction,  and  is  in  direct  proportion  to  the  vertical  depth  below  the  surface. 


304  HYDROSTATICS 

The  weight  of  1  cu.  ft.  of  fresh  water,  at  ordinary  temperature  of  the  atmos- 
phere, that  is,  from  32°  F.  to  80°  F.,  is  usually  assumed  at  62.5  Ib.  This  is  a 
trifle  more  than  the  actual  weight,  but  is  sufficiently  close  for  most  practical 
purposes. 

To  Find  Pressure  Exerted  by  Quiet  Water  Against  Side  of  Gangway  or 
Heading. — Multiply  the  area  of  the  side,  in  square  feet,  by  the  perpendicular 
distance  from  the  surface  of  the  water  to  a  point  equidistant  between  the  top 
and  bottom  of  the  submerged  heading  or  gangway,  and  multiply  the  product 
by  62.5.  The  result  will  be  the  pressure,  in  pounds,  exclusive  of  atmospheric 
pressure;  this  latter  need  not  be  considered  in  ordinary  mining  work. 

EXAMPLE. — If  an  abandoned  colliery,  opened  by  a  slope  on  a  pitch  of  25° 
and  100  yd.  long,  is  allowed  to  fill  with  water,  what  is  the  average  pressure 
exerted  on  each  square  foot  of  the  lower  rib  of  the  gangway,  assuming  that  the 
gangways  were  driven  dead  level,  and  that  the  length  of  the  slope  was  measured 
to  a  point  on  the  lower  rib  equidistant  between  top  and  bottom  of  gangway? 

SOLUTION.— Perpendicular  height  of  water  is  300 X  sin  25°  =126.78  ft. 
Then,  the  pressure  on  each  square  foot  of  the  lower  rib  of  gangway  is  126.78 
X  62.5  Ib. ,  =  7,923.75  Ib. ,  or  over  3  3  gross  tons.  The  total  pressure  exerted  along 
the  gangway  may  readily  be  found  by  multiplying  7,923.75  Ib.  by  the  number 
of  square  feet  in  the  lower  rib  against  which  it  rests. 

Pressure  Against  Dams,  Etc. — To  find  the  total  pressure  of  quiet  water 
against  and  perpendicular  to  any  surface  whatever,  as  a  dam,  embankment, 
or  the  bottom,  side,  or  top  of  any  containing  vessel,  water  pipe,  etc.,  no  matter 
whether  said  surface  is  vertical,  horizontal,  or  inclined;  or  whether  it  is  flat  or 
curved ;  or  whether  it  reaches  to  the  surface  of  the  water  or  is  entirely  below  it, 
apply  the  following  rule: 

Rule. — Multiply  the  area,  in  square  feet,  of  the  surface  pressed  by  the  vertical 
depth,  in  feet,  of  its  center  of  gravity  below  the  surface  of  the  water,  and  this  product 
by  62.5;  the  result  will  be  the  pressure  in  pounds. 

Thus,  assume  that  in  Figs.  1,  2,  and  3  the'depth  of  water  in  each  dam  is 
12  ft.,  and.  the  wall  or  embankment  is  50  ft.  long.  In  Fig.  1  the  total  pressure 
will  equal  12  X  50  X  6  X  62.5  =  225,000  Ib.  In  Figs.  2  and  3,  the  walls  or  embank- 
ments, being  inclined,  expose  a  greater  surface  to  pressure,  say,  18  ft.  from  A 
to  B.  Then  the  total  pressure  equals  18X50X6X62.5  =  337,500  Ib. 

The  results  obtained 
are  the  total  pressures 
without  regard  to  di- 
rection. In  Fig.  1  the 
total  pressure  calcu- 
lated, V  225,000  Ib.,  is 

_  _  horizontal,    tending 

FIG.  1  FIG.  2  PIG.  3  either  to  overturn  thi 

wall  or  make  it  slide  on  its  base.  The  center  of  pressure  is  at  C,  or  one-third 
of  the  vertical  depth  from  the  bottom.  In  Fig.  2,  the  pressure  is  exerted  in 
two  directions;  one  pressure,  acting  horizontally,  tends  to  overthrow  or  slide 
the  wall,  while  the  other,  acting  vertically,  tends  to  hold  it  in  place.  In  Fig.  3, 
the  pressure  is  also  exerted  in  two  directions;  one  pressure,  acting  horizon- 
tally, tends  to  overthrow  or  slide  the  wall,  while  the  other  tends  to  lift.  So 
long  as  the  vertical  depth  of  water  remains  the  same,  the  horizontal  pressure 
remains  the  same,  no  matter  what  inclination  is  given  the  wall.  Thus,  in 
Figs.  2  and  3,  the  horizontal  pressure  is  the  same  as  in  Fig.  1,  or  225,000  Ib. 

Distribution  of  Pressure. — The  total  pressure  of  the  water  is  distributed 
over  the  entire  depth  of  the  submerged  part  of  the  back  of  the  wall,  and  is  least 
at  the  top,  gradually  increasing  toward  the  bottom.  But  so  far  as  regards  the 
united  action  of  every  portion  of  it,  in  tending  to  overthrow  the  wall,  con- 
sidered as  a  single  mass  of  masonry  incapable  of  being  bent  or  broken,  it  may 
all  be  assumed  to  be  applied  at  C,  which  is  one-third  of  the  vertical  depth  from 
the  bottom  in  Fig.  1,  or,  what  is  the  same  thing,  one-third  of  the  slope  distance 
from  the  bottom  in  Figs.  2  and  3. 

No  matter  how  much  water  is  in  a  dam  or  vessel,  the  pressure  remains  the 
same,  so  long  as  the  area  pressed  and  the  vertical  depth  of  its  center  of  gravity 
below  the  level  surface  of  the  water  remains  unchanged.  Thus,  if  the  water 
in  dam  shown  in  Fig.  1  extended  back  1  m.,  it  would  exert  no  more  pressure 
against  the  wall  than  if  it  extended  back  only  1  ft. 

In  any  two  vessels  having  the  same  base,  and  containing  the  same  depth 
of  water,  no  matter  what  quantity,  the  pressures  on  the  bases  are  equal.  Thus, 
if  Figs.  4  and  5  have  the  same  base  and  are  filled  with  water  to  the  same  depth, 
the  pressure  on  the  bases  will  be  equal.  This  fact,  that  the  pressure  on  a  given 


HYDROSTATICS 


305 


surface,  at  a  given  depth,  is  independent  of  the  quantity  of  water,  is  called  the 

hydrostatic  paradox. 

As  the  pressure  of  water  against  any  point  is  at  right  angles  to  the  surface 

at  that  point,  props  or  other  strengthening  material  for  the  bracing  of 
such  structures  as  a  sloping  dam,  should 
be  so  placed  as  to  offer  the  greatest  re- 
sistance in  a  line  at  right  angles  to  the 
sloping  surf  ace,  and  these  supports  should 
be  strongest  and  closest  together  at  the 
bottom.  For  the  same  reason,  the  hoops 
on  a  circular  tank  should  be  strongest 
and  closest  at  the  bottom. 

Transmission  of  Pressure  Through 
Water. — Water,  in  common  with  other 
liquids,  possesses  the  important  property 
of  transmitting  pressure  equally  in  all 
directions.  Thus,  if  a  vessel  is  constructed 


FIG.  4       FIG.  5 


FIG.  6 


with  two  cylinders,  the  area  of  one  being  10  sq.  in.,  and  that  of  the  other  100 
sq.  in.,  and  the  vessel  is  filled  with  water,  as  in  Fig.  6,  and  pistons  are  fitted  to 
the  cylinders,  a  pressure  of  100  Ib.  applied  at  the  smaller  will  balance  1,000  Ib. 
at  the  larger.  This  is  the  principle  of  the  hydrostatic  press.  Air  and  other 
gaseous  fluids  transmit  pressure  equally  in  all  directions,  like  liquids,  but  not  as 
rapidly. 

To  Find  Pressure  on  Plane  Surface  at  Any  Given  Depth  of  Water. — For 
pounds  per  square  inch,  multiply  depth  in  feet  by  .434.  For  pounds  per 
square  foot,  multiply  depth  in  feet  by  62.5.  For  tons  per  square  foot,  multiply 

PRESSURE    AT   DIFFERENT   VERTICAL  DEPTHS  ALSO   TOTAL 
PRESSURE  AGAINST  A  PLANE    1    FT.  WIDE  EXTEND- 
ING VERTICALLY   FROM   SURFACE   OF 
WATER  TO    SAME   DEPTHS 


fl 

Pressure 
Pounds 
per  Sq.  Ft. 

Total 
Pressure 
Pounds 

H 

§  -d<£ 

C/J   £  rf 

8  gw 

£  ^  fe 

Total 
Pressure 
Pounds 

H 

Pressure 
Pounds 
per  Sq.  Ft. 

Total 
Pressure 
Pounds 

1 

62.5 

31 

27 

1,687 

22,781 

65 

4,062 

132,031 

2 

125 

125 

28 

1,750 

24.500 

70 

4,375 

153,125 

3 

187 

281 

29 

1,812 

26,281 

75 

4,687 

175,781 

4 

250 

500 

30 

1,875 

28,125 

80 

5,000 

200,000 

5 

312 

781 

31 

1,937 

30,031 

85 

5,312 

225,781 

6 

375 

1,125 

32 

2,000 

32,000 

90 

5,625 

253,125 

7 

437 

1,531 

33 

2,062 

34,031 

95 

5,937 

282,031 

8 

500 

2,000 

34 

2,125 

36,125 

100 

6,250 

312,500 

9 

562 

2,531 

35 

2,187 

38,281 

110 

6,875 

378,125 

10 

625 

3,125 

36 

2,250 

40,500 

120 

7,500 

450,000 

11 

687 

3,781 

37 

2,312 

42,781 

130 

8,125 

528,100 

12 

750 

4,500 

38 

2,375 

45,125 

140 

8,750 

612,500 

13 

812 

5,281 

39 

2,437 

47,531 

150 

9,375 

703,125 

14 

875 

6,125 

40 

2,500 

50,000 

160 

10,000 

800.000 

15 

937 

7,031 

41 

2,562 

52,531 

170 

10,625 

903,125 

16 

1,000 

8,000 

42 

2,625 

55,125 

180 

11,250 

1,012,500 

17 

1,062 

9,031 

43 

2,687 

57,781 

190 

11,875 

1,128,125 

18 

1,125 

10,125 

44 

2,750 

60,500 

200 

12,500 

1,250.000 

19 

1,187 

11,281 

45 

2,812 

63,281 

225 

14,062 

1,582,031 

20 

1,250 

12,500 

46 

2,875 

66,125 

250 

15,625 

1,953,125 

21 

1,312 

13,781 

47 

2,937 

69,031 

275 

17,187 

2,363,281 

22 

1,375 

15,125 

48 

3,000 

72,000 

300 

18,750 

2,812,500 

23 

1,437 

16,531 

49 

3,062 

75,031 

350 

21,875 

3,828,125 

24 

1,500 

18,000 

50 

3,125 

78,125 

400 

25,000 

5,000,000 

25 

1,562 

19,531 

55 

3,437 

94,531 

450 

28,125 

6,328,125 

26 

1,625 

21.12". 

60 

3.750 

112,500 

500 

31,250 

7,812,500 

306 


HYDROSTATICS 


depth  in  feet  by  .0279.  The  pressure  per  square  foot  at  different  depths 
increases  directly  as  the  depths.  The  total  pressure  against  a  plane  1  ft.  wide 
at  different  depths  increases  as  the  square  of  the  depths. 

Pressure  of  Water  in  Pipes. — As  water  exerts  a  pressure  equally  in  all 
directions,  it  is  important  that,  in  pipe  lines,  the  pipe  should  be  sufficiently 
thick  to  assure  strength  enough  to  resist  a  bursting  pressure.  In  ordinary 
practice,  the  thickness  of  cast-iron  water  pipes  of  different  bores  is  calculated 
by  Mr.  J.  T.  Fanning's  formula,  given  in  his  Hydraulic  Engineering,  which 
is  as  follows,  the  thickness  and  bore  being  given  in  inches  and  the  pressure  in 
pounds  per  square  inch: 

_,.  ,  (pressure  -f- 100)  X  bore          ooov^/i     b°re\ 

Thlckness  =  .4Xultimate  tensile  strength +'333X  (l~  w) 
This  formula,  worked  out  for  different  heads  and  different  sizes  of  bore, 
yields  the  results  given  in  the  accompanying  table.  In  this  table,  the  ultimate 
tensile  strength  of  cast  iron  is  taken  at  18,000  Ib.  per  sq.  in.  The  addition  of 
100  Ib.  to  the  pressure  is  made  to  allow  for  water  ram.  The  valves  of  water 
pipes  should  be  closed  slowly,  and  especially  as  the  pipes  increase  in  diameter. 
If  this  rule  is  not  observed,  the  momentum  of  the  water  which  is  suddenly 
stopped  creates  a  great  pressure  against  the  pipes  in  all  directions  and 
throughout  the  entire  length  of  the  line  above  the  valve,  even  if  it  is  many 
miles  long,  and  there  is  danger  of  the  pipes  bursting  at  any  point.  For  this 
reason,  stop-gates  are  shut  by  screws,  because  they  prevent  any  very  sudden 
closing;  but  in  pipes  of  large  diameters,  even  the  screws  must  be  worked 
very  slowly  to  prevent  the  pipes  bursting. 

THICKNESS   OF   PIPE   FOR   DIFFERENT   HEADS   AND    PRESSURES 


Head,  in  Feet  

50 

100 

200 

300 

500 

1,000 

Pressure,  in  Pounds 
per  Square  Inch 

21.7 

43.4 

86.8 

130 

217 

434 

Bore 

Inches 

Thickness  of  Pipe,  in  Inches 

2 

.36 

.37 

.38 

.39 

.42 

.48 

3 

.37 

.38 

.40 

.42 

.45 

.54 

4 

.39 

.40 

.42 

.45 

.50 

.61 

6 

.41 

.43 

.47 

.50 

.57 

.75 

8 

.45 

.47 

.52 

.57 

.66 

.90 

10 

.47 

.50 

.56 

.62 

.74 

1.04 

12 

.49 

.53 

.60 

.67 

.82 

1.18 

16 

.55 

.60 

.70 

.79 

.98 

1.46 

18 

.57 

.63 

.74 

.85 

1.06 

1.60 

20 

.61 

.67 

.79 

.91 

1.15 

1.75 

24 

.66 

.73 

.87 

1.02 

1.30 

2.03 

30 

.74 

.83 

1.01 

1.19 

1.55 

2.46 

36 

.82 

.93 

1.15 

1.36 

1.80 

2.88 

48 

.98 

1.13 

1.42 

1.70 

2.28 

3.73 

Wooden  Pipe. — The  sizes  of  wooden  pipes  up  to  6  in.,  and  sometimes  up 
to  12  in.  in  diameter  are  commonly  bored  from  a  single  log.  The  sizes  up  to 
48  in.  in  diameter  are  made  from  a  series  of  staves  placed  side  by  side  and 
wrapped  with  wire,  steel  bands,  etc.,  and  coated  with  tar  or  some  similar  pre- 
servative. The  sizes  given  in  the  accompanying  table  are  made  in  the  factories 
and  shipped  to  destination.  Larger  sizes  54-,  60-,  66-,  72-,  78-,  84-,  90-,  96-, 
108-,  and  120-in.  pipes  are  made  on  the  ground  where  used  from  staves  of  the 
proper  cross-section.  As  built,  the  staves  break  joint  at  least  24  in.  so  that 
they  interlock  longitudinally,  forming  a  continuous  pipe.  While  being  placed, 
the  completed  pipe  is  wrapped  with  steel  wire  or  bands.  For  heads  up  to 
400  ft.  (173  Ib.  per  sq.  in.)  wooden  pipe  has  been  used  for  many  years  and 
possesses  numerous  advantages  over  cast-  or  wrought-iron  pipe.  Owing  to  the 
smoothness  of  its  interior,  its  carrying  capacity  for  water  is  much  greater 


HYDRAULICS 
STANDARD  SIZES  OF  WOOD  PIPE 


307 


Inside  Diameter 
of  Pipe 
Inches 

Outside  Diameter 
of  Pipe 
Inches 

Weight  per  Foot 
80-lb.  Pressure 
Pounds 

Number  of  Feet  a 
40-Ft.  Car 
Will  Hold 

H 

3 

2 

17,000 

2 

4 

4 

11,000 

3 

6 

6* 

6,000 

4 

7 

7i 

4,500 

4 

8 

12 

4,000 

5 

9 

15 

3,000 

6 

10 

18 

2,700 

6 

10 

13 

2,700 

8 

12 

16 

2,000 

10 

14 

21 

1,600 

12 

16 

25 

1,200 

14 

18 

27 

1,000 

16 

20 

29 

800 

18 

22 

31 

700 

20 

24 

35 

600 

24 

28 

50 

425 

30 

36, 

90 

200 

36 

42 

110 

175 

48 

54  J 

160 

65 

than  is  that  of  cast  or  wrought  pipe.  This  difference  is  estimated  to  be  about 
10%  in  favor  of  the  wooden  pipe  when  it  and  the  iron  pipe  are  new  and  as 
much  as  30  or  40%  when  both  are  old.  Wooden  pipe  is  not  affected  by  acid 
mine  water  or  by  electrolysis  as  is  iron  pipe,  and  for  these  reasons  is  in  much 
favor  in  many  mines  where  the  head  is  not  too  great.  The  standard  thicknesses 
are  made  to  resist  pressures  due  to  100  ft.,  200  ft.,  300  ft.,  and  400  ft.  head,  or 
43  lb.,  87  lb.,  130  lb.,  and  173  |b.  per  sq.  in.  pressure.  In  exceptional  cases, 
wooden  pipe  has  been  built  to  work  under  700-ft.  head,  say,  under  a  pressure 
of  300  lb. 

Compressibility  of  Liquids. — Liquids  are  not  entirely  incompressible,  but 
they  are  so  nearly  so,  that  for  most  purposes  they  may  be  considered  as 
incompressible.  The  bulk  of  water  is  diminished  about  y^nr  by  a  pressure  of 
324  lb.  per  sq.  in.,  or  22  atmospheres;  varying  slightly  with  its  temperature. 
It  is  perfectly  elastic,  regaining  its  original  bulk  when  the  pressure  is 
removed. 


HYDRAULICS 


DEFINITIONS 

Hydraulics  treats  of  liquids  in  motion,  and  in  this,  as  in  hydrostatics,  water 
is  taken  as  the  type.  In  theory,  its  principles  are  the  same  as  those  of  falling 
bodies,  but  in  practice  they  are  so  modified  by  various  causes  that  they  can- 
not be  relied  on  except  as  verified  by  experiment.  The  discrepancy  arises 
from  changes  of  temperature  that  vary  the  fluidity  of  the  liquid,  from  friction, 
the  shape  of  the  orifice,  etc.  When  dealing  with  water  only,  the  first  cause 
need  not  be  considered.  In  theory  the  velocity  of  a  jet  is  the  same  as  that 
of  a  body  falling  from  the  surface  of  the  water. 

To  Find  Theoretical  Velocity  of  Jet  of  Water. — Let  v  =  velocity,  g  =  acceler- 
ation of  gravity  (32.16  ft.),  and  d  =  distance  of  orifice  below  surface  of  water. 
Then,  v=^2gd, 

EXAMPLE. — The  depth  of  water  above  the  orifice  is  64  ft.;  what  is  the 
velocity? 

SOLUTION. — Substituting  in  the  formula  64  for  d  and  32.16  for  g, 

v=  V2X  32. 16X64  =  64. 16. 


308  HYDRAULICS       ^ 

To  Find  Theoretical  Quantity  of  Water  Discharged  in  Given  Time.— Multi- 
ply the  area  of  the  orifice  by  the  velocity  of  the  water,  and  that  product  by 
the  number  of  seconds. 

EXAMPLE.— What  quantity  of  water  will  be  discharged  in  5  sec.  from  an 
orifice  having  an  area  of  2  sq.  ft.,  at  a  depth  of  16  ft.? 

SOLUTION. —  2X  V2X  32. 16X16  =  64. 16  cu.  ft.,  or  the  amount  discharged 
in  1  sec.,  and  in  5  sec.  the  amount  will  be  5X64.16  =  320.8  cu.  ft. 

The  foregoing  rules  are. only  theoretical,  and  are  only  useful  as  foundations 
on  which  to  build  practical  formulas. 

Flow  of  Water  Through  Orifices. — The  standard  orifice,  or  an  orifice  so 
arranged  that  the  water  when  flowing  from  it  touches  only  a  line,  as  is  the 
case  when  flowing  through  a  hole  in  a  very  thin  plate,  is  used  for  the  measure- 
ment of  water.  The  contraction  of  the  jet,  which  always  occurs  when  water 
issues  from  a  standard  orifice,  is  due  to  the  circumstance  that  the  particles 
of  water  as  they  approach  the  orifice  move  in  conyerging  directions,  and  that 
these  directions  continue  to  converge  for  a  short  distance  beyond  the  plane  of 
the  orifice.  This  contraction  causes  only  the  inner  corner  of  the  orifice  to  be 
touched  by  the  escaping  water,  and  takes  place  in  orifices  of  any  shape,  its  cross- 
section  being  similar  to  the  orifice  until  the  place  of  greatest  contraction  is 
passed.  Owing  to  this  contraction,  the  actual  discharge  from  an  orifice  is 
always  less  than  the  theoretical  discharge. 

Coefficient  of  Contraction. — The  coefficient  of  contraction  is  the  number 
by  which  the  area  of  the  orifice  is  to  be  multiplied  in  order  to  find  the  area 
of  the  least  cross-section  of  the  jet.  By  experiment,  this  coefficient  has  been 
found  to  be  about  .62  (Merriman's  "Hydraulics");  or,  in  other  words,  the 
minimum  cross-section  of  the  jet  is  62%  of  the  cross-section  of  the  orifice. 

Coefficient  of  Velocity. — The  coefficient  of  velocity  is  the  number  by  which 
the  theoretical  velocity  of  flow  from  the  orifice  is  to  be  multiplied  in  order  to 
find  the  actual  velocity  at  the  least  cross-section  of  the  jet.  This  may  be  taken 
for  practical  work  as  .98;  or,  in  other  words,  the  actual  flow  at  the  contracted 
section  is  98%  of  the  theoretical  velocity. 

Coefficient  of  Discharge. — The  coefficient  of  discharge  is  the  number  by 
which  the  theoretical  discharge  is  to  be  multiplied  in  order  to  obtain  the  actual 
discharge.  This  has  been  found  by  thousands  of  experiments  to  be  equal  to 
the  product  of  the  coefficients  of  contraction  .and  velocity,  and  for  practical 
work  it  may  be  taken  as  .61;  or,  the  actual  discharge  from  standard  orifices 
is  61%  of  the  theoretical  discharge. 

NOTE. — While  the  coefficients  for  standard  orifices  with  sharp  edges  have 
been  determined  fairly  close,  those  for  the  more  complicated  cases  of  weirs, 
and  especially  for  the  flow  of  water  through  long  pipes,  are  simply  the  nearest 
approximation  to  the  truth  that  it  has  been  possible  to  obtain.  In  all  cases, 
the  coefficient  should  be  one  that  has  been  determined  under  cpnditions  similar 
to  those  in  the  problem  in  hand.  For  instance,  it  is  not  practicable  to  use  the 
C9efficient  for  small  pipes  in  solving  problems  relating  to  large  ones,  or  for  short 
pipes  in  solving  problems  relating  to  long  ones. 

Suppression  of  Contraction.— When  a  vertical  orifice  has  its  lower  edge 
at  the  bottom  of  a  reservoir,  the  particles  of  water  flowing  through  its  lower 
portion  move  in  lines  nearly  perpendicular  to  the  plane  of  the  orifice,  and 
the  contraction  of  the  jet  does  not  form  on  the  lower  side.  The  same  thing 
occurs  in  a  lesser  degree  when  the  lower  edge  of  the  orifice  is  within  a  distance 
of  three  times  its  least  diameter  from  the  bottom.  The  suppression  of  con- 
traction will  occur  on  the  side  if  it  is  placed  within  a  distance  of  three  times 
its  least  diameter  trom  the  side  of  a  reservoir,  the  suppression  of  contraction 
being  the  greater  the  nearer  the  orifice  is  to  the  side.  By  rounding  the  edge 
of  the  orifice  sufficiently,  the  contraction  can  be  completely  suppressed,  and  the 
discharge  can  be  increased.  As  stated  before,  the  value  of  the  coefficient  of 
contraction  for  a  standard  square-edged  orifice  is  .62,  but  with  a  rounded 
orifice  it  may  have  any  value  between  .62  and  1.  depending  on  the  degree  of 
rounding  1  he  coefficient  of  discharge  for  square-edged  orifices  has  a  mean 
value  of  .61;  this  is  increased  with  rounded  edges  and  may  have  any  value 
between  .51  and  1,  although  it  is  not  probable  that  values  greater  than  .95 
can  be  obtained  except  by  the  most  careful  adjustment' of  the  rounded  edges 
to  the  exact  curve  of  a  completely  contracted  jet.  A  rounded  interior  orifice 
s  therefore  always  a  source  of  error  when  the  object  of  the  orifice  is  the  measure- 
ment of  the  discharge. 


HYDRAULICS 


309 


GAUGING  WATER 

Water  is  sold  by  two  methods;  i.  e.,  the  flowing  unit  and  the  capacity  unit. 
The  flowing  unit  is  1  cu.  ft.  per  sec.  In  the  western  part  of  North  America 
the  miners'  inch  has  come  into  use  quite  largely,  while  in  Australia  and  New 
Zealand  the  cubic  foot  per  second  is  the  common  measure;  1  cu.  ft.  per  sec. 
being  1  head,  10  heads  of  water  is  10  cu.  ft.  per  sec.,  regardless  of  the  actual 
hydrostatic  head  under  which  the  water  is  delivered.  Water  is  sometimes  sold 
for  irrigation  by  the  capacity  unit,  that  is,  so  much  land  covered  to  a  certain 
depth,  as,  for  instance,  the  acre-foot,  which  means  that  1  A.  has  been  covered 
to  a  depth  of  1  ft.,  or  that  43,560  cu.  ft.  of  water  has  been  furnished. 

Miners'  Inch. — The  miners'  inch  may  be  roughly  defined  as  the  quantity  of 
water  that  will  flow  in  1  min.  through  a  vertical  standard  orifice  having  a  sec- 
tion of  1  sq.  in.  and  a  head  of  65  in.  above  the  center  of  the  orifice.  This  quan- 
tity equals  1.53  cu.  ft.,  and  the  mean  quantity  may  be  taken  at,  approximately, 
1.5  cu.  ft.  per  min.  The  laws  or  customs  defining  the  miners'  inch  in  different 
districts  vary  so  that  the  amount  of  water  actually  delivered  varies  from  1.2  to 
1.76  cu.  ft.  per  min.  The  principal  reasons  for  these  variations  are  the  methods 
adopted  for  measuring  the  water  where  large  quantities  are  used;  as,  for 
instance,  at  Smartsville,  California,  an  opening  4  in.  deep,  250  in.  long,  with  a 
head  of  7  in.  above  the  top  edge,  is  said  to  furnish  1,000  miners'  inches,  while 
it  actually  furnishes  considerably  over  1,000.  In  other  places,  the  size  of  the 
opening  for  measuring  the  amounts  is  restricted,  and  may  actually  furnish  less 
than  the  rated  amount.  In  Montana  the  common  method  of  measurement 
was  formerly  through  a  vertical  rectangle  1  in.  high,  with  a  head  on  the  center 

DUTY  OF  MINERS'  INCH 

(Risdon  Iron  Works,  Evans's  Elevator  Catalogue) 

North  Bloomfield  Mine 


Years 

Amount 
of 
Gravel 
Washed 
Cubic 
Yards 

Miners' 
24-Hour 
Inches 

Grades 

Amount 
Washed 
per 
Miners' 
Inch 
Cubic 
Yards 

Water 
Used  per 
Cubic 
Foot  of 
Gravel 
Moved 
Cubic 
Feet 

Height 
of 
Bank 

Feet 

1870-74 

3,250,000 

710,987 

6    in.  to  12  ft. 

4.60 

18 

100 

1875 

1,858,000 

386,972 

6    in.  to  12  ft. 

4.80 

17 

100 

1876 

2,919,700 

700,000 

6    in.  to  12  ft. 

4.17 

20 

200 

1877 

2,993,930 

595,000 

6    in.  to  12  ft. 

3.86 

21 

265 

Totals 

11,021,630 

2,392,959 

4.60 

18 

La  Grange  Mine 


1874-76 

676,968 

624,745 

4  in.  to  16  ft. 

1.08 

74.0 

10  to  48 

1875-76 

683,244 

375,155 

4  in.  to  16  ft. 

1.82 

43.9 

6 

1874-76 

284,932 

207,010 

4  in.  to  16ft. 

1.37 

58.0 

50  to  80 

1875-78 

459,570 

302,960 

4  in.  to  16ft. 

1.52 

52.0 

40  to  50 

1880-81 

329,120 

203,325 

4  in.  to  16  It. 

1.57 

50.0 

10  to  80 

Totals 

2,433,834 

1,713,195 

1.42 

56.0 

310 


HYDRAULICS 


of  the  orifice  of  4  in.  The  number  of  miners'  inches  discharged  was  considered 
to  be  the  same  as  the  number  of  linear  inches  in  the  length  of  the  orifice;  thus, 
under  the  given  head,  an  orifice  1  in.  deep  and  60  in.  long  could  discharge 
60  miners'  inches. 

The  State  Legislature  of  Montana  has  now  passed  a  law  defining  the  miners' 
inch  as  the  number  of  gallons  of  water  discharged  in  a  given  time,  regardless 
of  the  character  of  the  openings  or  methods  of  measurement.  The  statement 
is  as  follows:  "Where  water  rights,  expressed  in  miners'  inches,  have  been 
granted,  100  miners'  inches  shall  be  considered  equivalent  to  a  flow  of  2£  cu. 
ft.  per  sec.  (18.7  gal.),  and  this  proportion  shall  be  observed  in  determining 
the  equivalent  flow  represented  by  any  number  of  miners'  inches."  If  this 
amount  is  reduced  to  cubic  feet  per  minute,  it  will  be  found  to  be  equal  to  a 
flow  of  1.5  cu.  ft.  per  min.,  which  is  the  value  given  for  the  miners'  inch. 

Duty  or  Work  Performed  by  a  Miners'  Inch  of  Water. — Few  tests  have  been 
made  in  regard  to  the  duty  of  a  miners'  inch  of  water,  but  the  North  Bloom- 
field  mine  and  the  La  Grange  mine,  in  California,  have'  carried  on  a  series  of 
experiments  extending  over  several  years.  At  the  La  Grange  mine,  the  obser- 
vations were  carried  on  simultaneously  upon  several  different  claims,  hence 
parallel  dates  appear.  The  following  table  gives  the  results  of  these  experi- 


Number  of 

Dimensions  of  Aperture,  in  Inches 

Depth  of  Pressure 
Board  Above 

Sluice  Heads 

Top  of  Aperture 

Width 

Depth 

Inches 

1 

16 

1 

IT 

2 

16 

2 

4! 

3 

16 

21 

4 

16 

2 

10  1 

5 

16 

3; 

91 

6 

32 

2. 

81 

7 

32 

21 

ftf 

8 

32 

2' 

10 

9 

32 

3 

10* 

10 

32 

3| 

Sf 

ments.  In  general  the  duty  is  governed  by  the  size,  capacity,  character 
of  pavement,  and  grade  of  sluices,  together  with  the  supply  of  water.  A 
heavy  grade  will  compensate  for  a  limited  supply.  With  an  abundant  supply 
of  water  and  material,  the  capacity  of  the  sluices  will  depend  on  the  character 
of  the  material  washed,  the  size  and  minimum  grade  of  the  sluices,  and  the 
character  of  the  riffles  used.  In  the  North  Bloomfield  mine  the  sluices  were 
6  ft.  wide,  and  32  in.  deep.  The  riffles  were  principally  blocks  (wood),  but 
rock  riffles  were  used  in  the  tail  sluices.  The  larger  portion  of  the  material 
moved  was  top  gravel.  In  the  La  Grange  mine  the  sluices  were  4  ft.  wide  and 
30  in.  deep,  and  were  paved  with  blocks. 

Sluice  Head. — In  Tasmania  and  the  Australian  Provinces,  water  is  sold 
by  the  sluice  head.  For  the  following  information  relating  to  Tasmania,  we 
are  indebted  to  Roy  Bamford,  Esq.,  South  Mt.  Cameron,  Tasmania. 

"The  sluice  head  as  leased  by  mining  companies  from  the  Government  at 
a  rental  of  £1  per  yr.  for  each  head,  amounts  to  24  cu.  ft.  per  min.  and  is 
measured  as  follows: 

"A  Government  gauge  box  for  measuring  water  is  12  ft.  long,  open  on  top, 

and  set  truly  horizontal.  The 
outlet  end  of  the  box  is  closed 
with  a  board  1  in.  in  thickness 
with  the  exception  of  an  aper- 
ture, which  is  always  the  full 
width  of  the  gauge  box.  In  all 
cases,  the  lower  end  of  the 
aperture  is  2  in.  above  the 
bottom  of  the  gauge  box. 
FIG.  1  When  measuring  the  discharge, 

through  the  aperture,  the  water  must  stand  on  a  level  with  the  top  of  the 


HYDRAULICS 


311 


board.     When    more   than  ten  sluice    heads  of    water  are  required  to   be 
measured,  two  or  more  of  such  gauge  boxes  shall  be  used." 

Gauging  by  V  Notch. — The  right-angled  V  notch  is  frequently  used  for  gaug- 
ing the  flow  of  comparatively  small  streams.  The  notch  is  usually  fitted  into 
a  box  provided  with  baffle  boards,  Fig.  1,  or,  where  this  is  not  practicable, 
the  water  should  be  so  impounded  above  the  notch  as  to  remove  all  possibility 
of  surface  currents  producing  a  perceptible  velocity  of  approach.  The  dis- 
tance a  of  the  surface  of  the  water  below  the  top  of  the  box  is  taken  at  a 
point  some  distance  back  from  the  notch  (at  least  18  to  20  in.),  where  the  sur- 

DISCHARGE    OF   WATER  THROUGH   A   RIGHT-ANGLED    V   NOTCH 


>v     «£ 

>>  «2 

jj    0) 

£  H  "3 

*«3 

>,-££ 

"S  "' 

I| 

w  Jj 

1|| 

•sl 

II 

H 

1  J 

.(J      4>  3 

||| 

1J 

1  -SS 
3  1*  w 

h 

Q* 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

1.05 

.3457 

3.25 

5.827 

5.45 

21.22 

7.65 

49.53 

9.85 

93.18 

1.10 

.3884 

3.30 

6.054 

5.50 

21.71 

7.70 

50.34 

9.90 

94.37 

1.15 

.4340 

3.35 

6.285 

5.55 

22.20 

7.75 

51.16 

9.95 

95.56 

1.20 

.4827 

3.40 

6.523 

5.60 

22.70 

7.80 

51.99 

10.00 

96.77 

1.25 

.5345 

3.45 

6.765 

5.65 

23.22 

7.85 

52.83 

10.05 

97.98 

1.30 

.5896 

3.50 

7.012 

5.70 

23.74 

7.90 

53.67 

10.10 

99.20 

1.35 

.6480 

3.55 

7.266 

5.75 

24.26 

7.95 

54.53 

10.15 

100.43 

1.40 

.7096 

3.60 

7.524 

5.80 

24.79 

8.00 

55.39 

10.20 

101.67 

1.45 

.7747 

3.65 

7.788 

5.85 

25.33 

8.05 

56.26 

10.25 

102.92 

1.50 

.8432 

3.70 

8.058 

5.90 

25.87 

8.10 

57.14 

10.30 

104.18 

1.55 

.9153 

3.75 

8.332 

5.95 

26.42 

8.15 

58.03 

10.35 

105.45 

.60 

.9909 

3.80 

8.613 

6.00 

26.98 

8.20 

58.92 

10.40 

106.73 

.65 

1.0700 

3.85 

8.899 

6.05 

27.55 

8.25 

59.82 

10.45 

108.02 

.70 

1.1530 

3.90 

9.191 

6.10 

28.12 

8.30 

60.73 

10.50 

109.31 

.75 

1.2400 

3.95 

9.489 

6.15 

28.70 

8.35 

61.65 

10.55 

110.62 

.80 

1.3300 

4.00 

9.792 

6.20 

29.28 

8.40 

62.58 

10.60 

111.94 

.85 

1.4240 

4.05 

10.100 

6.25 

29.88 

8.45 

63.51 

10.65 

113.26 

.90 

1.5220 

4.10 

10.410 

6.30 

30.48 

8.50 

64.45 

10.70 

114.60 

.95 

1.6250 

4.15 

10.730 

6.35 

31.09 

8.55 

65.41 

10.75 

115.94 

2.00 

1.7310" 

4.20 

11.060 

6.40 

31.71 

8.60 

66.37 

10.80 

117.29 

2.05 

1.8410 

4.25 

11.390 

6.45 

32.33 

8.65 

67.34 

10.85 

118.65 

2.10 

1.9550 

4.30 

11.730 

6.50 

32.96 

8.70 

68.32 

10.90 

120.02 

2.15 

2.0740 

4.35 

12.070 

6.55 

33.60 

8.75 

69.30 

10.95 

121.41 

2.20 

2.1960 

4.40 

12.420 

6.60 

34.24 

8.80 

70.30 

11.00 

122.81 

2.25 

2.3230 

4.45 

12.780 

6.65 

34.89 

8.85 

71.30 

11.05 

124.21 

2.30 

2.4550 

4.50 

13.140 

6.70 

35.56 

8.90 

72.31 

11.10 

125.61 

2.35 

2.5900 

4.55 

13.510 

6.75 

36.23 

8.95 

73.33 

11.15 

127.03 

2.40 

2.7300 

4.60 

13.890 

6.80 

36.89 

9.00 

74.36 

11.20 

128.45 

2.45 

2.8750 

4.65 

14.270 

6.85 

37.58 

9.05 

75.40 

11.25 

129.90 

2750 

3.0240 

4.70 

14.650 

6.90 

38.27 

9.10 

76.44 

11.30 

131.35 

2.55 

3.1770 

4.75 

15.040 

6.95 

38.96 

9.15 

77.49 

11.35 

132.81 

'2.  (30 

3.3350 

4.80 

15.440 

7.00 

39.67 

9.20 

78.55 

11.40 

134.27 

2.65 

3.4980 

4.85 

15.850 

7.05 

40.38 

9.25 

79.63 

11.45 

135.75 

2.70 

3.6660 

4.90 

16.260 

7.10 

41.10 

9.30 

80.71 

11.50 

137.23 

2.75 

3.8380 

4.95 

16.680 

7.15 

41.83 

9.35 

81.80 

11.55 

138.73 

2.80 

4.0140 

5.00 

17.110 

7.20 

42.56 

9.40 

82.90 

11.60 

140.23 

2.85 

4.1960 

5.05 

17.540 

7.25 

43.30 

9.45 

84.01 

11.65 

141.75 

2.90 

4.3820 

5.10 

17.970 

7.30 

44.06 

9.50 

85.12 

11.70 

143.28 

2.95 

4.5740 

5.15 

18.420 

7.35 

44.82 

9.55 

86.24 

11.75 

144.82 

3.00 

4.7700 

5.20 

18.870 

7.40 

45.58 

9.60 

87.37 

11.80 

146.36 

3.05 

4.9710 

5.25 

19.320 

7.45 

46.36 

9.65 

88.52 

11.85 

147.91 

3.10 

5.1780 

5.30 

19.790 

7.50 

47.14 

9.70 

89.67 

11.90 

149.48 

o.l5 

5.3880 

5.35 

20.260 

7.55 

47.92 

9.75 

90.83 

11.95 

151.05 

3.20 

5.6050 

5.40 

20.730 

7.60 

48.72 

9.80 

92.00 

12.00 

152.64 

*1  cu.  ft.  contains  7.48  U.  S.  gal.;  1  U.  S.  gal.  weighs  8.34  Lb. 


312 


HYDRAULICS 


in  which  Q  =  quantity,  in  cut 
h  =  '. 


feet  per  minute; 


face  of  the  water  is  unaffected  by  the  flow  through  the  notch.  The  distance 
a,  subtracted  from  the  total  depth  of  the  notch  H,  gives  the  head  h  of  the 
water  passing  over  the  notch.  The  discharge,  in  cubic  feet  per  second,  may 
be  found  by  the  formula 

0  =  .306VP= 
ubic 

•  head,  in  inches. 

The  accompanying  table  gives  the  discharge,  in  cubic  feet  per  minute, 
through  a  right-angled  V  notch,  as  shown  in  Fig.  1,  for  heads  varying  from 

1.05  in.  to  12  in. 

Gauging  by  Weirs. — A  weir  is 
an    obstruction    placed    across    a 
stream  for  the  purpose  of  diverg- 
ing the  water  so  as  to  make  it  flow 
through  a  desired  channel,  which 
may  be  a  notch  or  opening  in  the 
weir  itself.     The  term  usually  ap- 
_Ji  plies   to    rectangular    notches    in 
z^^=:  which  the  water  touches  only  the 
bottom    and    ends,    the    opening 

being  a  notch  without  any  upper 

%§zggp3!gH:3  edge.     Weirs  are  of  two  general 
classes:  weirs  with  end  contractions, 

•p       g  '  **'  Fig.  2  (a) ,  and  weirs  without  end 

contractions,  as  in  (6).  The  crest 
and  edges  of  the  weir  with  end  contractions  should  be  sharp,  as  shown  in 
(c)  and  (J).  The  head  of  water  H  producing  the  flow  over  the  weir  should 
be  measured  at  a  sufficient  distance  from  the  crest  to  avoid  the  effects  of  the 
curve  of  the  surface  as  it  flows  over  the  crest.  The  water  above  the  weir 
should  be  motionless,  or 
if  it  has  any  perceptible 
current  toward  the  weir, 
this  should  be  determined 
and  taken  into  account  in 
the  formula.  Fig.  3  illus- 
trates a  weir  constructed  ~ 
across  a  small  stream  for 
measuring  its  flow.  The 
head  is  measured  from  the 
stake  £  some  distance  back 
of  the  weir,  the  top  of  the 
stake  being  level  with  the 
crest  of  the  weir  B.  The 
discharge  over  the  weir 
may  be  calculated  from 
the  following  formula: 

Let  1  =  length  of  weir,  in  feet; 
#  =  head,  in  feet; 

v  =  velocity  with  which  water  approaches  weir,  in  feet; 
h  =  head  equivalent  to  velocity  with  which  water  approaches  weir; 
e  =  coefficient  of  discharge; 

Q  =  theoretic  discharge,  in  cubic  feet  per  second; 
Q'  =  actual  discharge,  in  cubic  feet  per  second. 

For  weirs  with  end  contractions  and  a  velocity  of  approach,  the  actual 
discharge  is 

Where  the  water  has  no  velocity  of  approach, 

Q'  =  5.347  C/V7/3 

For  weirs  without  end  contractions,  but  with  a  velocity  of  approach,  the 
actual  discharge  is 

=  5.347  cl 


pIG   3 


Where  the  water  has  no  velocity  of  approac 
Q'  =  5.347  cl^l~H* 

The  velocity  with  which  the  water  approaches  the  weir  may  be  found  by 
determining  the  approximate  discharge  from  the  stream  without  any  allowance 
for  velocity  of  approach,  and  then  dividing  this  discharge,  in  cubic  feet  per 


HYDRAULICS 


313 


second,  by  the  area  of  the  stream,  in  square  feet,  where  it  approaches  the 

weir,  which  will  give  the  velocity  of  approach,  in  feet  per  second.     Having 

obtained  the  value  of  v,  the  equivalent  head  h  may  be  found  by  the  formula 

fc  =  . 01555^2 

As  v  is  small  in  a  properly  constructed  weir,  it  is  usually  neglected  unless 
great  accuracy  is  required. 

The  values  of  coefficients  of  discharge,  as  determined  from  experiments, 
for  weirs  with  end  and  for  weirs  without  end  contractions  are  given  in  the 
accompanying  tables.  In  the  first  two  tables,  the  values  of  the  coefficients 
are  given  in  feet  and  tenths.  When  only  a  close  approximatioh  is  required, 
it  is  desired  to  take  all  of  the  measurement  in  feet  and  inches.  The  third 
table  should  not  be  used  unless  the  length  of  the  crest  is  at  least  three  or  four 
times  the  depth  of  water  passing  over  the  weir,  for  if  this  is  not  the  case,  there 
will  be  serious  errors  caused  by  end  contractions. 


COEFFICIENT  OF  DISCHARGE  FOR  WEIRS  WITH  END 
CONTRACTIONS 


Length  of  Weir,  in  Feet 

Effective  Head 

.66 

1              2 

3 

5 

10 

19 

Feet 

1 

Value  of  Coefficient 

.10 

.632 

.639 

.646 

.652 

.653 

.655 

.656 

.15 

.619 

.625 

.634 

.638 

.640 

.641 

.642 

.20 

.611 

.618 

.626 

.630 

.631 

.633 

.634 

.25 

.605 

.612 

.621. 

.624 

.626 

.628 

.629 

.30 

.601 

.608 

.616 

.619 

.621 

.624 

.625 

.40 

.595 

.601 

.609 

.613 

.615 

.618 

.620 

.50 

.590 

.596 

.605 

.608 

.611 

.615 

.617 

.60 

.587 

.593 

.601 

.605 

.608 

.613 

.615 

.70 

.590 

.598 

.603 

.606 

.612 

.614 

Qf\ 

.595 

.600 

.604 

.611 

.613 

.90 

.592 

.598 

.603 

.609 

.612 

1.00 

.590 

.595 

.601 

.608 

.611 

1.20 

.585 

.591 

.597 

.605 

.610 

1.40 

.580 

.587 

.594 

.602 

.609 

1.60 

.582 

.591 

.600 

.607 

COEFFICIENT  OF  DISCHARGE  FOR  WEIRS  WITHOUT  END 
CONTRACTIONS 


Length  of  Weir,  in  Feet 

Effective  Head 
Feet 

19 

10 

7 

5 

4 

3 

2 

Value  of  Coefficient 

.10 

.657 

.658 

.658 

.659 

.15 

.643 

.644 

.645 

.645 

.647 

.649 

.652 

.20 

.635 

.637 

.637 

.638 

.641 

.642 

.645 

25 

.630 

.632 

.633 

.634 

.636 

.638 

.641 

.30 

.626 

.628 

.629 

.631 

.633 

.636 

.639 

.40 

.621 

.623 

.625 

.628 

.630 

.633 

.636 

.50 

.619 

.621 

.624 

.627 

.630 

.633 

.637 

.60 

.618 

.620 

.623 

.627 

.630 

.634 

.638 

.70 

.618 

.620 

.624 

.628 

.631 

.635 

.640 

.80 

.618 

.621 

-.625 

.629 

.633 

.637 

.643 

.90 

.619 

.622 

.627 

.631 

.635 

.639 

645 

1.00 

.619 

.624 

.628 

.633 

.637 

.641 

648 

1.20 

.620 

.626 

.632 

.636 

.641 

.646 

1.40 

.^22 

.629 

.634 

.640 

.644 

1.60 

.623 

.631 

.637 

.642 

.647 

314 


HYDRAULICS 


DISCHARGE  PER  MINUTE  FOR  EACH  INCH  IN  LENGTH  OF  WEIR 
FOR  DEPTHS  FROM  1-8  IN.  TO  25  IN. 


Depth  of  Water,  in  Inches 

0 

i 

i 

1 

i 

! 

I 

I 

Discharge  per  Inch  of  Length  per  Minute,  in  Cubic  Feet 

0 

.01 

.05 

.09 

.14 

.20 

.26 

.33 

1 

.40 

.47 

.55 

.65 

.       .74 

.83 

.93 

1.03 

2 

1.14 

1.24 

1.36 

1.47 

1.59 

1.71 

1.83 

1.96 

3 

2.09 

2.23 

2.36 

2.50 

2.63 

2.78 

2.92 

3.07 

4 

3.22 

3.37 

3.52 

3.68 

3.83 

3.99 

4.16 

4.32 

5 

4.50 

4.67 

4.84 

5.01 

5.18 

5.36 

5.54 

5.72 

6 

5.90 

6.09 

6.28 

6.47 

6.65 

6.85 

7.05 

7.25 

7 

7.44 

7.64 

7.84 

8.05 

8.25 

8.45 

8.66 

8.86 

8 

9.10 

9.31 

9.52 

9.74 

9.96 

10.18 

10.40 

10.62 

9 

10.86 

11.08 

11.31 

11.54 

11.77 

12.00 

12.23 

12.47 

10 

12.71 

13.95 

13.19 

13.43 

13.67 

13.93 

14.16 

14.42 

11 

14.67 

14.92 

15.18 

15.43 

15.67 

15.96 

16.20 

16.46 

12 

16.73 

16.99 

17.26 

17.52 

17.78 

18.05 

18.32 

18.58 

13 

18.87 

19.14 

19.42 

19.69 

19.97 

20.24 

20.52 

20.80 

14 

21.09 

21.37 

21.65 

21.94 

22.22 

22.51 

22.79 

23.08 

15 

23.38 

23.67 

23.97 

24.26 

24.56 

24.86 

25.16 

25.46 

16 

25.76 

26.06 

26.36 

26.66 

26.97 

27.27 

27.58 

27.89 

17 

28.20 

28.51 

28.82 

29.14 

29.45 

29.76 

30.08 

30.39 

18 

30.70 

31.02 

31.34 

31.66 

31.98 

32.31 

32.63 

32.96 

19 

33.29 

33.61 

33.94 

34.27 

34.60 

34.94 

35.27 

35.60 

20 

35.94 

36.27 

36.60 

36.94 

37.28 

37.62 

37.96 

38.31 

21 

38.65 

39.00 

39.34 

39.69 

40.04 

40.39 

40.73 

41.09 

22 

41.43 

41.78 

42.13 

42.49 

42.84 

43.20 

43.56 

43.92 

23 

44.28 

44.64 

45.00 

45.38 

45.71 

46.08 

46.43 

46.81 

24 

47.18 

47.55 

47.91 

48.28 

48.65 

49.02 

49.39 

49.76 

CONVERSION  FACTORS 

Cubic  Feet  Into  Gallons. — 1  cu.  ft.  =  1,728  cu.  in.  =  1,728-^-231  gal. 
=  7.4805194  gal. 

Gallons  Into  Cubic  Feet.— 1  U.  S.  liq.  gal.  =  231  cu.  in.  =  23 1-5-1, 728  cu.  ft. 
=  .133680555  cu.  ft 

Feet  per  Second  Into  Miles  per  Hour. — 1  ft.  per  sec.  =  3,600  ft.  per  hr. 
-=»§*.  or«mi.  perhr. 

Miles  per  Hour  Into  Feet  per  Second. — 1  mi.  per  hr.  =  5,280  ft.  per  hr. 
=  «§»,  or  if  feet  per  sec. 

Second-Feet  per  Day  Into  Gallons. — 1  sec.-ft.,  or  7.4805194  gal.  per  sec.  for 
1  da.,  or  86,400  sec.  =  646,316.87616  gal. 

Millions  of  Gallons  Into  Second-Feet  per  Day.— 1,000,000  gal.  per  24  hr. 

~1  728X86400  CU*  **'  per  Se°"  Or  1>5472286  sec-  ft- 

Second-Feet  per  Day  Into  Acre-Feet. — 1  sec.-ft.  flow  for  1  da.  =  86,400  cu. 
ft.  =  86,400  +  43,560  =  1.983473  A.-ft. 

Acre-Feet  Into  Second-Feet  Flow  for  24  Hours.— 1  A.-ft.  each  24  hr. 
=  43,560  cu.  ft.  each  86,400  sec.  =  43 ,560-^86,400,  or  fflt  sec.-ft.  flow  for  24  hr. 

Acre-Feet  Into  Gallons.— 1  A.-ft.  =  43,560  cu.  ft.  (43.560X  1,728) -h 231 
=  325,851.428  gal. 

Millions  of  Gallons  Into  Acre-Feet.— 1,000,000  U.  S.  liq.  gal.,  or  231,000,000 
cu.  in.  - 133,680.555  cu.  ft.  =  133,680.555^-43,560  =  3.0688832  A.-ft. 


HYDRAULICS 


315 


Second-Feet  Into  Minute  Gallons. — 1  cu.  ft.  contains  1,728  cu.  in.;  1  gal.  has 
a  capacity  of  231  cu.  in.;  1  sec.-ft.  equals  [(1,728-4- 231) X 60]  gal.  per  min. 
=  448.831164  min.-gal. 

Minute-Gallons  Into  Second-Feet. — 1  gal.  contains  231  cu.  in.;  1  cu.  ft.  con- 
tains 1,728  cu.  in.;  1  gal.  per  min.  equals  [ (231-5-1,728)-^ 60]  sec.-ft., 
=  .0022280092  sec.-ft. 


FLOW  OF  WATER  IN  OPEN  CHANNELS 

Ditches. — In  the  case  of  hydraulic  mining  and  irrigation,  water  is  usually 
conveyed  through  ditches.  The  ditch  line  should  be  carefully  surveyed  and 
all  brush  and  trees  removed,  and  the  underbrush  cut  away  and  burned,  before 
beginning  to  excavate  the  ditch.  The  form  of  ditch  and  its  grade  will  depend 
largely  on  the  amount  of  water  to  be  conveyed  and  the  character  of  the  soil 
in  the  section  under  consideration.  As  a  general  rule,  the  average  flow  of  water 
in  a  ditch  should  not  be  less  than  2  ft.  per  sec.,  and  under  most  circumstances 
should  not  exceed  4  ft.,  though  in  rare  cases  where  the  formation  is  suitable, 
mean  velocities  of  5  ft.  per  sec.  are  employed.  Sand  will  deposit  from  a  current 
flowing  at  the  rate  of  1  j  ft.  per  sec.,  and  if  the  current  does  not  have  a  velocity 
of  at  least  2  ft.  per  sec.,  vegetation  is  liable  to  block  the  ditch  line. 

The  following  letters  will  be  used  in  the  formulas  for  determining  the 
various  factors  relating  to  ditches: 

h  =  difference  in  level  between  ends  of  canal  or  ditch,  or  between  two 

points  under  consideration; 
/  =  horizontal  length  of  portion  of  canal  or  ditch  under  consideration; 

s  =  slope  =  ratio  j  =  sine  of  slope ; 

a  =  area  of  water  cross-section  in  square  feet; 

p  =  wet  perimeter  =  portion  of  outline  of  cross-section  of  stream  in  contact 
with  channel,  in  feet; 

r  =  hydraulic  radius,  or  hydraulic  mean  depth  =  ratio  -; 

c'  =  coefficient,  depending  on  nature  of  surface  of  ditch; 

c  =  coefficient  depending  on  nature  of  surface  of  ditch,  as  determined  by 
Kutter's  formula; 

»  =  mean  velocity  of  flow,  in  feet  per  second; 

v'  =  surface  velocity  of  a  stream; 

vb  =  bottom  velocity  of  a  stream; 

x  =  bottom  or   one  side  of  a  section  the  form   of   which   is  one-half   a 
regular  hexagon,  in  feet; 

Q  =  quantity  of  water  flowing,  in  cubic  feet  per  second; 

n  =  coefficient  of  roughness  in  Kutter's  formula. 

Safe  Bottom  Velocity. — The  bottom  velocity  of  a  stream  may  be  obtained 
from  the  average  velocity  by  the  formula 

vb  =  v-  10.87  Vrs 

The  accompanying  table  gives  values  of  safe  bottom  and  mean  velocities, 
corresponding  with  certain  materials,  as  given  by  Ganguillet  and  Kutter: 

SAFE  BOTTOM  AND  MEAN  VELOCITIES  OF  STREAMS 


Material  of  Channel 

Safe  Bottom 
Velocity  vb 
Feet  per  Second 

Mean  Velocity  v 
Feet  per  Second 

Soft  brown  earth  
Soft  loam 

.249 
.499 

.328 
656 

Sand  

1.000 

1  312 

Gravel  

1.998 

2.625 

Pebbles  

2.999 

3.938 

Broken  stone,  flint  
Conglomerate,  soft  slate  
Stratified  rock  
Hard  rock 

4.003 
4.988 
6.006 
10009 

5.579 
6.564 
8.204 
13  127 

316  .  HYDRAULICS 

Resistance  of  Soils  to  Erosion  by  Water.  —  The  following  resistances  of 
various  soils  to  erosion  by  water  have  been  selected  from  the  experiments  of 
W.  A.  Burr: 

Soil  Feet  per  Second 

Pure  sand  resists  erosion  by  flow  9f  .....................     1.10 

Sandy  soil.  15%  clay,  resists  erosion  by  flow  of  ..........    1.20 

Sandy  loam,  40%  clay,  resists  erosion  by  flow  of  ........    1.80 

Loamy  soil,  65%  clay,  resists  erosion  by  flow  of  ..........    3.00 

Clay  loam,  85%  clay,  resists  erosion  by  flow  of  ..........    4.80 

Agricultural  clay,  95%  clay,  resists  erosion  by  flow  of  .....    6.20 

Clay,  resists  erosion  by  flow  of  ........................    7.35 

Carrying  Capacity  of  Ditches.  —  Ditches  should  never  be  run  full,  but  should 
be  constructed  large  enough  so  that  they  will  carry  the  desired  amount  of 
water  when  from  three-fourths  to  seven-eighths  full.  For  any  given  cross- 
section,  the  greatest  flow  will  be  attained  when  the  hydraulic  radius  or  hydraulic 
mean  depth  is  equal  to  one-half  of  the  actual  depth  of  the  channel.  The 
cross-section  of  a  ditch  or  conduit  that  has  the  greatest  possible  carrying  capac- 
ity is  a  half  circle,  and  the  nearest  practical  approach  to  this  is  a  half  hexagon. 
Knowing  the  cross-section  of  a  ditch,  its  dimensions  may  be  found  by  the 
formula: 


As  the  obtuse  angle  between  the  side  and  bottom  of  the  ditch  is  120°,  the 
form  can  be  easily  laid  off.  The  carrying  capacity  of  ditches  generally  increases 
after  they  have  been  in  use  some  time,  as  the  ditch  becomes  lined  with  a  fine 
scum  that  closes  the  pores  in  the  soil  and  prevents  leakage;  this  may  increase 
the  amount  by  as  much  as  10%. 

Grade.  —  The  grade  of  the  ditch  must  be  sufficient  to  create  the  desired 
velocity  of  flow,  and  depends  largely  on  the  character  of  the  material  com- 
posing the  surface  of  the  ditch.  If  the  surface  is  smooth,  as,  for  instance, 
where  the  ditch  is  cut  through  clay  or  is  lined  with  masonry,  the  grade  can 
be  considerably  less  than  where  the  surface  is  rough,  or  when  cut  through 
coarse  gravel  or  when  lined  with  rough  stone.  In  mountainous  countries, 
where  the  ground  is  hard,  deep  narrow  ditches  with  steep  grades  are  gener- 
ally preferred  to  larger  channels  with  gentle  slopes,  as  the  cost  of  excavation 
is  considerably  less;  but  steep  grades  and  narrow  ditches  are  suitable  only 
when  the  banks  can  resist  the  rapid  flow.  In  California,  grades  of  from  16  to 
20  ft.  per  mi.  are  used,  and  10  ft.  per  mi.  is  quite  common.  Water  channels 
of  a  uniform  cross-section  should  have  a  uniform  grade;  otherwise,  the  flow 
will  be  checked  in  places,  which  will  result  in  deposits  of  sand  or  silt  in  some 
portions  of  the  ditch,  which  are  liable  to  cause  the  banks  to  be  overflowed 
and  the  ditch  to  be  ultimately  destroyed.  When  designing  any  given  ditch, 
the  grade  is  generally  assumed  to  correspond  to  the  formation  of  the  country 
and  the  velocity  figured  from  the  grade.  In  case  v  is  found  to  be  so  great 
that  it  will  cut  the  banks,  it  will  be  necessary  either  to  reduce  the  grade  or  to 
change  the  form  of  the  ditch  so  as  to  reduce  the  velocity. 

Ditch  Banks,  when  possible,  should  be  composed  of  solid  material,  but  when 
necessary  to  use  excavated  material  care  must  be  taken  to  see  that  the  material 
is  so  placed  as  to  avoid  settling  and  cracking  as  much  as  possible.  All  stumps, 
roots,  etc.  should  be  separated  from  the  material  to  be  used  for  embankments. 
If  artificial  banks  are  necessary,  they  should  be  built  of  masonry  if  the  expense 
is  not  too  great  ;«  or,  the  water  may  be  carried  across  depressions  in  pipes  or 
flumes.  When  the  character  of  the  material  through  which  the  ditch  is  con- 
structed is  not  sufficiently  firm  to  resist  the  desired  current  vetocity,  it  is  neces- 
sary to  line  the  ditch.  In  some  locations  the  ditches  are  simply  smoothed 
on  the  inside  and  lined  with  from  f  in.  to  1  in.  of  cement  mortar,  made  up 
of  Portland  cement  and  sharp  sand.  In  other  cases,  they  are  lined  with  dry 
stonework  laid  up  in  order  and  carefully  bonded  together.  Sometimes  the 
stonework  is  pointed  with  cement  or  mortar  on  the  inside,  so  as  to  present  a 
more  uniform  surface  to  the  flow.  In  other  cases,  the  sides  are  simply  revetted 
with  stone. 

Influence  of  Depth  on  Ditch.  —  The  depth  of  the  flow  in  a  ditch  has  consider- 
able influence  on  the  scouring  or  eroding  of  the  bottom  and  the  banks,  owing 
to  the  fact  that  a  much  greater  average  velocity  can  be  attained  in  a  deep 
stream  than  in  a  shallow  stream,  without  causing  an  excessive  velocity  of  the 
water  in  contact  with  the  wet  perimeter.  For  this  reason,  in  cases  where 
banks  will  stand  it,  it  is  best  to  use  narrow  deep  ditches  rather  than  wide  flat 


HYDRAULICS 


317 


ditches,  though  each  location  has  to  be  treated  in  accordance  with  its  own 
special  conditions,  and  no  general  rule  can  be  laid  down. 

Measuring  the  Flow  of  Water  in  Channels. — The  laws  for  the  resistance  to 
the  flow  may  be  expressed  by  the  relation  ha  =  c'lpv2;  or 


VS3- 


If  c  —  \/— ,  the  formula  becomes 


The  coefficient  c  is  usually  found  by  means  of  Kutter's  formula,  one  form 
of  which  is  as  follows: 

23+l+;00155 


The  values  for  n,  the  coefficient  of  roughness  under  various  conditions, 
are  given  in  the  accompanying  table: 

COEFFICIENT  OF  ROUGHNESS  UNDER  VARIOUS  CONDITIONS 


Character  of  Channel 


Value  of  « 


Clean,  well-planed  timber 

Clean,  smooth,  glazed  iron,  and  stoneware  pipes 

Masonry,  smoothly  plastered  with  cement,  and  for  very  clean, 

smooth,  cast-iron  pipe 

Unplaned  timber,  ordinary  cast-iron  pipe,  and  selected  pipe 

sewers,  well  laid  and  thoroughly  flushed 

Rough  iron  pipes  and  ordinary  sewer  pipes,  laid  under  usual 

conditions 

Dressed  masonry  and  well-laid  brickwork 

Good  rubble  masonry  and  ordinary  rough  or  fouled  brickwork .  .  . 

Coarse  rubble  masonry  and  firm,  compact  gravel 

Well-made  earth  canals  in  good  alinement 

Rivers  and  canals  in  moderately  good  order  and  perfectly  free 

from  stones  and  weeds 

Rivers  and  canals  in  rather  bad  condition  and  somewhat 

obstructed  by  stones  and  weeds 

Rivers  and  canals  in  bad  condition,  overgrown  with  vegetation 

and  strewn  with   stones  and   other  detritus,   according  to 

condition . . . 


.009 
.010 

.011 
.012 

.013 
.015 
.017 
.020 
.0225 

.025 
.030 

.035  to  .05 


As  it  is  quite  difficult  to  obtain  the  value  of  c  by  Kutter's  formula,  the 
following  three  approximate  formulas  for  v  are  given: 
For  canals  with  earthen  banks, 


9r+35 

If  the  ditch  is  lined  with  dry  stonework, 


if  the  ditch  is  lined  with  rubble  masonry, 


IQO.OOOr^ 
7.3r+6 

To  find  the  quantity  Q  of  water  flowing  through  any  channel  in  a  given 
time,  multiply  the  velocity  by  the  area,  or  Q  =  av. 

Flow  in  Brooks  and  Rivers. — When  a  stream  is  so  large  that  it  becomes 
impracticable  to  employ  a  weir  for  measuring  its  flow,  fairly  accurate  results 
may  be  arrived  at  by  determining  the  velocity  of  the  current  at  various  points 


318  HYDRAULICS 

in  a  carefully  surveyed  cross-section  of  the  stream,  thus  determining  both  v 
and  o.  The  greatest  velocity  of  current  occurs  at  a  point  some  distance  below 
the  surface,  in  the  deepest  part  of  the  channel.  When  determining  the  current 
velocities  in  the  different  portions  of  a  stream,  it  is  frequently  advantageous 
to  divide  the  stream  into  divisions.  This  may  be  accomplished  by  stretching 
a  wire  across  and  tying  strings  or  rags  about  the  wire  at  various  points.  The 
mean  velocity  of  the  current  between  these  points  can  be  determined  by 
current  meters,  or  by  floats.  The  points  for  observation  should  be  chosen 
•where  the  channel  is  comparatively  straight  and  the  current  uniform.  Surface' 
floats  may  be  used,  in  which  case  the  mean  velocity  of  the  point  where  the  float 
is  used  may  be  found  as  follows:  If  v'  equals  the  observed  velocity,  then  the 
mean  velocity  will  be  v  =  .9»'. 

By  taking  observations  of  the  velocity  of  the  current  in  each  section  of 
a  stream,  the  amount  of  water  flowing  may  be  determined  for  each  separate 
section.  The  total  amount  of  water  flowing  in  the  stream  will  be  the  sum 
of  the  amounts  in  each  section.  The  average  velocity  of  the  entire  stream 
may  be  found  by  dividing  the  total  amount  of  water  flowing  by  the  total  area  of 
the  cross-section  of  the  stream.  The  correction  necessary  to  reduce  surface 
velocity  to  mean  velocity  may  be  made  as  follows:  Measure  off  nine-tenths 
of  the  ordinary  distance,  and  figure  the  time  as  though  for  the  full  distance. 
For  instance,  if  only  90  ft.  is  employed,  the  time  will  be  taken  and  the  problem 
figured  as  though  it  were  100  ft.,  because  the  mean  velocity  is  only  nine-tenths 
of  the  surface  velocity.  

FLUMES 

Flumes  are  used  for  conveying  water  when  a  ditch  line  would  be  abnormally 
long,  or  when  the  material  to  be  excavated  is  very  hard.  They  may  be 
constructed  of  timber  or  of  metal,  but  metal  flumes  are  comparatively  rare, 
as  piping  can  be  used  instead.  The  line  of  the  proposed  flume  should  be 
carefully  cleared  of  all  standing  timber,  and  the  brush  burned  for  at  least 
20  ft.  each  side  of  the  flume  line  to  prevent  danger  from  fire.  The  life  of  an 
ordinary  flume,  which  is  supported  on  or  constructed  of  timber,  is  always 
short,  varying,  as  a  rule,  from  10  to  20  yr.,  depending  on  whether  the  flume  is 
allowed  to  run  dry  a  portion  of  the  year  or  is  always  full  of  water,  the  care 
with  which  it  was  originally  constructed,  and  the  attention  paid  to  repairs. 
-Grade  and  Form  of  Flumes. — Flumes  are  usually  set  on  a  much  steeper 
grade  than  is  possible  in  ditches,  the  grade  frequently  being  as  much  as  25  to 
30  ft.  per  mi.,  and  in  special  cases  even  more.  The  result  of  this  is  that  the 
carrying  capacity  of  flumes  is  much  greater  than  that  of  ditches  of  the  same  size. 
The  form  of  flume  depends  largely  on  the  material  of  which  it  is  constructed. 
Metal  flumes  may  have  a  semicircular  form,  while  wooden  flumes  are  either 
rectangular  or  V-shaped.  The  former  is  used  almost  exclusively  for  con- 
veying water,  and  the  latter  quite  extensively  for  fluming  timber  or  cord 
wood  from  the  mountains  to  the  shipping  point  in  the  valley. 

Timber  flumes  should  be  so  constructed  that  the  water  will  meet  with  but 
small  resistance,  and  the  bottom  and  side  should  be  enclosed  in  a  frame  of 

timbers  so   braced   or  secured 

that  there  is  no  possible  chance 

of  the  sides  spreading  or  lifting 

from    the    bottom,    and    thus 

causing  leakage.     As  a  rule,  all 

mortised-and-tenoned  joints 
|  should  be  avoided  in  flume  con- 
struction. Fig.  1  shows  a  tim- 
ber flume  in  which  no  joints 

are   cut;    the   bottoms   of   the 

posts    are    kept    in    place    by 

stringers  spiked  on  the  sills  and 

the  tops  are  tied  together  by 

pieces  bolted  on.     Fig.  2  shows 
PIG.  1  a   construction   in    which    the  pIGi  2 

posts  are  let  into  the  sills  and 

supported  by  diagonal  braces.  The  ties  across  the  top  of  the  posts  are  also 
notched  to  receive  the  upper  ends  of  the  posts.  As  a  rule,  these  ties  are  only 
placed  on  every  third  or  fourth  frame,  the  diagonal  braces  being  depended 
on  to  hold  the  other  posts  in  place.  The  joints  between  the  planking  may  be 
battened  on  the  inside  with  strips  of  $-in.  lumber,  4  or  5  in.  wide,  or  the  edges 


HYDRAULICS  319 

of  the  planking  may  be  dressed  and  painted  before  they  are  put  together,  so 
as  to  form  a  tight  joint. 

Connection  With  Ditches. — Where  flumes  connect  with  ditches  or  dams, 
the  posts  for  several  boxes  should  be  made  longer,  so  that  they  may  receive 
another  sideboard  to  prevent  the  water  from  splashing  over  the  sides.  The 
flume  should  also  be  widened  out  or  flared,  both  at  its  entry  and  discharge  ends. 
Where  the  flume  passes  through  a  bank  of  earth,  an  outer  siding  may  be  nailed 
on  the  outside  of  the  posts,  to  protect  the  flume  from  rotting. 

Trestles. — Where  flumes  are  carried  on  trestles,  the  individual  frames 
supporting  the  flume  are  usually  placed  on  heavy  stringers,  which  in  turn  are 
supported  upon  trestle  bents  from  12  to  16  ft.  apart,  the  frames  supporting 
the  flume  being  placed  about  4  ft.  apart. 

Curves. — Where  flumes  are  laid  around  curves,  the  outer  edge  of  the  flume 
should  be  elevated  so  as  to  prevent  splashing  and  to  cause  the  flowing  water 
to  have  a  uniform  depth  across  the  width  of  the  flume.  It  is  impossible  to 
give  any  definite  rule  as  to  the  amount  that  the  outer  edge  of  the  flume  should 
be  raised,  but  this  is  usually  accomplished  by  judging  the  amount  when  the 
flume  is  first  constructed,  and  correcting  this  by  wedging  up  after  the  water 
is  flowing.  The  individual  boxes  of  the  flume  may  have  to  be  cut  into  two 
or  three  portions  on  curves,  and  at  times  the  side  planks  are  sawed  partly 
through,  so  as  to  enable  them  to  be  bent  to  the  desired  curve. 

Waste  Gates. — Waste  gates  should  be  placed  every  5  mi.,  to  empty  the 
flume  for  repairs,  or  in  case  of  accident.  They  are  also  useful  for  flushing 
snow  out  of  a  flume.  In  snowy  regions,  flumes  are  frequently  protected  by  sheds 
over  their  exposed  portions. 

Flow  of  Water  Through  Flumes. — As  smooth  wooden  surfaces  offer  consider- 
ably less  resistance  to  the  flow  of  water  than  earth  or  stone  canals,  the  coeffi- 
cients must  necessarily  be  somewhat  reduced,  and  the  following  formula  is 
useful  in  giving  the  flow  of  water  through  flumes; 

/100.000i*f 
\6.6r+0.46 

That  flumes  may  have  their  full  carrying  capacity,  they  have  to  be  of 
sufficient  length  to  get  the  water  in  motion,  or,  as  it  is  technically  expressed, 
"to  put  the  water  in  train."  It  is  largely  on  this  account  that  flumes  have 
to  be  made  of  a  larger  cross-section  at  both  the  entrance  and  the  exit. 

In  cold  countries  it  may  be  best  to  construct  the  flume  narrower  than  it  is 
deep,  as  in  cold  weather  the  ice  in  the  narrow  flume  freezes  a  crust  entirely 
across  the  surface,  thus  protecting  the  water  from  further  action  of  the  elements 
and  frequently  prolonging  the  flow  through  the  flume  for  several  weeks,  while 
wide  shallow  flumes  will  not  freeze  on  the  surface  so  quickly,  but  will  freeze 
in  from  the  bottom  and  sides  until  they  are  practically  a  solid  mass  of  ice. 

When  a  flume  is  laid  on  the  ground  along  a  bank,  it  should  be  laid  as  close 
to  the  bank  as  possible,  so  as  to  protect  it  from  snow  or  landslides,  and  so  that 
in  the  winter  the  snow  will  drift  in  under  and  behind  it,  thus  preventing  the 
circulation  of  the  air  about  the  flume.  This  will  protect  the  flume,  and  may 
prolong  the  flow  for  some  time  after  cold  weather  sets  in. 


TUNNELS 

Tunnels  are  sometimes  used  for  conveying  water,  in  connection  with  flume 
or  ditch  lines.  Where  a  tunnel  is  unlined,  it  is  best  to  give  the  roof  the  shape 
of  the  Gothic  arch,  because  this  stands  better  and  resists  scaling  to  a  greater 
extent  than  the  round  arch,  which  usually  scales  off  until  it  has  the  form  of  the 
Gothic  arch.  If  tunnels  are  to  be  used  as  water  conduits,  without  lining,  care 
should  be  taken  to  make  the  inside  of  the  tunnel  as  smooth  as  possible.  In 
some  cases,  in  order  to  increase  the  carrying  capacity,  the  tunnel  has  been 
lined  with  wooden-stave  pipe,  backed  with  concrete,  the  pipe  requiring  no 
metal  bands,  but  depending  on  the  concrete  to  keep  it  in  place.  When  such 
linings  are  employed,  it  is  not  practicable  to  have  them  exposed  to  the  alternate 
action  of  the  water  and  the  atmosphere;  hence,  the  tunnel  should  be  kept 
continually  full  of  water.  To  accomplish  this,  the  tunnel  may  be  dropped 
below  the  grade  of  the  ditch  or  flume  line,  so  that  it  is  always  under  a  slight 
hydrostatic  pressure,  and  even  if  the  water  is  turned  off  from  the  line,  the 
tunnel  will  remain  fu1!  of  water,  the  same  as  an  inverted  siphon.  Sometimes 
tunnels  are  lined  with  cement,  being  given  either  a  circular  or  oval  form,  or 
they  may  have  a  flat  bottom,  with  flat  sides  and  an  arched  roof.  The  cement 


320 


HYDRAULICS 


may  be  placed  directly  on  the  country  rock  composing  the  walls  of  the  tunnel 
or  the  tunnel  may  be  lined  with  brick  or  stone,  and  then  cemented  on  the  inside. 
Flow  Through  Tunnels. — The  flow  of  water  through  tunnels,  when  they  are 
only  partly  filled,  is  calculated  by  the  formulas  for  flow  in  open  channels, 
while  in  the  case  of  lined  tunnels  that  are  run  full,  the  flow  is  calculated  by 
formulas  for  calculating  the  flow  through  pipes. 


PIG.  1 


FLOW  THROUGH  PIPES 

Hydraulic  Gradient. — If  a  pipe  of  uniform  cross-section  is  connected  with 
a  reservoir,  and  water  is  allowed  to  discharge  through  its  open  end,  the  pressure 
on  the  pipe  at  any  point  is  equal  to  the  vertical  distance  from  the  center  of  the 
pipe  at  that  point  to  an  imaginary  line,  called  the  hydraulic  gradient  or  hydraulic 
grade  line.  This  is  a  line  drawn  from  a  point  slightly  below  the  surface  of  the 

water  in  the  reservoir  to 
the  outlet  of  the  pipe,  as 
ab,  Fig.  1.  The  distance 
from  the  surface  of  the 
water  to  the  point  a  is  equal 
to  the  head  lost  in  over- 
coming the  friction  at  the 
entrance  to  the  pipe,  and 
is  rarely  over  1  ft.  A  pipe 
laid  along  the  line  ab  will 
carry  exactly  the  same 
amount  of  water  as  when 
laid  horizontally,  as  shown, 
but  there  will  be  practically 
no  pressure  tending  to  burst 
the  pipe  at  any  point  along 
this  line;  while  if  it  is  laid 
along  the  line  from  the 
point  a'  (the  reservoir  being  made  deeper),  it  will  still  deliver  exactly  the 
same  amount  of  water,  but  the  pressure  tending  to  burst  the  pipe  will  be 
greatly  increased.  In  order  that  a  pipe  may  have  a  maximum  discharge,  no 
point  in  the  line  must  rise  above  the  hydraulic  gradient ;  it  makes  no  difference 
in  the  discharge  how  far  below  the  gradient  it  may  fall. 

In  Fig.  2,  the  pipe  rises  above  the  hydraulic  gradient  ac;  in  this  case  a  new 
hydraulic  gradient  ab  must  be  established  and  the  flow  calculated  for  this  head. 
The  pipe  be  simply  acts  to  carry  off  the  water  delivered  to  it  at  b.  If  the 
upper  side  of  the  pipe  is  open  at  the  point  b,  the  water  will  have  no  tendency 
to  escape,  but,  on  the  contrary,  air  will  probably  enter  and  the  pipe  flow  only 
partly  full  from  b  to  c. 

Flow  in  Pipes. — Darcy,  a  French  engineer,  made  a  series  of  experiments  on 
different  diameters  of  cast-iron  pipe,  with  different  degrees  of  internal  rough- 
ness, from  which  he  calculated 
a  series  of  formulas.  The  fol- 
lowing are  some  of  these  for- 
mulas, as  arranged  by  the  late 
E.  Sherman  Gould,  C.E..E.M. 
Darcy  found  that  the  character 
of  the  inside  surface  of  the  pipe 
played  a  very  important  part 
in  its  discharge,  and  he  deduced 

a   formula    and   determined    a  pIG  2 

series  of  coefficients  for  it,  but 

Mr.  Gould  calls  attention  to  the  fact  that  the  coefficients  for  pipes  from  8  to  48  in. 
in  diameter  practically  cancel  the  numerical  factor  employed  in  Darcy 's  formula, 
and  that  a  slightly  different  factor  applies  to  pipes  from  3  to  8  in.,  so  that  the 
following  simple  formulas,  in  which  the  factors  given  apply,  may  be  obtained: 
Q  =  discharge,  in  cubic  feet  per  second; 
q  =  discharge,  in  U.  S.  gallons  per  minute; 
D  —  diameter  of  pipe,  in  feet; 
d  =  diameter  of  pipe,  in  inches; 
H  =  total  head,  in  feet; 
h  =  head  per  1,000  ft.; 
V  =  velocity,  in  feet  per  second. 


HYDRAULICS  321 


Pipes  Between_3  and  8  In.  in  Diameter 
Rough  inside  surface,  Q  =  .89^~D*h  =  .89D*TJ'Dh;  V  = 
Smooth  inside  surface,  Q  =  .89  V2ZWz  =  1.25D2  VD/Z;  V 
Pipes  Above  8  In.  in  Diameter 
Rough  inside  surface,  Q  =  VZW*  =  D^T)h;  V  =  1.27  ^Dh 

Rough  inside  surface,  d  in  inches,  Q  =  o7^\/T 

^oo     \  o 


Smooth  inside  surface,  Q=lArWi  =  lAD*^jDh;  V  = 

As  a  rule,  it  is  best  to  calculate  any  pipe  line  by  the  formula  for  pipes  having 
a  rough  internal  surface,  for  if  this  is  not  done  the  results  are  liable  to  be 
disappointing,  as  all  pipes  become  more  or  less  rough  with  use. 
Eytelwein's  Formtfia  for  Delivery  of  Water  in  Pipes: 
D  =  diameter  of  pipe,  in  inches; 
//  =  head  of  water,  in  feet; 
L  =  length  of  pipe,  in  feet; 
W  =  water  discharged  per  minute,  in  cubic  feet. 


Hawksley's  Formula: 

G  —  number  of  gallons  delivered  per  hour; 

L  =  length  of  pipe,  in  yards; 

/Z  =  head  of  water,  in  feet; 

D  =  diameter  of  pipe,  in  inches. 

*L 


Neville's  General  Formula: 

v  —  velocity,  in  feet  per  second; 

r  =  hydraulic  mean  depth,  in  feet; 

5  =  sine  of  inclination,  or  total  fall  divided  by  total  length 


In  cylindrical  pipes,  vX 47. 124<22  =  discharge  per  minute,  in  cubic  feet, 
or  vX 293. 7286d2  =  discharge  per  minute  in  gallons,  d  being  the  diameter  of  the 
pipe  in  feet. 

Comparison  of  Formulas. — The  various  formulas  for  velocity  are  as  follows: 

R  =  mean  hydraulic  depth,  in  f eet  =  area  -4-  wet  perimeter  =  -  for  circular 

section  of  pipe; 
5  =  sine  of  slope  =  y ; 

v  —  velocity,  in  feet  per  second; 

d  =  diameter  of  pipe,  in  feet; 
L  =  length  of  pipe,  in  feet; 
#  =  head  of  water,  in  feet. 
Prony,  v  =  97.05  V/J5-.  08 

Eytelwein,  »  = 

Eytelwein,  »=  108V^5-.13 

Hawksley,  "  ?. 


Neville,  i 

Darcy,  v  =  C    ^RS 

For  the  value  of  C  see  the  following  table.      The  maximum  value  of  C  for 
very  large  pipes  is  113.3. 

Kutter,  v  =  C   ^RS 

in  which  C  = 


322 


HYDRAULICS 


Weisbach,  h  =  ~ 

~\v  '  "6 

in  which  /*  =  head  necessary  to  overcome  friction  in  the  pipe; 
r  =  mean  radius  of  pipe,  in  feet; 
g  =  gravity  =  32.2. 

.      .02L/,,     1  \»» 

,     Darcy'  ht — T\l+Wd)2g 

VALUE  OF  C  IN  DARCY'S  FORMULA 


Diameter  of  Pipes,  in  Inches 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

12 

14 

16 

18 

20 

22 

24 

Value  of  C. 


05 

80 

93 

99 

102 

103 

105 

106 

107 

108 

109 

109.5 

110 

110.5 

110.7 

111 

111.5 

111.5 

Loss  of  Head  in  Pipe  by  Friction.— In  each  100  ft.  in  length  the  loss  of  head, 
by  friction,  in  pipes  of  different  diameters,  when  discharging  various  quantities 
of  water  per  minute  is  given  in  the  accompanying  table,  which  has  been 
prepared  by  the  Pelton  Water  Wheel  Co. 


O/AOffAAf   Of    FftlCTIONM.     HEADS    IN    WATCff    HPf  flf/f    1000  FT.    LENGTH. 


FIG.  3 

EXAMPLE.— Having  200-ft.  head  and  600  ft.  of  11-in.  pipe,  carrying  119  cu. 
ft.  of  water  per  minute,  what  is  the  effective  head? 

SOLUTION. — In  right-hand  column,  under  11-in.  pipe,  find  119  cu.  ft. 
Opposite  this  will  be  found  the  coefficient  of  friction  for  this  amount  of  water, 
which  is  .444.  Multiplying  this  by  the  number  of  hundred  feet  of  pipe,  which 


HYDRAULICS 


323 


is  6,  gives  2.66  ft.,  which  is  the  loss  of  head.     Therefore,  the  effective  head 
is  200  -2.66  =  197.34. 

The  following  formula,  deduced  by  William  Cox,  gives  practically  the 
same  results  as  the  accompanying  table,  and  will  be  found  useful  in  many 
instances: 


in  which  F  =  friction  head ; 

L  =  length  of  pipe,  in  feet; 
D  =  diameter  of  pipe,  in  inches; 
V  =  velocity,  in  feet  per  second. 

The  diagram  shown  in  Fig.  3  gives  the  frictional  heads  in  1,000  ft.  of  water 
pipe.  It  shows  the  flow,  in  gallons  per  minute,  of  the  common  sizes  and  gives 
the  frictional  heads  in  both  feet  of  water  and  pounds  per  square  inch. 

Friction  of  Knees  and  Bends. — To  obtain  the  friction  of  knees  and  bends, 
the  following  formulas  may  be  taken  as  giving  close  approximate  results. 
It  is  well  to  bear  in  mind  that  right  angles  should  be  avoided  whenever  possi- 
ble, and  that  bends  should  be  made  with  as  large  a  radius  as  circumstances 
will  allow.  The  position  of  the  angle  A  is  shown  in  Fig.  4. 
Let  A  =  angle  of  bend  or  knee  with  forward 

line  of  direction; 

V  =  velocity  of  water,  in  feet  per  second; 
R  =  radius  of  center  line  of  bend; 
r  —  radius  of  bore  of  pipe  (or  f  diameter); 
K  =  coefficient  for  angles  of  knees; 
L  =  coefficient  for  curvature  of  bends; 
//  =  head  of   water,  in    feet,   necessary  to 

overcome  friction  of  bends,  or  knees.  FlG  4 


(a/ 


The  value  of  K  is  as  follows  for  different  angles: 


A°... 

20°  I  40° 

60°  |  80° 

90° 

100° 

120° 

K  

.046  [  .139 

.364  1   .74 

98 

1  26 

1  86 

For  bends, 

Values  of  L  for  various  ratios  of  the  radius  of  bend  to  radius  of  bore: 


When          -|  = 

K. 

•' 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

Circular  sec- 
tion L  
Rectangular 
section  L  .  .  . 

.131 
.124 

.138 
.135 

.158 
.18 

.206 
.25 

.294 
.4 

.44 
.64 

.66 
1.01 

.98 
1.55 

1.4 
2.3 

2.0 
3.2 

RELATIVE  QUANTITIES  OF  WATER  DELIVERED  IN  24  HOURS,  IN 
1  HOUR,  AND  IN  1  MINUTE 


Gal. 
in 
24  Hr. 

Gal. 
in 
1  Hr. 

Gal. 
in 
1  Min. 

Gal. 
in 
24  Hr. 

Gal. 
in 
IHr. 

Gal. 
in 
1  Min. 

Gal. 
in 
24  Hr. 

Gal. 
in 
1  Hr. 

Gal. 
in 
1  Min. 

2,500,000 
2,000,000 
1,500,000 
1,000,000 
950,000 
900,000 
850,000 
800,000 
750,000 
700,000 

104,166.6 
83,333.3 
62,500.0 
41,666.6 
39,583.3 
37,500.0 
35,416.6 
33,333.3 
31,250.0 
29,166.6 

1,736.0 

1,388.8 
1,041.7 
694.4 
659.7 
625.0 
590.2 
555.5 
520.8 
486.1 

650,000 
600,000 
550,000 
500,000 
450,000 
400,000 
350,000 
300,000 
250,000 
200,000 

27,083.3 
25,000.0 
22,916.6 
20,833.3 
18,750.0 
16,666.6 
14,583.3 
12,500.0 
10,416.7 
8,333.3 

451.3 

416.7 
381.9 
347.2 
312.5 
277.7 
243.0 
208.3 
173.6 
138.8 

150,000 
100,000 
75,000 
60,000 
50,000 
25,000 
20.000 
15,000 
10,000 
5,000 

6,250.0 
4,166.6 
3,125.0 
2,500.0 
2,083.3 
1,041.6 
833.3 
625.0 
416.6 
208.3 

104.1 
69.4 
52.1 
41.6 
34.7 
17.3 
13.8 
10.4 
6.9 
3.4 

324 


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326 


HYDRAULICS 


327 


RESERVOIRS 

When  selecting  a  site  for  a  reservoir,  the  following  points  should  be  observed: 

1.  A  proper  elevation  above  the  point  at  which  the  water  is  required. 

2.  The  total  supply  available,  including  observations  as  to  the  rainfall 
and  snowfall. 

3.  The  formation  and  character  of  the  ground,  with  reference  to  the 
amount  of  absorption  and  evaporation. 

The  most  desirable  formation  of  ground  for  a  reservoir  site  is  one  of  com- 
pact rock,  like  granite,  gneiss,  or  slate;  porous  rocks,  like  sandstones  and 
limestones,  are  not  so  desirable.  Steep  bare  slopes  are  best  for  the  country 
surrounding  a  reservoir,  as  the  water  escapes  from  them  quickly.  The  presence 
of  vegetation  above  the  reseryoir  causes  a  considerable  amount  of  absorption ; 
but,  at  the  same  time,  the  rainfall  is  usually  greater  in  a  region  covered  with 
vegetation  than  in  a  barren  region,  hence  the  streams  have  a  more  uniform 
flow.  A  reservoir  must  be  made  large  enough  to  hold  a  supply  capable  of 
meeting  the  maximum  demand.  The  area  of  a  reservoir  should  be  determined, 
and  a  table  made  showing  its  contents  for  every  foot  in  depth,  so  that  the 
amount  of  water  available  can  always  be  known. 


MINE  DAMS 

Dams  may  be  constructed  in  mines  to  isolate  a  portion  of  the  workings  so 
that  they  can  be  flooded  to  extinguish  fires,  or,  where  an  extremely  wet  formation 
has  been  penetrated,  they  may  be  constructed  to  prevent  the  water  flowing 
into  the  workings.  Mine  dams  should  be  of  sufficient  strength  to  resist  any 
column  of  water  that  will  be  likely  to  come  against  them.  The  dam  should 
be  arched  toward  the  direction  from  which  the  pressure  comes,  and  should  be 
given  a  good  firm  bearing  in  both  walls 
and  in  the  floor  and  roof.  Fig.  1  illus- 
trates a  brick  dam  that  was  constructed 
in  Kehley's  Run  Colliery,  at  Shenandoah, 
Pennsylvania,  to  isolate  a  portion  of  the 
seam  so  that  it  might  be  flooded  to  extin- 
guish a  mine  fire.  This  is  one  of  the  largest 
mine  dams  that  has  ever  been  constructed. 
It  is  composed  of  three  brick  arches,  each 
having  a  thickness  of  5  ft.,  placed  one 
against  the  other  so  that  they  act  as  one 
solid  structure.  The  gangway  at  this  point 
is  about  20  ft.  wide,  and  the  distance  to 
the  next  upper  level  is  about  119  ft.  It 
was  intended  that  this  should  be  the  maxi- 
mum head  of  water  that  the  dams  would 
ever  have  to  resist,  though  they  were  made 
sufficiently  strong  to  resist  a  head  of  water 
reaching  to  the  surface.  The  separate  walls 
were  constructed  one  at  a  time,  and  the 
cement  allowed  to  set  before  the  next  wall 
was  placed.  The  back  wall  was  carried  to 
a  greater.depth  and  height  than  the  others, 
so  as  to  make  sure  of  the  fact  that  all  slips 
or  partings  had  been  closed.  The  total 
pressure  upon  the  dam  when  the  water 
was  in  the  mine  was  about  70,000  lb. 
per  sq.  ft. 

Dams  constructed  to  permit  the  flood- 
ing of  a  mine  usually  require  no  passages 
through  them,  but  where  dams  are  con-  FIG.  1 

structed   to  confine  the  water  to  certain 

parts  of  the  workings,  and  so  reduce  pumping  charges,  it  may  be  necessary 
to  provide  both  manways  and  drain  pipes  through  the  dams.  Fig.  2 
illustrates  a  plan  and  cross-section  of  a  dam  in  the  Curry  Mine,  at  Norway, 
Michigan,  constructed  to  keep  out  of  the  mine  workings  the  water  that  came 
from  some  exploring  drifts.  As  originally  constructed,  it  was  a  sandstone 
dam  10  ft.  thick  and  arched  on  the  back  face  with  a  radius  of  6  ft.  A  piece 
of  20-in.  pipe  provided  a  manway  through  the  masonry  and  was  held  in  place 


328 


HYDRAULIC&- 


by  three  sets  of  clamps  and  bolts  passing  through  the  stonework.  A  5-in. 
drain  pipe  was  also  carried  through  the  dam  and  secured  by  clamps.  When 
the  pressure  came  upon  the  dam  it  was  found  to  leak,  so  the  water  was  drained 
off  and  a  22-in.  brick  wall  built  2  ft.  4  in.  back  of  the  dam,  the  space  between 
being  filled  with  concrete,  and  the  manway  and  drain  pipe  extended  through 
the  brick  wall.  Before  closing  the  drain  pipe,  horse  manure  was  fastened 
against  the  face  of  the  brick  wall  by  means  of  a  plank  partition.  After  this 

the  manway  and  drain  pipe  were 
closed,  and  when  the  pressure  came 
on,  the  dam  was  found  to  leak  a 
small  amount,  but  this  soon  prac- 
tically ceased,  showing  that  the 
manure  had  closed  the  leaks.  A 
gauge  in  the  head,  of  the  manway  on 
this  dam  showed  a  pressure  of  211 
lb.,  which  corresponded  to  a  static 
head  of  640  ft.  of  water.  The  total 
pressure  against  the  dam  was  some- 
thing over  800  T.,  which  it  success- 
fully resisted. 

Dams  are  now  successfully  made 
of  concrete,  which  may  be  used 
alone  or  as  a  support  to  and  sur- 
rounding an  inner  framing  of  wooden 
or  steel  beams,  steel  rods,  etc.  The 
roof  and  floor  as  well  as  the  two 
ribs  should  be  notched  deeply .  so 
that  the  dam  on  all  four  sides  may 
have  ample  bearing  in  order  that 
it  may  not  be  bodily  pushed  for- 
wards by  the  weight  of  the  water 
behind  it.  

OUTSIDE  DAMS 

Dams  are  used  for  retaining 
water  in  reservoirs,  for  diverting 
streams  in  mining,  and  for  storing 
d6bris  coming  from  coal  washeries 
in  canons  or  narrow  valleys. 

Foundations  for  dams  must  be 
pIG  0  solid  to  prevent  settling,  and  water- 

tight to  prevent  leakage  under  the 

base  of  the  dam.  Whenever  possible,  the  foundation  should  be  solid  rock. 
Gravel  is  better  than  earth,  but  when  gravel  is  employed  it  will  be  neces- 
sary to  drive  sheet  piling  under  the  upper  toe  of  the  dam,  to  prevent  water 
from  seeping  through  the  formation  under  the  dam.  Vegetable  soil  should  be 
avoided,  and  all  porous  material,  such  as  sand,  gravel,  etc.  should  be  stripped 
off  until  hard  pan  or  solid  rock  is  reached.  In  case  springs  occur  in  the  area 
covered  by  the  foundation  of  the  dam,  they  must  be  traced;  and  if  they 
originate  on  the  upper  side  their  flow  must  be  confined  to  that  side  of  the  dam, 
so  that  they  will  have  no  tendency  to  become  passageways  for  water  from  the 
upper  to  the  lower  face  of  the  dam,  thus  providing  holes  that  may  ultimately 
destroy  the  entire  foundation  of  the  structure. 

Wooden  Dams. — Wooden  dams  are  constructed  of  round,  sawed,  or  hewn 
logs.  The  timbers  are  usually  at  least  1  ft.  square,  or,  if  round,  from  18  to 
24  in.  in  diameter.  A  series  of  cribs  from  8  to  10  ft.  square  are  constructed  by 
building  up  the  logs  in  log-house  fashion  and  securing  them  together  with  tree- 
nails. The  individual  cribs  are  secured  to  one  another  with  treenails  or  by 
means  of  bolts.  The  cribs  are  usually  filled  with  loose  rock  to  keep  them  in 
place,  and  in  many  cases  are  secured  to  the  foundation  by  means  of  bolts. 
A  layer  of  planking  on  the  upper  face  of  the  dam  makes  it  watertight,  and  when 
the  spillway  is  over  the  crest  of  the  dam  the  top  of  the  cribs  must  be  planked. 
In  most  cases,  it  is  also  necessary  to  provide  an  apron  for  the  water  to  fall  9n. 
The  apron  may  be  set  on  small  cribs,  or  on  timbers  projecting  from  the  cribs 
of  the  dam  itself. 

Abutments  and  Discharge  Gates. — Abutments  are  structures  at  the  ends  of  a 
dam.  They  may  be  constructed  from  timber,  masonry,  or  dry  stonework. 


HYDRAULICS  329 

If  possible,  abutments  should  have  a  curved  outline,  and  should  be  so  placed 
that  there  is  no  possibility  of  the  water  overflowing  them,  or  getting  behind 
them  during  floods.  If  the  regular  discharge  from  a  dam  takes  place  from  the 
main  face,  the  gates  may  be  arranged  in  connection  with  one  of  the  abutments, 
or  by  means  of  a  tunnel  and  culvert  through  the  dam.  In  either  case,  some 
structure  should  be  constructed  above  the  outlet  so  as  to  prevent  driftwood, 
brush,  and  other  material  from  stopping  the  discharge  gates.  When  the 
discharge  gates  are  placed  at  one  side  of  the  dam,  they  are  usually  arranged 
outside  of  the  regular  abutment,  between  it  and  a  special  abutment,  the  dis- 
charge being  through  a  series  of  gates  into  a  flume,  ditch,  or  pipe. 

Spillways,  or  Waste  Ways. — Spillways,  or  waste  ways  are  openings  pro- 
vided in  a  dam  for  the  discharge  of  water  during  floods  or  freshets,  or  for  the 
discharge  of  a  portion  not  being  used  at  any  time.  The  spillway  may  be  over 
the  crest  of  the  dam;  though,  where  the  topography  favors  such  a  construction, 
the  main  dam  may  be  of  sufficient  height  to  prevent  water  from  passing  its 
crest  and  the  spillway  arranged  at  another  outlet  over  a  lower  dam.  Waste 
ways,  proper,  are  openings  through  the  dam,  and  are  intended  for  the  discharge 
of  the  large  quantities  of  water  that  come  do.wn  during  freshets  or  floods.  In 
the  case  of  timber  dams,  the  waste  ways  are  usually  surrounded  by  heavy 
cribs,  and  have  an  area  of  from  40  to  50  sq.  ft.  each. 

There  are  two  general  forms  of  construction  employed  for  waste  ways. 
One  consists  of  a  comparatively  narrow  opening  in  the  dam,  extending  to  a 
considerable  depth  (8  or  10  ft.).  Water  is  allowed  to  discharge  through  this 
during  flood  time,  but  when  it  is  desired  to  stop  the  flow,  planks  are  placed 
across  the  up-stream  face  of  the  opening  in  such  a  manner  as  to  close  it.  The 
opening,  which  is  usually  not  over  3  or  4  ft.  wide,  is  provided  with  guides  on 
the  upper  face  of  the  dam;  between  these  the  planks  are  slid  down,  the  indi- 
vidual pieces  of  planking  being  at  least  1  ft.  longer  than  the  opening  that  they 
are  to  cover.  The  other  device  frequently  used  consists  in  providing  the 
waste  way,  at  one  side  of  the  regular  spillway,  with  a  crest  2  or  3  ft.  lower 
than  the  regular  spillway.  The  crest  of  this  waste  way  is  composed  of  heavy 
timber,  and  4  or  5  ft.  above  there  is  placed  a  parallel  timber;  the  space  between 
the  two  is  then  closed  by  flash  boards,  which  are  pieces  of  2-  in.  or  3-in.  plank, 
6  or  8  in.  wide,  and  long  enough  to  extend  from  1  to  2  ft.  above  the  upper  • 
timber.  The  planks  are  placed  against  both  timbers  so  as  to  close  the  space. 
Through  the  upper  end  of  each  plank  is  bored  a  hole  through  which  a  piece 
of  rope  is  passed  and  a  knot  tied  in  the  end  of  the  rope;  these  ropes  are  secured 
by  staples  to  the  upper  timber.  When  it  becomes  necessary  to  open  the 
waste  way,  men  go  under  with  peevies,  cant  hooks,  or  pinch  bars,  and  pry 
up  the  planks  in  such  a  way  as  to  draw  the  longer  end  out  of  contact  with 
the  lower  timber,  when  the  force  of  the  water  will  immediately  carry  the 
plank  down  the  stream  as  far  as  the  rope  will  allow.  After  the  first  plank 
has  been  loosened,  the  succeeding  ones  can  be  pulled  up  with  comparative 
ease,  and  two  men  can  open  a  25-ft.  or  30-ft.  section  of  waste  way  in  a  very 
few  minutes.  The  ropes  keep  the  plank  from  being  lost,  and  the  opening 
can  be  closed  again  by  passing  the  planks  down  into  the  water  to  one  side  of 
the  opening  and  moving  them  into  the  current.  Some  skill  is  required  both 
in  opening  and  closing  the  waste  ways. 

Stone  Dams. — Where  cement  or  lime  is  expensive,  but  where  suitable 
rubble  stone  can  be  obtained,  dams  are  frequently  constructed  without  the  use 
of  mortar.  In  such  cases,  the  upper  and  lower  faces  of  the  dam  should  be  of 
hammer-dressed  stone,  carefully  bonded,  and  sometimes  the  stones  in  the 
lower  face  of  the  dam  are  anchored  by  means  of  bolts.  The  dam  can  be  made 
watertight  by  placing  a  skin  of  planking  on  the  upper  face.  In  case  water 
should  ever  pass  over  the  crest  of  such  a  dam,  much  of  it  will  settle  through 
the  openings  in  the  stone  into  the  interior  of  the  dam,  and  subject  the  stones 
in  the  lower  portion  of  the  face  to  a  hydrostatic  pressure,  provided  an  opening 
has  not  been  made  for  the  escape  of  such  water.  For  this  reason,  culverts  or 
"openings  should  be  made  through  the  lower  portion  of  the  dam,  to  discharge 
any  such  water.  When  such  dams  as  this  are  constructed,  the  regular  spillway 
is  not  placed  over  the  face  of  the  dam,  but  at  some  other  point,  and  usually 
over  a  timber  dam. 

Earth  Dams. — Earth  dams  are  used  for  reservoirs  of  moderate  height. 
They  should  be  at  least  10  ft.  wide  on  top,  and  a  height  of  more  than  60  ft.  is 
unusual.  When  the  material  of  which  the  dam  is  composed  is  not  water- 
tight, as  for  instance,  gravel,  sand,  etc.,  it  is  sometimes  necessary  to  construct 
a  puddle  wall  of  clay  in  the  center  of  the  regular  dam.  This  consists  of  a 
narrow  dam  of  clay  mixed  with  a  certain  proportion  of  sand.  The  puddle  wall 


HYDRAULICS 


should  not  be  less  than  from  6  to  8  ft.  thick  at  the  top  of  the  dam,  and  should 
be  given  a  slight  batter  on  each  side.  It  is  constructed  during  the  building 
of  the  dam,  and  should  be  protected  from  contact  with  the  water  by  a  con- 
siderable thickness  of  earth  on  the  upper  face.  The  upper  face  of  an  earthen 
dam  is  frequently  protected  by  means  of  plank  or  a  pavement  of  stone.  The 
lower  face  is  frequently  protected  by  means  of  sod,  or  sod  and  willow  trees. 
Sometimes  earth  dams  are  provided  with  a  masonry  core  in  place  of  the  puddle 


wall,  to  render  them  water-tight.  This  consists  of  a  masonry  wall  carried  to 
an  impervious  stratum,  and  up  through  the  center  of  the  dam.  The  masonry 
core  should  never  be  less  than  2  or  3  ft.  thick  at  the  top,  and  should  be  given 
a  batter  of  at  least  10%  on  each  side.  At  the  regular  water  level,  earthen  dams 
are  liable  to  have  a  small  bench  or  shelf  formed,  and  on  this  account,  during 
the  construction,  such  a  bench  or  shelf  is  sometimes  built  into  the  earth  dam. 
The  accompanying  figure  shows  a  dam  with  a  masonry  core,  with  the  upper 
face  covered  with  rubble  and  the  lower  face  covered  with  grass. 

IRRIGATION  QUANTITY  TABLES 


Amount  of  Water 
Required  to  Cover 
1  A.  to  Given  Depths 

Second-Feet  Reduced  to 
Gallons  and  Acre-Feet* 

Gallons  Required 
to  Cover  a  Given 
Number  of  Acres 
to  Depth  of  1  Ft. 

Depth 

11JS 

1 

1 

*o 

i 

fa 

U 

|P 

s°f 

$2% 

I 

o 

Ft. 

In. 

if!! 

13 
O 

i1 

Jl*a 

111 

<&< 

1 

1 

3.630 

27,154 

~~ 

112.2 

80,790 

.2479 

1 

325,851 

2 

7,260 

54,309 

i 

224.4 

161,579 

.4959 

2 

651,703 

3 

10,890 

81,463 

• 

336.6 

242,369 

.7438 

3 

977,554 

4 

14,520 

108,617 

i 

448.8 

323,158 

.9917 

4 

1,303,406 

5 

18,150 

135,771 

it 

561.0 

403,948 

1.2397 

5 

1,629,257 

6 

21,780 

162,926 

H 

673.2 

484,738 

1.4876 

6 

1,955,109 

7 

25,410 

190,080 

if 

785.5 

565,527 

1.7355 

7 

2,280,960 

8 

29,040 

217,234 

2 

897.7 

646,317 

1.9835 

8 

2,606,812 

9 

32,670 

244,389 

2* 

1122.1 

807.896 

2.4793 

9 

2,932,663 

10 

36,300 

271,542 

3 

1346.5 

969,475 

2.9752 

10 

3,258,515 

11 

39,930 

298,697 

4 

1795.3 

1,292,634 

3.9669 

15 

4,887,772 

00 

43,560 

325,851 

5 

2244.2 

1.615,792 

4.9586 

20 

6,517,029 

2 

50,820 

380,160 

6 

2693.0 

1,938,951 

5.9503 

25 

8,146,286 

4 

58,080 

434,469 

7 

3141.8 

2,262,109 

6.9421 

30 

9,775,544 

6 

65,340 

488,777 

8 

3590.6 

2,585,268 

7.9338 

40 

13,034,058 

8 

72,600 

543,086 

9 

4039.5 

2,908,426 

8.9255 

60 

19,551,087 

1 

10 

79,860 

597,394 

10 

4488.3 

3,231,585 

9.9173 

80 

26,068,116 

2 

00 

87,120 

651,703 

20 

8976.6 

6,463,170 

19.8345 

160 

52,136,232 

*One  cubic  foot  of  water  per  second  (exact  7.48052  gal.)  constant  flow  is 
known  as  the  second-foot. 

The  acre-foot  is  the  quantity  of  water  required  to  cover  1  A.  to  a  depth 


HYDRAULICS  331 

Refuse  Dams. — Refuse  dams  are  placed  across  the  bed  of  streams  to  hold 
back  refuse  from  mines  and  washeries,  and  to  prevent  damage  to  the  valleys 
below.  They  are  made  of  stone,  timber,  or  brush.  No  attempt  is  made  to 
render  the  refuse  dam  water-tight,  the  only  object  being  that  it  should  retard 
the  flow  of  the  stream  and  give  it  a  greater  breadth  of  discharge,  so  that  the 
water  naturally  drops  and  deposits  the  sediment  that  it  is  carrying.  The 
sediment  soon  silts  or  fills  up  against  the  face  of  the  dam,  the  area  above  the 
dam  becoming  a  flat  expanse  or  plain  over  which  the  water  finds  its  way  to 
the  dam.  When  these  dams  are  constructed  of  stone,  the  individual  stones 
on  the  lower  face  and  crest  of  the  dam  should  be  so  large  that  the  current  will 
be  unable  to  displace  them,  while  the  upper  face  and  core  of  the  dam  may  be 
composed  of  finer  material.  In  case  a  breach  should  occur  in  the  refuse  dam, 
it  will  not  necessarily  endanger  the  region  farther  down  the  stream,  as  is  the 
case  when  a  break  occurs  in  a  water  dam.  The  reason  for  this  is  that  the 
refuse  dam  is  not  made  watertight,  and  hence  there  is  never  much  pressure 
against  it,  or  a  large  volume  of  water  held  back  that  can  rush  suddenly  down 
the  stream  should  a  break  occur.  The  only  result  of  the  break  would  be  that 
more  or  less  of  the  gravel,  sand,  slate,  etc.,  behind  the  dam  would  be  washed 
through  the  breach. 

Wing  Dams. — Wing  dams  are  used  for  turning  streams  from  their  courses, 
so  as  to  expose  all  or  a  portion  of  the  bed  for  placer  mining  or  other  purposes. 
They  are  usually  of  a  temporary  nature,  and  are  constructed  of  brush  and 
stones,  light  cribs  filled  with  stones,  and  of  large  stones,  or  timber.  Some- 
times the  course  of  a  stream  is  turned  by  an  obstruction  made  of  sand  bags 
and  a  wing  dam  constructed  behind  this  of  frames  of  timber,  the  intervening 
space  being  filled  with  gravel  or  earth;  in  some  cases,  the  timber  is  covered  with 
stone  and  the  surface  riprapped  so  that  if  the  flow  ever  comes  over  the  top 
of  the  structure  it  will  not  destroy  it. 

Masonry  and  Concrete  Dams. — When  high  masonry  or  concrete  dams  are 
to  be  employed  they  should  be  designed  by  a  competent  hydraulic  engineer. 
Masonry  or  concrete  dams  are  not,  as  a  rule,  used  around  coal  mines,  owing 
to  the  fact  that  the  length  of  time  during  which  the  dam  is  required  rarely 
warrants  such  expensive  construction. 


WATER-POWER 

Theoretical  Efficiency  of  Water-Power.  —  The  gross  power  of  a  fall  of 
water  is  the  product  of  the  weight  of  water  discharged  in  a  unit  of  time,  and 
the  total  head  or  difference  in  elevation  of  the  surface  of  the  water,  above 
and  below  the  fall.  The  term  head,  used  in  connection  with  waterwheels, 
is  the  difference  in  height  between  the  surface  of  water  in  the  penstock  and 
that  in  the  tailrace,  when  the  wheel  is  running. 

If          Q  =  cubic  feet  of  water  discharged  per  minute; 
W  =  weight  of  1  cu.  ft.  of  water  =  62.5  lb.; 
H  =  total  head,  in  feet; 

WQH  =  gross  power,  in  foot-pounds  per  minute; 
WQH 


Substituting  the  value  for  W,  gives 

.  00189Q#,  as  horsepower  of  a  fall. 


The  total  power  can  never  be  utilized  by  any  form  of  motor,  because  there 
is  a  loss  of  head,  both  at  the  entrance  to,  and  exit  from,  the  wheel,  and 
there  are  also,  losses  of  energy  due  to  friction  of  the  water  in  passing  through 
the  wheel.  The  ratio  of  the  power  developed  by  the  wheel  to  the  gross 
power  of  the  fall,  is  the  efficiency  of  the  wheel.  A  head  of  water  can  be  made 
use  of  in  any  one  of  the  following  ways: 

1.  By  its  weight,  as  in  the  water  balance,  or  overshot  wheel. 

2.  By  its  pressure,  as  in  the  hydraulic  engine,  hydraulic  presses,  cranes, 
etc.,  or  in  a  turbine  water  wheel. 

3.  By  its  impulse,  as  in  the   undershot  and  impulse   wheels,  such  as 
Peltons,  etc. 

4.  By  a  combination  of  these. 

Horsepower  of  a  Running  Stream.  —  The  gross  horsepower  is 

QHX62.5 
H'  P<        33,000" 


332  HYDRAULICS 

in  which  Q  =  quantity  actually  impinging  on  float  or  bucket,  in  cubic  feet 

per  minute; 
H  =  theoretical  head  added  to  velocity  of  stream. 


in  which  v  =  velocity,  in  feet  per  second. 

For  example,  if  the  floats  of  an  undershot  waterwheel  are  2  ft.XlO  ft.,  and 
the  stream  has  a  velocity  of  3  ft,  per  sec.,  i.  e.,  z>  =  3,  #  =  9-^64.4  =  .139,  and  Q 
=  2X10X3X60  =  3,600  cu.  ft.  per  min. 

From  this,  H.  P.  =  3,600  X.  139  X.  00189  =  .945  H.  P.,  or  a  gross  horsepower 
for  practically  .05  sq.  ft.  of  wheel  surface;  but,  under  ordinary  circumstances, 
it  is  impossible  to  attain  more  than  40%  of  this,  or  practically  .02  H.  P.  per 
sq.  ft.  of  surface,  which  requires  50  sq.  ft.  of  float  surface  to  each  horsepower 
furnished. 

Current  Motors.  —  A  current  motor  fully  utilizes  the  energy  of  a  stream 
only  when  it  is  so  arranged  that  it  can  take  all  the  velocity  out  of  the  water; 
that  is,  when  the  water  leaves  the  floats  or  vanes  with  no  velocity.  In  practice, 
it  is  impossible  to  obtain  even  a  close  approximation  to  these  results,  and  hence 
only  a  small  fraction  of  the  energy  of  a  running  stream  can  be  utilized  by  the 
current  motor. 

Current  motors  are  frequently  used  to  obtain  small  amounts  of  power  from 
a  large  stream,  as,  for  instance,  for  pumping  a  limited  amount  of  water  for 
irrigation.  For  this  work,  an  ordinary  undershot  wheel  having  radial  paddles 
is  usually  employed.  At  one  end  of  the  wheel  a  series  of  small  buckets  are 
placed,  and  so  arranged  that  each  bucket  will  dip  up  water  at  the  bottom  of  the 
wheel  and  discharge  it  into  the  launder,  near  the  top  of  the  wheel.  The  shape 
of  the  buckets  should  be  such  that  only  the  amount  of  water  that  the  bucket 
is  capable  of  carrying  to  the  launder  will  be  dipped  up,  for,  if  the  bucket  is 
constantly  slopping  or  pouring  water  as  it  ascends,  a  large  amount  of  useless 
work  is  performed  in  raising  this  extra  water  and  then  pouring  it  out  again, 
as  only  the  portion  that  reaches  the  launder  can  be  of  any  service.  Current 
motors  are  not  practicable  for  furnishing  large  amounts  of  power. 

Utilizing  Power  of  Waterfall.  —  The  power  of  a  waterfall  may  be  utilized  by 
a  number  of  different  styles  of  motors,  but  each  has  certain  advantages. 

When  the  head  is  low  (not  over  5  or  6  ft.),  breast  or  undershot  wheels  are 
frequently  employed.  If  these  are  properly  proportioned,  it  is  possible  to 
realize  from  25%  to  50%  of  the  theoretical  power  of  the  fall,  but  the  wheels 
are  large  and  cumbersome  compared  with  the  duty  they  perform,  and  are  not 
often  installed  at  present,  especially  near  manufacturing  centers. 

For  falls  up  to  40  or  50  ft.,  overshot  wheels  are  very  commonly  employed, 
and  they  have  been  used  for  even  greater  heads  than  this.  The  overshot  wheel 
derives  its  power  both  from  the  impulse  of  the  water  entering  the  buckets,  and 
from  the  weight  of  the  water  as  it  descends  on  one  side  of  the  wheel  in  the 
buckets;  the  latter  factor  is  by  far  the  more  important  of  the  two.  When 
properly  proportioned,  overshot  wheels  may  realize  from  70%  to  90%  of  the 
power  of  the  waterfall,  but  they  are  large  and  cumbersome  compared  with  the 
power  that  they  give,  and  are  not  often  installed  except  in  isolated  regions, 
where  they  are  made  from  timber  by  local  mechanics. 

For  heads  varying  from  50  ft.  up,  impulse  wheels  are  very  largely  used. 
These  are  also  sometimes  called  hurdy  gurdies,  and  are  usually  of  the  Pelton 
type,  consisting  of  a  wheel  provided  with  buckets,  so  arranged  about  its  peri- 
phery that  they  receive  an  impinging  jet  of  water  and  turn  it  back  upon  itself, 
discharging  it  with  practically  no  velocity,  and  converting  practically  all  the 
energy  into  useful  work.  The  efficiency  of  these  wheels  varies  from  85%  to 
90%  under  favorable  circumstances.  This  style  of  wheel  is  especially  adapted 
for  very  high  heads  and  comparatively  small  amounts  of  water.  There  are  a 
number  of  instances  where  wheels  are  operating  under  a  head  of  as  much  as 
2,000  ft.  This  style  of  impulse  wheel  is  an  American  development;  in  Europe, 
a  style  of  impulse  turbine  has  been  used  to  some  extent,  but  has  not  found 
very  much  favor  in  the  United  States. 

Turbines,  or  reaction  wheels,  are  very  largely  employed,  especially  for 
moderate  heads.  When  properly  designed  to  fit  the  working  conditions,  they 
can  be  used  for  heads  varying  from  4  to  5  ft.  up  to  considerably  over  100  ft., 
and  when  properly  placed  are  capable  of  utilizing  the  entire  head,  a  factor 
that  gives  them  a  decided  advantage  over  any  other  style  of  waterwheel. 
Turbines  are  capable  of  returning  85%  to  90%  of  the  theoretical  energy  as 
useful  power,  and  are  largely  used,  especially  where  a  considerable  volume  of 
water  at  a  low  head,  or  a  smaller  volume  at  a  moderate  head,  can  be  obtained. 


HYDRAULICS 


333 


PUMP  MACHINERY 

CLASSIFICATION  OF  PUMPS 

f  Pumps  are  employed  for  unwatering  mines,  handling  water  at  placer  mines, 
irrigation,  water-supply  systems,  boiler  feeds,  etc.  For  unwatering  mines, 
two  general  systems  of  pumping  are  employed:  (1)  The  pump  is  placed  in 
the  mine  and  is  operated  by  a  motor  on  the  surface,  the  power  being  trans- 
mitted through  a  line  of  moving  rods.  (2)  Both  the  motor  and  pump  are 
placed  in  the  mine,  the  motor  being  an  engine  driven  by  steam,  compressed 
air,  hydraulic  motor,  or  an  electric  motor. 

Cornish  Pumps. — Any  method  of  operating  pumps  by  rods  is  commonly 
called  a  Cornish  system.  Formerly,  the  motor  in  the  Cornish  system  consisted 
of  a  steam  engine  placed  over  the  shaft  head,  which  operated  the  pump  by  a 
direct  line  of  rods.  With  this  arrangement,  there  is  great  danger  of  accident 
to  the  engine  from  the  settling  of  the  ground  around  the  shaft,  or  from  fire  in 
the  shaft;  also,  the  position  of  the  motor  renders  access  to  the  shaft  difficult. 
To  overcome  these  objections,  the  engine  is  frequently  placed  at  one  side  of 
the  shaft,  and  the  rods  operated  by  a  bob;  this  has  become  the  common  prac- 
tice, and  is  generally  called  the  Cornish  rig.  The  engine  employed  in  the  most 
modern  plants  is  generally  of  the  Corliss  type,  and  is  provided  with  a  governor 
to  guard  against  the  possibility  of  the  engine  running  away,  in  case  the  rods 
should  break. 

This  system  requires  no  steam  line  down  the  shaft,  and  is  independent  of 
the  depth  of  water  in  the  mine,  so  that  the  pump  is  not  stopped  by  the  drown- 
ing of  a  mine,  but  the  moving  rods  are  a  great  inconvenience  in  the  shaft,  and 
they  absorb  a  great  amount  of  power  by  friction. 

Simple  and  Duplex  Pumps. — In  the  simple  pumps  a  steam  cylinder  is  con- 
nected directly  to  a  water  cylinder,  and  the  steam  valves  are  operated  by 
tappets.  Such  a  pump  is  more  or  less  dependent  on  inertia  at  certain  points 
of  the  stroke  to  insure  the  motion  of  the  valves,  hence  will  not  start  from 
any  place,  but  is  liable  to  become  stalled  at  times. 

In  the  duplex  pump,  two  steam  cylinders  and  two  water  cylinders  are 
arranged  side  by  side,  and  the  valves  so  placed  that  when  one  piston  is  at  mid- 
stroke  it  throws  the  steam  valve  for  the  other  cylinder,  etc.  With  this  arrange- 
ment, the  pump  will  start  from  any  point,  and  can  never  be  stalled  for  lack  of 
steam,  due  to  the  position  of  the  valves.  Ordinarily,  duplex  pumps  are  to  be 
preferred  for  mine  work. 

The  pa  '  ' 
Any  form 

or  surrounding  the  ram, 
and  so  situated  that  any 
wear  will  allow  communi- 
cation between  the  op- 
posite ends  of  the  cylin- 
der, is  called  inside  pack- 
ing. It  may  consist  simply 
of  piston  rings  about  the 
piston,  as  in  the  case  of 
an  ordinary  steam:engine 
piston  G,  Fig.  1,  'or  sta- 
tionary rings  may  be  em- 
ployed about  the  outside 
of  a  moving  ram,  or  long 
piston  P.  In  either  case,  the  cylinder  heads  have  to  be  removed  before  the 
condition  of  the  packing  can  be  inspected,  and  any  leak  does  not  make  itself 
visible. 

When  outside  packing  is  employed,  separate  rams  are  used  in  opposite 
ends  of  the  cylinder,  there  being  no  internal  communication  between  the 
chambers  in  which  the  rams  work.  The  rams  are  packed  by  ordinary 
outside  stuffingboxes  and  glands.  The  arrangement  consists  practically  of 
two  single-acting  pumps  arranged  to  work  alternately,  so  that  one  is  forcing 
water  while  the  other  is  drawing  water.  Fig.  2  shows  a  horizontal  section 
of  a  cylinder  so  arranged,  together  with  the  yoke  rods  that  operate  the  ram 
at  the  farther  end  of  the  cylinder. 

As  a  rule,  inside-packed  pumps  should  be  avoided  in  mines,  because  acid 
or  gritty  waters  are  liable  to  cut  the  packing,  and  make  the  pumps  leak  in  a 


packing  for  the  water  piston  of  a  pump  may  be  either  inside  or  outside, 
•m  of  packing  that  is  inside  the  cylinder,  either  upon  a  moving  piston 


FIG.  1 


334  HYDRAULICS 

very  short  time.  For  dipping  work  in  single  stopes  or  entries,  small  single 
or  duplex  outside-packed  pumps  may  be  employed.  It  is  generally  best  to 
operate  such  pumps  by  compressed  air,  for  the  exhaust  will  then  be  beneficial 

to  the  mine  air.  If  steam 
iFThm  *dl?  is  employed,  it  is  fre- 

I, £T;~fi^'"_ -—••--- — -~—-.-7r?zzjm,  I  _  quently  necessary  to 

f~      =ia^^^^^3)BO  O O  Sbji^^^^^^a   j|^^  introduce   a   trap    and 

c:  ^^M^^^J^M^^  J   ^J^       remove  entrailed  water 

f  K.U  '    *u  ^  from  the  steam  before 

•pir   o  it  enters  the  pump,  and 

to  dispose  of  the  exhaust 

by  piping  it  out  or  condensing  it.  Such  isolated  steam  pumps  are  about  the 
most  wasteful  form  of  steam-driven  motor  in  existence. 

For  sinking,  center-packed  single  or  duplex  pumps  are  usually  employed, 
the  duplex  style  being  the  better.  For  station  work,  where  much  water  is  to 
be  handled,  large  compound,  or  triple-expansion,  condensing,  duplex  pumping 
engines  are  empk>yed.  They  may,  or  may  not,  be  provided  with  cranks  and 
a  flywheel.  Engineers  differ  greatly  upon  this  point,  and,  as  a  rule,  for  very 
high  lifts  and  great  pressures,  the  flywheel  is  employed.  , 

The  main  points  in  consideration  are  the  first  cost  of  the  pump,  and  the 
amount  that  will  be  saved  by  using  the  more  expensive  engine.  The  large 
flywheel  pumping  engines  are  several  times  as  expensive  as  the  direct-acting 
steam  pumps,  and  the  question  is  as  to  whether  their  greater  efficiency  will 
more  than  counterbalance  the  increased  outlay.  Most  engineers  favor  fly- 
wheel pumps  for  handling  large  volumes  of  water  where  the  work  is  approxi- 
mately constant,  and  direct-acting  pumps,  without  flywheels  or  cranks,  for 
handling  small  amounts  of  water,  or  for  very  irregular  service,  owing  to  the 
fact  that  if  the  flywheel  pump  is  driven  below  its  normal  speed  it  does  not 
govern  properly,  nor  work  economically.  Until  recently,  water  was  removed 
from  mines  in  lifts  of  about  300  to  350  ft.,  pumps  being  placed  at  stations  along 
the  shaft. 

While  a  series  of  station  pumps  are  still  employed  in  some  cases,  they  are 
generally  intended  to  take  care  of  water  coming  into  the  shaft,  or  workings 
at  or  near  their  level,  and  are  not  employed  for  handling  water  in  successive 
stages  or  lifts.  For  handling  the  bulk  of  the  water  from  the  bottom  of  the 
shaft,  large  pumping  engines  are  employed  that  frequently  force  the  water 
to  the  surface  from  depths  of  over  1,000  ft.  These  high-duty  pumping  plants, 
when  near  the  shaft  and  operated  by  steam  with  a  condenser,  frequently  show 
a  very  high  efficiency.  When  air  is  employed  to  operate  such  a  plant,  a  much 
higher  efficiency  can  be  obtained  if  the  compressed  air  is  heated  before  it  is 
used  in  the  high-pressure  cylinder  and  during  its  passage  from  the  high-pressure 
to  the  low-pressure  cylinder.  This  has  been  very  successfully  accomplished 
by  means  of  a  steam  reheater,  the  small  amount  of  steam  necessary  being 
conveyed  to  the  station  in  the  small  pipe,  and  entirely  condensed  in  the  reheater, 
from  which  it  is  trapped  as  water. 

The  duty  of  steam  pumps  is  approximately  as  follows:  For  small-sized 
steam  pumps,  the  steam  consumption  is  from  130  to  200  Ib.  per  H.  P.  per  hr., 
when  operating  in  the  workings  of  a  mine  at  some  distance  from  the  boiler. 
For  larger  sizes  of  simple  steam  pumps,  the  consumption  runs  from  80  to 
130  Ib.  per  H.  P.  per  hr.  Compound-condensing  pumps,  such  as  are  commonly 
used  as  station  pumps,  consume  from  40  to  70  Ib.  per  H.  P.  per  hr.  Triple- 
expansion,  condensing,  high-class  pumping  engines  consume  from  24  to  26  Ib. 
per  H.  P.  per  hr.  The  Cornish  pump  consumes  varied  amounts  of  steam  in 
proportion  to  the  water  delivered,  depending  largely  on  the  friction  of  the 
gearing,  bobs,  rods,  etc.,  but  its  efficiency  is  usually  considerably  below  the 
best  class  of  pumping  engines. 

Speed  of  Water  Through  Valves,  Pipes,  and  Pump  Passages. — The  speed  of 
water  through  the  valves  and  passages  of  a  pump  should  not  exceed  250  ft.  per 
min.,  and  care  should  be  taken  to  see  that  the  passages  are  not  too  abruptly 
deflected.  The  flow  of  water  through  the  discharge  pipe  should  not  exceed 
500  ft.  per  min.,  and  for  single-cylindered  pumps  it  is  usually  figured  at  between 
250  and  400  ft.  per  min.  In  the  case  of  very  large  pumps,  greater  velocities 
may  be  allowed.  The  suction  pipe  for  the  pump  should  be  larger  than  the 
discharge  pipe.  Ordinarily  the  suction  pipe  for  a  pump  should  not  exceed 
250  ft.  in  length,  and  should  not  contain  more  than  two  elbows.  The  following 
formula  gives  the  diameter  of  the  suction  and  discharge  pipes  of  a  pump: 

G  =  United  States  gallons  per  minute; 

d'  =  diameter  of  suction  pipe,  in  inches; 


HYDRAULICS 


335 


d"  =  diameter  of  discharge  pipe,  in  inches; 

v'  =  velocity  of  water,  in  feet  per  minute,  in  suction  pipe  =  from  .50»"  to  ,75v" 
v"  =  velocity  of  water,  in  feet  per  minute,  in  discharge  pipe. 


=  4.( 


RATIO  OF  STEAM  AND  WATER  CYLINDERS 
DIRECT-ACTING  PUMP 

Let  A  =area  of  steam  cylinder; 

D  =  diameter  of  steam  cylinder  ; 
F  =  steam  pressure,  in  pounds  per  square  inch; 
tf  =  head  of  water  =  2.309£; 
a  =  area  of  pump  cylinder; 
d  =  diameter  of  pump  cylinder; 
p  =  pressure  per  square  inch,  corresponding  to  head 


IN  A 


E  =  efficiency  of  pump  = 


EAP 


work  done  in  pump  cylinder 
work  done  in  steam  cylinder' 


.433/7 
EP 


EAP 


2.30QEPX~. 
a 


75%,  then  #  =  1.732PXJ 


E  is  commonly  taken  at  from  .7  to  .8  for  ordinary  direct-acting  pumps. 
For  the  highest  class  of  pumping  engines  it  may  amount  to  .9.  The  steam 
pressure  P  is  the  mean  effective  pressure,  according  to  the  indicator  diagram; 
the  pressure  p  is  the  mean  total  pressure  acting  on  the  pump  plunger  or  piston, 
including  the  suction,  as  would  be  shown  by  the  indicator  diagram  of  the 
water  cylinder.  The  pressure  on  the  pump  cylinder  is  frequently  much  greater 
than  that  due  to  the  height  of  the  lift,  on  account  of  the  friction  in  the  valves 
and  passages,  which  increases  rapidly  with  the  velocity  of  the  flow. 

Piston  Speed  of  Pumps. — For  small  pumps,  it  is  customary  to  assume  a 
speed  of  100  ft.  per  min.,  but,  in  the  case  of  very  small  short-stroke  pumps, 
this  is  too  high,  owing  to  the  fact  that  the  rapid  reverses  make  the  flow 
through  the  valves  and  change  in  the  direction  of  the  current  too  frequent. 
When  the  stroke  of  the  pump  is  somewhat  longer  (18  in.  or  more),  higher  speeds 
can  be  employed,  and  in  the  case  of  large  pumping  engines  having  long  strokes, 
speeds  of  as  much  as  200  to  250  ft.  per  min.  are  successfully  used  without  jar 
or  hammer. 

STROKES  FOR  PISTON  SPEED  OF  100  FT.  PER  MIN. 


Length  of 
Stroke 
Inches 

Number 
of 
Strokes 

Length  of 
Stroke 
Inches 

Number 
of 
Strokes 

Length  of 
Stroke 
Inches 

Number 
of 
Strokes 

4 
5 
6 
7 
8 
10 

300 
240 
200 
172 
150 
120 

12 
14 
16 
18 
20 
22 

100 
86 
75 
67 
60 
55 

24 
26 
28 
30 
36 
40 

50 
46 
43 
40 
33 
30 

Boiler  Feed-Pumps. — In  practice,  it  has  been  shown  that  a  piston  speed 
greater  than  100  ft.  per  min.  results  in  excessive  wear  and  tear  on  a  boiler 
feed-pump,  especially  when  the  water  is  warm.  This  is  because  vapor  forms  in 
the  cylinders,  and  results  in  a  water  hammer.  In  determining  the  proper 
size  of  a  pump  for  feeding  a  steam  boiler,  not  only  the  steam  employed  in 
running  the  engine,  but  that  necessary  for  the  pumps,  heating  system,  etc. 
must  be  taken  into  consideration. 


336 


HYDRAULICS 


THEORETICAL  CAPACITY  OF  PUMPS  AND  HORSEPOWER  REQUIRED 
TO  RAISE  WATER 

Let    Q  =  cubic  feet  of  water  per  minute; 
G  =  United  States  gallons  per  minute; 
G'  =  United  States  gallons  per  hour; 
d  =  diameter  of  cylinder,  in  inches; 
1  =  stroke  of  piston,  in  inches; 
2V  =  number  of  single  strokes  per  minute; 
v  =  speed  of  piston,  in  feet  per  minute; 


RATIOS  OF  AREAS  TO  DIAMETERS 


Diameter  of  Steam  Cylinder,  in  Inches 

TV          t 

of  Water 
Cylinders 
Inches 

5 

6 

8 

10 

12 

14 

Ratios  of  Areas 

I 

64,00 

92.16 

163.84 

256.00 

368.64 

501.76 

1 

44.44 

64.00 

113.77 

177.77 

256.00 

348.44 

1 

32.65 

47.02 

83.59 

130.61 

188.10 

256.00 

1 

25.00 

36.00 

64.00 

100.00 

144.00 

196.00 

H 

19.75 

28.44 

50.56 

79.01 

113.78 

154.86 

16.00 

23.04 

40.96 

64.00 

92.16 

125.44 

ij 

13.22 

19.04 

33.85 

52.89 

76.17 

103.66 

i; 

11.11 

16.00 

28.44 

44.44 

64.00 

87.11 

tj 

9.46 

13.63 

24.23 

37.87 

54.53 

74.22 

li 

8.16 

11.75 

20.90 

32.65 

47.02 

64.00 

11  • 

7.11 

10.24 

18.20 

28.44 

40.96 

55.75 

2 

6.25 

9.00 

16.00 

25.00 

36.00 

49.00 

2i 

4.93 

7.11 

12.64 

19.75 

28.44 

38.71 

21 

4.00 

5.76 

10.24 

16.00 

23.04 

31.36 

2f 

3.30 

4.76 

8.46 

13.22 

19.04 

25.91 

3 

2.77 

4.00 

7.11 

11.11 

16.00 

21.77 

3i 

2.37 

3.40 

6.06 

9.46 

13.63 

18.56 

3£ 

2.04 

2.93 

5.22 

8.16 

11.75 

16.00 

3! 

1.77 

2.56 

4.55 

7.11 

10.24 

13.93 

4 

1.56 

2.25 

4.00 

6.25 

9.00 

12.25 

4J 

1.38 

1.99 

3.54 

5.53 

7.97 

10.85 

4f 

1.23 

1.77 

3.15 

4.93 

7.11 

9.67 

4| 

1.10 

1.59 

2.83 

4.43 

6.38 

8.68 

5 

1.00 

1.44 

2.56 

4.00 

5.76 

7.84 

5* 

.82 

1.19 

2.11 

3.30 

4.76 

6.47 

6 

.69 

1.00 

1.77 

2.77 

4.00 

5.44 

61 

.59 

.85 

1.51 

2.37 

3.40 

4.63 

7 

.51 

.73 

1.30 

2.04 

2.93 

4.00 

71 

.44 

.64 

1.13 

1.77 

2.56 

3.48 

8 

.39 

.56 

1.00 

1.56 

2.25 

3.06 

|J 

.34 

.49 

.88 

1.38 

1.99 

2.71 

9 

.30 

.44 

.79 

1.23 

1.77 

2.42 

9* 

.27 

.39 

.70 

1.11 

1.59 

2.17 

10 

.36 

.64 

1.00 

1.44 

1.96 

11 

.29 

.52 

.82 

1.19 

1.62 

12 

.25 

.44 

.69 

1.00 

1.36 

13 

.37 

.59 

.85 

1.16 

14 

.33 

.51 

.73 

1.00 

15 

.28 

.44 

.64 

.87 

16 

.25 

.39 

.56 

.76 

17 

.34 

.49 

.67 

18 

.30 

.44 

.60 

HYDRAULICS 


337 


W 
P 
p 
H 
H.  P. 

Then, 


weight  moved,  in  pounds  per  minute  ; 
pressure,  in  pounds  per  square  foot  =  62.5ff; 
pressure,  in  pounds  per  square  inch  =  .433H; 
height  of  lift,  in  feet; 
horsepower. 


OF  STEAM  AND  WATER  CYLINDERS 


Diameter  of  Steam  Cylinders,  in  Inches 


16 

18 

20 

22 

24 

» 

28 

30 

Ratios  of  Areas 


455.11 

334  .  37 

256  .  00 

324.00 

400.00 

202  .  27 

256  .  00 

316.05 

163.84 

207.36 

256.00 

309  .  76 

135.41 

171.37 

211.57 

256  .  00 

113.77 

144.00 

177.77 

215.11 

256.00 

96.95 

122.70 

151.48 

183.29 

218.11 

83.59 

105.79 

130.61 

158.05 

188.10 

220  .  73 

72.82 

92.16 

113.78 

137.67 

163.85 

192.29 

64.00 

81.00 

100.00 

121.00 

144.00 

169.00 

196.00 

225.00 

50.56 

64.00 

79.01 

95.60 

113.78 

133.53 

154.86 

177  .77 

40.96 

51.84 

64.00 

77.44 

92.16 

108.16 

125.44 

144.00 

33.81 

42.84 

52.89 

64.00 

76.17 

89.39 

103.66 

119.01 

28.44 

36.00 

44.44 

53.77 

64.00 

75.11 

87.11 

100.00 

24.23 

30.67 

37.87 

45.82 

54.53 

64.00 

74.22 

85.21 

20.90 

26.44 

32.65 

39  .  51 

47.02 

55.18 

64.00 

73.47 

18.20 

23.04 

28.44 

34.42 

40.96 

48.07 

55.75 

64.00 

16.00 

20.25 

25.00 

30.25 

36.00 

42,25 

49.00 

56.25 

14.22 

17.93 

22.14 

26.79 

31.89 

37.43 

43.41 

49.83 

12.64 

16.00 

19.75 

23.90 

28.44 

33.38 

38.71 

44.44 

11.34 

14.36 

17.73 

21.45 

25.53 

29.96 

34.75 

39.89 

10.24 

12.96 

16.00 

19.36 

23.04 

27.04 

31.36 

36.00 

8.46 

10.71 

13.22 

16.00 

19.04 

22.35 

25.01 

29.75 

7.11 

9.00 

11.11 

13.44 

16.00 

18.77 

21.77 

25.00 

6.06 

7.66 

9.46 

11.45 

13.63 

16.00 

18.56 

21.30 

5.22 

6.61 

8.16 

9.87 

11.75 

13.79 

16.00 

18.37 

4.55 

5.76 

7.11 

8.60 

10.24 

12.00 

13.93 

16.00 

4.00 

5.06 

6.25 

7.56 

9.00 

10  .  56 

12.25 

14.06 

3.54 

4.48 

5.53 

6.69 

7.97 

9.35 

10.85 

12.45 

3.15 

4.00 

4.93 

5.98 

7.11 

8.34 

9.67 

11.11 

2.83 

3.59 

4.43 

5.36 

6.38 

7.49 

8.68 

9.97 

2  .  56 

3.24 

4.00 

4.84 

5.76 

6.76 

7.84 

9.00 

2.11 

2.67 

3.30 

4.00 

4.76 

5.58 

6.47 

7.43 

.77 

2.25 

2.77 

3.36 

4.00 

4.69 

5.44 

6.25 

.51 

1.91 

2.37 

2.86 

3.40 

4.00 

4.63 

5.32 

.30 

1.65 

2.04 

2.46 

2.93 

3.44 

4.00 

4.59 

.13 

1.44 

1.77 

2.15 

2.56 

3.00 

3.48 

4.00 

.00 

1.26 

1.56 

1.89 

2.25 

2.64 

3.06 

3.51 

.88 

1.12 

1.38 

1.67 

1.99 

2.34 

2.71 

3.11 

.79 

1.00 

1.23 

1.49 

1.77 

2.08 

2.41 

2.77 

338  HYDRAULICS 

The  diameter  of  piston  required  for  a  given  capacity  per  minute  will  be 


The  actual  capacity  of  a  pump  will  vary  from  60%  to  95%  of  the  theoretical 
capacity,  depending  on  the  tightness  of  the  piston,  valves,  suction  pipe,  etc. 
HP         QP    =Q#X144X.433^  QH  =     Gp 

"33,000,  33,000        "     529.2      1,714.5 

The  actual  horsepower  required  will  be  considerably  greater  than  the 
theoretical,  on  account  of  the  friction  in  the  pump;  hence,  at  least  20%  should 
be  added  to  the  power  for  friction  and  usually  about  50%  more  is  added  to 
cover  leaks,  etc.,  so  that  the  actual  horsepower  required  by  the  pump  is  about 
70%  more  than  the  theoretical. 

EXAMPLE  1. — What  size  of  pump  will  throw  30  gal.  of  water  per  min.  up 
125  ft.,  from  the  bottom  of  a  pit  or  prospect  shaft  to  the  station  pump  at  the 
main  shaft? 

SOLUTION. — An  allowance  of  probably  25%  should  be  made  with  a  small 
pump  of  this  character,  to  overcome  slippage  or  leaking  through  the  valves, 
past  the  piston,  etc.,  and  hence  the  total  amount  of  water  to  be  handled  is 

40  gal.  per  min.     The  formula  for  the  diameter  of  piston  is  d  =  4.95\/    ; 

therefore,  assuming  that  v  =  100  ft.  per  min.,  d  =  4.95  VH  =  4.95 X. 63  =  3. 12.     In 
practice,- a  3j-in.  pump  will  probably  be  employed. 

EXAMPLE  2. — Find  the  approximate  horsepower  necessary  to  lift  30  gal. 
per  min.  in  Example  1. 

SOLUTION.— 

TT   _         Gp         30X.433X125  ,.     ,      ,  TT   _ 

H"  R-  Tjlb IjfO '95'  or  Practlcallv  1  H-  p- 

In  order  to  cover  leakage  through  valves,  friction,  etc.,  an  addition  of  at 
least  75%  should  be  made  to  a  very  small  pump  like  this,  and  so  If  H.  P.  would 
be  counted  on. 

The  table  on  page  339  gives  theoretical  horsepowers  only.  Approxi- 
mately the  actual  horsepower  for  a  100-ft.  lift  may  be  found  by  multiplying 
the  tabular  figures  by  1.7;  for  a  200-ft.  lift,  by  1.45;  and  for  a  300-ft.  lift,  by  1.3. 
for  triplex  pumps. 

Depth  of  Suction. — Theoretically,  a  perfect  pump  will  raise  water  to  a 
height  of  nearly  34  ft.  at  the  sea  level;  but,  owing  to  the  fact  that  a  perfect 
vacuum  can  never  be  attained  with  the  pump,  that  the  water  always  contains 
more  or  less  air,  and  that  more  or  less  watery  vapor  will  form  below  the  piston, 
it  is  never  possible  to  reach  this  theoretical  limit,  and,  in  practice,  it  is  not 
possible  to  draw  water  much,  if  any,  over  30  ft.  at  the  sea  level,  even  when  the 
water  is  cold.  Warm  water  cannot  be  lifted  as  high  as  cold  Water  because  a 
larger  amount  of  watery  vapor  forms.  With  boiler  feed-pumps  handling  hot 
water,  the  water  should  flow  to  the  pumps  by  gravity. 

For  pumps  and  connections  in  the  best  possible  condition,  it  is  generally 
figured  that  the  suction  lift  will  be  three-fourths  of  that  theoretically  possible. 
However,  pumps  are  very  commonly  out  of  order  to  a  certain  degree  so  that  the 
lifts  given  in  the  following  table  agree  very  well  with  actual  practice. 

SUCTION  LIFT  OF  PUMPS  AT  DIFFERENT  ALTITUDES 


Altitude  Above  Sea  Level 

Atmospheric 
Pressure  at  Altitude 

Theoretical 

Practical 

Miles 

Feet 

Pounds  per 
Square  Inch 

Lift 
Feet 

Lift 
Feet 

14.70 

33.95 

22 

1 

1,320 

14.02 

32.38 

21 

S 

2,640 

13.33 

30.79 

20 

1 

3,960 

12.66 

29.24 

18 

1 

5,280 

12.02 

27.76 

17 

U 

6,600 

11.42 

26.38 

16 

H 

7,920 

10.88 

25.13 

15 

2 

10,560 

9.88 

22.82 

14 

HYDRAULICS  339 

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340 


HYDRAULICS 


Amount  of  Water  Raised  by  a  Single-Acting  Lift  Pump. — In  the  case  of  all 
pumps  having  a  piston  or  ram,  the  amount  of  water  lifted  is  usually  con- 
siderably less  than  the  piston  displacement,  owing  to  the  leakage  through 
the  valves,  etc.,  but  with  single-acting  lift  pumps,  having  bucket  plungers 
with  a  clack  valve  in  the  plunger,  the  amount  lifted  may  actually  exceed  the 
plunger  displacement;  that  is,  the  volume  of  water  may  actually  be  greater 
than  the  length  of  the  stroke  multiplied  by  the  number  of  strokes,  for,  during 
the  up-stroke,  the  water  both  above  and  below  the  piston  is  set  in  motion,  and 
during  the  down-stroke,  the  inertia  of  the  water  actually  carries  more  water 
through  the  valve  than  would  pass  through  it  on  account  of  the  space  passed 
through.  This  increases  as  the  speed  or  number  of  strokes  increases. 

Capacity  of  Pumps. — In  the  accompanying  table  are  given  the  capacities 
of  pumps;  these  values  are  for  single  strokes;  to  find  the  capacity  for  one 
revolution  the  capacity  for  a  stroke  must  be  multiplied  by  2. 

CAPACITY  OF  PUMPS 


Diameter 
of  Piston 
or  Plun- 
ger, Inches 

Length  of  Piston  or  Plunger  Stroke,  in  Inches 

2 

3 

,..|  j 

e    , 

12 

13 

Displacement  per  Stroke  of  Pump,  in  Gallons 

1 

.0106 

.0159 

.0212 

.0266 

.0319 

.0372 

.0638 

.0691 

1 

.0129 

.0193 

.0257 

.0321 

.0386 

.0450 

.0771 

.0835 

1 

.0153 

.0229 

.0306 

.0382 

,0459 

.0535 

.0918 

.0994 

1 

.0208 

.0312 

.0416 

.0521 

.0625 

.0729 

.1249 

.1353 

2 

.0272 

.0408 

.0544 

.0680 

.0816 

.0952 

.1632 

.1768 

2i 

.0344 

.0516 

.0688 

.0860 

.1033 

.1205 

.2065 

.2238 

24 

.0425 

.0638 

.0850 

.1063 

.1275 

.1488 

.2550 

.2763 

2f 

.0514 

.0771 

.1029 

.1286 

.1543 

.1800 

.3086 

.3343 

3 

.0612 

.0918 

.1224 

.1530 

.1836 

.2142 

.3672 

.3978 

3 

.0718 

.1077 

.1437 

.1796 

.2154 

.2514 

.4310 

.4668 

3 

.0833 

.1249 

.1666 

.2082 

.2499 

.2915 

.4997 

.5414 

>  3 

.0956 

.1484 

.1913 

.2391 

.2869 

.3347 

.5738 

.6216 

4 

.1088 

.1632 

.2176 

.2720 

.3264 

.3808 

.6530 

.7072 

4J 

.1228 

.1843 

.2457 

.3071 

.3684 

.4300 

.7370 

.7984 

4,1 

.1377 

.2065 

.2754 

.3443 

.4131 

.4819 

.8262 

.8950 

42- 

.1534 

.2301 

.3068 

.3835 

.4603 

.5370 

.9205 

.9972 

5 

.1700 

.2550 

.3400 

.4250 

.5100 

.5950 

.0200 

1  .  1050 

5| 

.1874 

.2811 

.3749 

.4686 

.  5623 

.6560 

.1245 

1.2183 

5 

.2057 

.3086 

.4114 

.5143 

.6171 

.7200 

.2342 

1  .  3370 

5 

.2248 

.3373 

.4497 

.5621 

.6745 

.7870 

.3490 

1.4614 

6 

.2448 

.3672 

.4896 

.6120 

.7344 

.8568 

.4690 

1.5912 

6 

.2656 

.3984 

.5312 

.6641 

.7969 

.9297 

.5940 

1  .  7270 

6 

.2872 

.4309 

.5745 

.7182 

.8618 

1.0050 

.7240 

1  .  8674 

6J 

.3099 

.4648 

.6197 

.7747 

.9296 

1.0850 

1.8590 

2.0140 

7 

.3332 

.4999 

.6665 

.8331 

.9997 

1.1660 

1.9990 

2.1660 

71 

.4084 

.6126 

.8168 

1.0210 

1.2250 

1.4290 

2  .  4500 

2  .  6540 

8 

.4352 

.6529 

.8704 

1.0890 

1.3060 

1.5230 

2.6110 

2  .  8290 

9 

.5508 

.8263 

.1020 

1.3770 

1  .  6520 

1  .  9280 

3  .  3050 

3  .  5800 

10 

.6800 

.0200 

.3600 

1.7000 

2.0400 

2  .  3800 

4.0800 

4  .  4200 

10* 

.7497 

.1250 

.4990 

1  .  8740 

2.2490 

2.6240 

4.4980 

4.8730 

11 

.8228 

.2340 

.6460 

2.0570 

2.4680 

2.8800 

4.9370 

5  .  3480 

12 

.9792 

.4690 

.9580 

2.4480 

2.9380 

3.4270 

5  .  8750 

6.3650 

13 

1.1490 

.7230 

2  .  2970 

2.8720 

3.4450 

4.0220 

6  .  8940 

7.4670 

14 

1.3320 

.9980 

2  .  6650 

3.3310 

3.9970 

4  .  6640 

7.9940 

8.6610 

15 

1  .  5300 

2.2950 

3.0600 

3.8250 

4  .  5900 

5.3540 

9.1800 

9.9430 

16 

1  .  7400 

2.6100 

3.4800 

4.3500 

5.2200 

6.0900 

10.4400 

11.3100 

18 

2.2030 

3.3050 

4.4060 

5  .  5080 

6.6100 

7.7110 

13.2200 

14.3200 

20 

2.7200 

4.0800 

5.4400 

6  .  8000 

8.1600 

9.5200 

16.3200 

17.6800 

22 

3.2910 

4.9360 

6  .  5820 

8.2280 

9.8740 

11.5200 

19.7500 

21.3900 

24 

3.9160 

5.8750 

7.8330 

9  .  7920 

11.7500  13.7100 

1 

23  .  5000  25  .  4600 

HYDRAULICS                                                341 

TABLE  —  (CONTINUED) 

Diam- 

Length of  Piston  or  Plunger  Stroke,  in  Inches 

eter  of 

Piston 

or 

1C 

18 

20 

24 

25 

33 

36 

38. 

Plun- 

ger, 

Inches 

Displacement  per  Stroke  of  Pump,  in  Gallons 

11 

.0850 

.0956 

.1062 

.1275 

.1328 

.1753 

.1912 

.2019 

If 

.1029 

.1157 

.1286 

.1543 

.1607 

.2121 

.2314 

.2442 

H 

.1224 

.1377 

.1530 

.1836 

.1912 

.2524 

.2754 

.2907 

1| 

.1666 

.1874 

.2082 

.2499 

.2603 

.3436 

.3748 

.3956 

2 

.2176 

.2448 

.2720 

.3264 

.3400 

.4488 

.4896 

.5168 

21 

.2754 

.3098 

.3442       .4131 

.4303 

.5680 

.6196 

.6541 

2J 

.3400 

.3825 

.4250 

.5100 

.5313 

.7013 

.7650 

.8075 

21 

.4114 

.4628 

.5143 

.6171 

.6428 

.8485 

.9257 

.9771 

3 

.4896 

.5508 

.6120 

.7344 

.7650 

.0100 

1.1020 

1.1630 

31 

.5746 

.6464 

.7183 

.8619 

.8978 

.1851 

1.2930 

1.3647 

3^- 

.6664 

.7497 

.8330 

.9996 

1.0410 

.3744 

1.4994 

1  .  5830 

3  1 

.7650 

.8610 

.9562 

1.1480 

1.1953 

.5778 

1.7212 

1.8169 

4 

.8704 

.9792 

.0880 

1.3060 

1  .  3600 

.7952 

1.9584 

2.0672 

41 

.9826 

1.1054 

.2282 

1.4740 

1.5353 

2.0270 

2.2110 

2.3336 

41 

.1010 

1.2393 

.3770 

1  .  6524 

1.7212 

2.2720 

2.4786 

2.6163 

4f 

.2274 

1.3780 

.5340 

1.8410 

1.9180 

2.5310 

2.7620 

2.9150 

5 

.3600 

1  .  5300 

.7000 

2.0400 

2.1250 

2.8050 

3.0600 

3.2300 

51 

.5000 

1.6870 

.8740 

2.2490 

2.3430 

3.0930 

3.3740 

3  .  5610 

5* 

.6460 

1.8510 

2.0570 

2.4680 

2.5710 

3.3940 

3.7030 

3.9080 

s| 

.7990 

2.0230 

2.2480 

2.6980 

2.8110 

3.7100 

4.0470 

4  .  2720 

6 

.9580 

2.2030 

2.4480 

2.9380 

3.0600 

4.0380 

4.4060 

4.6500 

61 

2.1250 

2.3900 

2  .  6560 

3.1880 

3.3200 

4.3830 

4.7810 

5.0470 

6* 

2.2980 

2.5850 

2.8730 

3.4470 

3.5910 

4.7400 

5.1710 

5  .  4580 

6f 

2.4790 

2.7880 

3.0990 

3.7180 

3.8730 

5.1130 

5.5780 

5  .  8870 

7 

2.6660 

2.9990 

3  .  3320 

3.9990 

4.1650 

5.4990 

5.9980 

6.3320 

7i 

3.2670 

3.6750 

4.0840 

4.9000 

5.1050 

6.7390 

7.3510 

7.7590 

8 

3.4820 

3.9170 

4.3520 

5.2230 

5.4400 

7.1810 

7.8340 

8  .  2690 

9 

4.4060 

4.9570 

5  .  5080 

6.6100 

6.8850 

9.0890 

9.9150 

10.4600 

10 

5.4400 

6.1200 

6.8000 

8.1600 

8.5000 

11.2200 

12.2400 

12.9200 

i(H 

5.9980 

6.7470 

7.4970 

8.9960 

9.3700 

12.3700 

13.4900 

14.2400 

11 

6.5820 

7.4050 

8.2280 

9.8730 

10.2800 

13.5800 

14.8100 

15.6300 

12 

7.8340 

8.8130 

9  .  7920 

11.7500 

12.2400 

16.1600 

17.6300 

18.6000 

13 

9  .  1920 

10.3400 

11.4900 

13.7800 

14.3600 

18.9600 

20  .  6900 

21.8300 

14 

10  .  6600 

11.9900 

13.3200 

15.9800 

16.6600 

21.9900 

23.9900 

25.3200 

15 

12.2300 

13.7700 

15.2900 

18.3600 

19.1200 

25.2400 

27  .  5400 

29.0700 

16 

13.9200 

15.6600 

17.4000 

20  .  8800 

21.7600 

28.7200 

31.3300 

33.0700 

18 

17.6200 

19.8200 

22.030026.440027.5400 

36.3500 

39  .  6600 

41.8600 

20 

21.7600 

24.4800 

27  .  2000  32  .  6400  34  .  0000 

44.8800 

48:9600 

51.6800 

22 

26.3300 

29  .  6200 

32.9100  39.490041.1400 

54  .  3000 

59.2400 

62.5300 

24 

31.330035.2500 

39.160047.000048.9600 

64  .  6300 

70  .  5000 

74.4200 

Pump  Valves. — As  a  rule,  a  large  number  of  small  valves  having  a  compara- 
tively small  opening  are  preferable  to  a  small  number  of  large  valves  with 
a  greater  opening,  and  most  modern  pumps  are  built  on  these  lines.  A  small 
valve  represents  a  proportionately  larger  surface  of  discharge  with  the  same 
lift  than  the  large  valve,  hence  whatever  the  total  area  of  the  valve-seat  open- 
ing, its  full  contents  can  be  discharged  with  less  lift  through  numerous  small 
valves  than  through  one  large  valve. 


large  metal  valve. 


Cornish  pumps  generally  have  one 

POWER  PUMPS 

In  a  power  pump  the  reciprocating  motion  is  transmitted  to  the  water 
plunger  or  piston  by  means  of  a  crank  driven  by  belting  or  gearing,  instead  of 
in  a  straight  line  directly  from  the  steam  or  air  piston.  Power  pumps  are  not 


342 


HYDRAULICS 


generally  used  for  pumping  against  heavy  pressures.  They  may  be  single, 
duplex,  or  triplex,  single-acting  or  double-acting,  and  either  of  piston  or  plunger 
types,  although  double-acting  and  triple-acting  plunger  pumps  are  the  most 
common.  The  triplex  pump  consists  of  three  single-acting  plunger  pumps 
driven  by  cranks  120°  apart  on  a  single  shaft.  A  tight  and  a  loose  pulley 
provide  the  means  for  starting  and  stopping  the  pump  without  disturbing 
the  engine  on  the  main  shaft.  The  pulley  shaft  is  geared  to  the  crank-shaft 
by  a  pinion  and  spur  wheel.  By  setting  the  cranks  120°  apart,  the  strokes 
follow  and  overlap  one  another  giving  a  uniform  flow  of  water  and  a  uniform 
expenditure  of  power.  In  the  case  of  duplex  single-acting  pumps,  the  cranks 
are  placed  180°  apart  and  the  discharge  is  the  same  as  from  one  double-acting 
pump  of  the  same  diameter  of  plunger  and  length  of  stroke.  Duplex,  double- 


ring  and  discharging 
these  pumps  is  sometimes  supplied  with  gears  at  each  end  to  equalize  the 
strain,  particularly  when  heavy  pressures  are  to  be  overcome. 

Electrically  Driven  Power  Pumps. — Where  water  is  to  be  delivered  from 
isolated  workings  to  the  sumps  for  the  large  station  pumps,  electrically  driven 
power  pumps  are  far  more  efficient  than  steam  pumps.  In  some  cases,  it  is 
probably  best  to  equip  the  entire  mine  with  electric  pumps,  both  in  the  isolated 
workings  and  at  the  stations,  because  they  can  be  driven  by  a  high-class 
compound-condensing  engine  on  the  surface,  directly  connected  to  a  generator, 
and  furnishing  electricity  through  conductors  to  the  various  pumps. 

The  total  efficiency  of  a  series  of  small  electric  pumps  that  aggregate  a 
sufficient  amount  of  power  to  enable  this  arrangement  to  be  used,  is  very 
much  higher  than  the  total  efficiency  of  a  number  of  small  isolated  steam  or 
compressed-air  pumps  introduced  into  the  workings.  With  compound- 
condensing  engines  upon  the  surface,  operating  electric  pumps  underground, 
the  steam  consumption  per  pump  horsepower  per  hour,  for  the  smaller  sizes, 
would  only  be  about  40  Ib.  per  H.  P.  per  hr.;  for  medium-sized  electric  pumps, 
about  30  Ib.  per  hr.,  and  larger  sizes  from  20  to  30  Ib.  per  H.  P.  per  hr.  These 
figures  show  that  for  pumping  from  isolated  portions  of  the  mine  the  electric 
pump  is  much  more  efficient  than  the  steam  pump,  as  the  current  can  fre- 
quently be  obtained  from  the  lines  operating  the  underground  haulage 
system,  furnishing  light,  etc. 

An  efficiency  of  at  least  50%  should  be  obtained  in  any  well-designed, 
well-built  pump,  so  that  a  close  approximation  to  "the  actual  current  consump- 
tion can  be  obtained  by  doubling  the  theoretical  consumption  given  in  the 
accompanying  table. 


THEORETICAL    CONSUMPTION    OF   ELECTRIC    CURRENT   FOR 
PUMPING  WATER  PER  1,000  GAL. 


Total 
Elevation 

Equivalent 
Pressure 

Kilowatts 

Total 
Elevation 

Equivalent 
Pressure 

Kilowatts 

Feet 

per 
Square  Inch 

1,000041. 

Feet 

per 
Square  Inch 

per 
1,000  Gal. 

10 

4.33 

.0312 

160 

69.29 

.500 

20 

8.66 

.0624 

170 

73.63 

.531 

30 

12.99 

.0937 

180 

77.96 

.562 

40 

17.32 

.124 

190 

82.29 

.593 

60 

21.65 

.156 

200 

86.62 

.624 

60 

25.99 

.187 

210 

91.14 

.655 

70 

30.32 

.218 

220 

95.48 

.686 

80 

34.65 

.249 

230 

99.82 

.717 

90 

38.95 

.281 

240 

104.16 

.748 

100 

43.31 

.312 

250 

108.50 

.779 

110 

47.64 

.343 

260 

112.84 

.813 

120 

51.97 

.374 

270 

116.91 

.841 

130 

56.30 

.406 

280 

121.24 

.875 

140 

60.63 

.437 

290 

125.57 

.903 

150 

64.96 

.468 

300 

129.90 

.934 

HYDRAULICS  343 

Precautions  Necessary  With  Electrically  Driven  Mine  Pumps. — Where 
electricity  is  used  in  mining,  the  prevailing  tendency  is  to  lay  the  blame  for 
troubles  of  various  kinds  to  its  use,  because  electricity  is  the  least  understood 
and  most  mysterious  force  employed.  It  is  especially  important,  therefore, 
that  every  precaution  be  taken  to  minimize  the  possibility  of  accident  from 
electric  causes,  either  by  shock  or  by  fire.  While  bare  wires  are  necessarily 
employed  as  trolley  wires,  all  wires  used  as  feeders,  on  the  headings,  and  wires 
leading  to  the  pump  should  be  well  insulated,  as  even  a  slight  shock  received 
by  the  attendant  working  at  or  near  the  pump,  or  trackmen,  or  timbermen 
working  on  the  entries,  may  prove  fatal  should  the  man  receiving  the  shock 
fall  against  the  exposed  wire.  Whenever  possible,  a  dry,  wooden  platform 
should  be  provided  about  the  pump;  or,  if  this  is  considered  objectionable 
on  account  of  the  fire  risk,  a  good,  dry,  cement  floor  should  be  laid  in  the 
pump  room.  A  small  stool  with  insulator  pins  and  glasses  for  legs  forms  a 
safeguard  and  should  be  used  whenever  it  is  necessary  to  adjust  or  change 
brushes  or  work  on  the  commutator  while  running. 

It  is  hardly  surprising  that  a  fire  should  originate  in  a  mine  when  a  small 
electric  pump  is  placed  on  a  wooden  floor  in  a  frame  pump  house  and  the  • 
attendant  has  a  seat  or  bunk  with  straw  mattress,  where  he  reclines  and  smokes; 
or  when  oil  and  waste  are  thrown  about  and  the  fuse  boxes  and  rheostat  are 
fastened  to  a  board  placed  against  an  inflammable  partition,  while  a  strong 
draft  passing  through  the  place,  and  no  available  means  at  hand  of  extinguish- 
ing a  fire  adds  to  the  danger. 

The  following  precautions  are  advised  in  placing  an  electric  pump:  Place 
the  pump,  if  possible,  in  a  special  room  excavated  for  the  purpose.  Where 
a  break-through  or  passage  between  two  rooms  must  be  used,  it  should  be 
closed  with  brick  or  stone  and  not  with  wooden  brattice.  Make  the  place 
fireproof;  allow  no  wooden  boxes  or  furnishings  of  inflammable  material; 
enforce  strict  regulations  in  regard  to  oil  and  waste  used  about  the  pump; 
have  a  dry,  cement  floor  and  keep  it  clean.  Matches  must  not  be  left  in  or 
around  the  pump  house,  or  any  illuminating  oil  kept  therein,  and  lubricating 
oils  should  be  carried  to  the  pump  house  only  in  small  quantities  and  in  closed 
cans.  Cotton  waste  when  saturated  with  oil  is  liable  to  spontaneous  com- 
bustion, and  should  be  thrown  into  a  tight  can  and  taken  out  of  the  mine  each 
day.  The  discharge  pipe  of  the  pump  should  be  tapped  with  1-in.  connections, 
and  a  length  of  hose  with  a  nozzle  kept  in  the  pump  house  ready  for  use  in 
case  of  fire. 

The  pump  house  should  be  well  lighted  by  incandescent  lamps.  Where 
lamps  are  used  in  series,  at  least  two  circuits  should  be  run,  since  one  burn-out 
will  extinguish  an  entire  series.  The  transmission  wire  for  the  pump  should 
be  strung  on  glass  or  porcelain  insulators  and  care  taken  to  prevent  contact 
with  the  pump  frame  or  the  mine  timbers.  The  line  should  be  taken  as  directly 
as  possible  to  the  switch  and  fuses,  and  should  be  protected  against  a  series 
ground  or  a  short  circuit. 

The  following  table  gives  the  gallons  per  minute  delivered  from  various 
sized  pumps  operating  at  different  piston  speeds. 

Centrifugal  Pumps. — In  mining  practice,  centrifugal  pumps  commonly 
driven  by  an  electric  motor  placed  on  the  same  shaft,  have  been  used  for  many 
years  in  raising  water  from  local  dips  and  swamps  into  the  main  sump.  The 
absence  of  valves  makes  them  well  adapted  to  pumping  dirty  or  gritty  water 
and  the  fact  that  the  moving  parts  have  a  rotatory  instead  of  a  reciprocating 
motion  makes  them  especially  suitable  where  electric  power  is  available. 
Their  small  size,  and  consequent  portability,  is  a  commending  feature  for 
underground  work.  Where  the  water  is  strongly  acid  these  pumps  probably 
wear  out  sooner  than  ordinary  reciprocating  pumps  unless  made  of  special 
acid-resisting  metal. 

The  original  form  of  single-stage  centrifugal  pump  was  designed  for  handling 
large  volumes  of  water  under  small  heads,  say,  from  60  to  100  ft.  In  modern 
installations,  heads  of  500  ft.,  750  ft.,  and  even  more,  are  overcome  by  the  use 
of  multistage  pumps,  so  that  this  type  is  now  frequently  used  in  pumping  from 
the  main  sump  to  the  surface  in  one  operation. 

The  pump  consists  of  a  series  of  revolving,  turbine-like  wheels  or  impellers, 
set  side  by  side  on  the  same  shaft.  The  water  thrown  off  by  the  first  wheel  is 
taken  up  by  the  second  and  by  it  passed  on  to  the  third,  and  similarly,  accord- 
ing to  the  number  of  stages.  If  there  is  but  one  revolving  part  or  impeller, 
which  throws  the  water  into  the  discharge  pipe,  the  pump  is  single-stage;  if 
there  are  two  revolving  parts,  the  second  discharging  the  water  forced  into  it 
by  the  first,  it  is  a  two-stage  pump,  and  similarly  for  each  additional  revolving 


344 


HYDRAULICS 


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HYDRAULICS  345 

part.     These  pumps  are  designated  by  the  size  of  their  outlet  as,  for  instance, 
a  2-in.  or  4-in.  pump,  meaning  with  a  2-in.  or  a  4-in.  discharge  pipe. 

The  height  of  lift  depends  on  the  quantity  of  water  to  be  discharged  and  the 
circumferential  velocity  of  the  revolving  disk  and  is  proportional  to  the  area 
of  the  discharge  orifices  at  the  circumference  of  the  disk.  The  circumferential 
velocity  depends  on  the  diameter  of  the  disks  as  well  as  on  the  number  of 
revolutions  per  minute.  As  the  number  of  revolutions  per  minute  is  com- 
monly limited  by  those  of  the  electric  driving  motor,  the  diameter  of  the  disks, 
that  is,  the  size  of  the  wheel  or  pump,  is  varied  to  suit  the  head  against  which 
the  machine  is  working.  For  a  given  lift,  the  total  efficiency  of  centrifugal 
pumps  increases  with  the  size  of  .the  pump,  being  about  .45  to  .50  for  the 
smallest  sizes  of  single  stage  pumps,  and  .70  to  .75  for  the  largest,  the  mul- 
tistage pumps  giving  better  results. 

One  of  the  most  important  points  to  investigate  when  selecting  a  centri- 
fugal pump  is  the  total  head  against  which  it  will  have  to  work,  as  this  head 
determines  the  speed  at  which  the  pump  can  most  economically  run  and  the 
speed  determines  the  size  necessary  to  throw  a  given  volume  of  water.  The 
horsepower  may  be  determined  by  the  same  formula  used  for  reciprocating 
pumps, 

BHP  =  (GFMXhead  in  feet)  4-  (3, 960 X efficiency  of  pump), 
in  which,  BHP  =  brake  horsepower; 

GPM  =  number  of  gallons  to  be  delivered  per  minute. 

In  this  formula,  if  the  efficiency  is  made  equal  to  unity,  the  horsepower 
determined  will  be  the  net  horsepower  theoretically  required  to  raise  the  given 
number  of  gallons  the  given  height.  As  stated,  the  efficiency  varies  widely, 
and  may  be  taken  at  .50  for  small  wheels  operating  under  low  heads  and  .75  for 
large  multistage  wheels  operating  under  high  heads.  However,  the  determi- 
nation of  the  proper  size  of  pump  had  better  be  left  to  the  manufacturer  who, 
on  receipt  of  the  proper  data,  will  supply  the  right  kind  and  size  of  pump  and 
will  guarantee  its  efficiency.  The  data  required  are  the  quantity  of  water  to 
be  pumped  per  minute  and  its  kind  (clean,  acid,  muddy,  gritty,  etc.,  size  of 
grains  of  impurity,  etc.),  the  suction  lift,  or  distance  from  the  water  level  in 
the  sump  to  the  center  line  of  the  pump,  the  discharge  lift,  or  difference  in 
elevation  between  the  center  line  of  the  pump  and  the  point  of  discharge, 
together  with  a  sketch  showing  a  plan  of  the  discharge  line  with  its  length  and 
size  and  the  number,  location,  and  radius  of  the  various  bends.  The  pressure, 
in  pounds  per  square  inch,  of  steam  or  compressed  air,  or  voltage  of  electric 
current  should  be  given,  all  estimates  being  made  for  the  power  available  at 
the  point  of  its  application. 

When  bolting  the  pump  to  the  foundation,  care  must  be  taken  not  to  spring 
the  bedplate.  Every  joint  in  the  suction  pipe  should  be  air-tight.  The  pump 
should  be  installed  to  run  in  the  direction  indicated  by  the  arrow,  wording,  or 
other  instruction  stamped  or  cast  on  the  casing.  The  stuffingboxes  should  be 
properly  packed  and  the  water-seal  ring  should  be  in  the  proper  position. 
The  bearings  should  be  cleaned  and  filled  with  a  good  grade  of  engine  oil. 
Long  sweep  elbows  only,  and  as  few  of  them  as  possible,  should  be  used  in  the 
suction  and  discharge  piping.  It  is  also  advisable  to  use  large  pipe  lines,  as 
this  reduces  the  power  necessary  to  drive  the  pump  and  will  save  money  in 
the  long  run.  To  prevent  freezing  in  cold  weather,  the  pump  should  always 
be  drained  when  not  in  use  by  unscrewing  the  plug  in  .the  bottom  of  the 
pump  casing. 

All  centrifugal  pumps  that  do  not  operate  with  pressure  on  the  suction 
side  (that  is,  all  pumps  drawing  water  from  a  sump  that  is  below  the  level 
of  the  center  of  the  pump)  must  have  the  casing  and  suction  pipe  filled  with 
water  before  starting.  This  may  'be  accomplished  in  various  ways.  Where 
steam  or  compressed  air  is  the  power  an  ejector  is  used,  but  this  method  of 
priming  is  not  available  in  mining  practice  where  electricity  is  used.  If  a 
hand  primer  is  used,  the  air  cock  on  the  top  of  the  pump  is  opened  and  the 
primer,  which  is  a  small  hand  pump,  is  worked  until  water  flows  through  this 
cock.  Then  the  pump  is  started. 

If  there  is  a  foot-valve  on  the  bottom  of  the  suction  pipe,  the  pump  can  be 
primed  by  running  water  into  it  from  an  overhead  tank,  or  any  other  source 
of  supply,  as  the  valve  will  hold  the  water  in  the  pump.  In  the  event  of  the 
column  pipe  being  full  of  water,  as  is  commonly  the  case  when  the  pump  has 
been  shut  down  temporarily  (as  during  the  night  shift),  a  by-pass  may  be 
arranged  by  which  the  water  in  the  column  pipe  may  be  drawn  off  in  sufficient 
quantity  to  prime  the 'pump.  After  priming,  the  pump  can  be  started  and, 
when  full  speed  has  been  attained,  the  discharge  valve  opened. 


346  HYDRAULICS 

PUMPS  FOR  SPECIAL  PURPOSES 

Sinking  Pumps. — Sinking  pumps  may  be  either  single  or  duplex  in  their 
action,  and  may  be  inside  or  outside  packed.  Outside-packed  single-acting 
pumps  are  in  many  ways  preferable,  owing  to  the  fact  that  they  are  less  liable 
to  get  out  of  order.  One  requisite  of  any  sinking  pump  is  that  it  should  have 
as  few  exposed  parts  as  possible,  and  that  these  parts  should  be  so  placed  that 
they  will  be  protected  to  as  great  an  extent  from  injury  by  blasting  as  possible. 
Sinking  pumps  are  usually  provided  with  a  telescopic  section  in  the  suction 
pipe,  and  sometimes  also  in  the  discharge  pipe,  so  that  they  can  be  moved 
down  several  feet  without  having  to  break  the  joints  of  the  piping. 

Pumps  for  Acid  Waters. — Where  mine  waters  are  acid  in  their  nature, 
bronze,  bronze-lined,  or  lead  lined  pumps  are  usually  employed,  and  in  some 
cases  even  wooden  pumps  have  been  used,  as, 
for  instance,  in  the  Swedish  copper  mines, 
though  this  practice  is  disappearing  in  favor  of 
the  use  of  bronze  or  copper  linings.  The  pipes 
for  such  pumps  should  be  of  bronze  or  copper 
tubing,  or  should  be  lined  with  some  sub- 
stance that  will  not  be  affected  by  the  acid 
of  the  water.  Sometimes  wooden  linings  are 
employed,  placed  as  shown  in  Figs.  1  and  2, 
Fig.  1  being  a  section  of  the  pipe  with  the  lining 
complete,  and  Fig.  2  a  cross-section  of  one 
of  the  individual  boards  used  in  the  lining. 
These  are  usually  made  of  pine  about  f  in. 
thick,  and  are  gro9ved  on  each  end  as  shown. 
FIG.  1  r  IG.  2  They  are  sprung  in  so  as  to  complete  a  circle 

on  the  inside  of  the  pipe,  and  then  long,  thin,  wooden  keys  driven  into  the 
grooves.  When  the  water  is  allowed  to  go  into  the  pipes,  the  linings  swell 
and  make  all  joints  perfectly  tight.  Elbows  and  other  crooked  sections  are 
lined  with  sheet  lead  beaten  in  with  a  mallet.  Concrete-lined  pumps  have 
been  recently  introduced  in  mines  where  there  is  acid  water. 

PUMP  FOUNDATIONS 

The  foundation  for  pumping  machinery  depends  entirely  on  the  type  of 
pump.  Direct-acting  duplex  pumps  probably  require  the  least  foundation,  for 
the  piston  and  plunger  moving  in  9pposite  directions  almost  balance  the 
machine  in  line  with  the  plunger  motion  and  the  strains  due  to  reversing  are 
contained  almost  wholly  within  the  machine  itself.  Small  duplex-pump 
foundations  are  made  of  a  solid  mass  of  brick  or  concrete,  while  large  pumps  are 
often  set  on  separate  piers,  one  for  the  water  end  and  one  for  the  steam  end. 
The  foundations  must  go  down  to  sufficiently  hard  material  to  bear  the  weight 
of  the  pump;  or,  if  the  substratum  consists  of  loose  sand  or  gravel,  the  founda- 
tion must  be  spread  so  that  the  pressure  does  not  exceed  1  T.  per  sq.  ft.  Single 
pumps  require  a  somewhat  heavier  foundation  than  duplex  pumps,  owing  to 
the  greater  shocks  to  which  they  are  subjected. 

Foundations  should  be  built  of  hard  brick  laid  in  cement  mortar,  or  of 
concrete;  or,  in  the  case  of  large  pumps,  stone  may  be  used.  The  pump  should 
be  secured  to  foundation  bolts  anchored  to  plates  underneath  the  masonry. 
If.  solid  rock  exists  at  the  place  where  the  pump  is  to  be  located,  the  surface 
of  the  rock  is  leveled  to  suit  the  bedplate  or  footings  of  the  pump;  holes  for  the 
foundation  bolts  are  then  drilled  to  a  sufficient  depth,  and  the  bolts,  which 
should  have  a  good  length  and  a  roughened  shank,  are  placed  in  the  holes  and 
fastened  by  pouring  molten  lead  around  them. 

Pump  houses,  or  pump  stations  as  they  are  often  called,  are  generally  placed 
near  the  foot  of  a  shaft  or  slope  in  a  room  excavated  for  the  purpose  in  the  solid 
rock  or  coal.  If  the  roof  needs  support,  timbers  or  steel  supports  may  be  used. 

PUMP  MANAGEMENT 

All  pumps,  when  new,  should  be  run  slowly  until  the  parts  have  become 
thoroughly  adjusted  to  their  bearings,  when  the  speed  may  be  increased. 
Because  a  new  pump  works  stiffly  is  no  cause  for  alarm,  for,  while  a  machinist 
can  properly  construct  the  parts,  he  cannot  always  forsee  the  strains  caused 
by  the  action  of  the  pump,  when  the  parts  are  assembled  and  which  require 
certain  adjustments  to  be  made  after  the  pump  is  at  work.  By  running  the 
pump  slowly  with  the  parts  properly  lubricated  and  making  such  adjustments 
as  may  be  necessary,  stiffness  will  gradually  disappear  and  the  highest  efficiency 


HYDRAULICS  347 

of  the  pump  will  be  attained,  provided  other  matters  on  which  the  pump's 
action  depend  have  received  proper  attention. 

The  causes  that  affect  a  pump,  impair  its  efficiency,  and  prevent  it  from 
performing  its  full  duty  are:  wear;  the  improper  adjustment  of  valves,  valve 
stems,  and  levers;  the  improper  packing  of  plungers  and  stuffingboxes;  draw- 
ing up  the  stuffingbox  glands  too  tightly;  lost  motion  due  to  permitting  the 
working  parts  to  wear  and  not  adjusting  them  to  the  new  conditions;  accumu- 
lations of  foreign  matter  under  the  valves  or  in  the  strainer;  broken  valves  and 
valve  springs;  leakage  in  valves;  taking  air  in  the  suction  pipe;  clogged  or 
broken  discharge  pipes;  and  the  use  of  poor  gaskets. 

At  many  mines,  the  pumps  are  capable  of  a  larger  capacity  than  is  obtained 
by  the  low  speed  at  which  they  are  run,  but  it  is  important  that  such  pumps 
be  run  continuously,  as  any  serious  interruption  in  pumping  might  cause  trouble 
elsewhere.  It  is  customary,  therefore,  to  keep  on  hand  a  supply  of  duplicate 
valves,  moving  parts,  and  packing,  in  order  that  when  it  becomes  necessary 
to  make  repairs  they  may  be  made  without  great  loss  of  time. 

A  common  cause  of  pumps  refusing  to  work  properly  is  due  to  their  taking 
air  below  the  suction  valves.  Small  leaks  will  cause  the  piston  to  jump,  owing 
to  the  water  not  entering  through  the  suction  valves  soon  enough  to  fill  the 
entire  chamber.  This  trouble  may  be  remedied  by  seeing  that  all  joints  in  the 
suction  pipe  and  between  the  pipe  and  the  pump  are  air-tight.  Leaks  may 
sometimes  be  detected  by  the  hearing  or  by  the  flame  from  a  candle  being 
drawn  toward  the  hole.  If  the  leaks  are  small  and  not  at  the  pipe  joints,  a 
coat  of  asphalt  paint  may  stop  them;  if  large,  they  should  be  drilled  larger,  the 
hole  threaded,  and  a  screw  plug  inserted.  If  the  leak  is  at  the  joint  between 
two  pipes,  the  pipes  should  be  uncoupled  and  screwed  together  again,  using 
graphite  pipe  grease  for  a  lubricant;  or,  if  the  joint  is  a  flanged  one,  a  new 
gasket  should  be  placed  between  the  flanges,  and  the  pipes  lined  up  before  the 
bolts  are  tightened. 

Sometimes,  a  pump  fails  to  catch  the  water  when  started  owing  to  leakage 
of  the  valves  in  the  suction  chamber.  The  trouble  may  be  caused  by  the 
valve  and  valve  seat  being  corroded;  by  chips  or  gravel  getting  under  the 
valves  and  preventing  them  from  seating  properly;  or  by  the  valves  and  seats 
becoming  worn  so  that  leakage  cannot  be  prevented  without  changing  the 
parts. 

Many  pumps  that  will  not  raise  water  in  the  suction  pipe  when  empty, 
owing  to  the  pump  having  been  idle  for  some  time,  will  continue  to  draw 
water  after  once  being  started.  In  such  cases,  it  is  necessary  to  prime  the 
pump,  by  which  is  meant  filling  the  suction  pipe  and  part  of  the  suction  cham- 
ber, if  there  is  one,  and  in  some  cases,  also,  the  pump  barrel,  with  water,  so  that 
the  pump  may  start  under  conditions  similar  to  those  under  which  it  must 
work.  To  prime  the  pump,  it  is  simply  necessary  to  open  the  cock,  or  valve, 
in  the  priming  pipe  and  allow  water  from  the  column  pipe  to  flow  down  into 
the  suction  pipe  and  the  pump.  When  these  are  full,  the  valve  is  again  closed 
and  the  pump  is  ready  to  start. 

Pumps  sometimes  fail  to  raise  the  water  when  the  full  head  is  resting  on  the 
valves  in  the  discharge  chamber.  This  may  be  due  to  air  accumulating 
between  the  suction  and  the  discharge  decks,  which  air  is  compressed  and 
expanded  by  the  motion  of  the  plunger.  Air  valves  should  be  provided  in  the 
water  cylinder  for  the  purpose  of  allowing  this  confined  air' to  escape.  Violent 
jarring  and  trembling  often  take  place  if  the  discharge  chamber  is  not  provided 
either  with  an  air  chamber  where  the  lift  is  not  above  150  ft.,  or  with  an  allevi- 
ator, for  lifts  above  that  distance.  This  jarring  is  due  to  the  column  of 
water  in  the  discharge  pipe  coming  to  rest  suddenly  between  strokes  and 
having  to  be  again  put  in  motion. 

In  case  the  pump  column  is  filled  with  water  and  the  pump  is  stopped, 
the  water  will  run  back  through  the  pump  if  the  foot-valve  is  not  tight.  To 
prevent  this,  a  gate  valve  or  a  check-valve  is  placed  a  short  distance  from  the 
pump  in  the  column  pipe.  A  gate  valve  wears  less  than  a  check-valve,  and 
presents  no  obstruction  to  the  flow  of  water  when  the  valve  is  open.  This 
valve  is  useful  in  the  column  pipe  to  keep  the  pressure  off  the  valves  when  the 
pump  is  not  at  work,  and  also  for  keeping  water  from  running  back  into  the 
pump  chamber  when  the  valves  are  being  repaired. 

When  starting  compound  pumps,  the  steam  on  the  high-pressure-cylinder 
piston  is  not  always  powerful  enough  to  move  the  plungers  against  the  resis- 
tance of  the  water  in  the  discharge  pipe;  but,  by  opening  the  gate  valve  in  the 
by-pass  piping,  the  pressure  on  the  plungers  is  relieved  for  a  sufficient  num- 
ber of  strokes  to  allow  the  steam  to  reach  the  low-pressure  piston,  when  the 


348  HYDRAULICS 

combined  force  of  the  two  pistons  will  do  the  work  and  the  by-pass  pipe  can 
be  closed. 

Valves  in  the  steam  end  sometimes  wear  unevenly  or  the  valve  stems  by 
continual  action  wear  and  cause  lost  motion,  thus  causing  a  back  pressure 
and  irregular  action.  Anything  wrong  in  the  steam  end  can  usually  be  deter- 
mined by  the  irregular  exhaust,  but  even  this  may  be  deceptive  in  case  the 
water-end  valves  are  leaking.  If  the  steam  valves  are  suspected,  the  steam- 
chest  cover  may  be  raised  for  their  inspection,  but  the  valves  should  not  be 
disturbed  until  it  has  been  determined,  by  moving  the  water  piston  backwards 
and  forwards  several  times,  that  they  do  not  open  and  close  properly.  The 
trouble  may  be  in  the  levers  or  toggles  that  throw  them,  and  the  adjustments 
may  be  properly  made  without  disturbing  the  valves.  In  many  duplex 
pumps,  there  are  very  slight  differences  between  the  two  sides,  and  the  amount 
of  lost  motion  between  the  valve  stem  and  the  valve  should  be  carefully 
adjusted.  Too  little  lost  motion  will  cause  short  stroking,  while  too  much  will 
allow  the  pistons  to  strike  the  heads.  The  adjustment  requires  skill. 

Sometimes,  the  valve  seat  or  the  valve  has  soft  spots  that  wear  faster  than 
the  rest  of  the  valve  and  seat.  Through  these  slight  depressions,  steam  will 
blow  and  cut  both  valve  and  seat  if  attention  is  not  given  them;  back  pressure 
will  then  seriously  interfere  with  the  working  of  the  pump.  If  the  defect  is 
in  the  valve,  a  new  one  can  take  its  place;  but  the  valve  seat,  if  a  part  of  the 
steam  cylinder,  will  require  an  entirely  new  cylinder,  and  hence  it  is  economy 
to  scrape  the  seat  until  the  depressions  are  removed.  A  try  plate  made  of  steel 
having  a  perfectly  level  surface  is  covered  with  chalk  and  carefully  rubbed 
over  the  valve  seat;  the  elevations  will  have  chalk  on  them,  the  depressions  will 
not.  The  elevations  are  scraped  with  a  chisel  made  of  the  best  steel  until  they 
are  worn  down  so  that  chalk  sticks  to  every  part  of  the  seat  alike.  The  valve 
is  treated  in  the  same  way  if  it  can  be  done  without  too  much  expense.  The 
valve  and  the  valve  seat  when  removable  should  be  sent  to  the  shop  to  be 
reground. 

The  first  step  after  a  pump  has  been  erected  is  to  clean  out  the  steam 
piping.  In  order  that  this  may  be  done  without  carrying  foreign  matter  into 
the  pump,  the  piping  is  left  disconnected  from  the  pump  and  steam  at  full 
boiler  pressure  is  allowed  to  blow  freely  through  the  piping  and  valves  for  a 
few  minutes.  Steam  is  then  shut  off  and  the  piping  is  connected  to  the  pump. 

The  next  step  is  to  blow  out  the  steam  cylinders.  To  do  this,  the  cylinder 
heads  should  be  put  on,  leaving  the  pistons  and  valves  out  of  the  cylinders. 
The  stuffingboxes  should  be  closed,  which  is  most  conveniently  done  by  placing 
a  piece  of  board  between  the  stuffingbox  and  the  reversed  gland  and  then 
setting  up  the  nut  on  the  stuffingbox  studs.  When  the  gland  is  drawn  home 
by  a  nut  outside  of  it,  a  circular  piece  of  pine  board  may  be  placed  between 
the  end  of  the  gland  and  the  inside  of  the  nut  in  order  to  close  the  opening 
through  which  the  piston  rod  passes.  Steam  may  now  be  turned  on  the 
main  steam  pipe  leading  to  the  pump;  by  opening  the  throttle  valve  wide  at 
short  intervals,  the  sand  and  scale  in  the  ports  and  other  passages  and  spaces 
of  the  steam  end  can  be  blown  out.  After  the  cylinders  have  been  blown  out, 
the  heads  and  covers  should  be  removed  and  all  foreign  matter  blown  into  the 
corners  and  chambers  of  the  cylinders  removed  by  hand.  The  pistons,  valves, 
cylinder  heads,  and  other  covers  can  then  be  put  in  place.  The  blowing  out 
of  the  pipes  and  cylinders  after  erection  is  often  neglected  or  but  imperfectly 
done,  with  serious  consequences  to  the  machine;  it  cannot  be  too  thoroughly 
done,  particularly  in  that  type  of  pump  where  the  steam  ports  and  exhaust 
ports  are  on  top,  for  in  this  particular  case  the  sand  and  grit  are  deposited  in 
the  bottom  of  the  cylinder  for  the  piston  to  ride  on. 

The  packing  of  all  rods  and  stems  is  the  next  step.  If  fibrous-  packing  is 
used,  the  boxes  should  be  filled  full  and  the  glands  tightened  down  very  moder- 
ately. The  tightening  of  the  glands  can  best  be  done  when  steam  is  on  and  the 
machine  is  in  motion,  when  they  should  be  tightened  only  sufficiently  to  stop 
leakage  and  no  more.  When  excessive  tightening  is  required  to  stop  leakage, 
the  packing  should  be  completely  renewed.  Some  pumps  are  fitted  with 
metallic  packing;  this  packing  is  usually  prepared  by  specialists  and  fully 
guaranteed,  and  their  directions  for  use  should  be  carefully  followed.  In  case 
of  failure  or  unsatisfactory  results,  the  makers  should  be  consulted. 

The  piling  of  the  machinery  is  the  next  step  and  is  a  very  important  one. 
All  rubbing  surfaces  should  be  provided  with  suitable  oiling  devices  appropriate 
to  the  particular  place  and  service.  The  quality  of  oil  should  be  carefully 
selected  to  suit  the  velocity  and  pressure  of  the  rubbing  surfaces  on  which  it 
is  used.  For  use  within  the  steam  cylinder,  heavy  mineral  oil  is  the  only  oil 


HYDRAULICS  349 

capable  of  withstanding  the  high  temperature;  and  when  starting  up  new 
pumps  only  the  best  quality  should  be  used,  regardless  of  price.  A  liberal 
use  of  this  oil  for  the  first  month  will  go  far  toward  reducing  subsequent  oil  bills. 

The  pumping  engine  must  often  run  continuously  or  without  interruption 
for  a  month  or  even  longer.  This  requires  that  all  oiling  devices  be  so  arranged 
that  they  can  be  supplied  and  adjusted  while  the  machine  is  in  motion.  It 
is  a  good  plan  to  provide  two  sets  of  oiling  systems  for  all  the  principal  journals, 
so  that  if  one  fails  the  other  can  be  used  while  the  disabled  one  is  being  over- 
hauled. All  oil  holes  are  generally  stopped  with  wooden  plugs  or  bits  of  waste 
twisted  into  the  hole,  or  are  otherwise  protected  while  the  machine  is  being 
erected.  These  should  now  be  removed  and  the  oil  holes  and  oil  channels 
thoroughly  cleaned.  Bearings  should  be  flooded  with  oil  at  first  to  wash  out 
any  dust  or  grit  that  may  have  reached  the  rubbing  surfaces. 

The  steam  end  is  then  ready  to  be  warmed  up,  and  it  may  be  mentioned 
that  from  now  on  the  method  of  starting  a  pump  is  the  same  whether  the 
pump  is  a  new  one  or  an  old  one.  To  warm  up  the  steam  end,  the  throttle  is 
opened  just  a  little  and  with  the  drain  cocks  opened  wide,  steam  is  allowed 
to  blow  through  the  cylinder  until  no  more  water  passes  out  of  the  drain  cocks, 
using  the  steam  by-pass  pipes  in  case  of  multiple-expansion  pumps.  If  the 
pump  has  a  valve  gear  that  can  be  operated  by  hand,  the  warming  up  can  be 
hastened  by  working  the  valve  back  and  forth  slowly.  While  the  steam  end 
is  warming  up,  the  water  end  should  be  made  ready  by  opening  the  stop-valve 
in  the  delivery  pipe  and  otherwise  seeing  to  it  that  the  pump  has  a  free  delivery. 
If  a  stop-valve  is  fitted  to  the  suction  pipe,  this  should  be  opened.  If  the 
machine  is  compound  or  triple  expansion,  the  water  by-pass  valves  must  be 
opened  until  the  machine  has  made  a  sufficient  number  of  strokes  to  bring  the 
intermediate  and  low-pressure  cylinders  into  action,  when  the  by-pass  valves 
should  be  closed.  If  the  pump  is  fitted  with  dash-relief  valves,  these  should 
be  closed  before  starting,  in  order  to  keep  the  pistons  as  far  from  the  heads 
as  possible  in  starting.  Should  the  pump  exhaust  into  an  independent  con- 
denser, this  should  be  started  and  a  vacuum  obtained  before  starting  the 
pumps. 

To  start  the  pump,  open  the  throttle  slowly  and  let  the  pistons  work  back 
and  forth  very  slowly  a  few  times,  gradually  increasing  the  velocity  until  full 
speed  is  attained.  After  the  pump  has  been  running  a  few  minutes,  close  the 
drain  cocks.  If  the  pump  has  dash-relief  valves,  the  length  of  stroke  may  now 
be  carefully  adjusted. 

To  stop  the  pump,  close  the  throttle,  open  the  drain  cocks,  and  close  the 
gate  valve  in  the  discharge  pipe,  if  one  is  fitted.  Afterwards,  shut  down  the 
condenser. 

MISCELLANEOUS  FORMS  OF  WATER  ELEVATORS 
Jet  Pump. — In  the  jet  pump,  the  energy  of  a  jet  of  water  is  utilized  for 
raising  a  larger  volume  through  a  small  distance,  or  a  mixture  of  water  and 
solid  material  through  a  short  distance. 

Vacuum  Pump. — The  pulsometer,  which  is  the  most  important  representa- 
tive of  the  vacuum  pumps,  consists  of  two  chambers  in  a  large  casting,  with 
suitable  automatic  valves  arranged  at  the  top  and  bottom  of  the  chambers. 
Steam  is  introduced  into  one  of  the  chambers,  then  the  valve  at  the  top  closed. 
This  steam  will  condense,  forming  a  vacuum  that  draws  water  from  the  suction 
into  the  chamber.  When  the  chamber  is  filled  with  water,  steam  is  again 
introduced  and  forces  the  water  out  through  the  discharge  pipe.  The  oper- 
ation is  then  repeated,  more  water  being  drawn  in  by  the  condensation  of 
the  steam.  The  two  chambers  work  alternately,  one  being  engaged  in  draw- 
ing water  in  while  the  other  forces  it  out.  The  total  steam  efficiency  of  this 
form  of  pump  is  small,  though  it  may  actually  be  above  that  of  small  steam 
pumps  employed  in  isolated  portions  of  a  mine.  The  advantages  are  that 
the  pump  possesses  no  intricate  mechanism  nor  reciprocating  parts,  requires 
no  lubrication,  and  is  not  injured  by  gritty  or  acid  materials.  On  this  account 
it  may  be  employed  for  pumping  water  in  concentration  works,  coal-washing 
plants,  and  similar  places  where  the  water  is  liable  to  contain  grit  or  dirt. 

Air-Lift  Pumps. — By  introducing  compressed  air  at  the  bottom  of  a  pipe 
submerged  in  any  liquid,  the  air  in  the  pipe  rises  as  bubbles,  and  so  reduces 
the  specific  gravity  of  the  fluid  in  the  pipe.  This  causes  the  fluid  in  the  pipe 
to  rise  above  the  level  of  that  surrounding  the  pipe.  The  difference  in  specific 
gravity  can  never  be  great,  and  hence  the  fluid  can  never  be  elevated  to  any 
considerable  height  without  having  the  lower  end  immersed  to  a  correspond- 
ingly great  depth.  On  this  account  it  is  frequently  necessary  to  drill  a  well 


350  HYDRAULICS 

considerably  below  the  water-bearing  strata,  so  as  to  pbtain  the  proper  ratio 
between  the  submerged  portion  of  the  pipe  and  the  height  to  which  the  water 
is  to  be  lifted.  Some  advantages  of  this  form  of  pump  are  that  there  are  no 
moving  parts,  no  lubrication  is  required,  and  gritty  material  does  not  inter- 
fere with  the  operation.  If  the  pump  is  constructed  of  suitable  material,  it 
may  be  employed  for  handling  acids  or  solutions  in  electrolytic  or  chemical 
works.  This  style  of  pump  is  also  quite  extensively  employed  for  pumping 
water  from  Artesian  wells.  It  has  not  been  successful  as  a  mine  pump,  owing 
to  the  ratio  between  the  part  immersed  and  the  lift. 

Water  Buckets. — Where  only  a  limited  amount  of  water  collects  in  the 
mine  workings,  it  is  frequently  removed  by  means  of  a  special  water  bucket 
or  water  car  during  the  hours  that  the  hoisting  engine  would  otherwise  be 
idle  Where  very  large  amounts  of  water  are  to  be  removed  from  deep 
shafts,  it  has  been  found  economical  to  do  this  with  special  water  buckets. 

One  of  the  best  illustrations  of  this  class  of  work  is  the  Gilberton  water 
shaft  which  has  been  equipped  at  the  Gilberton  Colliery  of  the  Philadelphia 
and  Reading  Coal  and  Iron  Co.  The  collieries  draining  to  this  shaft  require 
the  removal  of  6,000,000  gal.  of  water  per  24  hr.  during  the  wet  season,  and 
this  has  to  be  lifted  from  a  depth  of  1,100  ft.  In  order  to  accomplish  the  work 
by  means  of  steam  pumps,  it  required  a  number  of  pump  stations  in  different 
parts  of  the  mine,  each  of  which  had  to  be  attended  by  a  pumpman,  and  a 
large  number  of  steam  lines  were  required  in  the  mine.  In  order  to  remove  the 
danger  of  fire  caused  by  these  steam  lines,  and  to  dispense  with  the  large 
amount  of  labor  otherwise  necessary,  it  was  decided  to  hoist  the  water,  and  a 
shaft  22  ft.X26  ft.  8  in.  outside  of  timbers,  was  sunk.  This  shaft  contains 
two  compartments  7  ft.X7  ft.,  in  which  the  water  buckets  are  operated,  and 
two  compartments  7  ft.X  11  ft.  8  in.  that  are  utilized  for  cages  to  lower  men, 
timber,  and  other  supplies.  The  water  tanks  employed  in  the  special  water 
compartments  are  5  ft.  6  in.  in  diameter,  and  14  ft.  long.  They  are  provided 
with  special  devices,  sliding  on  regular  cage  guides,  and  empty  themselves 
automatically  at  the  surface  by  means  of  a  trip  or  sliding  valve.  Two  pairs 
of  direct-acting  hoisting  engines,  with  45-in.  X  60-in.  cylinders,  operating 
drums  14  ft.  8  in.  in  diameter  by  15-ft.  face,  are  employed.  These  operate  the 
water  buckets  in  cages  by  means  of  2-in.  crucible  steel  ropes,  at  50  rev.  per 
min.,  which  is  equivalent  to  a  piston  speed  of  500  ft.  per  min.  The  drums  will 
hoist  two  tanks  of  2,400  gal.  per  min.  This  gives  an  output  of  7,000,000  gal. 
per  24  hr.  By  slightly  increasing  the  speed  of  the  engine,  this  amount  can 
be  increased  10%,  which  is  25%  in  excess  of  the  calculated  maximum  demand 
on  the  shaft.  The  cages  in  the  cage  compartments  are  so  arranged  that  they 
can  be  disconnected,  and  water  buckets  substituted  for  them.  This  would  be  a 
total  output  of  over  14,000,000  gal.  per  24  hr.  at  the  normal  speed  of  the 
engine.  One  great  advantage  of  this  style  of  pumping  plant  is  that  there  is 
absolutely  no  fear  of  drowning  the  pumps. 

The  following  figures  by  Mr.  F.  E.  Brackett  give  the  cost  of  operation 
and  the  efficiency  of  the  water  hoist  at  the  Coleman  shaft,  Cambria  County, 
Pennsylvania.  The  Coleman  shaft  is  about  660  ft.  deep  and  the  water  hoist 
consists  of  two  Wellman-Seaver-Morgan  boiler-shaped  automatic  skips  of 
1,200  gal.  capacity  each,  with  the  customary  valves,  etc.  "The  bailing  of  the 
water  was  carried  on  intermittently  by  the  main  hoisting  engine.  It  was 
found  that  bailing  from  20  to  30  min.  per  hr.  was  sufficient  to  keep  the  water 
down. 

"When  bailing  with  one  skip,  one  skip  of  water  was  delivered  every  75  sec. 
but  by  a  slight  effort  a  skip  could  be  delivered  in  60  sec.  When  two  skips 
were  in  use,  the  time  necessary  to  deliver  a  skip  was  from  31  to  38  sec.,  averag- 
ing 34  sec.  Of  this  time.  20  sec.  were  occupied  in  hoisting  the  skip  700  ft.  and 
the  remaining  14  sec.  were  occupied  in  slowing  down  and  dumping.  The 
actual  dumping  only  occupied  about  5  sec.  The  capacity  of  the  two  skip  hoists 
was,  therefore,  (1,200-H 34) X  60  =  2,120  gal.  per  min. 

"The  amount  of  coal  consumed  in  hoisting  the  800  gal.  per  min.  made  by 
the  mine  at  this  time  was  23  gross  T.  per  da.  of  24  hr.  It  was  estimated  that 
85%  of  this,  or  19  T.,  was  consumed  in  hoisting  the  water.  The  consumption 
of  steam  by  the  hoisting  engine,  as  computed  from  its  dimensions,  was  74  Ib. 
per  useful  H.  P.  per  hr.  As  it  requires  141  H.  P.  to  hoist  800  gal.  of  water 
per  min.  700  ft.,  the  amount  of  steam  required  was  250,416  Ib.  per  da.  Divid- 
ing the  water  by  the  coal,  the  efficiency  of  the  boilers  on  this  kind  of  inter- 
mittent work  is  only  6  Ib.  of  steam  per  Ib.  of  coal.  The  duty  of  the  plant,  as 
computed  from  these  data,  is  about  15,400,000  ft.lb.  of  work  per  100  Ib.  of 
coal,  which  is  extremely  low.*' 


HYDRAULICS 


351 


Mr.  Brackett  reaches  the  conclusion  of  other  mining  engineers  that  water 
hoisting  from  shallow  depths  is  very  uneconomical  "as  there  is  very  little 
opportunity  to  use  the  steam  expansively.  Even  should  an  attempt  be  made 
to  do  so,  the  time  occupied  in  getting  up  speed,  when  the  steam  must  be 
admitted  at  nearly  full  stroke,  occupies  a  large  percentage,  sometimes  all,  of 
the  total  time  under  steam.  In  the  second  place,  there  is  a  large  amount  of 
power  wasted  during  every  winding  by  the  application  of  brakes  to  bring  the 
load  to  rest.  Besides  these,  the  intermittent  use  of  steam  necessarily  inter- 
feres with  the  economical  operation  of  the  boilers.  Enough  steam  cannot  be 
raised  during  the  demand  for  it  without  wasting  fuel  during  the  time  there  is 
little  or  no  demand  for  it.  By  careful  design,  especially  on  windings  of  greater 
length,  no  doubt  these  losses  can  be  reduced  to  some  extent,  but  as  a  general 
proposition  the  plan  of  hoisting  water  instead  of  pumping  it  should  not  be 
adopted,  unless  there  exists  some  other  reason  that  is  of  greater  weight  than 
the  economical  side  of  the  question." 

Some  years  ago  the  Hamilton  iron  mine,  in  Michigan,  was  drowned  by 
a  sudden  inrush  of  water  that  drove  the  pumpmen  from  the  pumps.  In  order 
to  remove  this  large  volume  of  water,  special  bailing  buckets  were  substituted 
for  the  ordinary  mine  skips.  These  bailing  buckets  ran  on  the  inclined  skip 
road,  and  unwatered  the  mine  in  a  remarkably  short  time. 


Siphons. — The  principle  on  which  the  siphon  works  is  shown  in  the  accom- 
panying figure.  The  atmospheric  pressure  on  the  surface  of  the  water  in  the 
upper  basin  will  force  the  water  up  the  short  leg  I  to  the  crown  or  summit, 
from  whence  it  will  flow  by  gravity  through  the  long  leg  h  into  the  lower 
basin.  The  vertical  height  h  is  called  the  lift,  and  the  vertical  fall  hi,  the  fall 
of  the  siphon.  The  difference  between  these  heights  (hi  —  h)  may  be  called  the 
siphon  head.  The  pressure  of  the  atmosphere  on  the  water  in  each  basin  acts 
to  keep  the  pipes  /,  h  filled  with  water. 

The  conditions  required  for  the  successful  operation  of  a  siphon  may  be 
stated  as  follows: 

1.  The  height  of  the  summit  of  the  siphon  above  the  surface  of  the  water 
in  the  upper  basin,  or  the  vertical  lift  of  the  siphon,  must  not  exceed  a  practical 
limit  to  which  the  atmpsphere  will  force  the  water.     This  height  is  theoretically 
34  ft.  at  sea  level,  but  is  less  at  points  above  the  sea  level.     A  safe  rule  to  apply 
in  determining  the  vertical  height  to  which  the  atmosphere  will  force  the 
water  in  the  suction  pipe  of  a  pump,  or  in  the  short  leg  of  a  siphon,  is  to  take  .8 

•of  the  barometric  height,  expressed  in  inches,  for  the  vertical  lift  of  the  pump, 
or  siphon,  in  feet.  Thus,  if  the  barometer  stands  at  30  in.,  the  lift  of  the  pump 
or  siphon,  may  be  taken  as  30 X. 8  =  24  ft.  Where  the  suction  pipe  is  nearly 
vertical,  and  consequently  of  shorter  length,  this  height  may  be  somewhat 
increased;  but  where  the  suction  pipe  is  inclined  and  its  length  therefore 
considerable,  the  vertical  lift  should  be  decreased  proportionately. 

2.  The  longer  leg,  or  the  discharge  pipe  of  the  siphon,  must  fall  through  a 
greater  vertical  height  than  the  short  leg,  or  draft  pipe. 

3.  When  the  fall  hi  of  the  siphon  exceeds  the  practical  limit  to  which  the 
atmosphere  will  force  the  water,  care  must  be  taken  to  arrange  the  fall  of  the 
siphon  relative  to  its  lift,  or  to  increase  the  length  of  the  long  leg,  or  to  use  a 
pipe  of  a  smaller  diameter,  or  to  throttle  the  discharge  by  means  of  a  valve, 
so  as  to  prevent  the  siphon  from  running  empty  in  a  few  hours,  which  it  will  do 
whenever  the  fall  is  so  great  that  the  water  in  the  long  leg  runs  away  from 
the  crown  faster  than  the  atmospheric  pressure  forces  it  up  the  short  leg. 


352  HEAT  AND  FUELS 

Another  important  condition  requisite  to  the  successful  operation  of  a 
siphon,  is  the  submerging  of  both  ends  of  the  siphon  pipe  in  their  respective 
basins,  in  order  to  prevent  air  from  being  drawn  into  the  pipe  and  reaching  the 
crown,  or  summit,  of  the  siphon.  This  takes  place  more  readily  in  the  short 
leg  of  the  siphon  than  in  the  long  leg,  due  to  the  direction  of  the  flow  of  the  water. 
The  submergence  of  the  discharge  end  of  the  siphon,  however,  is  important 
in  order  to  insure  a  full  flow  in  the  pipe.  Air  carried  into  a  siphon  by  the  water 
will  gradually  accumulate  at  the  highest  point  of  the  siphon  pipe  and  will 
interfere  with  the  working  unless  an  air  trap  is  provided  at  that  point  through 
which  the  air  can  be  let  off  from  time  to  time. 

In  order  that  a  siphon  may  operate  successfully  without  a  throttling  valve, 
its  length,  diameter,  lift,  and  fall  must  bear  a  certain  relation  to  one  another, 
or  fulfil  certain  conditions,  without  which  the  pipe  has  a  tendency  to  empty 
itself.  Referring  to  the  accompanying  figure,  and  calling  the  head,  length, 
and  diameter  of  pipe,  h,  I,  and  d,  respectively,  on  the  suction  end;  and  hi,  li, 
and  d\  on  the  discharge  end,  as  the  flow  is  uniform  throughout  the  pipe, 
hd6  hidi6 

1        IT 

But  the  pressure  of  the  atmosphere  acts  on  both  ends;  at  sea  level,  this  will 
support  a  water  column  of  14.7  -f-.  434  =  34  ft.,  practically.  Hence,  the  head 
producing  the  flow  of  water  from  the  suction  end  to  the  crown  is  34  —  h,  while 
the  head  causing  the  flow  from  the  crown  to  the  discharge  end  is  hi  —  34.  There- 
fore, the  formula  when  applied  to  siphons  at  sea  level,  becomes 


I  li 

Whenever  the  second  member  of  this  formula,  which  represents  the  flow 
in  the  discharge  end  of  the  siphon,  becomes  greater  than  the  first  member, 
which  represents  the  suction  end,  the  pipe  will  tend  to  empty  itself,  because 
the  water  will  then  flow  away  from  the  crown  faster  than  the  atmospheric 
pressure  can  supply  the  waste. 

Whenever  the  foregoing  equation  is  satisfied,  the  siphon  needs  no  throttling 
valve  to  restrict  its  flow,  although  a  valve  at  each  end  of  the  siphon  is  necessary 
for  filling  the  pipe.  The  discharge  is  then  given  by  the  following  formula, 


EXAMPLE.  —  A  siphon  pipe  4  in.  in  diameter  and  1,000  ft.  long,  has  a  rise 

of  15  ft.  and  a  fall  of  40  ft.;  how  may  gallons  of  water  will  it  discharge  in  1  hr.? 

SOLUTION.  —  Assuming  that,  for  mine  work,  /=.Q1.  and  substituting  the 


given  values  in  the  formula,  G  =  2.83X4*X    \  OIX*!^)?  =  143+  gal'  per  min' 
The  quantity  discharged  in  1  hr.  is  then  60  X  143  =  8,580  gal. 


HEAT  AND  FUELS 

Heat  is  a  form  of  energy  produced  by  the  rapid  vibrations  of  the  molecules 
of  a  body.  All  bodies  are  assumed  to  be  built  up  of  molecules  that  are  held 
together  by  cohesion  but  yet  are  in  a  state  of  rapid  movement  in  relation  to 
one  another.  The  application  of  heat  to  a  body  causes  a  more  rapid  vibration 
of  the  molecules,  and  the  withdrawal  of  heat  causes  a  less  rapid  vibration, 
thereof;  it  is  to  the  rate  of  vibration  that  the  sense  of  hotness  or  coldness  is  due. 

Thermometers. — Changes  in  the  temperature  of  a  body  are  commonly 
measured  by  a  thermometer,  although  very  high  temperatures  are  measured 
in  other  ways  as  by  means  of  a  pyrometer,  etc.  Because  of  its  uniform  expan- 
sion and  its  sensitiveness  to  heat,  mercury  is  commonly  used  in  the  construction 
of  thermometers,  provided  the  temperatures  to  be  measured  range  between, 
say,  -  35°  P.  and  +  625°  F.  This  is  because  mercury  freezes  at  about  -  38°  F. 
and  volatilizes  at  +675°  P.,  beginning  to  give  off  some  vapor  at  even  a  lower 
temperature.  For  measuring  temperatures  below  the  freezing  point  of  mercury, 
alcohol  is  commonly  employed  although  the  United  States  Bureau  of  Standards 
prefers  toluene. 

In  all  thermometers,  the  freezing  and  boiling  points  of  water  under  mean 
atmospheric  pressure  at  sea  level  determine  two  fixed  points,  but  the  division 
of  the  scale  between  these  points  is  made  in  one  of  three  different  ways.  In 


HEAT  AND  FUELS 


353 


the  Fahrenheit  thermometer,  which  is  in  universal  use  in  the  United  States  and 
Great  Britain,  the  boiling  point  of  water  is  called  212°  and  the  freezing  point  32°, 
the  0°  of  the  scale  being  32°  below  the  freezing  point  and  at  what  was  then 
supposed  to  be  the  lowest  temperature  attainable.  In  the  centigrade  ther- 
mometer, in  use  in  those  countries  that  employ  the  metric  system  and  in 
England  and  the  United  States  in  scientific  work,  the  freezing  point  of  water 
is  called  0°  and  the  boiling  point  100°.  In  the  Reaumur  thermometer,  in  use 
in  Russia  and  in  Germany  (for  domestic  purposes),  the  freezing  point  of  water 
is  called  0°  and  its  boiling  point  80°.  The  following  formulas  serve  to  convert 
the  readings  of  one  scale  into  those  of  the  others: 

F°  =  f  C°+32°  =  fR°+32° 

C°  =  t(F°-32°)=f  R° 

R°  =  £(F°-32°)  =  |C° 

Thus,  1,000°  C.  is  equal  to  1X1,000  +  32  =  1,832°  F.,  and,  similarly,  490°  F. 
is  equal  to  f  X  (490  —  32)  =  254.5°  C.  However,  when  the  relation  between  a 
given  number  of  degrees  of  the  scales  is  desired  other  formulas  must  be  used. 
Because  between  the  freezing  and  boiling  points  of  water  there  are  100°  on 
the  centigrade  scale  and  180°  on  the  Fahrenheit  scale,  1°  C.  =  1.8°  F.,  and  1° 
F.  =  .555°+C.  Thus,  a  range  of  temperature  represented  by  1,000°  C.  is  equal 
to  a  range  of  1,800°  F. 

COMPARISON  OF  THERMOMETER  SCALES 


Fahrenheit 
Degrees 

Centigrade 
Degrees 

Reaumur 
Degrees 

Absolute  zero  
Zero,  Fahrenheit  
Freezing  point  
Maximum  density  of  water 

-459.64 
0.00 
32.00 
39.10 

-273.13 

-    17.78 
0.00 
3.94 

-218.51 
-    14.22 
0.00 
3  15 

Boiling  point  

212.00 

100.00 

80.00 

Absolute  Zero. — At  32°  F.,  a  perfect  gas  expands  —    --  part  of  its  volume 

4"  l.t>4 

if  its  temperature  is  increased  1°,  the  pressure  remaining  unchanged.  Con- 
sequently, at  32°+491. 64°  =  523.64°  the  gas  will  occupy  double  its  original 
volume;  and  if  the  temperature  is  reduced  to  491.64°  — 32°= —459.64°,  the 
gas  will  disappear.  Presumably  some  change  in  the  rate  of  contraction  takes 
place  before  the  minimum  temperature  is  reached,  but  the  law  may  con- 
veniently be  used  within  the  range  of  temperature  where  it  is  known  to  hold 
good.  This  temperature  of  -459.64°  F.  (commonly  taken  as  -460°  F.)  is 
known  as  absolute  zero.  On  the  centigrade  scale,  this  point  is  reached  at 
—  273.13°,  usually  taken  as  —273°.  From  this,  any  perfect  gas  expands  ^5 
or  5f 3  of  its  volume  for  each  1  °  increase  in  temperature  above  that  of  absolute 
zero,  depending  on  whether  the  Fahrenheit  or  centigrade  thermometer  is  used. 

Temperatures  reckoned  from  the  absolute  zero  are  known  as  absolute 
temperatures.  To  find  the  absolute  temperature  on  the  Fahrenheit  scale, 
add  460°  to  the  reading  of  the  thermometer.  Thus,  62°  F.  =  460  +  62  =  522° 
absolute  F.,  and  -54°  F.  =  460-54  =  406°  absolute  F.  Similarly,  in  the 
centigrade  scale,  62°  C.  =  273  +  62  =  335°  absolute  C.,  and  -54°  C.  =  273-54 
=  219°  absolute  C. 

British  Thermal  Unit. — The  quantitative  measure  of  heat  in  use  by  English- 
speaking  nations  is  known  as  the  British  thermal  unit,  commonly  written 
B.  T.  U.  It  is  the  quantity  of  heat  required  to  raise  the  temperature  of 
1  Ib.  of  water  l°at  62°  F.;  that  is,  from  62°  to  63°.  For  accurate  work,  it 
is  necessary  to  specify  the  particular  degree  at  which  the  temperature  is 
measured  for  the  amount  of  heat  required  to  raise  the  temperature  of  1  Ib. 
of  water  is  not  the  same  for  all  parts  of  the  thermometric  scale.  British 
thermal  units  were  at  one  time  referred  to  the  temperature  of  the  maximum 
density  of  water,  39.1°  F.,  but  recent  practice  uses  62°  F.  as  being  nearer  the 
mean  value. 

The  heating  value  of  a  fuel  is  commonly  expressed  in  the  number  of  British 
thermal  units  per  pound  of  coal,  oil,  etc.,  it  will  yield  on  burning.  Thus, 
it  may  be  stated  that  a  certain  coal  has  a  fuel  or  heat  value  of  12,000  B.  T.  U. 


354  HEAT  AND  FUELS 

This  means  that  1  Ib.  of  the  fuel  when  burned  under  perfect  conditions  will 
yield  sufficient  heat  to  raise  the  temperature  of  12,000  Ib.  of  water  1°  F.,  or 
will  raise  the  temperature  of  1  Ib.  of  water  12,000°  F. 

Calorie.  —  The  calorie  is  the  equivalent  in  the  metric  system  of  the  British 
thermal  unit.  It  is  the  amount  of  heat  required  to  raise  the  temperature  of 
1  kilogram  of  pure  water  from  15°  to  16°  C.  As  in  the  case  of  the  British 
thermal  unit,  the  calorie  was  at  one  time  referred  to  as  the  temperature  of  water 
at  its  maximum  density,  or  3.94°  C.  The  French  and  English  systems  are 
not  exactly  equivalent  or  interchangeable  because  the  quantity  of  heat  required 
to  raise  the  temperature  of  a  given  mass  of  water  from  59°  F.  (15°  C.)  to  60.8°  F. 
(16°  C.)  is  not  exactly  the  same  as  that  required  to  raise  its  temperature  from 
62°  F.  to  63°  F.  This  difference,  however,  is  very  little,  but  .03%. 

There  are  two  calories  in  common  use.  The  one  just  defined,  in  which  the 
unit  weight  is  the  kilogram,  is  in  use  commercially  and  is  known  as  the  large 
calorie.  Chemists  use  the  small  calorie,  -nfer  of  the  former,  being  the  amount 
of  heat  required  to  raise  the  temperature  of  1  gram  of  water  from  15°  C.  to 
16°  C.  These  are  also  known  as  the  kilogram-calorie  and  gram-calorie, 
respectively. 

Pound  Calorie.  —  The  pound  calorie  is  the  quantity  of  heat  required  to 
raise  the  temperature  of  1  Ib.  of  water  from  15  to  16°  C.  This  unit  is  not 
infrequently  employed  in  stating  the  calorific  power  or  heat  value  of  coals  and 
in  metallurgical  calculations  where  the  weights  of  the  substances  involved  are 
given  in  pounds. 

Equivalence  of  Heat  Units.  —  Neglecting  the  difference  in  the  specific  heat 
of  water  at  different  temperatures  (as  noted  before),  the  relations  between  the 
different  thermal  units  may  be  determined  as  follows: 

1  B.  T.  U.  =  .252  large  cal.    =  252  small  cal.       =  .0555  Ib.-cal. 
1  large  cal.  =  1,000  small  cal.  =  3.968  B.  T.  U.      =  2.2046  Ib.-cal. 
1  small  cal.  =  .001  large  cal.    =  .003968  B.  T.  U.  =  .0022046  Ib.-cal. 
1  Ib.-cal.      =  1.8  B.  T.  U.       =  .4536  large  cal.     =453.6  small  cal. 

When  calories  are  expressed  per  kilogram  and  it  is  desired  to  find  the 
equivalent  number  of  British  thermal  units  per  pound,  the  factor  for  multiply- 
ing is  1.8  as  will  appear  from  the  following  fractions,  which  show  the  relation 
between  the  units  of  the  two  systems: 

B.  T.  U.  per  Ib.  =  Ib.  raised  deg.  F. 
Cal.  per  kg.       kg.  raised  deg.  C. 

As  pounds  are  in  each  numerator  and  kilograms  are  in  each  denominator 


they  may  be  canceled,  and  B"  ^-  U-     Beg.  ^  because  Xo  F>  =  1.8o  c> 


From  this  B.  T.  U.  (per  pound)  =  1.8  cals.  (per  kilo). 

Mechanical  Equivalent  of  Heat.  —  Heat  being  a  form  of  energy  is  capable 
of  performing  work.  Joule's  investigations  showed  that  1  B.  T.  U.  was  equiva- 
lent to  772  ft.-lb.  of  work,  but  later  determinations  indicate  that  the  true 
mechanical  equivalent  of  1  B.  T.  U.  is  777.52  ft.-lb.,  which  is  commonly  taken 
as  778  ft.-lb.  Thus,  if  1  Ib.  of  Pocahontas  coal  has  a  fuel  value  of  15,000  B. 
T.  U.,  it  is  capable  of  doing  15,000X778  =  11,670,000  ft.-lb.  of  work,  The 
unit  of  work  in  the  metric  system  is  the  meter-kilogram  (often  called  the  kilo- 
gram-meter) and  is  equal  to  1  kg.  raised  through  a  height  of  1  m.  One  calorie 
is  equal  to  426.8028  rn.-kg.  One  B.  T.  U.  =  107.5614  m.-kg.,  and  1  cal.  is 
equal  to  3,087.3531  ft.-lb.  The  number  778  is  called  the  mechanical  equivalent 
of  heat,  or,  sometimes,  Joule's  equivalent. 

Expansion  by  Heat.  —  All  bodies  change  in  volume  as  the  temperature  to 
which  they  are  subjected  is  changed;  they  commonly  expand  as  they  are  heated 
and  contract  as  they  are  cooled.  The  rate  of  expansion  is  commonly  expressed 
as  a  coefficient,  which  indicates  the  relative  amount  the  substance  expands 
in  length  for  an  increase  of  1°  in  temperature.  The  rate  of  expansion  is  not 
the  same  at  all  temperatures,  as  it  increases  slightly,  in  the  case  of  metals,  as 
higher  temperatures  are  reached. 

In  the  first  table  on  page  359  are  given  the  coefficients  of  linear  expansion 
for  1°  F.  of  some  of  the  more  common  materials.  The  coefficients  of  surface 
expansion  are  twice  the  values  in  the  table;  and  the  coefficients  of  cubic  expan- 
sion, or  expansion  in  volume,  are  three  times  the  tabular  values.  Thus,  a  bar 
of  wrought  iron  60  in.  long,  if  heated  from  60°  F.  to  460°  F.,  or  through  400°, 
will  expand  60  X.  00000677X400  =  .16248  in.  In  a  similar  way,  a  sphere  of 
brass  measuring  1,000  cu.  in.  at  32°  F.,  will  have  its  volume  increased  by  1,000 
X300X  (3X.  0000104)  =9.36  cu.  in.  if  heated  to  332°  F. 


HEAT  AND  FUELS  355 

EQUIVALENT  TEMPERATURES  BY  THE  FAHRENHEIT  AND 
CENTIGRADE  THERMOMETERS 


Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 

Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

-459.64 

-273.13 

2 

16.7 

62 

16.7 

122 

50.0 

400 

240.0 

3 

16.1 

63 

17.2 

123 

50.6 

350 

212.2 

4 

15.6 

64 

17.8 

124 

51.1 

300 

184.4 

5 

15.0 

65 

18.3 

125 

51.7 

250 

156.7 

6 

14.5 

66 

18.9 

126 

52.2 

200 

128.9 

7 

13.9 

67 

19.5 

127 

52.8 

150 

101.1 

8 

13.3 

68 

20.0 

128 

53.3 

100 

73.3 

9 

12.8 

69 

20.6 

129 

53.9 

50 

45.6 

10 

12.2 

70 

21.1 

130 

54.5 

49 

45.0 

11 

11.7 

71 

21.7 

131 

55.0 

48 

44.4 

12 

11.1 

72 

22.2 

132 

55.6 

47 

43.9 

13 

10.6 

73 

22.8 

133 

56.1 

46 

43.3 

14 

10.0 

74 

23.3 

134 

56.7 

45 

42.8 

15 

9.5 

75 

23.9 

135 

57.2 

44 

42.2 

16 

8.9 

76 

24.5 

136 

57.8 

43 

41.7 

17 

8.3 

77 

25.0 

137 

58.3 

42 

41.1 

18 

7.8 

78 

25.6 

138 

58.9 

41 

40.6 

19 

7.2 

79 

26.1 

139 

59.5 

40 

40.0 

20 

6.7 

80 

26.7 

140 

60.0 

39 

39.4 

21 

6.1 

81 

27.2 

141 

60.6 

38 

38.9 

22 

5.6 

82 

27.8 

142 

61.1 

37 

38.3 

23 

5.0 

83 

28.3 

143 

61.7 

36 

37.8 

24 

4.5 

84 

28.9 

144 

62.2 

35 

37.2 

25 

3.9 

85 

29.5 

145 

62.8 

34 

36.7 

26 

3.3 

86 

30.0 

146 

63.3 

33 

36.1 

27 

2.8 

87 

30.6 

147 

63.9 

32 

35.6 

28 

2.2 

88 

31.1 

148 

64.5 

31 

35.0 

29 

1.7 

89 

31.7 

149 

65.0 

30 

34.4 

30 

1.1 

90 

32.2 

150 

65.6 

29 

33.9 

31 

-.6 

91 

32.8 

151 

66.1 

28 

33.3 

32 

.0 

92 

33.3 

152 

66.7 

27 

32.8 

33 

+  .6 

93 

33.9 

153 

67.2 

26 

32.2 

34 

1.1 

94 

34.5 

154 

67.8 

25 

31.7 

35 

1.7 

95 

35.0 

155 

68.3 

24 

31.1 

36 

2.2 

96 

35.6 

156 

68.9 

23 

30.6 

37 

2.8 

97 

36.1 

157 

69.5 

22 

30.0 

38 

3.3 

98 

36.7 

158 

70.0 

21 

29.4 

39 

3.9 

99 

37.2 

159 

70.6 

20 

28.9 

40 

4.5 

100 

37.8 

160 

71.1 

19 

28.3 

41 

5.0 

101 

38.3 

161 

71.7 

18 

27.8 

42 

5.6 

102 

38.9 

162 

72.2 

17 

27.2 

43 

6.1 

103 

39.5 

163 

72.8  • 

16 

26.7 

44 

6.7 

104 

40.0 

164 

73.3 

15 

26.1 

45 

7.2 

105 

40.6 

165 

73.9 

14 

25.6 

46 

7.8 

106 

41.1 

166 

74.5 

13 

25.0 

47 

8.3 

107 

41.7 

167 

75.0 

12 

24.4 

48 

8.9 

108 

42.2 

168 

75.6 

11 

23.9 

49 

9.5 

109 

42.8 

169 

76.1 

10 

23.3 

50 

10.0 

110 

43.3 

170 

76.7 

9 

22.8 

51 

10.6 

111 

43.9 

•  171 

77.2 

8 

22.2 

52 

11.1 

112 

44.5 

172 

77.8 

7 

21.7 

53 

11.7 

113 

45.0 

173 

78.3 

6 

21.1 

54 

12.2 

114 

45.6 

174 

78.9 

5 

20.6 

55 

12.8 

115 

46.1 

175 

79.5 

4 

20.0 

56 

13.3 

116 

46.7 

176 

80.0 

3 

19.4 

57 

13.9 

117 

47.2 

177 

80.6 

2 

18.9 

58 

14.5 

118 

47.8 

178 

81.1 

—1 

18.3 

59 

15.0 

119 

48.3 

179 

81.7 

0 

17.78 

60 

15.6 

120 

48.9 

180 

82.2 

+  1 

17.2 

61 

16.1 

121 

49.5 

181 

82.8 

356 


HEAT  AND  FUELS 


Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

182 

83.3 

244 

117.8 

306 

152.2 

368 

186.7 

183 

83.9 

245 

118.3 

307 

152.8 

369 

187.2 

184 

84.5 

246 

118.9 

308 

153.3 

370 

187.8 

185 

85.0 

247 

119.5 

309 

153.9 

371 

188.3 

186 

85.6 

248 

120.0 

310 

154.5 

372 

188.9 

187 

86.1 

249 

120.6 

311 

155.0 

373 

189.5 

188 

86.7 

250 

121.1 

312 

155.6 

374 

190.0 

189 

87.2 

251 

121.7 

313 

156.1 

375 

190.6 

190 

87.8 

252 

122.2 

314 

156.7 

376 

191.1 

191 

88.3 

253 

122.8 

315 

157.2 

377 

191.7 

192 

88.9 

254 

123.3 

316 

157.8 

378 

192.2 

193 

89.5 

255 

123.9 

317 

158.3 

379 

192.8 

194 

90.0 

256 

124.5 

318 

158.9 

380 

193.3 

195 

90.6 

257 

125.0 

319 

159.5 

381 

193.9 

196 

91.1 

258 

125.6 

320 

160.0 

382 

194.5 

197 

91.7 

259 

126.1 

321 

160.6 

383 

195.0 

198 

92.2 

260 

126.7 

322 

161.1 

384 

195.6 

199 

92.8 

261 

127.2 

323 

161.7 

385 

196.1 

200 

93.3 

262 

127.8 

324 

162.2 

386 

196.7 

201 

93.9 

263 

128.3 

325 

162.8 

387 

197.2 

202 

94.5 

264 

128.9 

326 

163.3 

388 

197.8 

203 

95.0 

265 

129.5 

327 

163.9 

389 

198.3 

204 

95.6 

266 

130.0 

328 

164.5 

390 

198.9 

205 

96.1 

267 

130.6 

329 

165.0 

391 

199.5 

206 

96.7 

268 

131.1 

330 

165.6 

392 

200.0 

207 

97.2 

269 

131.7 

331 

166.1 

393 

200.6 

208 

97.8 

270 

132.2 

332 

166.7 

394 

201.1 

209 

98.3 

271 

132.8 

333 

167.2 

395 

201.7 

210 

98.9 

272 

133.3 

334 

167.8 

396 

202.2 

211 

99.5 

273 

133.9 

335 

168.3 

397 

202.8 

212 

100.0 

274 

134.5 

336 

168.9 

398 

203.3 

213 

100.6 

275 

135.0 

337 

169.5 

399 

203.9 

214 

101.1 

276 

135.6 

338 

170.0 

400 

204.5 

215 

101.7 

277 

136.1 

339 

170.6 

401 

205.0 

216 

102.2 

278 

136.7 

340 

171.1 

402 

205.6 

217 

102.8 

279 

137.2 

341 

171.7 

403 

206.1 

218 

103.3 

280 

137.8 

342 

172.2 

404 

206.7 

219 

103.9 

281 

138.3 

343 

172.8 

405 

207.2 

220 

104.5 

282 

138.9 

344 

173.3 

406 

207.8 

221 

105.0 

283 

139.5 

345 

173.9 

407 

208.3 

222 

105.6 

284 

140.0 

346 

174.5 

408 

208.9 

223 

106.1 

285 

140.6 

347 

175.0 

409 

209.5 

224 

106.7 

286 

141.1 

348 

175.6 

410 

210.0 

225 

107.2 

287 

141.7 

349 

176.1 

411 

210.6 

226 

107.8 

288 

142.2 

350 

176.7 

412 

211.1 

227 

108.3 

289 

142.8 

351 

177.2 

413 

211.7 

228 

108.9 

290 

143.3 

352 

177.8 

414 

212.2 

229 

109.5 

291 

143.9 

353 

178.3 

415 

212.8 

230 

110.0 

292 

144.5 

354 

178.9 

416 

213.3 

231 

110.6 

293 

145.0 

355 

179.5 

417 

213.9 

232 

111.1. 

294 

145.6 

356 

180.0 

418 

214.5 

233 

111.7 

295 

146.1 

357 

180.6 

419 

215.0 

234 

112.2 

296 

146.7 

358 

181.1 

420 

215.6 

235 

112.8 

297 

147.2 

359 

181.7 

421 

216.1 

236 

113.3 

298 

147.8 

360 

182.2 

422 

216.7 

237 

113.9 

299 

148.3 

361 

182.8 

423 

217.2 

238 

114.4 

300 

148.9 

362 

183.3 

424 

217.8 

239 

115.0 

301 

149.5 

363 

183.9 

425 

218.3 

240 

115.6 

302 

150.0 

364 

184.5 

426 

218.9 

241 

116.1 

303 

150.6 

365 

185.0 

427 

219.5 

242 

116.7 

304 

151.1 

366 

185.6 

428 

220.0 

243 

117.2 

305 

151.7 

367 

186.1 

429 

220.6 

HEAT  AND  FUELS 
TABLE— (Continued) 


357 


Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

430 

221.1 

459 

237.2 

488 

253.3 

925 

496.1 

431 

221.7 

460 

237.8 

489 

253.9 

950 

510.0 

432 

222.2 

461 

238.3 

490 

254.5 

975 

523.9 

433 

222.8 

462 

238.9 

491 

255.0 

1,000 

537.8 

434 

223.3 

463 

239.5 

492 

255.6 

1,050 

565.6 

435 

223.9 

464 

240.0 

493 

256.1 

1,100 

593.3 

436 

224.5 

465 

240.6 

494 

256.7 

1,150 

621.1 

437 

225.0 

466 

241.1 

495 

257.2 

1,200 

648.9 

438 

225.6 

467 

241.7 

496 

257.8 

1,250 

696.7 

439 

226.1 

468 

242.2 

497 

258.3 

1,300 

704.4 

440 

226.7 

469 

242.8 

498 

258.9 

1,350 

732.2 

441 

227.2 

470 

243.3 

499 

259.5 

1,400 

760.0 

442 

227.8 

471 

243.9 

500 

260.0 

1,450 

787.8 

443 

228.3 

472 

244.4 

525 

273.9 

1,500 

815.6 

444 

228.9 

473 

245.0 

550 

287.8 

1,600 

871.1 

445 

229.5 

474 

245.6 

575 

301.7 

1,700 

926.7 

446 

230.0 

475 

246.1 

600 

315.6 

1,800 

982.2 

447 

230.6 

476 

246.7 

625 

329.4 

1,900 

1,036.7 

448 

231.1 

477 

247.2 

650 

343.3 

2,000 

,093.3 

449 

231.7 

478 

247.8 

675 

357.2 

2,100 

,148.9 

450 

232.2 

479 

248.3 

700 

371.1 

2,200 

,204.4 

451 

232.8 

480 

248.9 

725 

385.0 

2,300 

,260.0 

452 

233.3 

481 

249.5 

750 

398.9 

2,400 

,315.6 

453 

233.9 

482 

250.0 

775 

412.8 

2,500 

,371.1 

454 

234.5 

483 

250.6 

800 

426.7 

2,600 

,426.7 

455 

235.0 

484 

251.1 

825 

440.6 

2,700 

,482.2 

456 

235.6 

485 

251.7 

850 

454.4 

2,800 

,537.8 

457 

236.1 

486 

252.2 

875 

468.3 

2,900 

,593.3 

458 

236.7 

487 

252.8 

900 

482.2 

3,000 

,648.9 

EQUIVALENT  TEMPERATURES  BY  THE  CENTIGRADE  AND 
FAHRENHEIT  THERMOMETERS 


Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

-273.13 

-459.64 

33 

27.4 

7 

19.4 

19 

66.2 

250 

418.0 

32 

25.6 

6 

21.2 

20 

68.0 

225 

373.0 

31 

23.8 

5 

23.0 

21 

69.8 

200 

328.0 

30 

22.0 

4 

24.8 

22 

71.6 

175 

283.0 

29 

20.2 

3 

26.6 

23 

73.4 

150 

238.0 

28 

18.4 

2 

28.4 

24 

75.2 

125 

193.0 

27 

16.6 

-1 

30.2 

25 

77.0 

100 

148.0 

26 

14.8 

0 

32.0 

26 

78.8 

75 

103.0 

25 

13.0 

+  1 

33.8 

27 

80.6 

50 

58.0 

24 

11.2 

2 

35.6 

28 

82.4 

49 

56.2 

23 

9.4 

3 

37.4 

29 

84.2 

48 

54.4 

22 

7.6 

4 

39.2 

30 

86.0 

47 

52.6 

21 

5.8 

5 

41.0 

31 

87.8 

46 

50.8 

20 

4.0 

6 

42.8 

32 

89.6 

45 

49.0 

19 

2.2 

7 

44.6 

33 

91.4 

44 

47.2 

18 

-.4 

8 

46.4 

34 

93.2 

43 

45.4 

17 

+  1.4 

9 

48.2 

35 

95.0 

42 

43.6 

16 

3.2 

10 

50.0 

36 

96.8 

41 

41.8 

15 

5.0 

11 

51.8 

37 

98.6 

40 

40.0 

14 

6.8 

12 

53.6 

38 

100.4 

39 

38.2 

13 

8.6 

13 

55.4 

39 

102.2 

38 

36.4 

12 

10.4 

14 

57.2 

40 

104.0 

37 

34.6 

11 

12.2 

15 

59.0 

41 

105.8 

36 

32.8 

10 

14.0 

16 

60.8 

42 

107.6 

35 

31.0 

9 

15.8 

17 

62.6 

43 

109.4 

34 

29.2 

8 

17.6 

18 

64.4 

44 

111.2 

HEAT  AND  FUELS 
TABLE— (Continued) 


Degrees 
Cent. 

Degrees 

Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 
Fahr. 

Degrees 
Cent. 

Degrees 

Fahr. 

45 

113.0 

108 

226.4 

171 

339.8 

234 

453.2 

46 

114.8 

109 

228.2 

172 

341.6 

235 

455.0 

47 

116.6 

110 

230.0 

173 

343.4 

236 

456.8 

48 

118.4 

111 

231.8 

174 

345.2 

237 

458.6 

49 

120.2 

112 

233.6 

175 

347.0 

238 

460.4 

50 

122.0 

113 

235.4 

176 

348.8 

239 

462.2 

51 

123.8 

114 

237.2 

177 

350.6 

240 

464.0 

52 

125.6 

115 

239.0 

178 

352.4 

241 

465.8 

53 

127.4 

116 

240.8 

179 

354.2 

242 

467.6 

54 

129.2 

117 

242.6 

180 

356.0 

243 

469.4 

55 

131.0 

118 

244.4 

181 

357.8 

244 

471.2 

56 

132.8 

119 

246.2 

182 

359.6 

245 

473.0 

57 

134.6 

120 

248.0 

183 

361.4 

246 

474.8 

58 

136.4 

121 

249.8 

184 

363.2 

247 

476.6 

59 

138.2 

122 

251.6 

185 

365.0 

248 

478.4 

60 

140.0 

123 

253.4 

186 

366.8 

249 

480.2 

61 

141.8 

124 

255.2 

187 

368.6 

250 

482.0 

62 

143.6 

125 

257.0 

188 

370.4 

251 

483.8 

63 

145.4 

126 

258.8 

189 

372.2 

252 

485.6 

64 

147.2 

127 

260.6 

190 

374.0 

253 

487.4 

65 

149.0 

128 

262.4 

191 

375.8 

254 

489.2 

66 

150.8 

129 

264.2 

192 

377.6 

255 

491.0 

67 

152.6 

130 

266.0 

193 

379.4 

256 

492.8 

68 

154.4 

131 

267.8 

194 

381.2 

257 

494.6 

69 

156.2 

132 

269.6 

195 

383.0 

258 

496.4 

70 

158.0 

133 

271.4 

196 

384.8 

259 

498.2 

71 

159.8 

134 

273.2 

197 

386.6 

260 

500.0 

72 

161.6 

135 

275.0 

198 

388.4 

275 

527.0 

73 

163.4 

136 

276.8 

199 

390.2 

300 

572.0 

74 

165.2 

137 

278.6 

200 

392.0 

325 

617.0 

75 

167.0 

138 

280.4 

201 

393.8 

350 

662.0 

76 

168.8 

139 

282.2 

202 

395.6 

375 

707.0 

77 

170.6 

140 

284.0 

203 

397.4 

400 

752.0 

78 

172.4 

141 

285.8 

204 

399.2 

425 

797.0 

79 

174.2 

142 

287.6 

205 

401.0 

450 

842.0 

80 

176.0 

143 

289.4 

206 

402.8 

475 

887.0 

81 

177.8 

144 

291.2 

207 

404.6 

500 

932.0 

82 

179.6 

145 

293.0 

208 

406.4 

550 

1,022.0 

83 

181.4 

146 

294.8 

209 

408.2 

600 

1,112.0 

84 

183.2 

147 

296.6 

210 

410.0 

650 

1,202.0 

85 

185.0 

148 

298.4 

211 

411.8 

700 

1,292.0 

86 

186.8 

149 

300.2 

212 

413.6 

750 

1,382.0 

87 

188.6 

150 

302.0 

213 

415.4 

800 

1,472.0 

88 

190.4 

151 

303.8 

214 

417.2 

850 

1,562.0 

89 

192.2 

152 

305.6 

215 

419.0 

900 

1,652.0 

90 

194.0 

153 

307.4 

216- 

420.8 

950 

1,742.0 

91 

195.8 

154 

309.2 

217 

422.6 

1,000 

1,832.0 

92 

197.6 

155 

311.0 

218 

424.4 

1,100 

2,012.0 

93 

199.4 

156 

312.8 

219 

426.2 

1,200 

2,292.0 

94 

201.2 

157 

314.6 

220 

428.0 

1,300 

2,372.0 

95 

203.0 

158 

316.4 

221 

429.8 

1,400 

2,552.0 

96 

204.8 

159 

318.2 

222 

431.6 

1,500 

2,732.0 

97 

206.6 

160 

320.0 

223 

433.4 

1,600 

2,912.0 

98 

208.4 

161 

321.8 

224 

435.2 

1,700 

3,092.0 

99 

210.2 

162 

323.6 

225 

437.0 

1,800 

3,272.0 

100 

212.0 

163 

325.4 

226 

438.8 

1,900 

3,452.0 

101 

213.8 

164 

327.2 

227 

440.6 

2,000 

3,632.0 

102 

215.6 

165 

329.0 

228 

442.4 

2,100 

3,812.0 

103 

217.4 

166 

330.8 

229 

444.2 

2,200 

3,992.0 

104 

219.2 

167 

332.6 

230 

446.0 

2,300 

4,172.0 

105 

221.0 

168 

334.4 

231 

447.8 

2,400 

4,352.0 

106 

222.8 

169 

336.2 

232 

449.6 

2,500 

4,532.0 

107 

224.6 

170 

338.0 

233 

451.4 

2,600 

4,712.0 

HEAT  AND  FUELS 
COEFFICIENTS  OF  LINEAR  EXPANSION  PER  1°  F. 


359 


Substance 

Coefficient 

Substance 

Coefficient 

Aluminum  
Brass  

.00001140 
.00001040 
.00000306 
.00000550 
.00000780 
.00000961 
.00000399 
.00000521 
.00000841 
.00000460 
.00000587 
.00000677 
.00001580 

Marble 

.00000400 
.00000206 
.00000490 
.00003334 
.00000494 
.00000200 
.00000400 
.00000670 
.00000599 
.00000702 
.00001160 
.00000276 
.00001634 

Mac,                    /from 

Brick 

Masonry  |to 

Mercury  
Platinum 

Cement,  concrete  |^om 

Porcelain  

Glass  .  .              .  .  (from 

Sandstone  {£om 

Steel,  untempered  
Steel,  tempered  

I  to 
Gold                           

Granite 

Iron  cast          

Tin  

Wood  pine 

Lead 

Zinc  

It  should  be  noted  that  if  the  length  of  a  bar  that  has  been  heated  is  deter- 
mined, and  then  its  length  is  found  after  its  temperature  has  been  reduced  by 
the  amount  it  has  been  heated,  the  value  obtained  for  the  contraction  in  length 
will  not  be  the  same  as  first  obtained  for  the  expansion.  Thus,  in  the  case  of 
the  wrought  iron  bar,  its  final  length  is  60.16248  in.,  the  expansion  from  60° 
to  460°  being  .16248  in.  If  the  same  bar  is  cooled  from  460°  to  60°,  the  con- 
traction will  be  60. 16248 X. 00000677X400  =  .16292  in.,  or  .00044  in.  more  than 
the  expansion  from  60°  to  460°. 

The  reason  for  this  difference  is  purely  a  mathematical  one.  If  C  is  the 
coefficient  of  expansion  and  Ti,  Tz,  L\,  and  Lz,  are,  respectively,  the  initial  and 
final  temperatures  and  the  initial  and  final  lengths,  the  formula  becomes, 


Conduction  of  Heat. — The  progress  of  heat  from  places  of  higher  to  places 
of  lower  temperature  in  the  same  body  is  called  conduction.  Good  conductors 
are  those  through  which  the  heat  wave  moves  rapidly;  poor  conductors  are 
those  in  which  this  movement  is  slow.  The  relative  heat  conductivities  of 
some  of  the  metals  are  given  in  an  accompanying  table. 

RELATIVE  HEAT  CONDUCTIVITIES  OF  METALS 


Metal 

Conductivity 

Metal 

Conductivity 

Silver 

100.0 

Iron  

11.9 

Copper  
Gold 

73.6 
53.2 

Steel  
Lead  

11.6 

8.5 

31.3 

Platinum  

8.4 

28  1 

Bismuth 

1.8 

Tin 

15.2 

Mercury  

1.3 

A  non-conductor  is  a  substance  that  will  not  conduct  heat.  No  perfectly 
non-conducting  substances  are  known,  although  a  number  of  substances  are 
such  poor  conductors  that  they  are  commonly  classed  as  non-conductors. 
The  metals  are  the  best  conductors,  silver  ranking  first,  while  liquids  and 
gases  are  very  poor  conductors.  Organic  substances,  as  cotton,  wool,  straw, 
bran,  etc.,  and  rocks  and  earths,  like  magnesia,  asbestos,  etc.,  are  very  poor 
conductors;  this  quality  is  taken  advantage  of  in  the  manufacture  of  boiler 
and  steam-pipe  coverings. 

Radiation  of  Heai. — The  communication  of  heat  from  a  hot  body  to  a 
colder  one  across  an  intervening  space  is  called  radiation.  The  best  example 
of  radiated  heat  is  that  received  from  the  sun.  The  intensity  of  heat  radiation 
from  a  given  source:  Varies  as  the  temperature  of  the  source;  varies  inversely 


360 


HEAT  AND  FUELS 


as  the  square  of  the  distance  from  the  source;  and  grows  less  as  the  inclination 
of  the  rays  to  the  surface  grows  less. 

The  radiating  power  of  heated  surfaces  depends  greatly  on  the  form,  shape, 
and  material  of  which  they  are  composed.  Thus,  in  the  case  of  a  cubic  vessel, 
filled  with  hot  water,  having  its  vertical  sides  coated,  respectively,  with  polished 
silver,  tarnished  lead,  mica,  and  lampblack,  the  radiating  power  of  the  sides 
was  experimentally  determined  to  be  as  25  :  45  :  80  :  100.  From  this,  bright 
surfaces  radiate  less  heat  than  dark  ones  having  the  same  temperature. 

Those  bodies  or  surfaces  that  reflect  heat  readily  do  not  absorb  it  to  any 
extent,  and  conversely.  Thus,  lampblack,  which  reflects  few  of  the  heat  rays 
impinging  upon  it,  absorbs  nearly  all;  and  polished  silver  absorbs  but  about 
2.5%  of  the  heat  rays,  reflecting  97.5%. 

Specific  Heat. — The  specific  heat  of  a  substance  is  the  ratio  between  the 
quantity  of  heat  required  to  raise  or  lower  the  temperature  of  that  substance  1° 
and  the  quantity  9f  heat  required  to  raise  or  lower  an  equal  weight  of  water  1°. 
Thus,  if  the  specific  heat  of  lead  is  .0299,  the  amount  of  heat  expressed  in 
British  thermal  units  required  to  raise  a  certain  weight  of  this  metal  1°  will 
raise  the  same  weight  of  water  only  .0299  of  1°,  or,  what  is  the  same  thing, 
as  1  B.  T.  U.  will  raise  the  temperature  of  1  Ib.  of  water  1°  F.,  .0299  B.  T.  U. 
will  raise  the  temperature  of  1  Ib.  of  lead  1°  F. 

For  strict  accuracy,  the  temperature  should  be  noted  at  which  the  specific 
heat  is  measured,  because  it  has  been  found  that  the  specific  heat  is  variable 
for  high  temperatures.  For  ordinary  temperatures,  however,  the  values  given 
in  the  accompanying  tables  may  be  considered  constant.  As  stated  before, 
the  specific  heat  of  water  varies  with  the  temperature. 


SPECIFIC  HEAT  OF  WATER  AT  VARIOUS  TEMPERATURES 


Temperature 

Temperature 

Specific 

Specific 

Degrees 

Degrees 

Heat 

Degrees 

Degrees 

Heat 

Centigrade 

Fahrenheit 

Centigrade 

Fahrenheit 

0 

32 

1.0094 

50 

122 

.9980 

5 

41 

1.0053 

55 

131 

.9985 

10 

50 

1.0023 

60 

140 

.9994 

15 

59 

1.0003 

65 

149 

1.0004 

16.11 

61 

1.0000 

70 

158 

1.0015 

20 

68 

.9990 

75 

167 

1.0028 

25 

77 

.9981 

80 

176 

1.0042 

30 

86 

.9976 

85 

185 

1.0056 

35 

95 

.9974 

90 

194 

1.0071 

40 

104 

.9974 

95 

203 

1.0086 

45 

113 

.9976 

100 

212 

1.0101 

SPECIFIC  HEATS  OF  SOLIDS 


Substance 

Specific 
Heat 

Substance 

Specific 
Heat 

Aluminum  .  . 

2143 

1152 

Ashes 

2100 

0299 

Brass  

.0883 

Platinum 

.0323 

Charcoal  

.2410 

Steel',  soft  

.1175 

Copper.  .  . 

0951 

Steel  hard 

1165 

Glass  

.1937 

2026 

Ice  

.5040 

Tin 

0518 

Iron,  cast  

.1189 

Zinc  

.0935 

HEAT  AND  FUELS 
SPECIFIC  HEATS  OF  LIQUIDS 


361 


Substance 

Specific 
Heat 

Substance 

Specific 
Heat 

Alcohol,  32°  
Alcohol,  176°  
Benzene,  50°  
Benzene,  122°  
Glycerine  
Lead,  melted  
Mercury,  32°  

.5475 
.6794 
.4066 
.4502 
.5760 
.0410 
.0335 

Petroleum  
Sea  water,  64°  
Sulphur,  melted  
Sulphuric  acid  
Tin,  melted  
Turpentine,  Oil  of  

.4980 
.9800 
.2350 
.3363 
.0637 
.4110 

In  the  table  of  the  specific  heats  of  certain  gases,  it  will  be  noted  that  two 
values  are  given  for  these.  This  is  because  it  requires  less  heat  to  raise  the 
temperature  of  a  gas  when  the  volume  remains  constant  than  when  the  pressure 
is  constant  and  the  volume  varies. 

SPECIFIC  HEATS  OF  GASES 


Substance 

Specific 
Heat  at 
Constant 
Pressure 

Specific 
Heat  at 
Constant 
Volume 

Substance 

Specific 
Heat  at 
Constant 
Pressure 

Specific 
Heat  at 
Constant 
Volume 

Air  
Carbon  dioxide  .... 
Carbon  monoxide.  . 
Hydrogen  

.2375 
.2170 
.2479 
3.4090 

.1690 
.1535 
.1758 
2.4123 

Methane  
Nitrogen  
Oxygen 

.5929 
.2438 
.2175 
.4805 

.4505 
.1727 
.1551 
.3460 

Superheated  steam 

EXAMPLE. — Assuming  that  all  the  heat  of  combustion  is  utilized,  how  many 
pounds  of  cast  iron,  which  has  a  specific  heat  of  .1189,  may  be  raised  from  60° 
to  260°  in  temperature,  by  the  burning  of  1  Ib.  of  Pocahontas  coal  with  a  heat- 
ing value  of  14,500  B.  T.  U.? 

SOLUTION. — The  number  of  British  thermal  units  required  to  raise  the 
temperature  of  1  Ib.  of  cast  iron  from  60°  to  260°  is  (260-60)  X.I  189 
=  23.78  B.  T.  U.  As  1  Ib.  of  the  coal  yields  14,500  B.  T.  U.,  it  will  raise  14,500 
-=-23.78  =  610  (about)  Ib.  of  cast  iron  from  60°  to  260°. 

The  specific  heat  of  an  alloy  or  of  a  mixture  of  gases,  etc.,  is  found  by 
multiplying  the  percentage  by  weight  of  each  one  of  the  several  constituents 
by  its  specific  heat  and  dividing  the  sum  of  these  products  by  100. 

EXAMPLE  1.— What  is  the  specific  heat  of  an  alloy  composed  of  21%  of 
copper,  40%  of  tin,  and  39%  of  zinc? 

SOLUTION. —  Copper    21 X  .0951  =  1.9971 

Tin          40X. 0518  =  2.0720 

Zinc         39  X. 0935  =  3.6465 

100  7.7156 

Hence,  the  specific  heat  is  7.7156 -MOO  =  .077156. 

EXAMPLE  2. — What  is  the  specific  heat  of  an  afterdamp  composed  of  4.5% 
COi,  1.5%  CO,  80.0%  N,  and  14%  O,  by  weight? 
SOLUTION.—  AT    80.0 X. 2438  =  19.50400 

O    14.0  X. 2 175=   3.04500 
COz      4.5  X. 2 170=      .97650 
CO      1.5X  .2479  =     .37185 
100.0  23.89735 

Hence  the  specific  heat  is  23.89735 -MOO  =  .2389735,  say,  2390. 
Sensible  and  Latent  Heat. — The  heat  that  serves  only  to  increase  the 
temperature  of  a  body  to  which  it  is  imparted,  and  which  may  be  measured  by 
means  of  a  thermometer,  is  known  as  sensible  heat.  For  illustration,  the  heat 
required  to  raise  the  temperature  of  a  volume  of  water  from  the  freezing 
point  at  32°  to  the  boiling  point  at  212°,  or  through  180°  is  sensible  heat.  In 
steam  engineering,  the  amount  of  heat  in  the  water  above  that  at  32°  is  com- 
monly called  the  heat  of  the  liquid. 


362  HEAT  AND  FUELS 

However,  heat  may  be  applied  to  ice  at  32°  and  to  water  at  212°  without 
increasing  the  temperature  of  either.  In  the  one  case  the  ice  is  changed  to 
water  at  the  same  temperature,  32°,  and  in  the  other  case  the  water  is  changed 
into  steam  at  the  same  temperature,  212°.  In  neither  case  can  the  heat  added 
be  measured  by  the  thermometer  until  all  the  ice  is  converted  into  water  and 
all  the  water  changed  into  steam.  This  heat  that  is  absorbed  in  changing  the 
state  or  condition  of  a  body,  which  does  work  in  overcoming  the  cohesion  of 
the  molecules,  is  called  latent  heat.  This  heat  is  given  up  when  the  body 
resumes  its  original  liquid  or  solid  state. 

The  heat  absorbed  in  melting  a  body  is  called  the  latent  heat  of  fusion  and  in 
the  case  of  melting  ice  into  water  is  equal  to  144  B.  T.  U.  The  heat  absorbed 
in  changing  a  body  from  the  liquid  to  the  gaseous  state  is  known  as  the  latent 
heat  of  volatilization.  In  the  case  of  water  this  is  called  the  latent  heat  of 
evaporation,  and  is  commonly  taken  as  being  equal  to  965.8  B.  T.  U.  Later 
investigations  by  Marks  and  Davis  indicate  that  the  true  value  of  the  latent 
heat  of  evaporation  of  water  is  970.4  B.  T.  U.  Using  the  former  value,  the 
number  of  British  thermal  units  required  to  change  1  Ib.  of  ice  at  32°  F.  into 
steam  at  212°  F.,  may  be  divided  as  follows: 

Latent  heat  of  fusion  =     144.0 

Sensible  heat  from  32°  to  212°=     180.0 

Latent  heat  of  evaporation       =    965.8 

1,289.8 

Should  the  ice  have  been  at  a  temperature  below  the  freezing  point  there 
must  be  added  to  the  1,289.8  B.  T.  U.  thus  obtained  the  amount  of  heat 
required  to  raise  the  ice  to  the  melting  point.  Thus,  if  the  ice  is  at  0°,  the 
amount  of  heat  required  to  raise  it  to  32°  will  be  equal  to  (32  —  0)  X  specific 
heat  of  ice  =  32 X. 504  =  16. 13  B.  T.  U.,  and  the  total  heat  required  to  convert 
1  Ib.  of  ice  at  0°  into  steam  at  212°  will  be  equal  to  16.13  +  1,289.8=1,305.93 
B.  T.  U.  Should  the  water  have  been  at,  say,  60°,  the  total  heat  required-  to 
evaporate  it  into  steam  at  212°  will  b'e: 

Sensible  heat  from  60°  to  212°=     152.0  B.  T.  U. 

Latent  heat  of  evaporation        =    965.8  B.  T.  U. 

1,117.8  B.  T.  U. 

In  those  cases  where  it  is  necessary  to  calculate  the  heat  of  formation  of 
steam  at  a  higher  temperature  than  212°,  Regnault's  formula  may  be  used. 
This  gives  the  number  of  heat  units  required  to  convert  water  at  32°  into 
steam  at  any  temperature,  T. 

Heat  units  =  1,081.4 +.305  T 

EXAMPLE  1. — How  many  British  thermal  units  are  required  to  convert 
1  Ib.  of  water  at  60°  into  steam  at  400°? 

SOLUTION.— From  the  formula,  heat  units  =  1,081.4 +(.305X400)  =  1,203.4 
B.  T.  U.  But  the  initial  temperature  of  the  water  was  60°  or  60-32  =  28° 
above  the  freezing  point.  Inasmuch  as  a  rise  of  1°  in  the  temperature  of  the 
water  requires  the  expenditure  of  1  B.  T.  U.,  28  heat  units  must  be  deducted 
from  the  total  previously  obtained,  and  the  required  number  is  1,203.4  —  28 
=  1,175.4  B.  T.  U. 

EXAMPLE  2. — How  many  pounds  of  water  at  60°  may  be  evaporated  into 
steam  at  400°  by  the  burning  of  1  Ib.  of  Pocahontas  coal  yielding  14,500  B.  T.  U. 
per  Ib.? 

SOLUTION. — From  example  1,  it  will  require  1,175.4  B.  T.  U.  to  convert 
1  Ib.  of  water  into  steam  under  the  assumed  conditions.  Consequently,  1  Ib.  of 
coal  will  evaporate  14,5004-1,175.4  =  12.3  Ib.  of  water  at  60°  into  steam  at  400°. 

MELTING  POINTS   AND   LATENT   HEAT   OF   FUSION   OF   METALS 


Fusing 

Latent 

Fusing 

Latent 

Metal 

Point 
Degrees 

Heat 
Fusion 

Metal 

Point 
Degrees 

Heat 
Fusion 

F. 

B.  T.  U. 

F. 

B.  T.  U. 

Aluminum  

1,157 

180.0 

Nickel     

2,642 

111.6 

Copper  

1,985 

77.9 

Platinum  

3,227 

49.0 

Gold.  

1,946 

29.3 

Silver  

1,764 

43.8 

Iron,  wrought.    . 

2,912 

126.0 

Sulphur  

237 

16.8 

Lead  

619 

7.2 

Tin 

446 

24.9 

Mercury  

-38 

5.1 

Zinc... 

788 

40.7 

HEAT  AND  FUELS 


363 


The  boiling  point  of  water  decreases  as  the  altitude  above  sea  level  increases, 
as  is  shown  in  an  accompanying  table. 

BOILING  POINT  OF  WATER  AT  VARIOUS  ALTITUDES 


Boiling 
Point 

Eleva- 
tion 
Above 

Atmos- 
pheric 
Pressure 

Barom- 
eter at 

Boiling 
Point 

Eleva- 
tion 
Above 

..Atmos- 
pheric 
Pressure 

Barom- 
eter at 

Degrees 

Sea 

Pounds 

32°  F. 

Degrees 

Sea 

Pounds 

32°  F. 

Fahren- 
heit 

Level 
Feet 

per 
Square 
Inch 

Inches 

Fahren- 
heit 

Level 
Feet 

per 
Square 
Inch 

Inches 

184 

15,221 

8.20 

16.70 

199 

6,843 

11.29 

22.99 

185 

14,649 

8.38 

17.06 

200 

6,304 

11.52 

23.47 

186 

14,075 

8.57 

17.45 

201 

5,764 

11.76 

23.95 

187 

13,498 

8.76 

17.83 

202 

5,225 

12.01 

24.45 

188 

12,934 

8.95 

18.22 

203 

4,697 

12.26 

24.96 

189 

12,367 

9.14 

18.61 

204 

4,169 

12.51 

25.48 

190 

11,799 

9.34 

19.02 

205 

3,642 

12.77 

26.00 

191 

11,243 

9.54 

19.43 

206 

3,115 

13.03 

26.53 

192 

10,685 

9.74 

19.85 

207 

2,589 

13.30 

27.08 

193 

10,127 

9.95 

20.27 

208 

2,063 

13.57 

27.63 

194 

9,579 

10.17 

20.71 

209 

1,539 

13.85 

28.19 

195 

9,031 

10.39 

21.15 

210 

1,025 

14.13 

28.76 

196 

£.481 

10.61 

21.60 

211 

512 

14.41 

29.33 

197 

7,932 

10.83 

22.05 

212 

0 

14.70 

29.92 

198 

7,381 

11.06 

22.57 

Combustion.  —  In  dealing  with  the  burning  of  fuels,  whether  solid,  liquid, 
or  gaseous,  combustion  may  be  defined  as  the  rapid  chemical  combination  of 
carbon,  hydrogen,  and  sulphur,  or  their  compounds,  with  the  oxygen  of  the 
air,  the  reaction  being  accompanied  by  the  production  of  light  and  heat. 
When  the  combustible  or  burnable  element  unites  with  all  the  oxygen  it  is 
capable  of  absorbing,  the  combustion  is  perfect;  otherwise  it  is  imperfect. 

The  more  common  chemical  reactions  in  the  burning  of  fuels  are  here  given. 
The  Roman  numerals  above  the  symbols  employed  in  expressing  the  reaction 
give  the  relative  volumes  of  the  gaseous  substances  involved,  and  the  Arabic 
numerals  below  the  reactions  are  the  approximate  molecular  weights  of  these 
substances.  The  actual  weights  concerned  in  the  reactions  are  proportional 
to  the  molecular  weights. 

In  the  complete  combustion  of  carbon  to  carbon  dioxide,  the  reaction  is 

C+02  =  C02 
12+32=  44 
giving  14,544  B.  T.  U.  per  Ib.  of  carbon  burned. 

In  the  incomplete  burning  of  carbon  to  carbon  monoxide,  the  reaction  is 


24  +  32=   56 
giving  4,450  B.  T.  U.  per  Ib.  of  carbon  burned. 

In  the  combustion  of  carbon  monoxide  to  carbon  dioxide,  the  reaction  is 
II        I        II 


56  +32=  88 
giving  4,325  B.  T.  U.  per  Ib.  and  347  B.  T.  U.  per  cu.  ft.  of  CO  burned. 

In  the  complete  combustion  of  hydrogen  to  form  water,  the  reaction  is 
II       I        II 


4   +32=    36 

giving  62,028  B.  T.  U  per  Ib.  and  349  B.  T.  U.  per  cu.  ft.  of  hydrogen  burned. 
In  the  complete  combustion  of  hydrogen  sulphide  to  carbon  dioxide  and 
sulphur  dioxide,  the  reaction  is 

II        III        II          II 
2HzS  +  3O2  =  2HsO  +  25O2 
.68  +  96=    36    +128 


364  HEAT  AND  FUELS 

giving  by  calculation  7.459  B.  T.  U.  per  Ib.  and  709  B.  T.  U.  per  cu.  ft.  of 
hydrogen  sulphide  burned. 

In  the  complete  combustion  of  methane  to  form  carbon  dioxide  and  water, 
the  reaction  is 


16  -j-  64  =  44  +  36 
giving  23.513  B.  T.  U.  per  Ib.  and  1,053  B.  T.  U.  per  cu.  ft.  of  methane  burned. 
In  the  complete  combustion  of  acetylene  to  form  carbon  dioxide  and  water, 
the  reaction  is  n         y  _  jy         n 

2C2#2+502  =  4C02+2#20 

52     +160=  176  +    36 

giving  21,465  B.  T.  U.  per  Ib.  and  1,556  B.  T.  U.  per  cu.  ft.  of  acetylene  burned. 
In  the  complete  combustion  of  olefiant  gas  to  carbon  dioxide  and  water, 
the  reaction  is 


28  +  96=   88  -f-  36 
giving  21,344  B.  T.  U.  per  Ib.  and  1,675  B.  T.  U.  per  cu.  ft.  of  plefiant  gas  burned. 
In  the  complete  combustion  of  ethane  to  carbon  dioxide  and  water,  the 
reaction  is 

II       VII       IV        VI 

2CzH6+  7O2  =  4C02+  6#2O 

60    +224=  176  +  108 

giving  22,230  B.  T.  U.  per  Ib.  and  1,862  B.  T.  U.  per  cu.  ft.  of  ethane  burned. 
In  the  complete  combustion  of  sulphur  to  sulphur  dioxide,  the  reaction  is 
I        I 


32+32=  64 
giving  4,050  B.  T.  U.  per  Ib.  of  sulphur  burned. 

The  following  reactions  are  important  in  dealing  with  fuels,  particularly 
of  the  gaseous  type,  as  one  or  all  of  them  are  concerned  in  the  manufacture  of 
producer  or  water  gas. 

If  carbon  dioxide  is  forced  through  a  bed  of  incandescent  coke,  it  absorbs 
a  certain  amount  of  carbon  to  form  carbon  monoxide  according  to  the  reaction 

I  II 

C02+C  =  2CO 
44  +12=  56 

This  reaction  is  not  accompanied  by  the  generation  of  heat  but  by  its 
absorption  at  the  rate  of  10,150  B.  T.  U.  per  Ib.  of  carbon  burned. 

If  steam  is  injected  into  white-hot  coke,  the  vapor  is  decomposed  into 
carbon  monoxide  and  hydrogen.  The  temperature  must  be  very  high  and  the 
steam  supply  partial,  the  reaction  being 

I         I        I 


12+  18  =28  +  2 

In  this  case,  also,  there  is  an  absorption  of  heat  and  to  the  extent  of  5,883  B. 
T.  U.  per  Ib.  of  carbon  involved. 

If  in  the  last  case  the  steam  supply  is  increased  and  the  temperature  lowered, 
the  reaction  is 

II          I         II 


12+   36    =44+4 

In  this  case  the  absorption  of  heat  is  6,066  B.  T.  U.  per  Ib.  of  carbon  consumed. 
When  using  any  of  the  foregoing  equations  as  a  basis  for  calculating  the 
volumes  and  weights  of  the  gaseous  substances  entering  into  a  reaction,  it  must 
be  remembered  that  the  same  is  assumed  to  have  taken  place  at  standard 
temperature  and  pressure,  viz.:  32°  P.,  and  29.92  in.  of  mercury.  Further 
discussion  of  the  nature  and  products  of  combustion  will  be  found  near  the 
end  of  this  section  and  in  the  section  on  Mine  Ventilation. 


FUELS  365 


FUELS 


FUELS  IN  GENERAL 

Substances  that  are  burned  for  the  purpose  of  generating  heat  for  com- 
mercial purposes  are  called  fuels.  As  regards  their  physical  state  they  are 
divided  into  solid,  liquid,  and  gaseous  fuels.  The  solid  fuels  include  wood, 
charcoal,  coal,  peat,  coke,  sawdust,  and  other  substances  of  vegetable  origin. 
Liquid  fuels  include  petroleum  and  its  derivatives,  naphtha,  gasoline,  and 
other  oils,  and  grain,  wood,  and  denatured  alcohol.  Caseous  fuels  include 
natural  gas  and  various  manufactured  gases,  such  as  coal  gas,  water  gas, 
producer  gas,  coke-oven  gas,  blast-furnace  gas,  etc.  The  products  of  com- 
bustion, or  gases,  from  beehive  coke  ovens  are  frequently  used  for  steam 
raising,  but  can  hardly  be  called  fuels  as  they  contain  no  combustible  con- 
stituents, their  value  being  in  their  actual,  sensible  heat. 

The  chief  combustible  element  in  all  fuels  is  carbon,  which  has  a  heat 
value  of  14,544  B.  T.  U.  per  Ib.  In  most  solid  fuels,  carbon  chiefly  exists  as 
such,  but  in  the  liquid  and  gaseous  fuels  and  to  a  less  extent  in  coal,  it  occurs 
as  a  hydrocarbon,  that  is,  as  a  gaseous  compound  of  carbon  and  hydrogen.  The 
heat  value  per  pound  of  gas  is  given  under  the  head  of  Combustion  in  the 
discussion  of  the  combustion  of  the  various  hydrocarbon  gases. 

The  second  important  combustible  element  is  hydrogen,  which  has  a  heat 
value  of  62,028  B.  T.  U.  per  Ib.  of  gas.  It  exists  in  the  free,  or  uncombined, 
state  in  natural  gas  and  in  certain  manufactured  fuel  gases,  such  as  water  gas, 
but  is  more  commonly  present  in  the  form  of  a  hydrocarbon,  or  combined 
with  oxygen  to  form  water.  If  both  hydrogen  and  oxygen  exist  in  a  fuel,  it 
is  assumed  that  all  the  oxygen  is  combined  with  the  hydrogen  in  the  form  of 
water,  HzO.  The  hydrogen  thus  combined  has  no  fuel  value  and  must  there- 
fore be  deducted  from  the  total  amount  of  hydrogen  present  in  calculating  the 
heating  value  of  the  fuel.  The  hydrogen  left  after  deducting  what  is  combined 
with  the  oxygen  is  called  the  available  hydrogen.  As  the  weight  of  hydrogen 
in  water  is  one-eighth  the  weight  of  the  oxygen,  the  percentage  of  available 

hydrogen  is  obtained  from  the  formula,  h  =  H——.  in  which  h,  H,  and  O,  are, 

o 

respectively,  the  percentages  of  available  hydrogen,  total  hydrogen,  and  oxygen, 
in  the  fuel. 


WOOD  AS  FUEL 

Wood  is  composed  of  woody  fiber,  or  cellulose,  CtHioOs,  which  makes  up  the 
chief  part  of  its  bulk;  the  constituents  of  the  sap;  and  water.  The  most 
important  of  the  sap  constituents  is  a  soluble  gum,  lignine,  amounting,  on  the 
average,  to  13%  of  the  wood.  The  cellulose  and  lignine  are  both  combustible, 
whereas  the  water  is  not  only  not  combustible,  but  its  evaporation  absorbs 
a  good  portion  of  the  heat  generated  by  the  burning  of  the  other  constituents. 
Dry  wood  is,  therefore,  a  much  better  fuel  than  undried  wood. 

Newly  felled  wood  contains  from  25  to  50%  of  water,  the  amount  varying 
greatly  with  different  kinds,  but  averaging  about  40%.  Exposed  to  the  air 
at  ordinary  temperatures,  wood  loses  a  large  part  of  its  moisture  and  shrinks, 
reaching  a  minimum  of  about  20%  of  moisture  after  about  2  yr.  of  air  drying, 
but  it  absorbs  water  and  swells  in  air  highly  charged  with  moisture. 

Ordinary  air-dried  wood  may  be  considered  as  having  the  following  com- 
position: hygroscopic  water,  20%;  oxygen  and  hydrogen  in  the  proportion  in 
which  they  unite  to  form  water,  40%;  and  charcoal,  including  1%  of  ash,  40%. 

The  effective  value  of  all  kinds  of  wood  per  pound,  when  dry,  is  substan- 
tially the  same,  and  is  v'ommonly  estimated  at  40%  of  that  of  the  same  weight 
of  average  coal.  In  the  accompanying  tables  are  given  the  weight  per 
cord  of  air-dried  woods  arranged  in  the  order  of  their  fuel  value  per  cord,  the 
weight  of  coal  equivalent  to  1  cord  of  air-dried  wood,  and  Gottlieb's  values 
for  the  composition  and  calorific  value  per  pound  of  different  varieties  of  wood. 


366 


FUELS 


WEIGHTS  PER  CORD  OF  DRY  WOOD  ARRANGED  ACCORDING  TO 
FUEL  VALUES 


Wood 

Weight 
Pounds 

Wood 

Weight 
Pounds 

Hickory  (shell  bark) 

4,469 

Beech  

3,126 

Hickory  (red  heart)  .... 
White  oak           

3,705 
3,821 

Hard  maple  
Southern  pine  

2,878 
3,375 

Red  oak  

3,254 

Virginia  pine  

2,680 

Spruce  

2,325 
2  137 

Yellow  pine  
White  pine 

1,904 
1  868 

yp 

WEIGHT  OF  COAL  EQUIVALENT  TO  1  CORD  OF  AIR-DRIED  WOOD 


Kind  of  Wood 

Weight  of 
1  Cord 
Pounds 

Weight  of  Coal  Equiv- 
alent to  1  Cord 
of  Wood 
Pounds 

4  500 

1,800  to  2,000 

White  oak  

3,850 

1,540  to  1,715 

Beech  red  and  black  oak     .  . 

3250 

1,300  to  1,450 

Poplar,  chestnut,  and  elm  

2,350 

940  to  1,050 

Pine  average  

2,000 

800  to     925 

COMPOSITION    AND    CALORIFIC    VALUE    PER    POUND    OF    WOOD 

(Gottlieb) 


Kind  of  Wood 

Composition 

Calorific  Value 

C 

H 

N 

o 

Ash 

Calories 

B.  T.  U. 

Oak 

50.16 
49.18 
48.99 
49.06 
48.88 
50.36 
50.31 

6.02 
6.27 
6.20 
6.11 
6.06 
5.92 
6.20 

.09 
.07 
.06 
.09 
.10 
.05 
.04 

43.36 
43.91 
44.25 
44.17 
44.67 
43.39 
43.08 

.37 
.57 
.50 
.57 
.29 
.28 
.37 

4,620 
4,711 
4,728 
4,774 
4,771 
5,035 
5,085 

8,316 
8,480 
8,510 
8,591 
8,586 
9,063- 
9,153 

Ash  
Elm 

Beech 

Birch  
Fir  

Pine 

It  is  safe  to  assume  that  from  2.25  to  2.5  Ib.  of  dry  wood  are  equivalent 
in  fuel  value  to  1  Ib.  of  soft  (bituminous)  coal  of  average  quality  and  that,  as 
stated,  the  fuel  value  of  the  same  weight  of  different  woods  is  very  nearly  the 
same;  that  is,  1  Ib.  of  hickory  is  worth  no  more  for  fuel  than  1.  Ib.  of  pine, 
assuming  both  to  be  dry. 

The  efficiency  of  wood  fuel  depends  largely  on  whether  it  is  wet  (as  cut) 
or  dry  and  in  a  measure  as  to  whether  it  is  fired  as  cord  wood,  in  4-ft.  lengths, 
or  as  sawdust  or  hogeed  wood,  the  latter  term  being  applied  to  the  fine  and 
shredded  material  produced  by  running  slabs  and  logs  through  a  macerator  or 
hogging  machine.  Such  refuse  may  contain  as  much  as  60%  of  moisture  and 
requires  that  a  large  combustion  chamber  be  provided  as  well  as  a  large  area  of 
heated  firebrick  to  radiate  heat  to  the  fuel  in  order  to  evaporate  the  water. 
To  secure  this  extra  space,  extension  furnaces  are  commonly  used,  and  added 
room  in  the  firebox  may  be  had  by  dropping  the  grate  to  the  level  of  the  boiler- 
house  floor  with  an  ashpit  below.  When  cord  wood  is  fired,  extension  furnaces 
are  not  generally  necessary,  although  the  grates  should  be  dropped.  Babcock 


FUELS  367 

&  Wilcox,  in  "Steam,"  state  that  "with  proper  draft  conditions,  150  Ib.  of  this 
fuel  (sawdust  and  hogged  chips)  containing  about  30  to  40%  of  moisture  can 
be  burned  per  square  foot  of  grate  surface  per  hour,  and  in  a  properly  designed 
furnace  1  sq.  ft.  of  grate  surface  can  develop  from  5  to  6  boiler  H.  P.  Where 
the  wood  contains  50%  of  moisture  or  over,  it  is  not  usually  safe  to  figure  on 
obtaining  more  than  3  to  4  H.  P.  per  sq.  ft.  of  grate  surface." 


PEAT  AS  FUEL 

Peat,  or  as  it  is  sometimes  called,  turf,  results  from  the  accumulation,  in 
place,  of  partly  decomposed  and  disintegrated  vegetable  matter,  chiefly  of 
varieties  of  moss  (sphagnum),  where  the  ordinary  decay  and  decomposition 
of  such  material  has  been  more  or  less  suspended,  although  the  form  and  a 
considerable  part  of  the  structure  of  the  plant  organs  are  more  or  less  destroyed. 
It  is  found  in  bogs  and  marshes,  where  periodic  overflows  or  times  of  saturation 
by  water  are  favorable  to  the  growth  of  plant  life  and  the  preservation  of  its 
remains  under  water.  According  to  its  origin  and  the  conditions  under  which 
it  has  accumulated,  peat  may  vary  in  color  from  brown  to  black.  In  texture  it 
may  vary  from  light,  spongy  matter,  that  is  porous,  coarse,  fibrous,  or  even 
woody,  and  easily  falls  to  pieces  when  flry,  to  forms  that  are  nearly  or  quite 
devoid  of  structure,  and  which,  when  wet,  are  as  plastic  as  clay,  and  when  dry 
form  dense,  hard  masses  resembling  lignite.  In  all  cases  peat  is  nearly  or  quite 
saturated  with  water,  containing,  under  usual  natural  conditions,  from  80  to  95%. 

When  dry,  peat  is  generally  lighter  colored  than  when  freshly  dug  and  will 
usually  float  if  placed  in  water,  although  this  is  not  always  true  of  the  dark- 
colored,  plastic  kinds  that  are  high  in  ash  and  when  thoroughly  dry  are  as 
compact  and  nearly  as  hard  as  coal.  Except  for  such  types,  raw  or  untreated 
peat  is  easily  crumbled  to  powder  when  handled,  and  makes  bulky  and  unsub- 
stantial fuel  that  does  not  bear  transportation  well.  The  name  muck  is  com- 
monly applied  to  black  impure  peats  of  the  more  completely  decomposed  types. 

It  is  estimated  that  the  12,000  sq.  mi.  of  workable  peat  bogs  in  the  United 
States  contain  13,000,000,000  T.  of  marketable  peat.  These  deposits  are 
mostly  found  in  the  colder  and  moister  sections  of  the  country,  in  New  Eng- 
land and  westwards  from  close  to  the  southern  boundary  of  New  York  nearly 
to  the  ninetieth  meridian  and  thence  northwards  to  Canada.  This  is  supple- 
mented by  a  narrow  strip  of  bog  land  extending  down  the  Atlantic  coast  to 
Florida,  includes  all  of  that  state,  and  reaches  westwards,  probably  across 
Texas,  to  the  Mexican  border.  Areas  of  unknown  extent  are  met  along  the 
Pacific  coast  in  California,  Oregon,  and  Washington.  The  Canadian  deposits 
of  peat  are  estimated  to  cover  35,000  sq.  mi. 

Peat  is  commonly  prepared  by  cutting  the  material  (after  the  bog  has 
been  properly  drained)  into  regular  shaped  pieces  somewhat  larger  than  an 
ordinary  building  brick,  which  are  subsequently  stacked  with  air  spaces  between 
and  dried  in  the  open  or  under  sheds.  In  some  cases,  the  peat  is  subjected  to 
a  process  of  grinding  or  macerating  and  pressing  before  being  pressed  into 
bricks  and  is  known  as  machine  peat,  pressed  peat,  condensed  peat,  or  machine- 
formed  peat.  Peat,  after  being  air-dried,  may  be  ground  to  a  powder,  further 
dried,  and  pressed  into  briquettes  under  a  pressure  of  18,000  to  30,000  Ib.  per 
sq.  in.  Either  charcoal  or  coke  may  be  made  from  peat  in  suitably  designed 
furnaces  or  retorts.  In  the  producer,  air-dried  peat  yields  large  volumes  of 
fuel  gas  of  the  most  excellent  quality;  this  seems  the  most  satisfactory  way 
of  using  it  in  manufacturing  operations. 

According  to  the  United  States  Geological  Survey,  freshly  dug  peat  from 
Bethel,  Conn.,  gave  by  analysis,  moisture,  88.72%;  volatile  matter,  6.54%; 
fixed  carbon,  3.13%;  ash,  1.61%;  and  sulphur  (separately  determined),  .08%. 
The  calorific  value  of  this  freshly  dug  peat  was  but  927  B.  T.  U.  per  Ib. 

A  consignment  of  compressed  or  machine  peat  from  near  Orlando,  Fla., 
and  tested  at  the  St.  Louis  Exposition  contained  by  analysis,  moisture,  21%; 
volatile  matter,  51.72%;  fixed  carbon,  22.11%;  ash,  5.17%;  and  sulphur  (separ- 
ately determined),  .4-5%.  The  ultimate  analysis  of  the  same  peat  was  carbon, 
46.57%;  hydrogen,  6.51%;  nitrogen,  2.33%;  oxygen,  38.97%;  ash,  5.17%;  and 
sulphur,  .45%.  The  calorific  value  of  the  peat  was  8,127  B.  T.  U.  per  Ib. 

As  a  general  rule  c  rdinary  air-dried  peat  has  about  one-half  the  fuel  value  of 
bituminous  coal,  say,  from  4,000  to  5,500  B.  T.  U.  per  Ib.;  the  calorific  value 
of  machined  peat  being  much  higher.  The  cost  of  machine  peat  will  range 
between  $.75  to  $1.50  per  T.,  so  that  in  fuel  value  it  is  about  equivalent  to 
bituminous  coal  at  $3  per  T. 


368 


FUELS 


COAL 

CONSTITUENTS  OF  COAL 

Coal  consists  of  the  finely  comminuted  remains  of  vegetable  matter  that 
have  been  preserved,  under  water,  from  complete  decay.  Whether  it  has 
resulted  from  the  accumulation  of  drift  material,  as  at  the  mouths  of  large 
rivers,  or  from  the  growth  of  trees,  shrubs,  and  mosses  in  place  in  bogs,  is 
an  undecided  question.  The  accompanying  table  shows  the  theoretical  change 
from  wood  to  anthracite. 

CHANGES  IN  CHEMICAL  COMPOSITION  FROM  WOOD  TO 
ANTHRACITE 


Substance 

Carbon 
Per  Cent. 

Hydrogen 
Per  Cent. 

Oxygen 
Per  Cent. 

Woody  fiber                                

52.65 

5.25 

42.10 

Peat  from  Vulcaire  .*.  .  . 

59.57 

5.96 

34.47 

66.04 

5.27 

28.69 

Earthy  brown  coal  -  

73.18 

5.58 

21.14 

Coal  from  Belestat  secondary  

75.06 

5.84 

19.10 

89.29 

5.05 

5.66 

Anthracite,  Mayenne,  transition  formation 

91.58 

3.96 

4.46 

The  chemical  elements  present  in  coal  are  the  carbon,  hydrogen,  oxygen, 
and  nitrogen  of  the  original  vegetable  matter,  together  with  the  ash  thereof, 
and  some  sulphur  and  phosphorus.  There  are  other  elements  and  their  combi- 
nations present,  but  the  ones  named  are  those  commonly  determined  by  the 
chemist.  The  carbon  exists  separately  and,  known  as  fixed  carbon,  is  the  chief 
combustible  substance  in  most  coals.  A  certain  amount  of  the  carbon  is  com- 
bined with  some  of  the  hydrogen  in  various  gases  called  hydrocarbons.  The 
nitrogen  exists  as  a  gas,  and  while  part  of  the  oxygen  may  also  exist  as  a  gas 
and  a  small  portion  is  probably  combined  with  the  carbon  as  carbon  dioxide, 
the  bulk  of  it  is  combined  with  hydrogen  in  the  proportions  necessary  to  form 
water.  The  water  is.  commonly  called  moisture,  and  the  other  gaseous  con- 
stituents are  called  volatile  matter,  volatile  combustible  matter,  or  volatile  hydro- 
carbons. 

Chemists  report  the  composition  of  coal  in  the  form  either  of  a  proximate 
analysis  or  of  an  ultimate  analysis.  In  the  former,  the  constituents  are 
reported  in  the  various  combinations  in  which  they  occur  in  the  coal,  as  mois- 
ture, fixed  carbon,  volatile  matter,  and  ash,  the  percentages  of  which  should 
add  up  100.  Both  the  sulphur  and  phosphorus  are  separately  determined; 
that  is,  their  amounts  are  not  included  to  make  up  the  100%  of  the  four  chief 
constituents.  In  an  ultimate  analysis,  the  constituents  are  determined  in  their 
elementary  or  ultimate  form  and  the  percentages  of  carbon,  hydrogen,  oxygen, 
nitrogen,  sulphur,  phosphorus  if  determined,  and  ash  should  add  up  100. 
Numerous  comparisons  of  proximate  and  ultimate  analyses  of  the  same  coals 
( are  given  in  an  accompanying  table. 

Moisture  in  coal  consists  of  two  portions,  first,  surface  moisture,  or  that 
which  is  on  the  exterior  surface  of  each  lump,  and  which  may  be  dried  off  in 
ordinary  dry  air;  second,  the  hygroscopic  moisture,  or  that  which  is  held  by 
capillary  attraction  in  the  pores  of  the  coal  and  can  only  be  driven  out  of  a 
lump  of  coal  by  heating  it  considerably  above  212°  P.  The  percentage  of 
surface  moisture  that  may  be  held  in  a  pile  of  coal  depends  on  the  size  of  the 
pieces;  the  smaller  the  coal,  the  greater  is  the  amount  of  moisture  that  it  will 
hold.  Thus,  buckwheat  anthracite,  or  slack  bituminous  coal,  after  exposure 
to  rain,  may  hold  as  much  as  8  or  10%. 

The  amount  of  hygroscopic  moisture  depends  on  the  kind  of  coal;  thus, 
anthracite  contains  practically  none,  or  less  than  1%;  semibituminous  coal 
rarely  over  1%;  bituminous  coal  from  Pennsylvania,  between  1  and  2%; 
from  Ohio,  about  4%;  from  Illinois,  8  to  14%;  while  lignite  may  contain  20% 
or  more.  A  sample  of  Illinois  coal  originally  containing  14%  of  moisture, 
and  thoroughly  dried  by  heating  to  from  240°  F.  to  280°  F.,  reabsorbed  the 
same  amount  of  moisture  when  exposed  to  ordinary  air  for  2  mo. 


FUELS  369 

In  addition  to  representing  20  Ib.  per  T.  of  worthless  material  for  each 
1%  present,  moisture  causes  an  actual  loss  of  heat  from  the  fact  that  every 
pound  of  water  has  to  be  evaporated  into  steam  at  212°  and  the  steam  then 
raised  to  an  uncertain  temperature,  which  is  approximately  that  of  the  fire 
and  may  be  from  1,500°  to  2,500°.  Thus,  the  water  contained  in  a  coal 
analyzing  10%  moisture  will  be  200  Ib.  per  T.  and  will  require  to  raise  it  from, 
say,  60°  to  1,500°,  200X[1,117.8  +  (1,500-32)X.48]  =  364,488  B.  T.  U.,  which 
is  all  the  heat  generated  by  the  combustion  of  about  33  Ib.  of  ordinary  coal 
having  a  calorific  value  of  11,000  B.  T.  U.  per  Ib. 

Fixed  carbon  is  the  chief  heat-producing  constituent  of  coal,  and,  the 
amount  of  impurities  remaining  the  same,  the  relative  heating  values  of  coals 
are  fairly  well  determined  by  a  comparison  of  their  content  of  this  substance. 
Although  the  fixed  carbon  of  a  coal  evaporates  much  less  water  than  an  equiva- 
lent weight  of  the  volatile  hydrocarbons  when  properly  burned,  in  ordinary 
practice  so  much  of  the  latter  is  lost  through  careless  firing  or  improper  furnace 
construction,  that  the  relative  heating  value  of  a  coal  may  be  fairly  approxi- 
mated by  assuming  that  the  fixed  carbon  is  the  only  useful  constituent. 

Volatile  matter  is  that  part  of  the  coal  that  is  driven  off  as  a  combustible 
gas  when  the  coal  is  heated.  When  a  large  percentage  of  volatile  matter  is 
present,  coals  ignite  easily  and  burn  with  a  long  yellow  flame,  and,  in  ordinary 
methods  of  combustion,  give  off  dense  smoke.  The  relative  proportions  of 
volatile  matter  and  fixed  carbon  in  a  coal,  other  things  being  equal,  determine 
its  adaptability  to  any  particular  purpose,  as  appears  under  the  Classification 
of  Coals. 

The  volatile  combustible  matter  in  coal  consists  of  carbon,  hydrogen,  and 
oxygen  in  various  proportions,  differing  with  the  character  of  the  coal.  It  is 
found  that,  with  the  exception  of  cannel  coal,  the  larger  the  percentage  of 
volatile  matter  in  a  coal,  the  greater,  usually,  is  the  proportion  of  oxygen  in 
the  volatile  matter.  It  also  appears  that  in  the  semibituminpus  coals,  after 
deducting  as  much  of  the  hydrogen  as  is  needed  to  form  water  with  the  oxygen, 
that  is,  one-eighth  as  much  as  the  oxygen,  the  remainder,  or  the  available 
hydrogen,  is  combined  with  carbon  in  about  the  proportion  forming  methane, 
or  marsh  gas,  C7/4,  or  three  parts,  by  weight,  of  carbon  to  one  part  of  hydrogen; 
while  in  the  bituminous  coals  it  is  combined  in  about  the  proportions  of  five 
parts,  by  weight,  of  carbon  to  one  part  of  hydrogen.  The  low  heating  values 
per  pound  of  combustible  in  coals  that  are  high  in  volatile  matter  and  in 
oxygen,  are  thus  accounted  for. 

The  following  calculations  made  on  coals  having  the  ultimate  analyses 
given  in  the  table  on  pages  382  to  385  illustrate  the  increase  in  moisture  and 
the  decrease  in  available  hydrogen  and  calorific  power  of  American  coals  in  pro- 
ceeding westwards  from  the  New.  River  field  of  West  Virginia  by  way  of 
Pittsburg,  Pa.,  to  Illinois. 

No.  114,  New  River,  available  H  =  4.66-^4^  =4.14;  B.  T.  U.  =  14,765 

O 

No.  85,  Pittsburg,  available  tf  =  4.63-^   =3.70;  B.  T.  U.=  13,952 

o 

No.  28,  Illinois,  available  #  =  5.44-^^  =  3.10;  B.  T.  U.  =  10,719 

The  ash  of  coal  comes  partly  from  that  properly  belonging  to  the  vege- 
table matter  from  which  it  was  formed  and  partly  from  sediments  washed 
into  the  coal  swamp  during  times  of  flood.  Just  what  proportion  of  coal  ash 
represents  that  of  the  original  plant  growth  will,  naturally,  depend  on  the 
composition  of  that  growth,  something  impossible  to  determine,  but  it  would 
seem  that  any  ash  in  coal  to  the  extent  of  more  than  2%,  is  due  to  extraneous 
mineral  matter.  In  composition,  coal  ash  approximates  that  of  fireclay,  with 
the  addition  of  ferric  oxide,  sulphate  of  lime,  magnesia,  potash,  and  phosphoric 
acid. 

White-ash  coals  are  generally  freer  from  sulphur  than  red-ash  coals,  which 
contain  iron  pyrites,  but  there  are  exceptions,  as  in  a  certain  Peruvian  coal, 
which  contains  more  than  10%  of  sulphur  and  yields  not  a  small  percentage 
of  white  ash. 

The  fusibility  of  ash  varies  according  to  its  composition.  It  is  the  more 
infusible  the  more  nearly  its  composition  approaches  fireclay,  or  silicate  of 
alumina,  and  becomes  more  fusible  with  the  addition  of  other  substances, 
such  as  iron,  lime,  etc.  Coals  high  in  sulphur  usually  give  a  very  fusible  ash, 
on  account  of  the  iron  with  which  the  sulphur  is  in  combination.  A  fusible 
ash  tends  to  form  a  clinker  on  the  grate  bars,  and  therefore  is  objectionable. 


370  FUELS 

The  quantity  of  ash  in  different  coals  as  they  are  sent  to  market  differs 
greatly  according  to  the  quality  of  the  coal  itself  and  the  care  taken  to  remove 
the  slate,  dirt,  etc.  that  accompany  them  as  they  come  from  the  mine.  A 
lump  of  coal  may  contain  only  5%  of  ash,  while  the  average  of  the  coal,  includ- 
ing slate  and  dirt  as  it  is  mined,  may  contain  15%.  A  considerable  part  of 
the  slate  may  be  removed  from  the  larger  sizes  by  picking  after  screening,  and 
from  the  smaller  sizes  by  washing. 

In  the  case  of  anthracite,  the  table  on  page  386  brings  out  the  increase  in  ash 
and  decrease  in  calorific  power  as  the  sizes  grow  smaller.  The  table  on  page  387 
is  of  value  in  showing  the  actual  commercial  ash  present  in  bituminous  coals, 
many  of  which,  in  the  case  of  carefully  selected  lumps,  will  yield  by  analysis 
less  than  one-half  the  ash  given  in  the  table. 

Sulphur,  having  a  calorific  value  of  4,050  B.  T.  U.  per  lb.,  is  always  present 
in  coal.  While  some  few  coals,  notably  the  Georges  Creek-Cumberland 
semibituminous,  occasionally  contain  but  a  trace  of  this  element,  it  is  com- 
monly present  to  the  extent  of  .5  to  5%  and  even  more.  Sulphur  is  generally 
classed  as  an  impurity  in  coals  because  of  the  corroding  action  of  its  fumes 
upon  metals.  The  terms  low  sulphur  and  high  sulphur  as  applied  to  coals, 
are  generally  relative,  although  a  coal  containing  less  than  1%  sulphur  would 
everywhere  be  placed  among  the  former  and  one  having  5%  among  the  latter. 
The  amount  of  this  element  that  will  render  a  coal  unfit  for  any  particular 
service  is  discussed  under  the  Classification  of  Coals. 

Sulphur  exists  in  coal  in  at  least  three  forms.  It  usually  occurs  in  combina- 
tion with  iron  as  the  bisulphide,  FeSi,  which  is  known  by  various  names  as 
fool's  gold,  brasses,  etc.,  and  very  commonly  only  as  sulphur.  In  pyrites, 
sulphur  has  about  one-half  the  heating  value  per  pound  of  carbon.  The 
pyrites  may  occur  in  minute  crystalline  grains  disseminated  through  the  mass 
of  the  coal  or  segregated  in  small  patches  upon  the  cleavage  planes;  as  sheets 
or  plates,  of  considerable  area  in  proportion  to  their  thickness,  that  are  parallel 
to  the  bedding;  as  regular  layers  interstratified  with  the  coal;  and  as  lense- 
shaped  masses,  sometimes  weighing  100  lb.,  known  as  sulphur  balls.  Sulphur 
balls,  when  pure,  contain  53.33%  sulphur  and  are  a  source  of  income  at  some 
mines  where  they  are  placed  in  the  gob  and  from  time  to  time  gathered  up  and 
shipped  to  the  chemical  works,  where  they  are  employed  in  the  manufacture 
of  sulphuric  acid.  X 

Sulphur  may  be  present  as  a  sulphate,  usually  that  of  calcium  or  lime, 
CaSOt,  less  commonly  as  magnesium  sulphate,  MgSOt,  and  sometimes  as 
the  salt  of  other  metals.  The  sulphates  are  commonly  found  in  thin  whitish 
or  grayish  plates  on  the  vertical  joint  planes  of  the  coal;  in  this  combination, 
sulphur  has  no  fuel  value. 

Sulphur  may  also  be  present  in  combination  with  the  organic  constituents 
of  the  coal,  in  which  form  it  is  known  as  vegetable  sulphur  and  has  a  fuel  value. 

Phosphorus,  as  a  natural  constituent  of  the  original  vegetable  matter,  is 
always  found  in  coal.  The  amount  of  phosphorus  is  always  very  small  and 
does  not  affect  the  heating  value  of  the  coal,  and  is  only  of  importance  if  the 
coal  is  destined  to  make  coke  for  use  in  furnaces  working  on  Bessemer  iron. 
Phosphorus  probably  exists  as  a  single  or  double  phosphate  of  lime  and  alumina. 
Mr.  Charles  Catlett  notes,  in  the  Big  seam  near  Columbiana,  Ala.,  the  existence 
of  light-colored,  resinous  grains  of  evansite,  hydrous  aluminum  phosphate, 


Phosphorus  is  commonly  segregated  near  both  the  roof  and  floor  of  the 
seam  and  by  rejecting  a  few  inches  of  the  top  and  bottom  coal,  the  coke  made  of 
the  remainder  may  often  be  brought  within  the  Bessemer  limits.  Its  amount 
also  varies  as  the  workings  are  extended  and  analyses  of  the  coal  should  be 
made  weekly  or  monthly  as  the  headings  advance. 

CLASSIFICATION  OF  COALS 

The  most  convenient  commercial  classification  of  coals  is  based  on  the 
relative  amounts  of  combustible  matter  therein,  both  fixed  carbon  and  volatile 
hydrocarbons,  as  determined  by  a  proximate  analysis;  this  is  shown  in  the 
accompanying  table. 

It  must  be  remembered  that  this  classification  is  decidedly  arbitrary  and 
that  the  coals  of  any  one  group  overlap  at  either  end  of  the  scale  into  those 
of  the  other  groups.  This  is  particularly  true  of  the  lignites,  many  varieties 
of  which  cannot  be.  distinguished  from  bituminous  coal  of  the  better  grades 
if  the  proximate  analysis  is  made  the  criterion.  Many  of  the  coals  of  Arkansas 
are  low  in  volatile  matter  and  may  be  grouped  with  either  the  semianthracite 
or  semibituminous.  Similarly,  the  low-volatile  coals  of,  say,  Somerset  County 


FUELS 


371 


CLASSIFICATION  OF  COALS  BASED  ON  THEIR  CONTENT  OF  FIXED 
CARBON  AND  VOLATILE  MATTER 


Kind  of  Coal 

Fixed 
Carbon 
Per  Cent. 

Volatile 
Matter 
Per  Cent. 

Anthracite  

97.0  to  92.5 

3.0  to    7.5 

Semianthracite  

92.5  to  87.5 

7.5  to  12.5 

Semibituminous 

87  5  to  75  0 

12  5  to  25  0 

Bituminous,  Eastern  United  States  
Bituminous,  Western  United  States  . 

75.0  to  60.0 
65.0  to  50.0 

25.0  to  40.0 
35  0  to  50.0 

und°r  50 

over  50 

and  Cambria  County,  Pa.,  may  be  classed  as  either  bituminous  or 
semibituminous. 

Owing  to  this  overlapping  of  the  different  groups  in  the  scale,  a  classi- 
fication based  on  calorific  values  is  also  unsatisfactory.  Likewise,  geological 
age  fails  to  furnish  a  satisfactory  basis  of  classification.  As  a  general  rule, 
the  younger  the  coal  geologically,  the  higher  is  its  content  of  moisture  and 
volatile  matter  and,  consequently,  the  lower  is  it  in  fixed  carbon.  Thus,  the 
coals  of  the  Tertiary  age  are  all  lignites  and  commonly  of  the  brown-coal  type; 
the  coals  of  the  underlying  Cretaceous  are  commonly  black  lignites  (subbitu- 
minous)  with  spme'true  bituminous  coals  among  them;  and  the  true  bitumin- 
ous, semibituminous,  semianthracite,  and  anthracite  coals  are  almost  entirely 
confined  to  the  true  coal  measures  of  the  Carboniferous  age,  in  which,  the 
lower  volatile  coals  are  found  near  the  base  of  the  series.  This  rule  appears 
to  hold  good  in  regions  where  the  rocks  have  either  remained  undisturbed  or 
at  best  have  been  but  slightly  folded,  but  metamorphism  has  played  an 
important  part  in  changing  the  characteristics  of  seams  in  mountain  districts. 
The  Cretaceous  of  Colorado  is  marked  by  beds  of  subbituminous  lignite  and 
bituminous  coals  in  the  level  country  and  foot-hills,  which  the  metamorphism 
incident  to  mountain  building  has  altered  to  anthracite  in  the  midst  of  the 
Rockies;  therefore,  the  same  seam  may  present  the  characteristics  of  bitu- 
minous coal  in  flat  unbroken  regions,  of  semibituminous  coal  in  the  foot-hills, 
and  of  semianthracite  and  possibly  of  true  anthracite  in  the  higher  and  more 
disturbed  mountains. 

Anthracite. — Anthracite,  or  hard  coal,  as  it  is  frequently  called,  is  the 
densest,  hardest,  and  most  lustrous  of  all  varieties.  It  has  a  conchoidal 
fracture,  frequently  displays  iridescence,  and  is  characterized  both  in  the  lump 
and  in  the  bed  by  the  absence  of  cleavage  planes.  Its  specific  gravity  ranges 
from  1.3  to  1.8  with  an  average  value  of  about  1.5.  It  contains  from  3  to  7% 
of  volatile  matter,  does  not  coke,  is  kindled  slowly  and  with  difficulty,  requires 
a  strong  draft  through  the  firebox,  and  burns  with  a  short  almost  colorless 
flame,  which  is  smokeless  or  essentially  so.  Practically  all  the  anthracite 
mined  in  the  United  States  comes  from  a  small  area  in  northeastern  Pennsyl- 
vania. A  series  of  analyses  of  anthracite  from  that  state  are  given  in  the 
table  on  page  386.  These  are  commercial  analyses  made  on  large  shipments 
and  show  that  on  account  of  the  uniformly  high  ash  content,  the  calorific  value 
of  anthracite  is  rather  low  in  comparison  with  standard  bituminous  coals. 
It  will  also  be  observed  that  the  smaller  sizes  (pea,  barley,  rice,  etc.)  are  much 
less  efficient  than  the  larger  broken,  egg,  and  the  like.  The  high  content  of 
ash  in  the  smaller  sizes  is  due  very  largely  to  imperfect  preparation. 

An  analysis  of  the  so-called  anthracite  from  Cranston,  R.  I.,  is  No.  92  of 
the  table  on  pages  382  to  385.  The  coal  is  highly  graphitic  in  character  and  of 
far  more  geological  interest  than  commercial  value.  Its  existence  has  been 
known  for  many  years,  during  which  time  the  numerous  attempts  to  exploit 
it  have  always  ended  in  failure. 

An  analysis  of  anthracite  from  the  Cretaceous  seam  near  Crested  Butte, 
Colo.,  and  from  the  same  formation  at  Madrid,  N.  Mex.,  are  given  in  the 
table  on  page  387. 

Analyses  of  anthracite  from  Alaska  will  be  found  in  the  table  on  page  390, 
from  New  Zealand  in  the  table  on  page  391,  and  of  the  so-called  anthracites 
(more  properly  semianthracites)  from  Banff,  Alberta,  Canada,  in  the  table  on 
page  388. 


372  FUELS 

In  the  Pocono  formation  of  the  Subcarboniferous  in  the  Sleepy  Creek 
and  Third  Hill  Mountains  of  Berkley  and  Morgan  Counties,  W.  Va.,  are 
found  a  series  of  deposits  of  anthracite  that  are  so  irregular  in  thickness,  uncer- 
tain in  area,  and  so  crushed  and  otherwise  disturbed  as  to  be  commercially 
worthless.  Their  content  9f  volatile  matter  is  about  10%,  which  more  properly 
groups  them  with  the  semianthracites. 

The  so-called  anthracites  of  Blacksburg,  Montgomery  County,  W.  Va., 
an  analysis  of  which  is  No.  105  of  the  table  on  pages  382  to  385,  are  really 
semi-anthracites  and  commercially,  are  of  but  little  more  value  than  those 
from  Sleepy  Creek  Mountains,  W.  Va.,  or  Cranston,  R.  I. 

Semianthracite. — Semianthracite  contains  from  7.5%  to  12.5%  of  volatile 
matter  and  passes  by  insensible  gradations  on  the  one  hand  into  anthracite 
and  on  the  other  hand  into  semibituminous  coal.  It  is  not  so  hard  or  dense 
as  true  anthracite,  is  not  so  lustrous,  and,  when  freshly  broken,  will  leave 
soot  upon  the  hands,  something  anthracite  will  not  do.  It  is  somewhat 
lighter  than  anthracite,  ignites  quite  readily,  and  burns  more  freely  than 
hard  coal. 

A  series  of  proximate  analyses  of  Pennsylvania  semianthracites  mined  in 
the  northward  extension  of  the  anthracite  region  is  given  in  the  table  on 
page  386.  The  average  of  eleven  analyses  of  Semianthracite  from  Alaska  will 
be  found  in  the  table  on  page  390,  and  an  analysis  of  this  grade  of  coal  from 
Banff,  Alberta,  Canada,  is  given  in  the  table  on  page  388.  Several  proximate 
analyses  of  Semianthracite  from  Arkansas,  and  one  from  Virginia  will  be  found 
in  the  table  on  page  387,  and  complete  analyses  and  calorific  values  of  the 
same  in  the  table  on  pages  382  to  385. 

Semibituminous  Coals. — The  semibituminous  coals  containing  from  12.5 
to  25%  of  volatile  matter,  and,  neglecting  the  ash  and  moisture,  from  75  to 
87.5%  of  fixed  carbon  are  everywhere  trie  favorites  for  steam  raising.  Typical 
examples  are  the  well-known  Pocahontas  and  New  River  coals  of  West  Virginia, 
the  Georges  Creek-Cumberland  coal  of  Maryland,  the  Broad  Top  coals  of 
Pennsylvania,  and  the  Kittanning  coals  of  Cambria,  Clearfield,  and  Somerset 
Counties  in  the  latter  state.  All  these  coals  contain  about  18%  of  volatile 
matter,  from  5%  to  10%  of  ash  and  water  and  from  70  to  80%  of  fixed  carbon, 
with  sulphur  little  if  any  over  1%  and  have  a  calorific  value  of  14,000  B.  T.  U. 
per  lb.,  in  some  cases  even  more.  Some  of  the  coals  in  this  group  are  fairly 
hard  and  blocky,  a  structure  noticeable  in  those  from  the  Pittsburg  seam  in  the 
Georges  Creek-Cumberland  and  Broad  Top  regions,  while  others  are  very  soft, 
as  typified  in  the  P9cahontas  and  New  River  coals.  The  Kittanning  coals 
of  Pennsylvania  are  intermediate  between  the  Pocahontas  and  Georges  Creek 
in  hardness.  Containing  more  volatile  matter  than  anthracite,  these  coals 
kindle  more  readily  and  burn  more  rapidly  with  a  steady  fire. 

Complete  analyses  and  calorific  values  of  these  coals  from  Arkansas  (so- 
called  Semianthracite) ,  Pennsylvania,  Maryland,  West  Virginia,  and  Oklahoma 
are  given  in  the  table  on  pages  382  to  385.  Other,  and  shorter  analyses  of 
these  coals  from  Maryland,  Pennsylvania,  and  West  Virginia  are  given  in  the 
table  on  page  387.  Coals  of  this  type  from  Alaska  are  -noted  in  the  table  on 
page  390,  and  some  foreign  and  Canadian  semibituminous  coals  are  listed  in 
the  tables  on  pages  388  and  389,  respectively. 

Bituminous  Coals. — The  bituminous  coals  include  about  75%  of  the  output 
of  the  mines  of  the  United  States.  Those  produced  in  the  eastern  states  contain 
from  25%  to  a  maximum  of  40%  of  volatile  matter,  or,  say,  30  to  32%  as  an 
average.  Those  mined  in  the  central  basin  and  west  thereof  range  as  high  as 
50%  in  volatile  matter,  a  general  average  being  about  40%.  The  western 
bituminous  coals  are  generally  characterized  by  a  very  much  higher  content 
of  water  than  their  eastern  namesakes,  which  frequently  runs  up  to  10%,  and 
usually  contain  more  sulphur.  These  coals  vary  from  hard  to  soft  and  from 
blocky  to  columnar  in  structure.  Their  specific  gravity  is  normally  about  1.3. 
They  burn  with  a  yellow  flame  and  much  smoke,  and,  on  distillation,  yield 
hydrocarbon  oils,  tar,  etc.  According  to  the  use  to  which  they  are  put  or  to 
certain  physical  and  chemical  characteristics,  theyare  subdivided  into  numerous 
groups. 

Subbituminous  Coals. — The  very  convenient  term  subbituminous  coals, 
which  originated  with  Dr.  M.  R.  Campbell,  of  the  United  States  Geological 
Survey,  is  given  to  that  large  and  valuable  group  of  coals,  that  possesses  some 
of  the  undesirable  features  of  the  true  lignites  or  brown-coals,  together  with 
many  of  the  desirable  features  of  the  true  bituminous  coals.  They  are  some- 
times called  black  lignites  from  their  color,  which  is  often  highly  lustrous  and 
not  to  be'  distinguished  from  that  of  bituminous  coals  proper.  They  have  a 


FUELS  373 

brown  streak  and  a  specific  gravity  of  1.22  to  1.25.  They  burn  with  a  long, 
bright  flame,  with  considerable  smoke  like  bituminous  coals  but  do  not  coke. 
In  composition  and  calorific  power,  they  closely  resemble  and  are,  in  some 
cases,  even  superior  to,  the  true  bituminous  coals  of  the  Central  Basin,  as 
will  be  seen  by  comparing  the  analyses,  in  the  table  on  pages  382  to  385  of 
subbituminous  coal  No.  14,  from  Lafayette,  Colo.,  or  Np.  125,  from  Hanna, 
Wyo.,  with  analysis  No.  28,  of  bituminous  coal  from  Livingston,  111.,  or  with 
No.  35,  from  Linton,  Ind. 

The  distinction  between  the  two  groups  lies  in  their  different  behavior  on 
weathering.  True  bituminous  coals  break  down  under  atmospheric  action 
into  smaller  and  smaller  cubes  or  prisms,  the  faces  of  which  are  more  or  less 
parallel  to  the  cleavage  planes  (butt,  face,  etc.)  of  the  coal  in  the  bed.  As 
Doctor  Campbell  remarks,  "Exception  is  to  be  noted,  however,  in  the  case  of 
cannel  coal,  splint  coal,  and  many  forms  of  block  coal,  of  which  the  Brazil 
block  of  Indiana  may  be  considered  the  type.  Such  coals  always  show  cleavage 
faces  on  large  blocks,  but  the  blocks  do  not  split  readily.  These  coals  generally 
have  other  characteristics  by  which  they  may  be  identified  without  recourse 
to  their  weathering  properties." 

On  the  other  hand,  subbituminous  coal,  on  weathering,  breaks  up  into 
irregularly  shaped  fragments,  and,  in  particular,  separates  along  the  bedding 
planes  into  plates.  This  latter  peculiarity  is  the  sole  distinction  between -the 
two  groups  of  coals.  To  quote  further  from  Doctor  Campbell:  "In  applying 
these  criteria  (weathering,  etc.)  some  coals  will  be  classed  as  bituminous  which 
have  a  brown  streak,  are  young  geologically,  and  generally  have  been  regarded 
as  lignites  or  lignitic  coals;  but  they  resist  the  weather,  stand  shipment  well, 
and  have  a  high  calorific  value,  which  makes  them  to  all  intents  and  purposes 
bituminous  coal." 

Lignite. — Primarily,  the  distinction  between  subbituminous  coal  and 
lignite  is  one  of  color  alone;  the  former  is  black  and  the  latter  brown.  As  the 
subbituminous  coals  have  been  segregated  from  the  lignites  and  given  a  dis- 
tinctive name,  the  original  term  is  now  confined  to  the  typical  lignite,  or  brown- 
coal.  Lignites  are  generally  inferior  as  fuels,  compared  to  the  subbituminous 
coals,  are  usually  higher  in  moisture  and  volatile  matter  and  lower  in  fixed 
carbon,  usually  show  their  vegetable  origin  more  plainly,  weather  more  rapidly, 
and  are  less  well  adapted  to  transportation.  It  should  be  noted  that  many 
subbituminous  coals  and  lignites,  even  in  the  dry  climate  of  the  Rocky  Moun- 
tain region  where  they  are  largely  mined,  will  completely  disintegrate  into 
slack  within  2  to  4  mo. 

Bituminous  coals,  for  trade  purposes,  are  subdivided  into  many  groups 
with  distinctive  names,  depending  on  the  use  to  which  they  are  put  or  to 
which  they  are  best  adapted,  or  depending  on  some  peculiarity  of  structure 
or  composition.  Some  of  these  varieties  are  here  noted. 

Gas  Coals. — The  coals  suitable  for  the  manufacture  of  illuminating  gas 
in  closed  retorts  by  the  destructive  distillation  of  the  coal  itself  without  the 
admission  of  either  air  or  steam  are  termed  gas  coals.  These  coals  yield  the 
original  type  of  gas  used  for  lighting,  a  type  now  quite  largely  superseded  by 
water  gas  made  by  forcing  steam  through  incandescent  anthracite  or  coke. 
Probably  the  best,  and,  in  any  event,  the  earliest  used  gas  coals  in  the  United 
States  are  those  mined  along  the  line  of  the  Pennsylvania  Railroad  near  Irwin 
and  along  the  Baltimore  &  Ohio  Railroad  on  the  Youghiogheny  River,  in 
Westmoreland  County,  Pa.  As  there  produced,  these  coals  commonly  contain 
as  much  as  37%  of  volatile  matter,  from  6  to  8%  of  ash  with  considerably 
less  than  1%  of  sulphur,  and  being  hard  and  blocky,  bear  transportation  well. 
Their  yield  is  rather  more  than  10,000  cu.  ft.  of  gas  per  T.  of  coal  charged  into 
the  retorts,  the  gas  being  of  17  to  21  c.  p.  The  residual  coke  amounts  to  about 
60%  of  the  weight  of  the  original  coal  and  is  shiny,  fairly  strong,  and  well 
adapted  to  domestic  purposes  or  steam  raising.  Their  yield  of  nitrogenous 
products,  such  as  ammonia,  is  also  high.  These  characteristics  of  Westmore- 
land coal,  particularly  the  low-  content  of  sulphur,  are  those  demanded  of 
standard  gas  coals. 

Domestic  Coals. — The  term  domestic,  as  applied  to  coal,  refers  as  much 
to  its  size  as  to  its  composition  or  other  features.  In  the  anthracite  consuming 
sections  of  the  eastern  states,  the  domestic  sizes  are  stove  and  chestnut  adapted 
to  burning  in  ranges  and  small  heaters,  and  egg  suitable  for  use  in  furnaces. 
In  the  bituminous  regions,  there  is  frequently  sold  a  domestic  lump,  which 
may  mean  a  coal  specially  screened  over  bars,  say,  3  in.  apart,  or  it  may  refer 
to  coal  that  will  pass  over  a  3-in.  bar  screen  and  through  one  with  bars  set, 
say,  6  in.  apart.  In  any  case,  coals  for  domestic  use  are  well  screened  and 


374  FUELS 

usually  over  bars  much  more  widely  spaced  than  those  used  in  preparing  coal 
for  steam  raising.  While  it  is  true  that  domestic  coals  are  classified  more  by 
size  than  anything  else,  the  possession  of  certain  qualities  will  make  one  coal 
more  desirable  than  another  for  household  purposes.  The  coal  that  sustains 
a  mild,  steady  combustion,  and  remains  ignited  at  a  low  temperature  with  a 
comparatively  feeble  draft,  is  the  best.  A  coal  burning  with  a  smoky  flame 
is  objectionable  as  producing  much  soot  and  dirt,  especially  for  open  grates  or 
cooking  purposes.  For  self-feeding  stoves,  or  for  base  burners,  a  dry  non- 
coking  coal  is  necessary.  A  very  free  and  fiercely  burning  coal  is  not  desirable, 
particularly  in  stoves,  as  the  temperature  cannot  be  easily  regulated.  A 
sulphurous  coal  is  also  bad,  as  it  produces  stifling  gases  with  a  defective  draft, 
and  corrodes  the  grates  and  fire-bowls.  The  difficulty  from  clinkering  is  not 
so  great  in  domestic  uses,  as  the  temperature  is  not  generally  high  enough  to 
fuse  the  ash.  A  stony,  hard  ash  that  will  not  pass  between  the  grate  bars  is 
bad,  and  light  pulverulent  ash  is  best. 

Blacksmith,  or  Smithing,  Coals. — A  coal  suitable  for  blacksmith  purposes 
should  have  a  high  heating  power,  should  contain  as  much  less  than  1%  of 
sulphur  as  possible,  should  be  low  in  ash,  and  should  coke  sufficiently  to  form 
a  hollow  fire,  that  is,  should  form  an  arch  on  the  forge.  The  semibituminous 
coals  from  the  Ne,w  River  and  Pocahontas  regions  of  West  Virginia,  that  from 
the  Georges  Creek-Cumberland  district  of  Maryland,  and  the  Broad  Top  (Hunt- 
ingdon County)  field  of  Pennsylvania,  make  excellent  blacksmith  coals  as 
mined.  The  slack  of  many  coking  coals,  if  washed  to  reduce  the  content  of 
sulphur  (especially)  and  ash,  serve  excellently  as  smithing  coal.  The  best 
known  blacksmith  coal  of  the  east  and  the  one  formerly  used  for  this  purpose 
to  the  practical  exclusion  of  all  others  is  known  by  the  name  of  Blossburg  from 
the  town  of  that  name  in  Tioga  County,  Pa.,  where  it  was  first  mined.  An 
average  analysis  of  this  coal  (commercial  sample)  from  the  Morris  Run  mines, 
wher.e  the  coal  is  at  its  best  gave  moisture,  1.12%;  volatile  matter,  18.57%; 
fixed  carbon,  72.10%;  ash,  7.63%;  and  sulphur,  .583%.  It  will  be  noted  that 
this  is  a  semibituminous  coal  essentially  the  same  as  those  already  described. 

Steam  Coals — In  the  Eastern  states  and  where  anthracite  is  concerned, 
the  term  steam  refers  entirely  to  the  size  of  the  fuel.  Thus,  if  (as  noted  under 
that  title)  the  domestic  sizes  of  anthracite  are  chestnut,  stove,  and  egg,  the 
steam  sizes  are  smaller  than  these  and  include  pea,  buckwheat,  barley,  rice, 
etc.  The  term  steam  coal  is  also  often  used  to  indicate  any  coal,  anthracite 
or  bituminous,  that  is  too  poor  to  be  used  for  any  purpose  except  steam 
raising;  the  idea  being  that  anything  that  will  burn  is  good  enough  to  find 
place  in  the  firebox. 

For  steam  making,  the  superiority  of  coals  high  in  combustible  constituents 
is  admitted,  and  those  with  the  higher  percentage  of  fixed  carbon  are  the  most 
desirable.  But  the  consideration  of  the  steaming  qualities  of  a  coal  involves, 
also,  a  consideration  of  the  form  of  furnace  and  of  all  the  conditions  of  com- 
bustion. The  evaporative  power  of  a  coal  in  practice  cannot  be  stated  without 
reference  to  the  conditions  of  combustion,  and  every  practical  test  of  a  coal, 
to  be  thorough,  should  lead  to  a  determination  of  the  best  form  of  furnace 
for  that  coal,  and  should  furnish  knowledge  as  to  what  class  of  furnaces  in 
actual  use  such  coal  is  specially  adapted.  It  is  not  sufficient  that  in  compara- 
tive tests  of  coals  the  same  conditions  should  exist  with  each,  but  there  should 
also  be  determined  the  best  conditions  for  each  coal. 

Of  coals  high  in  fixed  carbon,  the  semianthracites  and  the  semibituminous 
rank  as  high  as  the  anthracite  in  meeting  the  various  requirements  of  a  quick 
and  efficient  steaming  coal. 

For  railway  use,  these  coals  have  been  found  to  excel  anthracites  in  evapo- 
rating power.  The  comparative  absence,  in  semibituminous  coals,  of  smoke, 
which  means  loss  of  combustible  matter  as  well  as  discomfort  to  the  traveler, 
is  sufficient  to  suggest  their  superiority  over  bituminous  coals  for  such  use. 

Steaming  coal  should  kindle  readily  and  burn  quickly  but  steadily,  and 
should  contain  only  enough  volatile  matter  to  insure  rapid  combustion.  It 
should  be  low  in  ash  and  sulphur,  should  not  clinker,  and  when  it  is  to  be 
transported  should  not  easily  crumble  and  break. 

Coking  Coals. — Coking  coals  are  those  that  become  pasty  or  semiviscid 
in  the  fire  and  produce,  if  the  burning  or  heating  is  carried  on  with  the  partial 
or  entire  exclusion  of  air  and  the  process  is  not  allowed  to  proceed  too  far,  a 
hard  or  porous  mass  known  as  coke,  which  consists,  essentially,  of  the  fixed 
carbon  and  the  ash  of  the  original  coal,  the  peculiar  structure  being  due  to 
the  escape  from  the  partly  melted  mass  of  individual  bubbles  of  gas  driven  off 
by  the  heat. 


FUELS  375 

Commercial  coke  making  is  carried  on  in  firebrick  structures  known  as 
coke  ovens,  which  are  of  two  general  and  very  distinct  types.  The  original 
form  of  oven  and  still  the  chief  type  used  in  the  United  States  consists  of  a 
hemispherical  shell  of  firebrick  into  which  air  sufficient  to  burn  the  escaping 
gases  is  admitted  over  the  door  during  the  coking  process.  This  is  called, 
from  the  marked  similarity  in  form,  a  beehive  coke  oven.  The  modern  type, 
called  a  retort  oven,  usually  consists  of  a  long  (18  to  40  ft.)  and  narrow  (18  to 
30  in.)  rectangular  chamber  placed  like  a  book  on  edge,  the  height  being  10,  12, 
or  more  ft.  In  this  chamber  the  coal  is  heated  without  access  of  air,  the 
process  being  analogous  to  the  production  of  illuminating  gas.  Ovens  of  this 
type  are  frequently  called  by-product  ovens  as  they  are  well  adapted  to  the 
recovery  from  the  gases  of  the  tar,  ammonia,  etc.,  which  are  commonly  wasted 
in  coking  in  the  beehive  oven. 

Neither  anthracite  nor  semianthracite  on  one  end  of  the  scale  will  coke, 
nor  will  the  subbituminous  and  lignite  coals  on  the  other.  This  limits  the 
possible  possession  of  coking  qualities  to  the  semibituminous  and  bituminous 
coals,  ranging  between  12.5  and  50%  in  volatile  matter.  In  the  United  States, 
those  semibituminous  coals  so  low  in  volatile  matter  as  to  approximate  the 
semianthracite  in  composition  either  will  not  coke  at  all  or  but  very  indiffer- 
ently. The  same  is  true  at  the  other  end  of  the  scale  of  the  bituminous  coals 
very  high  in  volatile  matter,  as  these  coals  in  the  Western  states  are  almost 
invariably  non-coking.  The  difficulty  in  making  any  coke  at  all,  or  at  best 
but  a  very  indifferent  one,  from  Western  bituminous  coals  seems  to  be  due  to 
the  large  amount  of  water  they  contain.  Probably  90  or  95%  of  American 
coke  is  made  from  coal  containing  between  18  and  35%  of  volatile  matter. 
But  all  coals  falling  within  these  limits  will  not  coke,  and  the  reason  why,  of 
two  coals  having  essentially  the  same  analytic  composition,  one  should  coke 
and  the  other  not,  is  a  much  disputed  question. 

Even  if  a  coal  will  make  some  kind  of  a  coke,  whether  this  is  of  value  or  not 
depends  on  the  use  to  which  it  is  to  be  put.  For  the  manufacture  of  pig  iron 
in  the  blast  furnace,  the  coke  must  be  firm  and  tough  and  not  dense,  but  with  a 
pronounced  cellular  structure  and  a  hard  cell  wall.  If  the  pig  iron  from  the 
blast  furnace  is  to  be  used  in  the  manufacture  of  steel  by  the  Bessemer  process, 
the  makers  prefer  a  coke  containing  from  1  to  3%  of  volatile  matter  and 
moisture  combined,  10  to  12%  of  ash,  and  89  to  85%  of  fixed  carbon  with 
sulphur  and  phosphorus  not  over  1%  and  .02%,  respectively.  This  is  the 
composition  of  the  standard  so-called  Bessemer  coke.  Unfortunately,  very 
little  coke  is  now  obtainable  that  possesses  both  this  purity  and  the  proper 
physical  qualities.  The  objection  to  sulphur  in  the  coke  is  that  it  enters  the 
iron  and,  not  being  removed  in  the  Bessemer  converter,  remain^  in  the  steel, 
which  it  makes  red  short  or  brittle  when  hot.  Similarly,  phosphorus  is  not 
removed  in  this  process,  but  it  makes  the  steel  cold  short,  or  brittle  when  cold, 
a  very  serious  objection  in  structures  subject  to  shock,  as  rails.  Further,  low- 
phosphorus  iron  ores  are  becoming  more  and  more  difficult  to  obtain,  so  that 
the  lower  the  content  of  this  impurity  in  the  coke,  the  higher  may  it  be  in  the 
ore.  If  the  pig  iron  is  to  be  used  for  making  steel  by  the  basic  open-hearth 
process,  phosphorus  and  to  a  less  extent  sulphur  are  not  so  objectionable  in 
the  coke,  as  they  are  largely  removed  in  the  furnace. 

For  use  in  the  foundry  in  the  manufacture  of  castings,  the  coke  should 
possess  the  same  physical  qualities  demanded  of  good  blast-furnace  coke, 
but  the  percentage  of  both  sulphur  and  phosphorus  may  be  much  higher.  In 
fact,  many  foundry  managers  prefer  a  high  phosphorus  coke,  as  the  presence  of 
this  element  in  the  metal  makes  it  very  fluid  when  melted  so  that  it  readily 
fills  the  smallest  openings  in  the  mold.  It  is  generally  demanded  that  coke 
for  foundry  purposes  shall  be  capable  of  melting  10  Ib.  of  iron  per  pound  of  fuel. 
Such  a  result  is  not  often  obtained  and  in  ordinary  practice  1  Ib.  of  coke  will 
melt  but  8  Ib.  of  iron.  f 

In  smelting  operations  where  the  metals  are  recovered  as  matte  (sulphide  of 
iron,  etc.)  large  amounts  of  sulphur  in  the  coke  are  not  objectionable,  as  the 
element  is  essential  to  the  process. 

For  domestic  use,  it  is  desirable  that  the  coke  be  hard  so  that  it  will  bear 
crushing  and  screening  to  the  proper  sizes  and  subsequent  transportation  to 
market.  The  amount  of  sulphur  and  phosphorus  in  domestic  coke  is  not  of 
great  importance,  but  the  percentage  of  ash  should  be  as  low  as  is  consistent 
with  due  strength,  and  the  ash  should  not  clinker. 

From  the  foregoing,  it  is  evident  that  a  coal  that  will  make  a  coke  suitable 
for  one  purpose  will  not  make  a  coke  suitable  for  another.  The  fusibility  of 
the  carbon,  the  amount  of  disposable  hydrogen,  the  tenacity  with  which  the 


376  FUELS 

gaseous  constituents  are  held,  the  amounts  of  sulphur  and  phosphorus  in  the 
coal,  the  rapidity  and  temperature  of  the  coking  process,  the  state  of  the  coal 
when  charged  into  the  oven  (whether  as  run  of  mine  or  slack),  even  the  process 
itself,  all  affect  in  one  way  and  another  the  physical  and  chemical  qualities  of 
the  coke  and,  consequently,  the  use  to  which  it  is  best  adapted.  More  or  less 
weathered  coal  from  near  the  outcrop  will  not  make  as  good  coke  as  that  mined 
under  more  cover;  many  coals  that  will  coke  but  indifferently  as  run  of  mine 
coke  excellently  in  the  fine  state;  and  others,  which  make  a  poor  showing  in 
the  beehive  oven,  are  well  adapted  to  use  in  retort  ovens. 

Ordinary  analyses  do  not  indicate  whether  or  not  a  coal  is  a  good  coking 
coal,  and  they  indicate  simply  by  giving  the  amount  of  carbon,  ash,  and  sul- 
phur, what  will  be  the  probable  purity  of  the  coke  formed.  To  produce  a  stand- 
ard Bessemer  coke  in  the  beehive  oven,  the  typical  coal  has  essentially  the 
analysis  of  No.  18,  of  the  table  on  pages  382  to  385,  mined  from  the  Pittsburg 
seam  in  the  Connellsville  region  of  Pennsylvania.  Other  analyses  of  this  seam 
show  the  volatile  matter  to  be  as  high  as  32%,  with  the  fixed  carbon,  ash,  and 
sulphur  as  low  as  59%,  7%,  and  .5%,  respectively.  Coals  having  analyses 
that  differ  materially  from  this  give  most  excellent  cokes  that  are  in  every  way 
equal  to  that  from  the  Connellsville  region.  As  illustrations  of  this  may  be 
cited  the  cokes  made  from  the  semibituminous  coals  from  the  New  River  and 
Pocahontas  fields  of  West  Virginia,  which  coals  contain  only  about  18%  of 
volatile  matter,  as  well  as  coke  made  from  the  coal  mined  from  the  Freeport 
seam,  which  often  contains  over  35%  of  volatile  matter.  Coke  made  from 
coals  containing  less  than  5  or  6%  of  ash,  while  pure,  is  not  generally  desirable 
as  blast-furnace  fuel ,  as  it  lacks  the  strength  to  support  the  burden,  and  break- 
ing up  before  burning  tends  to  be  blown  out  the  stack  by  the  blast.  It  must 
be  remembered  that  coals  that  will  not  yield  a  satisfactory  coke  from  either 
the  chemical  or  physical  view  point  in  the  beehive  oven,  often  will  do  so  in 
the  retort  oven.  Thus,  when  investigating  the  coking  qualities  of  the  coal 
from  any  field  carload  lots  should  be  shipped  to  both  beehive  and  retort  oven 
plants  for  tests  under  actual  working  conditions. 

Yield  of  Coke.— There  are  several  methods  used  by  field  engineers  in 
arriving  at  an  estimate  of  the  quantity  and  quality  of  coke  that  a  given  coal 
will  produce.  It  is  obvious  that  if  there  is  no  loss  of  fixed  carbon  in  the  proc- 
ess, all  this  element  will  be  in  the  coke  together  with  all  the  ash.  In  the 
Connellsville  region,  it  is  found  that  about  40%  of  the  sulphur  is  volatilized, 
60%  remaining  in  the  coke.  With  this  understanding,  what  is  called  the 
theoretic  coke  obtainable  from  a  coal  such  as  No.  85  from  Connellsville  may 
be  figured  as  follows: 

;'-r*  Original     Remaining        Analysis 

Coal  in  Coke  of  Coke 

Moisture 97 

Volatile  matter 29.09 

Fixed  carbon 60.85  60.85  87.00 

Ash 9.09  9.09  13.00 

100.00  69.94  100.00 

Sulphur,  separate 90  X  .60        .54  .77 

The  figures  in  the  third  column  are  arrived  at  by  dividing  those  in  the 
second  column  by  .6994,  which  figure  is  often  spoken  of  as  the  theoretic  yield 
and  which  means  simply,  that  the  coal  in  question  should  yield  under  perfect 
conditions  69.94%  of  its  weight  as  coke,  which  should  have  the  composition 
given  in  the  third  column.  These  results  agree  very  closely  with  those  obtained 
in  actual  practice  in  the  Connellsville  region;  in  fact,  there  is  frequently  a 
greater  yield  than  the  theoretic  one  due  to  the  deposition  of  carbon  in  the  pores 
of  the  coke  during  the  process. 

Many  engineers  assume  that  under  average  conditions  1.5  T.  of  coal  are 
required  to  make  1  T.  of  coke,  and  that  there  is  enough  sulphur  volatilized 
to  insure  that  the  percentage  of  this  impurity  in  the  coke  shall  not  exceed  that 
in  the  original  coal.  Using  the  foregoing  coal,  the  figures  follow: 

Analysis 
of  Coke 
Per  Cent. 

Ash  in  coke 9.09X1.5=    13.63 

Fixed  carbon  by  difference 100.00-  13.63  =  86.37 

100.00 
Sulphur,  separate 90 


FUELS  377 

As  the  coking  process,  in  the  beehive  oven  at  least,  is  by  no  means  a  per- 
fect one,  the  analysis  will  be  affected  by  the  volatile  matter  in  the  coke  due  to 
imperfect  burning  and  to  the  moisture  resulting  from  watering  down  the  charge. 
The  sum  of  these  should  not  exceed  2%  in  fairly  good  practice. 

Either  of  the  foregoing  methods  of  estimating  the  yield  and  composition 
of  coke 'give  good  results  if  the  coal  contains  enough  volatile  matter  to  furnish 
the  necessary  heat  for  the  coking  process.  It  fails  in  the  case -of  the  semi- 
bituminous  coals,  as  a  certain  amount  of  their  fixed  carbon  is  burned  in  sup- 
plying the  heat  for  the  coking  operation.  Using  the  analysis  of  Pocahontas 
coal,  the  theoretic  yield  of  coke  is,  of  course,  the  sum  of  the  fixed  carbon 
and  ash  or  73.87  +  5.25  =  79.12%,  and  its  composition,  using  the  first  method 
given,  should  be,  fixed  carbon,  93.36%;  ash,  6.64%;  and  sulphur  (separately) 
.48%.  But  it  is  found  that  the  yield  in  the  beehive  oven  from  coals  of  this 
type  is  commonly  about  63%  of  the  weight  of  the  coal  charged.  Because  all 
the  ash  remains  in  the  coke  and  the  fixed  carbon  alone  is  consumed,  using  a  ton 
of  2,000  Ib.  as  a  basis,  the  composition  of  the  coke  is  as  follows: 

2,000  Ib.  of  coal  yields  2.000X. 6300=  1,260  Ib.;  fixed  carbon+ash 
2,000  Ib.  of  coal  yields  2,000 X. 0525=     105  Ib.;  ash 
2,000  Ib.  of  coal  yields  1,260-105    =  1,155  Ib.;  fixed  carbon 
Hence,  2,000  Ib.  of  coal  will  yield  63%,  or  1,260  Ib.,  of  coke,  which  con- 
tains 1,155  Ib.,  or  91.67%,  of  fixed  carbon  and  105  Ib.,  or  8.33%,  of  ash.     The 
sulphur  may  be  estimated  to  be  from  .64  as  in  the  coal  to  .48%  as  determined 
by  the  first  method. 

If  the  coal  is  coked  in  a  retort  oven,  the  yield  of  coke  will  exceed  the  theo- 
retic, and  a  fair  average  may  be  taken  as  78%  of  the  weight  of  the  charge. 
Using  the  Connellsville  coal  mentioned,'  the  yield  and  composition  of  coke  in  a 
retort  oven  will  be  about  as  follows: 

2,000  Ib.  of  coal  yields  2.0QOX. 7800  =  1,560  Ib.;  fixed  carbon+ash 
2,000  Ib.  of  coal  yields  2,000 X. 0909=     182  Ib.;  ash 
2,000  Ib.  of  coal  yields  1,560-182     =  1,378  Ib.;  fixed  carbon 
Hence  2,000  Ib.  of  coal  will  yield  78%,  or  1,560  Ib..  of  coke,  which  contains 
1,378  Ib.,  or  88.33%,  of  fixed  carbon  and  182  Ib.,  or  11.67%  of  ash.     It  is 
apparent  that  coking  in  a  retort  oven  gives  more  and  better  coke  than  coking 
in  the  beehive  oven.     The  increased  output  is  particularly  noticeable  in  coking 
semibituminous  coals. 

Of  the  total  coke  produced  in  the  beehive  oven,  between  95  and  96%  will 
be  of  large  size  suitable  for  shipment  to  any  market;  3  to  4%  will  be  fine  or 
small  coke  (breeze  or  braise)  which  may  be  separated  from  the  ash  by  screen- 
ing and  sold  for  domestic  use;  and  about  1%  of  ashes,  which  is  usually  worth- 
less but  is  sometimes  ground  and  used  for  foundry  facings.  The  foregoing 
represents  what  may  be  called  Connellsville  practice;  if  semibituminous  coal 
is  used,  the  resultant  coke  is  softer  and  the  amount  of  fine  coke  and  ashes  is 
considerably  greater. 

Pishel's  Test  for  Coking  Qualities  of  Coal. — There  has  recently  been 
developed,  by  Mr.  Max.  A.  Pishel,  a  simple  field  test  for  determining  the 
coking  or  non-coking  properties  of  coals  which  should  have  extensive 
application.  As  described  by  Mr.  Pishel  in  the  columns  of  the  Colliery 
Engineer,  the  procedure  is:  "Pulverize  in  a  mortar  a  small  quantity  of  the 
coal  to  be  tested  until  it  will  pass  through  a  100-mesh  sieve.  Pour  out  the 
loose  material  and  note  the  amount  that  adheres  to  the  mortar.  With 
some  coals,  the  mortar  and  pestle  will  be  deeply  coated  with  coal  dust  that 
adheres  so  strongly  that  it  can  be  removed  with  difficulty;  with  other  coals, 
there  will  be  only  a  thin  film  of  coal  dust  adhering  to  the  mortar  and  pestle; 
while  with  still  others  both  mortar  and  pestle  will  be  nearly  as  clean  after  the 
operation  is  completed  as  they  were  before  it  began.  The  degree  of  adhesion 
depends  on  the  grade  of  the  coal  with"  reference  to  its  coking  qualities.  If  it 
adheres  strongly,  the  coal  will  make  a  good  coke;  if  it  adheres  only  partly, 
the  coal  will  make  an  inferior  grade  of  coke;  and  if  it  does  not  adhere,  the  coal 
is  non-coking."  Porcelain,  glass,  earthenware,  iron,  or  agate  mortars  may  be 
used,  the  desideratum  being  that  the  material  is  hard  and  smooth.  The  results 
may  be  obtained  as  well  with  a  small  mortar  that  may  be  carried  in  the  pocket 
as  with  a  large  one. 

The  structure  of  the  coal  in  the  bed  affords  some  clue  to  its  coking  quali- 
ties; at  least,  it  has  been  often  noted  that  where  the  Pittsburg  and  Freeport 
seam  coals,  as  well  as  those  from  the  Pocahontas  and  New  River  districts, 
make  a  good  coke,  the  coal  shows  a  distinct  columnar  structure  and  tends  to 
break  out  of  the  bed  in  long  prisms  or  fingers. 


378  FUELS 

Non-Coking  Coals. — The  term  non-coking  coals  is  applied  to  those  bitu- 
minous coals  that  do  not  coke  even  when  highly  heated  but  which  retain  the 
shape  of  the  original  lump  until  reduced  to  ashes.  There  are  numerous  varieties 
known  by  distinctive  names,  and  all  are  valuable  domestic  fuels. 

Fat  and  Dry,  or  Lean,  Coals. — Fat  coals  are  those  that  possess  a  large 
amount  of  volatile  matter  and  consequently  burn  with  a  long  oily  flame.  Dry, 
or  lean,  coals  are,  obviously,  the  reverse  of  fat  coals  and  burn  with  short  flame 
and  little  smoke.  Cannel  coal  affords  an  illustration  of  the  first  and  Poca- 
hontas  of  the  second  of  these  groups. 

Free-Burning  Coal. — The  term  free-burning  is  applied  to  those  coals  that 
burn  easily  with  a  light  draft.  The  term  is  rather  loosely  used,  being  applied 
by  some  to  non-coking  coals,  by  others  to  semibituminous  «coals  as  opposed 
to  anthracite,  and  by  still  others  to  coals  containing  a  larger  amount  of  volatile 
matter. 

Cannel  Coal. — Cannel  coal  is  a  variety  of  bituminous  coal  that  is  very  rich 
in  volatile  matter,  which  makes  it  a  very  valuable  gas  coal.  It  kindles  readily 
and  burns  with  a  dense  smoky  flame.  It  is  compact,  with  little  or  no  luster  and 
without  any  appearance  of  banded  structure,  breaking  with  a  conchoidal 
fracture.  Its  content  of  volatile  is  commonly  about  50%,  its  color  is  dull 
black  to  grayish  black,  and  its  specific  gravity  is  about  1.23.  Certain  varieties 
show  what  appear  to  be  small  concretions  about  the  size  of  a  dime  scattered 
over  the  surface  of  a  fresh  fracture;  these  are  called  birds-eye  cannel  from  the 
fancied  resemblance  of  these  structures.  The  name  cannel  coal  is  a  corruption  of 
the  term  candle  coal  given  to  it  because  long  splints  of  it  readily  ignite  and  burn 
with  a  long  flame,  spitting  and  sputtering  like  a  candle  burning  in  a  draft. 
It  was  at  one  time  a  popular  grate  fuel  but,  although  extensive  deposits  exist, 
is  now  little  mined. 

Splint  Coal. — Splint  coal  has  a  dull  black  color,  and  is  much  harder  and  less 
breakable  than  ordinary  bituminous  coal.  It  is  readily  fissile,  like  slate,  but 
breaks  with  difficulty  on  cross-fracture.  It  ignites  less  readily  than  ordinary 
bituminous  coal,  but  makes  a  hot  fire,  and  is  a  good  house  coal,  although  its 
content  of  ash  is  usually  high.  Both  it  and  cannel  coal,  while  occurring  in 
distinct  seams,  are  very  commonly  found  as  a  layer  or  layers  interstratified 
in  seams  of  ordinary  coal. 

PROXIMATE  ANALYSIS  OF  COAL 

The  following  is  the  outline  of  the  method  recommended  for  the  proximate 
analysis  of  coal  by  a  committee  of  the  American  Chemical  Society,  Messrs. 
W.  F.  Hillebrand,  C.  B.  Dudley,  W.  A.  Noyes. 

Sampling. — At  least  5  Ib.  of  coal  should  be  taken  for  the  original  sample, 
with  care  to  secure  pieces  that  represent  the  average.  These  should  be  broken 
up  and  quartered  down  to  obtain  the  smaller  sample,  which  is  to  be  reduced 
to  a  fine  powder  for  analysis.  The  quartering  and  grinding  should  be  carried 
out  as  rapidly  as  possible,  and  immediately  after  the  original  sample  is  taken, 
to  prevent  gain  or  loss  of  moisture.  The  powdered  coal  should  be  kept  in  a 
tightly  stoppered  tube,  or  bottle,  until  analyzed.  Unless  the  coal  contains 
less  than  2%  of  moisture,  the  shipment  of  large  samples  in  wooden  boxes 
should  be  avoided. 

In  boiler  tests,  shovelfuls  of  coal  should  be  taken  at  regular  intervals  and 
put  in  a  tight  covered  barrel,  or  some  air-tight  covered  receptacle,  and  the 
latter  should  be  placed  where  it  is  protected  from  the  heat  of  the  furnace. 

In  sampling  from  a  mine,  the  map  of  the  mine  should  be  carefully  exam- 
ined and  points  for  sampling  located  in  such  a  manner  as  to  represent  fairly 
the  body  of  the  coal.  These  points  should  be  placed  close  to  the  working  face. 
Before  sampling,  a  fresh  cut  of  the  face  should  be  made  from  top  to  bottom 
to  a  depth  that  will  insure  the  absence  of  possible  changes  or  of  sulphur 
and  smoke  from  the  blasting  powders".  The  floor  should  be  cleaned  and  a 
piece  of  canvas  spread  to  catch  the  cuttings.  Then,  with  a  chisel,  a  cutting 
from  floor  to  roof,  say  3  in.  wide  and  about  1  in.  deep  should  be  made.  The 
shale  or  other  impurities  that  it  is  the  practice  at  that  mine  to  reject  should  not 
be  chiseled  out,  however.  The  length  of  the  cutting  made  should  then  be 
measured,  but  the  impurities  should  not  be  included  in  this  measurement. 
With  a  piece  of  flat  iron  and  a  hammer,  all  pieces  should  be  broken  to  $-in. 
cubes  or  less,  without  removing  from  the  cloth,  then  quartered,  and  trans- 
ferred to  a  sealed  bottle  or  jar.  For  the  "  run-of-mine "  sample,  samples  taken 
at  several  points  in  this  manner  should  be  mixed  and  quartered  down.  If  the 
vein  varies  in  thickness  at  different  points,  the  samples  taken  at  each  point 
should  correspond  in  amount  to  the  thickness  of  the  vein.  For  instance,  a 


FUELS  379 

small  measure  may  be  filled  as  many  times  with  the  coal  of  the  sample  as  the 
vein  is  feet  in  thickness.  Should  there  appear  differences  in  the  nature  of  the 
coal,  it  will  be  more  satisfactory  to  take,  in  addition  to  the  general  sample, 
samples  of  such  portions  of  the  vein  as  may  display  these  differences. 

Moisture. — Dry  1  g.  of  the  coal  in  an  open  porcelain  or  platinum  crucible 
at  104°  to  107°  C.  for  1  hr.,  best  in  a  double- walled  bath  containing  pure 
toluene.  Cool  in  a  desiccator  and  weigh  covered. 

Volatile  Combustible  Matter. — Place  1  g.  of  fresh,  undried  coal  in  a  platinum 
crucible  weighing  20  to  30  g.,  and  having  a  tightly  fitting  cover.  Heat  over 
the  full  flame  of  a  Bunsen  burner  for  7  min.  The  crucible  should  be  supported 
on  a  platinum  triangle  with  the  bottom  6  to  8  cm.  above  the  top  of  the  burner. 
The  flame  used  should  be  fully  20  cm.  high  when  burning  free,  and  the  determi- 
nation made  in  a  place  free  from  drafts.  The  upper  surface  of  the  cover  should 
burn  clear  but  the  under  surface  should  remain  covered  with  carbon.  To 
find  volatile  combustible  matter,  subtract  the  percentage  of  moisture  from  the 
loss  found  here. 

Ash. — Burn  the  portion  of  coal  used  for  the  •determination  of  moisture  at 
first  over  a  very  low  flame,  with  the  crucible  open  and  inclined,  until  free  from 
carbon.  If  properly  treated,  this  sample  can  be  burned  much  more  quickly 
than  the  dense  carbon  left  from  the  determination  of  volatile  matter. 

Fixed  Carbon. — The  fixed  carbon  is  found  by  subtracting  the  percentage 
of  ash  from  the  percentage  of  coke. 

Sulphur  (Eschka's  Method). — Mix  thoroughly  1  g.  of  the  finely  powdered 
coal  with  1  g.  of  magnesium  oxide  and  5  g.  of  dry  sodium  carbonate,  in  a  thin 
75  to  100  c.  c.  platinum  dish  or  crucible.  The  magnesium  oxide  should  be 
light  and  porous,  not  a  compact,  heavy  variety.  Heat  the  dish  on  a  triangle 
over  an  alcohol  lamp,  held  in  the  hand  at  first;  gas  must  not  be  used,  because 
of  the  sulphur  it  contains.  Stir  the  mixture  frequently  with  a  platinum  wire 
and  raise  the  heat  very  slowly,  especially  with  soft  coals.  Keep  the  flame  in 
motion  and  barely  touching  the  dish,  at  first,  until  strong  glowing  has  ceased, 
and  then  increase  gradually  until,  in  15  min.,  the  bottom  of  the  dish  is  at  a  low 
red  heat.  When  the  carbon  is  burned,  transfer  the  mass  to  a  beaker  and 
rinse  the  dish,  using  about  50  c.  c.  of  water.  Add  15  c.  c.  of  saturated  bromine 
water  and  boil  for  5  min.  Allow  to  settle,  decant  through  a  filter,  boil  a  second 
and  a  third  time  with  30  c.  c.  of  water,  and  wash  until  the  filtrate  gives  only 
a  slight  opalescence  with  silver  nitrate  and  nitric  acid.  The -volume  of  the 
filtrate  should  be  about  200  c.  c.  Add  1|  c.  c.  of  concentrated  hydrochloric 
acid,  or  a  corresponding  amount  of  dilute  acid  (8.  c  c.  of  an  acid  of  8%).  Boil 
until  the  bromine  is  expelled,  and  add  to  the  hot  solution,  drop  by  drop,  especi- 
ally at  first,  and  with  constant  stirring,  10  c.  c.  of  a  10%  solution  of  barium 
chloride.  Digest  on  the  water  bath,  or  over  a  low  flame,  with  occasional 
stirring"  until  the  precipitate  settles  clear  quickly.  Filter  and  wash,  using 
either  a  Gooch  crucible  or  a  paper  filter;  the  latter  may  be  ignited  moist  in  a 
platinum  crucible,  using  a  low  flame  until  the  carbon  is  burned. 

In  the  case  of  coals  containing  much  pyrites  or  calcium  sulphate,  the 
residue  of  magnesium  oxide  should  be  dissolved  in  hydrochloric  acid  and  the 
solution  tested  for  sulphuric  acid. 

When  the  sulphur  in  the  coal  is  in  the  form  of  pyrites,  that  compound  is 
converted  almost  entirely  into  ferric  oxide  in  the  determination  of  ash,  and, 
as  three  atoms  of  oxygen  replace  four  atoms  of  sulphur,  the  weight  of  the  ash 
is  less  than  the  weight  of  the  mineral  matter  in  the  coal  by  five-eighths  the 
weight  of  the  sulphur.  While  the  error  from  this  source  is  sometimes  con- 
siderable, a  correction  for  proximate  analyses  is  not  recommended.  When 
analyses  are  to  be  used  as  a  basis  for  calculating  the  heating  effect  of  the  coal, 
a  correction  should  be  made. 

FORMS  OF  REPORTING  ANALYSES 

The  proximate  analysis  of  a  coal  may  be  reported  in  one  of  several  ways. 

An  analysis  designated  as  received  refers  to  the  fact  that  the  sample  received 
no  preliminary  drying  before  analysis  and  usually  represents  the  coal  exactly 
as  mined  or  as  loaded  on  the  railroad  car,  etc. 

An  analysis  marked  as  fired  refers  to  the  fact  that  the  sample  for  analysis 
was  taken  from  the  fuel  in  the  boiler  room,  usually  at  the  time  of  a  test,  and 
represents  the  coal  as  fired  into  the  furnace. 

An  analysis  denoted  air  dried  refers  to  the  fact  that  the  sample  was  dried 
at  a  uniform  temperature,  usually  the  standard  one  of  62°  F.,  for  a  number  of 
hours  before  being  analyzed. 


380 


FUELS 


In  the  first  two  cases,  the  moisture  in  the  sample  is  commonly  reported 
as  moisture,  or  water,  although  the  temperature  at  which  the  water  is  driven 
off  is  sometimes  given.  Thus,  there  are  such  expressions  as  "moisture  at 
212°,"  or  "at  100°,"  "at  221°,"  or  "at  105°,"  depending  on  the  temperature 
and  thermometric  scale  employed. 

In  the  third  case,  the  water  is  reported  in  two  parts.  The  first,  which  rep- 
resents the  difference  in  the  amount  of  water  in  the  sample  as  received  and  after 
being  dried  in  the  laboratory  at  62°  F.  is  known  as  air  drying  loss,  or  as  loss  on 
drying.  The  second  part  represents  the  difference  between  the  water  in  the 
air-dried  sample  and  that  given  off  on  heating  at  105°  C.  This  is  commonly 
reported  as  explained  in  connection  with  the  first  two  cases,  the  temperature 
usually  being  stated. 

An  analysis  reported  moisture  free,  or  as  of  dry  coal,  is  one  in  which  the  sum 
of  the  percentages  of  fixed  carbon,  volatile  matter,  and  ash  equal  100.  The 
moisture  is  reported  as  a  separate  item  like  the  sulphur,  and  usually  as,  say, 
"moisture  at  105°  C." 

An  analysis  reported  as  dry  and  free  from  ash,  or  as  ash  and  moisture  free, 
and  even,  although  wrongly,  as  pure  coal,  is  one  in  which  the  percentages  of 
fixed  carbon  and  volatile  matter  equal  100,  the  moisture  and  ash  being  reported 
separately. 

Analyses  reported  in  one  form  may  readily  be  reduced  to  another.  A 
proximate  analysis  made  on  a  sample  as  received,  as  fired,  or  air-dried,  may  be 
reduced  to  a  moisture-free  basis  by  dividing  each  of  the  constituents,  except 
the  moisture,  by  100  -  moisture.  If  it  is  desired  to  reduce  the  analysis  to  a 
moisture-  and  ash-free  basis,  all  the  constituents  except  the  moisture  and  ash, 
which  are  dropped,  are  divided  by  100— (moisture + ash).  These  divisors  are 
applicable  to  the  sulphur  and  calorific  value  (British  thermal  units)  as  well. 

An  ultimate  analysis  may,  also,  be  reduced  from  the  as  received  to  the 
moisture  free,  or  to  the  ash-  and  moisture-free  basis  by  using  the  same  divisors 
as  before,  provided  the  amount  of  moisture  in  the  coal  is  known.  The  ash, 
sulphur,  carbon,  and  nitrogen  are  divided  in  the  regular  way,  but  from  the 
hydrogen  must  be  deducted  one-ninth  of  the  moisture  and  from  the  oxygen, 
eight-ninths  of  the  moisture. 


COAL  114  FROM  SEWELL  SEAM,  McDONALD,  W.  VA. 


IH      (U 
<g 

Divisor 

Moisture 
Free 

1 
s 

Ash  and 
Moisture 
Free 

Moisture  
Volatile  matter  .  .              

.68 
23.28 

.9932 

23.43 

.9418 

24.71 

4J  M 

70.91 

.9932 

71.40 

.9418 

75.29 

gl 

Ash  

5.14 

.9932 

5.17 

P3 

Total  

100.00 

100.00 

100.00 

ft* 

Sulphur,  separate 

91 

.9932 

.92 

.9418 

.97 

Carbon  

83  56 

.9932 

84.13 

.9418 

88.71 

Hydrogen  (  -  £  moisture)  
Nitrogen  
Oxygen  (  —  f  moisture) 

4.66 
1.60 
4  13 

.9932 
.9932 
.9932 

4.62 
1.61 
3.55 

.9418 
.9418 
.9418 

4.86 
1.70 
3.74 

•a  '35 

Sulphur  

91 

9932 

.92 

.9418 

.97 

6^ 

Ash 

5  14 

9932 

5  17 

11 

b<! 

Total  

100  00 

10000 

100.00 

Calorific  power  

14,765 

.9932 

14,866 

.9418 

15,680 

FUELS  .  *  381 

The  calculation  shown  in  the  table  on  page  380  is  made  upon  a  typical  coal 
from  the  New  River  field,  No.  114  of  the  table  on  pages  382  to  385,  mined  from 
the  Sewell  seam,  at  McDonald,  W.  Va.  The  second  C9lumn  contains  both  the 
proximate  and  the  ultimate  analyses  and  the  calorific  value,  or  power,  in 
British  thermal  units  per  pound.  The  divisor  in  the  third  column  is  obtained 
by  deducting  the  moisture  from  100  and  dividing  by  100,  or  divisor  =  (100 

—  .68)  -T-  100  =  .9932.     By  dividing  all  the  figures  in  the  second  column  by  this 
divisor,  those  in  the  fourth  column  are  obtained,  and  these  represent  the 
composition  of  the  coal  on  a  moisture-free,  or  dry-coal  basis.     The  second 
divisor,  that  in  the  fifth  column,  is  obtained  by  deducting  the  sum  of  the 
moisture  and  ash  from  100  and  dividing  the  result  by  100,  or  divisor  =  (100 

—  .68  — 5. 14) -T- 100  =  .94 18.     The  figures   in  the   second   column    (as  before) 
excepting  the  ash  and  moisture  if  divided  by  this  factor  will  give  the  figures 
in  the  sixth  column,  which  represent  the  composition  of  the  coal  on  an  ash- 
and  moisture-free,  or  on  the  dry-and-free-from-ash  basis. 

In  dealing  with  the  ultimate  analysis,  before  applying  either  divisor,  there 
must  be  deducted  from  the  hydrogen  and  oxygen  one-ninth  and  eight-ninths, 
respectively,  of  the  moisture  (.68)  as  given  in  the  proximate  analysis.  The 
two  dividends  will  be,  respectively,  4.66—  (.68-7-9)  =4.5844,  and  4.13—  (.68  -5-  9) 
X8  =  3.5256. 

Should  it  be  desired  to  give  the  percentage  of  moisture  on  a  moisture-free 
basis,  that  is,  as  a  separate  determination  similar  to  the  sulphur,  it  may  be 
obtained  by  dividing  the  moisture  in  the  original  sample  by  the  factor  in  the 
third  column,  or  moisture,  separately  determined  =  . 68  -4-.. 9932  =  .684.  If  the 
moisture  and  ash  are  desired  on  the  ash-  and  moisture-free  basis,  they  may  be 
had  by  dividing  the  percentage  of  these  constituents  in  the  second  column  by 
the  divisor  in  the  fifth  column,  and  are,  respectively,  .68-7- .94 19  =  .72,  and 
5. 14 -T- .94 19  =  5.45. 

ANALYSES  OF  TYPICAL  COALS 

The  table  on  pages  382  to  385  gives  the  proximate  and  the  ultimate  analyses 
and  the  calorific  values,  in  British  thermal  units  per  pound,  of  a  number  of 
typical  American  coals,  selected  largely  from  the  Reports  of  the  Fuel  Testing 
Plant  at  the  St.  Louis  Exposition  of  1904.  Other  anaylses  are  taken  from 
various  reports  of  the  United  States  Geological  Survey  and  the  United  States 
Bureau  of  Mines.  Except  as  noted,  all  the  analyses  and  heat  determinations 
represent  carload  lots  and  were  made  on  samples  air-dried  at  the  same  temper- 
ature. For  this  reason,  the  relative  values  of  the  different  coals  are  indicated 
by  their  calorific  power  as  given  in  British  thermal  units.  .  The  exceptions  are: 
The  proximate  and  the  ultimate  analyses  and  the  heating  values  of  coals  105, 
110,  and  111  were  made  upon  samples  marked  "as  received";  that  is,  the  pre- 
liminary air-drying  was  omitted,  and  the  analyses  indicate  more  moisture  and 
a  lower  calorific  value  in  these  coals  than  if  they  had  been  air-dried.  Also, 
the  ultimate  analyses,  but  not  the  calorific  values,  of  coals  15,  16,  17,  18,  and 
19,  were  made  upon  samples  as  received. 

In  the  column  headed  Kind,  A  =  anthracite;  B=  bituminous;  B.  L.  =  black 
lignite,  the  subbituminous  coal  of  the  United  States  Geological  Survey;  G.  A. 
=  graphitic  anthracite;  L  =  lignite,  the  true  lignite  or  brown  coal;  P  =  peat; 
S.  A.  =  semianthracite;  S.  B.  =  semibituminous. 

In  the  column  headed  Grade,  L  =  lump;  N  =  nut;  P  =  pea;  R  =  run  of  mine; 
S=^lack  or  culm.  L.  N.  refers  to  a  mixture  of  lump  and  nut;  S.  N.  refers  to  a 
mixture  of  slack  and  nut;  and,  similarly,  for  other  combinations  of  the  letters. 

In  the  proximate  analyses,  the  sums  of  the  moisture,  volatile  matter,  fixed 
carbon,  and  ash  should  equal  100%.  The  sulphur  is  separately  determined. 
In  the  ultimate  analyses,  the  sums  of  the  carbon,  hydrogen,  nitrogen,  oxygen, 
sulphur,  and  ash  should  equal  100%. 

In  the  table  on  page  386  is  given  a  series  of  proximate  analyses  of  Penn- 
sylvania anthracite  and  semianthracite.  Those  marked  C  were  made  on 
samples  of  the  coal  as  received  or  as  fired,  and  represent  a  series  of  monthly 
or  semimonthly  shipments,  usually  extending  over  a  year  and  in  some  cases 
aggregating  15,000  T.  in  weight.  They  were  made  with  great  care  in  order 
to  determine  the  proper  price  to  be  paid  for  the  coal,  which  was  sold  on  analysis. 
The  analyses  marked  D  were  made  on  air-dried  samples  previously  collected 
in  the  mine  by  breaking  down  a  full  section  of  the  working  face.  In  all  cases, 
regardless  of  the  origin  or  preliminary  treatment  of  the  sample  before  analysis, 
the  calorific  values  were  determined  on  air-dried  samples. 

In  the  table  on  page  387,  there  is  given  a  series  of  proximate  analyses  and 
calorific  values  of  some  important  coals  not  contained  in  the  table  on  pages 


382 


FUELS 


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25 


386  FUELS 

PROXIMATE  ANALYSES  AND  HEATING  VALUES  OF  PENNSYLVANIA 
ANTHRACITES 

(United  States  Bureau  of  Mines) 


Moisture 

Volatile 
Matter 

ll 

&CJ 

1 

1 

1 

t> 
H 
PQ 

Morea  broken 

c 

338 

4.86 

8245 

9  31 

60 

13  057 

Deringer,  egg  

c 

3.67 

5.29 

81.42 

9  62 

.66 

13,009 

Kingston,  grate         

c 

3.34 

4.74 

81.08 

10  84 

65 

12,717 

Wilkes-Barre,  screenings.  . 
Nanticoke,  barley  

c 
c 

4.17 
5.45 

5.95 
8.43 

79.02 
72.12 

10.86 
14  00 

.70 
64 

12,654 
12,045 

Mid  Valley,  pea 

r 

395 

7.38 

72  85 

15  82 

92 

11  989 

1 

Deringer,  pea  
Pittston,  pea   .          ... 

C 
r 

5.11 
3  62 

4.99 
5.82 

74.87 
7340 

15.03 
17  16 

.62 

82 

11,831 
11  798 

1' 

Mt.   Hope,   mammoth 
screenings  

r 

560 

6.61 

71  62 

16  17 

75 

11  581 

c 

Newcastle,  pea  

r 

4.93 

5.21 

72.96 

1690 

.65 

11,574 

< 

Schuylkill,  rice  

r 

507 

4.99 

71  58 

18  32 

75 

11  382 

Pittston,  No.  2  buckwheat 
Girard,  mammoth,  buck- 
wheat 

C 

r 

5.93 
6  21 

6.72 
564 

70.35 
70  70 

16.80 
17  45 

.95 
56 

11,359 
11  141 

Mt.  Hope,  barley  
Tower  City,  Lykens  Valley 
Bernice  egg 

C 

r 

6.55 
3.33 
2  12 

5.26 
3.27 
8  80 

70.83 

84.28 
73  43 

17.36 
9.12 
15  65 

.69 
.60 
58 

11,132 
13,351 
12  575 

.-tt 

Bernice,  Randall  &  Shaad 
mine   . 

p 

50 

9  go 

7790 

12  03 

83 

13  510 

1 

Bernice,  O'Boyle  &  Fay 
mine  

p 

60 

9  50 

77  40 

12  49 

1  41 

13  425 

1 

Bernice,  Connell  mine  
Lopez,  Northern  Anthra- 
cite Company  

D 
p 

.70 
.60 

8.65 
9.10 

76.75 
7895 

13.90 
11  35 

.66 
65 

13,185 
13  605 

1 

Loyalsock  

1.49 

11.07 

78.88 

7.09 

.86 

382  to  285.  Those  analyses  marked  C  are  of  commercial  lots  delivered  to  the 
various  government  departments  and  represent  the  coal  as  received  or,  as 
fired.  The  analyses  marked  D  were  made  from  air-dried  samples;  in  some 
cases  they  represent  carload  lots,  and  in  others  they  are  samples  taken  in  the 
mine.  The  calorific  values  were  determined  upon  air-dried  samples  except 
those  given  in  italics,  which  were  calculated  from  the  analysis  by  means  of 
Kent's  formula.  The  analyses  that  are  not  marked  with  a  C  or  a  D  are 
believed  to  represent  air-dried  samples,  but  those  reporting  them  failed  to 
state  the  facts  in  the  case. 

One  of  the  accompanying  tables  gives  a  series  of  analyses  of  Alaskan  coals 
taken  from  the  reports  of  the  United  States  Geological  Survey.  Among  them 
are  three  analyses  of  coals  from  the  Yukon  Territory  of  Canada.  The  report 
does  not  state  whether  the  analyses  are  of  air-dried  or  as-received  samples; 
judging  from  the  amount  of  water  in  some  specimens,  it  is  presumed  that  they, 
at  least,  were  of  samples  as  received.  The  sulphur  is  separately  determined. 

A  series  of  proximate  analyses  of  foreign  coals,  many  of  which  are  used  on 
the  Pacific  coast  of  the  United  States,  is  given  in  the  table  on  page  391. 
JLhe  sample  of  coal  from  Argentine  and  the  one  from  Rio  Grande  do  Sul, 
Brazil,  were  tested  at  the  United  States  Fuel  Testing  Plant,  St.  Louis,  Missouri. 
They  were  treated  in  the  same  way  as  the  samples  of  American  coal  given  in 
the  table  on  page  387.  These  two  analyses  are  of  air-dried  samples  and  the 
heating  values  are  6.320  and  9,058  B.  T.  U.,  respectively.  The  heating  value 
of  the  Victoria  coal  from  Windmill  shaft  is  given  as  12,871  B.  T.  U.  The 
other  analyses  are  taken  from  numerous  authorities,  who  fail  to  state  whether 
they  were  made  on  air-dried  or  on  as-received  samples;  judging  from  the  small 
amount  of  water  in  most  of  them,  the  samples  appear  to  have  been  air-dried 
before  analysis.  The  sulphur  is  usually  separately  determined. 


FUELS 


387 


PROXIMATE    ANALYSES    OF    MISCELLANEOUS    AMERICAN    COALS 

(United  States  Geological  Survey) 


State 

Kind  of  Coal 

Moisture 

Volatile 
Matter 

ll 
*0 

i 

& 
13 

CO 

S> 
H 

« 

Ala. 
Ark. 
Ark. 
Ark. 
Ariz. 
Ariz. 
Ariz. 
Cal. 
Cal. 
Cal. 
Cal. 
Col. 
Col. 
Col. 
Col. 
111. 
111. 
Kans. 
Ky. 
Ky. 
Ky. 
Ky. 
Md. 
Mich. 
Mich. 
Mich. 
Mont. 
Mont. 
Mont. 
N.  Mex. 
Ore. 
Ore. 
Ore. 
Pa. 
Pa. 
Pa. 
Utah 
Utah 
Utah 
Va. 
Va. 
Va. 
Va. 
W.  Va. 

W.  Va. 

W.  Va. 
W.  Va. 
W.  Va. 
W.  Va. 

W.  Va. 

D 
D 
D 
D 
D 
D 
D 
D 
D 

D 
D 
D 
D 
C 
C 
C 
D 
D 
D 
D 

D 
D 
D 
D 
D 
D 

D 

D 
C 
C 
C 
D 
D 
D 

D 
D 
D 

C 
C 
C 

C 
C 

1.33 
1.12 
1.03 
.68 
7.80 
8.10 
9.89 
4.86 
18.02 
12.20 
11.32 
6.80 
6.60 
5.50 
2.80 
7.93 
7.08 
3.50 
1.62 
1.78 
1.44 
1.68 
.70 
8.71 
3.78 
10.67 
1.00 
.60 
1.10 
5.70 
9.60 
10.41 
9.49 
2.42 
3.04 
2.56 
3.10 
4.04 
4.37 
2.98 
1.11 
1.01 
1.07 

.75 

.73 
2.50 
3.18 
2.36 

3.08 
2.63 

30.55 
11.54 
10.53 
9.93 
33.80 
33.30 
39.07 
47.74 
39.22 
35.20 
45.09 
36.50 
35.30 
37.80 
5.05 
34.23 
34.94 
33.73 
32.68 
34.27 
31.80 
33.20 
18.81 
38.45 
41.18 
33.59 
20.00 
30.30 
28.20 
2.18 
36.30 
46.15 
23.87 
20.31 
29.79 
16.47 
40.58 
43.23 
41.84 
10.94 
31.79 
32.70 
32.83 

38.16 

17.43 
20.58 
30.57 
18.56 

17.56 
18.25 

58.88 
78.62 
80.06 
79.94 
44.50 
47.80 
46.95 
41.03 
26.39 
41.40 
35.91 
50.28 
52.44 
48.49 
77.55 
49.78 
48.60 
52.43 
57.39 
55.55 
56.84 
61.35 
72.96 
41.16 
49.34 
53.80 
55.19 
57.75 
50.57 
86.13 
40.90 
36.85 
32.54 
70.13 
60.85 
71.58 
48.10 
47.27 
47.77 
64.14 
61.36 
60.39 
58.68 

54.63 

77.71 
71.70 
59.40 
71.70 

74.79 
73.87 

9.24 

8.72 
8.38 
9.43 
13.90 
10.84 
4.05 
6.37 
16.37 
11.20 
7.68 
6.42 
5.66 
8.21 
14.60 
8.06 
9.38 
10.34 
8.31 
8.40 
9.92 
3.77 
7.26 
11.68 
5.70 
1.94 
23.81 
11.35 
20.13 
5.99 
13.20 
6.59 
34.10 
7.14 
6.32 
9.39 
8.22 
5.46 
6.02 
21.94 
5.74 
5.90 
7.42 

6.45 

4.63 
5.22 
6.85 
7.38 

4.57 
5.25 

2.10 
2.01 
2.51 

1.76 
1.30 
1.14 
.42 
4.26 
3.07 
4.58 

.44 
.98 
.53 
.60 
1.79 
2.19 
4.60 
1.07 
.83 
.56 
.60 
1.01 
2.72 
2.50 
1.01 
.44 
.87 
1.37 
.69 

1.02 
1.18 
1.10 
1.23 
.93 
.54 
.58 
.89 
.68 
1.48 
.85 
.67 

2.30 

.62 

.74 
.92 
.81 

.66 
.64 

13,884 
13,853 
13,965 
13,896 
10,650 
11,020 
12,101 
12,727 
8,105 
10,130 

11,833 
12,001 
10,885 
12,563 
12,215 
12,151 
12,989 
18,664 
13,357 
13,473 
14,228 
14,626 
12,359 
13,489 
12,868 
11,420 
13,610 
11,790 
13,268 
9,720 

7,683 
14,087 
14,040 
13,748 
11,956 
11,729 
11,908 
11,669 
14,276 
14,203 
13,910 

13,509 

15,032 
14,533 
13,849 
14,135 

14,557 
14,528 

Semianthracite,  Spadra  
Semianthracite,  Clarksvil],e 
Semianthracite,  Russelville. 
Tuba,  Black  Mesa  Field  
Oraibi,  Black  Mesa  Field  .  .  . 
St.  Michael  

Stone  Canon  

Tesla 

Trafton  

Mean  of  ten  analyses 

Canon  City,  Chandler  
Canon  City  Nonac 

Colorado  Springs,  Cell  
Crested  Butte 

Pawnee,  washed  nut  
Pana,  washed  nut  
Cherokee  lump  
Elkhorn  Field.  Millard  
Elkhorn  Field,  Flatwoods.  .  . 
Elkhorn  Field,  L.  Elkhorn  .  . 
Elkhorn  Field,  U.  Elkhorn  .  . 
Georges  Creek,  av.  53  anal.  .  . 
Bay  City,  Lower  Verne  .... 
Bay  City,  Upper  Verne  .... 
Saginaw  

Electric  Field 

Electric  Field  

Electric  Field 

Madrid  
Coos  Bay  average.  . 

Coos  Bay,  average  
Rogue  Riv.  Valley,  Medford 
Cambria  Co.,  Beech  Creek.  . 
Reynoldsville  

Somerset  County,  C'  bed  .  .  . 
Castle  Gate  -.  
Price 

Winter  Quarters  
Blacksburg  .  . 

Dante,  Widow  Kennedy.  .  .  . 
Dante,  Lower  Banner  
Dante  Upper  Banner 

Fairmont,  average  of  sixty- 
three  mines  
Pocahontas,     "  average      of 
thirty-eight  mines  
Piney,  Raleigh  County  
Kanawha  Gas.  

Pocahontas,  No.  3,  3-in. 

Pocahontas,  No.  3,  M.R  

388 


FUELS 


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FUELS 


A  series  of  proximate  analyses  and  heating  values  of  Canadian  coals  arranged 
by  provinces,  coal  fields,  mines,  etc.,  is  given  in  the  table  on  pages  388  and  389. 
The  analyses  and  heating- value  determinations  were  made  on  samples  dried  at 
212°  P.,  consequently  the  sum  of  the  volatile  matter,  fixed  carbon,  and  ash 
equals  100.  Both  the  moisture  and  sulphur  were  separately  determined  and 
do  not  enter  in  this  total.  By  reason  of  the  analyses,  etc.  being  made  on  dry 
samples,  the  values  in  the  table  are  higher  than  if  made  on  air-dried  samples 
and  cannot  be  compared  with  those  given  in  the  table  on  pages  382  to  385.  The 
samples  were  collected  at  the  mine  either  at  the  working  face  or  from  coal  being 
shipped  and  represent  several  tons  in  each  case.  The  following  abbreviations 

PROXIMATE  ANALYSES  OF  ALASKAN  COALS 

(United  States  Geological  Survey) 


District  and  Kind  of  Coal 

Mois- 
ture 

Volatile 
Matter 

Fixed 
Carbon 

Ash 

Sul- 
phur 

Anthracite 
Bering    River,   average    of    seven 
analyses  

7.88 

6.15 

78.23 

7.74 

1.30 

Matanuska  River  

2.55 

7.08 

84.32 

6.05 

.57 

Semianthracite 
Bering   River,   average   of   eleven 

5.80 

887 

7606 

9  27 

1  08 

Semibituminous 
Bering  River,  average  of  twenty- 
eight  analyses  

4.18 

14.00 

72.42 

9.39 

1.73 

Cape  Lisburne,   average  of  three 
analyses  

3.66 

17.47 

75.95 

2.92 

.96 

Matanuska  River,  average  of  six- 
teen analyses    .  .  . 

2.71 

20  23 

6539 

11.60 

57 

Bituminous 
Lower  Yukon,  average  of  eleven 
analyses  

4.68 

31.14 

56.62 

7.56 

.48 

Subbituminous,  or  black  lignite 
Matanuska  River,  average  of  four 
analyses  

6.56 

3543 

49.44 

8.57 

.37 

Koyukuk  River  

4  47 

34  32 

48  26 

12.95 

1  39 

40  02 

55  55 

3  04 

2  98 

Alaska  Peninsula,  average  of  five 
analyses 

234 

38  68 

49  75 

9  22 

1  07 

Cape  Lisburne,  average  of  eleven 
analyses       

9  35 

3801 

47  19 

5  45 

35 

6  85 

36  39 

43  38 

13  38 

54 

Port  Graham  

16  87 

37  48 

39  12 

6.53 

.39 

Southeast  Alaska,  average  of  five 
analyses  
Wain  wright  Inlet  .  .    . 

1.97 
10  65 

37.84 
42  99 

35.18 
42  94 

24.23 
3  42 

.57 
62 

Colville  River 

11  50 

30  23 

30  27 

27  90 

50 

Upper  Yukon,  Canada,  average  of 
thirteen  analyses                            ' 

13  08 

39  88 

39  28 

7  72 

1  26 

Upper    Yukon,    Circle    Province, 
average  of  three  analyses 

10  45 

41  81 

40  49 

7  27 

1  30 

Upper  Yukon,  Rampart  Province, 
average  of  six  analyses  

11  42 

41  15 

36  95 

1048 

.33 

Seward  Peninsula  

24  92 

38  15 

33  58 

3  35 

68 

Chitistone  River.   . 

1  65 

51  50 

40  75 

6  10 

Katchemak    Bay,    average   of   six 
analyses  

19  85 

40  48 

30  99 

8  68 

35 

N  en  ana  River  .  . 

13  02 

48  81 

32  40 

5  77 

16 

Kodiak  Island  
Unga  Island,  average  of  two  analy- 
ses   

12.31 
10  92 

51.48 
53  36 

33.80 
28  25 

2.41 

7  47 

.17 
1  36 

Tyonck,  average  of  four  analyses.  .  . 
Chistochina  River  .  . 

8.55 
15  91 

54.20 
60  35 

30.92 
19  46 

6.53 
4  28 

3.38 

FUELS 


391 


are  used:  L,  lump;  R,  run  of  mine;  B,  buckwheat  (anthracite);  P,  pea  (anthra- 
cite); Sa,  mine  sample;  A.  Ry.  &  I.  Co.,  Alberta  Railway  and  Irrigation  Co.: 
B.  Mines,  Bankhead  Mines,  Ltd.;  C.  C.  &  Ry.  Co.,  Cumberland  Coal  and 
Railway  Co.;  C.  P.  C.  Co.,  Crowsnest  Pass  Coal  Co.;  C.  W.  C.  Co.,  Canada 
West  Coal  Co.;  Dom.  C.  Co.,  Dominion  Coal  Co.;  E.  C.  &  B.  Co.,  Eureka 
Coal  and  Brick  Co.;  H.  C.  &  C.  Co.,  Hillcrest  Coal  and  Coke  Co.;  H.  M., 
Hosmer  Mines,  Ltd.;  I.  C.  &  C.  Co.,  International  Coal  and  Coke  Co.;  I.  C. 

PROXIMATE  ANALYSES  OF  FOREIGN  COALS 

(Various  Authorities) 


Coal 

Mois- 
ture 

Vola- 
tile 
Matter 

Fixed 
Carbon 

Ash 

Sul- 
phur 

Argentine,  Province  of  Mendoza  
Brazil,  Rio  Grande  do  Sul  
Brazil,  Pernambuco  
British  Columbia,  Crowsnest  Pass, 

7.67 
10.96 
1.90 

1  09 

18.39 
26.78 
18.82 

21  07 

31.00 

38.82 
58.73 

7054 

42.85 
23.44 
20.55 

7  29 

1.21 
2.94 

37 

British  Columbia,  Comox,  average  .  .  . 
British  Columbia,  Nanaimo,  average  . 
Chili,  Straits  of  Magellan  
England,  Durham,  coking  average  
England,  South  Durham,  Brockwell.  . 
England,  South  Durham,  Busty  seam  . 
England,  Bearspark  colliery  

1.18 
2.12 
1.64 
.91 
1.12 
.86 
.85 
4  84 

28.41 
34.07 
24.85 
13.12 
22.05 
25.24 
27.06 
34  07 

62.91 
55.94 
69.52 
81.54 
72.17 
68.24 
68.97 
46.33 

7.49 
7.93 
3.99 
4.43 
4.66 
5.66 
3.12 
14.76 

1.54 
.64 
.97 
.92 
1.22 
1.30 
.78 
1.08 

6  00 

34  00 

4304 

1696 

1  20 

ndia  Johilla  

5  76 

33.03 

44.22 

16.99 

.42 

fapan,  average  eight  analyses  
apan  Yubari  mine          

2.62 
1.22 

42.49 
42.43 

50.07 
51.75 

4.82 
4.60 

.92 
.47 

1  63 

30  14 

6072 

7  51 

.27 

apan,  Poronai  mine,  Seam  2  

2.59 
1  77 

36.83 
4796 

56.32 
42  62 

4.26 
7  65 

.60 
.16 

Mexico,  Sabinas  Coal  Co.,  Sabinas  .  .  . 
Mexico,  Coahuila  Coal  Co.,  Coahuila. 
New  South  Wales,  Southern  Field, 

.69 
.39 

97 

22.46 
19.91 

23  10 

58.05 
64.93 

56  26 

18.80 
14.77 

10  67 

.86 
.46 

^ew  South  Wales,  Western,  average.  . 
^ew  South  Wales,  Northern,  average, 
^ew  South  Wales,  Killingworth  mine  . 
New  Zealand,  Lake  Coleridge  

1.87 
1.92 
1.24 
1  80 

31.49 
35.09 
38.82 
1  96 

52.61 
51.08 
32.46 
84.12 

14.03 
8.91 
27.48 
12.12 

.63 
.54 
3.50 

sTew  Zealand,  Millerton  Mines  
New  Zealand,  Paparoa,  Beds  1,  2,  3.  . 
slew  Zealand,  Paparoa,  Beds  4,  5  
New  Zealand,  Xaitongata  mines  

1.16 
1.03 

.78 
20.06 

20.50 
16.38 
23.55 
28.93 

74.83 
78.78 
72.77 
44.60 

3.51 
3.81 
2.90 
6.41 

.29 
.48 

New  Zealand  Westport  mines 

2  60 

37  17 

5601 

4.22 

Nova  Scotia,  Sydney,  average  

10.60 

39.20 

56.70 

5.10 

1.20 

Philippines,  Compostella,  Cebu  
Philippines  Mt.  Uling  Cebu 

7.80 
6  30 

37.56 
35  30 

51.96 
53  55 

2.68 
4  45 

.40 

3hilippines,    average   nine   analyses, 
Cebu                                    

1400 

31  08 

5035 

4.58 

Philippines  Batan 

5  82 

40  29 

52  40 

1  49 

66 

Philippines,  Batan  

4.53 

45.89 

46.96 

2.62 

.39 

Philippines  Batan  

5  62 

38  68 

54  42 

1.36 

.14 

Philippines,  Batan  

6.08 

40.36 

51.24 

2.32 

.40 

Philippines,  Batan,  average  five 

13  57 

3691 

44  92 

4  60 

Scotland,  Lanarkshire  splint  
Pransvaal,  Brugspruit  
Transvaal  Bethel 

6.86 
.80 
30 

34.42 
28.02 
41  23 

55.53 
64.62 
52  16 

3.19 
6.56 
631 

.70 
.86 
Trace 

Transvaal,  Springs  
Victoria,  Coal  Creek,  Bed  2  
Victoria  Windmill  shaft 

.57 
7.00 
594 

14.10 
21.60 
33  67 

63.00 
55.66 
55  23 

22.00 
12.35 
5  16 

392  FUELS 

&  Ry.  Co.,  Inverness  Coal  and  Railway  Co.;  I.  C.  Co.,  Intercolonial  Coal  Co.; 
L.  B.  C.  Co.,  Lund  Breckenridge  Coal  Co.;  Leitch,  Leitch  Collieries,  Ltd.; 
M.  Coal  Co.,  Minudie  Coal  Co.;  No.  Atl.  Cols.,  North  Atlantic  Collieries, 
Ltd.;  N.  S.  S.  &  C.  Co.,  Nova  Scotia  Steel  and  Coal  Co.;  N.  V.  C.  &  C.  Co., 
Nicola  Valley  Coal  and  Coke  Co.;  P.  C.  Co.,  Parkdale  Coal  Co.;  P.  C.  C.  Co., 
Pacific  Coast  Coal  Co.;  P.  H.,  R.  Ry.  &  C.  Co.,  Port  Hood,  Richmond,  Rail- 
way and  Coal  Co.;  S.  C.  Co.,  Strathcona  Coal  Co.;  St.  C.  Co.,  Standapd  Coal 
Co.;  W.  C.  Co.,  Wellington  Colliery  Co.;  W.  C.  Cols.,  West  Canadian  Col- 
lieries; W.  D.  Cols.  Co.,  Western  Dominion  Collieries  Co.;  W.  F.  Co.,  Western 
Fuel  Co.;  W.  P.  &  Y.  Ry.  Co.,  White  Pass  and  Yukon  Railway  Co.,  Ltd. 

DETERMINATION  OF  HEATING  VALUE  OF  COAL  FROM  A 
PROXIMATE  ANALYSIS 

A  very  good  idea  of  the  calorific  power  of  a  coal ,  from  a  commercial  stand- 
point at  least,  may  be  obtained  from  a  proximate  analysis  by  some  simple  cal- 
culations. Of  the  two  methods  of  doing  this,  that  devised  by  William  Kent 
and  known  by  his  name  has  a  fairly  general  application.  A  method  devised 
by  Lord  and  Haas  is  restricted  to  a  given  field,  but  for  the  coals  within  that 
field  it  is  probably  more  accurate  than  Kent's. 

Kent's  Method. — According  to  Kent,  a  relation  exists  between  the  amount 
of  fixed  carbon  in  the  combustible  portion  of  a  coal  (coal  ash-and-moisture 
free,  according  to  the  fifth  column  in  the  calculation  given  under  the  head 
Proximate  Analysis  of  Coal  ante)  and  its  calorific  value  per  pound  of  combus- 
tible, which  is  shown  in  the  following  table. 

These  figures  are  correct  within  2%  for  all  coals  containing  more  than  63% 
of  fixed  carbon  in  the  combustible,  but  for  coals  containing  less  than  60% 
fixed  carbon  or  more  than  40%  volatile  matter  in  the  combustible  they  are 
liable  to  an  error,  in  either  direction,  of  about  4%.  The  greater  variation 
in  the  coals  low  in  fixed  carbon  and  high  in  volatile  matter  is  due  to  the  fact 
that  they  differ  considerably  in  the  percentage  of  oxygen  in  the  volatile  matter. 

APPROXIMATE  HEATING  VALUE  OF  COALS 


Per  Cent,  of  Fixed  Carbon 

Heating  Value  per  Pound  Combustible 

in  Coal  Dry  tind.  Free 

From  Ash 

B.  T.  U. 

Calories 

100 

14,580 

8,100 

97 

14,940 

8,300 

94 

15,210 

8,450 

90 

15,480 

8,600 

87 

15,660 

8,700 

80 

15,840 

8,800 

72 

15,660 

8,700 

68 

15,480 

8,600 

;.V      63 

15,120 

8,400 

60 

14,760 

8,200 

57 

14,220 

7,900 

55 

13,860 

7,700 

53 

13,320 

7,400 

51 

12,420 

6,900 

B  T  U 


Method  of  Lord  and  Haas. — The  following  formula  is  based  on  extensive 
experiments  made  at  the  Ohio  State  University  by  Messrs.  Lord  and  Haas 
and  the  results  calculated  by  it  have  been  found  to  agree  very  closely  with  those 
obtained  with  the  Mahler  calorimeter. 

>-^A-5-M)  +  (5X4.050) 

100 

A,  sulphur  5,  and  moisture  M  are  expressed  as  percentages, 
and  K  is  a  constant  determined  from  a  number  of  chemical  and  calorimetric 
determinations  by  the  following  formula,  in  which  the  values  substituted  are 
the  averages  of  a  number  of  analyses: 

K_     B.  T.  U.- (sulphur X 4,050) 

100-  (ash + sulphur + moisture)  ™ 


FUELS  393 

These  gentlemen  found  that  the  value  of  K,  which  depends  on  the  amount 
of  moisture,  ash,  and  sulphur  in  the  coal,  is  practically  constant  for  the  same 
coal  in  the  same  field,  regardless  of  any  local  variation  in  the  relative  propor- 
tions of  these  constituents.  The  value  of  K  as  determined  by  them  for  various 
coals  from  Ohio,  Pennsylvania,  and  West  Virginia  is  given  in  the  following 
table. 

VALUE  OF  K  FOR  VARIOUS  COALS 


Coal 

Value  of  K 

Upper  Preeport,  Ohio  and  Pennsylvania  

15,116 

Pittsburg,  Pennsylvania  -.  

15,183 

Middle  Kittanning  (Darlington  coal),  Pennsylvania 

15062 

Middle  Kittanning  (Hocking  Valley  coal),  Ohio.  .  . 

14,265 

Thacker,  West  Virginia  

15,410 

Pocahontas,  West  Virginia 

15  829 

Fairmount,  West  Virginia  

15,675 

ILLUSTRATION  1.  —  Lord  and  Haas'  Method.  —  Using  coal  No.  103  from  Poca- 
hontas, Va.,  as  the  sulphur  is  separately  determined  in  the  usual  way,  the  per- 
centages of  ash  and  moisture  must  be  recalculated,  to  what  they  would  be  if 
the  sulphur  were  included.  This  is  done  by  dividing  them  by  (100  +S)  -f-  100 
=  1.0074,  as  the  coal  contains  .74%  of  sulphur.  Prom  this  the  adjusted 
moisture  and  ash  are,  respectively,  1.62%  and  5.82%.  The  value  of  K  to 
be  used,  15,829,  is  taken  from  the  table.  Substituting  in  formula  1: 
B  T  U  =  15.829X(100-5.82-.74- 


As  the  true  calorific  value  is  14,672,  the  difference  is  108  B.  T.  U.,  or  .736%. 

Kent's  Method.  —  Using  the  same  coal  as  before,  No.  103,  from  the  Poca- 
hontas field  in  Virginia,  the  heating  value  of  which  has  been  determined  by 
calorimeter  to  be  14,672  B.  T.  U.  per  lb.,  the  proximate  analysis  is:  Mois- 
ture, 1.63%;  volatile  matter,  17.17%;  fixed  carbon,  75.34%;  and  ash,  5.86%; 
the  sum  of  these  four  constituents  is  100%.  The  coal  dry  and  free  from  ash 
is  made  up  of  75.34-1-  (75.34  +  17.17  =  92.51)  =81.44%  of  fixed  carbon,  and 
17.17^7-  (75.34  +  17.17  =  92.51)  =  18.56%  of  volatile  matter.  By  interpolating 
in  the  second  column  of  the  table,  the  heating  value  per  pound  of  combustible 
of  a  coal  dry  and  free  from  ash,  and  containing  81.44%  of  fixed  carbon,  is  found 
to  be  15,803  B.  T.  U.  As  just  shown,  the  total  combustible  (the  sum  of  the  fixed 
carbon  and  volatile  matter)  in  the  coal  is  92.51.  Hence,  the  calorific  value 
of  this  coal  is  15,803  X.  9251  =  14,619  B.  T.  U.  This  agrees  very  closely  with 
the  calorimetric  value,  the  difference  being  but  48  B.  T.  U.,  or  .361%. 

ILLUSTRATION  2.  —  Kent's  Method.  —  Using  coal  No.  78,  of  the  table  given 
on  pages  382  to  385,  from  Henryetta,  Okla.,  the  heating  value  of  which  is 
12,620  B.  T.  U.,  and  which  contains  by  analysis:  Moisture,  3.87%;  volatile 
matter,  35.73%;  fixed  carbon,  50.05%;  and  ash,  10.35%.  The  fixed  carbon 
in  the  coal  dry  and  free  from  ash  is  58.35%  and  the  volatile  matter  is  41.65%. 
By  interpolating  in  the  second  column  of  the  table  giving  the  approximate 
heating  value  of  coals,  the  calorific  value  of  a  coal  per  pound  of  combustible  and 
containing  58.35%  of  fixed  carbon  on  a  dry  and  ash-free  basis,  is  14,463  B.  T.  U. 
But  the  total  combustible  (fixed  carbon  +  volatile  matter)  in  this  coal  is 
50.05+35.73  =  85.78%,  hence  its  heating  value  is  14,463  X.  8578=  12,406 
B.  T.  U.  This  differs  from  the  true  calorific  value  by  214  B.  T.  U.,  or  1.6%. 
It  will  be  noted,  however,  that  this  coal  contains  less  than  60%  of  fixed  carbon, 
and  is,  thence,  within  the  group  in  which  the  formula  does  not  apply  within  4%. 

Lord  and  Haas'  Method.  —  Taking  the  coal  just  used  and  recalculating  the 
analysis  to  include  the  sulphur,  the  analysis  is:  Moisture,  3.80%;  ash,  10.15%: 
and  sulphur,  1.95%.  The  recalculated  volatile  matter  is  35.03%,  and  fixed 
carbon  49.07%.  This  coal  is  not  included  in  the  table  of  those  for  which 
the  value  of  K  has  been  determined.  It  is  possible,  however,  for  illustrative 
purposes  only,  to  assume  a  value  for  this  constant. 

In  content  of  volatile  matter  this  coal  is  not  unlike  No.  82  from  the  Pitts- 
burg  seam,  at  Ellsworth,  Pa.,  35.73%  as  against  34.83%.  Using  the  value 
of  K,  15,183,  for  the  Pittsburg  seam,  and  substituting  in  formula  1,  gives  for 
the  calorific  value  of  this  coal  12,848  B.  T.  U.  per  lb.  This  is  228  B.  T.  U., 
or  1.80%,  greater  than  the  true  value,  12,620  B.  T.  U. 


394  FUELS 

In  the  amount  of  fixed  carbon,  49.07%,  this  coal  is  not  unlike  No.  75,  a 
Hocking  coal  from  Dixie,  Ohio,  carrying  46.08%  of  fixed  carbon.  Using  the 
value  of  K,  14,265,  for  Hocking  coal,  and  substituting  in  the  formula,  gives 
the  calorific  value  of  coal  No.  78  to  be  12,076  B.  T.  U.  This  is  544  B.  T.  U., 
or  4.31%  less  than  the  true  value. 

The  illustrations  show  that  while  this  method  gives  excellent  results  with 
those  coals  for  which  the  value  of  K  has  been  experimentally  determined,  it 
cannot  be  relied  on  to  give  good  results  where  K  is  unknown.  Nor  do  Messrs. 
Lord  and  Haas  make  any  such  claim  for  it. 

DETERMINATION  OF  HEATING  VALUE  OF  COAL  FROM  AN 

ULTIMATE  ANALYSIS 

Dulong's  Formula. — The  available  method  of  determining  the  heating 
value  of  coal  from  an  ultimate  analysis  is  based  on  the  formula  devised  by 
Dulong  and  known  by  his  name.  The  amount  of  heat  obtained  in  the  burning 
of  1  Ib.  of  coal  under  theoretically  perfect  conditions  is  expressed  as  follows: 

Lb.  Cal.  =  8,080C+34,462(tf-~)  +2,2505 

in  which  C,  H,  O,  and  5  are  the  percentages  of  the  elements  the  symbols  repre- 
sent and  the  coefficients  are  the  calories  evolved  in  burning  1  Ib.  of  carbon, 
hydrogen,  and  sulphur,  respectively.  The  figures  within  the  parenthesis 

(H )  represent  the  available  hydrogen,  i.  e.,  the  amount  of  that  element  over 

and  above  that  required  to  combine  with  the  oxygen  to  form  water.  American 
engineers  commonly  employ  the  British  thermal  unit  in  place  of  the  pound- 
calorie.  However,  if  calculations  are  made  in  pound-calories,  they  may 
readily  be  reduced  to  British  thermal  units  by  multiplying  by  1.8. 

In  terms  of  the  British  thermal  unit,  the  formula  becomes, 
B.  T.  U.  =  14,544C+62,032.ff +4,0505 

In  this  formula  C,  H,  O,  and  5  are  the  percentages  of  carbon,  hydrogen, 
oxygen,  and  sulphur,  respectively,  as  determined  by  an  ultimate  analysis,  and 
14,544,  62,032,  and  4,050,  are  the  number  of  British  thermal  units  evolved  in 
burning  1  Ib.  of  those  of  the  foregoing  elements  that  are  combustible. 

ILLUSTRATIONS. — Using  coal  No.  103  from  Pocahontas,  Va., 

B.  T.  U.  =  14,544X.8314+62,032X(.0458-^|^)+4,050X.0075  = 

This  is  within  69  B.  T.  U.,  or  .470%  of  the  calorimeter  value. 
In  the  case  of  coal  No.  78,  from  Henryetta,  Okla., 

B.  T.  U.  =  14,544X.6985+62,028x(.0514-1i^p)+4,050X.0199  = 

which  is  73  B.  T.  U.,  or  .58%,  too  low. 

Dulong's  formula  may  be  relied  on  to  give  results  within  2%  of  the  true 
calorimetrically  determined  value,  and  the  agreement  is  generally  much  closer, 
as  has  been  shown.  It  should  be  remembered  that  if  the  more  accurate  values 
for  the  calorific  powers  of  the  combustible  elements  are  substituted  in  the  for- 
mula, the  results  obtained  are  lower  than  those  had  through  the  use  of  the 
earlier  and  approximate  ones. 

A  comparison  of  the  results  obtained  in  calculating  the  heating  values  of 
coals  No.  103  and  No.  78,  by  the  different  methods  available  is  here  given  in 
tabular  form. 

No.  103        No.  78 
Method  Employed  B.  T.  U.      B.  T.  U. 

Actual  value  by  calorimeter 14,672  12,620 

Dulong's  formula 14,603  12,547 

Kent's  formula 14,619  12,406 

Lord  and  Haas'  formula 14,564 

Lord  and  Haas'  formula,  K  for  Pittsburg  coal,  in 

No.  78 12,848 

Lord  and  Haas'  formula,  K  for  Hocking  coal,  in 

No.  78 12,076 


•FUELS 


PETROLEUM  AS  FUEL 

Next  to  natural  gas,  petroleum  is  the  ideal  fuel,  1  Ib.  of  it  having  a  heating 
value  about  50%  greater  than  1  Ib.  of  average  coal.  Of  the  209,556,048  bbl. 
produced  in  the  United  States  in  1910,  24,586,108  bbl.  were  used  for  fuel  by 
the  railroads  along  the  Pacific  coast  and  in  the  Southwest,  displacing,  say, 
some  7,000,000  T.  of  coal.  If  to  the  consumption  of  the  railroads  is  added  that 
of  steamships,  central-station  power  plants,  and  other  large  industrial  con- 
cerns, it  is  probable  that  the  amount  of  oil  used  as  fuel  in  the  regions  named 
is  equivalent  to  about  20,000,000  T.  of  coal. 

Petroleum  is  a  dark  greenish-black  to  light-brown  oil  produced  by  the 
decomposition  of  organic  matter  contained  in  the  rocks,  but  whether  the 
organic  matter  is  of  vegetable  or  animal  origin  is  undetermined.  The  oil  con- 
sists of  a  series  of  hydrocarbons  that  may^be  distilled  off  in  a  series  of  gradually 
increasing  density  as  the  temperature  is  increased.  The  residue,  consisting  of 
the  least  volatile  portion,  which  comnwnly  remains  as  a  solid  known  as  the 
base,  affords  a  means  of  classifying  oils  into  three  groups:  paraffin  oils,  asphalt 
oils,  and  qlefin  oils. 

The  oils  in  the  first  group  are  those  produced  in  the  eastern  and  middle 
western  states  and  being  limited  in  production  and  high  in  yield  of  very  valu- 
able light  oils  (gasoline,  kerosene,  etc.)  are  too  high  in  cost  to  be  used  as  fuel. 
In  the  second  group  come  the  oils  of  California  and  Texas,  produced  in  large 
quantities  and  at  low  cost,  and  furnishing  the  vast  bulk  of  the  fuel  oil  used 
in  the  West  and  Southwest.  In  the  third  group  are  the  oils  of  Baku,  Russia, 
on  the  Caspian  Sea,  and,  except  in  so  far  as  they  possibly  displace  American 
coal  in  foreign  markets,  are  of  no  especial  interest  to  the  mining  engineer. 

Composition  of  Crude  Petroleum. — Petroleum  in  the  fo  rm  in  which  it  issues 
from  the  earth  is  known  as  crude  oil.  It  usually  contains  from  83  to  87%  of 
carbon;  from  10  to  16%  of  hydrogen;  and  small  amounts  of  oxygen,  nitrogen, 
and  sulphur.  Crude  oil  contains  from  less  than  1%  to  over  30%  of  water. 
The  amount  of  wa,ter  depends  largely  on  the  care  with  which  the  oil  is  pumped 
from  the  well.  The  oil  from  old  producing  wells  commonly  contains  more 
water  than  that  from  wells  newly  drilled.  In  fact,  in  many  districts,  the  per- 
centage of  water  gradually  increases  during  the  life  of  the  well,  eventually  the 
entire  output  being  salt  water.  As  the  amount  of  water  in  the  crude  oil  is 
uncertain  and  variable  and  as  it  separates  out  if  left  undisturbed,  allowance 
must  be  made  therefor  in  providing  storage  or,  as  more  commonly  called, 
tankage.  The  accompanying  table  gives  the  ultimate  analyses  of  oils  from 
various  sources. 

As  stated,  the  various  hydrocarbons  composing  crude  petroleum  may  be 
separated  by  distillation  at  different  temperatures;  thus,  gasoline  is  driven  off 
by  heating  from  140°  to  158°  P.;  a  light  benzine  or  naphtha  at  from  158°  to 
248°  P.;  heavier  benzines  at  248°  to  347°  P.;  kerosene,  or  ordinary  illuminating 
oil,  at  338°  P.  and  upwards;  lubricating  oils  at  482°  P.  and  above;  paraffin 
wax  at  a  higher  temperature;  leaving  a  tarry  residuum  that  may  be  further 
distilled  until  nothing  but  a  small  quantity  of  coke  remains  in  the  still.  If  the 
distillation  is  stopped  after  the  kerosene  has  been  driven  off,  the  residue  may 
be  used  for  fuel  oil. 

Flash  Point  and  Firing  Point. — If  a  sample  of  fuel  oil  or  of  crude  oil  is 
placed  in  an  open  cup  and  heat  is  applied,  the  oil  will  begin  to  vaporize  and 
inflammable  gases  will  be  driven  off.  If,  while  the  heating  proceeds,  a  lighted 
match  is  passed  at  intervals  over  the  surface  of  the  oil  and  about  f  in.  from  it, 
a  point  will  be  reached  at  which  the  vapor  rising  from  the  oil  will  ignite  and 
burn  with  a  flicker  of  blue  flame.  The  temperature  of  the  oil  when  this  flame 
first  becomes  apparent  is  termed  the  flash  point  of  the  oil.  If  the  heating  of  the 
sample  is  continued,  the  vapors  will  be  given  off  more  rapidly  and  eventually 
they  will  ignite  and  burn  continuously  at  the  surface  of  the  oil  when  the  lighted 
"  match  is  brought  near.  The  temperature  of  the  oil  when  the  burning  becomes 
continuous  is  termed  the  firing  point  of  the  oil.  The  flash  point  and  the  firing 
point  of  an  oil  depend  on  the  composition,  specific  gravity,  and  source  of  the  oil. 
As  a  general  rule,  the  heavier  oils  have  a  much  higher  flash  point  than  the 
lighter  ones  and  an  attempt  has  been  made  to  use  this  as  a  basis  for  classifying 
them.  A  specific  giavity  of  .85  is  taken  as  the  basis,  oils  heavier  than  this 
having  a  flash  point  above  60°  P.,  and  oils  lighter  than  this  having  a  flash  point 
lower  than  60°  P.,  although  this  is  very  far  from  always  being  true.  It  is 
obvious  that  a  high  flash  point  is  very  desirable  in  a  fuel  oil  in  order  to  avoid 
danger  of  explosion. 


FUELS 
ULTIMATE  ANALYSES  OF  CRUDE  PETROLEUM 


c 
U 

Hydrogen 

c 

| 

5 

1 
1 

fc 

I 

If 
SB 

wO 

Flash  Point 
Degrees 

Calorific 
Power  per 
Pound 
B.  T.  U. 

United  States 
California  

85.04 

11.52 

.991 

2.45 

1.40 

17,871 

California  
Kentucky  

81.52 
85.20 

11.51 
13.36 

6.92i 
l.ll2 

0.55 

230 

18,667 
20,6353 

Ohio  

83.40 

14.70 

1.30 

0.60 

19,580 

Ohio 

8420 

13  10 

702 

.887 

19  5393 

Ohio,  Mecca  
Pennsylvania, 
Franklin  

86.30 
84.90 

13.07 
14.10 

.632 
1.40 

.886 

20,6603 
19,210 

Pennsylvania,   O  i  1 
Creek 

82  00 

14  80 

3  202 

816 

20  5903 

Texas,  Beaumont  .  . 
Texas,  Beaumont  .  . 
Texas,  Beaumont.  . 
Texas  

84.60 
83.30 
86.10 
87  15 

10.90 
12.40 
12.30 
1233 

2.87 
3.83 
.92» 

1.63 
0.50 
1.75 
032 

.924 
.926 

.908 

180 
216" 

370 

19,060 
19,481 
19,060 
19338 

West  Virginia 

84  30 

14  10 

1  602 

841 

21  240 

West  Virginia  
Foreign  Countries 
Austria,  Galicia.  .  .  . 
Austria,  Galicia  
Borneo 

83.20 

85.30 
82.20 
85  70 

13.20 

12.60 
12.10 
11  00 

3.602 

2.102 
5.702 
3  31 

.857 

.855 
.870 

20,0523 

20,1053 
18,416 
19  240 

Burmah  

83  80 

12  70 

3  502 

875 

19  8353 

Canada,  West  

81.30 

13.40 

2.302 

.857 

19,9983 

Canada,  Petrolia... 
China,  Fu-li-fu  
Germany,  Hanover 
Germany,    Pechel- 
bronn 

84.50 
83.50 
80.40 

85  70 

13.50 
12.90 
12.70 

12  00 

2.002 
3.602 
6.902 

2  3Q2 

.870 
.860 
.892 

892 

20,5523 
19,9103 
19,0793 

19  7723 

Germany,  Schwab- 
weiler  

8620 

13  30 

502 

861 

20  794s 

Italy,  Parma  

8400 

1340 

1  802 

786 

20  436s 

Java,  Rembang.  .  . 
Java,  Tjabados.  .. 
Java,  Gagor  

87.10 
83.60 
8500 

12.00 
14.00 
11  20 

.902 
2.402 
2  802 

.923 

.827 
927 

19,7073 
20,7003 
19  1373 

Roumania  
Russia,  Baku  
Russia,  Baku  
Russia,  Baku  

83.00 
87.40 
86.60 
85.30 

12.20 
12.60 
12.30 
11.60 

4.802 

.102 
1.102 

3.102 

.901 
.882 
.938 
.954 

19,3503 
20,5663 
20,1873 
19.4043 

.  Calorific  Value  of  Fuel  Oil.— The  combustible  elements  in  oil  are  the  same 
as  those  m  coal,  namely,  carbon  and  hydrogen,  and  usually  some  sulphur. 
The  calorific  value  per  pound  may  be  determined  by  means  of  Dulong's  for- 
mula, which  is  applied  exactly  as  in  the  case  of  an  ultimate  analysis  of  coal. 
This  formula  v/as  used  to  calculate  the  greater  number  of  the  calorific  powers 
given  in  the  accompanying  table.  From  the  results  of  available  tests,  it  is 
found  that  the  heat  of  combustion  per  pound  of  fuel  oil  varies  from  17,000  to 
21,000  B.  T.  U.,  California  oil  averaging  about  18,600  B.  T.  U.,  and  Texas  oil 
some  1,000  B.  T.  U.  higher.  At  18,600  B.  T.  U.  per  Ib.  and  assuming  an  aver- 
age specific  gravity  of  .885,  1  gal.  of  oil  weighs  7.37  Ib.,  and  will  yield  137,082 
B-  T.  U.,  and  a  barrel  of  42  gal.  will  weigh  310  Ib.  and  will  yield  5,766,000 
B.  T.  U.  Using  the  same  specific  gravity  and  a  calorific  value  of  19,600  B.  T.  U. 
per  Ib.  1  gal.  of  oil  will  develop  144,452  B.  T.  U.,'and  a  barrel  6,076,000  B.  T.  U. 
rhe  theoretical  comparative  fuel  values  of  coals  of  different  heating  powers 

1  Includes  nitrogen. 

2  Oxygen,  by  difference. 

•  Calculated  by  means  of  Dulong's  formula. 


FUELS 


397 


and  of  fuel  oil  yielding,  respectively,  18,600  and  19,600  B.  T.  U.,  per  Ib.  are 
given  in  the  following  table. 

This  table,  however,  is  of  more  theoretical  than  practical  interest,  as  it  is 
based  on  the  assumption  that  combustion  is  perfect  whether  oil  or  coal  is  used, 
and  that,  in  consequence,  the  efficiency  of  an  oil-burning  and  of  a  coal-burning 
boiler  is  the  same.  This  is  far  from  the  case,  as  the  efficiency  of  a  properly 
designed  oil-burning  boiler  is  the  greater.  To  this  must  be  added  the  advan- 
tages outlined,  so  that  only  an  actual  test  of  the  two  fuels  will  determine  which 
is  the  more  economical  under  a  given  set  of  conditions. 

COMPARATIVE  VALUE  OF  COAL  AND  OIL  AS  FUEL 


At  18,600  B.  T.  U.  per  Lb. 

At  19,600  B.  T.  U.  per  Lb. 

Thermal 
Value  of 

Pounds 

Pounds 

Barrels 

Pounds 

Pounds 

Barrels 

Different 

of  Coal 

of  Coal 

of  Petro- 

of Coal 

of  Coal 

of  Petro- 

Coals 
B.  T.  U. 

Equiva- 
lent to 

Equiva- 
lent to 

leum 
Equiva- 

Equiva- 
lent to 

Equiva- 
lent to 

leum 
Equiva- 

per Pound 

1  Lb.  of 

1  Bbl.  of 

lent  to 

1  Lb.  of 

1  Bbl.  of 

lent  to 

Petro- 

Petro- 

1 T.  of 

Petro- 

Petro- 

1 T.  of 

leum 

leum 

Coal 

leum 

leum 

Coal 

10,000 

1.860 

577 

3.47 

1.960 

608 

3.29 

11,000 

1.691 

524 

3.82 

1.782 

552 

3.62 

12,000 

1.550 

481 

4.16 

1.633 

506 

3.95 

13,000 

1.431 

444 

4.51 

1.508 

467 

4.28 

14,000 

1.329 

412 

4.85 

1.400 

434 

4.61 

15,000 

1.240 

384 

5.21 

1.307 

405 

4.95 

Advantages  and  Disadvantages  of  Oil  Fuel. — Babcock  and  Wilcox  sum- 
marize the  advantages  of  fuel  oil  as  follows: 

1.  The  cost  of  handling  is  much  lower,  the  oil  being  fed  by  simple  mechani- 
cal means,  resulting  in 

2.  A  general  labor  saving  throughout  the  plant  in  the  elimination  of 
stokers,  coal  passers,  ash  handlers,  etc. 

3.  For  equal  heat  value,  oil  occupies  very  much  less  space  than  coal. 
This  storage  space  may  be  at  any  distance  from  .the  boiler  without  detriment. 

4.  Higher  efficiencies  and  capacities  are  obtainable  with  oil  than  with 
coal.     The   combustion   is   more   perfect   as   the   excess  air  is  reduced  to  a 
minimum;  the  furnace  temperature  may  be  kept  practically  constant,  as  the 
furnace  doors  need  not  be  opened  for  cleaning  or  working  fires;  smoke  may  be 
eliminated  with  the  consequent  increased  cleanliness  of  the  heating  surfaces. 

5.  The  intensity  of  the  fire  can  be  almost  instantaneously  regulated  to 
meet  load  fluctuations. 

6.  Oil,  when  stored,  does  not  lose  in  calorific  value  as  does  coal,  nor  are 
there  any  difficulties  arising  from  disintegration,  such  as  may  be  found  where" 
coal  is  stored. 

7.  Cleanliness  and  freedom  from  dust  and  ashes  in  the  boiler  room  with 
a  consequent  saving  in  wear  and  tear  on  machinery;  little  or  no  damage  to 
surrounding  property  due  to  such  dust. 

The  disadvantages  of  oil  are: 

1.  The  necessity  that  the  oil  have  a  reasonably  high  flash  point  to  mini- 
mize the  danger  of  explosions. 

2.  City  or  town  ordinances  may  impose  burdensome  conditions  relative 
to  location  and  isolation  of  storage  tanks,  which  in  the  case  of  a  plant  situated 
in  a  congested  portion  of  the  city,  might  make  the  use  of  this  fuel  prohibitive. 

3.  Unless  the  boilers  and  furnaces  are  especially  adapted  for  the  use  of 
this  fuel,  the  boiler  upkeep  cost  will  be  higher  than  if  coal  is  used. 

The  relative  cost  of  the  two  fuels  per  unit  of  power  produced  is,  of  course, 
the  deciding  factor  in  the  premises,  and  this  varies  so  greatly  in  such  short 
intervals  of  time,  even  from  day  to  day,  that  current  quotations  of  the 
delivered  cost  of  both  fuels  must  always  be  used  in  making  calculations  of  the 
savings  possible  when  substituting  oil  for  coal,  and  vice  versa. 


FUELS 


GASEOUS  FUELS 

Kinds  of  Gas.  —  The  different  gases  used  as  fuel  are  the  following,  arranged 
in  the  order  of  their  heating  value:  (1)  Natural  gas,  which  is  obtained  from 
wells  in  different  parts  of  the  world;  (2)  illuminating  gas,  or  coal  gas,  which  is 
made  either  by  distilling  coal  in  retorts  or  by  enriching  water  gas  with  the 
volatile  matter  distilled  from  cannel  coal  or  with  vapors  distilled  from  petro- 
leum; (3)  coke-oven  gases,  which  are  mainly  those  coming  from  by-product 
ovens,  although  occasionally  the  gases  from  the  beehive  ovens  are  used  under 
boilers;  (4)  water  gas,  which  is  made  by  blowing  steam  through  a  bed  of  glow- 
ing anthracite  or  coke,  by  the  reaction  C-f-  #20  =  CO  +2tf;  (5)  producer  gas, 
which  is  made  by  blowing  air  into  burning  bituminous  coal,  in  which  case  the 
volatile  matter,  including  condensible  tarry  vapors,  is  distilled,  and  the  coke 
is  burned  to  carbon  monoxide;  producer  gas  is  also  made  by  blowing  air  into 
burning  anthracite,  thus  producing  carbon  monoxide;  (6)  combined  water  gas 
and  producer  gas,  which  is  made  by  blowing  air  mixed  with  steam  into  a  pro- 
ducer charged  with  burning  bituminous  coal;  (7)  blast-furnace  gas,  which  is 
the  waste  gas  coming  from  the  top  of  a  blast  furnace,  and  which  contains  a 
certain  amount  of  carbon  monoxide  available  as  fuel. 

The  composition  and  heating  value  of  different  gases,  as  given  by  H.  A. 
Humphrey  in  the  Proceedings  of  the  Institution  of  Civil  Engineers  of  Great 
Britain,  are  shown  in  the  following  table. 


ANALYSES  AND  HEATING  VALUES  OF  VARIOUS  GASES 


Constituent  Gases 


II 

£ 


I 

S& 


P.  BO. 

N*3     <U 

*e  I 

PI 


Hydrogen,  H 

Marsh  gas  (methane),  CH* 

CnHzn  gases 

Carbon  monoxide,  CO 

Carbon  dioxide,  C02 

Nitrogen,  AT 

Total  volume  (approxi- 
mate)   

Total  combustible  gases . . 

Heating  value  (B.  T.  U. 
per  cubic  foot  at  64°  F.) 


22.0 

67.0 

6.0 

.6 

.6 

3.0 

100.0 
95.6 

892.4 


48.0 

39.5 

3.8 

7.5 

.5 

100.0 
98.8 

686.0 


56.9 
22.6 
3.0 
8.7 
3.0 
5.8 

100.0 
91.2 

511.0 


20.0 

4.0 
21.0 

5.0 
49.5 

100.0 
45.0 

207.5 


18.7 

!a 

25.1 

6.6 

49.0 

100.0 
160.0 


8.6 
2.4 

24.4 
5.2 

59.4 

100.0 
35.4 

134.5 


24.8 
2.3 

13.2 
12.9 
46.8 

100.0 
154.6 


Some  additional  analyses  of  natural,  producer,  and  coke-oven  gases, 
together  with  their  average  heating  values,  are  given  in  another  table. 

The  heating  value  per  pound  and  per  cubic  foot,  measured  at  32°  F.,  and 
atmospheric  pressure  of  the  several  constituents  of  a  mixed  fuel  are  given  in 
the  table  on  page  400.  The  figures  in  the  first  column  are  those  of  Favre  and 
Silbermann  except  in  the  two  cases  noted.  Other  heating  values  differing 
slightly  from  these  are  given  by  different  authorities,  owing  to  a  difference 
in  the  experiments  by  which  the  values  have  been  determined.  In  the  third 
column  are  shown  approximate  figures,  giving  the  British  thermal  units  per 
pound  of  combustible,  that  are  within  the  limits  of  error  of  chemical  analysis. 

Blast-Furnace  Gases. — Blast-furnace  gas  varies  greatly  in  its  composition , 
and  in  six  analyses  made  in  1  da.,  the  carbon  dioxide  varied  from  6.6  to  7.7%, 
the  carbon  monoxide  from  20.1  to  31.7%,  and  the  nitrogen  and  hydrocarbons 


FUELS 


o  a? 
#11 


883  3 §38 

^0     '     CO     COO^ 

qq^w     woqi 

OS  MT-lO         T}<COi-H 


oo 
cooo 


ooo 


ooo 
^H«5oo 


as 

!.i 


I 

uoowwSwiS    <J 


400 


FUELS 
HEATING  VALUE  OF  GASES  AT  32°  F. 


Substance 

Burned  in  Oxygen 

Approxi- 
mate 
Values 
per  Pound 
B.  T.  U. 

Per  Pound 
B.  T.  U. 

Per  Cubic 
Foot 
B.  T.  U. 

Hydrogen  to  HzO  
Carbon  to  carbon  dioxide,  COz 

62,032 
14,544 
4,451 

4,325 

23,513 

21,344 
17.847 
18,196* 
4,050t 

346.75 
338.00 

1,050.00 
1,568.00 
1,351.60 

62,000 
14,600 
4,450 

4,300 
10,150 

4,000 

Carbon  to  carbon  monoxide,  CO  
Carbon  monoxide,  CO,  to  carbon  dioxide 
COz  per  unit  of  CO 

Carbon  monoxide,  CO,  to  carbon  dioxide, 
COz  per  unit  of  carbon  C 

Marsh  gas  (methane),  CHi,  to  HzO  and 
COz..  

Ethvlene  (olefiant-gas)  ,  CzHt,  to  HzO  and 
COz  

Benzole  gas,  CeHe,  to  HzO  and  COz  

Acetylene,  CzHz,  to  HzO  and  COz  

Sulphur  to  SOz 

from  60.5  to  72.2%  by  volume.  The  heating  value  calculated  from  the  aver- 
age analyses  was  1,175  B.  T.  U.  per  lb.,  and  at  the  temperature  of  584°  P.,  at 
which  it  entered  the  steam  boiler  furnace,  it  carried  140  B.  T.  U.  per  lb. 
additional  heat.  The  1,175  B.  T.  U.  per  lb.  are  equal  to  about  94  B.  T.  U. 
per  cu.  ft.,  measured  at  32°  P.,  or  only  about  one-tenth  of  the  value  of  1  cu. 
ft.  of  natural  gas. 

Modern  blast  furnaces,  working  on  Bessemer  iron,  will  produce  about 
8,500  lb.  of  available  gas  per  ton  of  pig  iron  made.  This  gas  will  have  an  aver- 
age composition  of  about  COz,  10.80%;  CO,  28.00%;  H,  2.50%;  CHt,  .2%; 
and  N,  58.50%;  and  will  yield  85  to  100  B.  T.  U.  per  cu.  ft.,  or  1,050  to  1,250 
B.  T.  U.  per  lb.,  assuming  that  the  weight  of  1  cu.  ft.  thereof  is  .081  lb.  The 
heat  from  the  waste  gases  of  the  blast  furnaces  in  the  United  States,  which 
produced  about  26,700,000  T.  of  pig  iron  in  1910,  was  sufficient,  if  entirely  util- 
ized, to  have  displaced  10,400,000  T.  of  coal  having  a  fuel  value  of  12,000 
B.  T.  U.  per  lb. 

Natural  Gas. — Natural  gas,  produced  from  drilled  wells,  usually  in  or  near 
the  oil  fields,  is  a  valuable  fuel  in  many  states.  The  total  production  in 
1910  was  509,155,309,000,000  cu.  ft.  The  value  is  placed  at  $70,756,158,  or 
13.90  c.  per  1,000  cu.  ft.,  varying  from  7.16  c.  per  cu.  ft.  in  West  Virginia  to 
73.77  c.  in  South  Dakota.  Assuming  a  fuel  value  of  1,000  B.  T.  U.  per  cu.  ft., 
this  gas  displaced  21,000,000  T.  of  coal  rated  at  12,000  B.  T.  U.  per  lb. 
The  1,327,722  domestic  consumers  used  169,823,030,000.000  cu.  ft.  of  gas, 
for  which  they  paid  an  average  price  of  24.4  c.  per  1,000  cu.  ft.,  the  rate 
charged  varyingf  rom  16.9  c.  per  1,000  ft.  in  Oklahoma  to  $1  in  Michigan. 
The  18,267  industrial  establishments  used  339,332,279,000,000  cu.  ft.,  for 
which  they  paid  an  average  price  of  8.63  c.  per  1,000  cu.  ft.,  the  rate  charged 
varying  from  5.1  c.  per  1,000  cu.  ft.  in  West  Virginia  to  69.5  c.  in  South  Dakota. 
>  The  great  variation  in  the  composition  of  natural  gas  from  different  fields 
is  shown  in  the  table  on  page  399.  Assuming  a  calorific  value  of  1,000  B.  T.  U. 
per  cu.  ft.,  24,000  cu.  ft.  of  gas  will  yield  as  much  heat  as  1  T.  of  coal  rated  at 
12,000  B.  T.  U.  per  lb.  To  displace  1  T.  of  high-grade  Pocahontas  or  New 
River  coal  rated  at,  say,  14,750  B.  T.  U.  per  lb.,  will  require  29,500  cu.  ft.  of 
gas.  The  number  of  cubic  feet  of  gas  required  to  displace  1  T.  of  coal  when  the 
calorific  powers  of  each  are  known,  may  be  found  by  dividing  twice  the  calorific 
power  of  the  coal  per  pound  by  the  ratio  the  calorific  power  of  the  gas  bears 
to  1,000  B.  T.  U. 

EXAMPLE. — (a)  How  many  thousand  cubic  feet  of  gas  having  a  calorific 
power  of  925  B.  T.  U.  per  cu.  ft.,  will  be  required  to  displace  1  T.  of  coal  rated 
at  13,965  B.  T.  U.  per  lb.?  (b)  How  many  cubic  feet  will  be  required  if  the 
heating  value  of  the  gas  is  1,155  B.  T.  U.  per  lb.? 

*Calculated.     fN.  W.  Lord. 


FUELS  401 

SOLUTION. — (a)  It  is  assumed  that  the  efficiency  of  the  boiler  is  the  same 
regardless  of  the  fuel  used.  13'90605_X2  =  30.195  cu.  ft. 

,VAU 

-  =  24,181  cu.  ft. 

It  is  possible,  also,  to  deduce  from  this  that  1,000  cu.  ft.  of  the  first  gas 
=  2,000-^-30.195  =  66.23  Ib.  of  the  coal,  and  1,000  cu.  ft.  of  the  second  gas 
=  2,000-7-24.181  =  82.71  Ib.  of  the  coal.  Likewise,  1  Ib.  of  the  coal  is  equal 
to  1,000 -=-66.23  =  15.09  cu.  ft.  of  the  first  gas,  and  is  equal  to  l.OOO-r-82.71 
=  12.10  cu.  ft.  of  the  second  gas. 

In  the  matter  of  natural  gas  in  the  Pittsburg,  Pa.,  district,  a  committee  of 
the  Western  Society  of  Engineers  report  that  1  Ib.  of  good  coal  is  equal  to 
7|  cu.  ft.  of  natural  gas.  When  burned  with  just  enough  air,  its  temperature 
of  combustion  is  4.200°  F.  The  Westinghouse  Air  Brake  Company  found  from 
experiment  that  1  Ib.  of  Youghiogheny  coal  is  equal  12 \  cu.  ft.  of  natural  gas, 
or  1,000  cu.  ft.  of  natural  gas  is  equal  81.6  Ib.  of  coal.  Indiana  natural  gas 
gives  1,000,000  B.  T.  U.  per  1,000  cu.  ft.,  and  weighs  .045  Ib.  per  cu.  ft. 

Natural  gas,  when  used  for  steam  raising,  is  commonly  under  a  pressure 
of  about  8  oz.  and  is  fired  through  a  large  number  of  small  burners  to  prevent 
what  is  known  as  lancing,  or  the  issuing  of  the  flame  in  a  long  jet  similar  in 
appearance  and  largely  in  action  to  that  of  a  blow-pipe. 

By-Product  Gas. — By-product  gas,  so  called,  is  given  off  in  large  amount 
in  connection  with  the  numerous  by-product  processes  of  coking.  When  the 
coking  plant  is  situated  at  a  steel  works,  the  gas  is  used  for  the  generation  of 
steam;  if  situated  in  or  near  a  city,  the  gas  is  enriched  and  used  for  illuminating 
and  general  fuel  purposes,  as  is  done  at  the  plant  of  the  New  England  Gas  and 
Coke  Company  at  Everett,  near  Boston,  Mass. 

In  1910  there  were  4,078  by-product  ovens  in  the  United  States,  of  which 
all  but  27  were  in  blast.  They  consumed  9,529,042  T.  of  coal  and  produced 
7,138,734  T.  of  coke,  an  average  yield  of  74.9%.  A  certain  amount  of  the  gas 
given  off  by  the  coking  coal  is  required  to  furnish  the  heat  demanded  by  the 
process;  the  gas  not  so  used,  the  surplus  or  available  gas,  amounted,  in  1910, 
to  27,692,858,000  cu.  ft.,  valued  at  $3,017,908,  or  about  11  c.  per  1,000  cu.  ft. 
The  production  appears  to  be,  from  these  statistics,  at  the  rate  of  2,900  cu.  ft. 
per  T.  of  coal  charged,  or  3,880  cu.  ft.  per  T.  of  coke  drawn.  These  figures 
are  approximate  and  to  be  used  with  caution  because  at  a  small  number  of 
plants  no  attempt  was  made  to  save  the  gas,  and  at  another,  the  yield  of  gas 
had  to  be  estimated. 

The  amount  of  gas  available  depends  on  so  many  factors  that  it  is  impossible 
to  predicate  just  how  much  and  what  grade  of  gas  a  given  coal  will  yield. 
Obviously,  the  amount  of  gas  available  from  coking  1  T.  of  high-volatile  Con- 
nellsville  coal  is  much  greater  than  that  to  be  had  from  a  lean  semibituminous 
coal.  The  composition  of  the  gas  will  vary  with  the  composition  of  the  coal 
and  with  the  process  employed  in  coking.  The  gas  will  also  depend,  in  a  very 
great  measure,  on  whether  the  ovens  are  designed  primarily  for  coke  making, 
as  at  a  steel  or  iron  plant,  or  whether  intended  for  the  manufacture  of  illuminat- 
ing gas  and  the  recovery  of  by-products  (in  this  case,  the  coke  being  a  by- 
product), as  at  Everett,  near  Boston. 

In  regard  to  the  yield  of  gas  per  ton  of  coal  charged,  the  280  Koppers  regen- 
erative ovens  at  Joliet,  111.,  when  charged  with  a  mixture  of  80%  Pocahontas 
and  20%  high -volatile  coal,  yielded  84%  of  the  coal  charged  as  coke  and 
10,000  cu.  ft.  of  gas  per  T.,  of  which  rather  more  than  5,000  cu.  ft.  was  surplus 
and  available  as  fuel.  The  same  oven,  operating  in  Germany  on  a  coal  not 
dissimilar  to  the  Connellsville,  Pa.,  yields  between  5,000  and  6,000  cu.  ft.  of 
available  gas  per  T.  Mr.  P.  E.  Lucas,  superintendent  of  the  coke-oven  depart- 
ment of  the  Dominion  Iron  and  Steel  Co.,  Sydney,  N.  S.,  estimates  the  average 
yield  of  surplus  gas  from  average  coal  in  by-product  ovens  as  5,000  cu.  ft.  per  T. 
of  coal  charged,  and  that  this  gas  has  a  fuel  value  of  from  450  to  500  B.  T.  U. 
per  cu.  ft.  At  Mulheim-on-the-Ruhr,  Germany,  a  plant  of  50  Koppers  ovens 
supplies  that  city  and  Barmen,  40  mi.  distant,  with  gas;  these  ovens  take  8  to 
10  T.  of  coal  at  a  cha-ge.  The  time  of  coking  is  24  hr.  but  only  the  richer 
portion  of  the  gas,  that  evolved  from  the  second  to  the  twelfth  hour,  which 
is  about  50%  of  the  yield,  is  distributed.  During  these  10  hr.,  each  oven 
produces  70,600  cu.  ft.  of  gas  of  a  calorific  value  well  over  600  B.  T.  U.  per 
cu.  ft.,  with  the  average  composition:  COt,  1.2%;  CO,  6.8%;  H,  49.5%; 
CHt,  38.3%;  and  N,  4.2%.  Mr.  Edwin  A.  Moore,  estimates  that  a  plant  of 
100  United-Otto  ovens  consuming  750  T.  of  coal  will  produce  3,472,000  cu.  ft. 


402  FUELS 

of  available  gas,  or  at  the  rate  of  4,630  cu.  ft.  of  gas  per  T.  of  coal  charged. 
Mr.  Moore  calls  attention  to  the  fact  that  the  gases  given  off  during  the  early 
portion  of  the  coking  process  (first  10  hr.)  have  a  fuel  value  of  650  B.  T.  U. 
per  cu.  ft.,  and  during  the  latter  period,  but  525  B.  T.  U.  It  would  appear  that 
the  average  coal  will  yield  about  4,500  cu.  ft.  of  available  gas  per  T.,  and 
that  the  gas  has  a  heating  value  of  some  500  B.  T.  U.  per  cu.  ft.;  on  which 
basis  the  gas  has  about  8.5%  of  the  heating  value  of  the  coal  from  which  it  is 
made,  assuming  the  latter  to  be  rated  at  around  13,000  B.  T.  U.  per  Ib. 

On  the  basis  of  containing  500  B.  T.  U.  per  cu.  ft.,  the  27,692,858,000  cu.  ft. 
of  by-product  gas  marketed  in  1910  displaced  about  580,000  T.  of  coal  with  a 
fuel  value  of  12,000  B.  T.  U.  per  Ib. 

As  this  gas  is  highly  charged  with  moisture,  arrangements  must  be  made 
for  getting  rid  of  the  condensed  water.  Further,  as  the  gas  carries  large 
amounts  of  tar  and  heavy  hydrocarbons  that  clog  the  burners,  arrangements 
must  be  made  whereby  they  may  be  cleaned  out  by  blowing  steam  through 
them. 

Coke-Oven  Gas. — Beehive  coke-oven  gases  are  used  at  numerous  mines 
for  the  generation  of  the  necessary  steam  for  operating  the  power  plant  con- 
nected therewith.  As  these  gases  do  not  contain  any  combustible  portion, 
their  value  lies  in  their  sensible  heat.  Ihe  total  horsepower  available  may  be 

obtained  from  the  formula,        HP  = 

in  which  W= weight  of  gases  passing  per  hour;       T»    ' 

T  =  temperature  of  gases  entering  boiler; 
t  =  temperature  of  gases  leaving  boiler; 
s  =  specific  heat  of  gases. 

As  the  temperature  of  the  gases  entering  the  boiler  is  rarely  as  great  as 
2,000°  F.,  and  as  with  coal  firing  the  furnace  temperature  ranges  from  2,500° 
to  3,000°,  the  heating  surface  first  passed  over  will  not  absorb  as  much  heat 
in  the  waste-heat  boilers,  and,  consequently,  the  heating  surface  per  boiler 
horsepower  should  be  increased.  From  12  to  15  ft.  in  water-tube  boilers  is 
about  right,  and  from  15  to  20  ft.  in  return  tubular  and  shell  boilers. 

In  a  series  of  tests  with  a  high-class  water-tube  boiler,  the  following  results 
were  obtained  with  the  waste  heat  from  the  coke  ovens:  Temperature  of  the 
gases  entering  the  boiler,  1,720°  F.;  temperature  of  gases  leaving  the  boiler, 
650°  F.;  boiler  heating  surface,  1,611  sq.  ft.;  water  evaporated  per  hour  from 
and  at  212°  F.,  mean  result,  6,465  Ib.;  water  evaporated  from  and  at  212°  per 
oven  per  hour,  294  Ib.;  water  evaporated  from  and  at  212°  per  Ib.  of  coal 
coked,  1.7  Ib.;  water  evaporated  from  and  at  212°  per  sq.  ft.  of  heating  surface, 
4  Ib. 

At  the  Sydney  Mines  of  the  Nova  Scotia  Steel  and  Coal  Company,  the  waste 
heat  from  coke  ovens  of  the  Bauer  type  is  used  in  the  generation  of  steam.  In 
referring  to  a  test  run  made  upon  a  single  boiler,  Mr.  Thomas  J.  Brown,  the 
superintendent,  obtained  these  results:  Average  horsepower  per  hour,  331; 
maximum  horsepower  per  hour,  436;  minimum  horsepower  per  hour,  179; 
evaporation  from  and  at  212°  per  Ib.  of  coal  charged  into  the  ovens,  1.18  Ib. 
of  water;  coal  charged  into  the  ovens  per  boiler  horsepower,  29.23  Ib.  Mr.  Brown 
further  states,  that  the  boilers  have  3,140  sq.  ft.  of  heating  surface,  with  a 
flue  temperature  at  the  rear  of  the  boilers  of  between  600°  and  700°,  and  that 
the  proportion  of  about  9.5  sq.  ft.  of  heating  surface  per  horsepower  developed 
seems  to  be  about  right  for  this  class  of  fuel. 

At  Marianna,  Pa.,  2,000  H.  P.  are  developed  from  a  battery  of  75  beehive 
ovens  at  a  cost  of  $2.50  per  da.  as  opposed  to  a  cost  of  $63.50  if  coal  were  used. 
At  the  Stag  Canon  Mines,  Dawson,  N.  Mex.,  2,400  H.  P.  are  developed  from  the 
waste  gases  of  218  beehive  ovens,  the  gases  being  delivered  under  the  boilers 
at  temperatures  ranging  from  1,800°  F.  to  2,600°  F.  and  leaving  the  stack  at 
from  600°  to  1,150°  F.  Mr.  R.  D.  Martin,  referring  to  the  waste  heat  ovens 
in  use  at  Agujita  and  Lampacitos,  Coahuila,  Mex.,  estimates  that  each  oven 
is  capable  of  developing  12  boiler  H.  P.  from  a  coal  containing,  volatile  matter, 
21.1%;  fixed  carbon,  67.4%;  and  ash,  11.5%.  Here  the  temperature  in 
the  firebox,  as  determined  with  Saeger  cones,  was  as  high  as  2,600°  F. 
Mr.  Howard  N.  Eavenson,  in  connection  with  the  Continental  Coke  Co., 
No.  1  plant,  estimates  that  the  waste  heat  from  6  T.  of  coal  charged  into  a 
coke  oven  will  yield  as  many  boiler  horsepower  as  1  T.  of  coal  directly  fired. 

Coal  Gas.— Coal  gas,  frequently  called  illuminating  gas  from  the  use  to 
which  it  is  ordinarily  put,  is  made  by  heating  bituminous  coal  high  in  volatile 
matter  in  fireclay  retorts  of  a  semielliptic  cross-section.  The  retorts  are  about 


FUELS 


403 


15  in.  high  by  26  in.  wide  inside,  and  9  to  10  ft.  long  if  single-ended,  or  18  to  20  ft. 
long  if  double-ended.  The  retort  walls  are  about  4  in.  thick  and  each  retort  is 
connected  with  a  pipe  that  allows  the  gases  to  escape  as  fast  as  formed.  After 
passing  through  various  devices  to  remove  the  ammonia,  tar,  and  sulphur,  the 
gas  passes  into  a  gas  holder  and  is  ready  for  distribution. 

Analyses  of  typical  gas  coals  from  the  Pittsburg,  Pa.,  field  are  given  in  the 
following  table. 

ANALYSES  OF  GAS  COALS 


Constituents 

Westmoreland  Coal 
Company 

Pennsylvania  Gas  Coal 
Company 

South 
Side 
Mine 

Foster 

Mine 

Larri- 
mer 
No.  2 

Irwin 

No.  1 

Irwin 

Sewick- 
ley 

Water  
Volatile  matter.  .  .  . 
Fixed  carbon  
Sulphur  
Ash     

1.410 
37.655 
54.439 
.636 
5.860 

1.310 
37.100 
55.004 
.636 
5.950 

1.560 
39.185 
54.352 
.643 
4.260 

1.78 
35.36 
59.29 
.68 
2.89 

1.280 
38.105 
54.383 
.792 
5.440 

1.490 
37.153 
58.193 
.658 
2.506 

Total  

100.000 

100.000 

100.000 

100.00 

100.000 

100.000 

Under  ordinary  conditions  1  T.  of  such  coal  should  produce  about  10,000 
cu.  ft.  of  gas  of  17  c.  p.,  1,400  Ib.  of  coke,  12  gal.  of  tar,  and  4  Ib.  of  ammonia. 
The  following  may  be  considered  as  the  average  composition  of  purified 
coal  gas: 

Per  Cent. 

Hydrocarbon  vapors .6 

Heavy  hydrocarbons 4.4 

Carbon  dioxide,  COz 3.4 

Carbon  monoxide.  CO 10.1 

Marsh  gas,  CH\ 30.6 

Oxygen,  O 3 

Hydrogen,  H 45.9 

Nitrogen,  N 4.7 

Total 100.0 

The  use  of  illuminating  gas  as  fuel  for  steam-raising  is  limited  by  its  cost 
which,  while  sometimes  as  low  as  80  c.  per  1,000  cu.  ft.,  is  usually  about  $1. 
A  certain  amount  is  used  directly  in  small  gas  engines  in  the  larger  cities,  but 
the  larger  amount  is  used  for  illumination  or  in  cooking  ranges,  domestic 
heating  stoves,  and  the  like.  Coal  gas  made  from  gas  coals  in  retorts  is  being 
largely  displaced  by  water  gas. 

Water  Gas. — Water  gas  contains  the  same  combustible  constituents  as  coal 
gas  but  not  in  the  same  proportions.  ^  It  is  made  commercially  by  the  contact 
of  steam  with  incandescent  carbon,  in  the  form  of  anthracite  or  coke,  which 
decomposes  the  steam  separating  the  hydrogen  from  the  oxygen.  The  oxygen 
takes  up  carbon  from  the  coal  or  coke  and  forms  carbon  monoxide,  along  with 
a  small  amount  of  carbon  dioxide.  The  resultant  gases  therefore  are  mainly 
hydrogen  and  carbon  monoxide  mechanically  mixed  together.  This  is  what 
is  called  blue,  or  uncarbureted,  water  gas.  It  burns  with  a  non-luminous  flame 
and  is  consequently  useless  for  lighting  purposes,  except  in  incandescent  lamps 
of  the  Welsbach  type.  In  actual  practice,  this  water  gas  is  always  enriched 
with  oil  gas,  which  furrishes  the  hydrocarbons  necessary  to  make  a  luminous 
flame.  The  oil  gas  was  made  separately  in  many  of  the  older  forms  of  ap- 
paratus, but  it  is  now  commonly  produced  in  the  same  apparatus  in  which  the 
water  gas  is  made. 

The  only  impurity  that  must  be  removed  from  water  gas  is  hydrogen 
sulphide,  which  is  formed  from  the  sulphur  that  is  always  present  in  varying 
amounts  in  the  coal  or  coke  and  sometimes  in  the  oil.  The  hydrogen  sulphide 


404 


FUELS 


is  removed  by  purification  with  lime  or  iron  oxide  in  the  same  way  that  the 
purification  of  coal  gas  is  accomplished. 

Carbon  dioxide,  which  is  formed  either  by  imperfect  contact  of  the  steam 
with  the  incandescent  carbon,  or  because  the  temperature  of  the  carbon  is  too 
low,  is  not  a  dangerous  impurity,  but  is  merely  an  inert  gas  incapable  of  com- 
bustion. It,  however,  absorbs  heat  when  the  gas  is  burned,  and  is  conse- 
quently injurious  to  the  heating  and  lighting  power.  It  can  be  removed  by 
purification  with  lime,  but  this  is  not  necessary  if  the  generating  apparatus  is 
handled  properly,  as  the  quantity  made  will  be  very  small.  No  ammonia 
is  produced. 

The  following  is  a  volumetric  analysis  of  purified  water  gas: 

Per  Cent. 


Hydrocarbon  vapors 

Heavy  hydrocarbons 

Carbon  dioxide,  COz . . 

Carbon  monoxide,  CO 

Marsh  gas,  CHt 

Oxygen,  O 

Hydrogen,  H 

Nitrogen,  N 

Total.., 


1.2 
12.6 
3.0 
28.0 
20.2 

4 

31.4 

3.2 

.    100.0 


Water  gas  requires  from  30  to  40  Ib.  of  coal  or  coke  per  1,000  cu.  ft.  of  gas 
made,  and  from  4  to  5  gal.  of  oil,  depending  on  the  candlepower  required. 
Usually  between  5  and  6  c.  p.  is  obtained  from  each  gallon  of  oil  used.  The 
specific  gravity  of  24  c.  p.  water  gas  is  about  .625,  air  being  taken  as  unity. 

Pure  uncarbureted  water  gas  has  no  perceptible  odor,  but  the  carbureted 
gas  has  an  odor  fully  as  strong  as  coal  gas.  This  is  mainly  due  to  the  hydro- 
carbons from  the  oil  that  is  used  for  enriching.  It  should  be  noted  that  these 
hydrocarbons  are  not  added  if  the  gas  is  to  be  used  for  heating  or  in  gas  engines. 

Producer  Gas. — Producer  gas  is  made  in  a  cylindrical  riveted  shell  of  boiler 
plate,  lined  with  firebrick.  A  thick  bed  of  fuel  is  maintained  in  the  bottom  of 
the  producer  and  through  this  is  passed  a  moderate  supply  of  air,  with  or 
without  water  vapor  or  steam.  By  properly  regulating  the  air  supply,  a  partial 
or  incomplete  combustion  of  the  fuel  is  maintained,  resulting  in  the  gradual 
consumption  of  all  the  combustible  matter.  The  coke,  instead  of  remaining  as 
a  by-product,  as  in  the  manufacture  of  coal  gas  or  in  by-product  or  retort  coke 
ovens,  is  all  consumed  in  making  the  gas.  When  dry  air  alone  is  forced  through 
the  fire,  the  resulting  gas  is  known  as  air  gas  and  is  the  true  producer  gas;  when 
the  air  is  mixed  with  steam  or  water  vapor  the  resulting  gas  is  called  mixed  gas, 
and  is  frequently  made  in  producers;  and  when  air  is  not  used  at  all  and  steam 
alone  is  forced  through  the  fire,  the  product  is  called  water  gas  as  previously 
explained. 

The  quantity  of  producer  gas  derivable  from  1  T.  of  fuel  will  vary  according 
to  the  fuel  used,  the  type  of  producer  plant,  and  the  method  of  operating. 
The  United  States  Geological  Survey,  at  its  Fuel  Testing  Plant  at  the  Louisiana 
Purchase  Exposition,  held  in  St.  Louis,  in  1904,  made  an  exhaustive  series  of 
tests  of  American  coals  used  in  gas  producers,  and  from  its  reports  the  follow- 
ing tables,  etc.,  are  taken. 

QUANTITY    OF    GAS    PRODUCED    PER    POUND    OF    FUEL    IN    AN 
UP-DRAFT   PRESSURE    PRODUCER 


Fuel 

Maximum 

Minimum 

Average 

As  Fired 
Cubic 
Feet 

Dry 
Cubic 
Feet 

As  Fired 
Cubic 
Feet 

Dry 

Cubic 
Feet 

As  Fired 
Cubic 
Feet 

Dry 
Cubic 
Feet 

Bituminous  coal  .  .  . 
Lignite  .  .  . 

100.8 
45.9 

100.3 
52.8 

37.0 
26.1 

40.9 
38.8 

60.5 
35.8 
30.3 

64.7 
45.7 
38.3 

Peat  

FUELS 


405 


The  yield  of  gas,  in  cubic  feet  per  pound  of  dry  fuel,  which  may  be  expected 
in  the  up-draft  producer  from  various  fuels  is,  roughly,  as  follows:  Coke  or 
charcoal,  90;  anthracite,  75;  bituminous  coal,  65;  lignite,  46;  and  peat,  38. 
On  the  basis  of  the  Survey's  tests  the  yield  of  gas  and  the  heat  value  of  the 
gas  per  ton  of  fuel  as  fired  are  approximately  as  in  the  table  here  given. 

YIELD  AND  HEAT  VALUE  OF  GAS  PER  TON  OF  FUEL  AS  FIRED  IN 
AN  UP-DRAFT  PRESSURE  PRODUCER 


Kind  of  Fuel 

Cubic  Feet 
of  Gas  per 
Ton  of  Fuel 
as  Fired 

British 
Thermal  Units 
in  Gas,  per 
Cubic  Foot 

British 
Thermal  Units 
in  Gas,  per 
Ton  of  Fuel 
as  Fired 

Coke  or  charcoal  

170,000 

140 

23,800,000 

Anthracite  
Bituminous  coal 

140,000 
120000 

135 
152 

19,000,000 
18300000 

Lignite  
Peat 

72,000 
60000 

158 
175 

11,400,000 
10  000,000 

It  will  be  noted  from  this  table  that  while  the  inferior  fuels  yield  less  gas 
per  ton,  as  might  be  expected,  the  heating  value  of  the  gas,  in  British  thermal 
units  per  cubic  foot,  is  greater  than  in  gas  made  from  high-class  coals. 

Gas  Producers. — There  are  three  general  types  of  gas  producer  in  use.  In 
the  suction  type,  the  drawing  of  the  air  and  steam  through  the  fire  and,  con- 
sequently, the  generation  of  the  gas,  is  accomplished  by  the  suction  in  the 
engine  cylinder  in  which  the  gas  is  used.  While  the  gases  are  scrubbed,  etc., 
to  get  rid  of  the  tar  that  otherwise  would  clog  the  cylinders,  the  absence  of 
storage  tanks  for  the  gas  and  the  fact  that  the  suction  of  the  engine  causes  the 
operation  of  the  producer,  renders  absolute  separation  of  the  tar  difficult  if 
not  impossible.  Hence,  only  low  volatile  coals  are  adapted  to  use  in  this  type 
of  producer,  and  because  the  price  of  such  coals  is  always  high,  suction  plants, 
though  numerous,  are  of  comparatively  small  power,  few  exceeding  300  H.  P. 
each,  and  most  of  them  not  exceeding  100  H.  P. 

The  up-draft  pressure  producer  is  the  common  American  type  in  which 
the  gas  is  developed  under  a  slight  pressure  due  to  the  introduction  of  the  air 
and  steam  blasts,  and  the  gas  is  stored  in  holders  until  required  by  the  engine. 
As  the  generation  of  the  gas  is  independent  of  the  suction  stroke  of  the  engine, 
tar  and  other  impurities  may  be  removed  by  suitable  devices  and  hence  the  use 
of  bituminous  coal,  lignite,  and  peat  is  possible.  This  form  of  producer  is 
offered  in  many  types,  some  of  which  are  without  gas  holders  and  are  proving 
eminently  satisfactory.  If  the  holder  is  omitted,  automatic  devices  must  be 
introduced  for  controlling  the  pressure  and  the  supply  of  gas  to  the  engine. 

TYPICAL  ANALYSES  BY  VOLUME  OF  PRODUCER  GAS 


From 

Bituminous 

From  Lignite 

From  Peat 

Coal 

Per  Cent. 

Per  Cent. 

Per  Cent. 

U.  D. 

D.  D. 

U.  D. 

D.  D. 

U.  D. 

D.  D. 

Carbon  dioxide,  COz  

9.84 

6.22 

10.55 

11.87 

12.40 

10.94 

.04 

.13 

.16 

.01 

.41 

Ethylene,  CiH*  

.18 

.01 

.17 

.40 

.06 

Carbon  monoxide,  CO.  .  .  . 

18.28 

21.05 

18.72 

16.01 

21.00 

16.91 

Hydrogen,  Hz  

12.90 

12.01 

13.74 

14.66 

18.50 

10.19 

Methane,  CH*  

3.12 

.49 

3.44 

.98 

2.20 

.66 

Nitrogen,  Nz  

55.64 

60.09 

53.22 

56.37 

45.50 

60.83 

406  BOILERS 

In  both  the  foregoing  types  of  producer,  the  extraction  of  the  tar  removes 
a  large  part  of  the  heat  value  of  the  gas.  If  the  tar  can  be  sold  at  a  good  price 
this  may  not  make  much  difference,  but  where  the  tar  is  thrown  away  the  loss 
is  sufficient  to  warrant  the  attempt  to  devise  some  means  of  converting  this 
tar  into  gas  of  suitable  quality  for  engine  use.  To  this  end  down-draft  producers 
are  coming  into  general  use  and  in  them  the  gases  are  drawn  down  through  the 
bed  of  coal  and  the  tar  is  thereby  decomposed  into  fixed,  combustible  gases. 

Typical  analyses  of  gases  made  from  the  same  fuels  in  the  up-draft  (U.  D). 
and  down-draft  (D.  D.)  producer,  the  percentages  being  by  volume,  are  given 
in  the  preceding  table. 

In  the  matter  of  steam  raising  it  is  questionable  if  better  results  are  obtained 
by  using  the  gas  made  from  the  coal  than  by  firing  the  coal  directly  under  the 
boilers,  especially  in  the  case  of  good  grades  of  coal  from  subbituminous  to 
anthracite,  but  many  fuels,  notably  peat  and  some  of  the  true  lignites,  that 
give  indifferent  results  when  fired  directly  under  a  steam  boiler,  give  most 
excellent  results  when  fired  as  gas.  Further,  almost  any  material  containing 
carbon  will  yield  fuel  gas  in  the  producer,  even  bituminous  shale,  saw-dust, 
wood  pulp,  cornstalks,  and  the  like.  It  is  practically  impossible  to  predicate 
the  yield  of  gas  and  the  quality  thereof  of  a  coal  from  its  analysis.  Tests  in 
the  various  types  of  producers  are  required  for  this  purpose. 

Strictly  speaking,  the  gaseous  fuels  previously  described  are  all  producer 
gases,  except  natural  gas,  coal  gas  (illuminating  gas),  and  the  waste  heat  gases 
from  beehive  coke  ovens.  These  various  producer  gases  are  not  commonly 
used  for  steam  raising  under  boilers,  but  are  a  direct  source  of  power  in  internal 
combustion  engines.  It  must  be  noted  that  as  carbon  monoxide  is  one  of  the 
most  important  heat-producing  constituents  of  all  these  gases,  extreme  caution 
must  be  observed  in  inhaling  them  owing  to  their  highly  poisonous  nature. 

BOILERS 


STEAM 

PROPERTIES  OF  STEAM 

Saturated  Steam. — If  water  is  put  in  a  closed  vessel  and  heat  is  applied  until 
boiling  occurs  and  steam  is  given  off,  the  pressure  and  the  temperature  of  the 
steam  will  be  the  same  as  those  of  the  water.  The  steam  thus  produced  is 
known  as  saturated  steam;  that  is,  saturated  steam  is  steam  whose  temperature 
is  the  same  as  that  of  boiling  water  subjected  to  the  same  pressure.  Its 
nature  is  such  that  any  loss  of  heat  will  cause  some  of  the  steam  to  condense, 
provided  the  pressure  is  not  changed.  Saturated  steam  that  carries  no  water 
particles  with  it  is  called  dry  saturated  steam;  if  it  contains  moisture  it  is  called 
•wet  steam.  At  every  different  pressure,  saturated  steam  has  certain  definite 
values  for  the  temperature,  the  weight  per  cubic  foot,  the  heat  per  pound,  and 
so  on.  These  various  values,  collected  and  arranged  in  order,  form  the  table 
of  the  Properties  of  Saturated  Steam,  more  commonly  termed  the  Steam 
Table,  which  is  given  on  the  following  pages. 

The  various  properties  of  steam,  with  their  symbols,  as  given  in  the  Steam 
Table,  are  as  follows: 

The  temperature,  t,  of  the  steam,  which  is  the  boiling  point  of  the  water 
from  which  the  steam  is  formed. 

The  heat  of  the  liquid,  q,  which  is  the  number  of  British  thermal  units  required 
to  raise  the  temperature  of  1  Ib.  of  water  from  32°  F.  to  the  boiling  point  corre- 
sponding to  the  given  pressure. 

The  latent  heat  of  vaporization,  r,  often  termed  the  latent  heat,  which  is  the 
number  of  British  thermal  units  required  to  change  1  Ib.  of  water  at  the  boiling 
point  into  steam  at  the  same  temperature. 

The  total  heat  of  vaporization,  H,  often  termed  the  total  heat,  which  is  the 
number  of  British  thermal  units  required  to  raise  1  Ib.  of  water  from  32°  F.  to 
the  boiling  point  for  any  given  pressure  and  to  change  it  into  steam  at  that 
pressure.  It  is  the  sum  of  the  heat  of  the  liquid  and  the  latent  heat. 

The  specific  volume,  V,  which  is  the  volume,  in  cubic  feet,  of  1  Ib.  of  steam 
at  the  given  pressure. 

The  density,  w,  which  is  the  weight,  in  pounds,  of  1  cu.  ft.  of  steam  at  the 
given  pressure.  It  is  the  reciprocal  of  the  specific  volume. 


BOILERS 
PROPERTIES  OF  SATURATED  STEAM 


407 


p 

t 

q 

H 

r 

V 

w 

1 

101.99 

70.0 

1,113.1 

1,043.0 

334.6 

.00299 

2 

126.27 

94.4 

1,120.5 

1,026.1 

173.6 

.00576 

3 

141.62 

109.8 

1,125.1 

1,015.3 

118.4 

.00844 

4 

153.09 

121.4 

1,128.6 

1,007.2 

90.31 

.01107 

5 

162.34 

130.7 

1,131.5 

1,000.8 

73.22 

.01366 

6 

170.14 

138.6 

1,133.8 

995.2 

61.67 

.01622 

7 

176.90 

145.4 

1,135.9 

990.5 

53.37 

.01874 

8 

182.92 

151.5 

1,137.7 

986.2 

47.07 

.02125 

9 

188.33 

156.9 

1,139.4 

982.5 

42.13 

.02374 

10 

193.25 

161.9 

1,140.9 

979.0 

38.16 

.02621 

11 

197.78 

166.5 

1,142.3 

975.8 

34.88 

.02866 

12 

201.98 

170.7 

1,143.6 

972.9 

32.14 

.03111 

13 

205.89 

174.6 

1,144.7 

970.1 

29.82 

.03355 

14 

209.57 

178.3 

1,145.8 

967.5 

27.79 

.03600 

14.7 

212.0 

180.8 

1,146.6 

965.8 

26.60 

.03760 

16 

216.32 

185.1 

1,147.9 

962.8 

24.59 

.04067 

18 

222.40 

191.3 

1,149.8 

958.5 

22.00 

.04547 

20 

227.95 

196.9 

1,151.5 

954.6 

19.91 

.05023 

22 

233.06 

202.0 

1,153.0 

951.0 

18.20 

.05495 

24 

237.79 

206.8 

1,154.4 

947.6 

16.76 

.05966 

26 

242.21 

211.2 

1,155.8 

944.6 

15.55 

.06432 

28 

246.36 

215.4 

1.157.1 

941.7 

14.49 

.06899 

30  , 

250.27 

219.4 

1,158.3 

938.9 

13.59 

.07360 

32 

253.98 

223.1 

1,159.4 

936.3 

12.78 

.07820 

34 

257.50 

226.7 

1,160.4 

933.7 

12.07 

.08280 

36 

260.85 

230.0 

1,161.5 

931.5 

11.45 

.08736 

38 

264.06 

233.3 

1,162.5 

929.2 

10.88 

.09191 

40 

267.13 

236.4 

1,163.4 

927.0 

10.37 

.09644 

42 

270.08 

239.3 

1,164.3 

925.0  ' 

9.906 

.1009 

44 

272.91 

242.2 

1,165.2 

923.0 

9.484 

.1054 

46 

275.65 

245.0 

1,166.0 

921.0 

9.097 

.1099 

48 

278.30 

247.6 

1,166.8 

919.2 

8.740 

.1144 

50 

280.85 

250.2 

1,167.6 

917.4 

8.414 

.1188 

52 

283.32 

252.7 

1,168.4 

915.7 

8.110 

.1233 

54 

285.72 

255.1 

1,169.1 

914.0 

7.829 

.1277 

56 

288.05 

257.5 

1,169.8 

912.3 

7.568 

.1321 

58 

290.31 

259.7 

1,170.5 

910.8 

7.323 

.1366 

60 

292.51 

261.9 

1,171.2 

909.3 

7.096 

.1409 

62 

294.65 

264.1 

1,171.8 

907.7 

6.882 

.1453 

64 

296.74 

266.2 

1,172.4 

906.2 

6.680 

.1497 

66 

298.78 

268.3 

1,173.0 

904.7 

6.490 

.1541 

68 

300.76 

270.3 

1,173.6 

903.3 

6.314 

.1584 

70 

302.71 

272.2 

1,174.3 

902.1 

6.144 

.1628 

72 

304.61 

274.1 

1,174.9 

900.8 

5.984 

.1671 

74 

306.46 

276.0 

1,175.4 

899.4 

5.834 

.1714 

76 

308.28 

277.8 

1,176.0 

898.2 

5.691 

.1757 

78 

310.06 

279.6 

1,176.5 

896.9 

5.554 

.1801 

80 

311.80 

281.4 

1,177.0 

895.6 

5.425 

.1843 

82 

313.51 

283.2 

1,177.6 

894.4 

5.301 

.1886 

85 

316.02 

285.8 

1,178.3 

892.5 

5.125 

.1951 

90 

320.04 

290.0 

1,179.6 

889.6 

4.858 

.2058 

95 

323.89 

294.0 

1,180.7 

886.7 

4.619 

.2165 

100 

327.58 

297.9 

1,181.9 

884.0 

4.403 

.2271 

105 

331.13 

301.6 

1,182.9 

881.3 

4.206 

.2378 

110 

334.56 

305.2 

1,184.0 

878.8 

4.026 

.2484 

115 

337.86 

308.7 

1,185.0 

876.3 

3.862 

.2589 

120 

341.05 

312.0 

1,186.0 

874.0 

3.711 

.2695 

125 

344.13 

315.2 

1,186.9 

871.7 

3.572 

.2800 

130 

347.12 

318.4 

1,187.8 

869.4 

3.444 

.2904 

135 

350.03 

321.4 

1,188.7 

867.3 

3.323 

.3009 

140 

352.85 

324.4 

1,189.5 

865.1 

3.212 

.3113 

408 


BOILERS 
TABLE — (Continued) 


p 

/ 

Q 

H 

r 

V 

w 

145 

355.59 

327.2 

1,190.4 

863.2 

3.107 

.3218 

150 

358.26 

330.0 

,191.2 

861.2 

3.011 

.3321 

155 

360.86 

332.7 

,192.0 

859.3 

2.919 

.3426 

160 

363.40 

335.4 

,192.8 

857.4 

2.833 

.3530 

165 

365.88 

338.0 

,193.6 

855.6 

2.751 

.3635 

170 

368.29 

340.5 

,194.3 

853.8 

2,676 

.3737 

175 

370.65 

343.0 

,195.0 

852.0 

2.603 

.3841 

180 

372.97 

345.4 

,195.7 

850.3 

2.535 

.3945 

185 

375.23 

347.8 

,196.4 

848.6 

2.470 

.4049 

190 

377.44 

350.1 

,197.1 

847.0 

2.408 

.4153 

195 

379.61 

352.4 

,197.7 

845.3 

2.349 

.4257 

200 

381.73 

354.6 

,198.4 

843.8 

2.294 

.4359 

205 

383.82 

356.8 

,199.0 

842.2 

2.241 

.4461 

210 

385.87 

358.9 

,199.6 

840.7 

2.190 

.4565 

215 

387.88 

361.0 

,200.2 

839.2 

2.142 

.4669 

220 

389.84 

363.0 

,200.8 

837.8 

2.096 

.4772 

225 

391.79 

365.1  . 

,201.4 

836.3 

2.051 

.4876 

230 

393.69 

367.1 

,202.0 

834.9 

2.009 

.4979 

235 

395.56 

369.0 

,202.6 

833.6 

1.968 

.5082 

240 

397.41 

371.0 

,203.2 

832.2 

1.928 

.5186 

250 

400.99 

374.7 

,204.2 

829.5 

1.854 

.5393 

•260 

404.47 

378.4 

1,205.3 

826.9 

1.785 

.5601 

275 

409.50 

383.6 

1,206.8 

823.2 

1.691 

.5913 

300 

417.42 

391.9 

1,209.3 

817.4 

1.554 

.644 

325 

424.82 

399.6 

1,211.5 

811.9 

1.437 

.696 

The  pressures,  p,  given  in  the  first  column  are  absolute  pressures.  The 
pressure  registered  by  the  gauge  on  the  boiler  is  the  gauge  pressure,  or 
the  pressure  of  the  steam  above  that  of  the  atmosphere.  The  pressure  of  the 
atmosphere  at  sea  level,  with  the  barometer  at  about  30  in.,  is  approximately 
14.7  Ib.  per  sq.  in.  Therefore,  the  absolute  pressure  at  sea  level  is  equal  to  the 
gauge  pressure  plus  14.7.  In  using  the  Steam  Table,  the  atmospheric  pressure, 
14.7  Ib.  per  sq.  in.,  must  always  be  added  to  the  gauge  pressure. 

Use  of  Steam  Table.  —  For  any  absolute  pressure  p  given  in  the  first  column 
of  the  Steam  Table,  the  corresponding  temperature  t,  total  heat  H,  or  other 
property  is  found  in  the  same  horizontal  line,  under  the  proper  column  heading  ; 
but  if  the  pressure  lies  between  two  of  the  values  given  in  the  first  column, 
the  corresponding  temperature,  total  heat,  etc.  must  be  found  by  interpolation, 
as  illustrated  in  the  following  examples: 

EXAMPLE  1.  —  Find  the  temperature  corresponding  to  a  pressure  of  147  Ib. 
per  sq.  in.,  absolute. 

SOLUTION.—  Referring  to  the  Steam  Table, 

for  p  =  150  Ib.,  *  =  358.26° 

and  for  p  =  145  Ib.,  t  =  355.59° 

Difference,  5  Ib.,  2.67° 

Difference  for  1  Ib.  difference  of  pressure  is  2.67°  -^  5  =  .534°.  147  Ib.  -  145  Ib. 
=  2  Ib.,  the  given  difference  of  pressure;  and  for  this,  the  difference  in 
temperature  is  2X.  534°=  1.068°  or  1.07°,  taking  two  decimal  places.  Hence, 
the  increase  of  2  Ib.  from  145  Ib.  -to  147  Ib.  is  accompanied  by  an  increase  in 
temperature  of  1.07°.  Therefore,  adding  the  increase  1.07°  to  the  tempera- 
ture 355.59°  corresponding  to  145  Ib.,  the  temperature  for  147  Ib.  is  355.59° 
+  1.07°  =  356.66°. 

EXAMPLE  2.  —  The  pressure  in  a  steam  boiler  as  shown  by  the  gauge  is 
87  Ib.  per  sq.  in.  What  is  the  temperature  of  the  steam? 

SOLUTION.  —  The  absolute  pressure  is  87+14.7  =  101.7  Ib.  per  sq.  in.     This 

ssure,  in  the  Steam  Table,  lies  between  the  values  100  and  105. 


pressure 


for  £  =  1051b.,  *  =  331.13° 
for  p  =  100  Ib..  *  =  327.58° 
Difference,  5  Ib.,  3.55° 


BOILERS  409 

For  1  Ib.  change  of  pressure,  the  difference  in  temperature  is  3.55°  -i-5  =  .71°. 
From  100  Ib.  to  101.7  Ib.,  the  change  of  pressure  is  1.7  Ib.,  and  the  corresponding 
change  of  temperature  is  .71°  X  1.7  =  1.207°,  or  1.21°  as  the  values  in  the 
Steam  Table  contain  but  two  decimal  places.  For  101.7  Ib.,  therefore,  the 
temperature  is  327.58°+ 1.21°  =  328.79°. 

EXAMPLE  3. — What  is  the  pressure  of  steam  at  a  temperature  of  285°  P.? 
SOLUTION. — From  the  Steam  Table, 

for  t  =  285.72°,  p  =  54  Ib. 

for  t  =  283.32°,  p  =  52  Ib. 

Difference,  2.40°,          2  Ib. 

From  t  =  283.32°  to  t  =  285°,  the  increase  of  temperature  is  1.68°.  Now,  as 
an  increase  of  temperature  of  2.40°  gives  an  increase  of  pressure  of  2  Ib.,  the 
increase  of  1.68°  must  give  an  increase  of  pressure  of 

^|X2  Ib.-  1.4  Ib, 

Hence,  the  required  pressure  is  52  lb.  +  1.4  lb.  =  53.4  Ib. 

EXAMPLE  4. — Find,  from  the  Steam  Table,  the  total  heat  of  1  Ib.  of  satu- 
rated steam  at  a  pressure  of  63  Ib.  per  sq.  in.,  gauge. 

SOLUTION. — The  absolute  pressure  is  63  +  14.7  =  77.7  Ib.  per  sq.  in.  From 
the  Steam  Table, 

for  £  =  78  Ib.,  #  =  1,176.5  B.  T.  U. 

for  £  =  76  Ib.,  #=1. 176.0  B.  T.  U. 

Difference,  2  Ib.,  .5    B.  T.  U. 

Difference,  1  Ib.,  .25  B.  T.  U. 

The  difference  between  the  given  pressure  and  76  Ib.  is  77.7  —  76  =  1.7  Ib. 
For  a  difference  of  1.7  Ib.,  the  change  of  total  heat  is  1.7 X. 25  =  .425  B.  T.  U. 
Hence,  for  77.7  Ib.,  H  =  l,176.0+.425  =  1,176.425,  say  1,176.4  B.  T.  U. 

EXAMPLE  5. — Find  the  volume  occupied  by  14  Ib.  of  steam  at  30  Ib.  gauge 
pressure. 

SOLUTION. — Absolute  pressure  =  30 +14.7  =  44.7  Ib.  per  sq  in.  From  the 
Steam  Table, 

for  £  =  44  Ib.,  V  =  9.484  cu.  ft.* 

for  p  =  46  Ib. ,  V  =  9.Q97cu.  ft. 

Difference,  2  Ib.,          .387  cu.  ft. 

The  difference  for  1  Ib.  is  .387  +•  2  = .  1935.  44.7  -  44  =  .7  Ib.  actual  difference 
in  pressure.  .1935X  .7  =  .135  difference  in  volume.  As  the  pressure  increases, 
the  volume  decreases;  and  to  obtain  the  volume  at  44.7  Ib.,  it  is  necessary 
to  subtract  the  difference  .135  from  the  volume  at  44  Ib.;  thus,  for  £  =  44.7, 
V  =  9.484 -.135  =  9.349  cu.  ft.  The  volume  of  14  Ib.  is  14X9.349  cu.  ft. 
=  130.89  cu.  ft. 

EXAMPLE  6. — Find  the  weight  of  40  cu.  ft.  of  steam  at  a  temperature  of 
254°  F. 

SOLUTION. — From  the  Steam  Table,  the  weight  w  of  1  cu.  ft.  of  steam  at 
253.98  is  .07820  Ib.  254 -253.98  =  .02.  Neglecting  the  .02°,  the  weight  of 
40  cu.  ft.  is  therefore  .07820X40  =  3.128  Ib. 

EXAMPLE  7. — How  many  pounds  of  steam  at  64  Ib.  pressure,  absolute,  are 
required  to  raise  the  temperature  of  300  Ib.  of  water  from  40°  to  130°  F.,  the 
water  and  steam  being  mixed  together? 

SOLUTION. — The  number  of  heat  units  required  to  raise  1  Ib.  from  40°  to 
130°  is  130° -40°  =  90  B.  T.  U.  Actually,  a  little  more  than  90  would  be 
required  but  the  above  is  near  enough  for  all  practical  purposes.  Then,  to 
raise  300  Ib.  from  40°  to  130°  requires  90X300  =  27,000  B.  T.  U.  This  quan- 
tity of  heat  must  necessarily  come  from  the  steam.  Now,  1  Ib.  of  steam  at 
64  Ib.  pressure  gives  up,  in  condensing,  its  latent  heat  of  vaporization,  or 
906.2  B.  T.  U.;  but,  in  additipn  to  its  latent  heat,  each  pound  of  steam<on  con- 
densing must  give  up  an  additional  amount  of  heat  in  falling  to  130°.  As  the 
original  temperature  of  the  steam  was  296.74°  F.  (see  Steam  Table),  each  pound 
gives  up  by  its  fall  of  temperature  296.74-130  =  166.74  B.  T.  U.  Conse- 
quently, each  pound  of  the  steam  gives  up  a  total  of  906.2  +  166.74  =  1,072.94 
B.  T.  U.,  and  27,000-M,072.94  =  25.16  Ib.  of  steam  will  therefore  be  required 
to  accomplish  the  desired  result. 

SUPERHEATED  STEAM 

If  saturated  steam  in  contained  in  a  vessel,  out  of  contact  with  water,  and 
heat  is  added  to  it,  its  temperature  will  begin  to  rise  and  its  weight  per  cubic 


410  BOILERS 

foot  will  begin  to  decrease,  provided  the  pressure  remains  constant.  As  more 
heat  is  added,  the  temperature  rises  farther  above  that  of  saturated  steam  at 
that  pressure,  and  the  steam  is  then  called  superheated  steam.  Superheated 
steam  cannot  exist  in  contact  with  water. 

The  following  distinction  is  usually  made  between  saturated  and  super- 
heated steam:  For  a  given  pressure,  saturated  steam  has  one  temperature 
and  one  weight  per  cubic  foot,  neither  of  which  can  change  so  long  as  the 
steam  remains  in  immediate  contact  with  water.  Superheated  steam  at  the 
same  pressure  has  a  greater  temperature  and  less  weight  per  cubic  foot  than 
saturated  steam,  and  both  the  temperature  and  weight  per  cubic  foot  may  vary 
while  the  pressure  remains  constant  if  the  volume  increases  or  decreases  accord- 
ingly. In  other  words,  both  the  pressure  and  the  volume  of  superheated  steam 
must  be  constant  in  order  to  maintain  a  constant  temperature  and  a  constant 
weight  per  cubic  foot. 

QUALITY  OF  STEAM 

Moisture  in  Steam. — The  steam  furnished  by  the  average  steam  boiler 
is  not  dry  saturated  steam,  but  is  usually  wet  steam.  A  good  boiler  should 
not  show  more  than  2  or  3%  of  water  in  the  steam.  In  a  quantity  of  wet 
steam,  or  a  mixture  of  steam  and  water,  the  percentage  of  dry  steam,  expressed 
as  a  decimal,  is  called  the  quality  of  the  steam.  For  example,  suppose  that  a 
certain  boiler  generates  wet  steam  that  contains  3%,  or  .03,  of  moisture;  then 
the  quality  of  the  steam,  or  the  percentage  of  dry  steam,  is  .97.  In  other 
words,  the  quality  of  the  steam  is  equal  to  1  minus  the  percentage  of  moisture, 
expressed  decimally,  or  Q  =  \  —  m, 

in  which  Q  =  quality  of  steam; 

m  =  percentage  of  moisture,  expressed  decimally. 

EXAMPLE. — What  is  the  quality  of  steam  that  contains  2.7%  of  moisture? 

SOLUTION. — Expressed  as  a  decimal,  2.7%  =  .027.  Then,  substituting  this 
value  for  m  in  the  formula,  Q  =  1  —  .027  =  .973. 

Heat  in  Wet  Steam. — The  total  heat  contained  in  1  Ib.  of  dry  steam  is  the 
sum  of  the  heat  required  to  raise  1  Ib.  of  water  from  32°  F.  to  the  boiling  point 
and  the  heat  required  to  change  the  boiling  water  into  steam  of  the  same  tem- 
perature. That  is,  in  the  Steam  Table,  each  value  given  in  the  fourth  column 
is  the  sum  of  the  values  given  in  the  third  and  fifth  columns  and  lying  in  the 
same  horizontal  row.  In  a  mixture  of  1  Ib.  of  steam  and  water  at  the  same 
temperature  there  is  less  heat  than  in  1  Ib.  of  dry  steam  at  the  same  temper- 
ature; for  all  the  water  has  not  been  changed  to  steam,  and  consequently  the 
latent  heat  of  1  Ib.  of  steam  has  not  been  utilized.  Instead,  there  is  present 
only  that  part  of  the  latent  heat  which  is  used  to  evaporate  the  portion  of  the 
mixture  that  is  dry  steam,  which  is  represented  by  the  quality  of  the  steam. 
Thus,  using  the  symbols  given  in  the  Steam  Table, 

H  =  q+r  (1) 

which  is  the  formula  for  the  total  heat  of  1  Ib.  of  dry  steam.  But  if  the  steam 
is  wet,  and  Q  represents  the  quality  of  the  steam,  expressed  decimally,  the 
total  heat  of  1  Ib.,  represented  by  Hi,  is 

Hi  =  q+Qr  (2) 

EXAMPLE. — What  is  the  total  heat  of  10  Ib.  of  steam  at  150  Ib.  gauge 
pressure,  if  the  steam  contains  5%  of  moisture? 

SOLUTION. — From  the  Steam  Table,  the  heat  of  the  liquid  of  1  Ib.  of  dry 
steam  at  150  Ib.,  gauge,  or  150  +  14.7  =  164.7  Ib.,  absolute,  is  q  =  337.84  B.  T.  U.. 
and  the  latent  heat  of  1  Ib.  at  the  same  pressure  is  r  =  855.71  B.  T.  U.  As  the 
moisture  is  5%,  the  quality  of  the  steam  is  1.00  — .05  =  .95.  Then,  applying 
formula  2,  fli  =  337.84  +  .95X855.71  =  l,150.76  B.  T.  U. 
FLOW  OF  STEAM 

Weight  of  Steam  Discharged. — The  number  of  pounds  of  steam  that  will 
flow  continuously  through  a  pipe  of  given  diameter  in  1  min.  at  specified  pres- 
sure may  be  calculated  by  the  formula 


in  which    W= weight  of  steam  discharged,  in  pounds  per  minute; 

w  =  weight  of  1  cu.  ft.  of  steam  at  pressure  Pi; 

Pi  =  pressure  of  steam  at  entrance  to  pipe,  in  pounds  per  square  inch; 
Pa  =  pressure  of  steam  at  discharge,  in  pounds  per  square  inch; 

L  =  length  of  pipe,  in  feet; 

d  =  diameter  of  pipe,  in  inches. 


BOILERS 


411 


In  applying  the  preceding  formula  in  determining  the  diameter  of  the  steam 
pipe  for  an  engine,  it  must  be  remembered  that,  in  steam-engine  work,  the 
steam  is  drawn  intermittently  from  the  pipe.  Thus,  assume  that  an  engine 
of  100  H.  P.,  consuming  30  Ib.  of  steam  per  H.  P.  per  hr.,  cuts  off  at  one-fourth 
stroke.  In  that  case,  the  steam  consumption  per  hour  would  be  100X30 
=  3,000  Ib.  But  as  the  steam  used  at  each  stroke  is  drawn  into  the  cylinder 
during  only  one-fourth  of  the  time  required  to  complete  the  stroke,  the  3,000  Ib. 
of  steam  flows  through  the  pipe  in  {  hr.  Then,  in  order  to  determine  the 
quantity  of  steam  that  would  now  continuously  at  the  same  velocity  at  which 
it  flows  during  admission  to  the  cylinder,  the  actual  steam  consumption  per 
hour  should  be  divided  by  the  fraction  representing  the  cut-off  and  the  quotient 
should  be  taken  as  the  weight  of  steam  discharged  per  hour.  This  value, 
divided  by  60,  should  be  substituted  for  w  in  the  formula.  Thus,  in  the  case 
mentioned,  the  amount  of  steam  discharged  per  hour,  flowing  continuously 
at  the  same  velocity  as  during  the  admission  period,  is  3,000-^  =  12,000,  and 
the  value  of  W  to  be  used  in  the  formula  is  therefore  12,000-7-60  =  200  Ib.  per 
min.  Knowing  the  pressures,  the  length  of  pipe,  and  the  weight  of  the  enter- 
ing steam  per  cubic  foot,  different  values  of  d  may  be  assumed,  until  a  value  is 
found  that  will  give  the  necessary  discharge  W.  This  is  the  required  pipe 
diameter. 

WEIGHT  OF  STEAM  DELIVERED  PER  MINUTE  THROUGH  100  FT. 
OF  PIPE  WITH  1  LB.  DROP  OF  PRESSURE 


Initial 
Gauge 
Pressure 
Pounds  per 
Square  Inch 

Nominal  Diameter  of  Pipe,  in  Inches 

3 

3* 

4 

« 

5 

6 

7 

8 

9 

10 

Weight,  in  Pounds,  of  Steam  Delivered  per  Minute 
Through  100  Ft.  of  Pipe  with  1  Lb.  Drop  of  Pressure 

70 
80 
90 
100 
110 
120 
130 
140 
150 

43.2 
45.5 
47.6 
49.7 
51.7 
53.6 
55.4 
57.2 
58.9 

64.5 
68.0 
71.2 
74.3 
77.3 
80.2 
82.9 
85.5 
88.1 

91.7 
96.6 
101.2 
105.7 
109.9 
113.9 
117.8 
121.5 
125.2 

124.3 
130.9 
137.2 
143.2 
148.9 
154.4 
159.7 
164.7 
169.6 

168.7 
177.7 
186.3 
194.4 
202.1 
209.5 
216.7 
223.6 
230.2 

277.2 
292.1 
306.0 
319.8 
332.2 
344.3 
356.1 
367.4 
378.3 

410.5 
432.5 
453.3 
473.0 
491.8 
509.9 
527.4 
544.6 
560.2 

577.2 
608.2 
637.3 
665.1 
691.5 
717.0 
741.6 
765.7 
787.7 

793.3 
835.8 
875.9 
914.1 
950.4 
985.4 
1,019.6 
1,052.9 
1,082.6 

1.051.7 
1,108.4 
1,161.3 
1,211.8 
1,259.9 
1,306.3 
1,351.1 
1,393.9 
1,428.1 

The  approximate  weights  of  steam  delivered  per  minute  through  100  ft.  of 
pipe  of  various  diameters,  with  a  drop  of  pressure  of  1  Ib.,  are  given  in  the 
foregoing  table.  On  the  whole,  these  values  are  slightly  higher  than  those 
that  would  be  obtained  by  the  foregoing  formula  for  the  same  conditions.  If 
the  drop  of  pressure  is  more  or  less  than  1  Ib.,  the  value  in  the  table  must  be 
multiplied  by  the  square  root  of  the  drop,  to  obtain  the  discharge.  Also, 
if  the  length  of  the  pipe  is  more  or  less  than  100  ft.,  divide  100  by  the  length, 
in  feet,  and  multiply  the  square  root  of  this  quotient  by  the  value  given  in  the 
table.  The  following  example  illustrates  this  point. 

EXAMPLE. — How  many  pounds  of  steam  will  be  discharged  per  minute, 
with  an  initial  gauge  pressure  oi  120  Ib.  per  sq.  in.,  through  a  pipe  3  in.  in 
diameter  and  400  ft.  long,  with  a  drop  of  pressure  of  2  Ib.? 

SOLUTION. — From  the  table,  the  amount  discharged  through  100  ft.  of  3-in. 
pipe  with  a  drop  of  1  Ib.  and  an  initial  pressure  of  120  Ib.  per  sq.  in.,  is_53.6  Ib. 
per  min.  But  as  the  drop  is  2  Ib.,  the  table  value  isjnultiplied  by  V2  and  as 
the  length  is  400  ft.,  it  must  also  be  multiplied^  "N/H8-  Hence,  the  discharge 
for  the  given  conditions  will  be  53.6X  V2X  Vi88  =  37.9  Ib.  per  min. 

Resistance  of  Elbows  and  Valves. — The  presence  of  elbows,  bends,  and 
valves  in  a  steam  pipe  increases  the  resistance  to  the  flow  of  steam  and  thus 
increases  the  drop  of  pressure  between  the  inlet  and  outlet  ends.  It  has  been 
found  that  the  resistance  caused  by  an  elbow  or  a  sharp  bend  is  approximately 


412  BOILERS 

the  same  as  the  resistance  of  a  length  of  pipe  equal  to  60  times  the  diameter, 
and  that  a  stop- valve  has  a  resistance  equal  to  that  of  a  length  ot  pipe  ol 
40  diameters.  In  using  the  foregoing  formula  for  the  weight  of  steam  dis- 
charged, therefore,  the  value  of  L  should  be  the  equivalent  length  of  pipe, 
taking  into  account  the  bends  and  valves. 

EXAMPLE.— What  is  the  equivalent  length  of  300  ft.  bf  3-in.  pipe  containing 
four  elbows  and  six  stop- valves? 

SOLUTION.— Each  elbow  has  a  resistance  the  same  as  that  of  60  diameters 
of  pipe,  or  60X3  =  180  in.  =  15  ft.,  and  four  elbows  have  the  resistance  of 
4X16  =  60  ft.  of  pipe.  Each  stop-valve  has  a  resistance  that  is  equivalent  to 
adding  40X3  =  120  in.  =  10  ft.  of  pipe,  and,  as  there  are  six  valves,  their  com- 
bined resistance  is  that  of  6X10  =  60  ft.  of  pipe.  The  equivalent  length  of 
pipe  is,  therefore,  300+60+60  =  420  ft. 

Steam  Pipes  for  Engines. — In  practice,  the  velocity  of  flow  of  steam  in  the 
supply  pipes  of  engines  and  pumps  is  usually  not  greater  than  6,000  ft.  per 
min.,  although  it  is  increased  to  as  much  as  8,000  ft.  per  mm.  in  some  cases. 
For  exhaust  pipes,  a  common  value  is  4,000  ft.  per  mm.  The  assumptions 
made  are  that  the  cylinder  is  filled  with  steam  at  boiler  pressure  at  each  stroke 
and  that  a  volume  of  steam  equal  t9  the  volume  of  the  cylinder  is  released  at 
each  stroke,  so  that  the  flow  is  practically  continuous.  The  areas  of  the  steam 
and  exhaust  pipes  may  then  be  calculated  by  the  formula 

AS 
a  =  - — , 

5 

in  which          a  =  area  of  steam  or  exhaust  pipe,  in  square  inches; 
A  =  area  of  cylinder,  in  square  inches; 
5  =  piston  speed,  in  feet  per  minute; 
s  =  velocity  of  steam  in  pipe,  in  feet  per  minute. 

EXAMPLE. — Find  the  areas  of  the  steam  and  exhaust  pipes  _for  an  engine 
whose  cylinder  is  20  in.  in  diameter  and  whose  piston  speed  is  450  ft.  per  mm. 
SOLUTION. — By  the  formula,  the  area  of  the  steam  pipe,  assuming  that  s 
-6,000  ft.  per  min.,  is 

.7854X202X450 

°  = 6^00 23.6  sq.m 

Similarly,  for  the  exhaust  pipe,  assuming  that  5  =  4,000,  the  area  is 


BOILER  PIPING 

Principal  Considerations. — The  piping  of  an  engine  and  boiler  plant  requires 
that  careful  attention  be  paid  to  all  the  details  as  well  as  to  the  general  design, 
not  only  in  order  to  make  it  suitable  for  the  purpose,  but  also  in  order  to  reduce 
the  likelihood  of  a  breakdown.  The  main  considerations  regarding  steam 
piping  are  the  size  of  the  pipes,  the  arrangement  and  construction  of  the  piping 
system,  the  method  of  providing  for  expansion,  and  proper  drainage. 

Materials  for  Pipes.— Most  of  the  piping  for  steam  and  water  is  built  up  of 
wrought-iron  or  steel  pipe  of  standard  size.  The  various  grades  of  wrought- 
iron  and  steel  pipe  are  known  as  standard,  extra  strong,  and  double  extra  strong. 
Both  wrought-iron  and  steel  pipe  are  used  in  the  piping  systems  of  power 
plants.  Formerly,  wrought  iron  was  chiefly  used,  but  of  late  steel  has  been 
employed,  especially  for  the  larger  sizes  of  steam  pipes.  The  two  kinds  are 
equally  reliable  when  made  into  expansion  bends,  copper  bends  as  a  general 

rule  being  used  only  for  very  heavy  work. 
Expansion  Joints. — In  installing  steam 
piping,  provision  must  be  made  for  ex- 
^\  pansion  and  contraction,  which  ordinarily 
1  amounts  to  about  lj  in.  per  100  ft.  of  pipe. 
""^  Generally,  this  may  be  provided  for  in  the 
arrangement  of  the  piping,  but  for  great 
lengths  that  are  straight,  or  nearly  so,  it 
is  necessary  to  use  expansion  joints,  which 
may  be  made  in  various  ways.  One  form,  shown  in  Fig.  1,  is  called  the 
slip  joint.  The  ends  a  and  b  of  the  sections  of  pipe  come  together  in  a  stuf- 
fingbox  c  in  order  to  make  a  steam-tight  joint.  The  stud  bolts  are  extra 
long,  so  as  to  extend  through  holes  in  a  flange  d  riveted  to  the  pipe  b. 


«=£ 


BOILERS 


413 


^- -^ 


Check-nuts  e  on  the  ends  of  the  studs  prevent  the  two  ends  of  the  pipe  from 

being  forced  apart  by  the  steam  pressure.     The  nuts  e  are  not   intended 

ordinarily  to  be  in  contact  with  the  flange;  their 

distance  from  the  flange  is  adjusted  so  that  the 

proper  expansion  may  occur. 

In  Fig.  2  is  shown  a  corrugated  expansion 

joint,  which  is  sometimes  used  on  large  exhaust  pIG  2 

pipes.     It  consists  of  a  short  section  of  flanged 

corrugated  pipe,  usually  copper,  which  is  put  in  the  steam  pipe  wherever 

necessary.     The  elasticity  of  this  section,  due  to  the  corrugations,  permits 

expansion  and  contraction. 

Expansion  Bends. — The  best  way  of  allowing  for  expansion  is  by  using 

expansion  bends,  or  bent  pipes;  but  the 
space  they  occupy  often  limits  their 
use.  The  forms  of  bends  more  com- 
monly used  are  shown  in  Fig.  3,  the 
trade  name  being  given  below  each 
bend.  Where  a  bent  pipe  is  used,  the 
radius  r  of  the  bend  should  not  be  less 
than  six  times  the  diameter  of  the  pipe, 
for  wrought  iron  or  steel;  to  secure  the 
proper  spring  in  bends  used  on  long 
lines  of  piping,  the  radius  should  be 
greater  than  this.  Bends  of  copper  pipe 
may  be  of  shorter  radius,  as  copper 
yields  more  readily  than  iron  or  steel. 

Bends  made  from  iron  or  steel  pipe 
must  be  bent  while  red  hot.  Iron  and 
steel  pipe  bends  generally  have  iron 
flanges  fastened  on;  copper  bends  either 
have  composition  flanges  riveted  and 
brazed  on,  or  have  steel  flanges,  the 
edges  of  the  pipe  being  turned  over. 
The  piping  is  usually  installed  so  that  it 
is  under  a  slight  tension  when  cold; 
when  filled  with  steam,  the  expansion 
of  the  pipes  removes  the  tension,  and 
there  is  no  stress  on  the  pipe  except 
that  due  to  the  steam  pressure. 

Arrangement  of  Piping. — The  pipes 
and  fittings  must  be  so  proportioned 
as  to  permit  of  free  flow  of  steam  or 
water.  Water  pockets  should  be 
avoided;  and  where  such  pockets  are 
unavoidable,  they  must  be  drained  to 
free  them  from  water.  By-pass  pipes 
should  be  arranged  around  feedwater 
heaters,  economizers,  pumps,  etc.  The 
system  must  be  so  designed  as  to  give 
perfect  freedom  for  expansion  and 
contraction. 

Perfect  drainage  must  be  provided 
in  order  that  all  water  of  condensation 
shall  be  fully  separated  from  the  steam. 
Reliability  is  insured  by  careful 
design  and  superior  workmanship,  com- 
bined with  the  use  of  high-class  mate- 
rials and  fittings  and  the  judicious 
S'acing  of  cut-out  and  by-pass  valves, 
rainage  is  best  effected  by  arranging 
the  piping  so  that  all  the  water  of 
condensation  will  flow  by  gravity  to- 
ward a  point  close  to  the  delivery  end 
of  the  pipe,  and  then  providing  a  drip 

pipe  at  that  point.     A  trap  may  be  placed  at  the  end  of  the  drip  pipe  for 

automatic  draining. 


414 


BOILERS 


BOILER  FITTINGS 

SAFETY  VALVES 

The  safety  valve  is  a  device  attached  to  the  boiler  to  prevent  the  steam 
pressure  from  rising  above  a  certain  point.  When  _  steam  is  made  more 
rapidly  than  it  is  used,  its  pressure  must  necessarily  rise;  and  if  no  means  of 
escape  is  provided  for  it,  the  result  must  be  an  explosion.  Briefly  described, 
the  safety  valve  consists  of  a  plate,  or  disk,  fitting  over  a  hole  in  the  boiler 
shell  and  held  to  its  place  by  a  dead  weight,  by  a  weight  on  a  lever,  or  by  a 
j.  The  weight  or  the  spring  is  so  adjusted  that  when  the  steam  reaches 
desired  pressure  the  disk  is  raised  from  its  seat,  and  the  surplus  steam 
escapes  through  the  opening  in  the  shell. 


rl 

n 

B                       j 

H 

G 

FIG.  1 

Weight  of  Ball  for  Lever  Safety  Valve. — A  simple  diagram  of  a  lever  safety 
valve  is  shown  in  Fig.  1.     The  valve  stem  and  the  ball  are  attached  to  the 
lever  at  C  and  B,  respectively,  and  the  fulcrum  is  at  F. 
Let  d  =  FB  =  distance  from  fulcrum  to  weight,  in  inches; 

c  =  FG  =  distance  from  fulcrum  to  center  of  gravity  of  lever,  in  inches; 
a  =  FC  —  distance  from  fulcrum  to  center  line  of  valve,  in  inches; 
A  =area  of  orifice  beneath  bottom  of  valve,  in  square  inches; 
W= weight  of  ball  P,  in  pounds; 
Wi  =  weight  of  valve  and  stem,  in  pounds; 
Wz  =  weight  of  lever,  in  pounds; 

p  =  blow-off  pressure,  in  pounds  per  square  inch. 

Then,  if  the  position  of  the  ball  P  on  the  lever  is  fixed,  the  required  weight 
of  the  ball  may  be  found  by  the  formula 

,,,_a(PA-Wi)-W* 

d 

EXAMPLE. — The  area  of  the  orifice  is  10  sq.  in.,  the  distance  from  the  valve 
to  the  fulcrum  is  3  in.,  and  the  length  of  the  lever  is  32  in.  The  valve  and 
stem  weigh  5  lb.,  the  lever  weighs  12  lb.,  and  the  gauge  pressure  is  90  Ib. 
What  should  be  the  weight  W,  if  placed  2  in.  from  the  end  of  the  lever,  assuming 
the  lever  to  be  straight? 

SOLUTION.— In  this  case,  c  =  32-J-2  =  16  in.,  and  d  =  32-2  =  30  in.  Then, 
substituting  in  the  formula, 

TT/_  3XQOX10  -5)  -12X16     __ 

§0  -83.  lib. 

Position  of  Ball  for  Lever  Safety  Valve.— If  the  ball  of  a  lever  safety  valve 
has  a  known  weight  and  it  is  desired  to  find  at  what  distance  from  the  fulcrum 
it  must  be  placed  so  as  to  give  a  required  blow-off  pressure,  the  formula  to  be 
used  is 

,_a(pA-Wi)-Wzc 

W 
in  which  the  various  letters  have  the  same  meanings  as  before. 

EXAMPLE.— Suppose  all  the  quantities  to  remain  the  same  as  in  the  solution 
of  the  preceding  example,  except  that  it  is  desired  that  the  boiler  should  blow 
off  at  75.  lb.  gauge  pressure,  instead  of  90  lb.  What  will  be  the  distance  of 
the  weight  from  the  fulcrum? 

SOLUTION. — Applying  the  formula 

,     3X(75X10-5)-12X16     0, 
o  =  —      gg^ —  =  24.58  in. 

Roper's  Safety-Valve  Rules.— Some  inspectors  of  the  United  States  Steam- 
boat Inspection  Service  prefer  to  have  lever  safety-valve  problems  worked 


BOILERS  415 

out  by  the  rules  that  follow,  known  among  American  marine  engineers  as 
Roper's  rules. 

Let  A  =  area  of  valve,  in  square  inches; 

D  —  distance  from  center  line  of  valve  to  fulcrum,  in  inches; 

L  =  distance  of  weight  from  fulcrum,  in  inches; 

P  =  steam  pressure,  in  pounds  per  square  inch; 

W  =  weight  of  load  or  weight  on  lever,  in  pounds; 

V  =  weight  of  valve  and  stem,  in  pounds; 

w  =  weight  of  lever,  in  pounds; 

/  =  distance  from  fulcrum  to  center  of  gravity  of  lever,  in  inches. 
Then,  the  pressure  at  which  the  safety-valve  will  blow  off  is  found  by  the 
formula 


If  the  distance  L  is  known,  the  weight  W  to  be  hung  on  the  lever  is  found 
by  the  formula 

w  =  APD-(wl+VD)  (2) 

The  distance  L  from  the  fulcrum  to  the  point  at  which  the  weight  W  is 
hung  is  found  by  the  formula 

T     APD-(wl+VD)  (3) 

W 

Area  of  Safety  Valve.  —  By  area  of  safety  valve  is  meant  the  area  of  the 
opening  in  the  valve  seat;  that  is,  the  area  of  the  surface  of  the  valve  in  con- 
tact with  steam  when  the  valve  is  closed.  The  size  of  the  valve  relative  to  the 
size  of  the  boiler  and  the  working  pressure  is  prescribed  by  law  in  many  locali- 
ties, and  must  be  made  to  conform  to  the  law  wherever  such  law  is  in  existence. 
In  localities  having  no  law  governing  this  matter,  the  size  of  the  safety  valve 
may  be  calculated  by  the  accompanying  formulas,  which  are  based  on  practice 
and  recommended  by  leading  authorities. 

For  natural  draft, 


For  artiacial  draft, 

(2) 


in  which  G  =  grate  surface,  in  square  feet  ; 

p  =  steam,  gauge  pressure,  in  pounds  per  square  inch; 
10  =  weight  of  coal  burned  per  hour,  in  pounds; 
A  =  least  area  of  safety  valve,  in  square  inches. 

Location  of  Safety  Valve.  —  The  safety  valve  should  be  placed  in  direct  con- 
nection with  the  boiler,  so  that  there  can  be  no  possible  chance  of  cutting  off 
the  communication  between  them.  A  stop-valve  placed  between  the  boiler 
and  the  safety  valve  is  a  very  fruitful  cause  of  boiler  explosions.  Again,  the 
safety  valve  must  be  free  to  act,  and  to  prevent  it  from  corroding  fast  to  its 
seat,  it  should  be  lifted  from  the  seat  occasionally.  Care  must  be  taken  to 
prevent  persons  ignorant  of  the  importance  of  safety  valves  from  raising  the 
blow-off  pressure  by  adding  to  the  weights  or  increasing  the  tension  of  the 
spring.  To  this  end,  the  weights  of  lever  safety  valves  are  often  locked  in 
position  by  the  boiler  inspector. 

FUSIBLE  PLUGS 

Fusible  plugs  are  devices  placed  in  the  crown  sheets  of  furnaces,  or  in 
similar  places,  to  obviate  danger  from  overheating  through  lack  of  water. 
The  plug  often  consists  of  an  alloy  of  tin,  lead,  and  bismuth,  which  melts  at  a 
comparatively  low  temperature.  In  many  localities,  the  law  requires  that 
fusible  plugs  shall  be  attached  to  all  high-pressure  boilers. 

The  fusible  plugs  in  common  use  are  shown  in  section,  on  the  next 
page.  They  consist  of  brass  or  iron  shells  threaded  on  the  outside  with  a 
standard  pipe  thread.  The  plugs  have  some  form  of  conical  filling,  the  larger 
end  of  the  filling  receiving  the  steam  pressure.  The  conical  form  of  the  filling 
prevents  it  from  being  blown  out  by  the  pressure  of  the  steam.  Fusible  plugs 
applied  from  the  outside  differ  from  those  applied  from  the  inside,  as  shown. 

Location  of  Fusible  Plugs.  —  In  the  absence  of  local  laws,  the  following 
rules  issued  by  the  Board  of  Boiler  Rules  of  the  State  of  Massachusetts  may 
be  adopted.  Fusible  plugs  must  be  filled  with  pure  tin,  and  the  least  diameter 


416  BOILERS 

shall  not  be  less  than  \  in.,  except  for  working  pressures  over  175  lb.,  gauge, 
or  when  it  is  necessary  to  place  a  fusible  plug  in  a  tube,  in  which  cases  the  least 
diameter  of  fusible  metal  shall  not  be  less  than 
|  in.  The  location  of  fusible  plugs  shall  be  as 
follows: 

In  horizontal  return-tubular  boilers,  in  the 
back  head,  not  less  than  2  in.  above  the  upper 
row  of  tubes  and  projecting  through  the  sheet 
not  less  than  1  in. 

In  horizontal  flue  boilers,  in  the  back  head, 
on  a  line  with  the  highest  part  of  the  boiler 
exposed  to  the  products  of  combustion,  and 

projecting  through  the  sheet  not  less  than  1  in. 

Sns/afe  Type    Oute/de  Type  jn  iOCOmotive-type  or  star  water-tube  boil- 

ers, in  the  highest  part  of  the  crown  sheet  and  projecting  through  the  sheet 

In  vertical  fire-tube  boilers,  in  an  outside  tube,  placed  not  less  than  one- 
third  the  length  of  the  tube  above  the  tower  tube-sheet. 

In  vertical  submerged-tube  boilers,  in  the  upper  tube-sheet. 

In  water-tube  boilers  of  the  Babcock  &  Wilcox  type,  in  the  upper  drum,  not 
less  than  6  in.  above  the  bottom  of  the  drum  and  projecting  through  the  sheet 

In  Stirling  boilers  of  standard  type,  in  the  front  side  of  the  middle  drum 
not  less  than  6  in.  above  the  bottom  of  the  drum  and  projecting  through  the 
sheet  not  less  than  1  in. 

In  Stirling  boilers  of  the  superheated  type,  in  the  front  drum,  not  less  than 
6  in.  above  the  bottom  of  the  drum,  and  exposed  to  the  products  of  combustion, 
projecting  through  the  sheet  not  less  than  1  in. 

In  water-tube  boilers  of  the  Heine  type,  in  the  front  course  of  the  drum, 
not  less  than  6  in.,  from  the  bottom  of  the  drum,  and  projecting  through  the 
sheet  not  less  than  1  in. 

In  Robb-Mumford  boilers  of  standard  type,  in  the  bottom  of  the  steam  and 
water  drum,  24  in.  from  the  center  of  the  rear  neck,  and  projecting  through  the 
sheet  not  less  than  1  in. 

In  water-tube  boilers  of  the  Almy  type,  in  a  tube  directly  exposed  to  the 
products  of  combustion.  . 

In  vertical  boilers  of  the  Climax  or  Hazleton  type,  in  a  tube  or  center  drum, 
not  less  than  one-half  the  height  of  the  shell,  measuring  from  the  lowest  circum- 
ferential seam. 

In  Cahall  vertical  water-tube  boilers,  in  the  inner  sheet  of  the  top  drum, 
not  less  than  6  in.  above  the  upper  tube  sheet. 

In  Scotch  marine-type  boilers,  in  the  combustion-chamber  top,  and  pro- 
jecting through  the  sheet  not  less-than  1  in. 

In  dry-back  Scotch-type  boilers,  in  the  rear  head,  not  less  than  2  in.  above 
the  top  row  of  tubes,  and  projecting  through  the  sheet  not  less  than  1  in. 

In  Economic-type  boilers,  in  the  rear  head,  above  the  upper  row  of  tubes. 

In  cast-iron  sectional  heating  boilers,  in  a  section  over  and  in  direct  contact 
with  the  products  of  combustion  in  the  primary  combustion  chamber. 

In  other  types  and  new  designs,  fusible  plugs  shall  be  placed  at  the  lowest 
permissible  water  level,  in  the  direct  path  of  the  products  of  combustion,  as 
near  the  primary  combustion  chamber  as  possible. 

CONNECTION  OF  STEAM  GAUGE 

A  steam  gauge  should  be  connected  to  the  boiler  in  such  a  manner  that  it 
will  neither  be  injured  by  heat  nor  indicate  incorrectly  the  pressure  to  which 
it  is  subjected.  To  prevent  injury  from  heat,  a  so-called  siphon  is  placed 
between  the  gauge  and  the  boiler.  This  siphon  in  a  short  time  becomes  filled 
with  water  of  condensation,  which  protects  the  spring  of  the  gauge  from  the 
injury  the  hot  steam  would  cause.  Care  should  be  taken  not  to  locate  the 
steam-gauge  pipe  near  the  main  steam  outlet  of  the  boiler,  as  this  may  cause 
the  gauge  to  indicate  a  lower  pressure  than  really  exists.  In  locating  the  steam 
gauge,  care  must  also  be  taken  not  to  run  the  connecting  pipe  in  such  a  manner 
that  the  accumulation  of  water  in  it  will  cause  an  extra  pressure  to  be  shown. 

BLOW-OFFS 

For  the  double  purpose  of  emptying  the  boiler  when  necessary  and  of 
discharging  the  loose  mud  and  sediment  that  collect  from  the  feed  water,  every 
boiler  is  provided  with  a  pipe  that  enters  the  boiler  at  its  lowest  point.  This 


BOILERS  417 

pipe,  which  is  provided  with  a  valve  or  a  cock,  is  commonly  known  as  the 
bottom  blow-off.  The  position  of  the  blow-off  pipe  varies  with  the  design  of 
the  boiler;  in  ordinary  return-tubular  boilers,  it  is  usually  led  from  the  bottom 
of  the  rear  end  of  the  shell  through  the  rear  wall.  Where  the  boiler  is  fitted 
with  a  mud-drum,  the  blow-off  is  attached  to  the  drum. 

Blow-Off  Cocks  and  Valves. — While  in  many  boiler  plants  globe  valves 
are  used  on  the  blow-off  pipe,  they  have  the  disadvantage  that  the  valve 
may  be  kept  from  closing  properly  by  a  chip  of  incrustation  or  similar  matter 
getting  between  the  valve  and  its  seat,  with  the  result  that  water  may  leak  out 
of  the  boiler  unnoticed.  Plug  cocks  packed  with  asbestos  are  widely  used, 
the  asbestos  packing  obviating  the  objectionable  features  of  the  ordinary  plug 
cock.  Gate  valves  are  also  used  to  some  extent,  but  have  the  same  disadvant- 
age as  globe  valves.  In  the  best  modern  practice,  the  blow-off  pipe  is  fitted 
with  two  shut-off  devices.  The  one  shut-off  may  be  an  asbestos-packed  cock 
and  the  other  some  form  of  valve,  or  both  may  be  cocks  or  valves,  the  idea 
underlying  this  practice  being  that  leakage  past  the  shut-off  nearest  the  boiler 
will  be  arrested  by  the  other. 

Protection  of  Blow-Off  Pipe. — When  exposed  to  the  gases  of  combustion, 
the  bottom  blow-off  pipe  should  always  be  protected  by  a  sleeve  made  of  pipe, 
by  being  bricked  in,  or  by  a  coil  of  plaited  asbestos  packing.  If  this  precaution 
is  neglected,  the  sediment  and  mud  collecting  in  the  pipe,  in  which  there  is  no 
circulation,  will  rapidly  become  solid.  The  blow-off  pipe  should  lead  to  some 
convenient  place  entirely  removed  from  the  boiler  house  and  at  a  lower  level 
than  the  boiler.  Sometimes  it  may  be  connected  to  the  nearest  sewer.  In 
many  localities,  however,  ordinances  prohibit  this  practice;  the  blow-off  is  then 
connected  to  a  cooling  tank,  whence  the  water  may  be  discharged  into  the  sewer. 


FURNACE  FITTINGS 

Bridge  Wall. — The  bridge,  also  termed  the  bridge  wall,  is  a  low  wall  at  the 
back  end  of  the  grate;  it  forms  the  rear  end  of  the  furnace  and  causes  the  flame 
to  come  into  close  contact  with  the  heating  surface  of  the  boiler.  It  is  usually 
built  of  common  brick  and  faced  with  firebrick.  The  passage  between  the 
bridge  and  the  boiler  shell  should  not  be  too  small;  its  area  may  be  approx- 
imately one-sixth  the  area  of  the  grate.  The  space  between  the  grate  and  the 
shell  should  be  ample  for  complete  combustion,  and  the  distance  between 
the  grate  and  the  boiler  shell  may  be  made  about  one-half  the  diameter 
of  the  shell. 

Fixed  Grates. — The  grate,  which  is  nearly  always  made  of  cast  iron,  fur- 
nishes a  support  for  the  fuel  to  be  burned  and  must  be  provided  with  spaces 

for  the  admission  of  air.  The  area 
of  the  solid  portion  of  the  grate  is 
usually  made  nearly  equal  to  the 
combined  area  of  the  air  spaces. 

[— • • ri — r— i        The  common  type  of  fixed  grate 

I— *-^_^^  a    I  ^ — *— '  is  made  of  single  bars  a,  Fig.   1, 

"~~ LL "*  placed  side  by  side  in  the  furnace. 

PJQ  *  The  thickness  of  the  lugs  cast  on 

the  sides  of  the  bars  determines  the 

width  of  the  open  spaces  of  the  grate.  It  is  the  general  practice  to  make  the 
thickness  across  the  lugs  twice  the  thickness  of  the  top  of  the  bar.  For  long 
furnaces,  the  bars  are  generally  made  in  two  lengths  of  about  3  ft.  each,  with 
a  bearing  bar  in  the  middle  of  the  grate.  Long  grates  are  generally  set  with  a 
downward  slope  toward  the  bridge  wall  of  about  f  in.  per  ft.  of  length. 

For  the  larger  sizes  of  anthracite  and  bituminous  coal,  the  air  space  may 
be  from  f  to  f  in.  wide,  and  the  grate  bar  may  have  the  same  width.  For 
pea  and  nut  coal,  the  air  space  may 
be  from  f  to  £  in.,  and  for  finely 
divided  fuel,  like  buckwheat,  rice, 
bird's-eye,  culm,  and  slack,  air  spaces 
from  &  to  f  in.  may  be  used. 

The  grate  bar  shown  in  Fig.  2,  pIG  2 

and  known  as  the  herring-bone  grate 

bar,  has  in  many  places  superseded  the  ordinary  grate  bar,  because  it  will  usually 
far  outlast  a  set  of  ordinary  grate  bars.  Herring-bone  grate  bars  can  be 
obtained  in  a  great  variety  of  styles  and  with  different  widths  of  air  spaces. 
They  are  usually  supported  on  cross-bars,  and,  like  many  other  forms  of  grate 
27 


418 


BOILERS 


bars,  may  be  arranged  with  trunnions,  so  as  to  rock  the  individual  bars  by  means 
of  hand  levers. 

A  form  of  cast-iron  grate  bar  for  the  burning  of  sawdust  is  shown  in  Fig.  3. 
The  bar  is  semicircular  in  cross-section  and  is  provided  with  circular  openings 

for  the  introduction  of  air.     Lugs 
are  cast  on  each  side  of  the  bar 
to  serve  as  distance  pieces  in  pro- 
vid  ing  air  spaces  between  the  bars. 
Dead  Plate.— The  front  ends 
of  the  grate  bars  are  usually  sup- 
•  -TIG-  6  ported  on  the  dead  plate,  which 

is  a  flat  cast-iron  plate  placed  across  the  furnace  just  inside  the  boiler  front 
and  on  a  level  with  the  bottom  of  the  furnace  door.  The  purpose  of  the 
dead  plate  is  twofold:  It  forms  a  support  for  the  firebrick  lining  of  the  boiler 
front,  and  a  resting  place  on  which  bituminous  coal  may  be  coked  before  it  is 
placed  on  the  fire.  To  support  the  grate  bars,  the  inner  edge  of  the  dead  plate 
is  either  beveled  or  a  lip  is  provided,  as  at  a,  Fig.  4. 

Objection  to  Stationary  Grate  Bars. — The  greatest  objection  to  stationary 
grate  bars  is  that  with  them  the  furnace  door  must  be  kept  open  for  a  con- 
siderable length  of  time  when  the  fire  is  being  cleaned.  Cleaning  fires  when  the 
boiler  has  a  stationary  grate  not  only  severely  taxes  the  fireman,  but  the  inrush 
of  cold  air  chills  the  boiler  plates,  thus  producing  stresses  that  in  the  course 
of  time  will  crack  them. 

Shaking  Grates. — There  are  on  the  market  many  designs  of  shaking  grates 
for  large  steam  boilers,  differing  chiefly  in  detail  and  arrangement.  Usually 
the  grate  bars  are  hung  on  trunnions  at  each 
end  and  are  connected  together  with  bars  to 
which  are  attached  shaking  rods  that  extend 
forwards  through  the  furnace  front.  Levers  or 
handles  are  attached  to  the  shaking  rods,  and 
by  working  them  back  and  forth  the  grate  bars  rlG.  4 

receive  a  rocking  motion  that  breaks  up  the  bed  of  coal  on  the  grate  and  serves 
to  shake  the  ashes  through  into  the  ash-pit.  The  fires  may  thus  be  kept  clean 
without  the  necessity  of  opening  the  fire-doors. 

Classes  of  Mechanical  Stokers. — A  mechanical  stoker  is  a  power-driven 
rocking  grate  arranged  so  as  to  give  a  uniform  feed  of  coal  and:  to  rid  itself 
continuously  of  ashes  and  clinkers.     The  principal  designs   of  mechanical 
stokers  and  automatic  furnaces  may  be  divided  into 
two  general  classes,  overfeed  and  underfeed. 

Overfeed    Stoker. — In    overfeed    stokers    the 
fixed   carbon   of   the   coal  is  burned  on  inclined 
grates.     The  coal  is  pushed   on  to  these  grates, 
which  are  given  a  sufficiently  rapid  vibratory  mo- 
tion to  feed  it  down  at  such  a  rate  that  practically 
all  the  carbon  is  burned  before  reaching  the  lower 
end,  where  the  ashes  and  clinkers  are  discharged. 
In  Fig.  5  is  shown  a  sectional  view  of  a  stoker  of 
this  class.     The 
coal  is  fed  into 
the    hopper    a, 
from  which  it  is 
pushed   by  the 
pusher  plate  6 
on  to  the  dead 
plate   c,   where 
it  is    heated. 
From  c  it  passes 
to  the  grate  d. 
Each  bar  is  sup- 
ported   at  its 

«__    _  ends  by  trunn- 

FlG-  5  ions  and  is  con- 

nected by  an  arm  to  a  rocker  bar  »,  which  is  slowly  moved  to  and  fro  by  an 
eccentric  on  the  shaft  s,  so  as  to  rock  the  grates  back  and  forth;  the  grates 
thus  gradually  move  the  burning  fuel  downwards.  The  ashes  and  clinkers 
are  discharged  from  the  lower  grate  bar  on  to  the  dumping  grate  e.  A  guard  / 
may  be  raised,  as  shown  by  the  dotted  lines,  so  as  to  prevent  coke  or  coal  from 
falling  from  the  grate  bars  into  the  ash-pit  when  the  dumping  grate  is  lowered. 


BOILERS 


419 


Air  for  burning  the  gases  is  admitted  in  small  jets  through  holes  in  the  air 
tile  g,  and  the  mixture  of  gas  and  air  is  burned  in  the  hot  chamber  between  the 
firebrick  arch  h  and  the  bed  of  burning  coke  below. 

Underfeed  Stoker. — The  stoker  shown  in  Fig.  6  illustrates  the  principle  of 
operation  and  the  construction  of  the  underfeed  stoker.  Coal  is  fed  into  the 
hopper  a,  from  which  it  is  drawn  by  the  spiral  conveyer  b  and  forced  into  the 
magazine  d.  The  incoming  supply  of  fresh  coal  forces  the  fuel  upwards  to  the 
surface  and  over  the  sides  of  the  magazine  on  the  grates,  where  it  is  burned. 
A  blower  forces  air  through  a  pipe  /  into  the  chamber  g  surrounding  the  maga- 


FIG.  6 

zine.  From  g  the  air  passes  upwards  through  hollow-cast  iron  tuyere  blocks 
and  out  through  the  openings,  or  tuyeres  e.  The  gas  formed  in  the  magazine, 
mixed  with  the  jets  of  air  from  the  tuyeres,  rises  through  the  burning  fuel 
above,  where  it  is  subjected  to  a  sufficiently  high  temperature  to  secure  its 
combustion.  Nearly  all  the  air  for  burning  the  coal  is  supplied  through  the 
tuyeres,  only  a  very  small  portion  of  the  supply  coming  through  the  grate. 
The  ashes  and  clinkers  are  gradually  forced  to  the  sides  of  the  grate  against 
the  side  walls  of  the  furnace,  from  which  they  are  removed  from  time  to  time 
through  doors  in  the  furnace  front  similar  to  the  fire-doors  of  an  ordinary 
furnace.  In  other  words,  owing  to  the  construction  of  the  underfeed  stoker, 
the  fire  must  periodically  be  cleaned  from  clinkers  and  the  ashes  removed 
by  hand. 


COVERING  FOR  BOILERS,  STEAM  PIPES,  ETC. 

The  losses  by  radiation  from  uncovered  pipes  and  vessels  containing  steam 
are  considerable,  and  in  the  case  of  pipes  leading  to  steam  engines,  are  mag- 
nified by  the  action  of  the  condensed  water  in  the  cylinder.  It  therefore  is 
important  that  such  pipes  should  be  well  protected.  The  accompanying 
table  gives  the  loss  of  heat  from  steam  pipes  naked,  and  covered  with  wool  or 
hair  felt  of  different  thickness,  the  steam  pressure  being  assumed  at  75  lb., 
and  the  exterior  air  at  60°. 

There  is  a  wide  difference  in  the  value  of  different  substances  for  protection 
from  radiation,  their  values  varying  nearly  in  the  reverse  ratio  to  their  con- 
ducting power  for  heat,  up  to  their  ability  to  transmit  as  much  heat  as  the 
surface  of  the  pipe  will  radiate,  after  which  they  become  detrimental,  rather 
than  useful,  as  covering.  This  point  is  reached  nearly  at  baked  clay  or  brick. 


420 


8 


BOILERS 


t-       OOO 
O       CO  i-l 


O       N  » 

•^     eo 


00       COM<NOC<3 


>o  O  t^  c<  oo  i-^  co 


oo  o;  <N  O5  1>;  i-;  •* 


(NOOi-ilNO'* 
CC  00  Tf<  CO  <N  «O 


O  t^  t^  00  •«*  00 


BOILERS 


421 


A  smooth  or  polished  surface  is  of  itself  a  good  protection,  polished  tin  or 
Russia  iron  having  a  ratio,  for  radiation,  of  53  to  100  for  cast  iron.  Mere 
color  makes  but  little  difference. 


CONDUCTING  POWER  OF  VARIOUS  SUBSTANCES 

(From  Peclet) 


Substance 

Conducting 
Power 

Substance 

Conducting 
Power 

.274 

Wood,  across  fiber 

83 

Eiderdown  
Co'tton    or    wool,    any 

.314 

Cork  
Coke,  pulverized  ... 

1.15 
1.29 

density  

.323 

India  rubber  

1.37 

.418 

Wood,  with  fiber  

1.40 

.523 

Plaster  of  Paris 

3  86 

Wood  ashes     

.531 

Baked  clay  

4.83 

Straw 

.563 

Glass     .  . 

660 

Charcoal  powder  

.636 

Stone  

13.68 

Hair  or  wool  felt  has  the  disadvantage  of  becoming  soon  charred  from 
the  heat  of  steam  at  high  pressure,  and  sometimes  of  taking  fire  therefrom. 
This  has  led  to  a  variety  of  cements  for  covering  pipes — composed  generally 
of  clay  mixed  with  different  substances,  as  asbestos,  paper  fiber,  charcoal, 
etc.  A  series  of  careful  experiments,  made  at  the  Massachusetts  Institute 
of  Technology  showed  the  condensation  of  steam  in  a  pipe  covered  by  one 
of  them,  as  compared  with  a  naked  pipe,  and  one  covered  with  hair  felt,  was 
100  for  the  naked  pipe,  67  for  the  cement  covering,  and  27  for  the  hair  felt. 

The  presence  of  sulphur  in  the  best  coverings  and  its  recognized  injurious 
effects  make  it  imperative  that  moisture  be  kept  from  the  coverings,  for,  if 
present,  it  will  surely  combine  with  the  sulphur,  thus  making  it  active.  Stated 
in  other  words,  the  pipes  and  coverings  must  be  kept  in  good  repair.  Much 
of  the  inefficiency  of  coverings  is  due  to  the  lack  of  attention  given  them; 
they  are  often  seen  hanging  loosely  from  the  pipe  that  they  are  supposed 
to  protect. 

RELATIVE  VALUE  OF  NON-CONDUCTORS 

(From  Chas.  E.  Emery,  Ph.  D.) 


Material 

Value 

Material 

Value 

3.35 

Wood  across  the  grain 

.40  to  .55 

Loose  lampblack  
Goose  feathers 

1.12 
1.08 

Loam,  dry  and  open  .  .  . 
Chalk  ground 

.55 
.51 

Pelt,  hair  or  wool  

1.00 

Coal  ashes  

.35  to  .49 

Carded  cotton  ...    . 

1.00 

Gas-house  carbon  

.47 

Charcoal  from  cork  .... 

.87 

Asbestos  paper  

.47 

Mineral  wool  

.68  to  .83 

Paste  of  fossil  meal  and 

Fossil  meal 

.66  to  .79 

.47 

Straw  rope,  wound  spir- 
ally 

.77 

Asbestos,  fibrous  
Plaster  of  Paris,  dry 

.36 
.34 

Rice  chaff,  loose  

.76 

Clay,    with    vegetable 

Carbonate  of  magnesia 

.67  to  .76 

fiber  

.34 

Charcoal  from  wood  .  .  . 
Paper                   

.63  to  .75 
.50  to  .74 

Anthracite  powdered.  .  . 
Coke,  in  lumps  

.29 
.27 

Cork 

.71 

Air  space,  undivided  . 

.14  to  .22 

Sawdust  

.61  to  .68 

Sand  

.17 

Paste  of  fossil  meal  and 

.63 

Baked  clay,  brick  
Glass 

.07 
.05 

Wood  ashes     

.61 

Stone  

.02 

422 


BOILERS 


The  preceding  table  is  deduced  from  tests  of  raw  materials  contained 
in  commercial  pipe  coverings  and  does  not  indicate  the  relative  values  of  cover- 
ings into  whose  composition  they  enter.  Mineral  wool,  a  fibrous  material  made 
from  blast-furnace  slag,  is  a  good  protection,  and  is  incombustible.  Cork 
chips,  cemented  together  with  water  glass  make  one  of  the  best  coverings 
known. 

A  cheap  jacketing  for  steam  pipes,  but  a  very  efficient  one,  may  be  applied 
as  follows:  First,  wrap  the  pipe  in  asbestos  paper,  though  this  may  be  dis- 
pensed with;  then  lay  from  6  to  12  strips  of  wood  lengthwise,  according  to 
size  of  pipe,  binding  them  in  position  with  wire  or  cord,  and  around  the  frame- 
work thus  constructed  wrap  roofing  paper,  fastening  it  by  paste  or  twine. 
For  flanged  pipe,  space  may  be  left  for  access  to  the  bolts,  which  space  should 
be  filled  with  felt.  If  exposed  to  weather,  tarred  paper  should  be  used  or  the 
exterior  should  be  painted.  A  French  plan  is  to  cover  the  surface  with  a  rough 
flour  paste,  mixed  with  sawdust  until  it  forms  a  moderately  stiff  dough.  It 
should  be  applied  with  a  trowel,  in  four  or  five  layers  each  \  in.  thick.  If  iron 
surfaces  are  well  cleaned  from  grease,  the  adhesion  is  perfect;  for  copper,  a 
hot  solution  of  clay  in  water  should  be  applied.  A  coating  of  tar  renders  the 
composition  impervious  to  the  weather. 


BOILER  FEEDING  AND  FEEDWATER 

INJECTORS 

Classification  of  Injectors. — Injectors  may  be  divided  into  two  general 
classes,  namely,  non-lifting  and  lifting  injectors.  Non-lifting  injectors  are 
intended  for  use  where  there  is  a  head  of  water  available.  When  the  water 
comes  to  a  non-lifting  injector  under  pressure,  as  from  a  city  main,  it  can  be 
placed  in  almost  any  convenient  position  close  to  the  boiler.  Lifting  injectors 
are  of  two  distinct  types,  called  automatic  injectors  and  positive  injectors.  As 
positive  injectors  generally  have  two  sets  of  tubes,  they  are  frequently  called 
double-tube  injectors.  Automatic  injectors  are  so  called  from  the  fact  that  they 
will  automatically  start  again  in  case  the  jet  of  water  is  broken  by  jarring  or 
other  means.  Positive,  or  double-tube  injectors  are  provided  with  two  sets  of 
tubes,  one  set  of  which  is  used  for  lifting  the  water,  and  the  other  set  for  forcing 
the  water  thus  delivered  to  it  into  the  boiler.  A  positive  injector  has  a  wider 
range  than  an  automatic  injector  and  will  handle  a  hotter  feed- water  supply; 
it  will  also  lift  water  to  a  greater  height  than  the  automatic  injector. 

Advantages  and  Disadvantages  of  Injectors. — The  advantages  of  the  injec- 
tor as  a  boiler  feeding  apparatus  are  its  cheapness,  compared  with  a  pump  of 
equal  capacity;  it  occupies  but  little  space;  the  repair  bills  are  low,  owing  to  the 
absence  of  moving  parts;  no  exhaust  piping  is  required,  as  with  a  steam  pump; 
it  delivers  hot  water  to  the  boiler. 

The  disadvantages  of  the  injector  are  that  it  will  not  start  with  a  steam  pres- 
sure less  than  that  for  which  it  is  designed,  and  that  it  will  stand  but  little 
abuse,  being  poorly  adapted  for  handling  water  containing  grit  or  other  matter 
liable  to  cut  the  nozzles. 

Size  of  Injector. — Most  engineers  prefer  to  select  a  size  of  injector  having 
a  capacity  per  hour  about  one-half  greater  than  the  maximum  evaporation 
per  hour  in  order  to  have  some  reserve  capacity.  The  maximum  evaporation, 

WATER  DELIVERED  BY  INJECTORS 


Diameter  of 
Throat 
Decimals  of  an 
Inch 

Delivery,  in  Gallons  per  Hour,  with  a  Pressure 
per  Square  Inch  of 

30  Lb. 

45  Lb. 

60  Lb. 

75  Lb. 

90  Lb. 

.10 
.15 
.20 
.25 
.30 

56 
127 
226 
354 
505 

69 
156 
278 
434 
624 

80 
180 
321 
502 
722 

89 
201 
360 
561 

807 

98 
221 
393 
615 

884 

BOILERS 


when  not  known,  may  be  estimated  in  United  States  gallons  by  one  of  the  fol- 
lowing rules,  which  hold  good  for  ordinary  combustion  rates  under  natural 
draft: 

Rule  I. — For  plain  cylindrical  boilers,  multiply  the  product  of  the  length  and 
diameter  in  feet  by  1 .3. 

Rule.  II. — For  tubular  boilers,  either  horizontal  or  vertical,  multiply  the  product 
of  the  square  of  the  diameter,  in  feet,  and  the  length,  in  feet,  by  1.9. 

Rule  III. — For  water-tube  boilers,  multiply  the  heating  surface,  in  square  feet, 
by  .4. 

Rule  IV. — For  boilers  not  covered  by  the  foregoing  rules,  multiply  the  grate 
surface,  in  square  feet,  by  12. 

Rule  V. — //  the  coal  consumption,  in  pounds  per  hour,  is  known,  it  may  be 
taken  as  representing  the  number  of  gallons  evaporated  per  hour, 

No  standard  method  of  designating  the  size  of  an  injector  is  followed  by 
all  makers;  therefore,  such  an  instrument  must  be  selected  from  the  lists  of 
capacities  published  by  the  different  makers. 

WATER  REQUIRED  PER  MINUTE  TO  FEED  BOILERS 


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20 

1.2 

60 

3.6 

110 

6.6 

190 

11.4 

400 

24.0 

25 

1.5 

65 

3.9 

120 

7.2 

200 

12.0 

450 

27.0 

30 

1.8 

70 

4.2 

130 

7.8 

225 

13.5 

500 

30.0 

35 

2.1 

75 

4.5 

140 

8.4 

250 

15.0 

600 

36.0 

40 

2.4 

80 

4.8 

150 

9.0 

275 

16.5 

700 

42.0 

45 

2.7 

85 

5.1 

160 

9.6 

300 

18.0 

800 

48.0 

50 

3.0 

90 

5.4 

170 

10.2 

325 

19.5 

900 

54.0 

55 

3.3 

100 

6.0 

180 

10.8 

350 

21.0 

1,000 

60.0 

NOTE. — A.  S.  M.  E.  standard  of  30  lb.,  or  3.6  gal.,  per  H.  P.  per  hr.,  evapo- 
rated from  100°  F.,  to  70  lb.  steam  pressure  per  square  inch. 

Location  of  Injector. — An  injector  must  always  be  placed  in  the  position 
recommended  by  the  maker.  There  must  always  be  a  stop- valve  in  the  steam- 
supply  pipe  to  the  injector.  While  lifting  injectors,  when  working  as  such, 
scarcely  need  a  stop-valve  in  the  suction  pipe,  it  is  advisable  to  supply  it. 
When  the  water  flows  to  the  injector  under  pressure,  a  stop- valve  in  the  water- 
supply  pipe  is  a  necessity.  A  stop-valve  and  a  check- valve  must  be  placed  in 
the  feed-delivery  pipe,  with  the  stop-valve  next  to  the  boiler.  The  check- 
valve  should  never  be  omitted,  even  if  the  injector  itself  is  supplied  with  one. 
No  valve  should  ever  be  placed  in  the  overflow  pipe,  nor  should  the  overflow 
be  connected  directly  to  the  overflow  pipe,  but  a  funnel  should  be  placed  on 
the  latter  so  that  the  water  can  be  seen.  This  direction  does  not  apply  to  the 
inspirator  or  to  any  other  injector  that  has  a  hand-operated,  separate  over- 
flow valve.  In  the  inspirator,  the  overflow  pipe  is  connected  directly  to  the 
overflow,  but  the  end  of  the  pipe  must  be  open  to  the  air.  In  general,  where 
the  injector  lifts  water  it  is  not  advisable  to  have  a  foot-valve  in  the  suction 
pipe,  as  it  is  desirable  that  the  injector  and  pipe  may  drain  themselves  when  not 
in  use.  A  strainer  should  be  placed  on  the  end  of  the  suction  pipe. 

Steam  Supply  to  Injector. — The  steam  for  the  injector  must  be  taken  from 
the  highest  part  of  the  boiler,  as  it  must  be  supplied  with  dry  steam.  Under 
no  consideration  should  the  steam  be  taken  from  another  steam  pipe.  The 
suction  pipe  should  be  as  straight  as  possible  and  must  be  air-tight.  When 
connecting  up  an  injector,  the  pipes  should  be  cleaned  by  being  blown  out  with 
steam  before  the  connection  is  made,  because  if  a  small  bit  of  dirt  gets  into  the 
injector  it  will  interfere  seriously  with  its  operation. 

Injector  Troubles. — In  the  following  discussion  of  injector  troubles,  the 
suction  pipe,  strainer,  feed-delivery  pipe,  and  check-valve  are  considered  as 
parts  of  the  injector.  When  searching  for  the  cause  of  a  trouble,  therefore, 


424  BOILERS 

the  suction  and  delivery  pipes  should  be  carefully  inspected  as  well  as  the 

1 .  Failure  to  Raise  Water — The  causes  that  prevent  an  injector  from  raising 
water  are: 

Suction  pipe  stopped  up,  due,  generally,  to  a  clogged  strainer  or  to  the  pipe 
itself  being  stopped  at  some  point.  In  case  the  suction  pipe  is  clogged,  steam 
should  be  blown  back  through  the  pipe  to  force  out  the  obstruction. 

Leaks  in  suction  pipe,  which  prevent  the  injector  forming  the  vacuum 
'required  to  raise  the  water.  To  test  the  suction  pipe  for  air  leaks,  plug  up  the 
end  and  turn  the  full  steam  pressure  on  the  pipe;  leaks  will  then  be  revealed 
by  the  steam  issuing  therefrom.  Have  the  suction  pipe  full  of  water  before 
steam  is  turned  on,  as  the  presence  of  small  leaks  will  be  revealed  better  by 
water  than  by  steam. 

Water  in  the  suction  pipe  too  hot;  a  leaky  steam  valve  or  leaky  boiler  check- 
valve  and  leaky  injector  check- valve  may  allow  hot  water  or  steam  to  enter 
the  source  of  supply  and  heat  the  water  until  the  injector  refuses  to  handle  it. 

Obstruction  in  the  lifting  or  combining  tubes;  or,  the  spills  (or  openings)  in 
the  tubes  through  which  the  steam  and  water  escape  to  the  overflow  may  be 
clogged  up  with  dirt  or  lime. 

2.  Injector  Primes  But  Will  Not  Force — In  some  cases  an  injector  will  lift 
water,  but  will  not  force  it  into  the  boiler;  or,  it  may  force  part  of  it  into  the 
boiler  and  the  rest  out  of  the  overflow.     When  it  fails  to  force,  the  trouble 
may  be  due  to  one  or  the  other  of  the  following  causes: 

Choked  Suction  Pipe  or  Strainer. — If  the  suction  pipe  or  strainer  is  partly 
choked,  the  injector  will  be  prevented  from  lifting  sufficient  water  to  condense  all 
the  steam  issuing  from  the  steam  valve.  The  uncondensed  steam,  therefore,  will 
gradually  decrease  the  vacuum  in  the  combining  tube  until  it  is  reduced  so  much 
that  the  injector  will  not  work.  The  remedy,  when  the  supply  valve  is  partly 
closed,  is  to  open  it;  when  the  suction  pipe  is  choked,  blow  out  the  obstruction. 

Suction  Pipe  Leaking. — The  leak  may  not  be  sufficient  to  prevent  the 
injector  from  lifting  water,  but  the  quantity  lifted  may  be  insufficient  to  con- 
dense all  the  steam,  which,  therefore,  destroys  the  vacuum  in  the  combining 
tube.  A  slight  leak  will  pimply  cut  down  the  capacity  of  the  injector.  In 
such  a  case  an  automatic  injector  will  work  noisily,  on  account  of  the  overflow 
valve  seating  and  unseating  itself  as  the  pressure  in  the  combining  tube  varies, 
due  to  the  leak. 

Boiler  Check-Valve  Stuck  Shut. — If  the  boiler  check-valve  is  completely 
closed,  the  injector  may  or  may  not  continue  to  raise  water  and  force  it  out 
of  the  overflow;  this  depends  on  the  design  of  the  injector.  If  the  boiler  check 
is  partly  open,  the  injector  will  force  some  of  the  water  into  the  boiler  and  the 
remainder  out  of  the  overflow.  In  case  the  check-valve  cannot  be  opened 
wide,  water  may  be  saved  by  throttling  both  steam  and  water  until  the  over- 
flow diminishes,  or,  if  possible,  ceases.  The  steam  should  be  throttled  at  the 
valve  in  the  boiler  steam  connection.  If  a  check-valve  sticks,  it  can  sometimes 
be  made  to  work  again  by  tapping  lightly  on  the  cap  or  on  the  bottom  of  the 
valve  body. 

Obstruction  in  Delivery  Tube. — Any  obstruction  in  the  deliverv  tube  w411 
cause  a  heavy  waste  of  water  from  the  overflow.  To  remedy  this,  the  tube 
will  have  to  be  removed  and  cleaned. 

Leaky  Overflow  Valve. — A  leaky  overflow  valve  is  indicated  by  the  boiler 
check  chattering  on  its  seat.  To  remedy  this  defect,  grind  the  valve  on  its 
seat  until  it  forms  a  tight  joint. 

Injector  Choked  With  Lime. — It  is  essential  to  the  proper  working  of  an 
injector  that  the  interior  of  the  tubes  be  perfectly  smooth  and  of  the  proper 
bore.  As  in  course  of  time  the  tubes  become  clogged  with  lime,  the  capacity 
of  the  injector  decreases  until,  finally,  it  refuses  to  work  at  all.  If  the  water 
used  is  very  bad,  it  is  frequently  necessary  to  cleanse  the  tubes  of  the  accumu- 
lated lime.  This  may  be  done  by  putting  the  parts  in  a  bath  consisting  of 
1  part  of  muriatic  acid  to  10  parts  of  water.  The  tubes  should  be  removed 
from  it  as  soon  as  the  gas  bubbles  cease  to  be  given  off. 

INCRUSTATION  AND  CORROSION 

Incrustation. — Broadly  speaking,  any  deposit  that  is  formed  on  the  plates 
and  tubes  of  a  boiler  is  termed  scale,  or  incrustation;  it  is  caused  by  impurities 
that  enter  with  the  water  and  that  are  left  behind  in  the  boiler  when  the  water 
is  evaporated.  In  passing  through  the  soil,  water  dissolves  certain  mineral 
substances,  the  most  important  of  which  are  carbonate  of  lime  and  sulphate 
of  lime.  Other  substances  frequently  present  in  small  quantities  are  chloride 


BOILERS  425 

of  sodium,  or  common  salt,  and  chloride  of  magnesium.  The  water  also  often 
contains  other  troublesome  substances. 

Impurities  in  Feedwater. — Some  of  the  more  common  impurities  found  in 
feedwater,  together  with  their  properties,  are  as  follows: 

Carbonate  of  lime  will  not  dissolve  in  pure  water,  but  will  dissolve  in  water 
that  contains  carbonic-acid  gas.  It  becomes  insoluble  and  is  precipitated 
in  the  solid  form  when  the  water  is  heated  to  about  212°  F.;  the  carbonic-acid 
gas  is  driven  off  by  the  heat. 

Sulphate  of  lime  dissolves  readily  in  cold  water,  but  not  in  hot  water.  It 
precipitates  in  the  solid  form  when  the  water  is  heated  to  about  290°  P.,  corre- 
sponding to  a  gauge  pressure  of  45  Ib. 

Chloride  of  sodium  will  not  be  precipitated  by  the  action  of  heat  unless  the 
water  has  become  saturated  with  it.  As  it  generally  is  present  in  but  very 
small  quantities  in  fresh  water,  it  will  take  a  very  long  time  for  the  water  in 
a  boiler  to  become  troublesome,  and  with  the  ordinary  blowing  down  of  a  boiler 
once  a  week  or  every  2  wk.,  there  is  little  danger  of  the  water  becoming  satu- 
rated with  it.  Consequently,  it  is  one  of  the  least  troublesome  scale-forming 
substances  contained  in  fresh  water. 

Chloride  of  magnesium  is  one  of  the  worst  impurities  in  water  intended  for 
boilers,  for  while  not  dangerous  as  long  as  the  water  is  cold,  it  makes  the  water 
very  corrosive  when  heated,  and  when  present  in  large  quantities,  it  attacks 
the  metal  and  rapidly  destroys  it. 

Organic  matter  by  itself  may  or  may  not  cause  the  water  to  become  corrosive, 
but  will  often  cause  foaming;  when  it  is  present  in  small  quantities  in  water 
containing  carbonate  or  sulphate  of  lime,  or  both,  it  usually  serves  to  keep 
the  deposits  from  becoming  hard. 

Earthy  matter,  like  organic  matter,  is  not  dissolved  in  the  water,  but  is  in 
mechanical  suspension.  It  is  very  objectionable,  especially  when  it  is  clay, 
and  when  other  scale-forming  substances  are  present  is  liable  to  form  a  hard 
scale  resembling  Portland  cement. 

Acids,  such  as  sulphuric  acid,  nitric  acid,  tannic  acid,  and  acetic  acid,  are 
often  present  in  the  feedwater.  The  sulphuric  acid  is  the  most  dangerous 
one  of  these  acids,  attacking  the  metal  of  which  the  boiler  is  composed  and 
corroding  it  very  rapidly.  The  other  acids,  while  not  so  violent  in  their  action 
as  the  sulphuric  acid,  are  also  dangerous,  and  water  containing  any  one  should 
be  neutralized  when  it  must  be  used. 

Formation  of  Scale. — The  small  solid  particles  due  to  precipitation  of  sub- 
stances in  solution  or  matter  in  mechanical  suspension,  remain  for  a  time 
suspended  in  the  water,  especially  the  carbonate  of  lime  which  will  float  on  the 
surface  of  the  water.  These  particles  will  gradually  settle  on  the  plates,  tubes, 
and  other  internal  surfaces.  A  large  part  of  the  impurities  will  be  carried  by 
the  circulation  of  the  water  to  the  most  quiet  part  of  the  boiler  and  there  settle 
and  form  a  scale.  In  a  few  weeks,  if  no  means  of  prevention  are  used,  the  inner 
parts  of  the  boiler  may  be  covered  with  a  crust  from  &  to  5  in.  in  thickness. 

Danger  of  Scale. — A  scale  &  in.  or  less  in  thickness  is  thought  by  many  to 
be  an  advantage,  as  it  protects  the  plates  from  the  corrosive  action  of  acids 
in  the  water.  When,  however,  the  scale  becomes  i  in.  thick  or  more,  heat  is 
transmitted  through  the  plates  and  tubes  with  difficulty,  more  fuel  is  required, 
and  there  is  danger  of  overheating  the  plates.  The  chief  danger  from  a  heavy 
incrustation  is  the  liability  of  overheating  the  plates  and  tubes.  Scale  also 
prevents  a  proper  examination  of  the  inside  of  the  boiler,  as  it  may  hide  a 
dangerously  corroded  piece  of  plate  or  a  defective  rivet  head. 

Scale  Containing  Lime. — The  carbonate  of  lime  forms  a  soft,  muddy  scale, 
which  when  dry,  becomes  fluffy  and  flourlike.  This  scale  may  be  easily  swept 
or  washed  out  of  the  boiler  by  a  hose,  provided  it  is  not  baked  hard  and  fast. 
A  carbonata  scale  is  much  harder  to  deal  with  when  grease  is  allowed  to  enter 
the  boiler.  The  grease  settles  and  mixes  with  the  floury  scale,  making  a  spongy 
crust  that  remains  in  contact  with  the  plates,  being  too  heavy  to  be  carried 
off  by  the  natural  circulation  of  the  water.  The  sulphate  of  lime  forms  a 
scale  that  soon  bakes  to  the  plates. 

Kerosene  as  Scale  Remover. — Some  substances  seem  to  soften  and  aid  in 
detaching  scale.  Of  these,  kerosene  oil  has  met  with  much  favor.  Its  action 
appears  to  be  mechanical  rather  than  chemical,  the  oil  penetrating  or  soaking 
through  the  scale  and  softening  and  loosening  it.  It  is  somewhat  useful,  too, 
in  preventing  the  formation  of  scale,  enveloping  the  fine  particles  of  the  scale- 
forming  substances  that,  after  precipitation,  float  on  the  surface  of  the  water 
for  a  little  while.  It  seems  that  this  prevents  the  particles  from  adhering 
firmly  to  one  another  and  to  the  metal  when  they  finally  settle. 


426 


BOILERS 


Removal  of  Scale  by  Chipping. — A  hard  scale,  when  once  formed,  is  gen- 
erally removed  by  chipping  it  off  with  scaling  hammers  and  scaling  bars;  soft 
scale  can  be  largely  removed  during  running  by  a  periodic  use  of  the  bottom 
and  surface  blow-offs,  and  the  remainder  can  usually  be  washed  out  and  raked 
out  when  the  boiler  is  blown  down  and  opened.  In  order  to  prevent  the  scale- 
forming  substances  deposited  on  the  metal  from  baking  hard,  it  is  advisable 
to  let  the  boiler  cool  down  slowly  until  entirely  cold  preparatory  to  blowing 
off,  whenever  circumstances  permit  this  to  be  done.  This  cooling  process 
will  generally  take  from  24  to  36  hr. 

Removal  of  Mud. — Mud  and  earthy  matter  by  itself  will  not  form  any 
hard  scale,  but  will  often  do  so  when  carbonate  of  lime  and  sulphate  of  lime 
are  present.  An  accumulation  of  such  matter  can  be  prevented,  and  most  of. 
it  can  be  removed,  by  a  periodic  use  of  the  bottom  blow-off,  removing  any 
remainder  whenever  the  boiler  is  opened. 

Internal  Corrosion. — Corrosion  of  boiler  plates  may  be  denned  as  the  eating 
away  or  wasting  of  the  plates  due  to  the  chemical  action  of  water.  Corrosion 
may  be  internal  and  external.  Internal  corrosion  may  present  itself  as  uniform 
corrosion,  pitting  or  honeycombing,  and  groov- 
ing. In  cases  of  uniform  corrosion  large  areas 
of  plate  are  attacked  and  eaten  away.  There 
is  no  sharp  line  of  division  between  the  cor- 
roded part  and  the  sound  plate.  Corrosion 
often  violently  attacks  the  staybolts  and  rivet 
heads. 

Pitting  or  Honeycombing. — Pitting  or  honey- 
combing of  the  boiler  plates  is  readily  per- 
ceived. The  plates  are  indented  in  spots  with 
holes  and  cavities  from  -fa  to  i  in.  deep.  The 
appearance  of  a  pitted  plate  is  shown  in  Fig.  1. 
On  the  first  appearance  of  pitting,  the 
surface  so  affected  should  be  thoroughly 
cleaned  and  a  good  coating  of  thick  paint 
made  of  red  lead  and  boiled  linseed  oil  shpuld 
be  applied.  This  treatment  should  be  given 


FIG.  1 


from  time  to  time  to  insure  protection  to  the  metal. 

Grooving. — Grooving,  which  means  the  formation  of  a  distinct  groove,  is 
generally  caused  by  the  buckling  action  of  the  plates  when  under  pressure. 
Thus,  the  ordinary  longitudinal  lap  joint  of  a  boiler  slightly  distorts  the  shell 
from  a  truly  cylindrical  form,  and  the  steam  pressure  tends  to  bend  the  plates 
at  the  joint.  This  bending  action  is  liable  to  start  a  small  crack  along  the 
lap,  which,  being  acted  on  by  corrosive  agents  in  the  water, 
soon  deepens  into  a  groove,  as  shown  in  Fig.  2. 

External  Corrosion. — External  corrosion  frequently  attacks 
stationary  boilers,  particularly  those  set  in  brickwork.  The 
causes  of  external  corrosion  are  dampness,  exposure  to  weather, 
leakage  from  joints,  moisture  arising  from  the  waste  pipes  or 
blow-off,  etc.  External  corrosion  should  be  prevented  by 
keeping  the  boiler  shell  free  from  moisture,  and  the  stoppage  of 
all  leaks  as  soon  as  they  appear. 

Leakage  at  rivets  and  the  calking  edges  of  seams  may  be 
caused  by  the  delivery  of  the  cold  feed  water  on  to  the  hot  plates ; 
another  cause  is  the  practice  of  emptying  the  boiler  when  hot 
and  then  filling  it  with  cold  water.  The  leakage  in  both  cases 
is  due  to  the  sudden  contraction  of  the  plates. 

In  horizontal  water-tube  boilers  of  the  inclined-tube  type, 
external  corrosion  principally  attacks  the  ends  of  the  tubes, 
especially  the  back  ends,  close  up  to  the  headers  into  which 
they  are  expanded.  In  the  course  of  time  this  will  cause 
the  tubes  to  leak  around  the  expanded  portion  in  the  headers. 

If  leaks  are  attended  to  as  soon  as  they  occur,  no  corrosion  will  take  place, 
as  the  gases  of  combustion  are  harmless  unless  acting  in  conjunction  with 
water  or  dampness,  or  unless  the  coal  is  rich  in  sulphur.  Should,  however, 
the  ends  of  several  tubes  be  found  badly  corroded  but  not  yet  leaking  from  that 
cause,  the  tubes  should  by  all  means  be  removed  and  replaced. 

Lamination. — Sometimes  what  is  called  lamination,  or  the  splitting  of  a 
plate  into  thin  layers,  is  revealed  by  the  action  of  the  fire  in  causing  a  bag  or 
blister  to  appear.  Laminations  due  to  slag  and  other  impurities  in  the  metal 
which  become  flattened  out  when  the  plates  are  rolled,  are  shown  at  a,  Fig.  3. 


FIG.  2 


BOILERS 


427 


Under  the  action  of  the  heat  the  part  exposed  to  the  fire  will  form  a  blister 
which  may  finally  open  at  the  point  6  or  c.  If  the  laminated  portion  of  the 
plate  is  small,  it  may 
be  cut  out  and  a  patch 


laminations  in  the  same 
plate,  it  is  advisable 
to  put  in  a  new  plate. 

Overheating. — The  heating  of  a  plate  beyond  its  normal  temperature  is 
called  overheating,  and  may  be  caused  by  low  water  or  by  incrustation.  When 
the  plate  is  covered  by  a  heavy  scale,  the  plate  becomes  overheated,  so  that 
it  yields  to  the  steam  pressure,  forming  a  pocket,  as  shown  in  Fig.  4,  which 
represents  the  shell  sheet,  or  the  sheet  of  a  horizontal  return-tubular  boiler 
directly  oyer  the  fire.  If  the  pogket  is  not  discovered  in  time  for  the  plate 
to  be  repaired,  it  stretches  until  finally  the  material  becomes  too  thin  to  with- 
stand the  steam  pressure;  the  pocket  then  bursts  with  more  or  less  liability 
of  an  explosion.  The  vegetable  or  animal  oils  carried  into  the  boiler  from  a 
surface  condenser  are  particularly  liable  to  cause  the  formation  of  pockets. 
Prevention  of  Incrustation  and  Corrosion. — Incrustation  can  best  be  pre- 
vented by  purifying  the  feedwater  prior  to  its  entering  the  boiler,  but  can  be 

fairly  satisfactorily  prevented 
by  a  chemical  treatment  of  the 
water  in  the  boiler.  When  the 
water  contains  large  quantities 
of  substances  that  float  on  the 
surface,  mechanical  means  may 
be  resorted  to,  using  the  surface 
blow-off  at  frequent  intervals 
or  some  equivalent  skimming 
device.  Corrosion  is  prevented 


FIG.  4 


by  neutralizing  the  acids  in  the 


water  by  an  alkali.  Corrosion  due  to  a  perfectly  fresh  water  can  be  prevented 
by  giving  a  protective  coating  to  the  metal,  which  may  be  a  thick  red-lead 
paint  made  up  with  boiled  linseed  oil.  Sometimes  organic  substances  con- 
taining tannic  acid,  such  as  oak  bark,  hemlock,  or  sumac,  are  used  to  loosen 
or  prevent  scale.  They  should  not  be  used,  as  they  are  liable  to  injure  the 
plates  by  corrosion.  The  accompanying  table  gives  a  list  of  scale-forming 
substances  and  the  means  of  preventing  or  neutralizing  them. 

SCALE-FORMING  SUBSTANCES  AND  THEIR  REMEDIES 


Troublesome  Substance 

Trouble 

Remedy  or  Palliation 

Sediment,  mud,  clay,  etc. 

Incrustation 

Filtration 

Blowing  off 

Readily  soluble  salts 

Incrustation 

Blowing  off 

Heating  feed 

Bicarbonates  of  lime,  magnesia,  iron 

Incrustation 

Addition  of  caustic  soda, 

lime,  or  magnesia 

Sulphate  of  lime 

Incrustation 

Addition  of  carbonate  of 

soda  or  barium  chloride 

Chloride  and  sulphate  of  magnesium 

Corrosion 

Addition  of  carbonate  of 

soda,  etc. 

Carbonate  of  soda  in  large  amounts 

Priming 

Addition  of  barium  chlo- 

ride 

Acid  (in  mine  water) 

Corrosion 

Alkali 

Heating  feed 

Dissolved  carbonic  acid  and  oxygen 

Corrosion 

Addition  of  caustic  soda, 

slaked  lime,  etc. 

Grease  (from  condensed  water) 

Corrosion 

Slaked  lime  and  filtering 

Carbonate  of  soda 

Substitute  mineral  oil 

Organic  matter  (sewage) 

Priming 

Precipitate  with  alum  or 
chloride  of  iron  and  filter 

Organic  matter 

Corrosion 

Same  as  last 

428  BOILERS 

Use  of  Zinc  in  Boilers. — Zinc  is  much  used  in  marine  boilers  for  the  pre- 
vention of  both  incrustation  and  corrosion.  The  zinc  is  distributed  through 
the  boiler  in  the  form  of  slabs.  About  1  sq.  in.  of  zinc  surface  should  Be 
supplied  for  every  50  Ib.  of  water  in  the  boiler. 

TESTING  OF  FEEDWATER 

Testing  for  Corrosiveness. — It  is  a  good  plan  to  occasionally  test  the  feed- 
water  and  also  the  water  in  the  boiler  for  corrosiveness.  This  may  be  done  by 
B'acing  a  small  quantity  in  a  glass  and  adding  a  few  drops  of  methyl  orange, 
the  sample  of  water  is  acid,  and  hence  corrosive,  it  will  turn  pink.  If  it  is 
alkaline,  and  hence  harmless,  it  will  remain  yellow.  The  acidity  may  also  be 
tested  by  dipping  a  strip  of  blue  litmus  paper  in  the  water.  If  it  turns  red,  the 
water  is  acid.  This  method  is  not  so  sensitive  as  the  previous  one,  which 
should  be  used  in  preference.  If  litmus  paper  is  kept  in  stock,  it  should  be 
kept  in  a  bottle  with  a  glass  stopper,  as  exposure  to  the  atmosphere  will  cause 
the  paper  to  deteriorate.  If  the  water  in  the"  boilers  has  become  corrosive  and 
corrosion  has  set  in,  the  water  in  the  gauge  glass  will  show  red  or  even  black. 
As  soon  as  the  color  is  beyond  a  dirty  gray  or  straw  color,  it  is  advisable  to 
introduce  lime  or  soda  to  neutralize  the  acid. 

Testing  for  Carbonate  of  Lime. — Pour  some  of  the  water  to  be  tested  into 
an  ordinary  tumbler.  Add  a  little  ammonia  and  ammonium  oxalate,  and  then 
heat  to  the  boiling  point.  If  carbonate  of  lime  is  present,  a  precipitate  will 
be  formed. 

Testing  for  Sulphate  of  Lime.— Pour  some  of  the  feed  water  into  a  tumbler 
and  add  a  few  drops  of  hydrochloric  acid.  Add  a  small  quantity  of  a  solution 
of  barium  chloride  and  slowly  heat  the  mixture.  If  a  white  precipitate  is 
formed,  which  will  not  redissolve  when  a  little  nitric  acid  is  added,  sulphate 
of  lime  is  present. 

Testing  for  Organic  Matter. — Add  a  few  drops  of  pure  sulphuric  acid  to  the 
sample  of  water.  Then  add  enough  of  a  pink-colored  solution  of  potassium 
permanganate  to  make  the  whole  mixture  a  faint  rose  color.  If  the  solution 
retains  its  color  after  standing  a  few  hours,  no  organic  substances  are  present. 

Testing  for  Matter  in  Mechanical  Suspension. — Keep  a  tumblerful  of  the 
feedwater  in  a  quiet  place.  If  no  sediment  is  formed  in  the  bottom  of  the 
tumbler  after  standing  for  a  day,  there  is  no  mechanically  suspended  matter 
in  the  water. 

PURIFICATION  OF  FEEDWATER 

Means  of  Purification. — Water  intended  for  boilers  may  be  purified  by 
settlement,  by  filtration,  by  chemical  means,  and  by  heat.  Filtration  will 
remove  impurities  in  mechanical  suspension,  such  as  oil  and  grease,  and  earthy 
matter,  but  will  not  remove  substances  dissolved  in  the  water.  Chemical 
treatment  of  the  water  will  render  the  scale-forming  substances  and  corrosive 
acids  harmless,  and  may  be  applied  either  before  or  after  the  water  enters  the 
boilers,  but  preferably  the  former.  Purification  by  heat  is  based  on  the  fact 
that  most  of  the  scale-forming  substances  become  insoluble  and  are  precipi- 
tated when  the  water  containing  them  is  heated  to  a  high  temperature. 

Purification  by  Settlement.— For  feedwater  containing  much  matter  in 
mechanical  suspension,  one  of  the  simplest  methods  of  purifying  it  is  to  provide 
a  relatively  large  reservoir,  or  a  large  tank  for  small  steam  plants,  where  the 
impurities  can  settle  to  the  bottom.  While  this  method  is  fairly  satisfactory 
in  removing  earthy  matter,  it  will  not  clear  the  water  of  finely  divided  organic 
matter,  which  is  usually  lighter  than  the  water  and  often  so  finely  divided 
as  to  be  almost  dissolved  it  in. 

Purification  by  Filtration. — Organic  and  earthy  matter  in  mechanical  sus- 
pension is  most  satisfactorily  removed  by  a  filter,  passing  the  water  through 
layers  of  sand,  gravel,  hay,  or  equivalent  substances,  or  through  layers  of 
cloth.  Hay  and  cloth  are  of  service,  especially  where  the  feedwater  contains 
oil  or  grease,  as  is  the  case  where  a  surface  condenser  is  used  and  the  condensed 
steam  is  used  over  again. 

Purification  by  Chemicals.— Chemical  purification  may  take  place  before 
or  after  the  water  enters  the  boiler,  the  former  method  being  somewhat  more 
expensive.  However,  the  purification  is  better  carried  out  before  the  water 
enters  the  boiler,  as  the  amount  of  impurities  entering  the  boiler  will  be  greatly 
reduced.  The  process  adopted  depends  on  the  impurities. 

Use  of  Quicklime. — When  the  water  contains  only  carbonate  of  lime,  it 
may  be  treated  with  slaked  quicklime,  using  28  gr.  of  lime  for  every  50  gr.  of 
lime  present  in  the  water,  the  quicklime  precipitating  the  carbonate  of  lime  and 
being  transformed  into  carbonate  of  lime  itself  during  the  process. 


BOILERS  429 

Use  of  Caustic  Soda. — Water  containing  carbonate  of  lime  may  be  treated 
with  caustic  soda,  which  precipitates  the  former  and  leaves  carbonate  of  soda, 
which  is  harmless.  For  every  100  gr.  of  carbonate  of  lime  80  gr.  of  caustic 
soda  should  be  added. 

Use  of  Sal  Ammoniac. — Sal  ammoniac  is  sometimes  added  to  water  con- 
taining carbonate  of  lime  and  will  cause  the  latter  to  precipitate.  Its  use  is 
not  advisable,  however,  because  if  used  in  excess  there  is  danger  of  forming 
hydrochloric  acid,  which  will  attack  the  boiler. 

Treatment  for  Sulphate  of  Lime. — While  slaked  lime  will  precipitate  car- 
bonate of  lime,  it  will  nave  no  effect  on  sulphate  of  lime,  and  water  containing 
the  latter,  either  alone  or  in  conjunction  with  carbonate  of  lime,  must  be  treated 
with  other  chemicals.  The  most  available  chemicals  for  water  containing 
both  are  carbonate  of  soda  and  caustic  soda.  These  are  often  fed  into  the 
boiler  and  will  precipitate  the  carbonate  and  sulphate  of  lime,  requiring  the 
sediment  to  be  blown  out  or  otherwise  removed  periodically. 

Quantity  of  Chemicals  to  Use. — When  treating  water  containing  carbonate 
and  sulphate  of  lime,  caustic  soda  may  be  used  either  by  itself  or  in  combina- 
tion with  carbonate  of  soda,  depending  on  the  relative  proportions  of  the 
lime  compounds  present  in  the  water.  The  amount  of  caustic  soda  or  car- 
bonate of  soda  to  be  used  per  gallon  of  feed  water  can  be  found  as  follows: 

Rule  I. — Multiply  the  number  of  grains  of  carbonate  of  lime  per  gallon  by  1.36. 
If  this  product  is  greater  than  the  number  of  grains  of  sulphate  of  lime  per  gallon, 
only  caustic  soda  is  to  be  used.  To  find  the  quantity  of  caustic  soda  required  per 
gallon,  multiply  the  number  of  grains  of  carbonate  of  lime  in  1  gal.  by  .8. 

Rule  II. — Multiply  the  number  of  grains  of  carbonate  of  lime  per  gallon 
by  1.36.  If  this  product  is  less  than  the  number  of  grains  of  sulphate  of  lime  per 
gallon,  multiply  the  difference  by  .78  to  obtain  the  number  of  grains  of  carbonate 
of  soda  required  per  gallon.  To  find  the  amount  of  caustic  soda  required  per 
gallon,  multiply  the  number  of  grains  of  carbonate  of  lime  in  1  gal.  by  .8. 

EXAMPLE. — A  quantitative  analysis  of  a  certain  feedwater  shows  it  to 
contain  23  gr.  of  sulphate  of  lime  and  14  gr.  of  carbonate  of  lime  per  gallon. 
How  much  caustic  soda  and  carbonate  of  soda  should  be  used  per  gallon  to 
precipitate  the  scale-forming  substances? 

SOLUTION. — By  rule  I,  14X1.36  =  19  gr.  As  this  product  is  less  than  the 
number  of  grains  of  sulphate  of  lime  per  gallon,  rule  II  is  to  be  used.  Applying 
rule  II,  (23 - 19) X. 78  =  3. 12  gr.  of  carbonate  of  soda,  and  14X.8  =  11.2  gr.  of 
caustic  soda. 

Use  of  Carbonate  of  Soda. — Water  containing  sulphate  of  lime,  but  no 
carbonate  of  lime,  may  be  treated  with  carbonate  of  soda.  The  amount  of  the 
latter  that  is  required  per  gallon  to  precipitate  the  sulphate  of  lime  is  found  by 
multiplying  the  number  of  grains  per  gallon  by  .78.  When  using  soda,  it  is 
well  to  keep  in  mind  that  it  will  not  remove  deposited  lime  from  the  inside  of  a 
boiler.  All  that  the  soda  can  do  is  to  facilitate  the  separating  of  the  lime,  that 
is,  cause  it  to  deposit  in  a  soft  state.  This  sediment  must  be  removed 
periodically. 

Use  of  Trisodium  Phosphate. — For  decomposing  sulphate  of  lime,  tribasic 
sodium  phosphate,  more  commonly  known  as  trisodium  phosphate,  is  often 
used.  This  is  claimed  to  act  on  the  sulphate  of  lime,  forming  sulphate  of 
sodium  and  phosphate  of  lime,  the  former  of  which  remains  soluble  and  is 
harmless,  and  the  latter  of  which  is  a  loose,  easily  removed  deposit.  Trisodium 
phosphate  also  acts  on  carbonate  of  lime  and  carbonate  of  magnesia,  forming 
phosphate  of  lime  and  phosphate  of  magnesia,  at  the  same  time  neutralizing 
the  carbonic  acid  released  from  the  carbonate  of  lime  and  magnesia,  and  the 
sulphuric  acid  released  from  the  sulphates. 

Neutralization  of  Acids. — Acid  water  can  be  neutralized  by  means  of  an 
alkali,  soda  probably  being  the  best  one.  The  amount  of  soda  to  be  used  can 
best  be  found  by  trial,  adding  soda  until  the  water  will  turn  red  litmus  paper 
blue. 

Purification  by  Heat. — Carbonate  of  lime  and  sulphate  of  lime  become 
insoluble  if  the  water  is  heated,  the  former  precipitating  at  about  212°  F.  and 
the  latter  at  about  290°  F.  This  fact  is  taken  advantage  of  in  devices  that 
may  be  called  combined  feedwater  heaters  and  purifiers;  as  they  generally  use 
live  steam,  they  are  also  called  live-steam  feedwater  heaters.  As  no  feedwater 
heater  can  effect  a  direct  saving  of  fuel  except  when  the  heat  is  taken  from  a 
source  of  waste,  a  live-steam  feedwater  heater  can  affect  the  fuel  C9nsumption 
but  indirectly.  This  it  does  by  largely  preventing  the  accumulation  of  scale 
in  the  boiler  and  the  attendant  loss  in  economy  due  to  the  lowering  of  the 
rate  of  heat  transmission  through  a  plate  heavily  covered  with  incrustation. 


430  BOILERS 

FEEDWATER  HEATING 

The  feedwater  furnished  to  steam  boilers  must  be  raised  from  its  normal 
temperature  to  that  of  steam  before  evaporation  can  commence,  and  if  not 
otherwise  accomplished,  it  will  be  done  at  the  expense  of  fuel  that  should  be 
utilized  in  making  steam.  At  75  Ib.  gauge  pressure,  the  temperature  of  boiling 
water  is  about  320°  F.,  and  if  60°  is  taken  as  the  average  temperature  of  feed- 
water,  320-60  =  260  B.  T.  U.  is  required  to  raise  1  Ib.  of  water  from  60°  to  320°. 
It  requires  1,151.5  B.  T.  U.  to  convert  1  Ib.  of  water  at  60°  into  steam  at  75  Ib. 
gauge  pressure,  so  that  the  260  B.  T.  U.  required  for  heating  the  water  rep- 
resents 260-r-l,151.5  =  22.6%  of  the  total.  All  heat  taken  from  a  source  of 
waste,  therefore,  that  can  be  imparted  to  the  feedwater  before  it  enters  the 
boilers  is  just  so  much  saved,  not  only  in  cost  of  fuel  but  in  boiler  capacity. 

Types  of  Exhaust-Steam  Feedwater  Heaters. — The  impurities  contained 
in  the  water  will  largely  determine  the  type  of  exhaust-steam  heater  to  be  used 
in  any  given  plant.  These  heaters  are  divided  into  two  general  classes,  namely, 
open  heaters  and  closed  heaters. 

An  open  heater  is  one  in  which  the  water  space  is  open  to  the  atmosphere. 
In  a  direct-contact  open  heater,  the  exhaust  steam  comes  in  contact  with  the 
water,  which,  by  means  of  some  one  of  a  number  of  suitable  devices,  is  broken 
into  spray  or  thin  sheets  so  that  it  will  readily  absorb  the  heat  of  the  steam. 
In  a  coil  heater,  the  exhaust  steam  passes  through  coils  of  pipe  submerged  in 
a  vessel  containing  the  water  to  be  heated,  and  open  at  the  top. 

A  closed  heater  is  a  heater  in  which  the  feedwater  is  not  exposed  to  the 
atmosphere,  but  is  subjected  to  the  full  boiler  pressure.  The  steam  does  not 
come  in  contact  with  the  water;  the  latter  is  heated  through  contact  with 
metallic  surfaces,  generally  those  of  tubes,  that  are  heated  by  the  exhaust 
steam. 

Selection  of  Heater. — When  the  boiler  feedwater  is  free  from  acids,  salts, 
sulphates,  and  carbonates,  so  that  no  scale  is  formed  at  a  high  temperature 
the  closed  feedwater  heater  will  be  found  satisfactory.  Heaters  of  the  coil 
type  may  be  used  with  pure  water,  but  should  not  be  used  with  water  that 
will  precipitate  sediment  or  scale-forming  matter  of  any  kind.  The  coil 
heater  is  very  efficient  as  a  heater,  as  the  water  circulating  through  the  coils 
is  a  long  time  in  contact  with  the  surface  surrounded  and  heated  by  the  exhaust 
steam.  Heaters  of  the  closed  type  with  straight  tubes  and  a  sediment  chamber 
can  be  cleaned  more  readily  than  those  having  curved  tubes,  but  the  curved 
tubes  allow  more  freedom  for  expansion  and  contraction.  Heaters  of  the 
tubular  type  should  have  ample  sediment  chambers  and  may  be  used  with 
water  that  contains  organic  or  earthy  matter,  but  not  with  water  containing 
scale-forming  ingredients.  Carbonate  of  lime  is  likely  to  combine  with  earthy 
matter  and  form  an  exceedingly  hard  scale. 

Heaters  of  the  open  exhaust-steam  type  have  the  advantage  of  bringing 
the  exhaust  steam  in  direct  contact  with  the  feedwater;  some  of  the  exhaust 
steam  is  condensed,  thus  effecting  a  saving  in  feedwater,  and  sediment  and 
scale-forming  ingredients,  except  sulphates  of  lime  and  magnesia,  are  precipi- 
tated or  will  settle  to  the  bottom  of  the  heater.  The  oil  in  the  exhaust  steam 
must  be  intercepted  by  special  oil  extractors,  filters,  or  skimmers,  generally 
combined  with  the  heater  and,  by  automatic  regulation,  sufficient  fresh  feed- 
water  must  be  added  to  make  up  the  total  quantity  required.  When  the 
system  is  properly  arranged,  all  live-steam  drips  and  discharges  from  traps 
are  led  to  the  heater. 


BOILER  TRIALS 

Purposes  of  Boiler  Trials.— A  boiler  trial,  or  boiler  test,  as  it  is  often  called, 
may  be  made  for  one  or  more  of  several  purposes,  the  method  of  conducting 
the  trial  depending  largely  on  its  purpose.  The  boiler  trial  may  vary  from  the 
simplest  one,  in  which  the  only  observations  are  the  fuel  burned  and  the  water 
fed  to  the  boiler  in  a  stated  period  of  time,  to  the  elaborate  standard  boiler  trial, 
in  which  special  apparatus  and  several  skilled  observers  are  essential.  The 
object  of  a  boiler  trial  may  be  to  determine  the  efficiency  of  the  boiler  under 
given  conditions;  the  comparative  value  of  different  boilers  working  under 
the  same  conditions;  the  comparative  value  of  fuel;  or  the  evaporative  power, 
or  horsepower,  of  the  boiler. 

Observations  During  Trial.— The  essential  operations  of  a  boiler  trial  are 
the  weighing  of  the  feedwater  and  fuel,  and  the  observation  of  the  steam 
pressure,  temperature  of  feedwater,  and  various  other  less  important  pressures 


BOILERS  431 

and  temperatures.  These  observations  should  be  made  simultaneously  at 
intervals  of  about  15  min. 

Weighing  the  Coal. — The  coal  supplied  to  the  furnace  is  weighed  out  in  lots 
of  500  or  600  Ib.  It  is  a  convenient  plan  to  have  a  box  with  one  side  open 
placed  on  a  platform  scale.  A  weight  is  then  placed  on  the  scale  beam  sufficient 
to  balance  the  box.  The  scale  may  then  be  set  at  500  or  600  Ib.,  the  coal 
shoveled  in  until  the  beam  rises,  and  then  fed  directly  from  the  box  to  the 
furnace.  After  the  test,  the  ashes  and  clinkers  must  be  raked  from  the  ash-pit 
and  grate  and  weighed.  This  weight  subtracted  from  the  weight  of  the  coal 
used  gives  the  amount  of  combustible. 

Measurement  of  Feedwater. — The  amount  of  water  evaporated  in  a  test 
for  comparative  fuel  values  may  be  taken  as  equal  to  the  amount  of  feedwater 
supplied  without  introducing  any  serious  error.  The  most  reliable  method 
of  measuring  the  feedwater  delivered  to  the  boilers  is  to  weigh  it. 

Standard  of  Boiler  Horsepower. — When  making  a  horsepower  or  an 
efficiency  test,  a  more  elaborate  method  of  procedure  is  required  than  for  a 
comparative  fuel-value  test.  The  reason  for  this  is  that  different  boilers 
generate  steam  at  different  pressures,  different  feedwater  temperatures,  and 
different  degrees  of  dryness;  hence,  to  compare  the  performances  of  boilers  so 
as  to  determine  their  comparative  efficiencies,  it  is  necessary  to  reduce  the 
actual  evaporation  to  an  equivalent  evaporation  from  and  at  212°  F.  per  Ib.  of 
combustible. 

A  committee  of  the  American  Society  of  Mechanical  Engineers  has  recom- 
mended as  a  commercial  horsepower  an  evaporation  of  30  Ib.  of  water  per  hr. 
from  a  feedwater  temperature  of  100°  F.  into  steam  at  70  Ib.  gauge  pressure,  which 
is  equivalent  to  34f  units  of  evaporation;  that  is,  to  34  £  Ib.  of  water  evaporated 
from  a  feedwater  temperature  of  212°  F.  into  steam  at  the  same  temperature. 

As  965.8  B.  T.  U.  is  required  to  evaporate  1  Ib.  of  water  from  and  at  212°,  a 
boiler  horsepower  is  equal  to  965.8X34^  =  33,320  B.  T.  U.  per  hr. 

Equivalent  Evaporation. — The  equivalent  evaporation  is  readily  deter- 
mined by  means  of  the  formula 

w  _W(H-t+32) 
965.8        ' 
in  which    W  =  actual  evaporation,  in  pounds  of  water  per  hour; 

H  =  total  heat  of  steam  above  32°  F.  at  observed  pressure  of  evap- 
oration; 

t  =  observed  feedwater  temperature; 

W\  =  equivalent  evaporation,  in  pounds  of  water  per  hour,  from  and 
at  212°  F. 

EXAMPLE. — A  boiler  generates  2,200  Ib.  of  dry  steam  per  hr.  at  a  pressure 
of  120  Ib.  gauge;  the  temperature  of  the  feedwater  being  70°  F.:  (a)  What  is 
the  equivalent  evaporation?  (b)  What  is  the  horsepower  of  the  boiler? 

SOLUTION. — (a)  According  to  the  Steam  Table,  the  total  heat  H  correspon- 
ding to  a  gauge  pressure  of  120  Ib.  is  1,188.6  B.  T.  U.  Applying  the  formula, 

_ 

(b)  The  horsepower  is  obtained  by  dividing  the  total  equivalent  evapora- 
tion by  34.5,  the  equivalent  of  1  H.  P.,  and  is 

2,621 -=-34.5  =  76  H.  P.,  nearly 

Factor  of  Evaporation. — The  quantity  —  —  that  changes  the  actual 

96o.o 

evaporation  of  1  Ib.  of  water  to  the  equivalent  evaporation  from  and  at  212°  F. 
is  called  the  factor  of  evaporation.  To  facilitate  the  calculating  of  equivalent 
evaporation,  the  accompanying  table  of  factors  of  evaporation  is  inserted. 
The  equivalent  evaporation  is  found  by  multiplying  the  actual  evaporation 
by  the  factor  of  evaporation  taken  from  the  table. 

EXAMPLE  1. — A  boiler  is  required  to  furnish  1,800  Ib.  of  steam  per  hr.  at 
a  gauge  pressure  of  80  Ib.;  if  the  temperature  of  the  feedwater  is  48°  F.,  what 
will  be  the  rated  horsepower  of  the  boiler? 

SOLUTION. — From  the  table,  the  factor  of  evaporation  for  80-lb.  pressure 
and  a  feedwater  temperature  of  40°  is  1.214,  and  for  the  same  pressure  and  a 
feedwater  temperature  of  50°  it  is  1.203;  the  difference  is  1.214  — 1.203  =  .011. 
The  difference  of  temperature  is  50°  — 40°  =10°,  and  the  difference  between 
the  lower  temperature  and  the  required  temperature  is  48°  — 40°  =  8°.  Then, 
10°  :  8°=.011  :  x,  or  x=.009;  1.2 14 -.009  =  1.205.  1,800X1.205  =  2,169  Ib., 
and  2,169-7-34.5  =  63  H.  P.,  nearly. 


432 


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BOILERS  433 

EXAMPLE  2.  —  What  is  the  factor  of  evaporation  when  the  feedwater  tem- 
perature is  122°  F.  and  the  gauge  pressure  72? 

SOLUTION.  —  In  the  table,  under  the  column  headed  70  and  opposite  120  in 
the  left-hand  column  is  found  1.128;  in  column  headed  80  and  opposite  120  is 
found  1.131;  difference  is  .003.  In  the  same  vertical  columns  and  opposite  130 
are  found  1.117  and  1.120;  difference  is  .003,  same  as  before.  Hence,  for  an 
increase  of  10  Ib.  in  gauge  reading,  there  is  an  increase  of  .003  in  the  factor  of 
evaporation,  or  an  increase  of  .0003  for  1  Ib.  and  of  .0003  X  2  =  .0006  for  2  Ib. 
Therefore,  for  a  feedwater  temperature  of  120°  and  72  Ib.  pressure,  the  factor 
of  evaporation  is  1.128  +  .  0006  =  1.1286.  The  difference  between  the  numbers 
opposite  120  and  130  in  the  two  columns  headed  70  and  80,  respectively,  is 
1.  128-1.  117  =  .011,  and  1.31-1.  120  =  .011,  showing  that,  for  an  increase  of 
temperature  in  the  feedwater  of  10°,  there  is  a  decrease  in  the  factor  of  .011 
and  for  1°  a  decrease  of  .0011,  or  for  2°  of  .0022.  Hence,  the  value  of  the 
factor  for  a  temperature  of  122°  and  a  gauge  pressure  of  72  Ib.  is  1.1286  —  .0022 
=  1.126. 

Boiler  Efficiency.  —  The  efficiency  of  a  boiler  may  be  denned  as  the  ratio  of 
the  heat  utilized  in  evaporating  water  to  the  total  heat  supplied  by  the  fuel. 
The  efficiency  thus  calculated  is  really  the  combined  efficiency  of  the  furnace  and 
boiler,  as  it  is  not  easily  possible  to  determine  separately  the  efficiency  of  each. 

The  amount  of  heat  supplied  is  determined  by  first  accurately  weighing 
the  fuel  'used  during  the  test  and  deducting  all  the  ash  and  unconsumed  por- 
tions. This  weight,  in  pounds,  is  multiplied  by  the  total  heat  of  combustion 
of  1  Ib.  of  the  fuel,  as  determined  by  an  analysis,  the  product  being  the  total 
number  of  heat  units  supplied  during  the  test  under  the  assumpton  that  com- 
bustion was  perfect.  The  heat  usefully  expended  in  evaporating  water  is 
obtained  by  first  weighing  the  feedwater  and  correcting  this  weight  according 
to  the  quality  of  the  steam  ;  the  corrected  weight  is  then  multiplied  by  the  num- 
ber of  heat  units  required  to  change  water  at  the  temperature  of  the  feed  into 
steam  at  the  observed  pressure.  The  efficiency  of  the  boiler,  expressed  as  a 
per  cent.,  may  be  found  by  the  formula 


in  which  E  =  efficiency  of  boiler; 

A  =  heat  utilized  in  evaporating  water  ; 
B  =  total  heat  supplied  by  fuel. 

EXAMPLE.  —  A  boiler  trial  shows  a  useful  expenditure  of  186,429,030  B.  T.  U. 
and  a  total  supply  of  270,187,000  B.  T.  U.  What  is  the  efficiency  of  the 
boiler? 

SOLUTION.  —  Applying  the  formula, 

186.429  .030  _  fiq_fiw 
E~  270,187,000  ~-69      >9% 

Standard  Code.  —  For  elaborate  boiler  trials,  the  standard  code  recom- 
mended by  the  American  Society  of  Mechanical  Engineers  should  be  used. 


BOILER  MANAGEMENT 

FILLING  BOILERS 

Preparation  for  Filling  Boiler. — Before  starting  the  flow  of  water  into  the 
boiler,  the  manhole  plates  or  handhole  plates  that  were  removed  preparatory 
to  cleaning  and  overhauling  must  be  replaced,  and  the  blow-off  valve  must 
be  closed.  The  gaskets,  and  also  the  surfaces  with  which  they  come  in  contact, 
should  be  examined  to  see  that  they  are  in  good  condition.  It  is  customary 
to  place  a  mixture  of  cylinder  oil  and  graphite  on  the  outer  surface  of  each 
gasket,  so  that  it  may  be  removed  without  tearing.  It  is  important  that  the 
manhole  plates  and  handhole  plates  be  properly  replaced  and  secured  in  order 
to  prevent  leakage. 

Height  of  Water. — In  some  cases  the  water  can  flow  in  and  fill  the  boiler 
to  the  required  height  by  means  of  the  pressure  that  exists  in  the  main  supply 
pipe.  In  other  cases,  it  may  be  necessary  to  use  a  hose  or  to  fill  the  boiler 
with  a  steam  pump  or  a  hand  pump.  The  boiler  should  be  filled  until  the  water 
shows  half  way  up  in  the  gauge  glass. 

Escape  of  Air. — While  filling  a  boiler  it  is  necessary  to  make  provision  for 
the  escape  of  the  contained  air,  as  otherwise  the  pressure  caused  by  the  com- 
pression of  the  air  may  prevent  the  boiler  from  being  filled  to  the  proper  height. 

28 


434  BOILERS 

Most  boilers  have  some  valve  that  can  be  used  for  this  purpose;  a  gauge-cock 
may  be  left  open  until  water  issues  therefrom,  when  it  may  be  closed,  borne- 
times  the  manhole  plate,  if  the  manhole  is  on  top,  is  left  off  while  filling  a  boiler. 

MANAGEMENT  OF  FIRES  WHEN  STARTING 

Precautions  in  Starting. — After  the  boiler  has  been  filled  and  before  start- 
ing the  fire,  the  attendant  should  see  that  the  water  column  and  connections 
are  perfectly  clear  and  free,  that  is,  that  the  valves  in  the  connections  and 
the  gauge-glass  valves  are  open  so  that  the  water  level  may  show  in  the  glass; 
he  should  also  see  that  the  gauge-cocks  are  in  good  working  order  and  should 
open  the  top  cock  or  the  safety  valve;  he  should  take  care  that  the  stress  on  the 
stop-valve  spindle  is  relieved  by  just  unscrewing  the  valve  from  the  seat 
without  actually  opening  it.  He  should  make  sure  that  the  pump,  or  injector, 
or  whatever  device  is  used  to  feed  the  boiler,  is  in  good  working  order,  and 
ready  to  start  when  required. 

Starting  the  Fires. — It  is  customary  to  coyer  the  grates  with  a  layer  of  coal 
first,  and  then  to  add  the  wood,  among  which  may  be  thrown  oily  waste  or 
other  combustible  material  that  may  be  at  hand.  To  start  the  fire,  light  the 
waste  or  other  easily  ignited  material  and  open  the  damper  and  ashpit  doors 
to  produce  draft.  Then  close  the  furnace  door.  After  the  wood  has  started 
to  burn  well,  spread  it  evenly  over  the  grate  and  add  a  fine  sprinkling  of  coal, 
until  this  in  turn  begins  to  glow,  when  more  coal  may  be  added  and  the  fire 
occasionally  leveled  until  the  proper  thickness  of  fuel  has  been  obtained. 
Should  the  chimney  refuse  to  draw,  the  draft  can  generally  be  started  by 
building  a  small  fire  in  the  base  of  the  chimney. 

Value  of  Slow  Fires. — When  getting  up  steam,  the  fire  should  not  be  forced 
but,  instead,  should  be  allowed  to  burn  up  gradually.  By  forcing  the  fire, 
the  plates  or  tubes  that  are  nearest  the  fire  suffer  extreme  expansion,  while 
those  parts  that  are  remote  from  the  fire  are  still  cold;  under  such  conditions 
the  seams  and  rivets,  and  also  the  tube  ends,  which  are  expanded  into  the  tube 
plates,  are  liable  to  be  severely  strained,  and,  possibly,  permanently  injured. 
It  is  not  desirable  to  raise  steam  in  any  boiler,  except  in  steam  fire-engines,  in 
less  than  from  2  to  4  hr.,  according  to  the  size,  from  the  time  the  fire  is  first 
started.  When  steam  begins  to  issue  from  the  opened  top  gauge-cock  or  the 
raised  safety  valve,  as  the  case  may  be,  the  cock  or  the  valve  may  be  closed 
and  the  pressure  still  allowed  to  rise  slowly  until  the  desired  pressure  has  been 
reached. 

Trying  the  Fittings. — After  the  pressure  at  which  the  boiler  is  to  run  has 
been  reached,  and  before  cutting  it  into  service,  all  the  valves  and  cocks  should 
be  tried.  The  safety  valve  should  be  raised  and  its  action  noted;  the  water 
column  should  be  blown  out  and  the  gauge-cocks  tested ;  the  feeding  apparatus 
should  be  tried ;  and  it  should  be  noted  particularly  whether  the  check- valves 
seat  properly  and  the  valve  in  the  feedpipe  is  open.  All  the  accessible  parts 
should  be  examined  for  leaks. 

CONNECTING  BOILERS 

Cutting  Boiler  Into  Service. — Cutting  a  boiler  into  service  is  accomplished 
by  opening  the  stop-valve,  thus  permitting  the  steam  to  flow  to  the  engine 
or  other  destination.  The  stop-valve  should  be  opened  very  slowly  to  prevent 
a  too  sudden  change  in  the  temperature  and  consequent  expansion  of  the  piping 
through  which  the  steam  flows,  and  also  to  prevent  water  hammer.  The  steam- 
pipe  drain  should  be  kept  open  until  the  pipe  is  thoroughly  warmed  up.  In 
large  plants  with  many  boilers  and  long  steam  mains,  it  takes  several  hours  to 
warm  these  pipes  thoroughly  by  the  slow  circulation  of  the  steam,  but  the  main 
stop-valve  should  not  be  fully  opened  until  these  pipes  are  warm. 

Connecting  Boilers  to  Main. — Before  connecting  the  different  boilers  of  a 
battery  to  the  same  steam  main,  the  precaution  of  equalizing  the  pressures  in 
the  different  boilers  must  be  observed  in  order  to  prevent  a  sudden  rush  of 
steam  from  one  boiler  to  another.  All  the  pressures  should  be  within  about 
2  Ib.  before  an  attempt  is  made  to  connect  the  boilers. 

Changing  Over. — In  plants  where  there  are  duplicate  sets  of  boilers,  one  set 
being  in  operation  while  the  other  is  undergoing  repairs,  overhauling,  and 
cleaning,  the  method  of  changing  over,  or  connecting,  is  as  follows:  Start  the 
fires  and  raise  steam  in  the  boilers  that  are  to  be  cut  into  service.  Allow  the 
pressure  to  rise  in  all  to  within  5  Ib.  of  that  which  is  in  the  boilers  in  operation. 
All  arrangements  before  changing  over  should  be  made  with  a  view  of  getting 
all  the  heat  that  can  be  obtained  from  the  fires  in  the  boilers  that  are  to  be  cut 


BOILERS  435 

out.  This  can  be  accomplished  by  running  until  the  fires  have  given  up  all 
their  available  heat  for  making  steam,  as  indicated  by  the  gradual  fall  in 
pressure  when  the  dampers  are  wide  open,  and  then  making  the  change. 
While  the  fires  in  one  set  of  boilers  are  burning  low  and  the  pressure  is  falling, 
the  pressure  in  the  boilers  to  be  cut  in  is  gradually  rising  and  meeting,  so  to 
speak,  the  falling  pressure  of  the  set  in  operation.  When  the  difference  of 
5  Ib.  is  reached,  change  over.  A  man  should  be  stationed  at  each  stop-valve, 
and  while  pne  is  being  opened  the  other  should  be  closed;  the  engine  will  con- 
tinue running  uninterruptedly  while  the  change  is  being  made. 

EQUALIZING  THE  FEED 

When  the  boilers  of  a  battery  have  been  cut  into  service  and  hence  are  all 
connected  together  through  the  steam  main,  the  regulation  and  equalization 
of  the  feedjvater  becomes  an  important  factor.  Each  boiler  has  its  own  check- 
valve  and  Teed  stop-valve,  and  generally  all  the  boilers  are  supplied  from  one 
pump,  which  is  running  constantly.  The  quantity  of  water  admitted  to  each 
boiler  is  regulated  by  its  feed  stop-valve.  When  the  w'ater  gets  low  in  any  boiler 
the  feed  stop-valve  should  be  opened  wider,  while  at  the  same  time  the  feed 
stop-valves  on  one  or  more  of  the  other  boilers  in  operation  may  be  closed 
partly  and  thus  divert  the  feedwater  to  the  one  most  requiring  it.  Some  boiler 
plants  have  check-valves  with  an  adjustable  lift;  in  that  case  the  feed  is  equal- 
ized by  adjusting  the  lifts  of  the  check-valves,  the  stop-valves  being  left  wide 
open  while  running.  It  will  be  understood  from  the  foregoing  that  the  object 
in  view  is  the  maintaining  of  an  equal  water  level  in  all  the  boilers  through 
the  manipulation  of  the  feed  stop-valves  or  check-valves.  A  boiler  that  is 
not  doing  its  legitimate  share  in  generating  steam  may  be  known  by  the  fact 
that  the  feed  stop-valve  or  check-valve  on  that  boiler  will  be  nearly,  if  not 
entirely,  closed  most  of  the  time. 

FIRING  WITH  SOLID  FUEL 

The  safe  and  economical  operation  of  steam  boilers  calls  for  careful  and 
intelligent  management.  The  fires  should  be  kept  in  such  condition  as  to 
maintain  the  desired  pressure  and  to  burn  the  fuel  with  economy.  Different 
fuels  require  different  handling  and  hence  only  general  rules  can  be  given; 
much  will  depend  on  the  skill  and  judgment  of  the  attendant,  who  must  him- 
self discover  in  each  case  by  actual  trial  the  best  method  to  pursue.  The  fires 
must  be  cleaned  at  intervals;  the  time  and  method  of  cleaning  depend  on  the 
nature  of  the  fuel  and  the  rapidity  with  which  it  is  being  consumed,  the  style 
of  grate  in  use,  and  the  construction  of  the  furnace. 

Cleaning  of  Fires. — There  are  two  methods  employed  in  cleaning  the  fires: 
first,  that  of  cleaning  the  front  half  and  then  the  rear  half;  second,  that  of  cleaning 
one  side  of  the  fire  and  then  the  other  side.  In  the  first  method,  previous  to 
cleaning,  green  fuel  is  thrown  on  and  allowed  to  burn  partly  until  it  glows 
over  the  entire  surface.  The  new  and  glowing  fuel  is  then  pushed  to  the 
back  of  the  furnace  with  a  hoe,  leaving  nothing  on  the  front  half  of  the 
grate  but  the  ashes  and  clinkers,  which  are  then  pulled  out,  leaving  the  front 
end  of  the  grate  entirely  bare.  The  new  fire,  which  was  pushed  back,  is  drawn 
forwards  and  spread  over  the  bare  half  of  the  grate.  The  ashes  and  clinkers 
that  are  on  the  rear  half  of  the  grate  are  then  pulled  over  the  top  of  the  front 
half  of  the  fire  and  out  through  the  furnace  door;  this  leaves  the  rear  half  of 
the  grate  bare,  which  must  be  covered  by  pushing  back  some  of  the  new  front 
fire.  The  clean  fire  having  been  spread  evenly,  some  new  fuel  must  be  spread 
over  the  entire  surface. 

The  second  method  is  substantially  the  same  in  principle,  but  the  fire  is 
pushed  to  one  side  instead  of  to  one  end  of  the  furnace.  The  condition  of  the 
fires  themselves  and  the  nature  of  the  service  of  the  plant  will  determine  just 
how  often  and  at  what  time  the  cleaning  of  fires  should  take  place.  In  general, 
the  fires  in  stationary  boilers  require  cleaning  at  intervals  of  from  8  to  12  hr. 
Fires  require  cleaning  more  often  when  forced  draft  is  used  than  when  working 
with  natural  draft. 

Rapidity  in  cleaning  fires  is  of  great  importance,  as  during  the  operation 
a  large  volume  of  cold  air  enters  the  furnace  and  chills  the  metallic  surfaces 
with  which  it  comes  in  contact;  consequently,  the  boiler  is  damaged,  however 
slightly.  It  is  the  greatest  advantage  of  shaking  grates  that  they  allow  the 
fire  to  be  cleaned  without  opening  the  furnace  door;  the  inrush  of  cold  air  and 
consequent  chilling  of  the  plates,  etc.  is  thus  avoided. 

Before  starting  to  clean  fires,  the  steam  pressure  and  the  water  level  should 
be  run  up  as  high  as  is  safe  and  the  feed  should  be  shut  off  in  order  to  reduce 


436  BOILERS 

the  loss  in  pressure  while  cleaning.  The  condition  of  the  fire  during  cleaning 
and  the  opening  of  the  furnace  doors  cause  the  pressure  to  drop  quite  rapidly, 
but  the  rapidity  and  the  amount  of  drop  will  be  reduced  by  taking  the  precau- 
tions mentioned  and  cleaning  quickly. 

The  amount  of  drop  in  pressure  while  cleaning  fires  depends  on  several 
conditions.  For  example,  with  a  boiler  that  has  a  small  steam  space  and, 
in  addition,  is.  too  small  for  the  work  required  of  it  without  forcing,  it  is  to  be 
expected  that  the  drop  in  pressure  will  be  much  more  than  if  the  reverse  con- 
ditions exist.  Furthermore,  it  may  be  necessary  to  clean  fires  while  steam  is 
being  drawn  from  the  boiler,  instead  of  being  able  to  clean  at  a  time  when 
the  engine  is  stopped.  In  that  case  a  greater  drop  must  be  expected  than 
when  cleaning  while  no  steam  is  being  drawn  from  the  boiler.  It  is  advisable 
when  possible  to  do  the  cleaning  at  a  time  when  no  steam  is  being  drawn  from 
the  boiler  or  when  the  demand  for  steam  is  light.  t 

UNIFORM  STEAM  PRESSURE 

Desirability  of  Uniform  Pressure. — The  attendant  should  aim  to  carry  the 
pressure  in  the  boiler  as  uniform  as  possible.  A  steady  steam  pressure  and  a 
steady  water  level  are  conducive  to  economy  in  the  use  of  a  fuel  because,  with 
these  conditi9ns,  in  a  properly  designed  plant  there  will  be  a  fairly  steady 
temperature  in  the  furnace,  which,  under  normal  conditions,  is  sufficiently 
high  to  insure  a  thorough  ignition  of  the  volatile  matter  in  the  coal.  With  a 
constant  demand  for  steam,  a  fluctuation  in  the  steam  pressure  is  caused  by 
a  change  in  the  furnace  temperature,  assuming  the  feedwater  supply  to  be 
constant,  and  whenever  the  steam  pressure  is  down,  the  furnace  temperature 
is  low  at  the  same  time.  In  consequence  of  this,  large  quantities  of  the  volatile 
matter  in  the  coal  often  escape  unconsumed  and  cause  a  serious  loss  of  heat. 
Furthermore,  with  a  steady  steam  pressure  the  stresses  on  the  boiler  are 
constant,  and  hence  the  life  of  the  boiler  will  be  increased  and  repair  bills  will 
be  smaller  than  otherwise. 

Maintenance  of  Uniform  Pressure. — During  the  period  of  time  between  the 
cleaning  of  the  fires,  the  pressure  may  be  carried  nearly  uniform  by  manipu- 
lating the  feed  apparatus  so  that  just  the  necessary  amount  of  water  constantly 
enters  the  boiler.  Intermittent  feeding  is  practiced  under  certain  local  con- 
ditions, as,  for  example,  where  there  is  an  injector  or  a  pump  that  is  so  large 
that  it  is  impossible  to  run  it  continuously  without  increasing  the  height  of 
the  water  level.  In  such  a  case,  the  feeding  must  be  stopped  just  before  firing, 
and  is  not  resumed  until  the  new  fire  begins  to  make  steam,  as  indicated  by 
the  rise  of  pressure  on  the  gauge.  If  the  pressure  tends  to  rise  above  the 
standard  or  normal  the  dampers  must  be  partly  closed  and  the  quantity  of 
feed  increased,  assuming  in  this  case  that  no  damper  regulator  is  fitted  and 
that,  hence,  the  damper  is  regulated  by  hand.  A  damper  regulator,  system- 
atic firing,  and  proper  feeding  are  essential  for  carrying  a  practically  uniform 
pressure.  Should  the  pressure  continue  to  rise,  more  green  fuel  must  be 
thrown  on,  the  damper  closed,  the  feed  increased,  and  only  as  a  last  resort 
should  the  furnace  door  be  opened. 

A  uniform  steam  pressure  cannot  be  kept  without  proper  firing.  To 
maintain  such  a  pressure  the  following  directions  should  be  observed:  Keep 
the  fire  uniformly  thick;  allow  no  air  holes  in  the  bed  of  fuel;  fire  evenly  and 
regularly;  be  careful  not  to  fire  too  much  at  a  time;  keep  the  fire  free  from 
ashes  and  clinkers;  and  do  not  neglect  the  sides  and  corners  while  keeping 
the  center  clean.  Do  not,  however,  clean  the  fires  oftener  than  is  necessary. 
Keep  the  ash-pit  clear. 

Keeping  Water  Level  Constant. — In  connection  with  the  maintenance  of  a 
constant  water  level,  the  following  instructions  should  be  followed:  On  start- 
ing to  work,  remember  that  the  first  duty  of  the  fireman  is  to  examine  the 
water  level.  Try  the  gauge-cocks,  as  the  gauge  glass  is  not  always  reliable. 
If  there  is  a  battery  of  boilers,  try  the  gauge-cocks  on  each  boiler. 

PRIMING  AND  FOAMING 

Priming. — The  phenomenon  called  griming  is  analogous  to  boiling  over; 
the  water  is  carried  into  the  steam  pipes  and  thence  to  the  engine,  where 
considerable  damage  is  liable  to  take  place  if  the  trouble  is  not  checked  in  time. 
There  are  several  causes  for  priming,  the  most  common  ones  of  which  are: 
insufficient  boiler  power,  defective  design  of  boiler,  water  level  carried  too 
high,  irregular  firing,  and  sudden  opening  of  stop-valves. 

When  the  boiler  power  is  insufficient,  the  best  remedy  is  to  increase  the 
boiler  plant;  the  next  best  thing  to  do  is  to  put  in  a  separator,  which,  obviously, 


BOILERS  437 

will  only  prevent  the  entrained  water  from  reaching  the  engine,  and  will  not 
stop  the  priming. 

Defective  design  of  a  boiler  generally  consists  of  a  steam  space  that  is  too 
small  or  a  bad  arrangement  of  the  tubes,  which  may  be  spaced  so  close  in  an 
effort  to  obtain  a  large  heating  surface  as  to  interfere  seriously  with  the  circu- 
lation. In  horizontal  return-tubular  boilers,  a  sufficiently  large  steam  space 
can  be  obtained  by  the  addition  of  a  steam  drum;  sometimes  the  top  row  of 
tubes  can  be  taken  out  to  advantage,  which  permits  a  lower  water  level. 
Defective  circulation  in  horizontal  fire-tube  boilers  is  difficult  to  detect  and 
to  remedy;  if  it  is  due  to  a  too  close  spacing  of  the  tubes,  a  marked  betterment 
may  be  effected  by  the  removal  of  one  or  two  vertical  rows  of  tubes.  The 
remedy  for  a  water  level  that  is  too  high  is  to  carry  the  water  at  a  lower  level. 

Evidences  of  Priming. — Priming  manifests  itself  first  by  a  peculiar  clicking 
sound  in  the  cylinder  of  the  engine,  due  to  water  thrown  against  the  heads. 
In  cases  of  very  violent  priming,  the  water  will  suddenly  rise  several  inches  in 
the  gauge  glass,  thus  showing  more  water  in  the  boiler  than  there  really  is. 
When  priming  takes  place,  it  can  be  checked  temporarily  as  follows:  Close 
the  damper,  and  thereby  check  the  fires  until  the  water  is  quiet;  the  engine 
stop-valve  should  also  be  partly  closed  to  check  the  inrush  of  water.  Observe 
whether  the  water  drops  in  the  gauge  glass,  and  then,  if  more  feed  is  needed, 
increase  the  feed.  To  prevent  damage  to  the  engine,  open  the  cylinder  drains. 
Regular  and  even  firing  tends  to  prevent  priming. 

Foaming. — The  phenomenon  called  foaming  is  not  the  same  as  priming, 
though  frequently  considered  so.  Foaming  is  the  result  of  flirty  or  greasy 
water  in  the  boiler;  the  water  foams  and  froths  at  the  surface,  but  does  not 
lift.  A  boiler  may  prime  and  foam  simultaneously,  but  a  foaming  boiler  does 
not  always  prime.  Foaming  while  taking  place  is  visible  in  the  gauge  glass 
and  is  best  remedied  by  using  the  surface  blow-off.  If  no  surface  blow-off  is 
fitted,  the  bottom  blow-off  may  be  used  in  order  to  get  rid  of  the  dirty  water. 
Like  priming,  foaming  will  cause  a  wrong  level  to  be  shown,  and  hence  the 
first  thing  to  do  in  case  of  foaming  is  to  quiet  the  water  by  checking  the  outrush 
of  steam,  either  by  slowing  the  engine  down  or  by  checking  the  fire,  or  by  both. 

SHUTTING  DOWN  AND  STARTING  UP 

Preparations  for  Shutting  Down. — Before  shutting  down  for  the  night  it  is 
advisable  to  fill  the  boiler  to  the  top  of  the  glass,  so  as  to  be  sure  to  have  suffi- 
cient water  to  start  with  in  the  morning.  The  presence  of  possible  leaks 
through  the  valves,  tube  ends,  or  seams  necessitates  this  course  of  action. 
Even  if  no  leaks  exist,  it  is  good  practice  to  dp  this,  if  for  no  other  reason  than 
to  admit  of  blowing  out  a  portion  before  raising  steam  in  the  morning.  All 
the  gauge-cocks  should  be  tried  and  the  water  column  should  be  blown  out  to 
insure  their  being  free  and  clear. 

Banking  of  Fires. — The  fires  may  be  banked  at  such  a  time  that  there  will 
be  about  enough  steam  to  finish  the  day's  run,  thus  shutting  down  under  a 
reduced  pressure  with  only  a  remote  possibility  of  its  rising  again  through 
the  night.  If  the  fires  are  properly  banked  and  the  steam  worked  off  while 
the  feed  is  on,  it  will  be  remotely  possible  for  the  pressure  to  rise  during  the 
night  to  a  dangerous  extent.  To  bank  the  fires  they  should  be  shoved  to  the 
back  of  the  grate  and  well  covered  with  green  fuel,  leaving  the  front  part  of 
the  grate  bare,  thus  preventing  any  possibility  of  the  banked  fire  burning  up 
through  the  night. 

Closing  Valves  and  Damper. — The  steam  stop-valve,  feed  stop-valve, 
whistle  valve,  and  other  steam  valves  should  be  closed;  the  valves  at  the  top 
and  bottom  of  the  gauge  glass  also  should  be  shut  off  to  prevent  loss  of  water, 
etc.  in  case  the  glass  should  break  during  the  night.  If  there  is  a  damper 
regulator,  it  should  be  so  arranged  that  the  damper  may  be  left  closed,  but 
not  quite  tight,  because  a  small  opening  must  be  left  to  permit  the  collecting 
gases  from  the  banked  fire  to  escape  up  the  chimney;  otherwise,  there  is  danger 
that  the  gas  will  ignite  and  cause  an  explosion.  It  is  very  important  to  take 
this  precaution  and  also  to  make  a  mark  by  means  of  which  the  distance 
the  damper  is  open  can  be  ascertained  at  a  glance.  In  fact,  a  damper  should 
be  so  made  that  when  shut  to  the  full  extent  of  its  travel  there  will  be  still 
sufficient  space  around  it  to  allow  the  gas  to  escape.  The  damper  regulator 
should  be  rendered  positivelv  inoperative  in  any  manner  permitted  by  its 
design  so  that  when  closed  it  will  remain  in  that  position  until  connected  prop- 
erly by  the  attendant  in  the  morning. 

Starting  the  Fires. — On  entering  the  boiler  room  in  the  morning,  the  quan- 
tity of  water  in  the  boiler  should  first  be  noted.  The  gauge  glass  and  the 


438  BOILERS 

gauge-cocks  should  be  tried  and  the  water  level  determined.  After  it  has  been 
found  that  the  water  is  not  too  low,  the  banked  fires  may  be  pulled  down  and 
spread  over  the  grates  and  allowed  to  burn  up  slowly,  the  damper  regulator, 
if  one  is  fitted,  in  the  meantime  having  been  connected. 

Blowing  Down. — While  the  fires  are  burning  up  and  before  the  pressure 
begins  to  rise,  the  blow-off  cock  or  valve  should  be  opened  and  the  boiler  blown 
down;  that  is,  a  small  quantity  of  the  water  should  be  blown  out.  This  should 
be  done  every  morning,  so  that  any  impurities  in  mechanical  suspension  in  the 
water  that  settled  during  the  night  may  be  removed.  Great  care  should  be 
exercised  while  doing  this  so  that  too  much  water  is  not  blown  out;  from  3  to 
4  in.  as  shown  by  the  gauge  glass,  is  sufficient.  Under  no  circumstances  should 
the  attendant  leave  the  blow-off  while  it  is  open.  Disaster  to  the  boiler  is 
liable  to  follow  a  disregard  of  this  injunction.  Next,  all  the  valves,  except 
the  stop- valve,  which  were  shut  the  night  before  should  be  opened  and  tried 
to  see  that  they  are  free  and  in  good  working  order. 

CARE  OF  BOILERS 

Safety  Valves. — Great  care  should  be  exercised  to  see  that  the  safety  valves 
are  ample  in  size  and  in  working  order.  Overloading  or  neglect  frequently 
lead  to  the  most  disastrous  results.  Safety  valves  should  be  tried  at  least 
once  every  day,  to  see  that  they  act  freely. 

Pressure  Gauge. — The  steam  gauge  should  stand  at  zero  when  the  pres- 
sure is  off,  and  it  should  show  the  same  pressure  as  that  at  which  the  safety 
valve  is  set  when  that  is  blowing  off.  If  the.  pressures  do  not  agree,  the 
gauge  should  be  compared  with  one  known  to  be  correct. 

Water  Level. — The  first  duty  of  an  engineer  before  starting,  or  at  the  begin- 
ning of  his  watch,  is  to  see  that  the  water  is  at  the  proper  height.  He  should 
not  rely  on  glass  gauges,  floats,  or  water  alarms,  but  try  the  gauge-cocks. 
If  they  do  not  agree  with  the  water  gauge,  the  cause  should  be  learned  and  the 
fault  corrected. 

Gauge-Cocks  and  Water  Gauges. — All  gauge-cocks  and  water  gauges  must 
be  kept  clean.  Water  gauges  should  be  blown  out  frequently,  and  the  glasses 
and  passages  to  them  kept  clean.  The  Manchester,  England,  Boiler  Associa- 
tion attributes  more  accidents  to  inattention  to  water  gauges  than  to  all  other 
causes  put  together. 

Feed-Pump  or  Injector. — The  feed-pump  or  injector  should  be  kept  in 
perfect  order,  and  be  of  ample  size.  No  make  of  pump  can  be  expected 
to  be  continuously  reliable  without  regular  and  careful  attention.  It  is 
always  safe  to  have  two  means  of  feeding  a  boiler.  Check- valves  and  self- 
acting  feed-valves  should  be  frequently  examined  and  cleaned.  The  attend- 
ant should  satisfy  himself  frequently  that  the  valve  is  acting  when  the 
feed-pump  is  at  work. 

Low  Water. — In  case  of  low  water,  immediately  cover  the  fire  with  ashes 
(wet  if  possible)  or  any  earth  that  may  be  at  hand.  If  nothing  else  is  handy, 
use  fresh  coal.  Draw  fire  as  soon  as  it  can  be  done  without  increasing  the  heat. 
Neither  turn  on  the  feed,  start  nor  stop  engine,  nor  lift  safety  valve  until  fires 
are  out  and  the  boiler  cooled  down. 

Blisters  and  Cracks. — Blisters  and  cracks  are  liable  to  occur  in  the  best 
plate  iron.  When  the  first  indication  appears,  there  must  be  no  delay  in  having 
the  fault  carefully  examined  and  properly  cared  for. 

Fusible  Plugs. — When  used,  fusible  plugs  must  be  examined  when  the  boiler 
is  cleaned,  and  carefully  scraped  clean  on  both  the  water  and  fire  sides,  or  they 
are  liable  not  to  act. 

Firing. — Fire  evenly  and  regularly,  a  little  at  a  time.  Moderately  thick 
fires  are  most  economical,  but  thin  firing  must  be  used  where  the  draft  is  poor. 
Take  care  to  keep  grates  evenly  covered,  and  allow  no  air  holes  in  the  fire. 
Do  not  clean  fires  oftener  than  necessary.  With  bituminous  coal,  a  coking 
fire,  i.  e.,  firing  in  front  and  shoving  back  when  coked,  gives  best  results,  if 
properly  managed. 

Cleaning. — All  heating  surfaces  must  be  kept  clean  outside  and  in,  or 
there  will  be  a  serious  waste  of  fuel.  The  frequency  of  cleaning  will  depend 
on  the  nature  of  fuel  and  water.  When  a  new  feed  water  supply  is  intro- 
duced, its  effect  on  the  boiler  should  be  closely  observed,  as  this  new  supply 
may  be  either  an  advantage  or  a  detriment  as  compared  with  the  working  of 
the  boiler  previous  to  its  introduction.  As  a  rule,  never  allow  over  f§  in.  of 
scale  or  soot  to  collect  on  surfaces  between  cleanings.  Handholes  should  be 
frequently  removed  and  surfaces  examined,  particularly  in  the  case  of  a  new 
boiler,  until  proper  intervals  have  been  established  by  experience. 


BOILERS  439 

The  exterior  of  tubes  can  be  kept  clean  by  the  use  of  blowing  pipe  and 
hose  through  openings  provided  for  that  purpose.  When  using  smoky  fuel, 
it  is  best  to  occasionally  brush  the  surfaces  when  steam  is  off. 

Hot  Feedwater. — Cold  water  should  never  be  fed  into  any  boiler  when 
it  can  be  avoided,  but  when  necessary  it  should  be  caused  to  mix  with  the 
heated  water  before  coming  in  contact  with  any  portion  of  the  boiler. 

Foaming. — When  foaming  occurs  in  a  boiler,  checking  the  outflow  of  steam 
will  usually  stop  it.  If  caused  by  dirty  water,  blowing  down  and  pumping  up 
will  generally  cure  it.  In  cases  of  violent  foaming,  the  draft  and  fires  should 
be  checked. 

Air  Leaks. — Be  sure  that  all  openings  for  admission  of  air  to  boiler  or  flues, 
except  through  the  fire,  are  carefully  stopped ;  this  is  frequently  an  unsuspected 
cause  of  serious  Waste  of  fuel. 

Blowing  Off. — If  feedwater  is  muddy  or  salt,  blow  off  a  portion  frequently, 
according  to  condition  of  water.  Empty  the  boiler  every  week  or  two,  and 
fill  up  afresh.  When  surface  blow  cocks  are  used,  they  should  be  often  opened 
for  a  few  minutes  at  a  time.  Make  sure  no  water  is  escaping  from  the  blow-off 
cock  when  it  is  supposed  to  be  closed.  Blow-off  cocks  and  check- valves  should 
be  examined  every  time  the  boiler  is  cleaned.  Never  empty  the  boiler  while 
the  brickwork  is  hot. 

Leaks. — When  leaks  are  discovered,  they  should  be  repaired  as  soon  as 
possible. 

Filling  Up. — Never  pump  cold  water  into  a  hot  boiler.  Many  times  leaks, 
and,  in  shell  boilers,  serious  weaknesses,  and  sometimes  explosions  are  the 
result  of  such  an  action. 

Dampness. — Take  care  that  no  water  comes  in  contact  with  the  exterior 
of  the  boiler,  as  it  tends  to  corrode  and  weaken  it.  Beware  of  all  dampness 
in  seatings  and  coverings. 

Galvanic  Action. — Examine  frequently  parts  in  contact  with  copper  or 
brass,  where  water  is  present,  for  signs  of  corrosion.  If  water  is  salt  or  acid, 
some  metallic  zinc  placed  in  the  boiler  will  usually  prevent  corrosion,  but  it 
will  need  attention  and  renewal  from  time  to  time. 

Rapid  Firing. — In  boilers  with  thick  plates  or  seams  exposed  to  the  fire, 
steam  should  be  raised  slowly,  and  rapid  or  intense  firing  avoided.  With  thin 
water  tubes,  however,  and  adequate  water  circulation,  no  damage  can  come 
from  that  cause. 

Standing  Unused. — If  a  boiler  is  not  required  for  some  time,  empty  and 
dry  it  thoroughly.  If  this  is  impracticable,  fill  it  quite  full  of  water,  and  put 
in  a  quantity  of  common  washing  soda.  External  parts  exposed  to  dampness 
should  receive  a  coating  of  linseed  oil. 

Repair  of  Coverings. — All  coverings  should  be  looked  after  at  least  once 
a  year,  given  necessary  repairs,  refitted  to  the  pipe,  and  the  spaces  due  to 
shrinkage  taken  up.  Little  can  be  expected  from  the  best  non-conductors  if 
they  are  allowed  to  become  saturated  with  water,  or  if  air-currents  are  per- 
mitted to  circulate  between  them  and  the  pipe. 

General  Cleanliness. — All  things  about  the  boiler  room  should  be  kept 
clean  and  in  good  order;  negligence  tends  to  waste  and  decay. 


BOILER  INSPECTION 

NATURE  OF  INSPECTION 

The  inspection  of  a  boiler  usually  consists  in  an  external  examination  of 
the  complete  structure,  and  of  the  setting  if  the  boiler  is  externally  fired,  and 
an  internal  inspection.  The  examination  of  the  boiler  consists  of  an  ocular 
inspection  for  visible  defects,  and  a  hammer  test  or  sounding  for  hidden  defects 
of  plates,  stays,  braces,  and  other  boiler  parts.  The  hammer  test  is  made 
by  tapping  the  suspected  parts  with  a  light  hammer  and  judging  the  existence 
and  extent  of  defects  from  the  sound  produced  by  the  blow.  If  the  examina- 
tion discloses  marked  wear  and  tear,  a  series  of  calculations  is  often  required 
to  find  the  safe  pressure  that  may  be  allowed  on  the  worn  parts,  using  such 
formulas  or  rules  as  laws,  ordinances,  and  regulations  may  prescribe.  In  the 
absence  of  officially  prescribed  formulas  and  rules,  the  inspector  should  use 
such  rules  as  he  deems  in  best  accordance  with  good  practice.  The  inspection 
is  usually,  but  not  always,  completed  by  a  so-called  hydrostatic  test,  which  is 
generally  prescribed  by  official  regulations. 


440  BOILERS 

EXTERNAL  INSPECTION 

Preparation. — Before  a  boiler  that  has  been  in  use  can  be  inspected,  it  must 
be  blown  out  and  must  be  allowed  to  cool  off.  As  soon  as  the  water  has  been 
removed,  the  manhole  covers,  handhole  covers,  and  washout  plugs  should  be 
taken  out  and  all  loose  mud  and  scale  washed  out  with  a  hose.  If  the  boiler 
is  externally  fired,  the  tubes  must  be  swept  and  the  furnace,  the  ash-pit,  the 
smokebox,  and  the  space  back  of  the  bridge  wall  must  be  cleaned  out.  Any 
removable  insulating  covering  that  prevents  the  inspector  from  having  free 
access  to  the  exterior  of  the  boiler  must  be  removed  to  the  extent  deemed 
necessary  by  him;  it  may  even  be  necessary  to  take  down  some  of  the  bricks 
of  the  setting. 

Inspection  of  Externally  Fired  Boilers. — In  the  inspection  of  an  externally 
fired  fire-tube  or  flue  boiler,  the  exterior  is  first  examined.  The  seams  are 
gone  over  inch  by  inch;  the  rivet  heads  and  calking  edges  of  the  plates  are  care- 
fully scrutinized  for  evidence  of  leaks;  and  possible  cracks  are  looked  for 
between  the  rivet  heads,  especially  in  the  girth  seams  and  on  the  under  side  of 
the  boiler.  The  plates  must  also  be  examined  for  corrosion,  bulges,  blisters,  and 
cracks.  The  heads  are  inspected  for  cracks  between  the  tubes  or  flues,  cracks 
in  the  flanges,  leaky  tubes,  and  leaks  in  the  seams.  The  condition  of  the  fire- 
brick lining  of  the  furnace  and  bridge  and  the  top  of  the  rear  combustion  cham- 
ber is  noted  while  making  the  exterior  examination  of  the  underside  of  the 
boiler.  Every  defect  that  is  found  should  be  clearly  marked.  Attention  must 
also  be  paid  to  the  condition  of  the  grate  bars  and  their  supports. 

Inspection  of  Internally  Fired  Boilers. — The  inspection  of  the  shell  and 
heads  must  be  followed  by  examination  of  the  fire-box  or  furnace  tubes  or 
flues,  and  of  the  combustion  chambers  if  these  are  fitted  inside  the  boiler. 
In  fire-boxes,  special  attention  must  be  paid  to  the  crown  sheet.  The  ends  of 
the  staybolts  require  close  examination;  if  such  ends  are  provided  with  nuts, 
these  must  be  examined,  as  they  are  liable  to  loosen  and  are  also  liable  to  be 
burned  off  in  time.  Each  staybolt  should  be  tested  for  breakage,  which  is 
done  by  holding  a  sledge  against  the  outside  end  of  the  staybolt  and  striking 
the  inner,  or  fire-box,  end  with  a  light  hammer;  in  making  this  test  on  the 
boilers  of  locomotives  it  is  customary,  when  practical,  to  subject  the  boiler 
to  an  internal  air  pressure  of  from  40  to  50  Ib.  per  sq.  in.  The  internal  pressure, 
by  bulging  the  sheets,  separates  the  ends  of  a  broken  staybolt,  which  renders 
it  comparatively  easy  to  find  them  by  the  hammer  test. 

Inspection  of  New  Boilers. — As  made  in  boiler  shops,  the  external  inspection 
of  new  boilers,  whether  they  are  internally  or  externally  fired,  and  whether 
they  are  of  the  water-tube  or  the  fire-tube  type,  usually  consists  in  a  thorough 
examination  for  visible  defects  and  testing  under  water  pressure  to  locate 
leaks.  If  a  new  boiler  subject  to  official  inspection  during  construction 
successfully  passes  such  a  hydrostatic  test  as  the  regulations  prescribe,  it  will 
usually  be  permitted  the  working  pressure  it  was  designed  for,  the  design 
having  been  approved  officially  before  construction.  The  working  pressure 
will  be  reduced,  however,  if  the  inspection  discloses  poor  workmanship. 

In  the  external  inspection  of  water-tube  boilers  that  have  been  in  use,  the 
tubes  that  are  exposed  directly  to  the  heat  of  the  fire  must  be  particularly 
well  examined  for  evidence  of  overheating.  The  plugs  or  handholes  placed 
in  headers  to  permit  the  insertion  of  the  tubes  and  the  cleaning  of  them  are 
inspected  for  leakage,  and  the  headers  are  inspected  for  cracks.  Steam  drums 
and  mud-drums  should  be  examined  as  carefully  and  for  the  same  defects  as 
the  shells  of  externally  fired  fire-tube  boilers.  The  fire-brick  lining  of  the 
furnace,  and  the  interior  of  the  brick  setting  in  general,  as  well  as  the  baffle 
plates  controlling  the  direction  of  flow  of  the  gases  of  combustion,  must  be 
examined  for  cracks  and  any  other  defects.  The  external  inspection  of  the 
setting  can  usually  be  made  very  rapidly,  as  everything  is  in  plain  sight. 

INTERNAL  INSPECTION 

Preparation. — Before  the  internal  inspection  is  begun  all  loose  mud  should 
be  washed  out  with  a  hose.  In  a  horizontal  return-tubular  boiler  and  flue 
boiler,  the  shell  plates  and  heads  should  be  examined  for  corrosion  and  pitting; 
if  the  boiler  has  longitudinal  lap  seams,  these  should  be  inspected  at  the  inside 
calking  edere  for  incipient  grooving  and  cracks.  All  seams  should  be  examined 
for  cracks  between  the  rivet  holes.  Obviously,  if  the  boiler  is  scaled  to  an 
appreciable  degree,  the  scale  must  be  removed  before  inspection.  The  tubes 
or  flues  should  be  examined  for  pitting,  as  well  as  for  uniform  corrosion.  All 
braces  should  be  inspected  by  sounding  them  with  a  hammer,  and  if  they  are 
attached  by  cotter  pins,  it  should  be  seen  to  that  these  are  firmly  in  place. 


BOILERS  441 

All  defects  found  should  be  marked;  it  is  good  practice  to  make  a  memorandum 
of  them  as  well.  If  any  of  the  bracing  seems  to  have  worn  considerably,  it 
should  be  measured  at  the  smallest  part  in  order  that  the  safe  working  pressure 
thereon  may  be  calculated  afterwards.  To  determine  to  what  thickness  a 
plate  attacked  by  uniform  corrosion  has  been  reduced  the  inspector  will  have 
one  or  more  holes  drilled  through  the  plate  in  the  worn  part  to  enable  him  to 
measure  the  thickness.  These  holes  are  afterwards  plugged,  generally  by 
tapping  out  and  then  screwing  in  a  plug. 

Inspection  of  Locomotive-Type  Boilers. — In  internally  fired  boilers  of  the 
fire-box  and  locomotive  type,  particular  attention  must  be  paid  to  the  crown 
bars,  crown  bolts,  and  sling  stays;  in  boilers  having  the  crown  sheet  stayed 
by  radial  staybolts,  special  attention  is  also  paid  to  these.  As  a  general  rule, 
the  inspector  can  make  only  an  ocular  inspection  of  most  of  them,  as  they  are 
beyond  his  reach;  where  the  outer  sheets  of  the  firebox  contain  inspection  or 
washout  holes  above  the  level  of  the  crown  sheet,  a  lighted  candle  tied  or 
otherwise  fastened  to  a  stick  can  usually  be  introduced  through  these  holes 
from  the  outside  by  a  helper.  In  inspecting  above  the  crown  sheet,  the  inspec- 
tor should  look  for  mud  betv/een  the  crown  sheet  and  crown  bars  and  sight 
over  the  top  of  the  bars  to  see  if  any  have  been  bent.  As  the  inspector  can 
reach  from  the  inside  of  the  boiler  only  a  few  of  the  staybolts  staying  the  sides 
of  the  firebox,  he  must  rely  on  the  hammer  test  applied  from  the  inside  of  the 
furnace  for  finding  broken  staybolts. 

Flues  and  Combustion  Chambers. — In  boilers  having  circular  furnace  flues 
and  internal  combustion  chambers,  the  top  of  the  furnace  flues  must  be  care- 
fully inspected  for  deposits  of  grease  and  scale,  which  are  especially  liable  to 
be  found  if  the  feedwater  is  obtained  from  a  surface  condenser.  Even  a  light 
deposit  of  grease  on  the  furnace  flue  is  liable  to  lead  to  overheating  and  sub- 
sequent collapse  of  the  top.  The  tops  of  the  combustion  chambers,  together 
with  their  supports,  are  usually  easily  inspected,  there  being  ample  space  to 
reach  every  part. 

Inspection  of  Vertical  Boilers. — Vertical  boilers  as  a  general  rule,  except  in 
the  largest  sizes,  have  no  manhole  to  admit  a  person  to  the  inside,  and  such 
internal  inspection  as  is  possible  must  be  made  through  the  handholes.  Defects 
to  be  looked  for  are  pitting  and  uniform  corrosion  of  the  shell  and  tubes  near 
the  usual  water-line,  and  cracks  in  the  heads  between  the  tubes,  the  lower 
head  being  especially  liable  to  show  this  injury. 

INSPECTION  OF  FITTINGS 

Inspection  of  Safety  Valve. — The  safety  valve  requires  very  careful  inspec- 
tion. If  this  valve  is  known  to  leak,  it  should  be  reseated  and  reground  before 
the  hydrostatic  test  is  made.  After  a  boiler  passes  the  hydrostatic  test,  the 
clamp  locking  the  safety  valve  is  removed,  and  by  running  the  pressure  up 
once  more,  the  point  at  which  the  safety  valve  opens  can  be  noted  by  watching 
the  steam  gauge,  which  is  supposed  to  have  been  tested  and  corrected.  If  the 
safety  valve  does  not  open  at  the  working  pressure  allowed  or  opens  too  soon, 
it  is  readjusted.  If  the  safety  valve  is  locked  by  a  seal,  as  is  often  required 
by  official  regulations,  the  seal  is  applied  after  adjustment  of  the  valve. 

Testing  of  Steam  Gauge. — The  steam  gauge  should  be  tested  before  the 
hydrostatic  test  and  at  each  inspection  with  a  so-called  boiler  inspector's  test- 
ing outfit.  If  the  gauge  under  test  is  more  than  5%  incorrect  most  inspectors 
will  condemn  it  although  some  will  condemn  gauges  showing  a  much  smaller 
error.  In  most  cases  the  gauge  can  be  repaired  at  small  expense  by  the  makers. 

Inspection  of  Water  Gauge  and  Blow-off. — The  connections  of  water 
column  and  water-gauge  glasses  require  examination  in  order  to  see  that  they 
are  clear  throughout  their  whole  length.  The  blow-off  pipe  also  requires 
examination  in  order  to  see  that  it  is  clear. 


SELECTION  OF  BOILERS 

General  Requirements. — When  choosing  a  boiler,  the  facts  to  be  kept  in 
mind  are: 

1.  The  grate  surface  must  be  sufficient  to  burn  the  maximum  quantity  of 
coal  expected  to  be  used  at  any  time,  taking  into  consideration  the  available 
draft,  the  quality  of  coal,  its  percentage  of  ash,  whether  or  not  the  ash  tends 
to  run  into  clinker,  and  the  facilities,  such  as  shaking  grates,  for  getting  rid  of 
the  ash  or  clinker. 

2.  The  furnace  must  be  adapted  to  burn  the  particular  kind  of  coal  used. 


442  BOILERS 

3.  The  heating  surface  must  be  sufficient  to  absorb  so  much  of  the  heat 
generated  that  the  gases  escaping  into  the  chimney  will  be  not  over  450°  F. 
with  anthracite,  and  550°  F.  with  bituminous  coal. 

4.  The  gas  passages  must  be  so  designed  and  arranged  as  to  compel  the  gas 
to  traverse  at  a  uniform  rate  the  whole  of  the  heating  surface,  being  not  so 
large  at  any  point  as  to  allow  the  gas  to  find  a  path  of  least  resistance,  or  short- 
circuiting,  or,  on  the  other  hand,  so  contracted  at  any  point  as  to  cause  an 
obstruction  to  the  draft. 

When  these  elements  are  found  in  any  boiler — and  they  may  be  found  in 
boilers  of  many  of  the  common  types — the  relative  merits  of  the  different 
types  may  be  C9nsidered  with  reference  to  their  danger  of  explosion;  their 
probable  durability;  the  character  and  extent  of  repairs  that  may  be  needed 
from  time  to  time,  and  the  difficulty,  delay,  and  expense  that  these  may  entail; 
the  accessibility  of  every  part  of  the  boiler  to  inspection,  internal  and  external; 
the  facility  for  removal  of  mud  and  scale  from  every  portion  of  the  inner  sur- 
face, and  of  dust  and  soot  from  the  exterior;  the  water  and  steam  capacity; 
the  steadiness  of  water  level;  and  the  arrangements  for  securing  dry 

Liability  to  Explosion. — All  boilers  may  be  exploded  by  overpressure,  such 
as  might  be  caused  by  the  combination  of  an  inattentive  fireman  and  an  inopera- 
tive safety  valve,  or  by  corrosion  weakening  the  boiler  to  such  an  extent  as 
to  make  it  unable  to  resist  the  regular  working  pressure;  but  some  boilers  are 
much  more  liable  to  explosion  than  others.  When  selecting  a  boiler,  it  is  well 
to  see  whether  or  not  it  has  any  of  the  features  that  are  known  to  be  dangerous. 

The  plain  cylinder  boiler  is  liable  to  explosion  from  strains  induced  by  its 
method  of  suspension,  and  by  changes  of  temperature.  Alternate  expansion 
and  contraction  may  produce  a  line  of  weakness  in  one  of  the  rings,  which 
may  finally  cause  an  explosion.  A  boiler  should  be  so  suspended  that  all  its 
parts  are  free  to  change  their  position  under  changes  of  temperature  without 
straining  any  part.  The  circulation  of  water  in  the  boiler  should  be  sufficient 
to  keep  all  parts  at  nearly  the  same  temperature.  Cold  feedwater  should 
not  come  in  contact  with  the  shell,  as  this  will  cause  contraction  and  strain. 

The  horizontal  tubular  boiler,  and  all  externally  fired  shell  boilers,  are 
liable  to  explosion  from  overheating  of  the  shell,  due  to  accumulation  of  mud, 
scale,  or  grease,  on  the  portion  of  the  shell  lying  directly  over  the  fire,  to  c. 
double  thickness  of  iron  with  rivets,  together  with  some  scale,  over  the  fire, 
or  to  low  water  uncovering  and  exposing  an  unriveted  part  of  the  shell  directly 
to  the  hot  gases. 

Vertical  tubular  boilers  are  liable  to  explosion  from  deposit  9f  mud,  scale, 
or  grease,  upon  the  lower  tube-sheet,  and  from  low  water  allowing  the  upper 
part  of  the  tubes  to  get  hot  and  cease  to  act  as  stays  to  the  upper  tube-sheet. 

Locomotive  boilers  may  explode  from  deposits  on  the  crown  sheet,  from 
low  water  exposing  the  dry  crown  sheet  to  the  hot  gases,  and  from  corrosion 
of  the  staybolts. 

Double-cylinder  boilers,  such  as  the  French  elephant  boiler,  and  the  boilers 
used  at  some  American  blast  furnaces,  have  exploded  on  account  of  the  forma- 
tion of  a  steam  pocket  on  the  upper  portion  of  the  lower  drum,  the  steam 
being  prevented  from  escaping  from  out  of  the  rings  of  the  drum  by  the  lap 
joint  of  the  adjoining  ring,  thus  making  a  layer  of  steam  about  J  in.  thick 
against  the  shell,  which  was  directly  exposed  to  the  hot  gases.  In  the  case  of 
vertical  or  inclined  tubes  acting  as  stays  to  an  upper  sheet,  the  upper  part 
of  the  tubes  may  become  overheated  in  case  of  low  water;  also,  when  there 
are  stayed  sheets,  the  stays  are  liable  to  become  corroded. 

In  addition  to  these  features  of  design,  all  boilers  are  liable  to  explosion  due 
to  corrosion.  Internal  corrosion  is  usually  due  to  acid  feedwater,  and  all 
boilers  are  equally  liable  to  it.  External  corrosion,  however,  is  more  liable 
to  take  place  in  some  designs  of  boilers  than  others,  and  in  some  locations 
rather  than  others.  If  any  portion  of  a  boiler  is  in  a  cold  and  damp  place,  it 
is  liable  to  rust  out.  For  this  reason  the  mud-drums  of  many  modern  forms  of 
boilers  are  made  of  cast  iron,  which  resists  rusting  better  than  either  wrought 
iron  or  steel.  If  any  part  of  a  boiler,  other  than  a  part  made  of  cast  iron,  is 
liable  to  be  exposed  to  a  cold  and  damp  atmosphere,  or  covered  with  damp 
soot  or  ashes,  or  exposed  to  drip  from  rain  or  from  leaky  pipes,  and  especially 
if  such  part  is  hidden  by  brickwork  or  otherwise  so  that  it  cannot  be  seen, 
that  part  is  an  element  of  danger. 

The  causes  of  boiler  explosions  may  be  summarized  as  follows:  (1)  Bad 
materials;  (2)  bad  workmanship;  (3)  bad  water,  which  eats  away  the  plates 
by  internal  corrosion;  (4)  water  lying  upon  plates,  bringing  about  external 


BOILERS  443 

corrosion;  (5)  overpressure;  (6)  safety  valves  sticking;  (7)  water  .getting  too 
low;  (8)  excessive  firing;  (9)  hot  gases,  acting  on  plates  above  water  level; 
(10)  choking  of  feedpipes;  (11)  insufficient  provision  for  expansion  and  con- 
traction; (12)  insufficient  steam  room  and  too  sudden  a  withdrawal  of  a  large 
quantity  of  steam;  (13)  getting  up  steam,  or  knocking  off  a  boiler  too  suddenly; 
(14)  allowing  wet  ashes  to  lie  in  contact  with  plates.  The  probable  causes 
suggest  their  several  remedies. 

Durability. — The  question  of  durability  is  partly  covered  by  that  of  danger 
of  explosion,  but  it  also  is  related  to  the  question  of  incrustation  and  scale. 
The  plates  and  tubes  of  a  boiler  may  be  destroyed  by  internal  or  external 
corrosion  and  by  being  burned  out.  It  may  be  regarded  as  impossible  to 
burn  a  plate  or  tube  of  iron  or  steel,  no  matter  how  high  the  temperature  of 
the  flame,  provided  one  side  of  the  metal  is  covered  with  water.  However, 
if  a  steam  pocket  is  formed,  or  if  there  is  a  layer  of  grease  or  hard  scale,  so 
that  the  water  does  not  touch  the  metal,  the  plate  or  tube  may  be  burned. 
In  a  water  tube  that  is  horizontal,  or  nearly  so,  and  in  which  the  circulation 
of  water  is  defective,  it  is  possible  to  form  a  mass  of  steam  that  will  drive  the 
water  away  from  the  metal,  and&thus  al^w  the  tube  to  burn  out.  When 
considering  the  probable  durability  of  a  boiler,  it  is  necessary  to  consider  the 
same  things  as  when  investigating  the  danger  of  explosion.  There  are,  how- 
ever, many  chances  of  burning  out  a  minor  part  of  a_boiler  without  serious 
danger,  to  one  chance  of  a  disastrous  explosion.  Thus  the  tubes  of  a  water- 
tube  boiler,  if  allowed  to  become  thickly  covered  with  scale,  might  be  burned 
out  again  and  again  without  causing  any  further  destruction  at  any  one  time 
than  the  rupture  of  a  single  tube.  A  new  type  of  boiler  should  be  considered 
with  regard  to  the  likelihood  of  frequent  small  repairs  being  necessary,  as  well 
as  with  regard  to  its  liability  to  complete  destruction.  The  most  important 
of  these  considerations  are:  The  circulation  through  all  parts  of  the  boiler 
must  be  such  that  the  water  cannot  be  driven  out  of  any  tube  or  from  any 
portion  of  a  plate,  so  as  to  form  a  steam  pocket  exposed  to  high  temperature; 
there  must  be  proper  facilities  for  removing  the  scale  from  every  portion  ot 
the  plates  and  tubes. 

Repairs. — The  questions  of  durability  and  of  repairs  are,  in  some  respects, 
related  to  each  other;  the  more  infrequent  and  the  less  extensive  the  repairs, 
the  greater  the  durability.  The  tubes  of  a  boiler,  where  corroded  or  burnt 
out,  may  be  replaced  and  made  as  good  as  new.  The  shell,  when  it  springs 
a  leak,  may  be  patched,  but  is  then  likely  to  be  far  from  as  good  as  new.  When 
the  shell  corrodes  badly  it  must  be  replaced,  and  to  replace  the  shell  is  the 
same  as  getting  a  new  boiler.  Herein  is  the  advantage  of  the  sectional  water- 
tube  boilers.  The  sections,  or  parts  of  a  section,  may  be  renewed  easily,  and 
made  as  good  as  new,  while  the  shell,  being  far  removed  from  the  fire  and  easily 
kept  dry  externally,  is  not  liable  either  to  burning  out  or  to  external  corrosion. 
When  considering  the  merits  of  a  new  style  of  boiler,  with  reference  to  repairs, 
it  may  be  asked  what  parts  of  the  boiler  are  most  likely  to  give  out  and  need 
to  be  repaired  or  replaced?  Are  these  repairs  easily  effected,  how  long  will 
they  require,  and,  after  they  are  made,  is  the  boiler  as  good  as  new? 

Facility  for  Removal  of  Scale  and  for  Inspection. — The  matter  of  facility 
for  the  removal  of  scale  and  for  inspection  has  already  been  discussed  to  some 
extent  under  the  head  of  durability.  Some  early  water-tube  boilers  had  no 
facilities  for  the  removal  of  scale,  it  being  claimed  that  they  did  not  need  any, 
because  their  circulation  was  so  rapid.  If  there  is  scale-forming  material  in 
the  water  it  will  be  deposited  when  the  water  is  evaporated,  and  no  amount  or 
kind  of  circulation  will  keep  it  from  accumulating  on  every  part  of  the  boiler, 
and  in  every  kind  of  tubes,  vertical,  horizontal,  or  inclined.  The  nearly  vertical 
circulating  tubes  of  a  water-tube  boiler,  in  which  the  circulation  is  nine  times 
as  fast  as  the  average  circulation  in  the  inclined  tubes,  have  been  found  nearly 
full  of  scale;  that  is,  a  4-in.  tube  had  an  opening  in  it  of  less  than  1  in.  in  diam- 
eter. This  was  due  to  carelessness  in  blowing  off  the  boiler,  or  to  exceptionally 
bad  feedwater,  or  both. 

Water  and  Steam  Capacity. — It  is  claimed  for  some  forms  of  boilers  that 
they  are  better  than  others  because  they  have  a  larger  water  or  steam  capacity. 
Great  water  capacity  is  useful  where  the  demands  for  steam  are  extremely 
fluctuating,  as  in  a  rolling  mill  or  a  sugar  refinery,  where  it  is  desirable  to  store 
up  heat  in  the  water  in  the  boilers  during  the  periods  of  the  least  demand 
to  be  given  out  during  periods  of  greatest  demand.  Large  water  capacity  is 
usually  objectionable  in  boilers  for  factories,  especially  if  they  do  not  run  at 
night  and  the  boilers  are  cooled  down,  because  there  is  a  large  quantity  of  water 
to  be  heated  before  starting  each  morning.  If  rapid  steaming,  or  the  ability 


444 


BOILERS 


to  get  up  steam  quickly  from  cold  water,  or  to  raise  the  pressure  quickly,  is 
desired,  large  water  capacity  is  a  detriment. 

The  advantage  of  large  steam  capacity  is  usually  overrated.  It  is  useful  to 
enable  the  steam  to  be  drained  from  water  before  it  escapes  into  the  steam 
pipe,  but  the  same  result  can  be  effected  by  means  of  a  dry  pipe,  as  in  loco- 
motive and  marine  practice,  in  which  the  steam  space  in  the  boiler  is  very  small 
in  proportion  to  the  horsepower.  Large  steam  space  in  the  boiler  is  of  no 
importance  for  storing  energy  or  equalizing  the  pressure  during  the  stroke 
of  an  engine.  The  water  in  the  boiler  is  the  place  to  store  heat,  and  if  the 
steam  pipe  leading  to  an  engine  is  of  such  small  capacity  that  it  reduces  the 
pressure,  the  remedy  is  a  steam  reservoir  close  to  the  engine  or  a  large  steam  pipe. 

To  secure  steadiness  of  water  level  requires  either  a  large  area  of  water 
surface,  so  that  the  level  may  be  changed  slowly  by  fluctuations  in  the  demand 
for  steam  or  in  the  delivery  of  the  feed-pump,  or  else  constant,  and  preferably 
automatic,  regulation  of  the  feedwater  supply  to  suit  the  steam  demand.  _  A 
rapidly  lowering  water  level  is  apt  to  expose  dry  sheets  or  tubes  to  the  action 
of  the  hot  gases,  and  thus  be  a  source  of  danger.  A  rapidly  rising  level  may, 
before  it  is  seen  by  the  fireman,  cause  water  to  be  carried  over  into  the  steam 
pipe,  and  endanger  the  engine. 

Water  Circulation. — Positive  and  complete  circulation  of  the  water  in  a 
boiler  is  necessary  to  keep  all  parts  of  the  boiler  at  a  uniform  temperature, 
and  to  prevent  the  adhesion  of  steam  bubbles  to  the  surface,  which  may  cause 
overheating  of  the  metal.  It  is  claimed  by  some  manufacturers  that  the 
extremely  rapid  circulation  of  water  in  their  boilers  tends  to  make  them  more 
economical  than  others.  However,  proof  is  lacking  that  increased  rapidity 
of  circulation  of  water  beyond  that  usually  found  in  any  boiler  will  give  increased 

RATIO  OF  HEATING  SURFACE  TO  HORSEPOWER  AND  TO 
GRATE  AREA 


Ratij     Heating  Surface 

^   4_.       Heating  Surface 

Horsepower 

Grate  Area 

Plain  cylindrical  
Flue 

6  to  10 
8  to  12 

12  to    15 
20  to    25 

Return-tubular  
Vertical  

14  to  18 
15  to  20 

25  to    35 
25  to    30 

Water-tube  
Locomotive  

10  to  12 
Ito    2 

35  to    40 
50  to  100 

economy.  It  is  known  that  increased  rate  of  flow  of  air  over  radiating  surfaces 
increases  the  amount  of  heat  transmitted  through  the  surface,  but  this  is 
because  by  the  increased  circulation,  cold  air  is  continually  brought  into  con- 
tact with  the  surface,  making  an  increased  difference  of  temperature  on  the 
two  sides,  which  causes  increased  transmission.  But  by  increasing  the  rapidity 
of  circulation  in  a  steam  boiler,  it  is  not  possible  to  vary  the  difference  of 
temperature  to  any  appreciable  extent,  for  the  water  and  the  steam  in  the 
boiler  are  at  about  the  same  temperature  throughout.  The  ordinary  or 
"Scotch"  form  of  marine  boiler  shows  an  exception  to  the  general  rule  of 
uniformity  of  temperature  of  water  throughout  the  boiler,  but  the  temperature 
above  the  level  of  the  lower  fire-tubes  is  practically  uniform. 

Heating  Surface. — In  the  various  types  of  boilers,  there  is  a  nearly  constant 
ratio  between  the  water-heating  surface  and  the  horsepower,  and  also  between 
the  heating  surface  and  the  grate  area.  These  ratios  are  given  in  an  accompany- 
ing table.  If  the  heating  surface  of  a  boiler  is  known,  the  horsepower  can  be 
found  roughly;  thus,  if  a  return-tubular  boiler  has  a  heating  surface  of  900  sq.  ft., 
its  horsepower  lies  between  900-^18  =  50  H.  P.  and  900-^14  =  64.3  H.  P.,  say 
about  57  H.  P. 

The  heating  surface  of  a  boiler  is  the  portion  of  the  surface  exposed  to  the 
action  of  flames  and  hot  gases.  This  includes,  in  the  case  of  a  multitubular 
boiler,  the  portions  of  the  shell  below  the  line  of  brickwork,  the  exposed  heads 
of  the  shell,  and  the  interior  surface  of  the  tubes.  In  the  case  of  a  water-tube 
boiler,  the  heating  surface  comprises  the  portion  of  the  shell  below  the  brick- 
work, the  outer  surface  of  the  headers,  and  the  outer  surface  of  the  tubes.  In 
any  given  case,  the  heating  surface  may  be  calculated  by  the  rules  of  mensuration. 


BOILERS 


445 


The  following  example  will  show  the  method  of  calculating  the  heating  surface 
of  a  return-tubular  boiler: 

EXAMPLE. — What  is  the  heating  surface  of  a  horizontal  return -tubular 
boiler  that  has  the  following  dimensions:  Diameter,  60  in.;  length  of  tubes, 
12  ft.;  internal  diameter  of  tubes,  3  in.;  number  of  tubes,  82. 

SOLUTION. — Assume  that  two-thirds  of  the  shell  is  in  contact  with  hot 
gases  or  flame,  and  two-thirds  of  the  two  heads  are  heating  surface. 

Circumference  of  shell  is  60X3.1416  =  188.496  =  188.5  in.,  say. 

Length  of  shell  is  12  X 12  =  144  in. 

Heating  surface  of  shell  is  188.5  X 144  X  ?  =  18,096  sq.  in. 

Circumference  of  tube  is  3X3.1416  =  9.425  in.,  nearly. 

Heating  surface  of  tubes  is  82X144X9.425  =  111,290.4  sq.  in. 

Area  of  one  head  is  60' X. 7854  =  2,827.44  sq.  in. 

Two-thirds  area  of  both  heads  is  1X2X2,827.44  =  3,769.92  sq.  in. 

From  the  heads  must  be  subtracted  twice  the  area  cut  out  by  the  tubes; 
this  is  82X32X.7854X2  =  1,159.26  sq.  in. 

Total  heating  surface  in  square  feet  is 

18,096  +  111,290.4+3,769.92-1,159.26 


144 


=  916.64  sq.  ft. 


PROBABLE  MAXIMUM  WORK  OF  A  PLAIN  CYLINDRICAL  BOILER  OP 

120  SQ.  FT.  HEATING  SURFACE  AND  12  SQ.  FT.  GRATE 

SURFACE 


Rate  of  driving; 

pounds  of  wa- 

ter evapor- 

ated per  sq.  ft. 

of    heating 

surface    per 

hour  

2 

3 

3.5 

4 

4.5 

5 

6 

7 

8 

Total    water 

evaporated 

by  120  sq.  ft. 

heating  s  u  r- 

face  per  hour, 
pounds  

240.00 

360.00 

420.0O 

480.00 

540.00 

600.00 

720.00 

840.00 

960.00 

Horsepower 

34.5    Ib.    per 

hour=l  H.P. 

6.96 

10.43 

12.17 

13.91 

15.65 

17.39 

20.87 

24.35 

27.83 

Pounds     water 

evaporated 

per   pound 

combustible  . 

10.88 

11.30 

11.36 

11.29 

11.20 

11.05 

10.48 

9.48 

8.22 

Pounds  combus- 

tible   burned 

per  hour  

22.10 

31.90 

37.00 

42.50 

48.20 

54.30 

68.70 

88.60 

116.80 

Pounds  combus- 

tible per  hour 

per  square 
foot  of  grate  . 

1.85 

2.65 

3.08 

3.55 

4.02 

4.52 

5.72 

7.38 

9.73 

Pounds  combus- 

tible per  hour 

per  horse- 

power  

3.17 

3.05 

3.04 

3.06 

3.08 

3.12 

3.30 

3.64 

4.16 

The  figures  in  the  last  line  show  that  the  amount  of  fuel  required  for  a 
given  horsepower  is  nearly  37%  greater  when  the  rate  of  evaporation  is  8  Ib. 
than  when  it  is  3.5  Ib. 

The  figures  in  the  foregoing  table  that  represent  the  economy  of  fuel, 
viz.,  Pounds  water  evaporated  per  pound  combustible  and  Pounds  combustible 
per  hour  per  horsepower,  are  what  may  be  called  maximum  results,  and  they 
are  the  highest  that  are  likely  to  be  obtained  with  anthracite,  with  the  most 
skillful  firing  and  with  every  other  condition  most  favorable.  Unfavorable 
conditions,  such  as  poor  firing,  scale  on  the  inside  of  the  heating  surface,  dust 


446  BOILERS 

or  soot  on  the  outside,  imperfect  protection  of  the  top  of  the  boiler  from  radi- 
ation, leaks  of  air  through  the  brickwork,  or  leaks  of  water  through  the  blow-off 
pipe,  may  greatly  reduce  these  figures. 


CHIMNEYS 

Products  of  Combustion.  —  The  weight  and  volume  of  the  various  gases 
that  enter  into  problems  relating  to  combustion  when  measured  at  32°  F.  and 
the  average  atmospheric  pressure  at  sea  level  of  approximately  14.7  Ib.  per 
sq.  in.,  corresponding  to  a  height  of  the  mercurial  barometer  of  29.92  in.  are 
given  under  the  subject  of  Ventilation.  To  find  the  volume  at  any  other 
temperature  and  pressure,  the  following  formula  is  used, 

ft-«£P. 

piTz 
in  which  vz  =  volume   corresponding   to    absolute   pressure   Pz   and   absolute 

temperature  T*  (or  460  +<2); 
/>2  =  any  given  absolute  pressure; 
vi  =  volume  at  any  other  pressure  pi  and  absolute  temperature  Ti 

(or46Q+/i). 

EXAMPLE.  —  What  is  the  volume  of  4  Ib.  of  dry  air  at  75°  F.  and  under  an 
absolute  pressure  of  20  Ib.  per  sq.  in.? 

SOLUTION.  —  From  the  table,  it  is  found  that  1  Ib.  of  air,  at  32°  F.  and  14.7  Ib. 
per  sq.  in.  absolute  pressure,  occupies  12.388  cu.  ft.,  hence,  under  the  same 
conditions,  4  Ib.  occupies  4X12.388  =  49.552  cu.  ft.  Substituting,  in  the 
formula,  the  values  vz  =  49.  552,  pz  =  14.  7  Ib.  per  sq.  in.,  pi  =  20  Ib.  per  sq.  in., 
fa-75"  P.,  we  get  ,1  =  49.552XX  =  39.6  cu.  ft. 


Hitherto  it  has  been  considered  that  the  fuel  was  burned  in  oxygen.  When 
burning  with  air,  the  chemical  reactions  are  the  same,  for  the  nitrogen  in  the  air 
passes  through  the  furnace  unchanged.  In  calculations  of  temperature,  how- 
ever, account  must  be  taken  of  the  nitrogen,  as  it  is  heated  by  the  combustion 
and  therefore  absorbs  heat  and  causes  the  furnace  to  have  a  lower  temperature 
than  if  oxygen  alone  were  used. 

The  first  table  on  page  447  gives  the  weights  -of  air,  water  vapor,  and 
saturated  mixtures  of  air  and  water  vapor  at  different  temperatures,  under  the 
ordinary  atmospheric  pressure  of  14.7  Ib.  per  sq.  in.,  or  29.92  in.  of  mercury. 

EXAMPLE.—  A  coal  whose  heating  value  is  12,000  B.  T.  U.  per  Ib.,  is  burned 
with  20  Ib.  of  air  (not  including  water  vapor)  per  Ib.  of  coal.  The  relative 
humidity  of  the  air  is  90%,  and  its  temperature  is  92°  F.  How  much  heat  is 
lost  in  the  chimney  gases  on  account  of  the  moisture  in  the  air,  if  the  chimney 
gases  escape  at  512°  F.? 

SOLUTION.  —  From  the  table,  it  is  found  that  1  Ib.  of  air  will  hold,  when  fully 
saturated,  .03289  Ib.  of  water  vapor  at  92°  F.;  hence,  20  Ib.  of  air  will  hold  20 
X  .03289  =  .6578  Ib.  of  water  vapor;  at  90%  relative  humidity,  it  will  hold 
.6578  X.  90  =  .59202  Ib.  water  vapor. 

The  amount  of  heat  absorbed  in  heating  1  Ib.  of  water  from  92°  F.  to  512°  F. 
is:  (a)  From  92°  to  212°,  or  through  120°,  is  120  X.1  (specific  heat  of  water) 
=  120  B.  T.  U.;  (6)  from  212°  to  512°,  or  through  300°,  is  300X.48  (specific 
heat  of  superheated  steam)  =  144  B.  T.  U.  The  total  absorption  is  120+144 
=  264  B.  T.  U.  .59202  Ib.  water  will  absorb  264  X.  59202  =  156.29  B.  T.  U. 

or  1561|9(^)100  =  1.3%.  of  the  heating  value  of  the  coal. 

EXAMPLE.  —  How  many  cubic  feet  of  dry  air  per  pound  of  coal  are  used  in 
the  preceding  example,  if  the  air  is  at  the  mean  atmospheric  pressure  of  14.7  Ib. 
per  sq.  in.? 

SOLUTION.  —  From  the  table,  by  calculation,  it  is  found  that  1  Ib.  of  air 
at  32°  and  at  the  mean  atmospheric  pressure  occupies  1  ^  .0807  =  12.39  cu.  ft. 

no   I  4.AA 

At  92°  it  occupies  12.39X  ^  =13.9  cu.  ft.;  20  Ib.  will  occupy  13.9X20 
=  278cu.  ft. 

EXAMPLE.—  How  many  cubic  feet  of  air  must  be  delivered  per  minute  by 
a  fan,  to  drive  1.000  H.  P.  of  boilers  under  the  conditions  of  the  preceding 
examples,  if  4  Ib.  of  coal  is  burned  per  H.  P.  per  hr.? 

SOLUTION.-      4*  1,000X278  =  18t533  cu  ft  per  min 


BOILERS 


447 


WEIGHT  OF  AIR,  WATER  VAPOR,  AND  SATURATED   MIXTURES  AT 
DIFFERENT  TEMPERATURES 


Mixtures  of  Air  Saturated  With  Vapor 

Weight 
of  1  Cu. 

Elastic 

Elastic 

Weight  of  1  Cu.  Ft.  of 

Ft.  of 

Force  of 

Force  of 

Mixture  of  Air  and 

Temper- 
ature 
Degrees 
P. 

Dry  Air 
at 
Different 
Temper- 

Water 
Vapor 
Inches 
of 

Air  in 
Mixture 
of  Air 
and 

Water  Vapor 

Weight 
of  Vapor 
Mixed 
With 

Total 

atures 

Mercury 

Vapor 

Weight 

Weight 

Weight 

1  Lb. 

of  Air 

Pound 

Inches 

of 

of 

of 

of 

Air 

Vapor 

Mixture 

Pounds 

Mercury 

Pound 

Pound 

Pound 

0 

.0864 

.044 

29.877 

.0863 

.000079 

.086379 

.00092 

12 

.0842 

.074 

29.849 

.0840 

.000130 

.084130 

.00155 

22 

.0824 

.118 

29.803 

.0821 

.000202 

.082302 

.00245 

32 

.0807 

.181 

29.740 

.0802 

.000304 

.080504 

.00379 

42 

.0791 

.267 

29.654 

.0784 

.000440 

.078840 

.00561 

52 

.0776 

.388 

29.533 

.0766 

.000627 

.077227 

.00819 

62 

.0761 

.556 

29.365 

.0747 

.000881 

.075581 

.01179 

72 

.0747 

.785 

29.136 

.0727 

.001221 

.073921 

.01680 

82 

.0733 

1.092 

28.829 

.0706 

.001667 

.072267 

.02361 

92 

.0720 

1.501 

28.420 

.0684 

.002250 

.070717 

.03289 

102 

.0707 

2.036 

27.885 

.0659 

.002997 

.068897 

.04547 

112 

.0694 

2.731 

27.190 

.0631 

.003946 

.067046 

.06253 

122 

.0682 

3.621 

26.300 

.0599 

.005142 

.065042 

.08584 

132 

.0671 

4.752 

25.169 

.0564 

.006639 

.063039 

.11771 

142 

.0660 

6.165 

23.756 

.0524 

.008473 

.060873 

.16170 

152 

.0649 

7.930 

21.991 

.0477 

.010716 

.058416 

.22465 

162 

.0638 

10.099 

19.822 

.0423 

.013415 

.055715 

.31713 

172 

.0628 

12.758 

17.163 

.0360 

.016682 

.052682 

.46338 

182 

.0618 

15.960 

13.961 

.0288 

.020536 

.049336 

.71300 

192 

.0609 

19.828 

10.093 

.0205 

.025142 

.045642 

1.22643 

202 

.0600 

24.450 

5.471 

.0109 

.030545 

.041445 

2.80230 

212 

.0591 

29.921 

.000 

.0000 

.036820 

.036820 

Infinite 

OXYGEN  AND  AIR  REQUIRED  FOR  THE  COMBUSTION  OF  CARBON, 
HYDROGEN,  ETC. 


Fuel 


Chemical  Reaction 


Carbon  to  COt 

Carbon  to  CO i 

Carbon  monoxide  toCO2j 

Hydrogen  to  H^O | 

Marsh  gas  (methane),  1  ! 

Sulphur  to  SO2 ! 


C+O  = 

CO  +  0: 


=  CO 
=  C02 


5+2O  =  SOz 


I? 


8.85 

4.43 

1.90 

26.56 

13.28 
3.33 


fe-gx 

" 


11.52 
5.76 
2.47 

34.56 

17.28 
4.32 


12.52 
6.76 
3.47 

35.56 

18.28 
5.32 


The  preceding  table  contains,  in  convenient  form,  the  reactions  involved 
in  the  combustion  of  various  fuels,  as  explained  more  in  detail  before,  as  well 
as  the  weight  of  air,  oxygen,  and  nitrogen,  required  to  burn  1  Ib.  of  the  fuel, 


448 


BOILERS 


and  the  weight  of  the  products  of  combustion  resulting  therefrom.  It  is  found, 
in  practice,  that  if  air  is  blown  through  a  bed  of  hot  anthracite  or  coke,  and  the 
resulting  gases  are  analyzed,  they  always  contain  some  carbon  monoxide, 
showing  imperfect  combustion,  unless  they  contain  a  considerable  quantity  of 
uncombined  oxygen,  or  air.  The  excess  of  air  required  to  effect  complete 
combustion  to  carbon  dioxide  is  usually  not  less  than  50%  of  that  theoretically 
necessary,  so  that  about  17  Ib.  of  air  is  required  to  insure  the  complete  com- 
bustion of  1  Ib.  of  carbon  instead  of  11.52  Ib.,  the  figure  given  in  the  table. 
It  is  probable,  also,  that  more  than  34.56  Ib.  of  air  is  required  to  effect  the 
combustion  of  each  pound  of  hydrogen  in  a  furnace,  although,  experimentally, 
one  volume  of  oxygen  and  two  volumes  of  hydrogen  mixed  together,  or  eight 
parts  by  weight  of  oxygen  to  one  of  hydrogen  may  be  exploded  by  a  spark,  and 
converted  into  water  vapor.  The  excess  of  air  required  in  furnaces  may^be 
due  to  the  presence  of  the  great  volumes  of  nitrogen  and  carbon  dioxide,  which 
dilutes  the  oxygen  and  makes  it  less  active  in  causing  combustion. 

EXAMPLE. — How  much  air  is  required  for  the  complete  combustion  of 
1  Ib.  of  coal  containing  5%  moisture,  20%  volatile  matter,  60%  fixed  carbon, 
15%  ash,  assuming  the  volatile  matter  to  be  of  the  composition  of  marsh  gas 
(methane),  C£U? 

SOLUTION. — The  molecular  weight  of  marsh  gas  is  12+4  =  16;  hence,  three- 
fourths  of  the  weight  of  the  volatile  matter  is  carbon  and  one-fourth  hydrogen. 
The  carbon  of  the  volatile  matter  is  |  X  20  =  15%  of  the  fuel.  The  fixed  carbon 
is  given  as  60%.  The  total  carbon  is  15+60  =  75%.  The  hydrogen  of  the 
volatile  matter  is  iX20  =  5%  of  the  fuel. 

As,  from  the  table,  11.52  Ib.  of  air  is  required  to  burn  1  Ib.  of  carbon  to  COi, 
and  34.56  Ib.  of  air  is  required  to  burn  1  Ib.  of  hydrogen,  the  theoretical  amount 
of  air  required  to  burn  the  fuel  will  be:  For  the  carbon  .75X  11.52  =  8.640  Ib.; 
for  the  hydrogen  .05X34.56  =  1.728  Ib.;  making  a  total  of  10.368  Ib.  If  an 
excess  of  50%  of  air  is  allowed,  the  amount  will  be  1.5  X  10.368=  15.552  Ib. 

EXAMPLE. — How  many  cubic  feet  of  dry  air  at  62°  F.  will  be  required 
in  the  preceding  example? 

SOLUTION. — The  weight  of  1  cu.  ft.  of  air  at  a  temperature  of  62°  F.  and  a 
barometric  pressure  of  29.92  is  .0761  Ib.;  hence,  10.368  Ib.  =  10.368-7- .0761 
=  136.24  cu.  ft.  and  15.552  lb.  =  15.552 -=-.0761  =  204.36  cu.  ft. 

Temperature  of  Ignition. — Every  combustible  must  be  heated  to  a  certain 
temperature,  known  as  the  temperature  of  ignition,  or  kindling  point,  before 
it  will  combine  with  oxygen,  or  burn.  The  accompanying  table  gives  the 
temperatures  of  ignition  of  various  fuels  as  determined  by  different  authorities. 
It  appears  from  this  table  that  it  requires  a  considerably  higher  temperature 
to  ignite  the  gases  distilled  from  coal  than  to  ignite  the  coal  itself,  the 
temperature  of  ignition  of  the  carbon  being  lower  than  that  of  the  gases. 


TEMPERATURE  OF  IGNITION  OF  VARIOUS  FUELS 


Fuel 

Temperature  of 
Ignition 
Degrees  F 

Marsh  gas  (methane),  CHt  

1,202* 

Carbon  monoxide,  CO.    ,    . 

1  202  to  1  211 

Carbon  monoxide,  CO,  in  presence  of  a  large  quantity  of 
carbon  dioxide  COz  

1  292 

Ethylene  (olefiant  gas),  C^^i^ 

1  022 

Hydrogen 

1  031  to  1  130 

Anthracite  

925 

Semibituminous  coal 

870 

Bituminous  coal  

766 

Cannel  coal  

668 

Soft  charcoal,  prepared  at  500°  F 

650 

Sulphur  

470 

*The  temperature  of  ignition  of  marsh  gas  diluted  with  carbon  dioxide  and 
nitrogen  in  the  proportions  ordinarily  found  in  a  furnace  is  given  by  the  French 
Coal  Commission  as  1,436°  F. 


Temperature  of 
Fire. — Assuming  that  a 
pure  fuel,  such  as  car- 
bon, is  thoroughly 
burned  in  a  furnace,  all 
the  heat  generated  will 
be  transferred  to  the 
gaseous  products  of 
combustion,  raising 
their  temperature  above 
that  at  which  the_  fuel 
and  the  oxygen  or  air  are 
supplied  to  the  furnace. 
Suppose  that  1  Ib.  of 
carbon  is  burned  with 
2f  Ib.  of  oxygen,  form- 
ing 3 |  Ib.  of  carbon 
dioxide,  both  the  carbon 
and  the  oxygen  being 
supplied  at  0°  F.  The 
combustion  of  1  Ib.  of 
carbon  generates 
14,600  B.  T.  U.,  which 
will  all  be  contained  in 
the  3f  Ib.  of  carbon 
dioxide.  The  specific 
heat  of  carbon  dioxide 
is  .217  at  constant  pres- 
sure; that  is,  it  requires 
.217  B.  T.  U.  to  raise 
the  temperature  of  1  Ib. 
of  carbon  dioxide  1°  F. 
To  raise  3|  Ib.  of  car- 
bon dioxide  1°  F.  will 
require  3  |X. 2 17  =  .7957 
B.  T.  U.,  and  14,600  B. 
T.  U.  will  therefore  raise 
its  temperature  14,600 
-4- .7957  =  18,348.6°  F. 
(approximately  18,350 
F.)  above  the  tempera- 
ture at  which  the  car- 
bon and  the  oxygen  were 
supplied.  The  tempera- 
tures thus  calculated 
are  known  as  theoret- 
ical temperatures,  and 
are  based  on  the  assump- 
tions of  perfect  com- 
bustion and  no  loss  by 
radiation.  The  temper- 
ature of  18,350°  is  far 
beyond  any  tempera- 
ture known,  and  it  is 
probable  that  long  be- 
fore it  could  be  reached, 
the  phenomenon  of  dis- 
sociation would  take 
place;  that  is,  the  car- 
bon dioxide  would  be 
split  into  carbon  and 
oxygen,  and  the  ele- 
ments would  lose  their 
affinity  for  each  other. 

The  theoretical  ele- 
vation of  temperature 
of  the  fare  may  be  calcu- 
lated by  the  formula 

29 


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B.  T.  U.  generated  by  the  combustion 
Elevation  of  temperature  - 


Weight  of  gaseous  products  X  their  specific  heats 
It  is  evident  from  this  formula  that  the  rapidity  of  the  combustion,  or  the 
time  required  to  burn  a  given  weight  of  fuel,  has  nothing  to  do  with  the  tem- 
perature that  may  theoretically  be  attained.  In  practice,  the  temperature 
of  a  bed  of  coal  in  a  furnace  and  that  of  the  burning  gases  immediately  above 
the  coal  are  reduced,  to  some  extent,  by  radiation;  and  as  the  quantity  of  heat 
radiated  from  a  given  mass  of  fuel  is  a  function  of  the  time  during  which  it 
takes  place,  a  considerable  portion  of  the  heat  generated  may  be  lost  by  radi- 
ation when  the  combustion  is  very  slow.  With  ordinary  rates  of  combustion, 
however,  that  is,  of  about  10  Ib.  of  coal  per  square  foot  of  grate  surface 
per  hour,  and  firebrick  furnaces,  the  percentage  of  loss  of  heat  by  radiation 
is  1%  or  less,  and  the  actual  temperature  that  may  be  attained  will  be  very 
nearly  as  high  with  that  rate  of  combustion  as  witri  a  rate  of  20  or  40  Ib. 

The  elevations  of  temperature  given  in  the  foregoing  table  were  deter- 
mined by  means  of  the  preceding  formula,  the  specific  heat  of  the  chimney  gases 
being  taken  as  .24. 

To  burn  1  Ib.  of  hydrogen,  8  Ib.  of  oxygen  is  required,  and  there  is  also 
present  8X3.32  =  26.56  Ib.  of  nitrogen,  which  is  mixed  with  the  oxygen  in  the 
air.  The  gaseous  products  are  9  Ib.  of  water,  in  the  shape  of  superheated  steam 
(specific  heat  .48),  and  26.56  Ib.  of  nitrogen  (specific  heat  .2438).  The  heat 
produced  is  62,000  B.  T.  U.  If  the  temperature  of  the  atmosphere  is  62°  F., 
150  B.  T.  U.  is  absorbed  during  the  combustion  in  heating  1  Ib.  of  water,  HiO, 
from  62°  to  212°  F.  per  Ib.,  965.8  B.  T.  U.  in  evaporating  it  at  that  temper- 
ature, and  .48  (T+t  —  212)  in  superheating  it  from  212°  to  the  temperature  T 
+/  of  the  fire,  T  being  the  increase  of  temperature  and  t  the  temperature  of 
the  atmosphere,  which  in  this  case  is  62°  F.  All  this  heat  may  be  recovered 
by  condensing  the  steam  and  cooling  the  water  of  condensation  to  62°.  There- 
fore, the  following  equation  is  obtained : 


which,  being  solved,  gives  T  =  4,873°  F.  T+t  =  4,935°  F.  Showing  that  hydro- 
gen and  carbon,  when  perfectly  burned,  give  about  the  same  maximum  theo- 
retical temperature. 

By  a  process  of  reasoning  similar  to  the  preceding,  the  following  formula 
is  derived,  to  obtain  the  maximum  theoretical  temperature  of  the  fire,  when  the 
fuel  contains  hydrogen  and  moisture  with  a  varying  supply  of  air: 
616C+2,220fl-327Q-44PF 

f+.02W+A8H 

in  which       T  =  elevation  of  temperature  above  that  of  atmosphere; 
C  =  percentage  of  carbon  in  fuel; 
H  =  percentage  of  hydrogen  in  fuel; 
O  =  percentage  of  oxygen  in  fuel; 
W= percentage  of  water  in  fuel; 
/=  pounds  of  dry  gases  of  combustion  (HiO  excluded) 

per  pound  of  fuel. 
EXAMPLE. — What  would  be  the  temperature  of  the  fire,  the  temperature 
of  the  atmosphere  being  62°  P.,  when  burning  a  coal  having  the  composition 
excluding  ash  and  sulphur,  carbon  75%,  hydrogen  5%,  oxygen  10%,  moisture 
10%;  the  dry  chimney  gases  amount  to  20  Ib.  per  Ib.  of  this  combustible 
including  the  moisture? 

SOLUTION.— Applying  the  formula, 

r_616X75+2.220X5-327X10-44X10 
20  +  .02X10+.18X5 
T+/  =  2,5400-r-62°  =  2,6020  F. 
EXAMPLE. — What  is  the  maximum  temperature  attainable  by  burning 
moist  wood  of  the  composition  carbon  38%,  hydrogen  5%,  oxygen  32%,  nitro- 
gen and  ash  1%,  moisture  24% ;  the  dry  gases  are  15  Ib.  per  Ib.  of  wood,  and  the 
temperature  of  the  atmosphere  is  62°  P.? 
SOLUTION.— Applying  the  formula, 

616X38+2,220X5-327X32-44X24 
15+.02X24+.18X5 
r+*  =  l,403°+62°  =  1,465°  F. 
EXAMPLE.— What  will  be  the  temperature  of  a  fire  of  Pocahontas  coal 
analyzing  carbon  84.22%,  hydrogen  4.26%,  oxygen  3.48%,  nitrogen  .84%, 
sulphur  .59%,  ash  5.85%,  water  .76%;  the  dry  gases  are  20  Ib.  per  Ib.  of  com- 
bustible, the  heating  value  of  the  sulphur  being  neglected? 


BOILERS  451 

SOLUTION.  —  The  combustible,  carbon  and  hydrogen,  is  88.48%  of  the  coal, 
hence  /=  20  X  .8848  =  17.69.  Applying  the  formula, 

616X84.22+2.220X4.26-327X3.48-44X.76 

17.69  +  .02X.  76  +  .  18X4.26  SM°' 

r+*  =  3,257°  +62°  =  3,319°  F. 

When  the  combustion  is  perfect,  and  the  furnace  is  entirely  enclosed  in  walls 
of  firebrick,  highly  heated,  the  temperatures  calculated  by  the  formula  are 
nearly  attained,  the  only  loss  being  that  due  to  external  radiation.  In  ordinary 
practice,  with  the  boiler  immediately  above  the  fire,  the  temperature  is  lowered 
by  radiation,  and  also,  when  soft  coal  is  used,  by  imperfect  combustion. 

Estimation  of  Air  Supply.  —  The  theoretical  amounts  of  air  required  to  burn 
the  several  combustible  elements  in  a  fuel  were  given  in  the  table  on  page  447, 
but  when  burning  coal  in  a  furnace  only  a  rough  estimate  of  the  quantity  of 
air  supplied  may  be  obtained  by  direct  measurement  by  an  anemometer,  or  by 
counting  the  revolutions  of  a  fan.  The  only  available  method  of  closely 
approximating  the  amount  of  air  supplied,  is  by  making  a  proximate  analysis 
of  the  gases  of  combustion,  taken  from  a  point  close  to  the  furnace,  but 
beyond  the  point  of  visible  flame.  If  taken  from  the  chimney,  the  gas  may 
be  of  different  composition  on  account  of  inward  leaks  of  air  through  cracks 
in  the  brickwork. 

The  analysis  of  the  gases  gives  the  percentage  of  carbon  dioxide,  oxygen, 
and  carbon  monoxide,  in  this  order,  the  quantity  of  these  gases  being  deter- 
mined by  absorption;  nitrogen  is  determined  by  difference;  that  is,  the  remain- 
der after  subtracting  the  sum  of  the  other  three  gases  from  100.  Unburned 
hydrogen  or  hydrocarbon  gases  cannot  be  conveniently  determined  by  ordinary 
analysis.  If  the  combustion  is  complete,  the  percentage  of  nitrogen  will 
always  be  found  between  79  and  80.  If  it  exceeds  80%,  unburned  hydrogen, 
or  hydrocarbons  are  present,  an  error  has  been  made  in  the  analysis,  or,  possibly, 
the  hydrogen  of  a  gaseous  fuel  has  been  burned  leaving  the  carbon  unburned. 
Thus,  in  burning  marsh  gas  (methane),  CHt,  with  an  insufficient  supply  of  air, 
the  hydrogen  only  may  be  burned  to  water,  HzO,  leaving  the  carbon  unburned 
in  the  shape  of  soot,  which  is  caught  in  a  filter  attached  to  the  gas-collecting 
apparatus.  The  water,  or  water  vapor,  is  condensed,  and  is  not  determined 
in  the  analysis,  leaving  the  nitrogen  that  accompanied  the  oxygen  alone  to 
be  determined.  In  this  manner,  the  nitrogen  in  the  gases  may  actually 
exceed  80%. 

The  following  formula  may  be  used  for  calculating  the  air  supply: 

3.032.ZV 
Pounds  of  dry  air  per  pound  of  carbon  =  -.      \CQ 

in  which  COt,  CO,  and  N  are  percentages,  by  volume,  of  the  dry  gas. 

EXAMPLE.  —  How  many  pounds  of  air  are  supplied  per  pound  of  carbon  in 
burning  a  coal,  if  the  gases  analyze  carbon  dioxide  11.74%,  carbon  monoxide 
.10%,  oxygen  7.71%,  nitrogen  80.45%? 

SOLUTION.  —  Substituting  in  the  formula, 
3.032X80.45 


Production  and  Measurement  of  Draft.  —  It  is  well  known  that  any  volume 
of  gas  is  lighter  when  heated  than  the  same  volume  of  gas  when  cool.  When 
hot  gases  pass  into  the  chimney  they  have  a  temperature  of  from  400°  to  600°  F., 
while  the  air  outside  the  chimney  has  a  temperature  of  from  40°  to  90°  F. 
Roughly  speaking,  the  air  weighs  twice  as  much,  bulk  for  bulk,  as  the  hot 
gases.  Naturally,  then,  the  pressure  in  the  chimney  is  less  than  the  pressure 
of  the  outside  air.  The  production  of  draft  and  the  satisfactory  operation  of 
a  chimney  depend  on  this  pressure  difference.  The  pressure  of  the  draft 
depends  on  the  temperature  of  the  furnace  gases  and  the  height  of  the  chimney. 
Chimney  draft  is  affected  by  so  many  varying  conditions  that  no  absolutely 
reliable  rules  can  be  given  for  proportioning  chimneys  to  give  a  certain  desired 
draft  pressure.  The  rules  given  for  chimney  proportions  are  based  on  successful 
practice  rather  than  on  pure  theory. 

The  intensity  of  the  draft  may  be  measured  by  means  of  a  water  gauge 
such  as  is  shown  in  the  accompanying  illustration.  This  is  a  glass  tube  open 
at  both  ends,  bent  to  the  shape  of  the  letter  U  ;  the  left  leg  communicates  with 
the  chimney.  The  difference  in  the  two  water  levels  H  and  Z  in  the  legs 
represents  the  intensity  of  the  draft,  and  is  expressed  in  inches  of  water. 

The  draft  produced  by  a  chimney  may  vary  from  J  in.  to  2  in.  of  water, 
depending  on  the  temperature  of  the  chimney  gases  and  on  the  height  of  the 
chimney.  Generally  speaking,  it  is  advantageous  to  use  a  high  chimney  and 


452 


BOILERS 


as  low  a   chimney  temperature  as  possible.     The  draft  pressure  required 
depends  on  the  kind  of  fuel  used.     Wood  requires  but  little  draft,  say,  $  in.  of 
water  or  less;  bituminous  coal  generally  requires  less  draft  than  anthracite. 
To  burn  anthracite  slack,  or  culm,  the  draft  pressure  should  be 
about  1  1  in.  of  water. 

Erection  of  Chimneys.  —  The  form  of  a  chimney  has  a  pro- 
nounced effect  on  its  capacity.  A  round  chimney  has  a  greater 
capacity  for  a  given  area  than  a  square  one.  If  the  flue  is  taper- 
ing, the  area  for  calculation  is  measured  at  its  smallest  section. 
The  flue  through  which  the  gases  pass  from  the  boilers  to  the  chim- 
ney should  have  an  area  equal  to,  or  a  little  larger  than,  the  area 
of  the  chimney.  Abrupt  turns  in  the  flue  or  contractions  of  its 
area  should  be  carefully  avoided.  Where  one  chimney  serves 
several  boilers,  the  branch  flue  from  each  furnace  to  the  main  flue 
must  be  somewhat  larger  than  its  proportionate  part  of  the  area 
of  the  main  flue. 

Chimneys  are  usually  built  of  brick,  though  concrete,  iron, 
and  steel  are  often  used  for  those  of  moderate  height.  Brick 
chimneys  are  usually  built  with  a  flue  having  parallel  sides  and  a 
taper  on  the  outside  of  the  chimney  of  from  ^g  to  i  in.  per  ft.  of 
height.  A  round  chimney  gives  greater  draft  area  for  the  same 
amount  of  material  in  its  structure  and  exposes  less  surface  to  the 
wind  than  a  square  chimney.  Large  brick  stacks  are  usually  made 
with  an  inner  core  and  an  outer  shell,  with  a  space  between  them. 
Such  chimneys  are  usually  constructed  with  a  series  of  internal 
pilasters,  or  vertical  ribs,  to  give  rigidity.  The  top  of  the  chim- 
ney should  be  protected  by  a  coping  of  stone  or  a  cast-iron  plate 
to  prevent  the  destruction  of  the  brickwork  by  the  weather. 

Iron  or  steel  stacks  are  made  of  plates  varying  from  |  to  £  in.  thick.  The 
larger  stacks  are  made  in  sections,  the  plates  being  about  1  in.  thick  at  the  top 
and  increasing  to  |  in.  at  the  bottom;  they  are  lined  with  firebrick  about  18  in. 
thick  at  the  bottom  and  4  in.  at  the  top.  Sometimes  no  lining  is  used  on 
account  of  the  likelihood  of  corrosion  and  the  difficulty  of  inspection,  and  also 
because  the  inside  of  lined  stacks  cannot  be  painted. 

On  acdount  of  the  great  concentration  of  weight,  the  foundation  for  a 
chimney  should  be  carefully  designed.  Good  natural  earth  will  support  from 
2,000  to  4,000  Ib.  per  sq.  ft.  The  footing  beneath  the  chimney  foundation 
should  be  made  of  large  area,  in  order  to  reduce  the  pressure  due  to  the  weight 
of  the  chimney  and  its  foundation  to  a  safe  limit. 

Height  and  Area  of  Chimneys.  —  The  relation  between  the  height  of  the 
chimney  and  the  pressure  of  the  draft,  in  inches  of  water,  is  given  by  the 
formula  =  fl  /T.6  _  7.9\ 

in  which  .          p  =  draft  pressure,  in  inches  of  water; 

H  =  height  of  chimney,  in  feet; 
Ta  and  Tc  =  absolute  temperatures  of  outside  air 
and  of  chimney  gases  respectively. 

EXAMPLE.  —  What  draft  pressure  will  be  produced  by  a  chimney  120  ft. 
high,  the  temperature  of  the  chimney  gases  being  600°  F.,  and  of  the  external 
air  60°  P.? 

SOLUTION.  —  Substituting  in  the  formula, 


To  find  the  height  of  chimney  to  give  a  specified  draft  pressure,  the  preced- 
ing formula  may  be  transformed.     Thus, 


H 


6_.9x 
Ta     Tc) 

EXAMPLE.  —  Required,  the  height  of  the  chimney  to  produce  a  draft  of  \\  in. 
of  water,  the^temperature  of  the  gases  and  of  the  external  air  being,  respectively, 

SOLUTION.—  Substituting  in  the  formula, 


n 
ti 


7.6 
522' 


167  ft. 


_ 
1,010 


BOILERS  453 

In  determining  the  height  of  a  chimney  in  cities,  it  should  be  borne  in 
mind  that  the  chimney  must  almost  always  be  carried  to  a  height  above  the 
roofs  of  surrounding  buildings,  partly  in  order  to  prevent  a  nullification  of  the 
draft  by  opposing  air-currents  and  partly  to  prevent  the  commission  of  a 
nuisance. 

The  height  of  the  chimney  being  decided  on,  its  cross-sectional  area  must 
be  sufficient  to  carry  off  readily  the  products  of  combustion.     The  following 
formulas  for  finding  the  dimensions  of  chimneys  are  in  common  use: 
Let  H  =  height  of  chimney,  in  feet; 

H  .P.  =  horsepower  of  boiler  or  boilers; 

A  =  actual  area  of  chimney,  in  squa're  feet; 
E  =  effective  area  of  chimney,  in  square  feet; 
5  =  side  of  square  chimney,  in  inches; 
d  =  diameter  of  round  chimney,  in  inches. 


Then,  E  =  =  A-.6A         (1) 

Vfl 


(2) 
(3) 

d=  13.54  VE+4  (4) 

The  table  on  page  454  has  been  computed  from  these  formulas. 
EXAMPLE.  —  What  should  be  the  diameter  of  a  chimney  100  ft.  high  that 
furnishes  draft  for  a  600-H.  P.  boiler? 

SOLUTION.  —  Substituting    in    formula    1,    E  =  '-  —          =18.     Now,    using 

VlOO 
formula  4,  d  =  13.54V  18+4  =  61.44  in. 

EXAMPLE.  —  For  what  horsepower  of  boilers  will  a  chimney  64  in.  sq.  and 
125  ft.  high  furnish  draft? 

SOLUTION.  —  By  simply  referring  to  the  table,  the  horsepower  is  found 
to  be  934. 

Maximum  Combustion  Rate.  —  The  maximum  rates  of  combustion  attain- 
able under  natural  draft  are  given  by  the  following  formulas,  which  have  been 
deduced  from  the  experiments  of  Isherwood: 

Let        F  —  weight  of  coal  per  hour  per  square  foot  of  grate  area,  in  pounds; 
H  =  height  of  chimney  or  stack,  in  feet, 

Then,  for  anthracite  burned  under  the  most  favorable  conditions, 

F  =  2V#-1  (1) 

and  under  ordinary  conditions, 

F  =  1.5V#-1  (2) 

For  best  semianthracite  and  bituminous  coals, 

F  =  2.25Vfl  (3) 

and  for  less  valuable  soft  coals, 

F  =  3Vfl  (4) 

The  maximum  rate  of  combustion  is  thus  fixed  by  the  height  of  the 
chimney;  the  minimum  rate  may  be  anything  less. 

EXAMPLE.  —  Under  ordinary  conditions,  what  is  the  maximum  rate  of  com- 
bustion of  anthracite  if  the  chimney  is  120  ft.  high? 

SOLUTION.  —  By  formula  2,  _ 

F  =  1.5X  Vl20  -  1  =  15|  Ib.  per  sq.  ft.  per  hr. 

Forced  Draft.  —  The  use  of  forced  draft  as  a  substitute  for,  or  as  an  aid  to, 
natural  chimney  draft  is  becoming  quite  common  in  large  boiler  plants.  Its 
advantages  are  that  it  enables  a  boiler  to  be  driven  to  its  maximum  capacity 
to  meet  emergencies  without  reference  to  the  state  of  the  weather  or  to  the 
character  of  the  coal;  that  the  draft  is  independent  of  the  temperature  of  the 
chimney,  gases,  and  that,  therefore,  lower  flue  temperatures  may  be  used  than 
with  natural  draft;  and  in  many  cases  that  it  enables  a  poorer  quality  of  coal 
to  be  used  than  is  required  with  natural  draft.  Forced  draft  may  be  obtained: 

(1)  by  a  steam  jet  in  the  chimney,  as  in  locomotives  and  steam  fire-engines; 

(2)  by  a  steam-jet  blower  under  the  grate  bars;  (3)  by  a  fan  blower  delivering  air 
under  the  grate  bars,  the  ash-pit  doors  being  closed;  (4)  by  a  fan  blower  deliver- 
ing air  into  a  closed  ftreroom,  as  in  the  closed  stake-hold  system  used  in  some 
ocean-going  vessels;  and  (5)  by  a  fan  placed  in  the  flue  or  chimney  drawing 
the  gases  of  combustion  from  the  boilers,  commonly  called  the  induced-draft 
system.     Which  one  of  these  several  systems  should  be  adopted  in  any  special 


454  STEAM  ENGINES 

SIZE  OF  CHIMNEYS  AND  HORSEPOWER  OF  BOILERS 


1     1 

to 

•d  m 

Height  of  Chimney,  in  Feet 

ct 

pi 

§1 

2  | 

§1 

00 

50 

60 

70 

80 

90 

100 

110 

125 

150 

175 

200 

>     4> 

•a  8 

JT 

°" 
fe  ^ 

t£  co 

<  CO 

|l 

IE 

Commercial  Horsepower 

cog 

&s 

23 

25 

27 

.97 

1.77 

16 

18 

35 

38 

41 

1.47 

2.41 

19 

21 

49 

54 

58 

62 

2.08 

3.14 

22 

24 

65 

72 

78 

83 

2.78 

3.98 

24 

27 

84 

92 

100 

107 

113 

3.58 

4.91 

27 

30 

115 

125 

133 

141 

4.47 

5.94 

30 

33 

141 

152 

163 

173 

182 

5.47 

7.07 

32 

36 

183 

196 

208 

219 

6.57 

8.30 

35 

39 

216 

231 

245 

258 

271 

7.76 

9.62 

38 

42 

311 

330 

348 

365 

389 

10.44 

12.57 

43 

48 

402 

427 

449 

472 

503 

551 

13.51 

15.90 

48 

54 

505 

r>3',» 

565 

593 

632 

692 

748 

16.98 

19.64 

54 

60 

658 

694 

728 

776 

849 

918 

981 

20.83 

23.76 

59 

66 

792 

835 

876 

934 

1,203 

1,105 

1,181 

25.08 

28.27 

64 

72 

995 

1,038 

1,107 

1,212 

1,310 

1,400 

29.73 

33.18 

70 

78 

1,163 

1,214 

1,294 

1,418 

1,531 

1,637 

34.76 

38.48 

75 

84 

1,344 

1,415 

1,496 

1,639 

1,770 

1,893 

40.19 

44.18 

80 

90 

1,537 

1,616 

1,720 

1,876 

2,027 

2,167 

46.01 

50.27 

86 

96 

case  will  usually  depend  on  local  conditions.  The  steam  jet  has  the  advantage 
of  lightness  and  compactness  of  apparatus,  and  is  therefore  most  suitable  for 
locomotives  and  steam  fire-engines,  but  it  also  is  the  most  wasteful  of  steam, 
and  therefore  should  not  be  used  when  one  of  the  fan-blower  systems  is  avail- 
able, except  for  occasional  or  temporary  use,  or  when  very  cheap  fuel,  such  as 
anthracite  culm  at  the  mines,  is  used. 


STEAM  ENGINES 


PRINCIPLES  AND  REQUIREMENTS 

A  good  steam  engine  should  be  as  direct  acting  as  possible;  that  is,  the 
connecting  parts  between  the  piston  and  the  crank-shaft  should  be  few  in 
number,  as  each  part  wastes  some  power.  The  movin g  parts  of  an  engine  should 
be  strong,  to  resist  strains,  and  light,  so  as  to  offer  no  undue  resistance  to 
motion;  parts  moving  upon  each  other  should  be  well,  truly,  and  smoothly 
finished,  to  reduce  resistances  to  a  minimum;  the  steam  should  get  into  the 
cylinder  easily  at  the  proper  time,  and  the  exhaust  should  leave  the  cylinder  as 
exactly  and  as  easily.  The  steam  pipes  supplying  steam  should  have  an 
area  one-tenth  the  combined  areas  of  the  cylinders  they  supply,  and  exhaust 
pipes  should  be  somewhat  larger.  The  cylinder  and  the  steam  pipes  and  the 
boiler  should  be  well  protected.  The  engine  should  be  capable  of  being  started 
and  stopped  and  reversed  easily  and  quickly. 

Clearance. — The  term  clearance  is  used  in  two  senses  in  connection  with  the 
steam  engine.  It  may  be  the  distance  between  the  piston  and  the  cylinder 
head  when  the  piston  is  at  the  end  of  its  stroke,  or  it  may  represent  the  volume 
between  the  piston  and  the  valve  when  the  engine  is  on  dead  center.  To  avoid 
confusion,  the  former  is  called  piston  clearance,  and  the  latter  is  termed  simply 
clearance.  Piston  clearance  is  always  a  measurement,  expressed  in  parts  of 
an  inch.  Clearance,  however,  is  a  volume. 


STEAM  ENGINES  455 

The  clearance  of  an  engine  may  be  found  by  putting  the  engine  on  a  dead 
center  and  pouring  in  water  until  the  space  between  the  piston  and  the  cylinder 
head,  and  the  steam  port  leading  into  it,  is  filled.  The  volume  of  the  water 
poured  in  is  the  clearance.  The  clearance  may  be  expressed  in  cubic  feet  or 
cubic  inches,  but  it  is  more  convenient  to  express  it  as  a  percentage  of  the 
volume  swept  through  by  the  piston.  For  example,  suppose  that  the  clearance 
volume  of  a  12"X18"  engine  is  found  to  be  128  cu.  in.  The  volume  swept 
through  by  the  piston  per  stroke  is  12*  X.  7854X18  =  2,035.8  cu.  in.  Then, 
the  clearance  is  128-^2,035.8  =  .063  =  6.3%.  The  clearance  may  be  as  low  as 
i%  in  Corliss  engines,  and  as  high  as  14%  in  high-speed  engines. 

Theoretically,  there  should  be  no  clearance,  because  the  steam  that  fills 
the  clearance  space  does  no  work  except  during  expansion;  it  is  exhausted 
from  the  cylinder  during  the  return  stroke,  and  represents  so  much  dead  loss. 
This  is  remedied,  to  some  extent,  by  compression.  If  the  compression  were 
carried  up  to  the  boiler  pressure,  there  would  be  very  little,  if  any,  loss,  as  the 
steam  would  then  fill  the  entire  clearance  space  at  boiler  pressure,  and  the 
amount  of  fresh  steam  needed  would  be  the  volume  displaced  by  the  piston 
up  to  the  point  of  cut-off,  the  same  as  if  there  were  no  clearance.  In  practice, 
however,  the  compression  is  made  only  sufficiently  great  to  cushion  the  recipro- 
cating parts  and  bring  them  to  rest  quietly. 

It  is  not  practicable  to  build  an  engine  without  any  clearance,  on  account 
of  the  formation  of  water  in  the  cylinder  due  to  the  condensation  of  steam, 
particularly  when  starting  the  engine.  Automatic  cut-off  high-speed  engines 
of  the  best  design,  with  shaft  governors,  usually  compress  to  about  half  the 
boiler  pressure,  and  have  a  clearance  of  from  7  to  14%.  Corliss  engines  require 
but  very  little  compression,  owing  to  their  low  rotative  speeds;  they  also  have 
very  little  clearance,  as  the  ports  are  short  and  direct. 

Cut-Off  .  —  The  apparent  cut-off  is  the  ratio  between  the  portion  of  the  stroke 
completed  by  the  piston  at  the  point  of  cut-off,  and  the  total  length  of  the  stroke. 
For  example,  if  the  length  of  stroke  is  48  in.,  and  the  steam  is  cut  off  from  the 
cylinder  just  as  the  piston  has  completed  15  in.  of  the  stroke,  the  apparent 
cut-off  is  if  =  -fe. 

The  real  cut-off  is  the  ratio  between  the  volume  of.  steam  in  the  cylinder 
at  the  point  of  cut-off  and  the  volume  at  the  end  of  the  stroke,  both  volumes 
including  the  clearance  of  the  end  of  the  cylinder  in  question.  If  the  volume 
of  steam  in  the  cylinder,  including  the  clearance,  at  the  point  of  cut-off  is 

4  cu.  ft.,  and  the  volume,  including  the  clearance,  at  the  end  of  the  stroke  is 
6  cu.  ft.,  the  real  cut-off  is  £  =  |. 

Ratio  of  Expansion.  —  The  ratio  of  expansion,  also  called  the  real  number  of 
expansions,  is  the  ratio  between  the  volume  of  steam,  including  the  steam  in 
the  clearance  space,  at  the  end  of  the  stroke,  and  the  volume,  including  the 
clearance,  at  the  point  of  cut-off.  It  is  the  reciprocal  of  the  real  cut-off.  For 
example,  if  the  volume  at  the  end  of  the  stroke  is  8  cu.  ft.,  and  the  cut-off  is 

5  cu.  ft.,  the  ratio  of  expansion  is  8-j-5  =  1.6;  in  other  words,  the  steam  would 
be  said  to  have  one  and  six-tenths  expansions.     The  corresponding  real  cut-off 
will  be  f  . 

Let  e  =real  number  of  expansions; 

*  =  clearance,  expressed  as  a  per  cent,  of  stroke; 
k  =real  cut-off; 

ki  =  apparent  cut-off;  j 

r  =  apparent  number  of  expansions  =  —. 

KI 

Then,  «=|andfe  =  -         (1) 

K  6 

*4£     <*> 

EXAMPLE.  —  The  length  of  stroke  is  36  in.;  the  steam  is  cut  off  when  the 
piston  has  completed  16  in.  of  the  stroke;  the  clearance  is  4%.  Find  the 
apparent  cut-off,  the  real  cut-off,  and  the  real  number  of  expansions. 

SOLUTION.  —  Apparent  cut-off  =  £|  =  $  =  .444. 
ki+i     .444  +  .04     .484 


Real  number  of  expansions  =  e  =  r  =  -j-^  = 


Mean  Effective  Pressure.  —  In  order  to  find  the  horsepower  of  an  engine, 
it  is  necessary  to  know  the  mean  effective    pressure  (abbreviated  M.  E.  P.), 


456 


STEAM  ENGINES 


which  is  defined  as  the  average  pressure  urging  the  piston  forwards  during  its 
entire  stroke  in  one  direction,  less  the  pressure  that  resists  its  progress.  If  an 
indicator  is  not  available,  so  that  diagrams  may  be  taken  in  order  to  determine 
the  mean  effective  pressure  of  an  engine,  the  value  of  this  pressure  may  be 
estimated  by  the  formula 

P  =  .Q[C(p+ 14.7)  — 17], 

in  which        P  =  M.  E.  P.,  in  pounds  per  square  inch; 

C  =  constant  corresponding  to   cut-off,   taken  from 

following  table; 

p  =  boiler  pressure,  in  pounds  per  square  inch,  gauge. 

The  foregoing  formula  applies  only  to  a  simple  noncondensing  engine.  If  the 
engine  is  a  simple  condensing  engine,  the  formula  should  be  altered  by  sub- 
stituting for  17  the  pressure  existing  in  the  condenser,  in  pounds  per  square 
inch. 

CONSTANTS  USED  IN  CALCULATING  MEAN  EFFECTIVE 
PRESSURE 


Cut-off 

Constant 

Cut-off 

Constant 

Cut-off 

Constant 

1 

.545 
.590 
.650 
.705 
.737 

I 

1 

.773 
.794 
.864 
.916 
.927 

.7 

1 

.943 
.954 
.970 
.981 
.993 

In  this  table,  the  fraction  indicating  the  point  of  cut-off  is  obtained  by  divid- 
ing the  distance  that  the  piston  has  traveled  when  the  steam  is  cut  off  by  the 
whole  length  of  the  stroke;  that  is,  it  is  the  apparent  cut-off.  It  is  to  be 
observed  that  this  rule  cannot  be  applied  to  a  compound  engine  or  to  any  other 
engine  in  which  the  steam  is  expanded  in  successive  stages  in  several  cylinders. 

EXAMPLE. — Find  the  approximate  mean  effective  pressure  of  a  non-con- 
densing engine  cutting  off  at  one-half  stroke,  if  the  boiler  pressure  is  80  lb., 

SOLUTION. — According  to  the  table,  the  constant  corresponding  to  cut-off 
at  one-half  stroke  is  C  =  .864.  Then,  applying  the  formula,  P  =  .9X[.864 
X  (80+14.7)  - 171  =  58.34  lb.  per  sq.  in. 

Horsepower. — The  indicator  furnishes  the  most  ready  method  of  measuring 
the  pressures  on  the  piston  of  a  steam  engine  and,  in  consequence,  of  determin- 
ing the  amount  of  work  done  in  the  cylinder  and  the  corresponding  horsepower. 
The  power  measured  by  the  use  of  the  indicator  is  called  the  indicated  horse- 
power. It  is  the  total  power  developed  by  the  action  of  the  net  pressures  of  the 
steam  on  the  two  sides  of  the  moving  piston.  The  indicated  horsepower  is 
generally  represented  by  the  initials  I.  H.  P. 

The  part  of  the  indicated  horsepower  that  is  absorbed  in  overcoming  the  fric- 
tional  resistances  of  the  moving  parts  of  the  engine  is  termed  the  friction  horse- 
power. If  the  engine  is  running  light,  or  with  no  load,  all  the  power  developed 
in  the  cylinder  is  absorbed  in  keeping  the  engine  in  motion,  and  the  friction 
horsepower  is  equal  to  the  indicated  horsepower.  This  principle  furnishes  a 
simple  approximate  method  of  finding  the  friction  horsepower  of  a  given  engine; 
as,  however,  the  friction  between  the  surfaces  increases  with  the  pressure,  the 
power  absorbed  in  overcoming  the  engine  will  be  greater  as  the  load  on  the 
engine  is  increased. 

The  difference  between  the  indicated  horsepower  and  the  friction  horse- 
power is  the  net  horsepower.  This  is  the  power  that  the  engine  delivers  through 
the  flywheel  or  shaft  to  the  belt  or  the  machine  driven  by  it,  and  is  sometimes 
called  the  delivered  horsepower.  As  the  power  that  an  engine  is  capable  of 
delivering  when  working  under  certain  conditions  is  often  measured  by  a 
device  known  as  a  Prony  brake,  the  net  horsepower  is  frequently  called  the 
brake  horsepower,  abbreviated  B.  H.  P. 

Finding  the  Indicated  Horsepower. — Knowing  the  dimensions  and  speed 
of  the  engine  and  the  mean  effective  pressure  on  the  piston,  all  the  data  for  find- 
ing the  rate  of  work  done  in  the  engine  cylinder  expressed  in  horsepower  are 
at  hand. 


STEAM  ENGINES  457 

Let  H  =  indicated  horsepower  of  engine; 

P  =  mean  effective  pressure  of  the  steam,  in 

pounds  per  square  inch; 
A  =  area  of  piston,  in  square  inches; 
L  —  length  of  stroke,  in  feet; 
N  =  number  of  working  strokes  per  minute. 


In  a  double-acting  engine,  or  one  in  which  the  steam  acts  alternately  on  both 
sides  of  the  piston,  the  number  of  working  strokes  per  minute  is  twice  the 
number  of  revolutions  per  minute.  For  example,  if  a  double-acting  engine 
runs  at  a  speed  of  210  R.  P.  M.  there  are  420  working  strokes  per  minute. 
A  few  types  of  engines,  however,  are  single-acting;  that  is,  the  steam  acts  on 
only  one  side  of  the  piston.  Such  are  the  Westinghouse,  the  Willans,  and 
others.  In  this  case,  only  one  stroke  per  revolution  does  work,  and,  conse- 
quently, the  number  of  strokes  per  minute  to  be  used  in  the  foregoing  formula 
is  the  same  as  the  number  of  revolutions  per  minute.  Unless  it  is  specifically 
stated  that  an  engine  is  single-acting,  it  is  always  understood,  when  the  dimen- 
sions of  a  steam  engine  are  given,  that  a  double-acting  engine  is  meant. 

EXAMPLE.  —  The  diameter  of  the  piston  of  an  engine  is  10  in.  and  the  length 
of  stroke  15  in.  It  makes  250  R.  P.  M.,  with  a  mean  effective  pressure  of 
40  Ib.  per  sq.  in.  What  is  the  horsepower? 

SOLUTION.  —  As  it  is  not  stated  whether  the  engine  is  single  or  double  acting, 
assume  that  it  is  double  acting;  then,  the  number  of  strokes  is  250X2  =  500  per 
min.  Hence, 

T   w   P      P  L  A  N     40Xf|X(102X.7854)X500 
LH-P'  =     33,000     =  33,000 

The  indicated  horsepower  of  a  compound  or  triple-expansion  engine  may  be 
calculated  from  the  indicator  diagrams  in  exactly  the  same  manner  as  with 
any  simple  engine,  considering  each  cylinder  as  a  simple  engine  and  adding  the 
horsepowers  of  the  several  cylinders  together.  In  taking  the  indicator  cards 
from  a  compound  engine,  the  precaution  of  taking  the  cards  simultaneously 
from  all  cylinders  must  be  observed,  especially  when  the  engine  runs  under  a 
variable  load,  because,  otherwise,  an  entirely  wrong  distribution  of  power  may 
be  shown,  and  there  may  also  be  a  great  variation  between  the  indicated  horse- 
power really  existing  and  that  calculated  from  diagrams  taken  at  different 
times. 

The  indicated  horsepower  of  compound  engines  is  sometimes  found  by  refer- 
ring the  mean  effective  pressure  of  the  high-pressure  cylinder  to  the  low-pressure 
cylinder  and  calculating  the  horsepower  of  the  engine  on  the  assumption  that 
all  the  work  is  done  in  the  low-pressure  cylinder.  To  do  this,  the  mean  effective 
pressures  of  the  two  cylinders  are  found  from  indicator  diagrams;  the  mean 
effective  pressure  of  the  high-pressure  cylinder  is  then  divided  by  the  ratio  of 
the  volume  of  the  low-pressure  cylinder  to  that  of  the  high-pressure  cylinder; 
and  the  quotient  is  added  to  the  mean  effective  pressure  of  the  low-pressure 
cylinder,  the  sum  being  the  referred  mean  effective  pressure.  This  sum  is  then 
taken  as  the  mean  effective  pressure  of  the  engine,  and  the  area  of  the  low- 
pressure  piston  as  the  piston  area;  with  these  data,  the  length  of  stroke  and  the 
number  of  strokes,  the  horsepower  is  computed  as  for  any  simple  engine.  In 
the  case  of  a  triple-expansion  engine,  the  mean  effective  pressures  of  the  high- 
pressure  and  intermediate  cylinders  are  referred  to  the  low-pressure  cylinder 
and  added  to  its  mean  effective  pressure.  Thus,  suppose  that  in  a  12", 
20",  and  34"X30"  engine  the  mean  effective  pressures  are  82.3  Ib.,  27.8  Ib., 
and  10.6  Ib.,  respectively.  Then,  the  referred  mean  effective  pressure  is 
&*i  2  27  8  106 
f^+^^H  —  —-  =  10.4  +  10  +  10.6  =  31  Ib.,  and  this  value  must  be  substituted 

o.Uo      ^./o          I 

for  P  in  finding  the  horsepower  of  the  engine.  While  this  method  shortens  the 
labor  of  computing  the  horsepower,  it  obviously  does  not  show  the  distribution 
of  work  between  the  cylinders. 

Stating  Sizes  of  Engines.  —  The  size  of  a  simple  engine,  that  is,  an  engine 
having  but  one  cylinder,  is  commonly  stated  by  giving  the  diameter  of  the 
cylinder,  followed  by  the  length  of  the  stroke,  both  in  inches.  Thus,  a  simple 
engine  having  a  cylinder  12  in.  in  diameter  and  a  stroke  of  24  in.  would  be 
referred  to  as  a  12"X24"  engine,  the  multiplication  sign  in  this  case  serving 
merely  to  separate  the  two  numbers.  The  sizes  of  compound  and  multiple- 
expansion  engines  are  designated  in  a  similar  fashion.  Thus,  a  compound 
engine  with  a  high-pressure  cylinder  11  in.  in  diameter,  a  low-pressure  cylinder 


458  STEAM  ENGINES 

20  in.  in  diameter,  and  a  stroke  of  15  in.  would  be  referred  to  as  an  11*  and  20* 
X15"  compound  engine.  In  the  same  way,  a  14",  22",  and  34"X18"  triple- 
expansion  engine  would  be  one  in  which  the  diameters  of  the  cylinders  are 
14  in.,  22  in.,  and  34  in.,  and  the  stroke  is  18  in. 

Mechanical  Efficiency.  —  The  mechanical  efficiency  of  an  engine  is  the  ratio 
of  the  net  horsepower  to  the  indicated  horsepower;  or  it  is  the  percentage  of 
the  mechanical  energy  developed  in  the  cylinder  that  is  utilized  in  doing  useful 
work.  To  find  the  efficiency  of  an  engine,  when  the  indicated  and  net  horse- 
powers are  known,  divide  the  net  horsepower  by  the  indicated  horsepower. 

Piston  Speed.  —  The  total  distance  traveled  by  the  piston  in  1  min.  is  called 
the  piston  speed.  As  it  is  customary  to  take  the  stroke  in  inches,  to  find  the 
piston  speed,  multiply  the  stroke  in  inches  by  the  number  of  strokes  and  divide 

IN 
by  12;  or,  letting  5  represent  the  piston  speed,  S  =  —,  where  /  is  the  stroke  in 

inches.  But  N  =  2R,  where  R  represents  the  number  of  revolutions  per 
minute.  Hence, 


^ 
12        12         6 

EXAMPLE.  —  An  engine  with  a  52-in.  stroke  runs  at  a  speed  of  66  R.  P.  M. 
What  is  the  piston  speed? 

CO  \/  Aft 

SOLUTION.  —  By  the  formula,  5  =  —  -  —  =  572  ft.  per  min. 

The  piston  speeds  used  in  modern  practice  are  about  as  follows: 


Small  stationary  engines  ..............................  300  to     600 

Large  stationary  engines  .............................  600  to  1,000 

Corliss  engines  ......................................  400  to     750 

Marine  engines  .....................................  200  to  1,200 

Allowance  for  Area  of  Piston  Rod.  —  It  is  generally  considered  sufficiently 
accurate  to  take  the  total  area  of  one  side  of  the  piston  as  the  area  to  be  used 
in  calculating  the  horsepower  of  an  engine.  The  effective  area  of  one  side  of 
the  piston  is,  however,  reduced  by  the  sectional  area  of  the  piston  rod,  and 
if  it  is  important  that  the  power  be  calculated  with  the  greatest  practical  degree 
of  accuracy,  an  allowance  for  the  area  of  the  piston  rod  must  be  made.  This 
is  done  by  taking  as  the  piston  area  one-half  the  sum  of  the  areas  exposed  to 
steam  pressure  on  the  two  sides  of  the  piston.  Thus,  if  a  piston  is  30  in.  in 
diameter  with  a  6-in.  piston  rod,  the  average  area  is 
302  X.  7854  +  (302  X.  7854-  62  X.  7854) 

—  2  —  —  =  o92.72  sq.  in. 

If  the  piston  rod  is  continued  past  the  piston  so  as  to  pass  through  the  head- 
end cylinder  head;  that  is,  if  the  piston  has  a  tailrod,  allowance  must  be  made 
for  the  tailrod.     Thus,  with  a  piston  30  in.  in  diameter,  a  piston  rod  6  in.  in 
diameter,  and  a  tailrod  5  in.  in  diameter,  the  average  area  is 
(3Q2  X  .7854  -  52  X  .7854)  +  (3Q2  X  .7854  -  62  X  .7854) 
—  2  —  — 

Cylinder  Ratios.  —  The  cylinders  of  compound  and  multiple-expansion 
engines  increase  in  diameter  from  the  high-pressure  to  the  low-pressure  end, 
and  it  is  customary  to  refer  to  their  relative  sizes  by  means  of  cylinder  ratios. 
As  all  the  cylinders  have  the  same  length  of  stroke,  the  volumes  of  the  several 
cylinders  are  in  proportion  to  the  areas  of  the  cylinders,  and  therefore  in  pro- 
portion to  the  squares  of  the  diameters.  The  area  of  the  high-pressure  cylinder 
is  taken  as  unity,  and  the  other  areas  are  referred  to  it,  and  the  ratios  of  these 
areas,  or  the  ratios  of  the  squares  of  the  diameters,  are  called  the  cylinder 
ratios.  For  example,  a  triple-expansion  engine  having  cylinders  12  in.,  20  in., 
and  34  in.  in  diameter  will  have  the  cylinder  ratios  of  122  :  202  :  342,  or  144  :  400. 
1,156,  which  reduces  to  1  :  2.78  :  8.03;  that  is,  the  intermediate  cylinder  is 
2.78  times  as  large  as  the  high-pressure  cylinder  and  the  low-pressure  cylinder 
is  8.03  times  as  large  as  the  high-pressure  cylinder.  If  there  are  two  cylinders 
to  one  stage  of  expansion,  as,  for  example,  two  low-pressure  cylinders,  the  sum 
of  their  areas  must  be  used  in  finding  the  cylinder  ratios.  Thus,  if  there  had 
been  two  24-in.  low-pressure  cylinders  instead  of  one  34-in.  cylinder,  in  the 
foregoing  case,  the  cylinder  ratios  would  have  been  12*  :  2Q2  :  2X242,  or  144  : 
400  :  1,152,  which  reduces  to  1  :  2.78  :  8. 


STB  AM  ENGINES  459 

CONDENSERS 

There  are  two  types  of  condensers  in  general  use,  namely,  the  surface  con- 
denser and  the  jet  condenser.  In  the  former,  the  exhaust  steam  comes  in  con- 
tact with  a  large  area  of  metallic  surface  that  is  kept  cool  by  contact  with  cold 
water.  In  the  latter,  the  exhaust  steam,  on  entering  the  condenser,  comes  in 
contact  with  a  jet  of  cold  water.  In  either  case,  the  entering  steam  is  con- 
densed to  water,  and  in  consequence  a  partial  vacuum  is  formed.  If  enough 
cold  water  were  used,  the  steam  on  entering  would  instantly  condense  and  a 
practically  perfect  vacuum  would  be  obtained  were  it  not  for  the  fact  that  the 
feedwater  of  the  boiler  always  contains  a  small  quantity  of  air,  which  passes 
with  the  exhaust  steam  into  the  condenser  and  therefore  partly  destroys  the 
vacuum.  To  get  rid  of  this  air,  the  condenser  is  fitted  with  an  air  pump, 
which  pumps  out  both  the  air  and  the  water  formed  by  condensation. 

Surface  Condensers. — In  the  surface  condenser,  the  exhaust  steam  and  the 
injection  water  are  kept  separate  throughout  their  course  through  the  con- 
denser; and  the  condensed  steam  leaves  the  condenser  as  fresh  water,  free  from 
the  impurities  contained  in  the  injection  water.  The  water  of  condensation 
from  a  surface  condenser  is  therefore  fit  to  be  used  as  boiler  feed,  except  that  it 
contains  oil  used  for  cylinder  lubrication,  which  can  b'e  eliminated  by  means  of 
an  oil  separator.  It  is  for  this  reason  that  the  surface  condenser,  in  spite  of  its 
greater  complication,  cost,  size,  and  weight,  as  compared  with  the  jet  con- 
denser, is  used  instead  of  the  latter  where  the  supply  of  injection  water  is  unfit 
for  use  as  boiler  feed.  Thus,  the  surface  condenser  is  used  altogether  in 
marine  work,  except  for  vessels  navigating  clean,  fresh  water  like  that  of  the 
Great  Lakes,  in  order  to  avoid  the  use  of  sea-water  in  the  boilers. 

In  the  surface  condenser  the  steam  may  be  outside  and  the  water  inside  the 
tubes,  or  the  reverse.  If  the  water  is  inside  the  tubes,  it  should  enter  at  the 
bottom  of  the  condenser  and  be  discharged  at  the  top.  This  brings  the  coldest 
water  into  contact  with  the  partly  condensed  steam,  and  the  warmest  water 
into  contact  with  the  hot  entering  steam.  When  the  water  is  outside  the  tubes, 
it  is  necessary  to  fit  baffle  plates  on  the  water  side  to  force  the  water  into  a 
definite  and  regular  circulation,  and  to  prevent  it  from  going  directly  from  inlet 
to  outlet  and  also  to  prevent  the  water  from  arranging  itself  in  layers  according 
to  temperature,  with  the  coldest  water  on  the  bottom  and  the  hottest  water 
on  top.  The  outlet  should  be  well  above  the  top  row  of  tubes.  A  solid  body 
of  water  above  the  top  row  of  tubes  is  thus  assured,  and  the  accumulation  of  a 
stagnant  body  of  hot  water  in  the  top  of  the  condenser  is  prevented  by  its  being 
continually  drawn  off  by  the  circulating  pump  and  replaced  by  cooler  water 
from  beneath. 

Air  tends  to  accumulate  in  the  top  of  the  water  side  of  a  surface  condenser. 
This  is  particularly  inconvenient  where  the  water  is  inside  the  tubes,  as  the 
air  fills  the  top  rows  of  tubes  and  excludes  the  water,  destroying  their  value  as 
cooling  surfaces.  To  prevent  this,  an  air  valve  must  be  provided,  as  high  up 
on  the  water  side  as  possible,  by  which  the  air  can  be  drawn  off  when  it  becomes 
troublesome.  Drain  valves  and  pipes  should  be  provided  at  the  bottom. 

As  the  condensed  steam  from  the  surface  condenser  is  generally  pumped 
back  into  the  boiler  as  feedwater,  it  is  desirable  to  have  it  as  hot  as  possible; 
but  it  must  be  remembered  that  it  is  impossible  to  get  the  feedwater  from  the 
condenser  at  a  higher  temperature  than  that  of  saturated  steam  at  the  absolute 
pressure  existing  in  the  condenser. 

It  will  be  considerably  cooler  than  this  if,  after  being  condensed,  it  is  allowed 
to  lie  in  the  bottom  of  the  condenser  and  give  up  its  heat  to  the  circulating 
water.  The  heat  thus  given  up  is  a  total  loss,  and  should  be  avoided  by  con- 
necting the  air-pump  suction  to  the  lowest  point  of  the  condenser  and  by  shaping 
the  bottom  of  the  condenser  so  that  the  water  will  drain  rapidly  into  the  air- 
pump  suction. 

Cooling  Water  for  Surface  Condenser. — The  amount  of  cooling  water 
required  in  the  case  of  a  surface  condenser  may  be  found  by  the  formula 


in  which  Q  =  number  of  pounds  of  cooling  water  required  to  condense 

1  Ib.  of  steam; 

H  =  total  heat  above  32°  of  1  Ib.  of  steam  at  pressure  at  release; 
t  =  temperature  of  condensed  steam  on  leaving  condenser; 
t\  =  temperature  of  cooling  water  on  entering  condenser; 
to  =  temperature  of  cooling  water  on  leaving  condenser. 


460  STEAM  ENGINES 

EXAMPLE.  —  Steam  exhausts  into  a  surface  condenser  from  an  engine  cylinder 
at  a  pressure  of  6  lb.,  absolute;  the  temperature  of  the  condensing  water  on 
entering  is  55°  F.,  and  en  leaving  it  is  100°  F.  ;  the  temperature  of  the  condensed 
steam  on  leaving  the  condenser  is  125°  F.  How  many  pounds  of  cooling  water 
are  required  per  pound  of  steam? 

SOLUTION.  —  The  total  heat  above  32°  of  1  lb.  of  steam  at  6  lb.,  absolute, 
from  the  Steam  Table,  is  1,133.8  B.  T.  U.  Then,  substituting  the  values  of 
H,t,h,  and  fe>  in  the  formula, 

• 


Injection  Water  for  Jet  Condenser.  —  The  quantity  of  injection  water  required 
for  a  jet  condenser  may  be  found  by  the  formula 
fl-q-32) 

t-h      ' 
in  which  Q  =  number  of  pounds  of  injection  water  required  to  condense 

1  lb.  of  steam; 

H  =  total  heat  above  32°  of  1  lb.  of  steam  at  pressure  at  release; 
t  =  temperature  of  mixture  of  injection  water  and  condensed 

steam  on  leaving  the  condenser; 

h  =  temperature  of  injection  water  on  entering  the  condenser. 
EXAMPLE.  —  Steam  is  exhausted  into  a  jet  condenser  from  an  engine  cylinder 
at  a  pressure  of    10  lb.,  absolute;    the  temperature  of   the  injection  water  on 
entering  is  60°  F.,  and  on  leaving  140°  F.     How  much  injection  water  is  required 
per  pound  of  steam? 

SOLUTION.—  The  total  heat  above  32°  of  1  lb.  of  steam  at  10  lb.  absolute, 
from  the  Steam  Table,  is  1,140.9  B.  T.  U.  Then,  substituting  the  values  of 
H,  t,  and  h  in  the  formula. 


ENGINE  MANAGEMENT 

STARTING  AND  STOPPING 

Warming  Up. — About  15  or  20  min.  before  starting  the  engine,  the  stop- 
valves  should  be  raised  just  off  their  seats  and  a  little  steam  should  be  allowed 
to  flow  into  the  steam  pipe.  The  drain  cock  on  the  steam  pipe  just  above  the 
throttle  should  be  opened.  When  the  steam  pipe  is  thoroughly  warmed  up 
and  steam  blows  through  the  drain  pipe,  the  drain  cock  should  be  closed  and  the 
throttle  opened  just  enough  to  let  a  little  steam  flow  into  the  valve  chest  and 
cylinder;  or  if  a  by-pass  around  the  throttle  is  fitted,  it  may  be  used.  The 
cylinder  relief  valves,  or  drain  cocks,  and  also  the  drain  cocks  on  the  valve  chest 
and  the  exhaust  pipe  should  be  opened,  if  the  engine  is  non-condensing.  If  the 
cylinders  are  jacketed,  steam  should  be  turned  into  the  jackets  and  the  jacket 
drain  cocks  should  be  opened.  While  the  engine  is  warming  up,  the  oil  cups 
and  the  sight-feed  lubricator  may  be  filled.  A  little  oil  may  be  put  into  all  the 
small  joints  and  journals  that  are  not  fitted  with  oil  cups.  The  guides  should 
be  wiped  off  with  oily  waste  and  oiled.  By  this  time  the  engine  is  getting 
warm.  If  the  cylinder  is  fitted  with  by-pass  valves,  they  should  be  used  to 
admit  steam  to  both  ends  of  the  cylinder.  In  general,  all  cylinders,  especially 
if  they  are  large  and  intricate  castings,  should  be  warmed  up  slowly,  as  sudden 
and  violent  heating  of  a  cylinder  of  this  character  is  very  liable  to  crack  the 
casting  by  unequal  expansion. 

An  excellent  and  economical  plan  for  warming  up  the  steam  pipe  and  the 
engine  is  to  open  the  stop- valves  and  throttle  valve  at  the  time  or  soon  after 
the  fires  are  lighted  in  the  boilers,  permitting  the'  heated  air  from  the  boilers 
to  circulate  through  the  engine,  thus  warming  it  up  gradually  and  avoiding  the 
accumulation  of  a  large  quantity  of  water  of  condensation  in  the  steam  pipe  and 
cylinder.  When  pressure  shows  on  the  boiler  gauge  or  steam  at  the  drain  pipes 
of  the  engine,  the  stop- valves  and  throttle  may  be  closed  temporarily,  but  not 
hard  down  on  their  seats.  When  this  method  of  warming  up  the  engine  is 
adopted,  the  safety  valves  should  not  be  opened  while  steam  is  being  raised. 

Stop-valves  and  throttle  valves  should  never  be  opened  quickly  or  suddenly 
and  thus  permit  a  large  volume  of  steam  to  flow  into  a  cold  steam  pipe  or  cylin- 
der. If  this  is  done,  the  first  steam  that  enters  will  be  condensed  and  a  partial 
vacuum  will  be  formed.  This  will  be  closely  followed  by  another  rush  of  steam 


STEAM  ENGINES  461 

with  similar  results,  and  so  on  until  a  mass  of  water  will  collect,  which  will  rush 
through  the  steam  pipe  and  strike  the  first  obstruction,  generally  the  bend  in 
the  steam  pipe  near  the  cylinder,  with  great  force  and  in  all  probability  will 
carry  it  away  and  cause  a  disaster.  This  is  called  water  hammer  and  has  caused 
many  serious  accidents.  Before  turning  steam  into  any  pipe  line  or  into  a 
cylinder,  all  drain  valves  should  be  opened. 

Another  precaution  that  should  be  taken  is  the  easing  of  the  throttle  valve 
on  its  seat  before  steam  is  let  into  the  main  steam  pipe;  otherwise,  the  unequal 
expansion  of  the  valve  casing  may  cause  the  valve  to  stick  fast  and  thereby 
give  much  trouble.  Even  if  a  by-pass  pipe  is  fitted  around  the  throttle,  it  is 
better  not  to  depend  on  it.  As  water  is  non-compressible,  it  is  an  easy  matter 
to  blow  off  a  cylinder  head  or  break  a  piston  if  the  engine  is  started  when  there 
is  a  quantity  of  water  in  the  cylinder. 

Oil  and  Grease  Cups. — The  last  thing  for  the  engineer  to  do  before  taking 
his  place  at  the  throttle  preparatory  to  starting  the  engine,  provided  he  has  no 
oiler,  is  to  start  the  oil  and  grease  cups  feeding.  It  is  well  to  feed  the  oil  liber- 
ally at  first,  but  not  to  the  extent  of  wasting  it;  finer  adjustment  of  the  oiling 
gear  can  be  made  after  the  engine  has  been  running  a  short  time  and  the 
journals  are  well  lubricated. 

Starting  and  Stopping  Non-Condensing  Slide-Valve  Engine. — A  non- 
condensing  slide-valve  engine  is  started  by  simply  opening  the  throttle;  this 
should  be  done  quickly  in  order  to  jump  the  crank  over  the  first  dead  center, 
after  which  the  momentum  of  the  flywheel  will  carry  it  over  the  other  centers. 
The  engine  should  be  run  slowly  at  first,  gradually  increasing  the  revolutions 
to  the  normal  speed.  When  the  engine  has  reached  full  speed,  the  drain  pipes 
should  be  examined;  if  dry  steam  is  blowing  through  them,  the  drain  cocks 
should  be  closed.  If  water  is  being  delivered,  the  drain  cocks  should  remain 
open  until  steam  blows  through  and  should  then  be  closed. 

To  stop  a  non-condensing  slide-valve  engine,  it  is  only  necessary  to  shut 
off  the  supply  of  steam  by  closing  the  throttle,  but  care  should  be  taken  not  to 
let  the  engine  stop  on  the  dead  center.  After  the  engine  is  stopped,  the  oil 
feed  should  be  shut  off  and  the  main  stop-valve  clpsed.  The  valve  should  be 
seated,  but  without  being  jammed  hard  down  on  its  seat.  The  drain  cocks  on 
the  steam  pipe  and  engine  may  or  may  not  be  opened,  according  to  circum- 
stances. It  will  do  no  harm  to  allow  the  steam  to  condense  inside  the  engine, 
as  the  engine  will  then  cool  down  more  gradually,  which  lessens  the  danger 
of  cracking  the  cylinder  casting  by  unequal  contraction.  All  the  water  of 
condensation  should  be  drained  from  the  engine  before  steam  is  again  admitted 
to  it. 

Starting  and  Stopping  Condensing  Slide-Valve  Engine. — In  the  case  of 
condensing  slide-valve  engines,  before  the  main  engine  is  started,  the  air  pump 
and  circulating  pump  should  be  put  into  operation  and  a  vacuum  formed  in 
the  condenser;  this  will  materially  assist  the  main  engine  in  starting  promptly. 
Prior  to  starting  the  air  and  circulating  pumps,  the  injection  valve  should  be 
opened  to  admit  the  condensing  water  into  the  circulating  pump;  the  delivery 
valve  should  also  be  opened  at  this  time.  If  an  ordinary  jet  condenser  is  used, 
no  circulating  pump  is  required,  the  water  being  forced  into  the  condenser  by 
the  pressure  of  the  atmosphere.  If  the  air  pump  is  operated  by  the  main  engine 
a  vacuum  will  not  be  formed  in  the  condenser  until  after  the  engine  is  started 
and  at  least  one  upward  stroke  of  the  air  pump  is  made.  In  this  case  the 
injection  valve  must  be  opened  at  the  same  moment  the  engine  is  started; 
otherwise,  the  condenser  will  get  hot  and  a  mixture  of  air  and  steam  accumulate 
in  it  and  prevent  the  injection  water  from  entering.  When  this  occurs  it  is 
necessary  to  pump  cold  water  into  the  condenser  by  one  of  the  auxiliary  pumps 
through  a  pipe  usually  fitted  for  that  purpose;  if  such  a  pipe  has  not  been  pro- 
vided, it  may  be  found  necessary  to  cool  the  condenser  by  playing  cold  water 
on  it  through  a  hose. 

The  operation  of  stopping  a  slide-valve  surface-condensing  engine  is  pre- 
cisely similar  to  that  of  stopping  a  non-condensing  engine  of  the  same  type, 
•  with  the  addition  that  after  the  main  engine  is  stopped  the  air  and  circulating 
pumps  are  also  stopped,  and  in  the  same  way,  that  is,  by  closing  the  throttle, 
after  which  the  injection  valve  and  the  discharge  valve  should  be  closed' and  the 
drain  cocks  opened.  With  a  jet  condenser,  the  operation  of  stopping  the 
engine  is  the  same  as  the  above,  with  the  exception  that  the  injection  valve 
should  be  closed  at  the  same  moment  that  the  engine  is  stopped. 

Starting  and  Stopping  Simple  Corliss  Engine. — In  the  Corliss  engine  the 
eccentric  rod  is  so  constructed  and  arranged  that  it  may  be  hooked  on  or 
unhooked  from  the  eccentric  pin  on  the  wrist-plate  at  the  will  of  the  engineer. 


462  STEAM  ENGINES 

After  all  the  preliminary  operations  have  been  attended  to,  the  starting  bar  is 
shipped  into  its  socket  in  the  wristplate  and  the  throttle  ,is  opened.  The 
starting  bar  is  then  vibrated  back  and  forth  by  hand,  by  which  the  steam  and 
exhaust  valves  are  operated  through  the  wristplate  and  valve  rods;  as  soon  as 
the  cylinder  takes  steam,  the  engine  will  start.  After  working  the  starting 
bar  until  the  engine  has  made  several  revolutions  and  the  flywheel  has  acquired 
sufficient  momentum  to  carry  the  crank  over  the  dead  centers,  the  hook  of  the 
eccentric  rod  should  be  allowed  to  drop  upon  the  pin  on  the  wristplate.  As 
soon  as  the  hook  engages  with  the  pin,  the  starting  bar  is  unshipped  and 
placed  in  its  socket  in  the  floor.  The  way  to  determine  in  which  direction 
the  starting  bar  should  be  first  moved  to  start  the  engine  ahead  is  to  note  the 
position  of  the  crank,  from  which  the  direction  in  which  the  piston  is  to  move 
may  be  learned.  This  will  indicate  which  steam  valve  to  open  first;  it  will 
then  be  an  easy  matter  to  determine  in  which  direction  the  starting  bar  should 
be  moved.  If  the  engine  is  of  the  condensing  type,  the  same  course  of  pro- 
cedure in  starting  the  air  and  circulating  pumps  should  be  followed  as  with  the 
simple  condensing  slide-valve  engine. 

A  Corliss  engine  is  stopped  by  closing  the  throttle  and  unhooking  the 
eccentric  rod  from  the  pin  on  the  wristplate;  this  is  done  by  means  of  the  unhook- 
ing gear  provided  for  the  purpose.  As  soon  as  the  ecentric  rod  is  unhooked 
from  the  pin,  the  starting  bar  is  shipped  into  its  socket  in  the  wristplate  and  the 
engine  is  worked  by  hand  to  any  point  in  the  revolution  of  the  crank  at  which 
it  is  desired  to  stop  the  engine.  The  procedure  is  then  the  same  as  for  the 
simple  slide-valve  engine.  After  stopping  a  Corliss  condensing  engine  the  same 
course  should  be  followed  as  with  a  slide-valve  condensing  engine  in  regard  to 
draining  cylinders,  closing  stop-valves,  etc. 

Starting  and  Stopping  Compound  Slide-Valve  Engine. — Before  starting  a 
compound  engine,  the  high-pressure  cylinder  is  warmed  up  in  the  same  manner 
as  a  simple  engine.  To  get  the  steam  into  the  low-pressure  cylinder  is,  however, 
an  operation  that  will  depend  on  circumstances.  If  the  cylinders  are  provided 
with  pass-over  valves,  it  will  be  necessary  only  to  open  them  to  admit  steam 
into  the  receiver  and  thence  into  the  low-pressure  cylinder.  If  the  cylinders 
are  not  fitted  with  pass-over  valves  the  steam  can  usually  be  worked  into  the 
receiver  and  low-pressure  cylinder  by  operating  the  high-pressure  valves  by 
hand.  Sometimes  compound  engines  are  fitted  with  starting  valves,  which 
greatly  facilitate  the  operations  of  warming  up  and  starting.  Usually  a 
compound  engine  will  start  upon  opening  the  throttle. 

If  the  high-pressure  crank  of  a  cross-compound  engine  is  on  its  center  and 
the  low-pressure  engine  will  not  pull  it  off,  it  must  be  jacked  off.  If  the  pressure 
of  steam  in  the  receiver  is  too  high,  causing  too  much  back  pressure  in  the  high 
pressure  cylinder,  the  excess  of  pressure  must  be  blown  off  through  the  receiver 
safety  valve;  if  the  pressure  in  the  receiver  is  too  low  to  start  the  low-pressure 
piston,  more  steam  must  be  admitted  into  the  receiver.  If  the  engine  is  stuck 
fast  from  gummy  oil  or  rusty  cylinders,  all  wearing  surfaces  must  be  well  oiled 
and  the  engine  jacked  over  at  least  one  entire  revolution.  If  the  cut-offs  are 
run  up,  they  should  be  run  down,  full  open.  If  there  is  water  in  the  cylinders, 
it  should  be  blown  out  through  the  cylinder  relief  or  drain  valves,  and  if  there 
is  any  obstruction  to  the  engine  turning,  it  should  be  removed. 

If  the  crank  of  a  tandem  compound  engine  is  on  the  center,  it  must  be  pulled 
or  jacked  off.  If  the  high-pressure  crank  of  a  cross-compound  engine  is  on 
the  center,  r^may  or  may  not  be  possible  to  start  the  engine  by  the  aid  of  the 
low-pressure  cylinder,  depending  on  the  yalve  gear  and  the  crank  arrangement. 
When  the  cranks  are  180°  apart,  which  is  a  very  rare  arrangement,  the  crank 
must  be  pulled  or  jacked  off  the  center.  When  the  cranks  are  90°  apart  and  a 
pass-over  valve  is  fitted,  live  steam  may  be  admitted  into  the  receiver  and 
thence  into  the  low-pressure  cylinder,  in  order  to  start  the  engine.  When 
no  pass-over  is  fitted,  but  the  engine  has  a  link  motion,  sufficient  steam  to 
pull  the  high-pressure  crank  off  the  center  can  generally  be  worked  into  the 
low-pressure  cylinder  by  working  the  links  back  and  forth.  When  no  pass- 
over  is  fitted,  but  the  high-pressure  engine  can  have  its  valve  or  valves  worked  . 
by  hand,  steam  can  be  got  into  the  low-pressure  engine  by  working  the  high- 
pressure  valve  or  valves  back  and  forth  by  hand.  If  no  way  exists  of  getting 
steam  into  the  low-pressure  cylinder  while  the  high-pressure  crank  is  on  a 
dead  center,  it  must  be  pulled  or  jacked  off. 

If  the  air  and  circulating  pumps  are  attached  to  and  operated  by  the  main 
engine,  a  vacuum  cannot  be  generated  in  the  condenser  until  after  the  main 
engine  has  been  started.  Consequently,  in  this  case,  there  is  no  vacuum  to 
help  start  the  engine;  therefore,  if  it  is  tardy  or  refuses  to  start,  it  will  be 


STEAM  ENGINES  463 

necessary  to  resort  to  the  jacking  gear  and  jack  the  engine  into  a  position  from 
which  it  will  start.  A  vacuum  having  been  generated  in  the  condenser  before- 
hand, the  pressure  in  the  receiver  acting  on  the  low-pressure  piston  causes  the 
engine  to  start  promptly,  even  though  the  high-pressure  crank  may  be  on  its 
center. 

Compound  slide-valve  engines,  whether  condensing  or  non-condensing,  are 
stopped  by  closing  the  throttle,  and,  if  a  reversing  engine,  throwing  the  valve 
gear  into  mid-position.  If  the  stop  is  a  permanent  one,  the  usual  practice 
of  draining  the  engine,  steam  chests,  and  receiver,  closing  stop- valves,  stopping 
the  oil  feed,  etc.  should  be  followed.  If  the  engine  is  intended  to  run  in  both 
directions  in  answer  to  signals,  as  in  the  cases  of  hoisting,  rolling-mill,  and 
marine  engines,  the  operator,  after  stopping  the  engine  on  signal,  should  imme- 
diately open  the  throttle  very  slightly,  in  order  to  keep  the  engine  warm,  and 
stand  by  for  the  next  signal.  If  the  engine  is  fitted  with  an  independent  or 
adjustable  cut-off  gear,  it  should  be  thrown  off;  that  is,  set  for  the  greatest 
cut-off,  for  the  reason  that  the  engine  may  have  stopped  in  a  position  in  which 
the  cut-off  valves  in  their  early  cut-off  positions  would  permit  little  or  no  steam 
to  enter  the  cylinders,  in  which  case  the  engine  will  not  start  promptly,  and 
perhaps  not  at  all.  While  waiting  for  the  signal,  the  cylinder  drain  valves 
should  be  opened  and  any  water  that  may  be  in  the  cylinders  should  be  blown 
out.  When  dry  steam  blows  through  the  drains,  the  cylinders  are  clear  of 
water. 

When  the  signal  to  start  the  engine  is  received,  it  is  only  necessary  to  throw 
the  valve  gear  into  the  go-ahead  or  backing  position,  as  the  signal  requires, 
and  to  operate  the  throttle  according  to  the  necessities  of  the  case,  for  which 
no  rule  can  be  laid  down  beforehand,  as  the  position  of  the  throttle  will  depend 
on  the  load  on  the  engine  at  the  time. 

Starting  and  Stopping  Compound  Corliss  Engine. — The  operation  of  starting 
and  stopping  a  compound  Corliss  engine  is  precisely  similar  to  that  of  starting 
and  stopping  a  simple  Corliss  engine.  The  high-pressure  valve  gear  only 
is  worked  by  hand  in  starting,  the  low-pressure  eccentric  hook  having  been 
hooked  on  previously.  The  low-pressure  valve  gear  is  worked  by  hand 
only  while  Warming  up  the  low-pressure  cylinder."  The  directions  given  for 
operating  the  simple  condensing  engine  apply  to  the  condensing  Corliss 
engine,  so  far  as  the  treatment  of  the  air  pump,  circulating  pump,  and 
condenser  is  concerned. 

POUNDING  OF  ENGINES 

Faulty  Bearings. — Loose  journal  brasses  are  the  most  frequent  cause  of 
pounding  in  engines.  The  remedy  for  pounding  of  this  nature  is  obvious. 
The  engine  should  be  stopped  and  the  brasses  set  up  gradually  until  the  pound- 
ing ceases.  In  the  case  of  shaft  journals,  they  may  be  set  up  without  stopping 
the  engine,  provided  the  engineer  can  reach  them  without  danger  of  being  caught 
in  the  machinery. 

It  may  so  happen  that  the  boxes  or  brasses  are  worn  down  until  the  edges 
of  the  upper  half  and  those  of  the  lower  half  are  in  contact  and  cannot  be  set 
up  on  thejjournal  any  farther;  they  are  then  said  to  be  brass  and  brass,  or  brass- 
bound.  In  a  case  of  this  kind,  the  journal  must  be  stripped,  as  it  is  called,  when 
the  cap  and  brasses  are  removed  from  a  journal.  The  edges  of  the  brasses  are 
then  chipped  or  filed  off,  in  order  to  allow  them  to  be  closed  in. 

It  is  a  most  excellent  plan  in  practice  to  reduce  the  halves  of  the  brasses  so 
that  they  will  stand  off  from  each  other  when  in  place  for  a  distance  of  J  to  ^  in. 
and  to  fill  this  space  with  hard  sheet-brass  liners  fro,m  No.  20  to  No.  22 
Birmingham  wire  gauge  in  thickness,  or  even  thinner.  Should  the  journal 
become  brass-bound,  the  cap  may  be  slacked  off  and  a  pair  of  the  liners  slipped 
out  without  the  necessity  of  stripping  the  journal. 

In  some  instances  journal-boxes  are  fitted  with  keepers,  or  chipping  pieces, 
as  they  are  sometimes  called.  These  usually  consist  of  cast-brass  liners  from 
1  to  5  in.  in  thickness,  having  ribs  or  ridges  cast  on  one  side,  for  convenience  of 
chipping  and  filing.  These  keepers  are  sometimes  made  of  hardwood  and  are 
capable  of  being  compressed  slightly  by  the  pressure  exerted  upon  them  during 
the  setting-up  process.  When  the  boxes  are  babbitted,  the  body  of  the  box  is 
occasionally  made  of  cast  iron,  in  which  case  iron  liners  and  keepers  are  used 
instead  of  brass  ones. 

In  engines  fitted  with  some  types  of  friction  couplings,  there  is  a  thrust 
exerted  upon  the  shaft  in  the  direction  of  its  length.  This  will  necessitate  having 
a  thrust  bearing,  or  thrust  block,  as  it  is  sometimes  called.  There  are  a  number 
of  types  of  thrust  bearings,  but  the  most  common  is  the  collar  thrust,  which 


464  STEAM  ENGINES 

consists  of  a  series  of  collars  on  the  shaft  that  fit  in  corresponding  depressions 
in  the  bearing.  If  these  collars  do  not  fit  in  the  depressions  rather  snugly 
the  shaft  will  have  end  play  and  there  probably  will  be  more  or  less  ppunding 
or  backlash  at  every  change  of  load  on  the  engine.  This  can  be  remedied  only 
by  putting  in  a  new  thrust  bearing  and  making  a  better  fit  with  the  shaft 
collars,  unless  the  rings  in  the  bearing  are  adjustable,  in  which  case  the  end  play 
may  be  taken  up  by  adjusting  the  rings. 

Pounding  in  Cylinders. — Pounding  in  the  cylinders  is  frequently  caused  by 
water  due  to  condensation  or  to  that  carried  over  from  the  boilers.  This  may 
be  a  warning  that  priming  is  likely  to  occur  in  the  boilers  9r  has  already  com- 
menced. If  the  cylinders  are  not  fitted  with  automatic  relief  valves,  the  drain 
cocks  should  be  opened  as  quickly  as  possible  and  the  throttle  closed  a  little 
to  check  the  priming. 

Another  source  of  pounding  in  the  cylinder  is  a  piston  loose  on  the  rod;  this 
will  result  if  the  piston-rod  nut  or  key  backs  off  or  the  riveting  becomes  loose, 
permitting  the  piston  to  play  back  and  forth  on  the  piston  rod.  If  due  to 
backing  off  of  the  nut,  the  engine  should  be  shut  down  instantly.  There  is 
generally  very  little  room  to  spare  between  the  piston-rod  nut  and  the  cylinder 
head;  therefore,  it  cannot  back  off.  very  far  before  it  will  strike  and  break 
the  cylinder  head.  After  the  engine  is  stopped  and  the  main  stop-valve  is 
closed,  the  cylinder  head  should  be  taken  off  and  the  piston  nut  set  up  as  tightly 
as  possible.  As  a  measure  of  safety,  a  taper  split  pin  should  in  all  cases  be  fitted 
through  the  piston  rod  behind  the  nut  or  a  setscrew  should  be  fitted  through 
the  nut. 

A  slack  follower  plate  or  junk  ring  will  cause  pounding  in  the  cylinder. 
It  seldom  happens  that  all  the  follower  bolts  back  out  at  one  time,  but  not 
infrequently  one  of  them  works  itself  out  altogether.  This  is  a  very  danger- 
ous condition  of  affairs,  especially  in  a  horizontal  engine:  If  the  bolts  should 
get  end  on  between  the  piston  and  cylinder  head,  either  the  piston  or  the  cylin- 
der head  is  bound  to  be  broken.  Therefore,  if  there  is  any  intimation  that  a 
follower  bolt  is  adrift  in  the  cylinder,  the  engine  should  be  shut  down  instantly, 
the  cylinder  head  taken  off,  the  old  bolt  removed,  and  one  having  a  tighter 
fit  put  in. 

Broken  packing  rings  and  broken  piston  springs  will  cause  noise  in  the 
cylinder,  but  it  is  more  of  a  rattling  than  a  pounding,  and  the  sound  will  easily 
be  recognized  by  the  practiced  ear.  There  is  not  so  much  danger  of  a  break- 
down from  these  causes  as  may  be  supposed,  from  the  fact  that  the  broken 
pieces  are  confined  within  the  space  between  the  follower  plate  and  the  piston 
flange. 

Pounding  in  the  cylinders  of  old  engines  is  often  produced  by  the  striking 
of  the  piston  against  one  or  the  other  cylinder  heads,  due  to  the  wearing  away 
of  the  connecting-rod  brasses.  Keying  up  the  brasses  from  time  to  time  has 
the  effect  of  lengthening  or  shortening  the  connecting-rod,  depending  on  the 
design,  and  this. change  in  length  destroys  the  clearance  at  one  end  of  the 
cylinder  by  an  equal  amount.  The  remedy  is  to  restore  the  rod  to  its  original 
length  by  placing  sheet-metal  liners  behind  the  brasses;  this  obviously  will 
move  the  piston  back  or  ahead  and  restore  the  clearance.  A  rather  rare  case 
of  the  piston  striking  the  cylinder  head  is  due  to  the  unscrewing  of  the  piston 
rod  from  the  crosshead,  in  case  it  is  fastened  by  a  thread  and  check-nut.  To 
obviate  any  danger,  the  check-nut  should  be  tried  frequently. 

Improper  Valve  Setting. — The  primary  cause  of  another  source  of  pound- 
ing is  the  improper  setting  of  the  steam  valve,  or  possibly  its  improper 
design.  In  the  case  of  improper  setting  of  the  valve,  insufficient  compression, 
insufficient  lead,  cut-off 'too  early,  and  late  release  may  all  cause  pounding  on 

the  centers. 

.-^       ""-x  Reversal  of  Pressure. — The  effect  of  a  reversal  of 
\x      pressure  is  clearly  shown  in  the  accompanying  illustra- 
\    tion.     With  the  crankpin  at  a  and  the  engine  running 
,   in  the  direction  indicated  by  the  arrow,  the  connecting- 
j  rod  is  subjected  to  a  pull,  but  after  the  crankpin  has 
,    passed  the  dead  center  c,  the  connecting-rod  is  subjected 
f    to  a  push,  in  which  case  the  rear  brass,  as  shown  at  b, 
/      bears  against  the  crankpin,  while  in  the  former  case, 
,''         as  shown  at  a,  the  front  brass  bears  against  the  crank- 
pin.     By  giving  a  sufficient  amount  of  compression,  the 

lost  motion  in  the  pins  and  journals  is  transferred  gently  from  one  side  to  the 
other  before  the  crankpin  reaches  the  dead  center.  If  the  compression  is 
insufficient,  there  will  be  pounding. 


STEAM  ENGINES  465 

Insufficient  Lead. — Insufficient  lead  causes  an  engine  to  pound  because  the 
piston  has  then  little  or  no  cushion  to  impinge  on  as  it  approaches  the  end  of 
its  stroke,  and  it  is  brought  to  rest  with  a  jerk.  A  similar  effect  will  be  pro- 
duced by  a  late  release;  the  pressure  is  retained  too  long  on  the  driving  side  of 
the  piston.  The  ideal  condition  is  that  the  pressures  shall  be  equal  on  both 
sides  of  the  piston  at  a  point  in  its  travel  just  in  advance  of  the  opening  of  the 
steam  port.  The  position  of  this  point  varies  with  the  speed  of  the  piston  and 
other  conditions  that  only  the  indicator  card  can  reveal. 

Pounding  at  Crosshead. — The  crosshead  is  a  source  of  pounding  from 
various  causes,  of  which  the  loosening  of  the  piston  rod  is  one  of  the  most 
common.  There  are  several  methods  of  attaching  the  piston  rod  to  the  cross- 
head.  The  rod  may  pass  through  the  crosshead  with  a  shoulder  or  a  taper,  or 
both,  on  one  side  of  the  crosshead  and  a  nut  on  the  other;  or  the  rod  may  be 
secured  to  the  crosshead  by  a  cotter,  instead  of  the  nut;  or  the  end  of  the  rod 
may  be  threaded  and  screwed  into  the  crosshead,  having  a  check-nut  to  hold 
the  rod  in  place.  In  the  case  first  mentioned,  the  nut  may  work  loose,  which 
will  cause  the  crosshead  to  receive  a  violent  blow,  first,  by  the  nut  on  one  side 
and  then  by  the  shoulder  or  taper  on  the  other,  at  each  change  of  motion  of  the 
piston;  the  remedy  is  to  set  up  the  nut.  A  similar  effect  will  be  produced  if 
the  cotter  should  work  loose  and  back  out.  In  case  the'piston  rod  is  screwed 
into  the  crosshead  and  the  rod  slacks  back,  the  danger  is  that  the  piston  will 
strike  the  rear  cylinder  head.  The  check-nut  should  be  closely  watched. 
Pounding  at  the  crosshead  may  be  due  to  loose  wristpin  brasses,  in  which  case 
they  should  be  set  up,  but  not  too  tightly.  In  case  a  crosshead  works  between 
parallel  guides,  pounding  may  be  caused  if  the  crosshead  is  too  loose  between 
the  guides,  and  the  crosshead  shoes  should  therefore  be  set  out. 

If  pounding  results  from  the  wearing  down  of  the  shoe  of  a  slipper  crosshead, 
a  liner  should  be  put  between  the  shoe  and  the  foot  of  the  crosshead  or  the  shoe 
should  be  set  put  by  the  adjustment  provided. 

Pounding  in  Air  Pump. — Pounding  in  the  air  pump  is  generally  produced 
by  the  slamming  of  the  valves,  caused  by  an  undue  amount  of  water  in  the 
pump,  which  will  usually  relieve  itself  after  a  few  strokes.  The  pump  piston, 
however,  may  be  loose  on  the  piston  rod  or  the  piston  rod  may  be  loose  in  the 
crosshead.  A  broken  valve  may  also  cause  pounding  in  the  air  pump,  all  of 
which  must  be  repaired  as  soon  as  detected. 

Pounding  in  Circulating  Pump. — In  a  circulating  pump  of  the  reciprocating 
type,  pounding  may  be  caused  by  admitting  top  little  injection  water,  and  the 
pounding  may  be  stopped  by  adjusting  the  injection  valve  to  admit  just  the 
right  quantity.  It  may  so  happen,  however,  that  the  injection  water  is  very 
cold,  and  to  admit  enough  of  it  to  stop  the  pounding  in  the  circulating  pump 
will  make  the  feed  water  too  cold.  To  meet  this  contingency,  an  air  check- valve 
is  often  fitted  to  the  circulating  pump  to  admit  air  into  the  barrel  of  the  pump 
as  a  cushion  for  the  piston;  this  check- valve  may  be  kept  closed  when  not 
needed  to  admit  air.  A  broken  valve,  a  piston  loose  on  its  piston  rod,  and  a 
piston  rod  loose  in  the  crosshead  will  all  cause  pounding  in  the  circulating 
pump;  they  should  be  treated  in  the  same  manner  as  was  specified  for  similar 
troubles  in  the  air  pump. 

HOT  BEARINGS 

_  Should  any  of  the  bearings  show  an  inclination  to  heat  to  an  uncomfortable 
point  when  felt  by  the  hand,  the  oil  feed  should  be  increased.  If  the  bearing 
continues  to  get  hotter,  some  flake  graphite  should  be  mixed  with  the  oil  and 
the  mixture  should  be  fed  into  the  bearing  through  the  oil  holes,  between  the 
brasses,  or  wherever  else  it  can  be  forced  in. 

If,  after  trying  the  remedies  just  mentioned,  the  bearing  continues  to  grow 
hotter,  to  the  extent,  for  instance,  of  scorching  the  hand  or  burning  the  oil,  it 
indicates  that  the  brasses  have  been  expanded  by  the  heat  and  that  they  are 
gripping  the  journal  harder  and  harder  the  hotter  they  get.  At  this  stage,  if 
the  engine  is  not  stopped  or  if  the  heating  is  not  checked,  the  condition  of  the 
bearing  will  continue  to  grow  worse,  and  may  become  so  bad  as  to  slow  down 
and  eventually  stop  the  engine  by  excessive  friction.  By  this  time  the  brasses 
and  journal  will  be  badly  cut  and  in  bad  condition  generally,  and  the  engine 
must  be  laid  up  for  repairs. 

After  the  simple  remedies  previously  given  have  been  tried  and  failed  to 
produce  the  desired  results,  the  engine  should  be  stopped  and  the  cap  or  key 
of  the  hot  bearing  should  be  slacked  back  and  the  engine  allowed  to  stand 
until  the  bearing  has  cooled  off.  If  necessary,  the  cooling  may  be  hastened 
by  pouring  ;cold  water  on  the  bearing,  though  this  is  objectionable,  as  it  may 


466  STEAM  ENGINES 

cause  the  brasses  to  warp  or  crack.  Putting  water  on  a  very  hot  bearing 
should  be  resorted  to  only  in  an  emergency,  that  is,  when  an  engine  must  be 
kept  running.  Water  may  be  used  on  a  moderately  hot  bearing  without  doing 
very  much  harm.  It  is  quite  common  in  practice,  when  sprinklers  are  fitted 
to  an  engine,  to  run  a  light  spray  of  water  on  the  crankpins  when  they  show  a 
tendency  to  heat,  with  very  beneficial  results. 

Dangerous  Heating.  —  Should  a  bearing  become  so  hot  as  to  scorch  the  hand 
or  to  burn  the  oil  before  it  is  discovered  it  is  imperative  that  the  engine  should 
be  stopped,  at  least  long  enough  to  loosen  up  the  brasses,  even  though  it  is 
necessary  to  start  up  again  immediately;  otherwise  the  brasses  will  be  damaged 
beyond  repair  and  deep  grooves  will  be  cut  into  the  journals.  If  the  brasses 
are  babbitted,  the  white  metal  will  melt  out  of  the  bearing  at  this  stage.  The 
engine  will  then  be  disabled,  and  if  there  is  not  a  spare  set  of  brasses  on  hand, 
it  will  be  inoperative  until  the  old  brasses  are  rebabbitted  or  until  a  new  set 
is  made  and  fitted. 

If  it  is  absolutely  necessary  in  an  emergency  to  keep  the  engine  running 
while  a  bearing  is  very  hot,  the  engineer  must  exercise  his  best  judgment  as 
to  how  he  shall  proceed.  After  slacking  off  the  brasses,  about  the  best  he  can 
do  is  deluge  the  inside  of  the  bearing  with  a  mixture  of  oil  and  graphite,  sulphur, 
soapstone,  etc.,  and  the  outside  with  cold  water  from  buckets,  sprinklers,  or 
hose,  taking  the  chances  of  ruining  the  brasses  and  cutting  the  journal. 

Refitting  Cut  Bearing.  —  The  wearing  surfaces  of  the  brasses  and  journal 
must  be  smoothed  off  as  well  as  circumstances  will  permit;  but  if  the  grooves 
are  very  deeply  cut,  it  will  be  useless  to  attempt  to  work  them  out  entirely,  and 
if  the  brasses  are  very  much  warped  or  badly  cracked,  it  will  be  best  to  put 
in  spare  ones,  if  any  are  on  hand.  If  not,  the  old  ones  must  be  refitted  and  used 
until  a  new  set  can  be  procured.  As  for  the  J9urnal,  it  is  permanently  damaged. 
Temporary  repairs  can  be  made  by  smoothing  down  the  journal  and  brasses; 
but  at  the  first  opportunity  the  journal  should  be  turned  in  a  lathe  and  the 
brasses  properly  refitted  or  replaced  with  new  ones. 

Newly  Fitted  Bearings.  —  The  bearings  of  new  engines  are  particularly 
liable  to  heat,  as  the  wearing  surfaces  of  the  brasses  and  journal  have  just  been 
machined  and  hence  are  comparatively  rough.  The  conditions  just  mentioned 
also  exist  with  new  brasses  and  the  journals  of  an  old  engine.  If  a  new  engine, 
or  one  with  new  brasses  is  run  moderately,  in  regard  to  both  speed  and  load, 
and  with  rather  loose  brasses,  there  will  be  little  danger  of  hot  bearings,  pro- 
vided proper  attention  is  given  to  adjustment  and  lubrication.  This  is  what 
is  familiarly  termed  wearing  down  the  bearings. 

Faulty  Brasses.  —  When  the  brasses  of  an  engine  bearing  are  set  up  too  tight, 
heating  is  inevitable.  Often,  an  attempt  is  made  to  stop  a  pound  in  an  engine 
by  setting  up  the  brasses  when  the  thump  should  be  stopped  in  some  other 
way.  The  brasses  should  be  slacked  off  as  soon  as  possible.  As  a  matter  of 
fact,  hot  bearings  should  never  occur  from  this  cause. 

Bearings  may  heat  because  the  brasses  are  too  loose.  The  heating  is  caused 
by  the  hammering  of  the  journal  against  the  brasses  when  the  crankpin  is 
passing  the  dead  centers.  The  derangement  is  easily  remedied,  however, 
by  setting  up  the  cap  nuts  or  the  key.  Most  engineers  have  their  own  views 
regarding  the  setting  up  of  bearings.  One  method  is  to  set  up  the  cap  nuts 
or  key  nearly  solid  and  then  slack  them  back  half  way;  if  the  brasses  are  still 
too  loose,  they  are  set  up  again  and  slacked  back  less  than  before,  repeating 
this  operation  until  there  is  neither  thumping  nor  heating. 

Another  method  of  setting  up  journal  brasses  is  to  fill  up  the  spaces  between 
the  brasses  with  thin  metal  liners,  from  No.  18  to  No.  22  Birmingham  wire 
gauge  in  thickness,  and  a  few  paper  liners  for  fine  adjustment.  Enough  of 
these  should  be  put  in  to  cause  the  brasses  to  set  rather  loosely  on  the  journal 
when  the  cap  nuts  or  keys  are  set  up  solid.  The  engine  should  be  run  for  a 
while  m  that  condition;  then  a  pair  of  the  liners  should  be  removed  and  the 
brasses  set  up  solid  again.  This  operation  should  be  repeated  until  there  is 
neither  thumping  nor  heating.  It  may  require  a  week  or  more,  and  with  a 
large  engine  longer,  to  reach  the  desired  point.  If  this  system  is  carefully 
earned  out,  there  will  be  very  little  danger  of  heating.  In  removing  the  liners, 
great  care  should  be  exercised  not  to  disturb  the  brasses  any  more  than  is 
absolutely  necessary. 

Warped  and  cracked  brasses  will  cause  heating,  because  they  do  not  bear 
evenly  on  the  journal,  and  hence  the  friction  is  not  distributed  evenly  over 
" 


l^j1"6  lurf.ace-  «  the  distortion  is  not  too  great,  the  brasses  may  be 
refitted  to  the  journal  by  chipping,  filing,  and  scraping;  but  if  they  are  twisted 
so  much  that  they  cannot  be  refitted,  nothing  will  do  but  new  brasses 


STEAM  ENGINES  467 

Brasses  and  journals  that  have  been  hot  enough  to  be  cut  and  grooved  are 
liable  to  heat  up  again  any  time  on  account  of  the  roughness  of  the  wearing 
surfaces.  As  long  as  the  grooves  in  the  journal  are  parallel  and  match  the 
grooves  in  the  brasses,  the  friction  is  not  greatly  increased;  but  if  a  smooth 
journal  is  placed  between  brasses  that  are  grooved  and  pressure  is  applied,  the 
journal  crushes  the  grooves  in  the  brasses  and  becomes  brazed  or  coated  with 
brass,  and  then  heating  results.  The  way  to  prevent  heating  from  this  cause 
is  to  work  the  grooves  out  of  the  journal  and  brasses  by  filing  and  scraping  as 
soon  as  possible  after  they  occur. 

Faulty  workmanship  is  a  common  cause  of  the  heating  of  crankpins,  wrist- 
pins,  and  bearings.  The  brasses  in  that  case  do  not  bear  fairly  and  squarely, 
even  though  they  appear  all  right  to  the  eye.  A  crankpin  brass  must  fit  squarely 
on  the  end  of  the  connecting-rod  and  the  rod  itself  must  be  square.  If  the 
key,  when  driven,  forces  the  brasses  to  one  side  or  the  other  and  twists  the  strap 
on  the  rod,  it  will  draw  the  brasses  slantwise  on  the  pin  and  make  them  bear 
harder  on  one  side  than  on  the  other,  thus  reducing  the  area  of  the  bearing 
surfaces.  The  same  is  true  of  the  shaft  bearings.  If  the  brasses  do  not  bed 
fairly  on  the  bottom  of  the  pillow-block  casting  or  do  not  go  down  evenly, 
without  springing  in  any  way,  heating  will  result 

If  the  brasses  are  too  long  and  bear  against  the  collars  of  the  journal  when 
cold,  they  will  most  surely  heat  after  the  engine  has  been  running  a  while.  It 
is  hardly  possible  to  run  bearings  stone  cold.  They  will  warm  up  a  little  and 
the  brasses  will  be  expanded  thereby,  which  will  cause  them  to  bear  still  harder 
against  the  collars.  This,  in  turn,  will  induce  greater  friction  and  more  expan- 
sion of  the  brasses.  The  evil  may  be  obviated  by  chipping  or  filing  a  little 
off  each  end  of  the  brasses  until  they  cease  to  bear  against  the  collars  while 
running.  A  little  side  play  is  a  good  thing  because  it  also  promotes  a  better 
distribution  of  the  oil  and  prevents  the  journal  and  brasses  from  wearing  into 
concentric  parallel  grooves. 


Edges  of  Brasses  Pinching  Journal. — Brasses,  when  first  heated  by  abnormal 
nd  along  the  surface  in  contact  with  the  journal ;  this  would 


friction,  tend  to  expand , 


open  the  brass  and  make  the  bore  of  larger  diameter  were  it  not  prevented  by 
the  cooler  part  near  the  outside  and  by  the  bedplate  itself.  If  the  brass  has 
become  hot  quickly  and  excessively,  the  resistance  to  expansion  produces  a 
permanent  set  on  the  layers  of  metal  near  the  journal,  so  that  on  cooling, 
the  brass  closes  and  grips  the  journal.  This  is  why 
some  bearings  always  run  a  trifle  warm  and  will  not 
work  cool.  A  continuance  of  heating  and  cooling 
will  set  up  a  bending  action  at  the  middle  of  the 
brass,  which  must  eventually  end  in  cracking  it.  Heat- 
ing produced  in  this  way  may  be  prevented  by  chip- 
ping off  the  brasses  at  their  edges  parallel  to  the  jour- 
nal, as  shown  at  a  in  the  accompanying  illustration, 
in  which  b  is  a  section  of  the  journal  and  c  and  d  repre- 
sent the  top  and  bottom  brasses,  respectively. 

Hot  Bearings  Due  to  Faulty  Oiling. — It  does  not 
take  long  for  a  bearing  to  get  very  hot  if  it  is  deprived 
of  oil.  The  two  principal  causes  of  dry  bearings 
are  an  oil  cup  that  has  stopped  feeding,  either  by 
reason  of  being  empty  or  by  being  clogged  up  from  dirt  in  the  oil,  and  oil  holes 
and  oil  grooves  stopped  up  with  dirt  and  gum. 

The  effect  produced  upon  a  bearing  by  an  insufficient  oil  supply  is  similar 
to  that  of  no  oil,  but  in  a  less  degree.  Of  course,  it  will  take  longer  for  a 
bearing  to  heat  with  insufficient  oil  than  with  none  at  all,  and  the  engineer 
has  more  time  in  which  to  discover  and  remedy  the  difficulty. 

Oils  that  contain  dirt  and  grit  are  prolific  sources  of  hot  bearings.  There 
is  a  great  deal  of  dirt  in  lubricating  oils  of  the  average  quality ;  therefore,  all  oil 
should  be  strained  through  a  cloth  or  filtered,  no  matter  how  clear  it  looks. 
All  oil  cups,  oil  cans,  and  oil  tubes  and  channels  should  be  cleaned  out  fre- 
quently. Oil  may  be  removed  from  the  cups  by  means  of  an  oil  syringe,  and 
all  oil  removed  from  the  cups  and  cans  should  be  strained  or  filtered  before 
being  used. 

There  are  on  the  market  many  lubricating  oils  whose  quality  cannot  be 
definitely  decided  on  without  an  actual  trial,  and  it  is  difficult  to  avoid  getting 
a  bad  lot  of  oil  sometimes.  About  the  only  safe  way  to  meet  this  trouble  is 
to  pay  a  fair  price  to  a  reputable  dealer  for  oil  that  is  known  to  be  of  good 
quality,  unless  the  purchaser  is  expert  in  judging  oils  or  is  able  to  pay  a 
competent  chemist  to  test  them. 


468  STEAM  ENGINES 

Bearings  carrying  very  heavy  shafts  sometimes  refuse  to  take  the  oil;  or, 
if  they  do,  it  is  squeezed  out  at  the  ends  of  the  brasses  or  through  the  oil  holes, 
and  then  the  journal  will  run  dry  and  heat.  Large  journals  require  oil  of  a 
high  degree  of  viscosity,  or  heavy  oil,  as  it  is  popularly  called.  Oil  of  this 
character  has  more  difficulty  in  working  'its  way  under  a  heavy  shaft  than  a 
thin  oil  has,  but  thin  oil  has  not  the  body  necessary  to  lubricate  a  large  journal. 

This  difficulty  may  be  met  by  chipping  oil  grooves  or  channels  in  the  brasses. 
A  round-nosed  cape  chisel,  slightly  curved,  is  generally  used  for  this  purpose; 
care  should  be  taken  to  smooth  off  the  burrs  made  by  the  chisel,  which  may 
be  done  with  a  steel  scraper  or  the  point  of  a  flat  file.  The  grooves  are  usually 
cut  into  the  brass  in  the  form  of  a  V  if  the  engine  is  required  to  run  in  only  one 
direction;  if  it  is  to  run  in  both  directions  the  grooves  should  form  an  X.  In 
the  first  instance,  care  must  be  taken  that  the  V  opens  in  the  direction  of 
rotation  of  the  shaft;  that  is,  the  grooves  should  spread  out  from  their  junction 
in  the  same  direction  as  that  in  which  the  journal  turns.  The  oil  grooves  may 
be  about  i  in.  wide  and  f  in.  deep,  and  semicircular  in  cross-section. 

Grit  in  Bearings. — Grit  is  an  ever-present  source  of  heating  of  bearings, 
and  only  by  persistent  effort  can  the  engineer  keep  machinery  running  cool 
in  a  dirty  atmosphere.  The  machinery  of  coal  breakers,  stone  crushers,  and 
kindred  industries  is  especially  liable  to  be  affected  in  this  way.  Work  done 
on  a  floor  over  an  engine  shakes  dirt  down  upon  it  at  some  time  or  other; 
hence,  all  floors  over  engines  should  be  made  dust-proof  by  laying  paper  between 
the  planks.  If  the  engine  room  and  firerooms  communicate,  and  piles  of  red- 
hot  clinkers  and  ashes  are  deluged  with  buckets  of  water,  the  water  is  instantly 
converted  into  a  large  volume  of  steam,  carrying  with  it  small  particles  of  ashes 
and  grit  that  penetrate  into  every  nook  and  cranny,  and  these  will  find  their 
way  into  the  bearings  sooner  or  later.  Hot  clinkers  and  ashes  should  be 
sprinkled,  and  the  fireroom  door  should  be  closed  while  the  ashes  and  clinkers 
are  being  hauled  or  wet  down  or  while  the  fires  are  being  cleaned  or  hauled. 
As  an  additional  precaution,  all  open  oil  holes  should-  be  plugged  with  wooden 
plugs  or  bits  of  clean  cotton  waste  as  soon  as  possible  after  the  engine  is  stopped, 
and  should  be  kept  closed  until  ready  to  oil  the  engine  again  preparatory  to 
starting  up.  Plaited  hemp  or  cotton  gaskets  should  also  be  laid  over  the 
crevices  between  the  ends  of  the  brasses  and  the  collars  of  the  journals  of  every 
bearing  on  the  engine  and  kept  there  while  the  engine  is  standing  still. 

Overloading  of  Engine. — The  effects  produced  by  overloading  an  engine 
are:  The  pressure  on  the  brasses  is  increased  to  a  point  beyond  that  for  which 
they  were  designed,  the  friction  exceeds  the  practical  limit,  and  the  bearing 
heats.  In  case  an  engine  is  run  at  or  near  its  limit  of  endurance,  or  if  the 
journals  are  too  small,  it  is  wise  and  economical  to  have  a  complete  set  of  spare 
brasses  on  hand  ready  to  slip  in  when  the  necessity  arises. 

Engine  Out  of  Line. — If  the  engine  is  not  in  line,  the  brasses  do  not  bear 
fairly  upon  the  journals.  This  will  reduce  the  area  of  the  bearing  surfaces  in 
contact  to  such  an  extent  as  to  cause  heating.  If  the  engine  is  not  very  much 
out  of  line,  matters  may  be  considerably  improved  by  refitting  the  brasses  by 
filing  and  scraping  down  the  parts  of  those  that  bear  most  heavily  on  the 
journal.  If  this  does  not  answer,  the  heating  will  continue  until  the  engine  is 
lined  up. 

The  crosshead  guides  of  an  engine  out  of  line  are  apt  to  heat.  The  guides 
may  also  heat  from  other  causes;  for  instance,  the  gibs  may  be  set  up  too 
much.  The  danger  of  hot  guides  may  be  very  much  lessened  by  chipping 
zigzag  oil  grooves  in  their  wearing  surfaces  and  by  attaching  to  the  crosshead 
oil  wipers  made  of  cotton  lamp  wicking  arranged  so  as  to  dip  into  oil  reser- 
voirs at  each  end  of  the  guides  if  they  are  horizontal,  and  at  the  lower  end 
if  they  are  vertical.  These  wipers  will  spread  a  film  of  oil  over  the  guides  at 
every  stroke  of  the  crosshead. 

Effect  of  External  Heat  on  Bearings. — Bearings  may  get  hot  by  the  appli- 
cation of  external  heat.  This  may  be  the  case  if  the  engine  is  placed  too  near 
furnaces  or  an  uncovered  boiler,  or  in  an  atmosphere  heated  by  uncovered 
steam  pipes  or  other  means.  The  excessive  heat  of  the  atmosphere  will  then 
expand  the  brasses  until  they  nip  the  journals,  which  will  generate  additional 
heat  and  cause  further  expansion  of  the  brasses,  and  so  on  until  a  hot  bearing 
is  the  result.  The  remedy  obviously  depends  upon  the  conditions  of  each  case. 

Springing  of  Bedplate. — If  the  bedplate  of  an  engine  is  not  rigid  enough  to 
resist  the  vibration  of  the  moving  parts,  or  if  it  is  sprung  by  uneven  settling 
or  the  instability  of  the  foundation,  the  engine  will  be  thrown  out  of  line  inter- 
mittently or  permanently,  and  the  bearings  will  heat.  But  it  will  do  no  good  to 
refit  the  brasses  unless  the  engine  bed  is  stiffened  in  some  way  and  leveled  up. 


STEAM  ENGINES  469 

Springing  or  Shifting  of  Pillow-Blqck. — The  effect  of  the  springing  or  shift- 
ing of  the  pedestal  or  pillow-block  is  similar  to  the  springing  of  the  engine  bed; 
that  is,  the  bearing  will  be  thrown  out  of  line,  with  the  consequent  danger  of 
heating.  As  the  pedestal  is  usually  adjustable,  it  is  an  easy  matter  to  readjust 
it,  after  which  the  holding-down  bolts  should  be  screwed  down  hard.  If  a 
pedestal  is  not  stiff  enough  to  resist  the  strains  upon  it  and  it  springs,  measures 
should  be  taken  to  stiffen  it.  

STEAM  TURBINES 

The  turbine  is  a  machine  by  which  the  energy  of  a  moving  fluid,  as  steam 
or  water,  is  transformed,  producing  a  rotary  motion.  The  rotating  part  of  the 
turbine  is  cylindrical  in  form,  comprising  a  shaft  carrying  a  wheel,  to  which 
are  fastened  blades,  also  called  vanes  or  buckets,  against  which  the  moving  fluid 
impinges.  This  wheel,  known  as  a  turbine  wheel,  is  enclosed  in  a  casing.  This 
form  of  motor  is  growing  in  popularity  particularly  in  electrical  work,  the  motor 
and  generator  being  keyed  on  the  same  shaft,  and  for  the  following  reasons: 

1.  The   ability  to  use   highly    superheated    steam,  resulting    in   greater 
economy. 

2.  Reduced  cost  per  unit  capacity  of  the  electrical  generator,  because  of 
increased  speed  and  less  weight  per  horsepower. 

3.  Reduced  floor  space,  resulting  in  less  cost  for  land  and  power-station 
building. 

4.  Reduced  cost  of  lubrication,  as  no  cylinder  oil  is  required  and  less  oil 
is  needed  for  bearings. 

5.  Saving  in  labor;    engine  oilers  are  not  required,  and  one  engineer  can 
attend  to  more  output  than  on  reciprocating  engines. 

6.  Reduced  cost  of  foundations,  as  the  turbine  is  balanced  and  has  no 
reciprocating  parts. 

7.  The  turbine  gives  good  steam  economy  over  a  wider  range  of  load  than 
the  reciprocating  engine;   this  is  an  important  advantage  in  favor  of  the  tur- 
bine, particularly  for  electric  power  stations  where  the  load  is  variable.     If  it 
becomes  necessary  to  operate  a  turbine  unit  at  a  comparatively  light  load,  say, 
one-fourth  or  one-half  load,  the  increase  in  steam  consumption  per  horsepower 
per  hour  is  not  so  great  as  it  would  be  with  a  reciprocating  engine  under  the 
same  conditions.     Also,  a  turbine  unit  will  work  more  efficiently  on  overloads. 
The  forces  acting  on  the  turbine  wheels  are  continuous;  hence,  a  uniform  rotary 
motion  is  secured  without  the  necessity  of  heavy  flywheels. 

Types  of  Turbines. — Steam  turbines  are  of  two  general  types,  velocity 
turbines  and  pressure  turbines.  In  the  velocity,  or  impulse,  turbine  the  rotation 
is  produced  by  the  direct  impact  or  blow  upon  the  blades  of  the  turbine  of 
steam  issuing  from  a  nozzle  at  high  velocity,  the  action  being  the  same  as 
that  of  water  in  impulse  water-wheels.  Leading  examples  of  this  type  of 
turbine  are  the  De  Laval,  which  is  a  single-stage,  expansion,  velocity  turbine,  in 
which  all  the  expansion  of  the  steam  takes  place  in  a  single  stage  in  one  set 
of  nozzles;  the  Curtis  turbine,  which  is  a  few-stage,  expansion,  velocity  turbine, 
in  which  the  steam  is  expanded  in  two,  three,  four,  or  five  stages;  the  Rateau 
turbine,  which  is  a  multistage,  expansion,  velocity  turbine,  in  which  the  steam  is 
expanded  in  many  stages. 

In  the  pressure,  or  reaction,  turbine,  the  steam  enters  the  central  space  and 
flows  out  through  a  series  of  guide  vanes  and  then  through  the  vanes  of  the 
moving  wheel.  In  this  type  of  wheel,  the  blades  run  full  of  steam,  and  there 
is  a  continual  fall  of  pressure  from  the  entrance  of  the  steam  until  it  leaves  the 
turbine.  The  pressure  turbine  is  always  a  multistage  expansion  turbine, 
the  number  of  stages  reaching  50  or  100.  The  leading  American  example 
is  the  Westinghouse-Parsons  turbine. 

When  referring  to  the  various  stages  of  expansion  in  a  turbine,  it  is  cus- 
tomary to  omit  the  term  expansion  and  speak  of  the  single-stage  velocity 
turbine  (instead  of  the  single-stage  expansion  velocity  turbine) ;  the  few-stage 
velocity  turbine;  the  multistage  velocity  turbine. 

In  the  turbines  named,  the  Curtis  turbine  has  a  vertical  shaft  around  which 
the  blades  rotate  in  a  horizontal  plane.  In  all  the  others  the  axis  is  horizontal 
and  the  blades  rotate  in  vertical  planes. 

Steam  Consumption. — The  relation  between  the  brake  horsepower  of  the 
steam  turbine  at  full  load  and  the  steam  consumption  is  shown  in  the  follow- 
ing table.  The  values  in  this  table  are  taken  from  published  tests  of  steam 
turbines  that  have  attained  the  greatest  commercial  success.  The  turbines  used 
saturated  steam  at  from  115  to  140  Ib.  per  sq.  in.,  gauge  pressure,  and  exhausted 


470 


STEAM  ENGINES 


into  a  vacuum  of  from  26  to  28.5  in.  of  mercury.  Better  results  than  those 
noted  in  the  table  can  be  obtained  by  the  use  of  highly  superheated  steam. 

The  better  the  vacuum,  the  greater  is  the  economy  in  the  use  of  steam,  both 
in  the  steam  engine  and  in  the  steam  turbine.  A  high  vacuum  is  of  greater 
value  to  the  turbine,  however,  because  the  turbine  can  take  advantage  of  a 
greater  range  of  expansion.  The  degree  of  vacuum  to  be  carried  is  a  matter 
of  dollars  and  cents;  that  is,  it  may  cost  more  to  create  and  maintain  a  high 
vacuum  than  may  be  saved  in  steam  consumption.  In  a  comparative  test  of  a 
turbine  and  a  triple-expansion  engine  under  like  conditions,  it  was  found  that, 
in  the  case  of  the  reciprocating  engine,  little  or  nothing  was  to  be  gained  by 
carrying  a  greater  vacuum  than  about  26  in.;  but  the  economy  of  the  turbine 
in  the  use  of  steam  increased  rapidly  as  the  vacuum  was  increased  above  26  in. 
The  conclusion  is  that  high  degrees  of  vacuum  are  more  desirable  for  turbines 
than  for  engines. 

Comparison  of  Turbines  and  Engines. — If  the  matter  of  steam  consump- 
tion alone  is  considered,  the  average  condensing  turbine  of  less  than  about 
700  H.  P.  is  not  so  economical  as  the  average  compound  or  triple-expansion 
condensing  engine,  although  the  turbine  may  be  preferred  to  the  engine 
for  other  reasons.  In  larger  sizes,  however,  and  particularly  in  very  large 
units,  the  economy  of  the  turbine  is  very  noticeable.  The  turbine  possesses 
the  ability  to  expand  the  steam  to  the  lowest  available  condenser  pressure 
without  difficulty;  but  to  do  this  in  a  reciprocating  engine  would  require  very 

STEAM  CONSUMPTION  PER  HOUR  OF  TURBINES 


Brake 
Horsepower 

Pounds  of 
Steam  Used 

Brake 
Horsepower 

Pounds  of 
Steam  Used 

100 
200 
300 
400 
500 

18.2 
17.5     :   v> 
16.9 
16.3 
15.8 

600 
700 
800 
900 
1,000 

15.3 
14.8 
14.3 
13.7 
13.2 

large  valves,  and  ports  and  heavy  pistons,  because  of  the  great  volume  of  steam 
to  be  handled  at  very  low  pressures. 

Finding  Horsepower  of  Turbines. — There  is  no  way  of  finding  the  indicated 
horsepower  of  a  steam  turbine,  because  no  form  of  indicator  applicable  to 
the  turbine  has  been  invented.  Nor  is  any  such  instrument  likely  to  be 
developed,  owing  to  the  very  great  difficulty  of  determining  the  energy  given 
up  to  the  blades  of  a  turbine  from  a  jet  of  steam.  The  usual  way  of  finding 
the  power  of  a  steam  turbine  is  to  use  a  brake  or  a  dynamometer  and  thus  to 
determine  the  brake  horsepower,  or  else  to  connect  an  electric  generator  to 
the  turbine  and  measure  the  electrical  output  at  the  switchboard.  In  case  the 
latter  method  is  used,  the  efficiency  of  the  generator  and  the  turbine  together 
is  involved. 

Turbine  Troubles.; — To  obtain  free  running,  it  is  necessary  to  allow  clear- 
ance between  the  stationary  and  the  moving  rows  of  blades,  as  well  as  between 
the  ends  of  the  blades  and  the  casing  or  the  rotor.  In  impulse  turbines,  such 
as  the  Curtis  and  the  Rateau,  the  clearance  between  the  rows  of  blades  is 
important;  however,  if  it  is  made  no  greater  than  is  necessary  for  mechanical 
reasons,  the  efficiency  will  not  be  affected  seriously.  In  the  reaction  turbine, 
such  as  the  Parsons,  the  clearance  between  the  rows  is  of  small  consequence 
as  compared  with  the  clearance  between  the  ends  of  the  stationary  blades  and 
the  rotor  and  between  the  ends  of  the  moving  blades  and  the  casing.  The 
former  may  vary  from  |  to  1  in.  or  more  from  the  high-pressure  to  the  low- 
pressure  stage;  but  the  tip  clearance  must  be  kept  between  a  few  hundredths 
and  a  few  thousandths  of  an  inch. 

The  stripping  of  the  blades  is  one  of  the  troubles  to  which  turbines  are 
subject.  It  may  be  due  to  the  interference  of  the  stationary  and  the  movable 
blades,  or  to  the  rubbing  of  the  blades  against  the  shell  or  the  rotor.  In  either 
of  these  cases  the  existing  clearances  are  reduced  by  wear  of  the  parts,  shifting 
of  the  rotor,  or  unequal  expansion  of  the  rotor  and  the  casing,  until  the  blades 
touch  and  tear  one  another  loose.  The  same  result  will  occur  if  some  foreign 
solid,  as  a  stray  nut  or  bolt,  is  carried  along  with  the  steam  into  the  turbine. 
If  a  turbine  is  started  too  quickly,  without  being  properly  warmed  up,  the 


STEAM  ENGINES  471 

sudden  unequal  expansion  set  up  in  the  heavy  casing  arid  the  lighter  rotor  may 
cause  the  blades  to  come  in  contact  and  be  stripped.  Stripping  is  claimed  by 
some  engineers  to  be  more  common  in  turbines  in  which  the  blades  are  not 
supported  at  their  outer  ends.  To  prevent  it,  some  manufacturers  apply 
shroud  rings  and  metal  lacings  to  the  outer  ends  of  the  blades. 

As  there  are  no  valves,  pistons,  or  piston  rings  in  the  turbine  to  be  main- 
tained free  from  leakage,  about  the  only  thing  that  can  affect  the  steam  con- 
sumption is  the  condition  of  the  blades.  The  blades  of  steam  turbines  are 
subjected  to  the  cutting  action  of  steam  flowing  at  high  velocities,  and  often 
carrying  water  particles  with  it.  This  cutting,  or  erosion,  wears  away  the 
edges  and  surfaces  of  the  blades.  From  the  data  available,  it  appears  that 
the  erosion  is  very  slight  if  the  steam  is  dry  or  superheated,  no  matter  what 
velocities  are  used;  but  if  the  steam  is  wet,  erosion  will  take  place,  and  it  will 
be  greatly  increased  if  the  velocity  of  the  steam  is  high.  The  horsepower  is 
not  affected  to  any  great  extent  by  blade  erosion,  according  to  the  results  of 
experience.  In  the  case  of  a  100-H.  P.  De  Laval  turbine,  the  steam  inlet  edges 
of  the  blades  were  worn  away  about  ^  in.,  yet  the  steam  consumption  was 
only  about  5%  above  that  with  new  blades. 

If  the  boiler  supplying  steam  to  a  reciprocating  engine  primes  badly,  a 
slug  of  water  may  be  carried  over  into  the  cylinder,  resulting  in  a  cracked  piston 
or  cylinder,  a  buckled  piston  rod  or  connecting-rod,  or  a  wrecked  frame.  In 
case  a  steam  turbine  is  used,  however,  the  danger  is  greatly  lessened.  In  tur- 
bines in  which  the  blades  are  not  supported  at  their  outer  ends,  the  water  may 
cause  stripping  of  the  blades;  but  this  is  not  very  likely,  as  the  blades  at  the  high- 
pressure  end  of  the  turbine  are  short.  A  rush  of  water  from  the  boiler  has  been 
known  to  bring  a  turbine  almost  to  a  stop  without  damaging  the  blades. 

On  account  of  the  high  speeds  attained  in  turbine  practice,  the  rotors  are 
balanced  accurately,  so  as  to  reduce  vibration.  But  in  spite  of  this  careful 
balancing,  vibration  may  manifest  itself  during  ordinary  running.  It  may  be 
caused  in  any  one  of  several  ways,  but  the  fundamental  cause  is  lack  of  balance. 
If  the  rotor  is  warmed  up  too  rapidly,  the  shaft  or  the  wheels  may  be  warped 
by  unequal  expansion,  producing  an  unbalanced  effect.  The  stripping  of  a 
blade  or  two  will  affect  the  balance  of  the  wheel  and  tend  to  produce  vibration. 
Even  water  carried  into  the  turbine  with  the  steam  will  bring  about  an  unbal- 
anced condition  and  will  lead  to  vibration.  When  vibration  is  observed,  it 
is  well  to  reduce  the  speed  a  little,  and  to  note  whether  this  causes  the  vibration 
to  cease.  If  it  does,  but  comes  back  again  as  soon  as  the  speed  is  increased, 
the  source  of  the  trouble  should  at  once  be  determined. 

Operation  of  Turbines. — If  the  steam  turbine  is  a  new  one,  or  if  it  has  been 
standing  idle  for  a  long  period,  it  should  not  be  started  until  it,  together  with 
its  auxiliary  apparatus,  has  been  thoroughly  inspected.  The  bearings  should 
be  properly  adjusted  and  freed  from  dirt,  and  the  entire  lubricating  system 
should  be  clean  and  filled  with  clean  oil.  The  steam  pipe  from  the  boilers 
should  be  blown  through,  so  as  to  clear  it  of  any  foreign  matter  that  could  be 
carried  into  the  turbine  by  the  steam.  The  governor  mechanism  should  be 
examined,  to  see  that  it  is  in  good  order;  the  oil  pump  shpuld  be  looked  after, 
to  ascertain  whether  it  is  in  condition  to  maintain  a  continuous  supply  of  oil; 
and,  finally,  before  the  turbine  is  started,  the  shaft  should  be  turned  over  by 
hand,  to  insure  that  the  rotor  will  turn  freely  in  the  casing. 

A  steam  turbine  should  be  started  slowly,  and  before  it  is  allowed  to  turn 
over  under  steam  it  should  be  warmed  up.  This  is  accomplished  by  opening  the 
throttle  valve  just  enough  to  let  steam  flow  into  the  turbine.  The  drains  should 
be  kept  open  until  the  turbine  is  well  started.  The  length  of  time  required 
for  warming  up  depends  on  the  size  of  the  turbine,  a  large  unit  requiring  more 
time  than  a  small  one.  As  the  warming  up  proceeds,  the  throttle  may  grad- 
ually be  opened  and  the  auxiliary  machinery  may  be  started.  Once  it  has  been 
started,  the  turbine  should  be  brought  up  to  speed  slowly.  If  it  is  speeded 
up  too  rapidly,  vibration  will  result.  After  the  normal  running  speed  has  been 
reached,  the  load  may  be  thrown  on;  but  this,  also,  should  be  done  gradually, 
to  prevent  a  rush  of  water  from  the  boiler  with  the  steam. 

If  superheated  steam  is  used,  extra  caution  must  be  employed  in  starting, 
for  during  the  warming  up,  with  the  throttle  valve  only  slightly  opened,  the 
passing  steam  will  be  cooled  considerably.  But  when  the  valve  is  opened 
wider,  the  greater  volume  passing  will  not  lose  so  much  of  its  superheat,  and  if 
care  is  not  exercised  the  turbine  will  be  subjected  to  sudden  expansion  because 
of  the  higher  temperature  of  the  steam.  The  main  point  in  starting  is  to 
avoid  any  sudden  changes  of  temperature  in  the  turbine.  If  a  turbine  must 
be  ready  to  be  put  in  operation  at  short  notice,  steam  may  be  allowed  to  flow 


472  STEAM  ENGINES 

through  it  continually,  by  means  of  a  by-pass  around  the  throttle  valve.     It  will 
always  be  warmed  up,  then,  and  can  be  brought  up  to  speed  with  less  danger  and 

The  shaft  or  spindle  of  a  turbine  rotates  at  high  speed,  and  therefore  the 
bearings  should  be  kept  well  lubricated;  for  if  the  oil  supply  fails,  or  if  a  bearing 
begins  to  heat  because  of  grit  carried  into  it,  the  resulting  trouble  will  come 
very  quickly.  The  presence  of  a  hot  bearing  will  usually  be  evidenced  by  the 
smell  of  burning  oil  or  by  the  appearance  of  white  smoke.  When  these  signs 
are  observed  the  oil  supply  should  immediately  be  increased  to  the  greatest 
possible  amount.  If  this  does  not  reduce  the  temperature  of  the  bearing  or 
prevent  its  further  heating,  the  turbine  should  be  shut  down.  To  continue 
will  result  in  burning  out  the  bearing,  and  it  is  better  to  stop  before  this  happens. 
The  high  speed  of  the  shaft  renders  it  impossible  to  nurse  a  hot  turbine  bearing 
as  is  done  frequently  in  the  running  of  reciprocating  engines. 

When  shutting  down  a  steam  turbine,  the  throttle  valve  should  be  closed 
partly  before  the  load  is  reduced,  so  as  to  prevent  any  possibility  of  racing 
when  the  load  is  finally  taken  off.  The  load  may  then  be  used  as  a  brake  to 
bring  the  rotor  to  a  stop.  When  the  throttle  valve  has  been  closed  and  the 
steam  supply  has  been  shut  off  completely,  the  auxiliary  machinery  may  be 
stopped.  If  the  load  is  taken  off  before  the  throttle  is  wholly  closed _  the 
turbine  may  continue  to  rotate  for  $  hr.,  as  the  rotor  is  then  running  in  a 
vacuum  and  under  no  load.  The  speed  may  be  reduced  by  opening  the  drains 
and  allowing  air  to  enter  the  casing.  The  oil  supply  to  the  bearings  must  be 
continued  until  the  turbine  has  come  to  rest,  and  the  oil  pump  should  be  the  last 
auxiliary  to  be  stopped. 

Economy  of  Turbine. — As  there  are  no  internal  rubbing  surfaces  in  the 
steam  turbine,  superheated  steam  may  be  employed  without  causing  any  of 
the  lubrication  troubles  attending  its  use  in  reciprocating  engines.  Because 
of  the  greater  amount  of  heat  contained  in  1  Ib.  of  superheated  steam,  the 
economy  of  a  turbine  working  with  superheated  steam  is  greater  than  that  of 
one  working  with  saturated  steam;  also,  the  efficiency  is  increased  because  the 
'  superheated  steam  causes  less  frictional  resistance  to  the  motion  of  the  blades. 
To  show  the  value  of  superheated  steam  in  turbine  work,  it  may  be  stated 
that  50°  F.  of  superheat  reduces  the  steam  consumption  about  6% ;  100°  F.  of 
superheat  reduces  it  about  10% ;  and  150°  F.  of  superheat  reduces  it  about  13£%. 
The  use  of  high  superheat,  however,  produces  expansion  of  the  rotor  and  the 
casing  and  may  cause  the  blades  to  interfere;  as  a  result,  the  usual  degree  of 
superheat  in  steam-turbine  practice  is  100°  F.,  and  seldom  exceeds  150°  F. 

The  steam  turbine  shows  better  economy  than  the  steam  engine  when  work- 
ing with  low-pressure  steam  in  connection  with  a  high  vacuum;  but  when  work- 
ing with  high-pressure  steam  and  a  vacuum  of  about  26  in.,  the  engine  is  the 
more  economical.  As  a  consequence,  a  combination  of  the  steam  engine  and 
the  steam  turbine  has  been  adopted.  The  engine  uses  the  high-pressure  steam 
from  the  boilers  and  expands  it  to  about  atmospheric  pressure.  This  exhaust 
steam  then  passes  into  the  turbine,  which  exhausts  into  a  condenser  carrying 
a  high  degree  of  vacuum,  and  the  expansion  is  carried  to  the  extreme  practicable 
limit.  The  turbine  thus  used  in  connection  with  an  engine  is  termed  an 
exhaust-steam  turbine, 

As  the  economy  of  the  steam  turbine  is  dependent  so  largely  on  the  degree 
of  vacuum  carried,  it  is  necessary  for  the  engineer  to  watch  the  vacuum  gauge 
closely.  With  reciprocating  engines,  the  loss  of  1  or  2  in.  of  vacuum  may  not 
be  of  much  consequence;  but  in  a  turbine  plant,  where  the  vacuum  is  from  27  to 
28  in.,  a  loss  of  1  or  2  in.  will  result  in  a  considerable  increase  in  the  steam 
consumption.  Because  of  the  high  vacuum  employed,  the  difficulty  of  keeping  ' 
pipes,  valves,  and  glands  from  leaking  is  greater  in  turbine  practice  than  in 
engine  practice,  but  the  greater  economy  obtained  by  keeping  everything 
tight  overbalances  the  increased  care  and  labor. 

Care  of  Gears  in  De  Laval  Turbines.— The  De  Laval  Steam  Turbine 
Company  in  their  directions  for  operating  their  turbines  state  that  in  order  to 
keep  the  gears  in  good  condition  the  teeth  should  be  cleaned  occasionally  when 
the  turbine  is  not  in  service.  They  recommend  that  a  wire  brush  and  kerosene 
be  employed  for  this  purpose.  At  the  same  time  the  gear-case  should  also  be 
thoroughly  cleaned,  and  after  the  cleaning  the  gears  should  be  well  lubricated. 

Should  an  engineer  for  any  reason  desire  to  take  the  gears  out  of  the  case,  it 
is  recommended  that  he  secure  special  directions  relating  to  their  removal 
from  the  manufacturers.  The  same  statement  also  applies  to  the  adjustment  of 
the  gears,  which  need  to  be  kept  in  perfect  adjustment. 


STEAM  ENGINES  473 

RULES  FOR  STATIONARY  ENGINEERS 

If  a  gauge  glass  breaks  turn  off  the  water  first  and  then  the  steam,  to 
avoid  scalding  yourself. 

Don't  buy  oil  or  waste  simply  because  it  is  very  cheap;  it  will  cost  more 
than  a  good  article  in  the  end. 

When  cutting  rubber  for  gaskets,  etc.,  have  a  dish  of  water  handy,  and  keep 
wetting  the  knife  blade;  it  makes  the  work  much  easier. 

Don't  forget  that  there  is  no  economy  in  employing  a  poor  fireman;  he 
can,  and  probably  will,  waste  more  coal  than  would  pay  the  wages  of  a  first- 
class  man. 

An  ordinary  steam  engine  having  two  cylinders  connected  at  right  angles 
on  the  same  shaft  consumes  one-third  more  steam  than  a  single-cylinder 
engine,  while  developing  only  the  same  amount  of  power. 

A  fusible  plug  ought  to  be  renewed  every  3  mo.,  by  removing  the  old 
metal  and  refilling  the  case;  and  it  should  be  scraped  clean  and  bright  on  both 
ends  every  time  that  the  boiler  is  washed  out,  to  keep  it  in  good  working  order. 

When  trying  a  gauge-cock,  don't  jerk  it  open  suddenly,  for  if  the  water 
happens  to  be  a  trifle  below  the  cock,  the  sudden  relief  from  pressure  at  that 
point  may  cause  it  to  lift  and  flow  out,  thus  showing  a  wrong  height.  Whereas, 
if  it  is  opened  quietly,  no  lift  will  occur,  and  it  will  show  whether  there  is  water 
or  steam  at  that  level. 

Always  open  steam  stop-valves  between  boilers  very  gently,  that  they 
may  heat  and  expand  gradually;  by  suddenly  turning  on  steam  a  stop- valve 
chest  was  burst,  due  to  the  expansive  power  of  heat  unequally  applied.  The 
same  care  must  be  exercised  when  shutting  off  stop- valves;  explosions  have  been 
caused  by  shutting  a  communicating  stop- valve  too  suddenly — due  to  the  recoil. 

In  order  to  obtain  the  driest  possible  steam  from  a  boiler,  there  should  be  an 
internal  perforated  pipe  (dry  pipe,  so  called)  fixed  near  the  top  of  the  boiler, 
and  suitably  connected  to  the  steam  pipe.  The  perforations  in  this  pipe  should 
be  from  one-quarter  to  one-half  greater  in  area  than  that  of  the  steam  pipe. 

If  a  glass  gauge  tube  is  too  long,  wet  a  triangular  file  with  turpentine,  then 
holding  the  tube  in  the  left  hand,  with  the  thumb  and  forefinger  at  the  place 
where  it  is  to  be  cut,  saw  it  quickly  and  lightly  two  or  three  times  with  the 
edge  of  the  file.  Take  the  tube  in  both  hands,  both  thumbs  being  on  the  side 
opposite  the  mark,  and  1  in.  or  so  apart,  and  then  try  to  bend  the  glass,  using  the 
thumbs  as  fulcrums,  and  it  will  break  at  the  mark,  which  has  weakened  the  tube. 

A  stiff  charge  of  coal  all  over  a  furnace  will  lower  the  temperature  200° 
or  300°  in  a  very  short  time.  After  the  coal  is  well  ignited  the  temperature 
will  rise  about  500°,  and  as  it  burns  will  gradually  drop  about  200°,  until  the 
fireman  puts  in  another  charge,  when  the  sudden  fall  again  takes  place. 
This  sudden  contraction  and  expansion  frequently  causes  the  bursting  of  a 
boiler,  and  it  is  for  this  reason  that  light  and  frequent  charges  of  coal,  or 
else  firing  only  one-half  of  the  furnace  at  a  time,  should  be  always  insisted  on. 

Be  careful  when  using  a  wrench  on  hexagonal  nuts  that  it  fits  snugly,  or 
the  edges  of  the  nut  will  soon  become  rounded. 

If  a  monkey-wrench  is  not  placed  on  the  nut  properly,  the  strain  will  often 
bend  or  fracture  the  wrench. 

The  area  of  grate  for  a  boiler  should  never  be  less  than  £  sq.  ft.  per  I.  H.  P. 
of  the  engine,  and  it  is  seldom  advisable  to  increase  this  allowance  beyond 
i  sq.  ft.  per  I.  H.  P. 

The  area  of  tube  surface  for  a  boiler  should  not  be  less  than  2|  sq.  ft.  per 
I.  H.  P.  of  the  engine. 

The  ratio  of  heating  surface  to  grate  area  in  a  boiler  should  be  30  to  1  as  a 
minimum,  and  may  often  be  increased  to  40  to  1,  or  even  more,  with  advantage. 

Lap- welded  pipe  of  the  same  fated  size  has  always  the  same  outside  diameter, 
whether  common,  extra,  or  double  extra,  but  the  internal  diameter  is  of  course 
decreased  with  the  increased  thickness. 

A  good  cement  for  steam  and  water  joints  is  made  by  taking  10  parts,  by 
weight,  of  white  lead,  3  parts  of  black  oxide  of  manganese,  1  part  of  litharge, 
and  mixing  them  to  the  proper  consistency  with  boiled  linseed  oil. 

To  harden  a  cutting  tool,  heat  it  in  a  coke  fire  to  a  blood-red  heat  and 
plunge  it  into  a  solution  of  salt  and  water  (1  Ib.  of  salt  to  1  gal.  of  water), 
then  polish  the  tool,  heat  it  over  gas,  or  otherwise,  until  a  dark  straw  and 
purple  mixed  color  shows  on  the  polish,  and  cool  it  in  the  salt  water. 

Small  articles  can  be  plated  with  brass  by  dipping  them  in  a  solution  of 
9\  gr.  each  of  sulphate  of  copper  and  chloride  of  tin,  in  If  pt.  of  water. 


474  COMPRESSED  AIR 

Don't  be  eternally  tinkering  about  an  engine,  but  let  well  enough  alone. 
Don't  forget  that  it  is  possible  to  drive  a  key  with  a  copper  hammer  just  as 
well  as  with  a  steel  one,  and  that  it  doesn't  leave  any  marks. 

Keep  on  hand  slips  of  thin  sheet  copper,  brass,  and  tin,  to  use  as  liners, 
and  if  these  are  shaped  properly,  much  time  will  be  saved  when  they  are  needed. 

A  few  wooden  skewer  pins,  such  as  butchers  use,  are  very  useful  for  many 
purposes  in  an  engine  room. 

In  running  a  line  of  steam  pipe  where  there  are  certain  rigid  points,  make 
arrangements  for  expansion  on  the  line  between  those  points. 

Arrange  the  usual  work  of  the  engine  and  firerooms  systematically,  and 
adhere  to  it. 

Don't  forget  that  cleanliness  is  next  to  godliness. 

Rubber  cloth  kept  on  hand  for  joints  should  be  rolled  up  and  laid  away 
by  itself,  as  any  oil  or  grease  coming  in  contact  with  it  will  cause  it  to  soften 
and  give  out  when  put  to  use. 

When  using  a  jet  condenser,  let  the  engine  make  three  or  four  revolutions 
before  opening  the  injection  valve,  and  then  open  it  gradually,  letting  the 
engine  make  several  more  revolutions  before  it  is  opened  to  the  full  amount. 

Open  the  main  stop- valve  before  the  fires  are  started  under  the  boilers. 

When  starting  fires,  don't  forget  to  close  the  gauge-cocks  and  safety  valve 
as  soon  as  steam  begins  to  form. 

An  old  Turkish  towel,  cut  in  two  lengthwise,  is  better  than  cotton  waste 
for  cleaning  brass  work. 

Always  connect  the  steam  valves  in  such  a  manner  that  the  valve  closes 
against  the  constant  steam  pressure. 

Turpentine  well  mixed  with  black  varnish  makes  a  good  coating  for  iron 
smoke  pipes. 

Ordinary  lubricating  oils  are  not  suitable  for  use  in  preventing  rust. 

It  is  possible  to  make  a  hole  through  glass  by  covering  it  with  a  thin  coating 
of  wax,  warming  the  glass  and  spreading  the  wax  on  it;  then  scrape  off  the  wax 
where  the  hole  is  wanted,  drop  a  little  fluoric  acid  on  the  spot  with  a  wire. 
The  acid  will  cut  a  hole  through  the  glass,  and  it  can  be  shaped  with  a  copper 
wire  covered  with  oil  and  rottenstone. 

A  mixture  of  1  oz.  of  sulphate  of  copper,  J  oz.  of  alum,  £  teaspoonful  of 
powdered  salt,  1  gill  of  vinegar  and  20  drops  of  nitric  acid  will  make  a  hole 
in  steel  that  is  too  hard  to  cut  or  file  easily.  Also,  if  applied  to  steel  and 
washed  off  quickly,  it  will  give  the  metal  a  beautiful  frosted  appearance. 


COMPRESSED  AIR 


CLASSIFICATION  AND  CONSTRUCTION  OF 
COMPRESSORS 

An  air  compressor  consists  essentially  of  a  cylinder  in  which  atmospheric 
air  is  compressed  by  a  piston,  the  driving  power  being  steam,  water,  oil,  gas, 
or  electricity.  Steam-driven  compressors  in  ordinary  use  may  be  classed  as 
follows: 

1.  _  Straight-line  type,  in  which  a  single  horizontal  air  cylinder  is  set  tandem 
with  its  steam  cylinder,  and  provided  with   two  flywheels;  this  pattern  is 
generally  adapted  for  compressors  of  small  size. 

2.  Duplex  type,  in  which  there  are  two  steam  cylinders,  each  driving  an 
air  cylinder,  and  coupled  at  90°  to  a  crank-shaft  carrying  a  flywheel. 

3.  Horizontal,  cross-compound  engines,  each  steam  cylinder  set  tandem 
with  an  air  cylinder,  as  in  2. 

4.  Vertical,  simple,  or  compound  engines,  with  the  air  cylinders  set  above 
the  steam  cylinders. 

5.  Compound  or  stage  compressors,  in  which  the  air  cylinders  themselves 
are  compounded;  the  compression  is  carried  to  a  certain  point  in  one  cylinder 
and  successively  raised  and  finally  completed  to  the  desired  pressure  in  the 
others.     They  may  be  either  of  the  straight-line  or  duplex  form,  with  simple 
or  compound  steam  cylinders.     The  principle  of  compound,  or  two-stage,air 
compression    is    recognized    as   applicable  for  even  the  moderate   pressures 
required  in  mining.     Compressors  of  class  5  are  frequently  employed,  as  well 
as  classes  1,  2,  and  3. 


COMPRESSED  AIR  475 

Theory  of  Air  Compression. — The  useful  effect  or  efficiency  of  a  compressor 
is  the  ratio  of  the  force  stored  in  the  compressed  air  to  the  work  that  has  been 
expended  in  compressing  it;  this  probably  never  reaches  80%  and  often  falls 
below  60%. 

Free  Air  is  air  at  ordinary  atmospheric  pressure  as  taken  into  the  com- 
pressor cylinder;  as  commonly  used,  this  means  air  at  sea-level  pressure 
(14.7  Ib.  per  sq.  in.)  at  60°  F.  The  absolute  pressure  of  air  is  measured  from 
zero,  and  is  equal  to  the  assumed  atmospheric  pressure  plus  gauge  pressure. 
Air-compression  calculations  depend  on  the  two  well-known  laws: 

1.  Boyle's  Law. — The  temperature  being  constant,  the  volume  varies 
inversely  as  the  pressure;  or  PV  =  P'V'  =  a  constant;  in  which  F  equals  the 
volume  of  a  given  weight  of  air  at  the  freezing  point,  and  the  pressure  P; 
V  equals  the  volume  of  the  same  weight  of  air  at  the  same  temperature  and 
under  the  pressure  P'. 

2  Cay-Lussac's  Law. — The  volume  of  a  gas  under  constant  pressure,  when 
heated,  expands,  for  each  degree  of  rise  in  temperature,  by  a  constant  pro- 
portional part  of  the  volume  that  it  occupied  at  the  freezing  point;  or, 
V'=  V  (1  +at°),  in  which  a  equals  2fo  for  centigrade  degrees,  or  *th:  for  Fahren- 
heit degrees. 

Theoretically,  air  may  be  compressed  in  two  ways,  as  follows: 

1.  I sothermally ,  when  the  temperature  is  kept  constant  during  compres- 
sion, and  in  this  case,  the  formula  PF  =  P'F'  is  true. 

2.  A  diabolically,  when  the  temperature  is  allowed  to  rise  without  check 
during  the  compression. 

As  the  pressure  rises  faster  than  the  volume  diminishes,  the  equation 

PV  =  P'V  no  longer  holds,  and  •p  =  (T?)W.  *n  which  n  equals  1.406.     The 

specific  heat  of  air  at  constant  pressure  is  .2375,  and  at  constant  volume 
.1689.  and  n  =  . 2375 -h.  1689  =  1.406. 

In  practice,  compression  is  neither  isothermal  nor  adiabatic,  but  inter- 
mediate between  the  two.  The  values  of  n  for  different  conditions  in  prac- 
tice as  determined  from  a  2,000-H.  P.  stage  compressor  at  Quai  de  la  Gare, 
Paris,  are  as  follows:  For  purely  adiabatic  compression,  with  no  cooling 
arrangements,  n=  1.406;  in  ordinary  single-cylinder  dry  compressors,  provided 
with  a  water-jacket,  n  is  roughly  1.3;  while  in  the  best  wet  compressors  (with 
spray  injection) ,  n  becomes  1.2  to  1.25.  In  the  poorest  forms  of  compressor,  the 
value  n  =  1.4  is  closely  approached.  For  large,  well-designed  compressors 
with  compound  air  cylinders,  the  exponent  n  may  be  as  small  as  1.15. 

Construction  of  Compressors. — Compressors  are  usually  built  with  a  short 
stroke,  as  this  is  conducive  to  economy  in  compression  as  well  as  the  attain- 
ment of  a  proper  rotative  speed.  In  ordinary  single-stage  compressors,  the 
usual  ratio  of  length  of  stroke  to  diameter  of  steam  cylinders  is  H  to  1  or  1J 
to  1.  In  some  makes,  such  as  the  Rand,  the  ratio  is  considerably  greater, 
varying  from  1£  to  If  to  1,  as  in  several  large  plants  built  for  the  Calumet 
&  Hecla  Mining  Co.  Many  compressors  have  length  and  diameter  of  steam 
cylinders  equal.  The  relative  diameters  of  the  air  and  steam  cylinders  depend 
on  the  steam  pressure  carried,  and  the  air  pressure  to  be  produced.  In  mining 
operations,  there  is  usually  but  little  variation  in  these  conditions.  For  rock- 
drill  work,  the  air  pressure  is  generally  from  60  to  80  Ib. 

In  using  water-power,  a  compressor  is  driven  most  conveniently  by  a  bucket 
impact  wheel,  such  as  the  Pelton  or  Knight.  The  waterwheel  is  generally 
mounted  directly  on  the  crank-shaft,  without  the  use  of  gearing.  As  the  power 
developed  is  uniform  throughout  the  revolution  of  the  wheel,  the  compressor 
should  be  of  duplex  form,  in  order  to  equalize  the  resistance  so  far  as  possible. 
The  rim  of  the  wheel  is  made  extra  heavy,  to  supply  the  place  of  a  flywheel. 
When  direct-connected,  the  wheel  is  of  relatively  large  diameter,  as  its  speed 
of  rotation  must  of  necessity  be  slow.  With  small  high-speed  wheels,  the 
compressor  cylinders  may  be  operated  through  belting  or  gearing.  In  most 
cases,  however,  the  waterwheel  may  be  large  enough  to  render  gearing  unneces- 
sary. Impact  wheels  may  be  employed  with  quite  small  heads  of  water,  by 
introducing  multiple  nozzles.  To  prevent  the  water  from  splashing  over  the 
compressor,  the  wheel  is  enclosed  in  a  tight  iron  or  wooden  casing.  The  force 
of  the  water  is  regulated  usually  by  an  ordinary  gate  valve.  If  the  head  is 
great,  it  may  be  necessary  to  introduce  means  for  deflecting  the  nozzle,  so  that, 
when  the  compressor  is  to  be  stopped  suddenly,  danger  of  rupturing  the  water 
main  will  be  avoided. 

Rating  of  Compressors. — Compressors  are  rated  as  follows:  (1)  In  terms 
of  the  horsepower  developed  by  the  steam  end  of  the  compressor,  as  shown  by 


476 


COMPRESSED  AIR 


indicator  cards  taken  when  running  at  full  speed  and  when  the  usual  volume 
of  air  is  being  consumed;  (2)  compressors  for  mines  are  often  rated  roughly 
as  furnishing  sufficient  air  to  operate  a  certain  number  of  rock  drills;  a  3-in. 
drill  requires  a  volume  of  air  at  60  Ib.  pressure,  equal  to  100  or  110  cu.  ft.  of 
free  atmospheric  air  per  minute;  (3)  in  terms  of  cubic  feet  of  free  air  com- 
pressed per  minute  to  a  given  pressure. 

As  the  actual  capacity  of  a  compressor  depends  on  the  density  of  the 
intake  air,  it  will  be  reduced  when  working  at  an  altitude  above  sea  level, 
because  of  the  diminished  density  of  the  atmosphere.  The  accompanying 
table  gives  the  percentages  of  output  at  different  elevations. 

EFFICIENCIES  OF  AIR  COMPRESSORS  AT  DIFFERENT  ALTITUDES 


Barometer  Pressure 

Volumetric 

Decreased 

Altitude 

Efficiency  of 

Loss  of 

Power 

Feet 

Inches 
Mercury 

Pounds  per 
Square  Inch 

Compressor 
Per  Cent. 

Capacity 
Per  Cent. 

Required 
Per  Cent. 

0 

30.00 

14.75 

100 

0 

0 

1.000 

28.88 

14.20 

97 

3 

1.8 

2,000 

27.80 

13.67 

93 

7 

3.5 

3,000 

26.76 

13.16 

90 

10 

5.2 

4,000 

25.76                12.67 

87 

13 

6.9 

5,000 

24.79 

12.20 

84 

16 

8.5 

6,000 

23.86 

11.73 

81 

19 

10.1 

7,000 

22.97 

11.30 

78 

22 

11.6 

8,000 

22.11 

10.87 

76 

24 

13.1 

9,000 

21.29 

10.46 

73 

27 

14.6 

10,000 

20.49 

10.07 

70 

30 

16.1 

11,000 

19.72 

9.70 

68 

32 

17.6 

12,000 

18.98 

9.34 

65 

35 

19.1 

13,000 

18.27 

8.98 

63 

37 

20.6 

14,000 

17.59 

8.65 

60 

40 

22.1 

15,000 

16.93 

8.32 

58 

42 

23.5      ' 

EXAMPLE.  —  Calculate  the  volume  of  air  furnished  by  an  18"X24"  com- 
pressor working  at  an  elevation  of  5,000  ft.  above  sea  level,  making  95  rev.  per 
min.,  and  having  a  piston  speed  of  380  ft.  per  min. 


SOLUTION.—  92X  3.14  =  254.3  sq.  in.  =  piston  area.  rrjX  380  =  668.8 
cu.  ft.  =  volume  displaced  per  minute  by  the  piston;  deducting  10%  for  loss 
gives  602  cu.  ft.  At  sea  level  at  80  Ib.  gauge  pressure,  this  equals 


X  602  =  95  cu.  ft.     At  an  elevation  of  5,000  ft.,  the  output  of  a  compressor 
would  be  95X84%  =  79.8  cu.  ft.  per  min. 

Cooling.  —  Compressor  cylinders  may  be  cooled  by  injecting  water  into  the 
cylinder,  in  which  case  they  are  known  as  wet  compressors;  or  by  jacketing  the 
cylinder  in  water,  when  they  are  known  as  dry  compressors. 


TRANSMISSION  OF  AIR  IN  PIPES 

The  actual  discharge  capacity  of  piping  is  not  proportional  to  the  cross- 
sectional  area  alone,  that  is,  to  the  square  of  the  diameter.  Although  the 
periphery  is  directly  proportional  to  the  diameter,  the  interior  surface  resis- 
tance is  much  greater  in  a  small  pipe  than  in  a  large  one,  because,  as  the  pipe 
becomes  smaller,  the  ratio  of  perimeter  to  area  increases. 

To  pass  a  given  volume  of  compressed  air,  a  1-in.  pipe  of  given  length 
requires  over  three  times  as  much  head  as  a  2-in.  pipe  of  the  same  length. 
The  character  of  the  pipe,  also,  and  the  condition  of  its  inner  surface,  have 
much  to  do  with  the  friction  developed  by  the  flow  of  air.  Besides  imper- 
fections in  the  surface  of  the  metal,  the  irregularities  incident  on  coupling 
together  the  lengths  of  pipe  must  increase  friction.  There  are  so  few  reliable 


COMPRESSED  AIR  477 

data  that  the  influences  by  which  the  values  of  some  of  the  factors  may  be 
modified  are  not  fully  understood;  and,  owing  to  these  uncertain  conditions, 
the  results  obtained  from  formulas  are  only  approximately  correct. 

Among  the  formulas  in  common  use,  perhaps  the  most  satisfactory  is  that 
of  D'Arcy.     As  adopted  for  compressed-air  transmission,  it  takes  the  form: 


in  which  D  =  volume  of  compressed  air  discharged  at  final  pressure  in  cubic  feet 

per  minute; 
c  =  coefficient  varying  with  diameter  of  pipe,   as   determined  by 

experiment; 

d  =  diameter  of  pipe  in  inches  (actual  diameters  of  1  J-  and  Ij-in.  pipe 
are  1.38  in.  and  1.61  in.,  respectively;  nominal  diameters  of  all 
other  sizes  may  be  taken  for  calculations)  ; 
I  =  length  of  pipe,  in  feet; 

pi  =  initial  gauge  pressure,  in  pounds  per  square  inch; 
pz  =  final  gauge  pressure,  in  pounds  per  square  inch; 
wi  =  density  of  air,  or  its  weight  at  initial  pressure  pi,  in  pounds  per 

cubic  foot. 
The  values  of  the  coefficients  c  for  sizes  of  piping  up  to  12  in.  are: 

1  in  ...........  45.3        5  in  ...........  59.0          9  in  ...........  61.0 

2  in  ...........  52.6        6  in  ...........  59.8        10  in  ...........  61.2 

3  in  ...........  56.5        7  in  ...........  60.3        11  in  ...........  61.8 

4  in  ..........  .58.0        8  in..  ......  ...60.7        12  in  ...........  62.0 

Some  apparent  discrepancies  exist  for  sizes  larger  than  9  in.,  but  they  cause 

no  very  material  differences  in  the  results. 

Another  formula,  published  by  Mr.  Prank  Richards,  is  as  follows: 


10,000  D*a 
in  which  H  =head  or  difference  of  pressure  required  to  overcome  friction  and 

maintain  flow  of  air; 

V  =  volume  of  compressed  air  delivered,  in  cubic  feet  per  minute; 
L  =  length  of  pipe,  in  feet; 
D  =  diameter  of  pipe,  in  inches; 
a  =  coefficient,  depending  on  size  of  pipe. 
Values  of  a  for  nominal  diameters  of  wrought-iron  pipe: 

lin  ..........  350        3  in  ...........  730          Sin  ..........  1.125 

IJin  .........  500        3£i«  ..........  787         10  in  ..........  1.200 

Hin  .........  662        4  in  ...........  840         12  in  .....  ......  1.260 

2  in  ..........  565        5  in  ...........  934 

2£in  .........  650        6  in....  ____  ..1.000 

The  values  of  a  for  1£  and  l|-in.  pipe  are  not  consistent  with  those  for 
other  sizes,  for  the  reason  already  stated.  When  using  this  formula  with  its 
constants,  the  calculated  losses  of  pressure  are  found  to  be  smaller,  and,  con- 
versely, the  volumes  of  air  discharged  are  larger,  under  the  same  conditions 
than  those  obtained  from  D'Arcy's  formula. 

It  must  be  remembered  that,  within  certain  limits,  the  loss  of  head  or 
pressure  increases  with  the  square  of  the  velocity.  To  obtain  the  best  results, 
it  has  been  found  that  the  velocity  of  flow  in  the  main  air  pipes  should  not 
exceed  20  or  25  ft.  per  sec.  When  the  initial  velocity  much  exceeds  50  ft. 
per  sec.,  the  percentage  loss  becomes  very  large;  and,  conversely,  by  using 
piping  large  enough  to  keep  down  the  velocity,  the  friction  loss  may  be  almost 
eliminated.  For  example,  at  the  Hoosac  tunnel,  in  transmitting  875  cu.  ft. 
per  min.  of  free  air  at  an  initial  pressure  of  60  lb.,  through  an  8-in.  pipe,  7,150  ft. 
long,  the  average  loss  including  leakage  was  only  2  lb.  A  volume  of  500  cu.  ft. 
per  min.  of  free  air,  at  75  lb.,  can  be  transmitted  through  1,000  ft.  of  3-in.  pipe 
with  a  loss  of  4.1  lb.,  while  if  a  5-in.  pipe  is  used  the  loss  will  be  reduced  to 
.24  lb.  The  velocity  of  flow  in  the  latter  case  is  only  10  ft.  per  sec. 

When  driving  the  Jeddo  mining  tunnel,  at  Ebervale,  Pa.,  two  3j-in.  drills 
were  used  in  each  heading,  with  a  6-in.  main,  the  maximum  transmission  dis- 
tance being  10,800  ft.  This  pipe  was  so  large  in  proportion  to  the  volume  of  air 
required  for  the  drills  (230  cu.  ft.  per  min.  of  free  air)  that  the  loss  was  reduced 
to  an  extremely  small  quantity.  A  calculation  shows  a  los's  of  .002  lb.,  and 
the  gauges  at  each  end  of  the  main  were  found  to  record  practically  the  same 
pressure. 

A  due  regard  for  economy  in  installation,  however,  must  limit  the  use  of 
very  large  piping,  the  cost  of  which  should  be  considered  in  relation  to  the 


478  COMPRESSED  AIR 

cost  of  air  compression  in  any  given  case.  Diameters  of  from  4  to  6  in.  for 
the  mains  are  large  enough  for  any  ordinary  mining  practice.  Up  to  a  length 
of  3,000  ft.,  a  4-in.  pipe  will  carry  480  cu.  ft.  per  min.  of  free  air  compressed 
to  82  lb.,  with  a  loss  of  2  Ib.  pressure.  This  volume  of  air  will  run  fpur  3-in. 
drills.  Under  the  same  conditions,  a  6-in.  pipe,  5,000  ft.  long,  will  carry 
1,100  cu.  ft.  per  min.  of  free  air,  or  enough  for  10  drills. 

A  mistake  is  often  made  by  putting  in  branch  pipes  of  too  small  a  diam- 
eter. For  a  distance  of,  say,  100  ft.,  a  Ij-in.  pipe  is  small  enough  for  a  single 
drill,  though  a  1-in.  pipe  is  frequently  used.  While  it  is,  of  course,  admissible 
to  increase  the  velocity  of  flow  in  short  branches  considerably  beyond  20  ft. 
per  sec.,  extremes  should  be  avoided.  To  run  a  3-in.  drill  from  a  1-in.  pipe  100 
ft.  long,  will  require  a  velocity  of  flow  of  about  55  ft.  per  sec.,  causing  a  loss 
of  10  lb.  pressure. 

The  piping  for  conveying  compressed  air  may  be  of  cast  or  wrought  iron. 
If  of  wrought  iron,  as  is  customary,  the  lengths  are  connected  either  by  sleeve 
couplings  or  by  cast-iron  flanees  into  which  the  ends  of  the  pipe  are  screwed 
or  expanded.  Sleeve  couplings  are  used  for  all  except  the  large  sizes.  The 
smaller  sizes,  up  to  lj  in.,  are  butt-welded,  while  all  from  1?  in.  up  are  lap- 
welded,  to  insure  the  necessary  strength.  Wrought-iron,  spiral-seam,  riveted, 
or  spiral- weld  steel  tubing  is  sometimes  used.  It  is  made  in  lengths  of  20  ft. 
or  less.  For  convenience  of  transport  in  remote  regions,  rolled  sheets  in  short 
lengths  may  be  had.  They  are  punched  around  the  edges,  ready  for  riveting, 
and  are  packed  closely — four,  six,  or  more  sheets  in  a  bundle. 

All  joints  in  air  mains  and  branches  should  be  carefully  made.  Air  leaks 
are  more  expensive  than  steam  leaks  because  of  the  losses  suffered  when  com- 
pressing the  air.  The  pipe  may  be  tested  from  time  to  time  by  allowing  the 
air  at  full  pressure  to  remain  in  the  pipe  long  enough  to  observe  the  gauge. 
A  leak  should  be  traced  and  stopped  immediately.  When  putting  together 
screw  joints,  care  should  be  taken  that  none  of  the  white  lead  or  other  cement- 
ing material  is  forced  into  the  pipe;  this  would  cause  obstruction  and  increase 
the  friction  loss.  Also,  each  length  as  put  in  place  should  be  cleaned  thor- 
oughly of  all  foieign  substances  that  may  have  lodged  inside.  To  render  the 
piping  readily  accessible  for  inspection  and  stoppage  of  leaks,  it  should,  if 
buried,  be  carried  in  boxes  sunk  just  below  the  surface  of  the  ground;  or,  if 
underground,  it  should  be  supported  upon  brackets  along  the  sides  of  the  mine 
workings.  Low  points  in  pipe  lines,  which  would  form  pockets  for  the  accu- 
mulation of  entrained  water,  should  be  avoided,  as- they  obstruct  the  passage 
of  the  air.  In  long  pipe  lines,  where  a  uniform  grade  is  impracticable,  pro- 
vision may  be  made  near  the  end  for  blowing  out  the  water  at  intervals,  when 
the  air  is  to  be  used  for  pumps,  hoists,  or  other  stationary  engines. 

For  long  lengths  of  piping,  expansion  joints  are  required,  particularly 
when  on  the  surface.  They  are  not  often  necessary  underground,  as  the 
temperature  is  usually  nearly  constant,  except  in  shafts,  or  where  there  may  be 
considerable  variations  of  temperature  between  summer  and  winter. 


LOSSES  IN  THE  TRANSMISSION  OF  COMPRESSED  AIR 

To  obtain  compressed  air,  an  engine  drives  a  compressor,  which  forces  air 
into  a  reservoir;  the  air  under  pressure  is  led  through  pipes  to  the  air  engine, 
and  is  there  used  after  the  manner  of  steam.  The  resulting  power  is  frequently 
a  small  percentage  of  the  power  expended.  In  a  large  number  of  cases  the 
losses  are  due  to  poor  designing,  and  are  not  chargeable  as  faults  of  the  system 
or  even  to  poor  workmanship. 

The  losses  are  chargeable,  first,  to  friction  of  the  compressor.  This  will 
amount  ordinarily  to  15%  or  20%,  and  can  be  helped  by  good  workmanship, 
but  cannot  probably  be  reduced  below  10%.  Second,  a  loss  is  occasioned  by 
pumping  the  air  of  the  engine  room,  rather  than  air  drawn  from  a  cooler  place; 
this  loss  varies  with  the  season,  and  amounts  to  from  3%  to  10%  and  can  all 
be  saved.  The  third  loss,  or  series  of  losses,  is  caused  by  insufficient  supply, 
difficult  discharge,  defective  cooling  arrangements,  poor  lubrication,  and  a 
host  of  other  causes,  in  the  compression  cylinder.  The  fourth  loss  is  found  in 
the  pipe,  it  varies  with  every  different  situation,  and  is  subject  to  somewhat 
complex  influences.  The  fifth  loss  is  chargeable  to  a  fall  of  temperature  in 
the  cylinder  of  the  air  engine.  Losses  arising  from  leaks  are  often  serious, 
but  the  remedy  is  too  evident  to  require  demonstration;  no  leak  can  be  so 
small  as  not  to  require  immediate  attention.  An  attendant  who  is  careless 
about  packings  and  hose  couplings  will  permit  losses  for  which  no  amount  of 
engineering  skill  can  compensate. 


COMPRESSED  AIR  479 

It  is  possible  to  realize  100%  efficiency  in  the  air  engine,  leaving  friction 
out  of  our  consideration,  only  when  the  expansion  of  the  air  and  the  changes 
of  its  temperature  in  the  expanding  or  air-engine  cylinder  are  precisely  the 
reverse  of  the  changes  that  have  taken  place  during  the  compression  of  the 
air  in  the  compressing  cylinder;  but  these  conditions  can  never  be  realized. 
The  air  during  compression  becomes  heated,  and  during  expansion  it  becomes 
cold.  If  the  air  immediately  after  compression,  before  the  loss  of  any  heat, 
was  used  in  an  air  engine  and  there  perfectly  expanded  back  to  atmospheric 
pressure,  it  would,  on  being  exhausted,  have  the  same  temperature  it  had 
before  compression,  and  its  efficiency  would  be  100%. 

But  the  loss  of  heat  after  compression  and  before  use  cannot  be  prevented, 
as  the  air  is  exposed  to  such  very  large  radiating  surfaces  in  the  reservoir  and 
pipes,  on  its  passage  to  the  air  engine.  The  heat  that  escapes  in  this  way, 
did,  while  in  the  compressing  cylinder,  add  much  to  the  resistance  of  the  air 
to  compression,  and  as  it  is  sure  to  escape,  at  some  time,  either  in  reservoir 
or  pipes,  the  best  plan  is  to  remove  it  as  fast  as  possible  from  the  cylinder  and 
thus  remove  one  element  of  resistance.  Hence,  compressors  are  almost  uni- 
versally provided  with  cooling  attachments  more  or  less  perfect  in  their  action, 
the  aim  being  to  secure  isothermal  compression,  or  compression  having  equal 
temperature  throughout. 

If  air  compressed  isothermally  is  used  with  perfect  expansion  and  the  fall 
of  temperature  during  expansion  is  prevented,  100%  efficiency  will  be  obtained. 
But  air  will  grow  cold  when  expanded  in  an  engine,  hence  warming  attach- 
ments have  the  same  economic  place  on  an  air  engine  that  cooling  attachments 
have  on  an  air  compressor.  In  fact,  attachments  of  this  kind  are  found  in 
large  and  permanently  located  engines,  but  their  use  on  most  of  the  engines 
for  mine  work  is  dispensed  with,  and  the  engines  expand  the  air  adiabatically, 
or  without  receiving  heat. 

The  practical  engineer,  therefore,  has  to  deal  with  nearly  isothermal  com- 
pression, and  nearly  adiabatic  expansion,  and  must  also  consider  that  the  air 
in  reservoirs  and  pipes  becomes  of  the  same  temperature  as  surrounding  objects. 
Consideration  must  also  be  had  for  the  friction  of  the  compressor  and  the  air 
engine.  For  the  pressure  of  60  lb.,  which  is  that  most  commonly  used,  the 
decrease  in  resistance  to  compression  secured  by  the  cooling  attachments 
is  almost  exactly  equaled  by  the  friction  of  the  compressor.  Hence  it  is  safe, 
when  calculating  the  efficiency  of  the  air  engine,  to  consider  the  compressor 
as  being  without  cooling  attachments,  and  also  as  working  without  friction. 
The  results  of  such  calculations  will  be  too  high  efficiencies  for  light  pressures, 
which  are  little  used;  about  correct  for  medium  pressures,  which  are  com- 
monly employed;  and  too  low  for  higher  pressures,  and  will  thus  have  the 
advantage  of  not  being  overestimated.  This  result  is  occasioned  by  the  fact 
that,  owing  to  the  slight  heat  in  compressing  low  pressures  of  air,  the  saying 
of  power  by  the  cooling  attachments  is  not  equal  to  the  friction  of  the  machine, 
but  at  high  pressures,  on  account  of  the  great  heat,  the  cooling  attachments 
are  of  great  value  and  save  very  much  more  power  than  friction  consumes. 

In  'expanding  engines,  the  expansion  never  falls  as  low  as  the  adiabatic 
law  would  indicate,  owing  to  a  number  of  reasons,  but  if  the  expansion  is  con- 
sidered as  adiabatic,  an  error  in  calculations  caused  thereby  will  be  on  the  safe 
side  and  the  actual  power  will  exceed  the  calculated  power.  Therefore,  the 
compressor  and  engine  may  be  considered  as  following  the  adiabatic  law  of 
compression  and  expansion,  and  as  working  without  friction. 

With  this  view  of  the  case,  the  efficiency  of  an  air  engine,  working  with 
perfect  expansion,  stated  in  percentages  of  the  power  required  to  operate 
the  compressor,  can  be  placed  as  here  shown  for  the  various  pressures  above  the 
atmosphere.  As  the  efficiencies  for  the  lower  pressures  are  very  much  greater 
than  for  the  high  pressures,  the  conclusion  is  almost  irresistible  that  to  secure 
economical  results  air  engines  should  be  designed  to  run  with  light  pressures. 

Pressure  Above  T? #•  • 

Atmosphere  Efficiency 

Pounds  PerCent- 

2.9  94.85 

14.7  81.79 

29.4  72.72 

44.1  66.90 
.58.8  62.70 

73.5  59.48 

88.2  56.88 


480  COMPRESSED  AIR 

In  the  foregoing  the  pipe  friction  has  been  entirely  neglected.  A  pressure 
of  2.9  Ib.  is  credited  with  an  efficiency  of  94.85%;  but,  if  the  air  were  con- 
veyed through  a  pipe,  and  the  length  of  the  pipe  and  the  velocity  of  flow 
were  such  that  2.9  Ib.  pressure  was  lost  in  friction,  the  efficiency  of  the  air, 
instead  of  being  94.85%,  would  be  absolutely  zero.  It  is  the  power  that  can  be 
obtained  from  the  air,  after  it  has  passed  the  pipe  and  lost  a  part  of  its  pressure 
by  friction,  that  must  be  considered  when  the  efficiency  of  an  apparatus  is  given. 

The  foregoing  table  of  efficiencies  with  a  loss  of  2.9  Ib.  in  the  pipe,  now  gives 
different  values  for  the  efficiencies  at  the  various  pressures. 

Pressure  Above  Efficiency 


2.9  00.00 

14.7  70.44 

29.4  68.81 

44.1  64.87 

58.8  61.48 

73.5  58.62 

88.2  56.23 

It  will  be  noticed  that  the  light  pressures  have  lost  most  by  the  pipe  fric- 
tion, 2.9  Ib.  having  lost  100%;  14.7  Ib.  11%,  and  88.2  Ib.  only  a  trifle  over  one- 
half  of  1%.  It  is  also  seen  now  14.7  Ib.  is  apparently  the  economical  pressure  to 
use.  But  a  further  careful  analysis  of  the  subject  shows,  that  when  the  loss  in 
the  pipe  is  2.9  Ib.,  then  20.5  Ib.  is  the  most  economical  pressure  to  use,  and  that 
the  efficiency  is  71%.  But  2.9  Ib.  is  a  very  small  loss  between  compressor  and 
air  engine,  and  cases  are  extremely  exceptional  where  the  friction  of  valves, 
pipes,  elbows,  ports,  etc.  does  not  far  exceed  this.  Yet,  with  these  conditions, 
which  are  very  difficult  to  fill,  20.5  Ib.  is  the  lightest  pressure  that  should  prob- 
ably ever  be  used  for  conveying  power,  and  71%  is  an  efficiency  scarcely  to  be 
obtained. 

Continuing  the  investigation  and  taking  examples  where  the  pipe  friction 
amounts  to  5.8  Ib.,  it  is  found  that  the  following  efficiencies  correspond  to  the 
stated  pressure: 

Pressure  Above  77  «,-,•„„,. 

Atmosphere  Efficiency 

Pounds  PerCenL 

14.7  57.14 

29.4  64.49 

44.1  62.71 

58.8  60.12 

73.5  57.73 

88.2  55.59 

As  friction  increases,  or,  in  other  words,  when  more  air  is  used  and  greater 
demands  are  made  on  the  carrying  capacity  of  the  pipe,  the  pressure  "must  be 
greatly  increased  to  attain  the  most  economical  results.  If  the  demands  are 
such  as  to  increase  the  friction  and  loss  in  pipe  to  14.7  Ib.,  the  air  of  14.7  Ib. 
pressure  at  the  compressor  is  entirely  useless  at  the  air  engine.  The  table  will 
therefore  stand  thus  : 

Pressure  Above  77  ./r  •  „- 

Atmosphere  Efficiency 

Pounds  Per  Cent' 

14.7  00.00 

29.4  48.53 

44.1  55.13 

58.8  55.64 

73.5  54.74 

88.2  53.44 

It  is  to  be  noticed  that  88.2  Ib.  pressure  has  lost  only  about  3?%  of  its 
efficiency  by  reason  of  as  high  a  friction  as  14.7  Ib.,  while  the  efficiency  of  the 
lower  pressures  has  been  greatly  affected.  As  the  friction  increases  the  most 
efficient,  and  consequently,  most  economical,  pressure  increases.  In  fact,  for 
any  given  friction  in  a  pipe,  the  pressure  at  the  compressor  must  not  be  carried 
below  a  certain  limit.  The  following  table  gives  the  lowest  pressures  that  should 
be  used  at  the  compressor,  with  varying  amounts  of  friction  in  the  pipe: 


COMPRESSED  AIR  481 

«**» 


Pounds  Per  Cent' 

2.9  20.5  70.92 

5.8  29.4  64.49 

8.8  38.2  60.64 

11.7  47.0  57.87 

14.7  52.8  55.73 

17.6  61.7  53.98 

20.5  70.5  52.52 

23.5  76.4  51.26 

26.4  82.3  50.17 

29.4  88.2  49.19 

So  long  as  the  friction  of  the  pipe  equals  the  amounts  there  given,  an 
efficiency  greater  than  the  corresponding  sums  stated  in  the  table  cannot  be 
expected.  In  a  case  that  corresponds  to  any  of  those  cited  in  the  table,  the 
efficiency  can  be  increased  only  by  reducing  the  friction.  An  increase  in  the 
size  of  pipe  will  reduce  friction  by  reason  of  the  lower  velocity  of  flow  required 
for  the  same  amount  of  air.  But  many  situations  will  not  admit  of  large  pipes 
being  employed,  owing  to  considerations  of  economy  outside  of  the  question 
of  fuel  or  prime  motor  capacity. 

An  increase  of  pressure  will  decrease  the  bulk  of  air  passing  in  the  pipe,  and 
in  that  proportion  will  decrease  its  velocity.  This  will  decrease  the  loss  by 
friction,  and,  as  far  as  that  goes,  a  gain  is  obtained,  but  there  is  a  new  loss, 
and  that  is  the  diminishing  efficiencies  of  increasing  pressures.  Yet  as  each 
cubic  foot  of  air  is  at  a  higher  pressure,  and,  therefore,  carries  more  power, 
as  many  cubic  feet  will  not  be  needed  for  the  same  work.  It  is  obvious  that 
with  so  many  sources  of  gain  or  loss  the  question  of  selecting  the  proper  pres- 
sure is  not  to  be  decided  hastily. 

As  an  illustration  of  the  combined  effect  of  these  different  elements,  a  very 
common  case  will  be  taken.  ^  The  compressor  makes  102  rev.  per  min.,  pres- 
sure is  52.8  lb.,  loss  in  pipe  is  14.7  lb.,  machine  in  mine  running  at  38.2  lb., 
efficiency  is  55.73%.  As  long  as  the  friction  of  the  pipe  amounts  to  14.7  lb., 
52.8  lb.  is  the  best  pressure  and  55.73%  the  greatest  efficiency,  but  friction 
may  be  reduced  by  reducing  the  bulk  of  air  passing  through  the  pipe  and  if 
the  cylinder  of  the  air  engine  is  reduced  until  it  requires  47  lb.  pressure  to  do 
the  same  work  as  before;  the  friction  of  pipe  will  then  drop  to  11.7  lb.  The 
pressure  on  the  compressor  will  rise  to  58.8  lb.,  its  number  of  revolutions  will 
fall  to  100,  and  the  resulting  efficiency  will  be  57.22%. 

Another  change  of  pressure  on  compressor  to  64.7  lb.  will  decrease  its  revo- 
lutions to  93,  friction  to  8.8  lb.,  and  its  efficiency  will  rise  to  57.94%.  If  the 
pressure  is  increased  to  73.5  lb.,  there  will  be  only  84  revolutions  of  compressor, 
5.8  lb.  loss  in  pipe,  and  an  efficiency  of  57.73%.  In  this  last  case  the  efficiency 
begins  to  fall  off  a  little,  and  higher  pressures  will  show  less  efficiency;  but,  in 
comparison  with  the  first  example,  the  same  work  will  be  done  with  a  trifle  less 
power  and  with  a  decrease  of  nearly  20%  in  the  speed  of  the  compressor. 

Other  common  examples  can  be  shown  where  an  increase  of  pressure  would 
result  in  wonderful  increase  in  efficiency  and  economy.  There  are  many  cases 
where  light  pressures  and  high  velocity  in  the  pipe  will  convey  a  given  power 
with  greater  economy  than  higher  air  pressures  and  lower  speed  of  flow  through 
the  pipe.  But  these  cases  arise  mostly  when  the  higher  air  pressures  become 
very  much  greater  than  are  at  present  in  common  use.  Therefore,  when  esti- 
mating the  efficiency  of  the  complete  outfit,  it  is  found  that  the  pipe  and  the 
pressure  are  very  important  elements,  and  must  be  determined  with  care  and 
skill  to  secure  the  most  satisfactory  results.  As  the  volume  and  power  of  air 
vary  with  its  pressure,  the  size  and  consequent  cost  of  compressor  for  a  certain 
work  will  also  be  affected  by  the  pressure.  To  plan  an  outfit  for  a  mine,  due 
regard  must  be  had  to  the  cost  of  fuel  or  prime  motor  power,  and  also  to  the 
cost  of  compressor,  pipes,  and  machinery,  as  the  saving  in  one  is  often  secured 
by  a  sacrifice  in  the  other. 

Next  to  determining  the  size  of  pipe,  the  skilful  engineer  has  need  of  fur- 
ther care  in  the  proper  position  of  reservoirs,  branches,  drains,  and  other 
attachments,  as  only  by  the  exercise  of  good  judgment  in  this  can  satisfactory 
working  be  secured.  The  fact  that,  on  account  of  the  diminished  density  of 
the  atmosphere  at  high  altitudes,  air  compressors  do  not  give  the  same  results 
as  at  sea  level,  should  also  be  taken  into  consideration  when  a  compressor  is  to 
be  installed  in  a  mountainous  region. 
31 


482  COMPRESSED  AIR 

LOSS  OF  PRESSURE,  IN  POUNDS  PER  SQUARE  INCH,  BY 
FLOW  OF  AIR  IN  PIPES  1,000  FT.  LONG 


Velocity 

J 

of  Air  at 
Entrance 

1-In.  Pipe 

2-In.  Pipe 

2^-In.  Pipe 

to  Pipe 

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23 

29 

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41 

2 

6.56 

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12 

15 

.3050 

46 

59 

.2562 

65 

82 

3 

9.84 

1.4545 

18 

22 

.7216 

69 

88 

.5818 

97 

124 

4 

13.12 

2.5620 

24 

29 

1.2566 

93 

117 

1.0248 

130 

165 

5 

16.40 

3.9345 

29 

37 

1.9642 

116 

146 

1.5738 

163 

207 

6 

19.68 

5.4225 

35 

44 

2.7120 

139 

175 

2.1690 

195 

247 

8 

26.24 

10.2480 

47 

59 

5.0264 

185 

234 

4.0992 

260 

330 

10 

32.80 

15.7380 

59 

74 

7.8568 

232 

294 

6.2952 

326 

413 

l 

3-In.  Pipe 

4-In.  Pipe 

5-In.  Pipe 

1 

3.28 

.0463 

48 

60 

.0347 

86 

109 

.0287 

134 

169 

2 

6.56 

.2092 

96 

121 

.1525 

172 

217 

.1281 

268 

239 

3 

9.84 

.4880 

144 

182 

.3608 

258 

326 

.2909 

402 

509 

4 

13.12 

.8381 

193 

243 

.6283 

343 

436 

.5124 

537 

678 

5 

16.40 

1.3176 

241 

304 

.9821 

429 

544 

.7869 

671 

844 

6 

19.68 

1.8080 

289 

364 

1.3560 

515 

653 

1.0845 

805 

1,017 

8 

26.24 

3.3525 

386 

486 

2.5132 

687 

871 

2.0496 

1,073 

1,357 

10 

32.80 

5.2704 

480 

607 

3.9284 

859 

1,088 

3.1476 

1,342 

1,696 

6-In.  Pipe 

8-In.  Pipe 

10-In.  Pipe 

1 

3.28 

.0232 

193 

244 

.0173 

343 

434 

.0143 

537 

680 

2 

6.56 

.1046 

386 

488 

.0762 

687 

864 

.0640 

1,073 

1,359 

3 

9.84 

.2440 

579 

633 

.1805 

1,030 

1,303 

.1455 

1,610 

2,039 

4 

13.12 

.4190 

772 

977 

.3141 

1,373 

1,736 

.2562 

2,146 

2,719 

5 

16.40 

.6588 

965 

1,221 

.4910 

1,717 

2,171 

.3934 

2,683 

3,399 

6 

19.68 

.9040 

1,158 

1,466 

.6780 

2,060 

2,605 

.5423 

3,220 

4,079 

8 

26.24 

1.6762 

1,544 

1,954 

1.2556 

2,747 

3,473 

1.0248 

4,293 

5,438 

10 

32.80 

2.6352 

1,931 

2,443 

1.9642 

3,434 

4,342 

1.5738 

5,367 

6,798 

Friction  of  Air  in  Pipes. — Air  in  its  passage  through  pipes  is  subject  to 
friction  in  the  same  manner  as  water  or  any  other  fluid;  therefore,  the  pressure 
at  the  compressor  must  be  greater  than  at  the  point  of  consumption,  m  order 
to  overcome  this  resistance.  The  power  that  is  needed  to  produce  the  extra 


COMPRESSED  AIR  483 

pressure  representing  the  friction  of  the  pipe  is  lost,  as  there  can  be  no  useful 
return  for  it.  The  friction  is  affected  by  very  many  circumstances;  it  is 
increased  in  direct  proportion  to  the  length  of  the  pipe  and  also  in  the  square 
of  the  velocity  of  the  flow  of  air.  The  pressure  of  the  air  does  not  affect  it. 

The  losses  by  friction  may  be  quite  serious  if  the  piping  system  is  poorly 
designed,  and,  on  the  other  hand,  extravagant  expenditure  in  pipe  may  result 
from  a  timid  overrating  of  the  evils  of  friction.  A  thorough  knowledge  of  the 
laws  governing  the  whole  matter,  as  well  as  a  ripe  experience,  is  necessary  to 
secure  true  economy  and  mechanical  success.  The  loss  of  power  in  pipe 
friction  is  not  always  the  most  serious  result.  When  a  number  of  machines 
are  in  use  in  a  mine,  and  the  pipes  are  so  small  as  to  cause  considerable  loss  of 
pressure  by  friction,  there  will  be  sudden  and  violent  fluctuations  in  pressure 
whenever  a  machine  is  started  or  stopped.  Breakages  will  be  common  occur- 
rences, as  the  changes  are  too  quick  to  be  entirely  guarded  against  by  the 
attendant;  perfectly  even  pressure  at  the  compressor  is  no  safeguard  against 
this  class  of  accidents.  The  trouble  arises  in  the  pipe,  and  the  remedy  must 
be  applied  there.  A  system  of  reservoirs  and  governing  valves  will  regulate 
these  matters  and  allow  successful  work  to  be  done  with  pipes  that  would 
otherwise  be  entirely  inadmissible. 

The  ordinary  formulas  for  calculating  the  volume  of  air  transmitted  through 
a  pipe  do  not  take  into  account  the  increase  of  volume  due  to  reduction  of 
pressure,  i.  e.,  loss  of  head.  To  transmit  a  given  volume  of  air  at  a  uniform 
velocity  and  loss  of  pressure,  it  is  necessary  to  construct  the  pipe  with  a  gradu- 
ally increasing  area.  This,  of  course,  is  impracticable,  and  in  a  pipe  of  uniform 
section  both  volume  and  velocity  must  increase  as  the  pressure  is  reduced  by 
friction.  The  loss  of  head  in  properly  proportioned  pipes  is  so  small,  how- 
ever, that  in  practice  the  increase  in  volume  is  usually  neglected.  The  table 
on  page  482  gives  the  loss  of  pressure  by  flow  of  air  in  pipes  calculated  for 
pipes  1,000  ft.  long;  for  other  lengths,  the  loss  varies  directly  as  the  length. 

The  resistance  is  not  varied  by  the  pressure,  only  so  far  as  changes  in  pres- 
sure vary  the  velocity.  It  increases  about  as  the  square  of  the  velocity,  and 
directly  as  the  length.  Elbows,  short  turns,  and  leaks  in  pipes  all  tend  to 
reduce  the  pressure  in  addition  to  the  losses  given  in  the  table.  An  elbow 
with  a  radius  of  one-half  the  diameter  of  the  pipe  is  as  short  as  can  be  made. 

LOSS  BY  FRICTION  IN  ELBOWS 

Radius  of  Elbow  Equivalent  Length  of  Straight  Pipe 

Diameters  Diameters 

5  •          7.85 

3  8.24 

2  9.03 

1*  10.36 

H  12.72 

17.51 

a  35.09 

121.20 


DESIGN,  OPERATION,  AND  INSTALLATION  OF  AIR 
COMPRESSORS 

With  regard  to  the  design,  installation,  and  operation  of  air  compressors, 
the  following  suggestions  made  by  Mr.  Alex.  M.  Gow,  Mechanical  Engineer, 
Oliver  Iron  Mining  Co.,  and  slightly  enlarged,  will  be  of  interest. 

Design  for  Avoiding  Explosions. — Clearance  space  should  be  reduced  to  a 
minimum.  Ingoing  air  should  traverse  as  small  a  surface  of  hot  metal  as 
possible.  Discharge  valves  and  passageways  should  contain  no  pockets  or 
recesses  for  the  accumulation  of  oil.  Cylinders  and  heads  should  be  water- 
jacketed;  in  some  cases  piston  water-cooling  may  be  resorted  to.  Stage  com- 
pression, with  adequate  intercooling  should  be  employed  wherever  final 
pressure  and  first  cost  of  installation  will  warrant.  Discharge  valves  must  be 
easy  of  access  for  cleaning  and  examination.  There  must  be  no  excuse  for 
dirty  or  leaky  valves. 

Installation  of  Compressor. — Air  should  be  drawn  from  the  coolest  and 
cleanest  place  possible,  and  never  from  the  engine  room.  _  Engine-room  air  is 
never  cool  nor  clean  and  an  open  intake  is  a  constant  invitation  to  squirt  oil 
in  from  a  can.  Around  collieries,  it  is  well  to  consider  the  washing  of  the  air. 
Coal  dust  drawn  in  with  the  air,  mixes  with  the  oil  and  forms  a  substance  that, 


484  ELECTRICITY 

on  heating,  cakes  and  may  take  fire.  The  discharge  pipe  should  be  of  ample 
size  and  have  as  few  bends  as  possible.  A  thermometer,  preferably  recording, 
should  be  placed  on  the  discharge  pipe.  Provision  for  aftercooling  should  be 
made,  a  water  spray  will  answer,  to  be  used  when  the  thermometer  indicates 
the  necessity.  The  receiver  should  be  provided  with  a  manhole  for  cleaning, 
and  a  drain  easy  of  access  and  ample  in  size.  Automatic  sight-feed  lubricators 
should  be  depended  on  f9r  regular  lubrication,  but  in  addition  an  oil  pump 
may  be  installed  for  the  introduction  of  soap  and  water  in  case  of  necessity. 

Operation  of  Compressors. — High  flash-test  cylinder  oil  of  the  best  obtain- 
able grade  should  be  used  for  regular  lubrication  of  the  air  cylinders.  Mr. 
L.  A.  Christian  advises  that  the  flash  point  be  625°  F.,  and  that  the  oil  should 
be  comparatively  free  from  unnecessary  volatile  carbon  compounds.  Volatile 
hydrocarbons  tend  to  reduce  the  flash  point,  and,  mixing  with  the  dust  from  the 
air,  form  combustible  deposits  in  the  receiver  and  outlet  passages.  Further, 
oil  of  low-flash  test,  on  reaching  the  interior  of  the  heated  air  cylinder  will  be 
vaporized  and  will  pass  out  with  the  air  into  the  receiver  without  affording  any 
lubrication  to  the  wearing  surfaces.  If  the  oil  is  too  dense  or  is  compounded 
with  animal  or  vegetable  oils,  as  is  the  case  with  many  steam-cylinder  oils,  it 
will  have  a  tendency  to  adhere  to  the  discharge  valves  and  passages,  and, 
being  subjected  to  the  dry  heat  of  the  compressed  air,  will  gradually  change  to 
a  hard,  brittle  crust,  which  in  time  will  completely  choke  up  the  air  passages 
or  will  prevent  the  valves  seating.  The  amount  of  oil  to  be  fed  into  the  air 
cylinder  should  be,  if  the  machine  makes  less  than  120  rev.  per  min.,  about 
1  drop  every  3  min.  Kerosene  should  never  be  used  to  cut  or  eat  away  deposits 
of  carbon,  as  is  sometimes  done,  as  its  flash  point  is  about  120°  F.  If  the 
cylinders  or  air  passages  need  cleaning,  soapsuds  made  of  1  part  of  soft  soap  and 
15  parts  of  pure  water  should  be  fed  into  the  cylinder  and  the  machine  worked 
with  a  liberal  solution  instead  of  oil  for  a  few  hours  or  a  day ;  then  the  blow-off 
valve  of  the  receiver  should  be  opened  and  the  accumulation  of  oil  and  water 
drained  off.  After  this  treatment  and  before  the  machine  is  shut  down,  oil 
should  be  fed  into  the  cylinder  for  an  hour  or  so,  in  order  that  the  valves  and  the 
parts  connected  with  the  cylinder  may  be  coated  with  oil  and  thus  prevent  rust. 

Discharge  valves  must  be  kept  tight;  to  this  end  the  use  of  the  steam 
engine  indicator  is  advised.  The  cards  may  not  tell  much  about  the  conditions 
of  the  valves,  but  one  of  the  greatest  values  of  the  indicator  is  the  moral  effect 
upon  the  engineer.  The  valves  should  be  cleaned  from  dust  and  oil  and  fre- 
quently examined. 

Accumulations  of  water  and  oil  must  be  blown  from  the  receiver  and  an 
internal  examination  made  at  stated  intervals. 

The  thermometer  on  the  discharge  pipe  should  be  watched  like  the  steam 
gauge.  Before  it  reaches  400°  F.,  the  after  cooling  spray  should  be  put  on,  and 
all  the  water-supply  pipes  and  the  discharge  valves  examined. 

The  engineer  in  charge  should  be  thoroughly  instructed  as  to  the  possibility 
of  an  explosion,  the  dangers  attendant  upon  the  use  of  any  but  the  prescribed 
oil,  and  the  effect  of  leaky  discharge  valves.  He  should  be  instructed  in  the 
use  of  the  steam-engine  indicator  and  required  to  submit  cards  at  stated 
intervals.  He  should  record  in  the  engine-room  log  the  daily  conditions  of  the 
machines  under  his  charge.  He  should  be  given  a  wholesome  respect  for  an 
air  compressor,  with  imperative  instructions  to  keep  it  clean,  inside  as  well 
as  out. 


ELECTRICITY 


PRACTICAL  UNITS 

In  electric  work,  it  is  necessary  to  have  units  in  terms  of  which  to  express 
the  different  quantities  entering  into  calculations.  The  unit  quantity  of  elec- 
tricity ftowing  through  a  circuit  is  called  a  coulomb.  A  coulomb  is  the  quantity 
of  electricity  that  will  deposit  from  a  solution  of  silver  nitrate  through  which 
it  flows  .U01118  gram  of  silver. 

Strength  of  Current. — The  strength  of  current  flowing  in  a  wire  may  be 
measured  in  several  ways.  If  a  compass  needle  is  held  under  or  over  a  wire 
it  will  be  deflected  and  will  tend  to  stand  at  right  angles  to  the  wire.  The 
stronger  the  current,  the  greater  is  the  deflection  of  the  needle.  If  the  wire 
carrying  the  current  is  cut  and  the  end  dipped  into  a  solution  of  silver  nitrate, 


ELECTRICITY  485 

silver  will  be  deposited  on  the  end  of  the  wire  toward  which  the  current  is 
flowing,  and  the  amount  of  silver  deposited  in  a  given  time  will  be  directly 
proportional  to  the  average  strength  of  current  flowing  during  that  time. 
When  the  current  flowing  in  a  wire  is  spoken  of,  the  strength  of  the  current  is 
meant. 

The  unit  used  to  express  the  strength  of  a  current  is  called  the  ampere. 
If  a  current  of  1  amp.  be  sent  through  a  bath  of  silver  nitrate,  .001118  g.  per  sec. 
of  silver  will  be  deposited.  The  expression  of  the  flow  of  current  through  a  wire 
as  so  many  amperes  is  analogous  to  the  expression  of  the  flow  of  water  through 
a  pipe  as  so  many  gallons  per  second.  If  1  amp.  flows  through  a  circuit  for 
1  sec.,  the  quantity  of  electricity  that  has  passed  through  the  circuit  during 
the  1  sec.  is  1  coulomb;  that  is,  1  coulomb  is  equal  to  1  amp.  for  1  sec. 

Electromotive  Force. — In  order  that  a  current  may  flow  through  a  wire, 
there  must  be  an  electric  pressure  of  some  kind  to  cause  the  flow.  In  hydraulics, 
there  must  always  be  a  head  or  pressure  before  water  can  be  made  to  flow 
through  a  pipe.  It  is  also  evident  that  there  may  be  a  pressure  or  head  without 
there  being  any  flow  of  water,  because  the  opening  in  the  pipe  might  be  closed; 
the  pressure  will,  however,  exist,  and,  as  soon  as  the  valve  closing  the  pipe  is 
opened,  the  current  will  flow.  In  the  same  way,  an  electric  pressure  or  electro- 
motive force  (often  written  E.  M.  F.)  may  exist  in  a  circuit,  but  no  current 
can  flow  until  the  circuit  is  closed  or  until  the  wire  is  connected  so  that  there 
will  be  a  path  for  the  current. 

The  practical  unit  of  electromotive  force  is  the  volt.  It  is  the  unit  of  elec- 
tric pressure,  and  fulfils  somewhat  the  same  purpose  as  head  of  water  and  steam 
pressure  in  hydraulic  and  steam  engineering.  The  electromotive  force  fur- 
nished by  an  ordinary  cell  of  a  battery  usually  varies  from  .7  to  2  volts.  A 
Daniell  cell  gives  an  electromotive  force  of  1.072  volts.  A  pressure  of  500  volts 
is  generally  used  for  street-railway  work,  and,  for  incandescent  lighting,  110 
volts  is  common. 

Resistance  — All  conductors  offer  more  or  less  resistance  to  the  flow  of  a 
current  of  electricity,  just  as  water  encounters  friction  in  passing  through  a 
pipe.  The  amount  of  this  resistance  depends  on  the  length  of  the  wire,  the 
diameter  of  the  wire,  and  the  material  of  which  the  wire  is  composed.  The 
resistance  of  all  metals  also  increases  with  the  temperature. 

The  practical  unit  of  resistance  is  the  ohm.  A  conductor  has  a  resistance 
of  1  ohm  when  the  pressure  required  to  set  up  1  amp.  through  it  is  1  volt.  In 
other  words,  the  drop,  or  fall,  in  pressure  through  a  resistance  of  1  ohm,  when 
a  current  of  1  ampere  is  flowing,  is  1  volt.  1,000  ft.  of  copper  wire  .1  in.  in 
diameter  has  a  resistance  of  nearly  1  ohm  at  ordinary  temperatures. 

Ohm's  Law. — The  law  governing  the  flow  of  current  in  an  electric  circuit 
was  first  stated  by  Dr.  G.  S.  Ohm,  and  is  known  as  Ohm's  law.  It  may  be 
briefly  stated  as  follows:  The  strength  of  the  current  in  any  circuit  is  equal  to 
the  electromotive  force  divided  by  the  resistance  of  the  circuit. 

Let  E  =  electromotive  force,  in  volts; 

R  =  resistance,  in  ohms; 
/  =  current,  in  amperes. 

Then,  /  =  !      R  =  j      E  =  IR 

EXAMPLE  1. — A  dynamo  D  generating  110  volts,  is  connected  to  a  coil  of 
wire  C  that  has  a  resistance  of  20  ohms;  what  .current  will  flow,  supposing  the 
resistance  of  the  rest  of  the  circuit  to  be  negligible? 

SOLUTION. — As  £  =  110  volts  and  R  =  20  ohms, 
by  Ohm's  law  7  =  110-:- 20  =  5.5  amp. 

EXAMPLE  2. — If  the  resistance  of  the  coil  C  is 
6  ohms,  what  electromotive  force  must  the  dynamo    (  j)  )E=110  Volts 

generate  in  order  to  set  up  a  current  of  15  amp.     V J  C 

through  it?  ' 

SOLUTION. — In  this  case  the  third  formula  will 
be  used;  that  is,  £  =  15X6  =  90  volts. 

In  case  the  current  and  electromotive  force  are  known,  the  resistance  of 
the  circuit  may  be  calculated  by  using  the  second  formula. 

EXAMPLE  3. — If  the  current  in  the  previous  examples  were  8  amp.  and  the 
electromotive  force  of  the  dynamo  110  volts,  what  is  the  resistance  of  the 
circuit? 

SOLUTION. —  1?  =  110-;- 8  =  13.75  ohms. 

Electric  Power. — The  electric  power  expended  in  any  circuit  is  found  by 
multiplying  the  current  flowing  in  the  circuit  by  the  pressure  required  to  force 


486 


ELECTRICITY 


the  current  through  the  circuit.  In  other  words,  W  =  EI,  where  W  is  the 
power  expended,  E  is  the  electromotive  force  and  /  is  the  current.  When  E 
is  expressed  in  volts  and  /  in  amperes,  then  W  is  expressed  in  watts.  The 
watt  is  the  unit  of  electric  power,  and  is  equal  to  the  power  developed  when 
1  amp.  flows  under  a  pressure  of  1  volt.  The  watt  is  equal  to  7j^  H.  P. 
Let  E  =  electronwtive  force,  in  volts; 

/  =  current,  in  amperes; 
R  =  resistance,  in  ohms; 
W= power,  in  watts;' 
H.  P.  =  horsepower. 

Then,  W=EI  =  PR  =  ^ 

The  energy  used  in  forcing  a  current  through  the  wire  reappears  in  the  form 
of  heat;  the  heating  effect  of  a  current  flowing  in  a  conductor  being  proportional 
to  the  square  of  the  current.  Furthermore, 

H'P'  =  746  =  746 

This  relation  is  very  useful  for  calculating  power  in  terms  of  electric  units. 
The  watt  is  too  small  a  unit  for  convenient  use  in^  many  cases,  so  that  the 
kilowatt  or  1,000  watts,  is  frequently  used.  This  is  sometimes  abbreviated 
to  K.  W. 

The  unit  of  work  is  the  watt-hour,  which  is  the  total  work  done  when  1  watt 
is  expended  for  1  hr.  For  example,  if  a  current  of  1  amp.  flows  for  1  hr.  through 
a  resistance  of  1  ohm,  the  total  amount  of  work  done  is  1  watt-hour.  A  kilo- 
watt-hour is  the  total  work  done  when  1  K.  W.  is  expended  for  1  hr.  It  is 
about  equivalent  to  If  H.  P.  for  1  hr.  The  work  done  when  1  watt  is  expended 
for  1  sec.  is  called  the  joule;  or  1  joule  is  expended  in  a  circuit  when  1  volt  causes 
1  amp.  to  pass  through  the  circuit  for  1  sec. 

ELECTRICAL  EXPRESSIONS  AND  THEIR  EQUIVALENTS 

(Arranged  for  Convenient  Reference  by  C.  W.  Hunt) 


Rate  of  doing  work 
1.            amp.  per  sec.  at 

Quantity  of  work 
2,654.28        ft.-lb. 

1  volt 

1TTT-  J.J. 

.503      mi.-lb. 

.7373    ft.-lb.  per  sec. 

Watt- 

T-Tnnp 

1.            amp.  hr.Xl 

1  Watt. 

44.238      ft.-lb.  per  min. 

riou.r 

volt 

2,654.28        ft.-lb.  per  hr. 

>:•/!"  v     ,- 

.00134  H.  P.-hr. 

.5027    mi.-lb.  per  hr. 

T&        H.  P.-hr. 

.00134  H.  P. 

[Quantity  of  work 

I                Tig            ±1.  r. 

{Rate  of  doing  work 
737.3    ft.-lb.  per  sec. 
44,238.      ft.-lb.  per  min. 
502.7    mi.-lb.  per  hr. 
1.34  H.  P. 
IRate  of  doing  work 
550.        ft.-lb.  per  sec. 
33,000.        ft.-lb.  per  min. 

1  Ampere- 
Hour       ' 

1,980,000.        ft.-lb. 
375.        mi.-lb. 
746.        watt-hr. 
.746  K.  W.-hr. 
[Quantity  of  current 
1  amp.  flowing  for  1  hr., 
irrespective  of  voltage 
Watt-hour  -j-  volts 

375.        mi.-lb.  per  hr. 

(  Force  moving  in  a  circle 

746.        watts 

Torque     < 

Force  of  1  Ib.  at  a  radius 

.746  K.  W.       • 

I     of  1  ft. 

CIRCUITS 

The  path  through  which  a  current  flows  is  generally  spoken  of  as  an  elec- 
tric circuit;  this  path  may  be  made  up  of  a  number  of  different  parts.  For 
example,  the  line  wires  may  constitute  part  of  the  circuit,  and  the  remainder 
may  be  composed  of  lamps,  motors,  resistances,  etc.  In  practice,  the  two 
kinds  of  circuits  most  commonly  met  with  are  those  in  which  the  different 
parts  of  the  circuit  are  connected  in  series  and  those  in  which  they  are  connected 
in  multiple  or  parallel. 

Series  Circuits. — In  a  series  circuit,  all  the  component  parts  are  connected 
in  tandem,  so  that  the  current  flowing  through  one  part  also  flows  through 
the  other  parts;  view  (a)  represents  such  a  circuit  made  up  of  a  different  number 


ELECTRICITY 


487 


of  parts.  The  current  leaves  the  dynamo  D  at  the  +  side  and  flows  through 
the  arc  lamps  a,  thence  through  the  incandescent  lamps  I,  thence  through  the 
motor  m  and  resistance  r,  back  to  the  dynamo,  thus  making  a  complete  cir- 
cuit. All  these  parts  are  here  connected  in  series,  so  that  the  current  flowing 
through  each  of  the  parts  must  be  the  same  unless  leakage  takes  place  across 
from  one  side  of  the  circuit  to  the  other,  and  this  is  not  appreciable  if  the  lines 
are  properly  insulated.  The  pressure  furnished  by  the  dynamo  must  evi- 
dently be  the  sum  of  the  pressures  required  to  force  the  current  through  the 
different  parts. 

The  most  common  use  of  this  system  is  in  connection  with  arc  lamps, 
which  are  usually  connected  in  series,  as  shown  in  (fc).     The  objections  to 


Trolley  Wire 


] this  system  of  distribution 

for  general  work  are  that 
6i       the  breaking  of  the  circuit 
at  any  point  cuts  off  the 
Ol       current  from  all  parts  of 
the  circuit;  also,  the  pres- 
1         sure  generated  by  the  dy- 
namo must  be  very  high 

(e)  if   many  pieces    of    appa- 

ratus are  connected  in 

series.  In  such  a  system,  the  dynamo  is  provided  with  an  automatic  regulator 
that  increases  or  decreases  the  voltage  of  the  machine,  so  that  the  current  in 
the  circuit  is  kept  constant,  no'  matter  how  many  lamps  or  other  devices  are 
in  operation.  For  this  reason,  such  circuits  are  often  spoken  of  as  constant- 
current  circuits. 

Parallel  Circuits. — In  a  parallel  circuit,  the  different  pieces  of  apparatus 
are  connected  side  by  side,  or  in  parallel,  across  the  main  wires  from  the  dynamo 
as  shown  in  (c).  In  this  case,  the  dynamo  D  supplies  current  through  the  mains 
to  the  arc  lamps  a,  incandescent  lamps  I,  and  motor  m.  This  system  is  more 
widely  used,  as  the  breaking  of  the  circuit  through  any  one  piece  of  apparatus 
will  not  prevent  the  current  from  flowing  through  the  other  parts.  Incan- 
descent lamps  are  connected  in  this  way  almost  exclusively.  The  lamps  are 
connected  directly  across  the  mains,  as  shown  in  (d).  Street  cars  and  mining 
locomotives  are  operated  in  the  same  way,  the  trolley  wire  constituting  one 
main  and  the  track  the  other,  as  shown  in  (e).  By  adopting  this  system,  any 
car  can  move  independently  of  the  others,  and  the  current  in  each  device 
may  be  turned  off  and  on  at  will  without  affecting  devices  in  other  parallel 
circuits.  In  all  these  systems  of  parallel  distribution,  the  pressure  generated 
by  the  dynamo  is  maintained  as  constant  as  practicable,  no  matter  what  cur- 
rent the  dynamo  may  be  delivering.  For  example,  in  the  lamp  system,  view  (d) , 
the  dynamo  will  maintain  a  constant  electromotive  force  of  110  volts.  Each 
lamp  has  a  fixed  resistance,  and  will  take  a  certain  current  (110  +  R  amperes) 
when  connected  across  the  mains.  As  the  lamps  are  turned  on,  the  current 
delivered  by  the  dynamo  increases,  the  pressure  remaining  constant.  In 
street-railway  work,  the  pressure  between  trolley  and  track  is  kept  in  the 
neighborhood  of  500  volts,  the  current  varying  with  the  number  of  cars  in 
operation.  In  mine-haulage  plants,  the  pressure  is  usually  250  or  500  volts, 
the  former  being  generally  preferred  as  being  less  dangerous.  Lamps  may  also 
be  connected  in  series  multiple,  as  shown  in  (e).  Here  the  two  125- volt  lamps  / 


488  ELECTRICITY 

are  connected  in  series  across  the  250-volt  circuit.     Such  an  arrangement  is 
frequently  used  in  mines  when  lamps  are  operated  from  the  haulage  circuit. 

Such  circuits  as  those  just  described  are  called  constant-potential  or  con- 
stant-pressure circuits,  to  distinguish  them  from  the  constant-current  circuit 
mentioned  previously.  _ 

RESISTANCES  IN  SERIES  AND  MULTIPLE 

Resistance  in  Lines.  —  If  two  or  more  resistances  are  connected  in  series, 
as  in  Fig.  1,  their  total  combined  resistance  is  equal  to  the  sum  of  their  sepa- 

rate  resistances.     If  R  equals 


tances  connected  in  series,  then, 
pIG.  1  R  =  Ri+R2+R3. 

For  example,  if  the  separate 

resistances  are  Ri  =  10  ohms,  Rz=l  ohm,  andJ?3  =  30  ohms,  the  three  combined 
will  be  equivalent  to  a  single  resistance  of  10  +  1+30  =  41  ohms. 

Resistances  in  Parallel.  —  If  a  number  of  resistances  are  connected  in  parallel, 
the  reciprocal  of  their  combined  resistance  is  equal  to  the  sum  of  the  reciprocals 
of  the  separate  resistances.  In  Fig.  2,  three  resis- 
tances are  shown  connected  in  parallel;  therefore,  the 
total  resistance  of  such  a  combination  must  be  lower 
than  that  of  the  lowest  resistance  entering  into  the 
combination.  If  the  resistances  in  this  case  were  all 
equal,  the  resistance  of  the  three  combined  would 
be  one-third  the  resistance  of  one  of  them,  because  — 

a     current    passing    through    the    three     combined 

could  split  up  equally  between  three  equal  paths,  instead  of  having  only 
one  path  to  pass  through.  If  R  represents  the  combined,  resistance, 
and  Ri,  Rz,  Rs,  and  Jfa,  the  separate  resistances,  the  following  relation 

is  true  for  any  number  of  resistances  in  parallel:     -^  =  -?r  +  ^  —  h^r+^r+etc. 

K     Ki     K.2     Ks     Kt 

from  which  R  =  ~^  -  ;  -  ;  -  ;  -  •     If  three  resistances  in  parallel  are 

E+S+S+J&+*'- 
13         „     #1 

^==^'orR=^- 

EXAMPLE.  —  Three  resistances  of  3,  10,  and  5  ohms  are  connected  in  par- 
allel; what  is  their  combined  resistance? 

SOLUTION.-        =    ++    or,  K  =  -  =      =  1.58  ohms. 


If  resistances  in  parallel  are  all  equal,  the  current  will  divide  equally 

through  them;  if  not  equal,  the  current  in  each  path  will  be  inversely  pro- 

_X_>O_-N  portional  to  the  resistance  of  the  path.     In  any 

—  r—  ^0000    -  1  —    case-  the  current  through  any  path  is  equal  to 

A  the  difference  of  potential  across  the  path  divided 

I      ^TWwWr^       *        by  its  resistance. 

UUWUU  Shunt.—  When  one  circuit  B,  Fig.   3,  is  con- 

„  nected    across    another    A,   so   as  to  form,  as  it 

^IG-  "  were,  a  by-pass,  or  side  track,  for  the  current, 

such  a  circuit  is  called  a  shunt,  or  it  is  said  to  be  in  shunt  with  the  other  circuit 


ELECTRIC  WIRING  (CONDUCTORS) 

Materials. — Practically  all  conductors  used  in  electric  lighting  or  power 
work  are  of  copper,  this  metal  being  used  on  account  of  its  low  resistance. 
Iron  wire  is  used  to  some  extent  for  conductors  in  telegraph  lines,  and  steel 
is  largely  used  as  the  return  conductor  in  electric-railway  or  haulage  plants 
where  the  current  is  led  back  to  the  power  station  through  the  rails.  The 
resistance  of  iron  or  steel  varies  from  six  to  seven  times  that  of  copper,  depend- 
ing on  the  quality  of  the  metal.  Aluminum  is  coming  into  use  in  electric 
transmission.  It  is  so  much  lighter  than  copper  that  it  is  able  to  compete 
with-it  as  a  conductor,  even  though  its  cost  per  pound  is  higher  and  its  con- 
ductivity only  about  60%  that  of  copper. 


ELECTRICITY 


489 


PROPERTIES  OF  ANNEALED  COPPER  WIRE;  AMERICAN,  OR 
BROWN  &  SHARPE,  GAUGE 


* 

^ 

Current 

* 

a 

Capacity 

<u 

m 

Weight 

National 

£f 

S 

a  ^ 

o 

Board  Fire 

Jo 

c 

3  1? 

oun 

T!1*  pc,' 

Underwriters 

N 

£ 

O 

P,  O  o 

Amperes 

£  <& 

§ 

S  o 

«  C 

, 

PQ 

5 

1 

g| 

fc.-S 

ll 

11 

• 

*! 

*E 

1~ 

!# 

&8 

0000 

460.00 

211,600.00 

641.0000 

3,380.000 

.0500 

312 

210 

000 

409.60 

167,805.00 

508.0000 

2,680.000 

.0630 

262 

177 

00 

364.80 

133,075.00 

403.0000 

2,130.000 

.0795 

220 

150 

0 

324.90 

105,534.00 

319.0000 

1,690.000 

.1000 

185 

127 

1 

289.30 

83,694.00 

253.0000 

1,340.000 

.1260 

156 

107 

2 

257.60 

66,373.00 

201.0000 

1,060.000 

.1590 

131 

90 

3 

229.40 

52,634.00 

159.0000 

841.000 

.2010 

110 

76 

4 

204.30 

41,742.00 

126.0000 

667.000 

.2530 

92 

65 

5 

181.90 

33,102.00 

100.0000 

529.000 

.3200 

77 

54 

6 

162.00 

26,251.00 

79.5000 

420.000 

.4030 

65 

46 

7 

144.30 

20,816.00 

63.0000 

333.000 

.5080 

8 

128.50 

16,509.00 

50.0000 

264.000 

.6410 

46 

33 

9 

114.40 

13,094.00 

39.6000 

209.000 

.8080 

10 

101.80 

10,381.00 

31.4000 

166.000 

1.0200 

32 

24 

11 

90.70 

8,234.00 

24.9000 

132.000 

1.2800 

12 

80.80 

6,529.90 

19.8000 

104.000 

1.6200 

23 

17 

13 

71.90 

5,178.40 

15.7000 

82.800 

2.0400 

14 

64.10 

4,106.80 

12.4000 

76.200 

2.5800 

16 

12 

15 

57.10 

3,256.70 

9.8600 

52.000 

3.2500 

16 

50.80 

2,582.90 

7.8200 

41.300 

4.0900 

8 

6 

17 

45.20 

2,048.20 

6.2000 

32.700 

5.1600 

18 

40.30 

1,624.30 

4.9200 

25.900 

6.5100 

5 

3 

19 

35.90 

1,288.10 

3.9000 

20.600 

8.2100 

20 

31.90 

1,021.50 

3.0900 

16.300 

10.4000 

21 

28.50 

810.10 

2.4500 

12.900 

13.1000 

22 

25.30 

642.40 

1.9400 

10.300 

16.5000 

23 

22.60 

509.40 

1.5400 

8.100 

20.8000 

24 

20.10 

404.00 

1.2200 

6.400 

•   26.2000 

25 

17.90 

.   320.40 

.9700 

5.100 

33.0000 

26 

15.90 

254.10 

.7690 

4.000 

41.6000 

27 

14.20 

201.50 

.6100 

3.200 

52.5000 

28 

12.60 

159.70 

.4840 

2.500 

66.2000 

29 

11.20 

126.70 

.3840 

2.000 

83.5000 

30 

10.00 

100.50 

.3040 

1.600 

105.0000 

31 

8.93 

79.70 

.2410 

1.270 

133.0000 

32 

7.95 

63.21 

.1910 

1.010 

167.0000 

33 

7.08 

50.13 

.1520 

.801 

211.0000 

34 

6.30 

39.75 

.1200 

.635 

266.0000 

35 

5.61 

31.52 

.0954 

.504 

336.0000 

36 

5.00 

25.00 

.0757 

.400 

423.0000 

37 

4.45 

19.83 

.0600 

.317 

533.0000 

38 

3.96 

15.72 

.0476 

.251 

673.0000 

39 

3.53 

12.47 

.0377 

.199 

848.0000 

40 

3.14 

9.89 

.0299 

.158 

1,070.0000 

i 

490  ELECTRICITY 

Most  of  the  conductors  used  are  in  the  form  of  copper  wire  of  circular 
cross-section.  Conductors  of  large  cross-section  are  made  up  of  a  number 
of  strands  of  smaller  wire  twisted  together.  For  electrolytic  plants,  copper- 
refining  plants,  etc.,  copper  bars  of  rectangular  cross-section  are  frequently 
used.  On  account  of  the  method  used  in  supporting  the  larger  sizes,  large 
trolley  wires  are  not  always  of  circular  cross-section. 

Wire  Gauge. — The  gauge  most  generally  used  in  America  to  designate 
the  different  sizes  of  copper  wire  is  the  American,  or  Brown  &  Sharpe  (B.  &  S.). 
The  sizes  as  given  by  this  gauge  range  from  No.  0000,  the  largest,  .460  in. 
diameter,  to  No.  40,  the  finest,  .003  in.  diameter.  Wire  drawn  to  the  sizes 
given  by  this  gauge  is  always  more  readily  obtained  than  sizes  according  to 
other  gauges;  hence,  when  selecting  wire  for  any  purpose  it  is  always  desirable, 
if  possible,  to  give  the  size  required  as  a  wire  of  the  B.  &  S.  gauge.  A  wire 
can  usually  be  selected  from  this  gauge,  which  will  be  very  nearly  that  required 
for  any  specified  case. 

The  diameter  of  round  wires  is  usually  given  in  the  tables  in  decimals  of 
an  inch  and  the  so-called  area  of  cross-section  is  given  in  terms  of  a  unit  called 
a  circular  mil.  This  is  done  simply  for  convenience,  as  it  makes  calculations 
involving  the  cross-section  much  simpler  than  if  the  square  inch  was  used  as 
the  unit  area.  A  mil  is  ^Vs  in.,  or  .001  in.  A  circular  mil  is  the  square  of 
the  diameter  of  a  wire  expressed  in  mils.  A  wire  having  a  diameter  of  1  in. 
has  a  sectional  area  of  .7854 XI2  =  .7854  sq.  in.,  and  is  said  to  have  a 
sectional  area  of  1,0002  =  1,000,000  circular  mils.  Hence,  the  area  of  cross- 
section  of  a  wire  in  circular  mils  is  equal  to  the  square  of  its  diameter  expressed 
in  mils.  CM  is  frequently  used  as  an  abbreviation  for  circular  mils. 

EXAMPLE. — A  wire  has  a  diameter  of  .101  in.;  what  is  its  area  in  circular  mils? 

SOLUTION.—     .101  in.  =  101  mils.     Hence,  (101)2  =  10,201  CM. 


CARRYING  CAPACITY  OF  COPPER  CABLES 


Area 

Current,  in  Amperes 

Area 

Current,  in  Amperes 

Mils 

Exposed 

Concealed 

Mils 

Exposed 

Concealed 

200,000 

299 

200 

1,200,000 

1,147 

715 

300,000 

405 

272 

1,300,000 

1,217 

756 

400,000 

503 

336 

1,400,000 

1,287 

796 

500,000 

595 

393 

1,500,000 

1,356 

835 

600,000 

682 

445 

1,600,000 

1,423 

873 

700,000 

765 

494 

1,700,000 

1,489 

910 

800,000 

846 

541 

1,800,000 

1,554 

946 

900,000 

924 

586 

1,900,000 

1,618 

981 

1,000,000 

1,000 

630 

2,000,000 

1,681 

1,015 

1,100,000 

1,075 

673 

COMPARISON  OF  PROPERTIES  OF  ALUMINUM  AND  COPPER 


Aluminum 

Copper 

Conductivity,  for  equal  sizes 

.54  to  .63 

1 

Weight,  for  equal  sizes 

33 

1 

Weight,  for  equal  length  and  resistance  .  . 
Price  of  bare  wire,  per  pound,  aluminum, 
29  o.;  copper,  16  c  
Price,  equal  length  and  resistance,  bare 
line  wire  

.48 
1.81 
868 

1 
1 
1 

Temperature  coefficient,  per  degree  F.  .  .  . 
Resistance  of  mil-foot,  at  20°  C. 

.002138 
18  73 

.002155 
10.5 

Specific  gravity  

2  5  to  2  68 

8  89  to  8  93 

Breaking  strength,  equal  sizes  

1 

1 

ELECTRICITY 


491 


The  table  on  page  489  gives  the  dimensions,  weight,  and  resistance  of 
annealed  copper  wire.  The  weights  given  are,  of  course,  for  bare  wire.  The 
first  column  gives  the  B.  &  S.  gauge  number,  the  second  the  diameter  in  mils. 
The  diameter  in  inches  will  be  the  number  given  in  this  column,  divided  by 
1,000.  The  third  column  gives  the  area  in  circular  mils,  the  numbers  in  this 
column  being  equal  to  the  squares  of  those  in  the  second  column.  The  safe 
carrying  capacity  is  also  given.  In  case  a  conductor  larger  than  that  given  in 
the  table  is  required,  stranded  cables  are  used;  these  are  made  in  various  sizes. 
The  first  table  on  page  490  gives  some  of  the  more  common  sizes  of  stranded 
copper  cables,  with  their  allowable  current  capacity,  while  a  comparison  of  the 
properties  of  aluminum  and  copper  is  given  in  the  second  table  on  page  490. 

Estimation  of  Resistance. — The  resistance  of  any  conductor  is  directly  pro- 
portional to  its  length,  and  inversely  proportional  to  its  area  of  cross-section, 

or  R  =  K  — ,  where  K  is  a  constant.     If  L  is  expressed  in  feet  and  A  is  expressed 

A 
in  circular  mils,  the  constant  K  must  be  the  resistance  of  1  ft.  of  the  wire  in 

BREAKING  STRENGTH  OF  COPPER  AND  ALUMINUM  WIRES 
AND  CABLES 


Breaking  Strain,  Pounds 

Wire 
Number 

Area 
Circular 

Copper,  Solid 

Aluminum 

B.  &S. 

Mils 

Gauge 

Annealed 

Hard- 
Drawn 

Solid 

Stranded 

0000 

211,600 

5,650 

8,310 

4,320 

6,830 

000 

167,805 

4,475 

6,580 

3,430 

5,420 

00 

133,079 

3,550 

5,226 

2,720 

4,290 

0 

105,592 

2,800 

4,558 

2,150 

3,410 

1 

83,695 

2,225 

3,746 

1,710 

2,700 

2 

66,373 

1,775 

3,127 

1,355 

2,143 

3 

52,634 

1,400 

2,480 

1,075 

1,700 

4 

41,743 

1,115 

1,967 

852 

1,350 

5 

33,102 

885 

1,519 

657 

1,070 

6 

26,251 

700 

1,237 

536 

850 

7 

20,817 

550 

980 

426 

8 

16,510 

440 

778 

337 

9 

13,094 

350 

617 

267 

10 

10,382 

275 

489 

212 

11 

8,234 

220 

388 

167 

12 

6,230 

175 

307 

133 

13 

5,178 

135 

244 

105 

14 

4,107 

110 

193 

84 

question  of  1  circular  mil  cross-section.     The  resistance  of  1  mil-ft.  of  copper 

wire  at  75°  P.  is  about  10.8  ohms.    Hence,  for  copper  wire,  R  =  — ~,  in  which  d 

a2 

is  the  diameter  in  mils.  This  formula  is  easily  remembered,  and  is  very  con- 
venient for  estimating  the  resistance  of  any  length  of  wire  of  given  diameter 
when  a  wire  table  is  not  at  hand,  9r  when  the  diameter  of  the  given  wire  does 
not  correspond  to  anything  given  in  the  table. 

EXAMPLE. — Find  the  resistance  of  1  mi.  of  copper  wire  .20  in.  in  diameter. 

SOLUTION.— 1  mi.  =  5,280  ft.;  .20  in.  =  200  mils,  or  40,000  C.  M.;  hence, 

10.8XL     10.8X5.280 
R  =  —^ 40,000      =L42ohms 

The  breaking  strengths  of  copper  and  aluminum  wires  and  cables  are  given 
in  the  preceding  table.  The  ultimate  strength  of  annealed  copper  is  taken 
as  34,000  Ib.  per  sq.  in.;  of  hard-drawn  copper,  as  60,000  Ib.  per  sq.  in.,  except 
that  for  Nos.  000  and  00  it  is  taken  at  50,000  Ib.,  for  No.  0  at  55,000  Ib., 
and  for  No.  1  as  57,000  Ib.  The  ultimate  strength  of  aluminum  is  taken  as 
26,000  Ib.  per  sq.  in.  The  table  gives  the  actual  breaking  strains  to  which 
a  suitable  factor  of  safety  must  be  applied  to  give  a  safe  working  load. 


492  ELECTRICITY 

CALCULATION  OF  WIRES  FOR  ELECTRIC 
TRANSMISSION 

Direct-Current  Circuits. — No  matter  how  large  a  wire  may  be,  some  energy 
must  always  be  expended  in  forcing  a  current  through  it,  because  no  con- 
ductor can  be  entirely  devoid  of  resistance.  It  is  true  that  the  loss  may  be 
made  as  small  as  desired  by  using  a  very  large  conductor,  but  in  practice  this 
will  not  pay,  because  the  interest  on  the  cost  of  the  copper  will  more  than 
counterbalance  the  gain  in  the  efficiency  of  transmission.  In  starting  out,  then, 
to  estimate  the  size  of  wire  to  transmit  a  given  amount  of  power  over  a  given 
distance,  one  of  the  first  things  to  be  decided  is  the  amount  of  power  that  may 
be  allowed  for  loss  in  the  line,  because  the  greater  the  power  lost  the  higher 
may  be  the  line  resistance,  and  hence  the  smaller  the  wire.  The  pressure 
required  to  force  a  current  I  through  a  wire  of  a  resistance  R  is  IXR.  This 
pressure  is  generally  spoken  of  as  the  drop,  for  the  reason  that  the  pressure 
necessary  to  set  up  the  current  through  the  line  is  lost,  and,  consequently,  the 
pressure  falls  off  or  drops  from  the  dynamo  to  the  receiving  end  of  the  line. 
In  all  cases,  the  pressure  at  the  end  of  the  line,  or  point  where  the  power  is 
delivered,  is  equal  to  the  pressure  .at  the  dynamo  less  the  drop  in  the  line,  and, 
conversely,  the  pressure  that  must  be  maintained  by  the  dynamo  in  order  to 
obtain  a  given  pressure  at  the  end  of  the  line  will  be  equal  to  the  pressure  at 
the  receiving  end  plus  the  drop  in  the  line. 

This  is  shown  in  the  accompanying  illustration,  where  a  dynamo  D  sup- 
plies current  to  a  motor  M  situated  1  mi.  distant.  In  order  that  the  motor 
may  operate  properly,  the  pressure  at  its  terminals  must  be  kept  constant  at, 
say  500  volts;  therefore,  the  pressure  between  a  and  b  (the  dynamo  terminals) 
must  be  more  than  500  volts  by  the  drop  or  pressure  necessary  to  force  the 
current  through  the  line.  If  the  motor  is  taking  very  little  current,  that  is, 
if  it  is  running  on  a  very  light  load,  the  current  will  be  small,  and  hence  the 
drop  in  the  line  will  be  small.  In  order,  then,  that  the  pressure  at  the  motor 
may  remain  constant,  or  nearly  so,  the  pressure  at  the  dynamo  must  auto- 
matically increase  as  the  load  increases  and  the  line  must  be  designed  with 
regard  to  the  maximum  current  it  has  to  carry.  It  will  be  supposed  that  the 
motor  takes  50  amp.  at  full  load  and  that  the  line  wire  has  a  resistance  of 
.2  ohm  per  mi.  The  current  has  to  pass  through  2  mi.  of  wire  (because  it  has 
to  flow  out  through  1  mi.  and  back  through  1  mi.),  and  hence  encounters  a 
resistance  of  .4  ohm.  The  drop  in  the  line  will  then  be  .4X50  =  20  volts, 
and  in  order  to  obtain  a  pressure  of  500  volts  at  the  motor,  the  pressure  at  the 
dynamo  will  have  to  be  520  volts.  The  loss  of  power  in  the  line  would  be 
current  X  drop  =  50X20  =  1,000  watts,  or  about  1J  H.  P.  The  drop  in  an 
electric-transmission  line  is  analogous  to  the  loss  in  pressure  due  to  the  fric- 
tion encountered  by  water  flowing  through  a  pipe  line. 

If,  in  the  illustration  just 
given,  the  wire  had  a  resistance 
of  .1  ohm  per  mi.',  the  loss  in 
the  line  would  be  halved,  but 
the  weight  of  copper  required 
doubled,  because  the  wire  would 
have  to  be  double  the  cross- 
section.  The  question  as  to 
whether  it  would  pay  better  to 
invest  more  money  in  the  line 
or  to  put  up  with  the  larger 

loss  is  something  that  must  be 

determined    in    each   case   by 
the  relative  cost  of  power  and  copper. 

In  many  cases,  the  loss  allowed  in  the  line  is  about  10%  of  the  power  to  be 
delivered,  though  sometimes  the  loss  may  be  allowed  to  run  as  high  as  15% 
or  25%.  This  applies  only  to  transmission  lines.  For  local  electric-light  or 
power-distributing  systems,  the  amount  of  drop  allowed  is  usually  about  2% 
for  the  former  and  5%  for  the  latter. 

The  problem  of  calculating  line  wires  usually  presents  itself  in  the  follow- 
ing form:  Given,  a  certain  amount  of  power  to  transmit  over  a  known  dis- 
tance with  a  certain  allowable  loss,  to  determine  the  cross-section  of  the  wire 
required. 

Let   P  =  power  to  be  delivered,  expressed  in  watts;  P  will  be  equal  to  horse- 
power delivered  at  end  of  line  multiplied  by  746; 


ELECTRICITY  493 

%  =  allowable  percentage  of  loss  in  line,  that  is,  percentage  of  power 

delivered  that  may  be  lost  in  transmission; 
E  =  voltage  at  end  of  line  where  power  is  delivered  ; 
/  =  current  at  full  load  ; 

L  =  length  of  wire  through  which  current  flows. 

The  cross-section  of  the  copper  conductor  will  then  be  given  by  the  for- 
mula: 


The  circular  mils  will  be  d2,  and  the  corresponding  size  of  wire  may  be  found 
by  consulting  the  wire  table.  It  should  be  noticed,  particularly,  that  in  this 
formula,  L  is  the  average  length  of  conductor  through  which  the  current  / 
flows.  The  application  of  distance  of  transmission  in  the  formula  is  shown 
in  the  following  example: 

EXAMPLE.  —  A  mine  pump,  driven  by  an  electric  motor,  is  situated  2  mi. 
from  the  power  station.  The  electric  input  of  the  motor  at  full  load  is  50  H.  P., 
and  the  voltage  at  its  terminals  is  to  be  500.  Estimate  the  size  of  line  wire 
necessary  to  supply  the  motor,  the  allowable  loss  in  the  line  being  15%  of  the 
power  delivered. 

SOLUTION.  —  The  actual  length  of  line  through  which  the  current  will  flow 
•will  be  4  mi.,  because  the  current  has  to  flow  out  to  the  motor  and  back  again. 
Then 

_     watts     50X746 
I  =  ~E  ----  500— 

Applying  the  formula, 

A      M     10-8X2X2X5,280X74.6X100     00.  C0ft  n    ., 
A  =  dz  =  —  —  =  226,880  C.  M.,  nearly 

ouuxio 

By  consulting  the  wire  table  it  is  found  that  this  calls  for  a  wire  a  little 
larger  than  No.  0000,  which  has  a  cross-section  of  211,600  C.  M.;  No.  0000 
wire  would  probably  be  used  in  this  case,  as  it  is  near  enough  to  the  calculated 
size  for  all  practical  purposes.  In  case  the  calculated  size  comes  out  larger 
than  any  size  given  in  the  table,  a  number  of  wires  may  be  used  in  multiple  to 
make  up  the  required  cross-section,  or,  what  is  better,  a  stranded  cable  may 
be  used.  These  heavy  stranded  cables  may  now  be  obtained  in  different  sizes, 
up  to  2,000,000  C.  M.  cross-section. 

If  it  were  allowable  to  waste  twice  as  much  power  in  the  line,  or  what  is 
equivalent  to  having  a  line  drop  of  150  volts  instead  of  75  volts,  the  cross- 
section  of  wire  required  would  be  one-half  of  that  just  found.  Such  a  large 
amount  of  loss  would,  however,  be  objectionable  unless  power  was  very  cheap. 
A  large  drop  in  the  line  is  in  any  case  objectionable,  because  the  voltage  at  the 
receiving  end  of  the  circuit  will  fall  off  greatly  unless  the  voltage  at  the  gen- 
erating station  is  raised  as  the  load  conies  on  in  order  to  compensate  for  the 
line  drop.  Most  of  the  uses  to  which  electricity  is  put,  in  mines  or  other  places, 
require  that  the  pressure  at  the  point  where  the  power  is  utilized  shall  be 
kept  approximately  constant.  For  example,  in  the  case  of  incandescent 
lights,  the  lamps  will  fall  off  greatly  in  brightness  if  the  pressure  decreases 
even  by  a  comparatively  slight  amount.  Also,  if  motors  are  being  operated, 
the  speed  will  vary  considerably  if  the  pressure  is  not  kept  constant,  and  it 
may  be  stated,  in  general,  that  a  large  line  loss  tends  to  poor  regulation  at 
the  end  of  the  circuit  where  power  is  delivered. 

From  these  considerations,  it  is  evident  that  the  size  of  wire  to  be  used 
under  given  conditions  is  determined  by  the  allowable  amount  of  drop.  In 
some  cases,  however,  especially  if  the  current  is  to  be  used  near  at  hand,  the 
size  of  wire  so  determined  might  not  be  large  enough  to  carry  .the  current  with- 
out overheating.  Of  course,  in  such  cases,  the  safe  carrying  capacity  of  the 
wire  determines  the  size  to  be  used,  and  the  drop  will  be  correspondingly  less. 
The  amount  of  current  that  a  given  wire  can  carry  without  overheating  depends 
very  largely  on  the  location  of  the  wire.  For  example,  a  wire  strung  in  the 
open  air  will  carry  a  greater  current,  with  a  given  temperature  rise,  than  the 
same  wire  when  boxed  up  in  a  molding  or  conduit. 

In  order  to  keep  down  the  size  of  wire  required  to  transmit  a  given  amount 
of  power  over  a  given  distance,  with  a  certain  allowable  loss,  the  current  must 
be  kept  as  small  as  possible.  Now,  for  a  given  amount  of  power,  the  current 
can  only  be  made  small  by  increasing  the  pressure,  because  the  number  of 
watts,  or  power  delivered,  is  equal  to  the  product  of  the  current  and  the  pressure. 
As  a  matter  of  fact,  if  the  pressure  in  any  given  case  is  doubled,  the  amount  of 
copper  required  will  be  only  one-fourth  as  great;  in  other  words,  for  a  given 


494 


ELECTRICITY 


amount  of  power  transmitted,  the  weight  of  copper  required  decreases  as  the 
square  of  the  voltage.  It  is  at  once  seen,  then,  that  if  any  considerable  amount 
of  power  is  to  be  transmitted  over  long  distances,  a  high  line  pressure  must  be 
used  or  else  the  cost  of  copper  becomes  prohibitory.  The  use  of  high  pressures 
in  power  transmission  will  be  taken  up  in  connection  with  alternating  currents. 
Insulated  Wires. — For  most  overhead  line  work  using  modern  voltages, 
weather-proof  insulated  wire  is  used.  This  wire  is  covered  with  two  or  three 
braids  of  cotton,  and  treated  with  insulating  compound.  For  inside  work, 
and  in  places  where  a  better  quality  of  insulation  is  required,  rubber-covered 
wires  are  used.  The  accompanying  table  gives  the  approximate  weight  of 
weather-proof  line  wire.  The  cost  of  the  wire  per  pound  varies  considerably, 
owing  to  variations  in  the  price  of  copper. 

WEATHER-PROOF  LINE  WIRE  (ROEBLING'S) 


Double  Braid 

Triple  Braid 

Number 
B.  &S. 

Outside 

Weight,  in  Pounds 

Outside 

Weight,  in  Pounds 

(jctllgC 

Diameter 

Diameter 

32ds  In. 

Per 

Per 

32ds  In. 

Per 

Per 

1,000  Ft. 

Mile 

1,000  Ft. 

Mile 

0000 

20 

716 

3,781 

24 

775 

4,092 

000 

18 

575 

3,036 

22 

630 

3,326 

00 

17 

465 

2,455 

18 

490 

2,587 

0 

16 

375 

1,980 

17 

400 

2,112 

1 

15 

285 

1,505 

16 

306 

1,616 

2 

14 

245 

1,294 

15 

268 

1.415 

3 

13 

190 

1,003 

14 

210 

1,109 

4 

11 

152 

803 

12 

164 

866 

5 

10 

120 

634 

11 

145 

766 

6 

9 

98 

518 

10 

112 

591 

8 

8 

66 

349 

9 

78 

412 

10 

7 

45 

238 

8 

55 

290 

12 

6 

30 

158 

7 

35 

185 

14 

5 

20 

106 

6 

26 

137 

16 

4 

14 

74 

5 

20 

106 

18 

3 

10 

53 

4 

16 

85 

For  high-tension  lines,  it  is  customary  to  use  bare  wires  and  insulate  them 
thoroughly  on  special  porcelain  insulators.  The  ordinary  weather-proof  wire 
insulation  is  of  little  or  no  use  as  a  protection  when  these  high  pressures  are 
used,  and  it  only  makes  the  line  more  dangerous  because  of  the  false  appear- 
ance of  security  that  it  gives.  In  many  cases,  it  is  also  better  to  use  bare 
feeders  for  mine:haulage  plants,  because  the  ordinary  insulation  soon  becomes 
defective  in  a  mine,  and  a  wire  in  this  condition  is  really  more  dangerous  than 
a  bare  wire,  because  the  latter  is  known  to  be  dangerous  and  will  be  left  alone. 


CURRENT  ESTIMATES 


Rr    |  1     at  this  will  de 

*    O     O    O     O     6    is  to  be  used 
^< ]_  are  usually  c 


FIG.  1 


Incandescent  Lamps. —  Before  cal- 
culating the  size  of  wire  required  for 
any  given  case,  it  is  necessary  to  know 
the  current,  and  the  method  of  getting 
at  this  will  depend  on  what  the  current 
for.  Incandescent  lamps 
operated  on  110- volt  cir- 
cuits, as  shown  in  Fig.  1,  or  on  the 
three-wire  system,  as  shown  in  Fig.  2. 


In  the  three-wire  system,  two  110- volt  dynamos  are  connected  in  series  so  that 
the  voltage  across  the  outside  wires  is  220.     The  neutral  wire  a  connects  at 


ELECTRICITY  495 

the  point  b  where  the  machines  are  connected  together.  The  wire  a  merely 
serves  to  carry  the  difference  in  the  currents  on  the  two  sides  of  the  system, 
in  case  more  lamps  should  be  burning  on  one  side  than  on  the  other.  The 
outside  wires  for  such  a  system  are  calculated  as  if  the  lights  were  operated 
two  in  series  across  220 
volts.  The  middle  wire 
is  usually  made  equal  in 
size  to  the  outer  wires. 
An  ordinary  16-c.  p. 
incandescent  carbon- 
filament  lamp  requires 
about  55  watts  for  its 
operation;  a  32-c.  p. 
lamp  requires  about  1 10 

watts.    Tungsten  lamps  ,,       0 

are  designated  by  the 
watts    required    rather 

than  by  the  candlepower  light  they  give.  Thus,  a  25-watt  tungsten  lamp 
gives  about  20  c.  p.  Hence,  in  the  case  of  ordinary  parallel  distribution,  as 
shown  in  Fig.  1,  the  dynamo  will  deliver  about  5  amp.  for  each  16-c.  p. 
carbon  lamp  operated,  and  1  amp.  for  each  32-c.  p.  carbon  lamp.  In  the 
case  of  the  three-wire  system,  each  pair  of  16-c.  p.  carbon  lamps  will  take 
J  amp.,  and  the  total  number  of  amperes  in  the  outside  wires  will  be  one-fourth 
the  number  of  lamps  operated. 

EXAMPLE  1. — A  certain  part  of  a  mine  is  to  be  illuminated  by  fifty  16-c.  p. 
carbon  lamps  and  ten  32-c.  p.  carbon  lamps.     This  portion  of  the  mine  is 
1,000  ft.  from  the  dynamo  room,  and  the  allowable  drop  in  pressure  is  5%. 
The  lamps  are  to  be  run  on  a  110-volt  system.     Find  the  size  of  wire  required. 
SOLUTION. — Fifty  16-c.  p.  carbon  lamps  require  ....25  amperes 
Ten  32-c.  p.  carbon  lamps  require 10  amperes 

Total  current 35  amperes 

10.8X1.000X2X35X100     ,.„  *-,  r   AT 
110X5  -  =  137,454  C.  M., 

or  about  a  No.  00  B.  &  S.  wire. 

EXAMPLE  2. — Take  the  same  case,  but  suppose  the  lights  to  be  operated 
on  the  three- wire  system. 

SOLUTION. — There  will  then  be  twenty-five  16-c.  p.  carbon  lamps  and  five 
32-c.  p.  carbon  lamps  on  each  side  of  the  circuit,  and  the  total  current  in  the 
outside  wires  will  be  17.5  amp.  The  voltage  between  the  outside  wires  will 
be  220,  and 

10.8X1.000X2X17.5X100  ft    r    . , 

220X5  —  34,363  C.M., 

or  about  a  No.  5  B.  &  S.  wire. 

If  the  central  wire  is  made  also  of  this  size,  this  system  would  require  three- 
eighths  the  amount  of  copper  called  for  by  the  plain  110-volt  system.  There 
is  the  disadvantage  that  two  dynamos  are  needed. 

NOTE. — The  length  to  be  used  in  the  wiring  formula  is  the  "average  dis- 
tance traversed  by  the  current  in  the  conductor.  For  example,  if,  as  in  Fig.  3  (a) , 
the  lamps  were  all  grouped  or  bunched  at  the  end  of  the  line,  the  length 
used  in  the  formula  would  be  twice  that  from  G  to  A,  because  the  whole  cur- 
rent has  to  flow  out  to  A  through  one  main  and  back  through  the  other.  In 
other  words,  the  whole  current  here  passes  through  the  whole  length  of  the 
line.  In  case  the  load  is  uniformly  distributed  all  along  the  line,  as  shown  in  (b), 
the  current  decreases  step  by  step  from  the  dynamo  to  the  end.  In  such  a 
case,  the  length  or  distance  to  be  used  in  the  formula  is  one-half  that  used  in 
the  former  case,  or  simply  the  distance  from  the  dynamo  to  the  end,  instead 
of  twice  this  distance. 

Arc  Lamps. — Arc  lamps  are  frequently  run  on  constant-potential  circuits, 
and  usually  consume  from  400  to  500  watts.  There  are  so  many  types  of 
these  lamps  that  it  is  difficult  to  give  any  current  estimates  that  will  be  gen- 
erally applicable.  Enclosed  arc  lamps  usually  take  from  3  to  5  amp.  when 
run  on  110-volt  circuits. 

Motors. — Practically  all  the  motors  used  in  mining  work  are  run  on  the 
constant-potential  system,  either  at  250  or  500  volts.  The  efficiency  of  ordi- 
nary motors  will  vary  from  65%  to  94%,  depending  on  the  size.  The  efficiency 
is  greater  with  the  larger  machines,  and,  for  the  ordinary  run  of  motors,  it  will 


496 

probably  lie  between 


ELECTRICITY 


3%  and  90%.     By  efficiency  is  here  meant  the  ratio 

of  the  useful  output  at  the  pulley  or  pinion  of  the  motor  to  the  total  input. 
The  following  table  gives  the  efficiency  of  motors  of  ordinary  size: 

Approximate  Motor  Efficiency 

|  to    li  H.  P.,  inclusive  =  70-75%  efficiency 

3    to    5    H.  P.,  inclusive  =  75-80%  efficiency 

1\  to  10    H.  P.,  inclusive  =  80-85%  efficiency 

15  H.  P.  and  upwards  =  85-90%  efficiency 

If  the  required  output,  in  horsepower,  of  a  direct-current  motor  is  known, 
the  input,  in  watts,  will  be  W  =  —  '     '.      -  —  ,  and  the  current  required  at  full 

W 
load  will  be  1  =    r,  where  E  is  the  voltage  between  the  mains  at  the  motor. 


CURRENT  REQUIRED  FOR  DIRECT-CURRENT  MOTORS 


Horse- 

'  Effi- 

Amperes 

Watts 

of 

ciency* 
Per  Cent. 

Input 

110 

220 

250 

500 

550 

Volts 

Volts 

Volts 

Volts 

Volts 

1 

65 

1,148 

10.4 

5.2 

4.58 

2.29 

2.08 

2 

65 

2,295 

20.8 

10.4 

9.16 

4.58 

4.16 

2i 

65 

2,870 

26.0 

13.0 

11.45 

5.72 

5.21 

31 

75 

3,481 

31.6 

15.8 

13.90 

6.90 

6.32 

5 

75 

4,973 

45.1 

22.6 

19.90 

9.95 

9.04 

7* 

80 

6,994 

63.5 

31.7 

27.90 

13.95 

12.70 

10 

80 

9,325 

84.6 

42.3 

37.20 

18.60 

16.90 

15 

85 

13,165 

119.8 

59.9 

52.70 

26.40 

23.90 

20 

85 

17,553 

159.6 

79.8 

70.20 

35.10 

31.90 

25 

90 

20,770 

189.0 

94.5 

83.10 

41.60 

37.80 

30 

90 

24,864 

225.8 

112.9 

99.40 

49.70 

45.20 

40 

90 

33,232 

302.6 

151.3 

133.00 

66.50 

60.50 

50 

90 

41,540 

378.0 

189.0 

166.20 

83.10 

75.60 

75 

90 

62,310 

567.0 

283.5 

249.30 

124.80 

113.40 

100 

93 

80,215 

729.0 

364.5 

320.50 

160.30 

145.70 

125 

93 

100,269 

912.0 

456.0 

401.00 

200.50 

182.30 

150 

93 

120,322 

1,094.0 

547.0 

481.00 

240.70 

219.00 

200 

94 

158,510 

1,442.0 

721.0 

634.00 

317.00 

288.00 

FIG.  3 

Conductors  for  Electric-Haulage  Plants.— In  electric-haulage  plants,  the 
rails  take  the  place  of  one  of  the  conductors,  so  that,  in  calculating  the  size  of 
feeders  required,  only  the  overhead  conductors  are  taken  into  account.  It 

*Efficiencies  are  taken  arbitrarily;  a  variation  in  these  percentages  will 
make  proportionate  changes  in  watts  and  amperes. 


ELECTRICITY  497 

is  a  difficult  matter  to  assign  any  definite  value  to  the  resistance  of  the  track 
circuit,  as  it  depends  very  largely  on  the  quality  of  the  rail  bonding  at  the 
joints.  If  this  bonding  is  well  done,  the  resistance  of  the  return  circuit  should 
be  very  low,  because  the  cross-section  of  the  rails  is  comparatively  large.  For 
calculating  the  supply  feeders,  the  following  approximate  formula  may  be  used : 
.,  14XLX/X100 

circular  mils  =  — ^..^    , 

£X%  drop 

In  this  case,  L  is  the  average  length  of  feeder  over  which  the  power  is  to  be 
transmitted.  It  will  be  noticed  that  the  constant  10.8  appearing  in  the  previous 
formulas  has  here  been  increased  to  14.  This  has  been  done  to  allow,  approxi- 
mately, for  the  track  resistance,  but  this  constant  might  vary  considerably 
depending  on  the  quality  of  the  rail  bonding.  If  the  load  is  all  bunched  at 
the  end  of  the  feeder,  L  is  the  actual  length  of  the  feeder  in  feet.  If  the  load 
is  uniformly  distributed,  as  it  would  be  if  a  number  of  locomotives  were 
continually  moving  along  the  line,  the  distance  L  in  the  formula  will  be  taken 
as  one-half  that  used  in  the  case  where  the  load  is  bunched  at  the  end.  In 
other  words,  the  whole  current  /  will  only  flow  through  an  average  of  one-half 
the  length  of  the  line. 


1200 41 400O- 


FIG.  4 

EXAMPLE. — In  Fig.  4,  ab  represents  a  section  of  track  4,000  ft.  long.  From 
the  dynamo  c  to  the  beginning  of  the  section,  the  distance  is  1,200  ft.  The 
trolley  wire  is  No.  00  B.  &  S.,  and  is  fed  from  the  feeder  at  regular  intervals. 
Two  mining  locomotives  are  operated,  each  of  which  takes  an  average  cur- 
rent of  75  amperes.  The  total  allowable  drop  to  the  end  of  the  line  is  to  be 
5%  of  the  terminal  voltage,  which  is  500  volts.  Calculate  the  size  of  feeder 
required,  assuming  that  the  constant  14,  in  the  formula,  takes  account  of  the 
resistance  of  the  return  circuit. 

SOLUTION. — Since  the  locomotives  are  moving  from  place  to  place,  the 
center  of  distribution  for  the  load  may  be  taken  at  the  center  of  the  4,000  ft. 
The  distance  L  will  then  be  1,200+2,000  =  3,200  ft.  The  total  current  will 
be  150  amperes;  hence,  we  have 

14X3,200X150X100 

circular  mils  =  —  —    —  =  268,800. 

oOUX  5 

This  would  require  either  a  stranded  cable  or  the  use  of  two  No.  00  wires 
in  parallel  from  c  to  a.  From  a  to  &  we  have  the  No.  00  trolley  wire  in  parallel 
with  the  feeder;  hence,  the  section  of  feeder  ab  may  be  a  single  No.  00  wire. 
In  many  cases,  the  drop  is  allowed  to  run  as  high  as  10%,  because  the  loads 
are  usually  heavier,  and  the  distances  longer,  than  in  the  example  given  above. 


DYNAMOS  AND  MOTORS 

DIRECT-CURRENT  DYNAMOS 

A  dynamo,  or  generator,  is  a  machine  for  converting  mechanical  energy  into 
electrical  energy  by  moving  conductors  relatively  to  a  magnetic  field.  An 
electric  motor  is  a  machine  for  converting  electrical  energy  into  mechanical 
energy  by  the  relative  motion  between  conductors  carrying  a  current  and  a 
magnetic  field.  In  the  case  of  a  dynamo  a  number  of  conductors  are  made  to 
move  across  a  magnetic  field  by  means  of  a  steam  engine  or  other  prime 
mover,  and  the  result  is  that  an  electromotive  force  is  set  up  in  the  conductors, 
and  this  electromotive  force  will  set  up  a  current  if  the  circuit  is  closed. 

In  the  case  of  a  motor,  a  number  of  conductors  are  arranged  so  that  they 
are  free  to  move  across  a  magnetic  field,  and  a  current  is  sent  through  these 
conductors  from  some  source  of  electric  current.  The  current  flowing  through 
these  conductors  reacts  on  the  magnetic  field  and  causes  the  conductors  to  move, 
thus  converting  the  electrical  energy  delivered  to  the  motor  into  mechanical 


ELECTRICITY 


energy.     As  far  as  mechanical  construction  goes,  dynamos  and  motors  are 

almost  identical,  and  the  operation  of  the  motor  is  about  the  reverse  of  that  of 

the  dynamo. 

Dynamos  and  motors  may  be  divided  into  two  general  classes:     Dynamos 

and  motors  for  direct  current;  dynamos  and  motors  for  alternating  current. 

Direct-current  dynamos  are  those  that 
furnish  a  current  that  always  flows  in  the 
same  direction.  This  kind  of  dynamo  is 
largely  used  for  incandescent  lighting,  and 
also  for  the  operation  of  street  railways. 
A  dynamo  generates  an  electromotive 
force  by  the  motion  of  conductors  across 
a  magnetic  field;  hence,  there  must  be  a 
magnet  of  some  kind  to  set  up  a  magnetic 
field,  known  as  the  field  magnet,  or  simply 
as  the  field;  and  a  series  of  conductors 
arranged  so  that  they  may  be  moved  or 
revolved  in  the  magnetic  field,  known  as 
the  armature.  The  field  is  supplied  by 
means  of  a  powerful  electromagnet  which 
is  magnetized  by  the  current  in  the  field 
coils.  Fig.  1  shows  a  typical  six-pole 
magnet  of  this  kind;  B  are  the  magnetizing 
coils,  which,  when  a  current  is  sent  through 
*  them,  form  powerful  magnetic  poles  at  N 

and  5.     The  framework  A  is  usually  made  of  cast  iron  or  cast  steel.     These 

field  mapnets  may  have  any  number  of  poles,  but  machines  of  ordinary  size 

are  usually  provided  with  from  two  to  eight  poles. 

The  armature  usually  consists  of  a  number  of  turns  of  insulated  copper 

wire,  arranged  around  the  periphery  of  a  ring  or  drum  built  up  of  soft  iron 

sheets.     Pig.  2  shows  the  construction  of  a  typical  armature  of  the  ring  type. 

The  winding  is  divided  into  a  number  of  sections,  and  the  terminals  connected 

to  the  commutator. 

This  commutator,  consists  of  a  number  of  copper  bars,  insulated  from  each 

other  by  means  of  mica,  the  bundle  of  bars  being  clamped  firmly  into  place 


COMPLETCARMATWC. 


nsulation,. 


•Binding-  wires? 


FlG.  2 

and  turned  up  to  form  a  true  cylindrical  surface.  The  sections  in  the  commu- 
tator correspond  with  those  in  the  armature,  and  the  use  and  operation  of  the 
commutator  will  be  described  later.  The  winding  on  the  ring  is  endless,  that 
is,  it  consists  of  a  number  of  coils  or  sections  c,  Pig.  3,  the  end  of  one  section 


ELECTRICITY 


499 


being  joined  to  the  beginning  of  the  next,  thus  forming  an  endless  coil.     The 
construction  of  such  a  ring  armature  would  be  as  shown  in  Fig.  2. 

Suppose  that  the  ring  shown  in  Fig.  3  with  its  endless  winding  is  rotated 
between  the  poles  of  a  two-pole  field  magnet.  Magnetic  lines  will  flow  from 
the  N  pole  of  the  field  magnet 
across  through  the  iron  core  of 
the  armature  and  enter  the  5 
pole  on  the  other  side.  As 
all  the  conductors  on  the  right- 
hand  face  of  the  ring  are  mov- 
ing upwards,  they  will  have  an 
electromotive  force  generated 
in  them  in  one  direction,  while 
the  conductors  on  the  left  side 
will  have  an  electromotive 
force  in  the  opposite  direction, 
because  all  the  conductors  on 
this  side  are  moving  down- 
wards, or  in  the  opposite  direc- 
tion, to  those  on  the  other  side. 
These  two  opposing  electro- 
motive forces  may  be  said  to 
start  at  a'  and  to  meet  at  a,  as 
shown  by  the  arrowheads  on 
the  conductors,  and  will  neu- 
tralize each  other  so  that  no  current  will  flow  through  the  windings  of  the 
armature.  Suppose,  however,  that  taps  are  connected  at  the  points  a 
and  a',  as  shown  by  the  dotted  lines,  and  these  taps  connected  to  two  con- 
ducting metal  rings  r  and  r',  mounted  so  as  to  revolve  with  the  armature. 
By  allowing  brushes  b  and  b'  to  press  on  these  rings,  connection  can  be  made 
with  an  outside  circuit  d,  which  may  consist  of  a  number  of  lamps  or  any 
other  device  through  which  it  is  desired  to  send  a  current.  By  putting  in  the 
taps  at  a  and  a',  the  two  opposing  electromotive  forces  may  set  up  a  current 
through  the  common  connections  to  the  rings,  and  thence  through  the  outside 
circuit.  Current  now  flows  in  each  half  of  the  armature  winding,  unites  at  a, 
flows  out  by  means  of  ring  r'  and  brush  b',  thence  through  the  outside  circuit  d 
to  brush  b  and  ring  r,  from  whence  it  passes  to  a',  and  thus  completes  the 
circuit.  When  the  ring  makes  a  half  revolution  from  the  position  in  the 
figure,  the  current  in  the  outside  circuit  will  flow  in  the  opposite  direction. 
In  fact,  an  arrangement  of  this  kind  will  deliver  a  current  that  will  be  periodi- 
cally reversing  in  the  outside  circuit;  it  will  be  what  is  known  as  an  alternating 
current. 

Instead  of  simply  bringing  out  two  terminals  to  rings,  suppose  the  winding 
to  be  tapped  at  a  fairly  large  number  of  points,  and  connections  brought  down 

to  a  number  of  metal  bars  insu- 
lated from  one  another,  as  shown 
in  Fig.  4.  When  the  armature  is 
revolved  the  brushes  will  come  in 
contact  with  successive  bars  and 
keep  the  outside  circuit  in  such 
relation  to  the  armature  winding 
that  the  current  will  always  flow 
through  it  in  the  same  direction. 
Moreover,  if  the  number  of  divis- 
ions in  the  armature  is  large,  the 
current  will  fluctuate  very  little, 
being  nearly  as  steady  as  that 
obtained  from  a  battery.  The 
arrangement  made  up  of  insulated 
bars  is  called  the  commutator, 
because  it  commutes  or  changes 
th3  relation  of  the  outside  circuit 
to  the  armature  winding  so  that 
the  current  in  the  outside  circuit 
always  flows  in  the  same  direction.  All  practical  machines  used  for  the  gener- 
ation of  direct  current  must  be  provided  with  such  a  commutator.  When 
alternating  currents  are  used  it  is  only  necessary  to  use  plain  collector  rings, 
as  shown  in  Fig.  3. 


500 


ELECTRICITY 


Factors  Determining  Electromotive  Force  Generated. — A  dynamo  should 
be  looked  upon  as  a  machine  for  maintaining  an  electric  pressure  rather  than 
as  a  machine  for  generating  a  current.  A  pump  does  not  manufacture  water — 
it  merely  maintains  a  head  or  pressure  that  causes  water  to  flow  wherever  an 
outlet  is  provided  for  it  to  flow  through.  In  the  same  way,  a  dynamo  main- 
tains a  pressure,  and  this  pressure  will  set  up  a  current  whenever  the  circuit  is 
closed,  so  that  the  current  can  flow.  The  important  thing  to  consider,  there- 
fore, is  the  electromotive  force  that  the  dynamo  is  capable  of  generating. 

The  electromotive  force  generated  by  an  armature  depends  on  the  total 
number  of  magnetic  lines  cut  through  per  second  by  the  armature  conductors. 
This  means  that  (1)  the  faster  the  armature  runs,  the  higher  will  be  the  electro- 
motive force;  (2)  the  greater  number  of  conductors  or  turns  there  are  on  the 
armature,  the  higher  will  be  the  electromotive  force:  and  (3)  the  stronger  the 
magnetic  field,  the  higher  will  be  the  electromotive  force.  The  electromotive 
force  in  terms  of  these  quantities  may  be  written 

nCN 

'     100,000,000 
in  which         n  =  speed,  in  revolutions  per  second; 

C  =  number  of  conductors  on  face  of  armature; 

N  =  number  of  magnetic  lines  flowing  from  one  pole. 

The  constant  100,000,000  is  necessary  to  reduce  the  result  to  volts.  This 
makes  it  possible  to  make  calculations  relating  to  any  two-pole  dynamo,  and 
with  slight  modification  it  is  applicable  to  machines  with  field  magnets  having 
a  number  of  poles. 

Field  Excitation  of  Dynamos. — In  the  earliest  form  of  dynamo,  the  magnetic 
field  in  which  the  armature  rotated  was  set  up  by  means  of  permanent  magnets. 
Permanent  magnets  are,  however,  very  weak  compared  with  electromagnets, 
which  are  excited  by  means  of  current  flowing  around  coils  of  wire  wound  on  a 
soft-iron  core.  As  soon  as  the  current  ceases  flowing  around  the  coils  of  an 
electromagnet,  the  magnetism  almost  wholly  disappears,  but  a  small  amount, 
known  as  the  residual  magnetism,  remains.  It  is  to  this  residual  magnetism 
that  the  dynamo  owes  its  ability  to  start  up  of  its  own  accord  and  excite  its 
own  field  magnets.  When  the  armature  is  first  started  to  revolve,  a  very  feeble 
electromotive  force  is  generated  in  it,  but  the  armature  is  connected  to  the  field 
coils  in  such  a  way  that  this  small  electromotive  force  is  able  to  force  a  small 
current  through  the  field  coils,  and  thus  set  up  a  larger  amount  of  magnetism 
in  the  field.  This  in  turn  increases  the  electromotive  force  in  the  armature,  and 
the  building-up  process  goes  on  rapidly  until  the  dynamo  generates  its  full 
pressure.  There  are  three  methods  in  use  for  supplying  the  field  coils  with 
current,  and  continuous-current  dynamos  are  divided  into  three  classes,  accord- 
ing to  the  method  used  for  exciting  their  fields.  These  three  classes  are: 
Series-wound  dynamos,  shunt-wound  dynamos,  and  compound-wound  dynamos. 


FIG.  5 


FIG.  6 


In  series-wound  dynamos  the  field  coils  are  connected  in  series  with  the 
armature,  and  all  the  current  that  passes  through  the  armature  also  passes 
through  the  field  and  the  outside  circuit.  This  arrangement  is  shown  in 
Fig.  5,  where  N  and  ^represent  the  poles  of  the  magnet,  +B  and  —B  the 
brushes,  and  Re  the  outside  circuit,  which  may  consist  of  lamps,  motors,  or 
any  other  device  in  which  it  is  desired  to  utilize  the  current.  With  an  arrange- 
ment of  this  kind,  and  as  long  as  the  speed  does  not  change,  the  electromotive 
force  will  increase  as  the  current  increases,  because  the  field  will  become 
stronger.  This  will  be  true  up  to  the  point  where  the  field  carries  all  the 


ELECTRICITY 


501 


magnetism  it  is  capable  of,  or,  in  other  words,  until  it  becomes  saturated. 
After  this  point  is  reached,  the  electromotive  force  will  increase  very  little 
with  increase  of  current.  In  most  of  the  work  connected  with  lighting  or 
power  transmission,  it  is  desirable  to  have  the  voltage  remain  nearly  constant. 
For  this  reason,  therefore,  the  series  method  of  excitation  has  not  been  very 
largely  used  for  dynamos.  The  only  style  of  generator  to  which  it  has  been 
applied  at  all  generally  is  the  arc-light  dynamo,  and  these  machines  are  pro- 
vided with  an  automatic  regulator  of  some  kind  to  vary  the  voltage  as  desired. 
The  series  field  winding  has,  however,  been  largely  used  in  connection  with  the 
motors  operated  on  constant-pressure  circuits. 

Shunt-wound  dynamos  have  not  been  used  largely  of  late  years,  although 
they  were  formerly  very  common.  In  this  method  of  excitation,  the  field  is 
connected  as  a  shunt  or  by-pass  to  the  armature;  that  is,  the  field  winding  is 
connected  in  parallel  with  the  armature.  This  winding  consists  of  a  large 
number  of  turns  of  fine  wire,  so  that  its  resistance  is  high  and  only  a  small  part 
of  the  total  current  flows  through  it.  Fig.  6  shows  the  connections  for  this 
kind  of  field  excitation.  An  adjustable  resistance  r  is  usually  inserted  in  the 
field  circuit,  and  by  cutting  this  resistance  in  or  out,  the  field  may  be  weakened 
or  strengthened  and  the  voltage  varied  accordingly.  With  this  type  of  machine, 
the  current  through  the  field  does  not  vary  greatly  from  no  load  to  full  load, 
and  if  the  dynamo  is  well  designed,  the  pressure  at  the  brushes  will  keep 
approximately  constant.  The  pressure  will,  however,  always  fall  off  more  or 
less  as  the  amount  of  current  produced  increases  on  account  of  the  drop  in  the 
armature,  due  to  its  resistance,  and  also  because  of  the  tendency  that  the  cur- 
rent in  the  armature  has  of  weakening  the  field.  The  shunt  winding  is  used 
quite  largely  for  motors. 

The  compound-wound  dynamo  is  the  one  most  largely  used  for  direct-current 
power  and  light  distribution,  and  it  is  so  called  because  the  winding  used  for 
exciting  the  field  is  a  combination  of  the  series  and 
shunt  windings.  The  series  winding  serves  to  keep 
up  the  field  strength  while  the  load  is  increased, 
and  thus  keeps  the  pressure  constant,  or  even  makes 
it  rise  with  increased  load,  if  so  desired.  When  the 
series  winding  is  so  adjusted  that  the  pressure  rises 
as  the  load  is  increased,  the  machine  is  said  to  be 
over  compounded.  Fig.  7  shows  the  connections  for 
such  a  machine.  It  will  be  seen  that  the  shunt 
winding  is  connected  as  before,  a  field  resistance 
or  rheostat,  not  shown  in  the  figure,  being  inserted 
for  the  purpose  of  adjusting  the  voltage.  One  brush 
connects  directly  to  one  terminal  of  the  machine 
+  T,  while  the  other  brush  connects  to  one  end  of 
the  series  winding  on  the  field.  The  other  end  of 
the  series  winding  forms  the  other  terminal  —  T,  to 


FIG.  7 


which  the  outside  circuit  Re  is  connected.  By  this  arrangement,  the  shunt  coil 
supplies  a  certain  amount  of  initial  magnetization  that  is  augmented  by  the 
magnetism  supplied  by  the  series  coils.  Care  must  be  taken  to  see  that  the 
current  in  the  series  coils  circulates  around  the  field  in  the  same  direction  as 
that  in  the  shunt  coils,  otherwise  the  electromotive  force  will  fall  off  with  an 
increasing  load  instead  of  keeping  it  up. 

DIRECT-CURRENT  MOTORS 

Direct-current  motors,  so  far  as  their  fundamental  construction  goes,  are 
almost  identical  with  direct-current  dynamos.  But  as  .  motors  are  often 
required  to  operate  under  very  trying  conditions,  as  in  mine  haulage  or  pump- 
ing plants  or  on  the  ordinary  street  car,  the  mechanical  construction  must  be 
so  designed  as  to  enclose  the  working  parts  as  completely  as  possible,  and  thus 
protect  them  from  dirt  and  injury.  The  two  kinds  of  motors  most  commonly 
used  are  the  series  and  shunt  varieties;  compound  -wound  motors  are  only  used 
for  a  few  special  kinds  of  work.  Practically  all  the  motors  in  use  are  operated 
from  constant-pressure  mains;  that  is,  the  pressure  at  the  terminals  of  the 
motor  is  practically  constant,  no  matter  what  load  it  may  be  carrying.  Only 
constant-potential  motors  will  be  considered  here. 

Principles  of  Operation.  —  If  the  fields  of  an  ordinary  constant-potential 
dynamo  are  excited  and  a  current  supplied  to  the  armature  from  some  outside 
source,  such  as  another  dynamo  D,  Fig.  1,  so  that  the  current  enters  at  -\-B, 
and  passing  through  the  winding  in  the  direction  indicated  by  the  arrowheads, 
leaves  at  brush  —  B,  all  the  conductors  under  the  5  pole  face,  b,  c,  d,  e,  f,  and  g, 


502 


ELECTRICITY 


will  tend  to  move  downwards,  and  all  those  under  the  N  pole  face,  j,  k,  I,  m,  n, 
and  o,  will  tend  to  move  upwards,  as  indicated  by  the  small  arrows. 

These  forces  combine  to  produce  a  tendency  of  the  armature  to  rotate  about 
its  axis  as  indicated  by  the  large  arrows,  which  tendency  is  called  the  torque  of 
the  motor. 

The  amount  of  this  torque — which  is  usually  expressed  in  pound-feet;  that 
is,  a  certain  number  of  pounds  acting  at  a  radius  of  a  certain  number  (usually  1) 
of  feet — depends  on  the  strength  of  the  field,  the  number  of  conductors,  their 
mean  distance  from  the  axis  of  the  armature,  and  the  amperes  in  each  con- 
ductor. In  any  given  machine,  the  second  and  third  conditions  are  constant,  so 
that  the  torque  depends  on  the  strength  of  the  field  and  the  current. 

If  the  armature  is  stationary,  the  electromotive  force  required  to  send  the 
current  through  the  winding  is  only  that  necessary  to  overcome  the  drop, 
which  is  due  to  the  resistance  of  the  winding.  If  the  torque  exerted  by  this 
current  is  greater  than  the  opposition  to  motion,  so  that  it  causes  the  armature 
to  revolve,  the  motion  of  the  conductors  through  the  field  generates  in  them 
an  electromotive  force  that  is  opposed  to  the  electromotive  force  that  is  sending 
the  current  through  the  armature.  This  opposing  electromotive  force  or 
counter  electromotive  force  as  it  is  called,  then  diminishes  the  effect  of  the  applied 
electromotive  force,  so  that  the  current  is  reduced,  thereby  reducing  the  torque. 
Should  the  torque  still  be  greater  than  the  opposition  to  motion,  the  speed  of 
the  armature  will  continue  to  increase,  increasing  the  counter  electromotive 
force,  and  thereby  further  reducing  the  current  and  the  corresponding  torque 
until  the  torque  just  balances  the  opposition  to  the  motion,  when  the  speed 
will  remain  constant. 

At  all  times,  the  drop  of  potential  through  the  armature  is  equal  to  the 
difference  between  the  counter  and  the  applied  electromotive  forces,  and  as  the 
product  of  this  drop  and  the  current  represents  energy  wasted,  it  is  desirable 

to  make  it  as  low 
as  possible.  In  good 
motors  of  about 
10  H.  P.  output,  the 
drop  in  the  arma- 
ture is  seldom  more 
than  about  5%  of 
the  applied  electro- 
motive force,  and  is 
less  in  larger  ma- 
chines. This  being 
the  case,  it  is  evident 
that  if  the  arma- 
ture is  at  rest,  so 
that  it  has  no  coun- 
ter electromotive 
force,  and  is  con- 
nected directly  to 
the  mains,  a  very 
large  current  will 
flow  through  it, 
which  would  be 
liable  to  damage  the 
armature.  On  this 
account  an  external 


FIG.  1 


resistance,  called  a  starting  resistance,  is  connected  in  series  with  the  armature 
when  it  is  to  be  started.  This  resistance  is  made  great  enough  to  prevent 
more  than  about  the  normal  current  from  flowing  through  the  armature  when 
it  is  at  rest;  as  the  armature  speeds  up  and  develops  some  counter  electromotive 
force,  this  resistance  is  gradually  cut  out,  until  the  armature  is  connected 
directly  to  the  mains,  and  is  running  at  normal  speed. 

The  energy  represented  by  the  product  of  drop  in  the  armature  and  the 
current  is  wasted;  that  represented  by  the  product  of  the  current  and  the  rest 
of  the  electromotive  force,  that  is,  the  counter  electromotive  force,  is  the  energy 
required  to  keep  the  armature  in  motion. 

Aside  from  the  comparatively  small  amount  of  current  required  to  furnish 
the  torque  necessary  for  overcoming  the  frictional  losses  in  the  motor  itself, 
which  are  practically  constant,  the  amount  of  current  taken  from  the  mains 
is  directly  proportional  to,  and  varies  automatically  with,  the  amount  of  the 
external  load;  for,  if  this  external  load  is  increased,  the  current  that  has  been 


ELECTRICITY  503 

flowing  in  the  armature  cannot  furnish  sufficient  torque  for  this  increased 
load,  so  that  the  machine  slows  down.  This  decreases  the  counter  electromotive 
force,  which  immediately  allows  more  current  to  flow  through  the  armature, 
increasing  the  torque  to  the  proper  amount.  If  the  external  load  is  decreased, 
the  current  flowing  furnishes  an  excess  of  torque,  which  causes  the  speed  to 
increase,  increasing  the  counter  electromotive  force,  and  decreasing  the  current 
until  it  again  furnishes  only  the  required  amount  of  torque. 

As  the  counter  electromotive  force  is  very  nearly  equal  to  the  applied,  it  is 
only  necessary  for  it  to  vary  a  small  amount  to  vary  the  current  within  wide 
limits.  For  example,  if  the  resistance  of  a  certain  armature  is  1  ohm,  and  it 
is  supplied  with  current  at  a  constant  potential  of  250  volts,  then,  when  a 
current  of  10  amp.  is  flowing  through  it,  the  drop  is  10X1  =  10  volts,  and  the 
counter  electromotive  force  is  250—10  =  240  volts.  Now,  if  the  current  is 
reduced  to  1  amp.,  the  drop  is  1 X 1  =  1  volt,  and  the  counter  electromotive  force 

g 
is  250  —  1  =  249  volts;  that  is,  the  counter  electromotive  force  only  varies  -^r~ 

or  3.75%,  while  the  current  varies  — ,  or  90%. 

As  stated  before,  the  field  magnets  of  constant-potential  motors  are  usually 
either  shunt-wound  or  series-wound.  If  shunt-wound  and  supplied  from  a 
constant-potential  circuit,  the  magnetizing  force  of  the  field  coils  is  constant, 
giving  a  practically  constant  field.  This  being  the  case,  the  counter  electro- 
motive force  is  directly  proportional  to  the  speed,  so  that  variations  of  the 
load  make  only  slight  variation  in  the  speed.  A  shunt- wound  motor  is  then 
(practically)  a  constant-speed  motor. 

With  series- wound  motors,  the  strength  of  the  field  varies  with  the  current; 
if  the  load  on  such_a  motor  is  reduced,  the  excess  of  torque  makes  the  armature 
speed  up,  but  the  increasing  counter  electromotive  force  produces  a  decreasing 
current,  thereby  decreasing  the  field  strength,  and,  consequently,  the  armature 
must  speed  up  to  a  much  greater  extent,  in  order  to  increase  the  counter 
electromotive  force  to  the  right  degree,  than  would  be  necessary  if  the  field 
were  constant.  If  the  load  is  increased,  the  increase  in  the  current  so  increases 
the  field  strength  that  the  speed  must  decrease  considerably,  in  order  to  decrease 
the  counter  electromotive  force  by  the  right  amount.  The  speed  of  a  series- 
wound  motor,  then,  varies  largely  with  variations  in  the  load. 

An  advantage  of  the  series  motor  is  that  if  a  torque  greater  than  the  normal 
is  required,  it  can  be  obtained  with  less  current  than  with  a  shunt  motor,  since 
the  increased  current  increases  the  field  strength,  which  remains  practically 
constant  in  a  shunt  motor,  and  the  torque  is  proportional  to  both  these  factors. 

It  is  not  practicable  to  make  the  field  strength  of  a  shunt  motor  as  great  as  is 
possible  to  get  with  a  series  motor,  because  it  would  require  a  very  large  magnet- 
izing force,  and  with  the  shunt  winding,  this  extra  magnetizing  force  would 
have  to  be  expended  all  the  time,  whether  the  strong  field  was  required  or  not, 
which  would  be  very  wasteful;  in  the  series-motor,  however,  this  extra  magnet- 
izing force  is  only  expended  while  it  is  needed. 

A  disadvantage  of  the  series  winding  is  that  if  all  the  load  is  taken  off, 
the  current  required  to  drive  the  motor  is  very  small,  making  a  weak  field, 
which  requires  such  a  high  speed  to  generate  the  proper  counter  electromotive 
force  that  the  armature  is  liable  to  be  damaged.  In  other  words,  the  motor 
will  race,  or  run  away,  if  the  load  is  all  removed.  This  cannot  occur  with  the 
shunt  motor  as  long  as  the  field  circuit  remains  unbroken. 

On  account  of  the  foregoing  features,  shunt  motors  are  used  to  drive 
machinery  that  requires  a  nearly  constant  speed  with  varying  loads,  or  which 
would  be  damaged  if  the  speed  should  become  excessive,  such  as  ordinary 
machinery  in  shops  and  _  factories,  pumps,  etc.  Series  motors  are  used  on 
street  cars,  to  operate  hoists,  etc.,  where,  on  account  of  the  gearing  used,  the 
load  cannot  be  entirely  thrown  off,  except  by  opening  the  motor  circuit,  and  the 
torque  required  at  starting  and  getting  quickly  up  to  speed  is  much  greater 
than  the  torque  required  when  the  car  is  running  at  ordinary  speed. 

Speed  Regulation  of  Motors. — The  speed  of  a  motor  may  be  varied  by 
varying  the  applied  electromotive  force  or  the  strength  of  the  field.  The 
simplest  way  to  vary  the  applied  electromotive  force  is  to  insert  a  resistance,  in 
series  with  the  armature,  similar  to  the  starting  resistance.  By  varying  this 
resistance,  the  applied  electromotive  force  at  the  terminals  of  the  motor  is  also 
varied,  although  the  electromotive  force  of  the  supply  circuit  remains  constant. 
It  is  evident  that  the  energy  represented  by  the  product  of  the  current  and 
the  drop  through  the  resistance  is  converted  into  heat,  and  is  thereby  wasted; 
therefore,  for  great  variations  in  speed,  this  method  is  not  economical,  though 


504 


ELECTRICITY 


often  very  convenient.  The  applied  electromotive  force  may  also  be  varied 
by  varying  the  electromotive  force  of  the  generator  supplying  the  current, 
but  this  can  only  be  done  where  a  single  generator  is  supplying  a  single  motor, 
or  several  motors,  whose  speed  must  all  be  varied  at  the  same  time;  so  that 

this    method   is 
only     used     in 
,  special  cases. 

-250  Volt» •+• — 250  Volts — >\         Varying  the 

-500  Volts • *4  strength  of  the 

pIG  2  field  gives  a  con- 

venient method 

of  varying  the  speed.  If  the  strength  of  the  field  is  lessened,  the  speed  will  in- 
crease, and  if  the  field  is  strengthened,  the  speed  will  decrease.  With  shunt  motors, 
the  field  may  be  weakened  by  inserting  a  suitable  resistance  in  the  field  circuit, 
as  in  shunt  dynamos;  with  series  motors  the  same  result  may  be  obtained  by 
cutting  out  some  of  the  turns  of  the  field  coils  or  by  placing  a  suitable  resistance 
in  parallel  with  the  field  coils.  This  method  of  regulation  is  also  of  limited 
range,  as  it  is  not  economical  to  maintain  the  strength  of  the  field  much  above 
or  below  a  certain  density.  The  resistance  method  described,  being  rather 
more  simple,  it  is  generally  used.  The  regulating  field  resistance  must  be  so 
constructed  as  to  remain  in  the  circuit  all  the  time  the  motor  is  running  without 
getting  hot  enough  to  be  thereby  damaged. 

For  special  cases,  such  as  street-railroad  work,  various  special  combinations 
of  the  foregoing  methods  of  regulation  are  used.  One  of  the  most  common 
of  these  is  known  as  the  series-parallel  method,  and  is  the  method  of  regulation 
generally  used  at  present  for  operating  street  cars.  This  method  is  equivalent 
to  the  method  of  cutting  down  the  _^^_<^  ^f~~\ 

speed  by  reducing  the  electromotive  t 0000 ""T     L** — 

force  applied  to  the  motor,  and  is    __^_ 

only  applicable  where  at  least  two    Trolley]  _  |  Ground 

motors  are  used.     It  is  also  used,  to 

some    extent,    in    haulage    plants. 

When  a  low  speed  is  desired,  or 

when  the  car  is  to  be  started  up,  the 

motors  are  thrown  in  series,  as  shown 

in  Fig.  2,  thus  making  the  voltage  across  each  motor  equal  to  one-half  the  voltage 

between  the  lines,  and  cutting  down  the  speed  accordingly.     When  a  high  speed 

is  desired,  the  motors  are  thrown  in  multiple,  as  shown  in  Fig.  3,  and  each 

motor  runs  at  full  speed  because  it  gets  the  full  line  pressure.     In  practice, 

starting  resistances  are  used  in  connection  with  the  foregoing  to  make  the 

starting  smooth,  but  the  two  running  positions  are  as  shown,  the  motors  being 

connected  in  series  in  the  one  case,  and  in  parallel  in  the  other. 

Connections  for  Continuous-Current  Motors. — Fig.  4  shows  the  manner  in 
which  a  shunt  motor  is  connected  to  the  terminals  +  and  —  of  the  circuit. 
The  current  through  the  shunt  field  does  not  pass  through  the  resistance  R 


FIG.  4 


FIG.  5 


which  is  connected  in  the  armature  circuit,  as  to  keep  the  field  strength  con- 
stant, the  full  difference  of  potential  of  the  supply  circuit  should  be  maintained 
between  the  terminals  of  the  field  coil.  This  would  not  be  the  case  if  the 
rheostat  were  included  in  the  field  circuit,  for  then  the  difference  of  potential 


ELECTRICITY 


505 


would  be  only  that  existing  between  the  brushes  +B  and  —  B.  As  on  starting 
the  motor  this  difference  of  potential  is  small,  only  a  small  current  will  flow 
through  the  field  coils,  which  will  generate  such  a  weak  field  that  an  excessive 
current  will  be  required  to  furnish  the  necessary  torque  for  starting  the  motor. 
When  connected  as  shown,  the  field  is  brought  up  to  its  full  strength  before 
arfy  appreciable  current  passes  through  the  armature;  so  this  difficulty  does 
not  arise.  The  current  through  the  armature  is  gradually  increased  as  the 
speed  increases  by  gradually  cutting  out  the  resistance  in  the  starting  box. 

As  in  a  series  motor  the  same  current  flows  through 
both  armature  and  field  coils,  the  starting  resistance 
may  be  placed  in  any  part  of  the  circuit.  The  diagram 
in  Pig.  5  illustrates  one  method  of  connecting  a  series 
motor  to  the  line  terminals  +  and  — ;  here  the  start- 
ing or  regulating  resistance  R  is  placed  between  the 
—  line  terminal  and  the  b-ush  —  B  of  the  motor.  To 
reverse  the  direction  of  rotation  of  a  motor  it  is  neces- 
sary to  reverse  either  the  direction  of  the  field  or  the 
direction  of  the  current  through  the  armature.  It  is 
usual  to  reverse  the  direction  of  the  current  in  the 
armature,  a  switch  being  used  to  make  the  necessary 
changes  in  the  connections. 

Fig.  6  shows  the  connections  of  one  form  of  reversing  switch.  Two  metal 
bars  B  and  Bi  are  pivoted  at  the  points  T  and  Ti\  one  is  extended  and  supplied 
with  a  handle  H,  and  the  two  bars  are  joined  together  by  a  link  L  of  some 
insulating  material,  such  as  fiber.  Three  contact  pieces  a,  b,  and  c  are  arranged 
on  the  base  of  the  switch  so  that  the  free  ends  of  the  bars  B  and  B\  may  rest 
either  on  a  and  b,  as  shown  by  the  full  lines,  or  on  b  and  c,  as  shown  by  the 
dotted  lines.  The  line  is  connected  to  the  terminals  T  and  T\,  and  the  motor 
armature  between  a  and  b,  or  vice  versa,  a  and  c  being  connected  together. 

When  the  switch  is  in  the  position  shown  by  the  full  lines,  T  is  connected 
to  a  by  the  bar  B,  and  Ti  to  b  by  the  bar  B\.  If  the  switch  is  thrown  by  means 
of  the  handle  H  into  the  position  indicated  by  the  dotted  lines,  T  is  connected 
to  b  by  the  bar  B,  and  T\  to  a  by  the  bar  B\  and  the  connection  between  c  and  a. 
The  direction  of  the  current  through  the  motor  armature,  or  whatever  circuit 
is  connected  between  a  and  b,  is  thus  reversed. 

In  order  to  reverse  only  the  current  in  the  armature,  the  reversing  switch 
must  be  placed  in  the  armature  circuit  only.  Fig.  7  represents  the  connection  for 
a  rever sing-shunt  motor  (a)  and  a  rever sing-series  motor  (&);  +  and  —  are  the 

line  terminals; 
R,  the  starting 
resistance;  B 
and  Bi.  the 
brushes  of  the 
motor,  and  F, 
the  field  coil  of 
the  motor. 
Some  manufac- 
turers combine 

«*>  FIG-  7  «  the  starting  re- 

sistance and  reversing  switch  in  one  piece  of  apparatus.  When  connecting 
up  motors,  some  form  of  main  switch  is  used  to  entirely  disconnect  the  motor 
from  the  line  when  it  is  not  in  use. 

To  prevent  an  excessive  current  from  flowing  through  the  motor  circuit 
from  any  cause,  short  strips  of  an  easily  melted  metal,  known  as  fuses,  mounted 
on  suitable  terminals,  known  as  fuse  boxes,  are  placed  in  the  circuit.  These 
fuses  are  made  of  such  a  sectional  area  that  a  current  greater  than  the  normal 
heats  them  to  such  an  extent  that  they  melt,  thereby  breaking  the  circuit  and 
preventing  damage  to  the  motor  from  an  excessive  current.  The  length  of 
fuse  should  be  proportioned  to  the  voltage  of  the  circuit,  a  high  voltage  requir- 
ing longer  fuses  than  a  low  voltage,  in  order  to  prevent  an  arc  being  maintained 
across  the  terminals  when  the  fuse  melts. 

If  desired,  measuring  instruments  (ammeter  and  voltmeter)  may  be  con- 
nected in  the  motor  circuit,  so  that  the  condition  of  the  load  on  the  motor  may 
be  observed  while  it  is  in  operation.  All  these  appliances,  regulating  resistance, 
reversing  switch,  fuses,  instruments,  etc.,  are  placed  inside  the  main  switch; 
that  is,  the  current  must  pass  through  the  main  switch  before  coming  to  any 
of  these  appliances,  so  that  opening  the  main  switch  entirely  disconnects  them 
from  the  circuit,  when  they  may  be  handled  without  fear  of  shocks. 


506  ELECTRICITY 

ALTERNATING-CURRENT  DYNAMOS 

An  alternating-current  dynamo  is  one  that  generates  a  current  that  periodi- 
cally reverses  its  direction  of  flow;  as  when  an  armature  is  provided  simply 
with  collector  rings.     This  current  may  be  represented  by  a  curve  such  as  that 
shown  in  Fig.  1.    The  complete  set  of  values 
that  the  current,  or  electromotive  force, 
passes  through  repeatedly  is  known  as  a 
cycle.     For  example,  the  values  passed 
through  during  the  interval  of  time  repre- 
-  sented  by  the  distance  ac  will  constitute 
FIG.  1  a  cycle.     The  set  of  values  passed  through 

during  the  interval  ab  is  known  as  an  alternation.  An  alternation  is,  there- 
fore, half  a  cycle.  The  number  of  cycles  passed  through  per  second  is  known 
as  the  frequency  of  the  current,  or  electromotive  force. 

Alternating-current  dynamos  are  now  largely  used  both  for  lighting  and 
power  transmission,  especially  when  the  transmission  is  over  long  distances. 
The  reason  that  the  alternating  current  is  specially  suitable  for  long-distance 
work  is  that  it  may  be  readily  transformed  from  one  pressure  to  another,  and 
in  order  to  keep  down  the  amount  of  copper  in  the  line,  a  high  line  pressure 
must  be  used.  Pressures  much  over  500  or  600  volts  cannot  be  readily  gener- 
ated with  direct-current  machines,  owing  to  the  troubles  that  are  likely  to 
arise  due  to  sparking  at  the  commutator.  On  the  other  hand,  an  alternator 
requires  no  commutator  or  even  collecting  rings,  if  the  armature  is  made 
stationary  and  the  field  revolving,  as  is  frequently  done.  Alternators  are  now 
built  that  generate  as  high  as  11,000  volts  directly.  If  a  still  higher  pressure 
is  required  on  the  line,  it  can  be  easily  obtained  by  the  use  of  transformers. 
Alternating-current  dynamos,  like  direct-current  machines,  consist  of  two 
main  parts,  the  field  and  armature.  Either  of  these  parts  may  be  the  revolving 
member,  and  in  many  modern  machines  the  armature,  or  the  part  in  which  the 
current  is  induced,  is  the 
revolving  member.  Fig.  2 
shows  a  typical  alternator 
of  the  belt-driven  type, 
having  a  revolving  arma- 
ture. It  is  not  unlike  a 
direct-current  machine  as 
regards  its  general  appear- 
ance. The  number  of  poles 
is  usually  large,  in  order  to 
secure  the  required  fre- 
quency without  running  the 
machine  at  a  high  rate  of 
speed.  The  frequencies  met 
with  in  practice  vary  all 
the  way  from  25  to  150. 
The  higher  frequencies  are, 
however,  passing  out  of  use, 
and  at  present  a  frequency 
of  60  is  very  common.  This 
frequency  is  well  adapted 

both  for  power  and  light-  F       „ 

ing  purposes.  When  ma- 
chines are  used  almost  entirely  for  lighting  work,  frequencies  of  125  or  higher 
may  be  used.  The  frequency  of  any  machine  may  be  readily  determined  when 
the  number  of  poles  and  the  speed  is  known,  as  follows: 

_,  number  of  poles     rev.  per  min. 

Frequency  =  —    — - — £ X ^ 

&  ou 

For  example,  if  an  eight-pole  alternator  runs  at  a  speed  of  900  rev.  per  min., 
the  frequency  will  be 

/=. 1X^  =  60  cycles  per  sec. 

Alternators  may  be  divided  into  single-phase  alternators  and  multiphase 
alternators. 

Single-phase  alternators  are  so  called  because  they  generate  a  single  alter- 
nating current  (as  represented  by  the  curve  shown  in  Fig.  1).  The  armature 
is  provided  with  a  single  winding  and  the  two  terminals  are  brought  out  to 
collector  rings.  Single-phase  machines  have  been  largely  used  for  lighting 
work,  but  they  are  gradually  being  replaced  by  multiphase  machines,  because 


ELECTRICITY 


507 


the  single-phase  machines  are  not  well  suited  for  the  operation  of  alternating- 
current  motors. 

Multiphase  alternators  are  so  called  because  they  deliver  two  or  more 
alternating  currents  that  differ  in  phase;  that  is,  when  one  current  is,  say,  at 
its  maximum  value,  the  other  currents  are  at  some  other  value.  This  is 
accomplished  by  providing  the  armature  with  two  or  more  distinct  windings 
which  are  displaced  relatively  to  each  other  on  the  armature.  One  set  of 
windings,  therefore,  comes  under  the  poles  at  a  later  instant  than  the  winding 
ahead  of  it,  and  the  current  in  this  winding  comes  to  its  maximum  value  at  a 
later  instant  than  the  current  in  the  first  winding.  In  practice,  the  two  types 
of  multiphase  alternators  most  commonly  used  are  two-phase  alternators,  and 
three-phase  alternators. 

Two-phase  alternators  deliver  two  alternating  currents  that  differ  in  phase 
by  one-quarter  of  a  complete  cycle;  that  is,  when  the  current  in  one  circuit 
is  at  its  maximum  value,  the  current  in  the  other  circuit  is  passing  through  its 
zero  value.  By  tapping  four  equidistant  points  of  a  regular  ring  armature, 
as  shown  in  Pig.  3,  and  connecting  these  points  to  four  collector  rings,  a  simple 
two-pole  two-phase  alternator  is  obtained.  One  circuit  connects  to  rings  1 
and  1',  the  other  circuit  connects  to  rings  2  and  2'.  When  the  part  of  the 
winding  connected  to  one  pair  of  rings  is  in  its  position  of  maximum  action,  the 
electromotive  force  in  the  other  coils  is  zero,  thus  giving  two  currents  in  the 


FIG.  3 


FIG.  4 


two  different  circuits  that  differ  in  phase  by  one-quarter  of  a  cycle  or  one-half 
an  alternation. 

Three-phase  alternators  deliver  three  currents  that  differ  in  phase  by  one- 
third  of  a  complete  cycle;  that  is,  when  one  current  is  flowing  in  one  direction 
in  one  circuit,  the  currents  in  the  other  two  circuits  are  one-half  as  great,  and 
are  flowing  in  the  opposite  direction.  By  tapping  three  equidistant  points  of 
a  ring  winding,  as  shown  in  Fig.  4,  a  simple  three-phase  two-pole  alternator 
is  obtained.  Three  mains  lead  from  the  collecting  rings. 

In  order  to  have  three  distinct  circuits,  it  would  ordinarily  be  necessary 
to  have  six  collecting  rings  and  six  circuits;  but  this  is  not  necessary  in  a  three- 
phase  machine  if  the  load  is  balanced  in  the  three  different  circuits,  because 
one  wire  can  be  made  to  act  alternately  for  the  return  of  the  other  two. 

Uses  of  Multiphase  Alternators. — Multiphase  alternators  are  extensively 
used  because  alternating-current  motors  can  be  readily  operated  from  two- 
phase  and  three-phase  circuits.  By  using  multiphase  machines,  motors  can 
be  operated  that  will  start  from  rest  under  load,  whereas  with  single-phase 
machines  most  motors  have  to  be  brought  up  to  speed  from  some  outside 
source  of  power  before  they  can  be  made  to  run.  For  this  reason,  such  machines 
are  used  for  the  operation  of  modern  power-transmission  plants.  As  far  as 
the  general  appearance  of  three-phase  machines  goes,  they  are  similar  to 
ordinary  single-phase  alternators,  the  only  difference  being  in  the  armature 
winding  and  the  larger  number  of  collector  rings.  The  multiphase  alternator 
is  also  adapted  for  the  operation  of  lights,  so  that  by  using  these  machines  both 
lights  and  motors  may  be  operated  from  the  same  plant.  They  are  well  adapted 
for  power-transmission  purposes  in  mines,  especially  for  the  operation  of 
pumping  and  hoisting  machinery,  because  the  motors  operated  by  them  are 
very  simple  in  construction  and  therefore  not  liable  to  get  out  of  order. 


508  ELECTRICITY 

ALTERNATING-CURRENT  MOTORS 

Alternating-current  motors  may  be  divided  into  synchronous  motors  and 
induction  motors. 

Synchronous  motors  are  almost  identical,  so  far  as  construction  goes,  with 
the  corresponding  alternator.     For  example,  a  two-phase  synchronous  motor 

will  be  constructed  in  the  same  way  as 
a  two-phase  alternator.  They  are  called 
synchronous  motors  because  they  al- 
ways run  in  synchronism,  or  in  step, 
with  the  alternator  driving  them. 
This  means  that  the  motor  runs  at 
the  same  frequency  as  the  alternator, 
and  if  the  motor  had  the  same  num- 
ber of  poles  as  the  alternator,  it  would 
run  at  the  same  speed,  no  matter  what 
load  it  might  be  carrying.  This  type 
of  motor  has  many  good  points,  and 
is  especially  well  suited  to  cases  where 
the  amounts  of  power  to  be  transmitted 
are  comparatively  large  and  where  the 
motor  does  not  have  to  be  started  and 
stopped  frequently.  Multiphase  syn- 
chronous motors  will  start  up  from 
rest  and  will  run  up  to  synchronous 
speed  without  aid  from  any  outside 
source.  Most  multiphase  synchron- 

pIG  ous  motors  will  not,  however,  start 

with  a  strong  starting  torque  or  effort, 

and  will  not,  therefore,  start  up  underload,  and  cannot  be  used  in  places 
where  a  strong  starting  effort  is  required .  For  this  reason  most  synchronous 
motors  are  not  suitable  for  intermittent  work.  Some  special  multiphase  syn- 
chronous motors  are  so  designed,  however,  that  they  may  be  used  where  a 
fairly  strong  starting  effort  is  required. 

Induction  motors  are  so  called  because  the  current  is  induced  in  the  arma- 
ture instead  of  being  led  into  it  from  some  outside  source.  Fig.  1  shows  a 
typical  induction  motor.  There  are  two  essential  parts  in  these  machines, 
viz.,  the  field,  into  which  multiphase  currents  are  led  from  the  line,  and  the 
armature,  in  which  currents  are  induced  by  the  magnetism  set  up  by  the  field. 
Either  of  these  parts  may  be  the  stationary  or  revolving  member,  but  in  most 
cases  the  field,  or  part  that  is 
connected  to  the  line,  is  sta- 
tionary. The  stationary  part 
of  an  alternating-current  motor 
is  called  the  stator  and  the  rota- 
ting part,  the  rotor.  Fig.  2 
shows  the  construction  of  the 
stationary  member  or  field. 
This  consists  of  a  v  number  of 
iron  laminations,  built  up  to 
form  a  core  and  provided  with 
slots  around  the  inner  periph- 
ery. Form-wound  coils  con- 
stituting the  field  winding  are 
placed  in  these  slots  and  con- 
nected to  the  mains.  This  wind- 
ing is  arranged  in  the  same  way 
as  the  armature  winding  of  a 
multiphase  alternator.  When 
alternating  currents  differing  in 
phase  are  sent  through  the  wind- 
ing, magnetic  poles  are  formed 
at  equidistant  points  abound 
the  periphery  of  the  field,  and 

the  constant   changing  of  the  FIG 

currents  causes  these  poles  to 
shift  around  the  ring,  thus  setting  up  what  is  known  as  a  revolving 
magnetic  field.  The  armature,  Fig.  3,  consists  of  a  laminated  iron  core 
provided  with  a  number  of  slots,  in  each  of  which  is  placed  a  heavy  copper 


ELECTRICITY 


509 


bar  b.  The  ends  of  these  bars  are  all  connected  together  by  two  heavy  short- 
circuiting  rings  r  running  around  each  end  of  the  armature.  The  bars  and 
end  rings  thus  form  a  number  of  closed  circuits.  When  such  an  armature  is 
placed  in  the  revolving  field,  the  magnetism  will  cut  across  the  armature  con- 
ductors, inducing  electromotive  forces  in  them,  and  as  the  conductors  are 
joined  up  into  closed  circuits,  currents  will  flow  in  them.  These  currents  will 
react  on  the  field  and  the  armature  will  be  forced  to  revolve.  Such  an  armature 
will  not  run  exactly  in  synchronism,  because  if  it  did,  it  would  revolve  just  as 
fast  as  the  magnetic  field,  and  there  would  be  no  cutting  of  lines  of  force. 
The  speed  drops  slightly  from  no  load  to  full  load,  but  if  the  motor  is  well 
designed,  this  falling  off  in  speed  is  slight. 

The  name  squirrel  cage  is  applied  to  a  rotor  of  the  type  shown  in  Fig.  3. 
Another  type  of  rotor  used  in  induction  motors  is  provided  with  a  coil  winding 
with  ends  brought  out  to  three  collector  rings  mounted  on  the  shaft.  By 
means  of  stationary  brushes  resting  on  these  rings,  the  resistance  in  the  circuit 
of  such  a  rotor  can  be  varied.  Motors  having  such  rotors  are  called  wound- 
rotor  motors,  or  slip-ring  motors.  Induction  motors  possess  many  advantages 
for  mine  work.  Squirrel-cage  mo- 
tors having  no  sliding  contacts 
operate  with  absolutely  no  spark- 
ing— a  desirable  feature  for  mine 
work.  Such  motors  are  also  very 
simple  in  construction,  and  are 
therefore  not  liable  to  get  out  of 
order.  They  have  the  additional 
advantage  over  the  synchronous 
motor  in  that  they  exert  a  strong 
starting  effort,  and,  in  fact,  behave 
in  most  respects  like  any  good  shunt- 
wound  direct-current  motor.  They 
are  used  quite  successfully  for  all 
kinds  of  stationary  work,  such  as 
pumping,  hoisting,  etc.,  but  are  not 
adapted  for  haulage  purposes. 
Wound-rotor  (slip-ring)  motors  are 
used  where  especially  strong  starting 
effort  or  variable  speed  is  required. 


FIG.  3 


At  no  load  the  speed  of  an  induction  motor  is  practically  the  quotient 
obtained  by  dividing  the  number  of  alternations  of  the  current  by  the  number 
of  magnetic  poles  for  which  the  motor  field  winding  is  connected.  Thus  with 
a  60-cycle  current,  or  7,200  alternations,  a  two-pole  motor  runs  at  3,600  rev. 
per  min.,  a  four-pole  motor  at  1,800  rev.,  a  six-pole  motor  at  1,200  rev.,  an 
eight-pole  motor  at  900  rev.,  a  ten-pole  motor  at  720  rev.,  a  twelve-pole  motor 
at  600  rev.,  and  a  fourteen-pole  motor  at  514  rev.  With  a  25-cycle  current, 
or  3,000  alternations,  the  corresponding  speeds  are  1,500,  750,  500,  375,  300, 
250,  and  214  rev.  per  min. 

The  full-load  speed  is  less  than  the  no-load,  or  synchronous,  speed,  and 
the  decrease  from  no-load  to  full-load  speed  is  called  the  slip.  The  slip  depends 
on  the  resistance  of  the  rotor  circuit  and  on  the  load,  and,  the  higher  the  slip 
with  a  given  load,  the  lower  the  efficiency  of  the  motor.  In  commercial  motors, 
slip  ranges  in  value  from  2  to  10%  of  the  no-load  speed,  depending  on  the 
size  of  the  motor,  large  motors  having  low  slip. 

Selection  of  Induction  Motors  for  Mine  Use. — Induction  motors  are  made 
for  operating  on  single-phase,  two-phase,  and  three-phase  circuits.  Single- 
phase  motors  can  be  used  advantageously  in  small  capacities  up  to,  say, 
10  H.  P.,  for  many  purposes.  They  start  with  fairly  strong  effort  and  operate 
with  efficiency  and  power  factor  approximately  the  same  as  two-phase  and 
three-phase  motors.  They  require  but  two  line  wires  and  one  transformer 
to  increase  or  decrease  the  voltage. 

In  cost  and  reliability  of  operation  there  is  little  choice  between  two-phase 
and  three-phase  motors,  but  because  the  latter  require  but  three  line  wires  as 
opposed  to  the  four  required  by  the  former  the  resulting  savinp  in  copper  has 
led  to  the  more  extensive  use  of  the  three-phase  type.  It  should  be  noted, 
however,  that  two-phase  systems  require  but  two  transformers  where  the 
voltage  has  to  be  changed  as  against  three  transformers  for  the  three-phase 
system. 

By  the  use  of  static  transformers  the  voltage  for  induction  motors  can  be 
made  independent  of  the  line  voltage.  For  long-distance  transmission  lines 


510  ELECTRICITY 

the  generator  voltage  is  usually  stepped-up  for  transmission  through  the  line, 
and  the  line  voltage  stepped-down  for  use  in  the  motors  at  the  end  of  the  line. 
Large  motors  can  be  advantageously  operated  directly  on  the  line  if  the  voltage 
does  not  exceed  6,600,  but  great  care  must  be  taken  to  keep  them  dry.  High- 
voltage  motors  cannot  be  used  successfully  in  damp  places;  and  low-  voltage 
motors  for  use  in  such  places  should  have  waterproof  insulation  on  the  windings. 
The  choice  of  frequency  generally  lies  between  the  two  prevailing  standards 
of  25  cycles  and  60  cycles  per  sec.  For  railroad  work  the  25-cycle  transmission 
system  is  preferred  because  a  better  regulation  is  obtainable  and  the  rotary 
(synchronous)  converters  Used  in  connection  therewith  cost  less.  For  general 
lighting  purposes,  both  arc  and  incandescent  lamps  operate  better  on  60-cycle 
circuits.  When  the  voltage  does  not  exceed  110,  incandescent  lamps  may  be 
used  without  flickering  on  25-cycle  circuits;  but  when  the  voltage  is  high, 
frequency-changers  should  be  employed  to  raise  the  frequency  of  that  portion 
of  the  current  used  for  lighting  from  25  to  60  cycles.  For  the  operation  of 
stationary  motors  about  mines,  the  60-cycle  system  is  generally  preferred 
because  the  transformers  are  less  costly,  because  the  choice  of  motor  speeds  is 
much  greater,  and  because  this  frequency  is  as  well  adapted  to  lighting  as  to 
power  purposes. 

The  full-load  torque  of  a  motor  is  the  turning  effort  it  must  develop  when 
revolving  at  its  rated  speed  in  order  to  produce  its  rated  horsepower;  that  is, 
„   p  =2*TXRPM 
'         33,000      ' 
in  which  ir  =  3.1416; 

T  =  torque,  in  foot-pounds; 
RPM  =  ihe  number  of  revolutions  per  minute. 

„,    33.000  HP     5,250  HP      _, 

By  transformation,  T=n   ..,„„,,,  =  —  --,--.  —  .     Thus,  the  full-load  torque 

KJrM 


of  a  10-H.  P.  motor  at  1,700  rev.  per  min.  is  5>25^10 

The  starting  torque  of  an  induction  motor  is  that  developed  at  starting  from 
a  state  of  rest  and  is  commonly  considerably  greater  than  the  full-load  torque. 
The  pull-out  torque  is  the  maximum  turning  effort  the  motor  can  exert  without 
stopping  and  is  usually  from  1.5  to  3  times  the  full-load  torque.  An  induction 
motor  cannot  operate  at  more  than  full-load  torque,  except  for  short  periods, 
without  overheating. 

Squirrel-cage  induction  motors  have  no  wearing  parts  except  the  bearings, 
and  these  can  be  made  dust-proof,  so  that  these  motors  rarely  need  to  be 
enclosed  unless  they  are  to  be  used  in  extremely  dusty  places.  A  free  circu- 
lation of  air  through  the  interior  of  the  motor  is  necessary  to  keep  it  cool. 
Ordinarily,  the  necessary  circulation  is  secured  by  arranging  the  casing  as 
shown  in  Fig.  1,  where  the  openings  are  covered  with  gratings  to  prevent 
objects  falling  into  and  injuring  the  motor.  "Where  the  air  is  only  moderately 
dusty,  a  supply  of  clean  air  may  be  drawn  through  a  special  pipe  from  outside 
the  motor  room  and,  after  circulating  through  the  motor,  is  discharged  through 
another  pipe.  For  use  in  very  dusty  or  damp  places,  the  openings  in  the 
casing  (shown  covered  by  gratings  in  Fig.  1)  are  closed  with  tight-fitting 
plates;  these  should  be  fitted  with  gaskets  to  keep  out  dampness.  It  must  be 
remembered  that  this  enclosing  reduces  the  capacity  of  the  motor  for  con- 
tinuous operation  owing  to  the  heating  through  lack  of  interior  ventilation; 
in  fact,  an  enclosed  motor  can  operate  at  full  rating  only  intermittently. 

Squirrel-cage  motors  are  generally  preferred  to  wound-rotor  motors  for 
driving  machinery,  such  as  mine  fans,  where  the  speed  is  constant.  By  pro- 
viding a  motor  of  this  type  with  a  high  resistance  rotor,  its  starting  and  pull- 
out  torque  with  a  given  input  of  current  can  be  made  high,  although  its 
efficiency,  when  running  under  load,  is  correspondingly  low.  For  intermittent 
service  where  a  high  torque  is  necessary  for  starting  or  while  in  operation, 
squirrel-cage  motors  with  high-resistance  rotors  are  sometimes  desirable,  as  in 
driving  elevators,  conveyers,  etc. 

Wound-rotor  motors  are  preferred  for  driving  machinery  such  as  hoisting 
engines,  which  must  be  frequently  started  and  stopped  with  a  high  torque 
and  where  ability  to  change  the  speed  is  important.  By  means  of  a  controller 
connected  with  the  collector  rings,  the  resistance  in  the  rotor  circuit  can  be 
varied  at  will,  thus  limiting  the  starting  current  and  giving  any  desired  speed. 
When  driving  machines  other  than  hoisting  engines  where  the  engineer  is  con- 
stantly on  duty,  it  should  be  noted  that  when  a  motor  of  this  type  is  operated 
with  external  resistance  in  its  rotor  circuit,  any  change  in  the  amount  of  the 


ELECTRICITY  511 

load  thrown  upon  it  causes  an  inverse  change  in  its  speed  so  that,  in  these 
cases,  also,  the  presence  of  an  attendant  may  be  necessary  to  keep  the  speed 
adjusted. 

Induction  motors  are  usually  purchased  under  guaranteed  heating  limits 
and  performance  characteristics,  such  as  efficiency,  power  factor,  starting  and 
pull-out  torque,  and,  sometimes,  slip.  The  heating  limits,  or  rise  in  temper- 
ature of  the  windings,  etc.,  of  the  motor  when  in  operation  are  at  present 
commonly  guaranteed  not  to  exceed  40°  C.  to  75°  C.  above  the  normal  temper- 
ature; the  amount  of  rise  guaranteed  depending  on  the  style  of  motor,  whether 
open,  semi -enclosed,  or  enclosed,  and  on  the  nature  of  the  service,  whether  . 
under  continuous  or  intermittent  operation.  High  efficiency  is  desirable  in  a 
motor  that  is  to  be  run  continuously  under  a  steady  load,  and  the  efficiency 
should  be  high  at  this  load;  the  importance  of  high  efficiency  in  such  a  motor 
increases  with  the  cost  of  electricity.  Efficiency  is  not  of  importance  in  a  motor 
that  opei  ates  intermittently,  or  where  the  cost  of  electricity  is  very  low. 

Low  power  factor  indicates  that  some  of  the  current  in  the  generator  and 
transmission  line  is  useless  or  idle,  in  that  the  energy  supplied  the  motors 
is  less  than  is  indicated  by  the  line  current.  The  actual  energy  that  can  be 
delivered  by  a  generator  within  its  guaranteed  heating  limits  decreases  with  the 
power  factor.  Thus,  a  generator  rated  at  1,000  K.  W.  at  100%  power  factor 
would  have  an  output  of  900  K.  W.  at  90%  power  factor;  and  similarly,  the 
carrying  capacity  of  transmission  lines  is  reduced  in  the  same  way.  The  power 
factor  9f  a  system  depends  on  the  power  factors  of  the  motors  operating 
on  the  lines.  A  small  number  of  motors  operating  at  low  power  factors  may  not 
affect  the  general  capacity  appreciably,  but  as  the  number  of  motors  is  increased, 
the  importance  of  operating  them  at  high  power  factor  increases,  as  the  genera- 
tor and  lines  may  be  overloaded  with  the  current. 

Installation  and  Care  of  Induction  Motors. — When  ordering  a  motor,  the 
manufacturer  should  be  advised  whether  it  is  to  be  placed  on  a  side  wall, 
suspended  in  a  reversed  position  overhead,  or  used  on  the  ordinary  horizontal 
floor,  or  pedestal,  mounting,  as  the  arrangement  of  the  housings,  oil  cups,  etc., 
will  be  different  in  the  several  cases.  The  machine  should  be  mounted  in  the 
driest,  cleanest,  and  best-ventilated  place  possible,  where  it  is  in  plain  sight 
and  within  easy  reach.  The  foundations  should  be  solid  enough  to  prevent 
vibration,  masonry  or  concrete  construction  being  preferred.  The  rails  upon 
which  the  motor  slides  in  being  adjusted  to  position  should  be  supported 
upon  an  absolutely  even  surface,  so  that  the  machine  may  rest  properly  upon 
them.  When  the  motor  is  belt-connected  to  the  driven  machine,  the  axles 
of  the  two  should  be  absolutely  parallel,  and  the  centers  of  the  faces  of  the 
driving  and  driven  pulleys  should  be  exactly  in  line,  so  that  the  rotor  will  not 
be  forced  from  its  central  position.  If  the  motor  is  geared  to  the  driven 
machine,  the  axles  of  the  two  must  be  parallel,  the  centers  of  the  faces  of  the 
-  gear-wheels  must  be  in  the  same  line,  and  the  distance  between  the  centers  of 
the  gear-wheels  must  be  exactly  that  demanded  by  the  designs,  that  the  pinion 
may  mesh  properly  with  the  gear.  If  a  thin  piece  of  paper  is  passed  through 
the  gears  while  slowly  turning  the  rotor,  it  should  show  by  its  crushing  or 
marking,  an  even  pressure  across  the  full  width  of  the  tooth. 

Before  starting  a  motor  for  the  first  time,  care  must  be  taken  that  all 
circuits,  connections,  etc.,  are  in  accordance  with  the  diagram  furnished  by  the 
manufacturer.  With  small  motors,  enclosed  type  fuses  are  used  in  connection 
with  the  starter,  but  with  larger  motors  circuit-breakers  are  used.  Fuses  that 
are  not  out  during  starting  should  have  a  current  capacity  at  least  2^  times 
that  of  the  motor.  Very  small  motors  require  no  starting  apparatus  and  may 
be  put  in  operation  by  closing  the  line  circuit.  In  motors  of  5  H.  P.  and 
upwards,  the  sudden  throwing  on  of  the  entire  current  will  cause  fluctuations 
in  the  line  current,  which -may  interfere  with  the  working  of  other  motors  on 
the  same  circuit  and  may  even  damage  the  motor  windings. 

To  permit  the  application  of  low  voltage  at  starting,  which  may  be  increased 
to  full  voltage  after  the  motor  has  been  brought  up  to  speed,  squirrel-cage 
induction  motors  are  provided  with  auto  or  compensating  starters.  These 
starters  differ  in  details  of  design,  but  in  all  cases  they  comprise  the  essential 
elements  of  two  or  three  single-coil  transformers  for  reducing  the  voltage,  and 
a  switch  for  changing  the  connections  between  the  line,  the  transformers,  and 
the  motor.  The  transformers  are  provided  with  taps,  and  by  adjusting  the 
tapping-in  point  the  voltage  at  starting  may  be  varied.  In  the  starting  posi- 
tion, the  switch  conrects  the  transformers  to  the  line  and  the  motor  to  the 
transformers.  In  the  running  position,  the  motor  is  connected  directly  to  the 
line,  no  current  passing  through  the  transformers.  Starters  commonly  have 


512  ELECTRICITY 

but  one  starting  position  and  open  the  circuit  when  passing  from  the  starting 
to  the  running  position.  They  are  designed  so  that  it  is  impossible  to  move 
from  the  off  to  the  running  position  without  passing  through  the  starting 
position,  or  to  introduce  the  starting  connection  in  passing  back  from  the 
running  to  the  off  position.  The  handles  of  most  starters  are  moved  clockwise 
to  start  and  stop  the  motor,  and  can  be  turned  in  the  reversed  position  only 
to  return  from  the  starting  to  the  off  position. 

The  power  should  not  be  thrown  on  in  one  rapid  operation  as  such  action 
will  cause  excessive  starting  current;  rather,  the  handle  should  be  left  at  the 
starting  position  for  a  short  time,  and  then  moved  quickly  either  to  the  second 
starting  position  (if  there  is  one)  or  to  running. 

When  setting  up  a  motor,  the  oil  wells  should  be  examined  and  if  dirty 
should  be  blown  out  or  cleaned  with  gasoline  if  they  are  badly  clogged.  After 
cleaning,  they  should  be  filled  with  a  high  grade  of  mineral  oil,  preferably 
dynamo  oil,  which  flows  easily  and  is  readily  carried  up  by  the  oil  rings.  Graph- 
ite and  similar  lubricants  are  not  satisfactory  for  use  in  motors  as  they  clog 
the  oil  ducts  and  interfere  with  the  operation  of  the  oil  rings.  When  starting 
the  motor  (which  may  be  turned  by  hand  for  testing  purposes)  care  must  be 
taken  that  the  rings  revolve  and  carry  up  the  oil.  At  all  times  enough  oil 
must  be  kept  in  the  bearings  that  the  rings  may  dip  well  below  its  surface. 
Bearings  using  oil  and  waste  should  be  packed  with  a  high-grade  wool  waste, 
which  should  fit  closely  against  the  shaft.  Cotton  or  the  poorer  grades  of  wool 
waste  become  soggy  and  drop  away  from  the  shaft.  The  waste  should  be 
thoroughly  saturated  with  oil,  preferably  by  immersing  it  for  48  hr.,  and  then 
letting  it  drip  for  10  to  12  hr.  Too  much  free  oil  will  result  in  an  overflow 
and  the  possible  introduction  of  oil  within  the  motor.  Dirty  oil  should  never 
be  used;  it  should  be  replaced  at  once  with  clean  oil,  and  to  this  end  an  oil 
filter  is  an  excellent  investment.  Bearings  using  grease  should  be  filled  with  a 
good  quality  of  grease  free  from  dirt  or  grit. 

The  distance  between  the  centers  of  the  driving  and  driven  pulleys  should 
be  great  enough  to  allow  some  sag  in  the  belt.  Kent  gives  the  following 
general  rules  for  belting.  With  narrow  belts  and  small  pulleys,  the  distance 
between  centers  should  be  15  ft.,  with  a  sag  in  the  loose  side  of  the  belt  of  1  ^  to 
2  in.  With  belts  of  medium  width  and  larger  pulleys,  the  center  distance 
of  the  pulleys  should  be  20  to  25  ft.,  and  the  sag,  2|  to  4  in.  With  main  belts  on 
very  large  pulleys,  the  center  distance  should  be  25  to  30  ft.,  and  the  sag  from 
4  to  5  in.  If  the  distance  between  pulley  centers  is  too  great,  the  belt  will  flap 
unsteadily  resulting  in  unnecessary  wear  of  the  belt  and  bearings;  if  the  distance 
is  too  short,  the  severe  tension  required  to  prevent  slipping  will  cause  rapid 
'wear  and  possible  overheating  of  the  bearings.  The  rules  given  represent  good 
practice  for  long  life  of  belt  and  bearings.  Shorter  distances  must  sometimes 
be  used,  in  which  cases  the  belt  may  be  tighter,  the  belt  and  pulleys  wider,  or 
the  pulleys  larger  and  the  belt  speed  greater.  Very  short  belts  will  work  satis- 
factorily if  idler  pulleys  are  used  to  increase  the  arc  of  contact  between  the 
belt  and  pulleys.  Belts  should  not  be  run  at  a  greater  angle  with  the  horizontal 
than  45°  if  this  is  possible,  and  never  vertically.  The  belt  should  be  just  tight 
enough  to  avoid  slipping  or  flapping;  the  slack  side  should  have  a  gently  undu- 
lating motion;  the  joints  should  be  as  smooth  as  possible,  and  a  lapped  joint 
should  always  trail,  never  lead  over  a  pulley.  A  sidewise  movement  of  the 
belt  indicates  poor  alinement  of  the  pulleys  or  unequal  stretching  of  the  edges 
of  the  belt. 

When  a  bearing  becomes  hot,  the  cause  of  the  trouble  should  be  looked  for 
at  once.  Some  of  the  common  causes  of  hot  bearings  are:  Poor  grades  of  oil, 
grit  and  dust  in  the  oil  well  and  bearings,  stopping  of  the  circulation  through 
foreign  particles  in  the  oil  grooves,  an  empty  oil  well,  too  tight  or  too  heavy  a 
belt,  too  much  end  thrust  on  the  rotor  due  to  poor  alining  or  leveling,  a  sprung 
shaft,  or  worn  or  cut  Babbitt  metal  in  the  bearings.  The  bearings  of  induction 
motors  should  be  inspected  daily,  because  the  air  gap  between  the  rotor  and 
stator  being  small,  any  excessive  wear  on  the  bearings  may  cause  these  parts 
to  rub.  Some  of  the  larger  sizes  of  induction  motors  are  provided  with  adjust- 
able bearings  so  that  the  rotor  may  be  shifted  to  secure  a  uniform  air  gap, 
but  in  the  smaller  sizes  the  effects  of  wear  can  be  overcome  only  by  renewing 
the  linings. 

Dust  and  grit  should  not  be  allowed  to  accumulate  around  the  windings 
and  bearings.  __  The  motor  should  be  regularly  and  thoroughly  wiped  and  the 
dust  blown  from  all  its  parts.  The  projecting  portions  of  the  stator  coils  of 
motors  running  in  damp  places  should  receive  an  occasional  coating  of  water- 
proof insulating  varnish. 


ELECTRICITY 


513 


The  temperature  of  all  induction  motors  will  rise  above  that  of  the  atmos- 
phere while  running  under  load.  As  long  as  the  hand  can  be  held  continuously 
on  the  machine  there  is  no  danger,  but  as  soon  as  the  heat  can  be  borne  but 
for  a  few  seconds,  and  particularly  if  the  odor  of  burning  oil  is  noticeable,  the 
danger  point  has  been  reached.  It  will  seldom  be  necessary  to  do  more  than 
supply  the  bearings  with  an  abundance  of  fresh  clean  lubricant,  care  being 
taken  that  the  oil  or  grease  reaches  the  bearing  surface;  sometimes  it  may  be 
necessary  to  remove  excessive  belt  tension.  If  relief  is  not  afforded  in  this 
way,  a  heavy  oil  should  be  poured  directly  on  the  journal  if  possible.  If 
necessary,  part  or  all  of  the  load  should  be  removed  but  the  rotor  should  be  kept 
in  motion  enough  to  prevent  the  bearing  from  becoming  set  or  frozen. 

When  an  induction  motor  is  overloaded  beyond  its  limit,  it  will  stop  or 
pull-out.  Should  a  motor  stop  when  it  is  not  overloaded,  and  an  examination 
of  the  bearings  and  air  gap  shows  that  the  motor  and  stator  are  not  rubbing, 
the  stoppage  may  be  due  to  abnormally  low  voltage  in  the  supply  circuit. 
The  torque  exerted  by  induction  motors  decreases  as  the  square  of  the  voltage; 
hence,  a  comparatively  small  drop  in  the  voltage  produces  a  large  decrease  in 
torque  and  the  motor  may  come  to  a  standstill  if  it  happens  to  be  carrying  a 
heavy  load  at  the  time  the  voltage  drops.  To  secure  the  best  results  from  an 
induction  motor,  full  voltage  should  be  maintained  and  it  is  better  to  have  the 
voltage  too  high  than  too  low  provided  excessive  heating  does  not  result 
therefrom. 


TRANSFORMERS 

Transformers  used  for  raising  the  voltage  are  known  as  step-up  transformers; 
those  used  for  lowering  the  pressure  are  known  as  step-down  transformers. 

The  transformer  consists  9f  a  laminated  iron  core  upon  which  two  coils 
of  wire  are  wound;  these  coils  are  entirely  distinct,  haying  no  connection 
with  each  other.  One  of  these  coils,  called  the  primary,  is  connected  to  the 
mains;  the  other  coil,  called  the  secondary,  is  connected  to  the  circuit  to  which 
. ,  current  is  delivered.  Fig.  1  shows  the  arrangement  of 

coils  and  core  for  a  common 

type-  of  transformer.     The 

secondary  coil  is  wound  in 

two   parts   5   and  S',  and 

the  primary  coil,  also  in  two 

parts  P  and  Pf,  is  placed 

over  the  secondary.     C  is 

the  core,  built  up  of  thin 

iron  plates.     Fig.  2  shows  a 

weather-proof  cast-iron  case 

for  this  transformer.    "When 

•  a  current  is  sent  through 

the  primary  it  sets  up    a 

magnetism  in  the  core  which 

rapidly  alternates  with  the 

changes  in  the  current. 

This   changing    magnetism 


FIG.  1 


FIG.  2 


sets  up  in  the  secondary  an  alternating  electromotive  force,  which  depends 
on  the  number  of  turns  in  the  secondary  coil.  If  the  secondary  turns  are 
greater  than  the  primary,  the  secondary  electromotive  force  will  be  higher 
than  that  of  the  primary.  The  relation  between  the  primary  electromotive 
force  and  secondary  electromotive  force  is  given  by  the  following: 

Second  E.  M.  P.-prfn^  E.  M. 


secondary  E.  M.  P. 


secondary  turns 

The  ratio    pnmary  tunl!L  js  known  as  the  ratio  of  transformation  of  the 

secondary  turns 

transformer.  For  example,  if  a  transformer  had  1,200  primary  turns  and 
60  secondary  turns,  its  ratio  of  transformation  would  be  20  to  1,  and  the  secon- 
dary voltage  would  be  one-twentieth  that  of  the  primary.  Transformers  are 
made  for  a  number  of  different  ratios  of  transformation,  the  more  common  ones 
being  10  to  1  or  20  to  1.  Of  course,  a  transformer  never  gives  out  quite  as  much 

33 


514 


ELECTRICITY 


power  from  the  secondary  as  it  takes  in  from  the  primary  mains  because  there 
is  always  some  loss  in  the  iron  core  and  in  the  wire  making  up  the  coils.     The 


l--ioootr— T 

l^oooooTdW-J 


FIG.  4 


efficiency  of  trans- 
formers is,  however, 
high,  reaching  as 
high  as  97%  or  98% 
in  the  larger  sizes. 
Transformers  are 
connected  in  paral- 
lel across  the 
mains,  and  if  they 
are  well  designed, 
will  furnish  a  very 
nearly  constant  sec- 
ondary pressure  at 


FIG.  5 


all  loads,  when  furnished  with  a  constant  primary  pressure.  Fig.  3  shows 
transformers  connected  on  a  single-phase  circuit,  Fig.  4  shows  the  con- 
nection for  a  two-phase  circuit,  and  Fig.  5  shows  one  method  of  connection 
for  a  three-phase  circuit. 

ELECTRIC  SIGNALING 

BATTERIES 

Batteries  are  used  for  various  purposes  in  connection  with  mining  work, 
principally  for  the  operation  of  bells  and  signals.  The  Leclanche  cell  is  one 
that  is  widely  used  for  bell  and  telephone  work.  It  is  made  in  two  or  three 
different  forms,  one  of  the  most  common  being  shown  in  (a)  of  the  accompany- 
ing illustration.  The  zinc  element  of  this  battery  is  in  the  form  of  a  rod  Z, 
and  weighs  about  3  oz.  The  other  electrode  is  a  carbon  plate  placed  in  a 
porous  cup  and  surrounded  with  black  oxide  of  manganese,  mixed  with  crushed 

coke  or  carbon.  The  electro- 
lyte used  in  the  battery  is  a 
saturated  solution  of  sal  am- 
moniac. The  electromotive 
force  of  this  cell  is  about  1.48 
volts  when  the  cell  is  in  good 
condition.  In  another  form  of 
the  cell,  known  as  the  Gonda 
type,  black  oxide  of  manganese 
is  pressed  into  the  form  of 
bricks  and  clamped  against  each 
side  of  a  carbon  plate  by 
means  of  rubber  bands.  The 
Leclanch6  type  of  cell  will  do 
good  work  if  it  is  only  used 

,  j  fft  intermittently  in  circuits  where 

the  insulation  is  good  and  where 

there  is  no  leakage  causing  the  cell  to  give  out  current  continuously.  If  cur- 
rent is  taken  from  it  for  any  length  of  time,  it  soon  runs  down,  but  will  recu- 
perate if  allowed  to  stand. 

Dry  cells  are  essentially  the  same  as  a  Leclanch6  liquid  cell,  but  the  electro- 
lyte is  limited  to  the  amount  that  can  be  retained  in  some  absorbent  material, 
such  as  paper,  that  is  placed  inside  a  zinc  can  which  forms  one  electrode.  The 
other  electrode  is  a  carbon  rod  in  the  center.  The  space  between  is  filled  with 
crushed  coke  and  peroxide  of  manganese  and  the  whole  interior  is  saturated 


ELECTRICITY 


513 


23       5 

c<i         o> 


foil 

^  OS     - 

•§-sS-S 
'•«  S  g  «.  & 

CX  ^  «»  a3 
§^«  «^ 

I88!* 


M  « 

^  w     ^ 

si  I 


I     I 

O         O 


H 


ft" 

ll 


1  bl 

(B  K  R»Q 


II 

«  <— '     O  . 


£       I 


m 
ted 


e-a  p  p 

N          < 


1  I 


l-l 


s     a 


516 


ELECTRICITY 


with  the  solution  and  the  top  sealed  to  prevent  its  evaporation.  Dry  cells  are 
extensively  used  in  place  of  wet  Leclanch6  cells  because  they  are  as  good  and 
so  much  cheaper  that  it  is  economical  to  throw  them  away  when  exhausted  and 
buy  new  ones  instead  of  spending  the  time  and  money  required  to  replenish 
the  wet  Leclanch6  cells.  The  internal  resistance  of  cells  not  over  1  yr.  old 
nor  entirely  exhausted  varies  from  .1  to  .8  ohm  and  the  electromotive  force 
from  1.3  to  1.5  volts. 

In  cases  where  the  insulation  is  apt  to  be  poor,  as  it  often  is  in  mines,  it  is 
best  to  use  a  battery  that  will  stand  a  continuous  delivery  of  current  and  that 
will  at  the  same  time  operate  all  right  on  intermittent  work  or  on  work  where 
the  circuit  is  open  most  of  the  time.  For  work  of  this  kind,  cells  of  the  Edison 
or  Gordon  type  are  excellent.  View  (b)  shows  the  Edison  cell.  The  elements 
consist  of  two  zinc  plates  Z  hung  on  each  side  of  a  plate  of  compressed  cupric 
oxide  C.  The  electrolyte  is  a  saturated  solution  of  caustic  potash,  which  is 
kept  covered  with  a  layer  of  heavy  paraffin  oil,  to  prevent  the  action  of  the 
air  on  the  solution.  The  voltage  .of  the  cell  is  only  .7  volt,  but  its  internal 
resistance  is  very  low  and  its  current  capacity  correspondingly  large.  The 
electrolyte  used  in  the  Gordon  cell  is  also  caustic-potash  solution,  and  the  two 
cells  are  much  the  same,  so  far  as  their  general  characteristics  are  concerned. 
The  preceding  table  gives  data  relating  to  a  number  of  different  types  of  cell. 

BELL  WIRING 

The  simple  bell  circuit  is  shown  in  Pig.  1,  where  p  is  the  push  button,  b  the 
bell,  and  c  the  cells  of  the  battery  connected  up  in  series.  When  two  or  more 


88 


PW.I 


FiG-2 


bells  are  to  be  rung  from  one  push  button,  they  may  be  connected  in  series, 
as  shown  in  Fig.  2,  or  arranged  in  parallel  across  the  battery  wires,  as  at  a  and  b, 
Fig.  3.  The  battery  B  is  indicated  in  each  diagram  by  short  parallel  lines,  this 
being  the  conventional  method.  In  the  parallel  arrangement,  the  bells  are 
independent  of  each  other,  and  the  failure  of  one  to  ring  will  not  affect  the 
others;  but  in  the  series  grouping,  all  but  one  bell  must  be  changed  to  a  single- 
stroke  action,  so  that  each  impulse  of  current  will  produce  only  one  move- 
ment of  the  hammer.  The  current  is  then  interrupted  by  the  vibrator  in 
the  remaining  bell,  the  result  being  that  each 
bell  will  ring  with  full  power.  The  only  change 


FIG.  3 


FIG.  4 


necessary  to  produce  this  effect  is  to  cut  out  the  circuit-breaker  on  all  but  one 
bell  by  connecting  the  ends  of  the  magnet  wires  directly  to  the  bell  terminals. 
When  it  is  desired  to  ring  a  bell  from  one  of  two  places  some  distance  apart, 
the  wires  may  be  run  as  shown  in  Fig.  4.  The  pushes  p  and  p'  are  located  at 
the  required  points,  and  the  battery  and  bell  are  put  in  series  with  each  other. 


ELECTRICITY 


517 


A  single  wire  may  be  used  to  ring  signal  bells  at  each  end  of  a  line,  the 
connections  being  given  in  Fig.  5.     Two  batteries  are  required,  B  and  B',  and 


FIG.  5 


a  key  and  bell  at  each  station.  The  keys  k  and  kf  are  of  the  double-contact 
type,  making  connections  normally  between  bell  b  or  b'  and  line  wire  L  When 
one  key  k  is  depressed,  a  current  from  one  battery  B  flows  along  the  wire 
through  the  upper  contact  of  the  other  key  k'  to  a  bell  b'  and  back  through  the 
ground  plates  G'  and  G. 

When  a  bell  is  intended  for  use  as  an  alarm  apparatus,  a  constant-ringing 
attachment  may  be  introduced,  which  closes  the  bell  circuit  through  an  extra 

wire  as  soon  as  the  trip  at  a  door  or 
window  is  disturbed.  In  the  diagram, 
Fig.  6,  the  main  circuit,  when  the 
push  p  is  depressed,  is  through  the  auto- 
matic drop  d  by  way  of  the  terminals 
a  and  b  to  the  bell  and  battery.  This 
current  releases  a  pivoted  arm  which, 
on  falling,  completes  the  circuit  be- 
tween b  and  c,  establishing  a  new  path 
for  the  current  by  way  of  e,  indepen- 
dent of  the  push  p.  The  bell  will  then 
ring  until  the  drop  d  is  restored 
by  some  one  or  the  battery  becomes 


FIG.  6 


exhausted.     For  operating  electric  bells,  any  good  type  of  open-circuit  battery 
may  be  used;  dry  and  Leclanche  cells  are  largely  used  for  this  purpose. 

Annunciator  System. — The  wiring  diagram  for  a  single  annunciator  system 
is  shown  in  Fig.  7.  The  pushes  1,  2,  8,  etc.,  are  located  in  various  places,  one 
side  being  connected  to  the  battery  wire  b,  and  the  other  to  the  leading  wire  I 
in  communication  with  the  annunciator  drop  corresponding  to  that  place.  A 
battery  B  of  two  or  three  Leclanch6  cells  is  placed  in  any  convenient  location. 
The  size  of  wire  used  throughout 
may  be  No.  18  annunciator  wire. 

Telephones  are  also  used  for 
signaling  and  communicating  pur- 
poses. The  mine  telephone  system 
performs  two  functions:  It  expe- 
dites the  work,  thereby  lowering  the 
cost  of  production,  and  it  enhances 
the  safety  of  the  mine  workers  and 
mine  property.  Its  value  was 
realized  first  by  some  of  the  leading 
mining  companies  and  several  states 
have  enacted  mine  laws  requiring 
its  use.  The  principles  involved 
in  a  mine  telephone  system  are 
identical  with  ordinary  telephone 
practice,  with  such  changes  in  de- 
tails as  are  necessary  to  meet  con- 
ditions existing  in  mines. 

The  telephone  case  in  mine  work 
must  be  damp-proof  and  dust-proof, 
and  wiring  must  be  of  such  a  nature 
as  to  resist  both  dampness  and  the 
corroding  influence  of  drops  of  acid-  pIG  7 

ulated  mine  water.     It  must  also  be 

suspended  so  as  to  be  protected  from  injury  due  to  falls  of  roof,  cars,  or  the 
carelessness  of  employes. 

It  has  been  found  that  a  first-class,  long-distance,  bridging  telephone  is 
the  best  type  to  use;  bridging  telephones  are  so  called  because  they  are  bridged 


Be// 


-+H- 


518 


ELECTRICITY 


ELECTRICITY 


519 


Arrester 


Residence 


fl 


£ngtrre  House 


l  r 


Ti'pp/e 


first  Left  Enfry 


eft  Entry 


Physician's 
Office 


f 


FIG.  9 


ELECTRICITY 


ELECTRICITY 


521 


FOOT  BELl  O 
J>-S\ 

U 

FBOM  EUGIlfE  ROOJf(j   1 

( 

TO  EfGlJft:  ROOM    &  J 

?       ^                                                     ^ 

1      FOOT  UKLl.^ 

^7 

•3 

^ 

O  « 

!< 

HMMIH- 

•^    •"' 

r 

i 

zr 

=TTT 

fOOT 

J    TELEPUOUE 

>^L 

or  connected  in  parallel 

across  the  line,  and  are 

not  connected  in  series. 

If  one  telephone  should 

get  o 

ut 

of  order,  tl 

ie  o 

thers 

are  n< 

3t  likely  to 

be  disabled.     Figs. 

8  and  9  show  the  system  of 

wiring  and  installation  used  by  the  Stromberg- 
Carlson  Telephone   Manufacturing  Company. 
It  will  be  noted  that  there  is  a  metallic  circuit 

*" 

8 

1ST.  LEVKL 

for  the 

telephones  separate  and  distinct  from 

that  used  for  either  lighting  or  emergency  bells. 

Fi 

0. 

10  shows  tl 

ie  c 

ombm 

ed  tel 

jphone  and 

^-o- 

$ 

fcyZX    LKFKT 

emergency  (alarm)  system  of  bells  employed  by 
the  Western  Electric  Company,  in  which  three 

wires  are  used.     As  in  the  case  shown  in  Fig.  8, 

a  separate  generator  is  employed  to  ring  the 
alarm  bells.     One  of  these  is  installed  at  some 

g 

yttD.  LEFISL 

** 

central 

ooint  on  the  surface 

where  some  one 

is  always  on  duty 

to  receive  telephone  calls 

from 

DO 

ints  inside  t 

he  1 

-nine  £ 

md,  if 

necessary, 

to  sound  the  alarm  bells 

Other  generators  may 

be  installed  at  other  points,  say,  at 

the  foot  of 

the  shaft  or  at  the  inside  parting,  from  which 
it  may  be  desirable  to  be  able  to  send  warn- 
ing signals  in  event  of  accident. 
Fig.  11  shows  a  complete  bell  annunciator 

g 

'\  *TH.  L& 

1 

and  telephone  outfit  as 
anthracite  mines  of  the 

installed  in 
D..  L.  &  W 

one  of  the 
.  R.  R.  Co. 

Bridging  instruments  are  used  and  each  bell  in 
the  shaft  is  provided  with  a  return-call  button. 

0- 

i 

era.  usrsi, 

This 

b« 

11  wiring  sr 

oul 

3  be 

put  u 

p  in  a  sub- 

stant 

al 

manner,  an 

d  it 

is  be 

3t.  if 

aossible,  to 

rur  all  the  wires  down  the  shaft  in  the  shape  of 

aleac 

l-c 

overed  cable 

Anoth 

er  sha 

ft-signaling 

apparatus  is  shown  in  Fig.  12,  as  used  at  the 
West  Vulcan  mines,   Mich.     Fig.  13  shows  a 
form  of  waterproof  push  button  used  at  the 

8 

T" 

same  mine.     Fig.   14  shows  the  arrangement 
of  flash  signals  as  used  in  Montana.     This  con- 

sists of 

a  switch  cut  into  a  lighting  circuit  at 

each 

Ie' 

/el  of  the  n 

line 

3.     By 

pulli 

ng  out  the 

hand 

e 

bar  of  the  s 

witc 

h,  all 

the  li 

*hts  on  this     v              »* 

V    ^=5L 

circu 

t 

can  be  flash 

ed 

at  one 

e,  anc 

by  a  prop- 

erly  arranged  code  of  flash  signals 

the  system                                    «L» 

can  1 

>e 

used  for  co 

mm 

unicat 

ing  b 

etween  the 

surface  to  any  part  of  the  mine,  and  between                                FlG.  11 
different  portions  of  the  mine. 

522 


ELECTRICITY 


Hoisting  Engine  House. 


/////                                     North  Cable  Be II. 
--i       •'••///  South Cab/e Bell,    r- 1   .- -• 


PIG.  12 


ELECTRICITY  523 

A  system  of  signaling  by  which  signals  can  be  sent  to  the  engine  room  from 
any  point  along  the  haulage  road  is  shown  in  Fig.  15.  The  bare  conductors  a 
and  b  leading  from  the  battery  are  sup- 
ported on  insulators  parallel  to  each  other 
along  the  roadside,  and  about  6  in.  apart. 
A  short  iron  rod,  placed  across  the  wires 
a,  signals  to  the  engineer,  or  by  simply 
bringing  the  two  wires  together  a  signal 


may  be  sent.     When  the  engineer  hauls 


FIG.  15 


from  different  roads,  the  signaling  system 
should  be  supplemented  with  indicators,  so  that  when  the  bell  rings  the  indi- 
cator will  show  from  which  point  the  signal  came,  and  in  case  several  signals 
were  given  at  the  same  time,  the  engineer  should  not  heed  any  until  the  indi- 
cator shows  that  a  complete  signal  came  from  one  place. 

A  system  of  signaling  for  showing  whether  or  not  a  section  of  track  is 
occupied  by  another  motor  is  shown  in  Fig.  16.     White  lights  indicate  a  clear 

track  and  darkness  an  occupied 
section.  A  single-center  hinge, 
double-handle  switch  at  each 
signal  station  is  used  and  a 
touch  of  the  handle  throws 
the  switch  in  the  desired  di- 
pIG<  IQ  rection.  The  switches  are 

placed     in    the    roof,    4§    ft. 

above  the  rails  within  easy  reach  of  the  motorman.  Each  switch  is  provided 
with  a  spring  (not  shown  in  the  figure)  which,  drawing  across  the  center  hinge 
when  the  handles  are  in  their  central  position,  insures  a  perfect  contact  when 
the  switch  is  inclined  toward  either  the  trolley  or  rail-terminal  plug. 


LT/I 

W  i 


DYNAMO  AND  MOTOR  TROUBLES 

SPARKING  AT  BRUSHES 

Faults  in  dynamos  and  motors  may  be  classed  as  follows:  Sparking  at 
the  brushes;  heating  of  armature,  field  coils,  and  bearings;  noise;  too  high  or 
too  low  speed.  Besides,  a  motor  may  stop,  fail  to  start,  or  may  run  backwards 
or  against  the  brushes  and  a  dynamo  may  fail  to  generate  electricity. 

Brush  Faults. — Sparking  at  brushes  may  be  due  to  some  fault  with  the 
brushes. 

1.  The  brushes  may  not  have  been  set  diametrically  opposite  one  another 
because  they  were  not  set  properly  while  at  rest  by  counting  the  bars,  by 
measurement,  or  by  the  use  of  reference  marks  on  the  commutator.     Brushes 
can  be  set  properly,  if  necessary,  in  an  emergency  while  the  machine  is  running 
by  bringing  the  brushes  on  one  side  to  the  least  sparking  point  by  moving 
the  rocker-arm,  and  then  adjusting  the  brushes  on  the  other  side  to  the  least 
sparking  point  by  moving  in  or  out  the  brush  holder  and  clamping  in  new 
positions. 

2.  The  brushes  may  not  have  been  set  at  a  neutral  point.     In  this  case, 
move  the  rocker-arm  slowly  back  and  forth  until  the  sparking  is  stopped  or 
reduced  to  a  minimum. 

3.  The  brushes  may  not  have  been  properly  trimmed.     If  sparking  begins 
from  this  cause  and  the  dynamo  cannot  be  shut  down,  bend  back  and  cut  off 
the  loose  and  ragged  wires;  retrim  as  soon  as  possible  after  the  machine  is  shut 
down.     If  there  are  two  or  more  brushes  in  each  set  they  may  be  changed  one 
at  a  time  on  a  low-voltage  machine  while  it  is  running.     If  there  is  a  singing 
or  hissing  at  the  brushes  apply  a  little  mineral  oil  or  better  yet  vaseline,  or  hold 
a  piece  of  stearic-acid  candle  on  the  commutator  a  moment  and  then  wipe  off, 
leaving  just  a  faint  trace  of  oil  or  grease.     To  eliminate  noise,  it  may  be  neces- 
sary to  lengthen  or  shorten  the  brushes  in  the  holders  until  a  firm  but  gentle 
pressure  is  maintained  free  from  vibration.     Use  only  a  cloth,  never  waste, 
to  wipe  off  commutator. 

4.  The  brushes  may  not  be'in  line.     In  this  case,  adjust  each  brush  until 
the  brushes  rest  on  the  same  line  and  square  with  the  commutator  bar,  bearing 
evenly  throughout  their  width,  unless  purposely  staggered.     In  case  of  a  broken 
circuit  in  an  armature  winding,  it  is  sometimes  necessary  to  bridge  the  break 
temporarily  by  staggering  the  brushes  until  the  machine  can  be  shut  down, 


624  ELECTRICITY 

when  it  should  be  repaired;  this  is  only  a  temporary  makeshift  to  reduce  spark- 
ing during  a  run  when  the  machine  cannot  be  stopped  for  repairs. 

5.  The  brushes  may  not  make  good  contact.  In  this  case,  clean  the 
commutator  of  oil,  dirt,  or  grit  so  that  the  brushes  will  bear  properly  on  it  and 
adjust  by  the  proper  tension  screws  and  springs  until  a  light  but  firm  and  even 
contact  is  secured. 

Commutator  Faults. — Sparking  at  the  brushes  may  also  be  due  to  some 
fault  with  the  commutator. 

1.  The  commutator  may  be  rough,  worn  in  grooves  and  ridges  or  out  of 
round.     In  any  case,  the  commutator  should  be  ground  down  with  fine  sand- 
paper (never  emery  in  any  form)  laid  in  a  piece  of  wood  curved  to  fit  the 
commutator,  or  a  curved  suitable  stone,  and  finally  polished  with  soft,  clean 
cloth.     If  the  commutator  is  too  bad  to  grind  down,  it  may  be  turned  down  with 
a  special  tool  and  rest  while  the  commutator  is  turning  slowly  in  its  own  bear- 
ings or  the  armature  may  be  removed  from  the  machine,  placed  in  a  lathe,  and 
the  commutator  turned  off  with  light  cuts.     An  armature  should  have  from  & 
to  i  in.  end  motion  so  as  to  distribute  the  wear  of  the  brushes  evenly  and  to 
prevent  their  wearing  ruts  in  the  commutator.     Brushes  may  be  shifted  side- 
wise  occasionally  to  assist  in  the  distribution  of  wear.     If  there  is  no  end  motion, 
the  shoulders  should  be  turned  off  of  the  shaft  or  filed  or  turned  off  of  bearings 
until  the  armature  has  some  free  end  play  while  in  motion. 

2.  One  or  more  commutator  bars  may  be  too  high.     A  high  bar  should  be 
forced  down  carefully  with  a  wooden  mallet  or  block  of  wood,  care  being  taken 
not  to  bend,  bruise,  or  injure  the  bar,  and  then  tighten  the  clamping  rings; 
if  this  does  not  remedy  the  fault,  the  high  bar  should  be  filed  or  trimmed 
down  to  the  level  of  the  other  bars,  or  the  commutator  ground  or  turned  down 
a  little.     High  bars  may  cause  the  brush  to  jump  or  vibrate  so  as  to  sing. 

3.  One  or  more  commutator  bars  may  be  too  low.     In  this  case,  the 
commutator  may  be  ground  or  turned  down  until  no  bearings  are  below  a  true 
cylindrical  surface. 

HEATING  OF  ARMATURE,  FIELD  COIL,  AND  BEARINGS 

Heating  of  Armature. — The  heating  of  an  armature  may  be  due  to  the 
machine  being  overloaded,  to  a  short  circuit,  a  broken  circuit,  or  a  cross- 
connection;  the  causes  and  remedies  for  such  conditions  are  given  under  the 
head  of  Miscellaneous  Troubles.  Moisture  in  the  armature  coils  should  be 
removed  by  drying  out  the  coils  with  a  slow  heat  secured  by  sending  through 
the  armature  current  that  is  regulated  so  as  not  to  exceed  the  proper  amount. 
If  the  moisture  is  so  bad  as  to  cause  a  short  circuit  or  a  cross-connection  or  to 
heat  the  armature  too  much,  it  may  be  dried  out  by  the  heat  produced  by 
its  under  current  while  running. 

The  heating  of  an  armature  may  also  be  due  to  eddy  currents  in  the  arma- 
ture coil.  If  the  iron  of  the  armature  is  hotter  than  the  coils  after  a  short 
run,  the  faulty  armature  core  should  have  been  more  laminated  and  the  lami- 
nations should  have  been  better  insulated  from  one  another.  There  is  no 
remedy  but  to  rebuild  the  armature. 

Heating  of  Field  Coils. — The  heating  of  field  coils  may  be  due  to  excessive 
current  in  the  field  circuit,  eddy  currents  in  the  pole  pieces,  or  moisture  in  the 
field  coils.  Excessive  currents  in  the  field  circuit  of  a  shunt  machine  may  be 
reduced  by  decreasing  the  voltage  at  the  terminals  by  reducing  the  speed  or 
increasing  the  resistance  of  the  field  coils  by  winding  on  more  wire,  by  rewinding 
with  finer  wire,  or  by  putting  a  resistance  in  series  with  the  field.  Excessive 
current  in  the  field  circuit  of  a  series  machine  may  be  reduced  by  shunting 
a  portion  or  otherwise  decreasing  the  current  in  the  field  coils  or  by  taking 
off  one  or  more  layers  of  wire  or  rewinding  the  field  coils  with  closer  wire. 
Excessive  current  in  a  shunt  or  series  machine  may  of  course  be  due  to  a  short 
circuit  or  from  moisture  in  the  coils  acting  as  a  short  circuit. 

Eddy  currents  in  pole  pieces  may  cause  the  pole  pieces  to  become  hotter 
than  the  coils  after  a  short  run.  This  is  due  to  faulty  construction  or  to 
fluctuating  current;  if  due  to  the  latter,  the  current  should  be  regulated. 

Moisture  in  the  field  coils  may  cause  the  coils  to  be  lower  in  resistance  than 
normal  or  it  may  cause  a  short  circuit  or  a  contact  between  the  coils  and  the 
iron  of  the  machine.  The  coil  should  be  c^ried  out,  as  already  explained. 
Excessive  current  may  be  due  to  a  short  circuit  or  to  moisture  in  the  coils 
acting  as  a  short  circuit. 

Heating  of  Bearings. — Heating  of  bearings  may  be  due  to  not  enough  or  a 
poor  quality  of  oil.  The  remedy  is  to  use  plenty  of  oil  and  see  that  it  is  fed 
properly.  Only  the  best  quality  of  mineral  oil,  filtered  clean  and  free  from 


ELECTRICITY  525 

grit  should  be  used,  and  care  must  be  taken  not  to  flood  the  bearings  so  as  to 
force  the  oil  upon  the  commutator  or  into  the  insulation  of  the  brush  holders, 
as  it  will  then  gradually  char  and  gather  copper  dust  and  form  a  short  circuit. 
Vaseline,  cylinder  oil,  or  other  heavy  lubricant  may  be  used  if  the  ordinary 
oil  fails  to  remedy  the  hot  boxes;  such  lubricant  should  be  used  until  the  run  is 
over,  when  the  bearings  should  be  cleaned  and  adjusted. 

When  ice  is  used  to  cool  the  bearings,  care  must  be  exercised  not  to  let  it 
get  into  the  commutator  or  armature,  which  it  may  ruin  unless  they  are  water- 
.  proof  as  in  the  case  of  street-car  and  some  other  motors.  A  machine  must 
never  be  shut  down  because  of  a  hot  bearing  until  all  the  remedies  given  there- 
for have  been  tried  and  proved  of  no  avail.  If  it  is  absolutely  necessary  to 
shut  down  a  machine,  take  the  belt  off  as  soon  as  possible,  do  not  allow  the  shaft 
to  stick  in  stopping,  get  the  bearings  out  and  cool  off  as  soon  as  possible,  but 
not  in  water,  as  this  may  ruin  them.  Then  scrape,  fit,  clean,  and  polish  the 
bearings  and  shaft  and  see  if  it  can  be  turned  freely  by  hand  before  putting  on 
the  belt  and  starting  again.  Use  none  but  the  best  of  mineral  lubricating 
oil.  New  oil  and  oil  from  self-oiling  bearings  should  be  filtered  before  being 
used. 

Heating  of  bearings  may  be  due  to  dirt,  grit,  or  other  matter  in  bearings. 
In  this  case  wash  out  the  grit  by  flooding  with  clean  oil  until  the  run  is  over; 
then  clean  out  the  bearings,  being  careful,  however,  not  to  flood  the  commu- 
tator or  brush  holders.  When  the  run  is  over,  remove  the  cap  of  the  bearing 
and  clean  the  journals  and  bearings  very  carefully,  then  replace  caps  and 
lubricate  well.  Allow  bearings  to  cool  off  naturally.  It  may  be  necessary  to 
entirely  remove  the  bearings  and  clean  the  grit  away,  polish  all  parts,  and  set 
up  again. 

Should  rough  journals  or  bearings  cause  hot  bearinps,  polish  the  bearings 
in  a  lathe,  remove  cuts,  scratches,  and  marks;  then  fit  new  bearings  of  Babbitt 
or  other  metal. 

If  journals  are  too  tight  in  bearings,  loosen  the  bolts  in  the  cap  of  the  bearing, 
put  in  very  thin  pieces  of  packing  or  sheet  metal  between  the  caps  and  the  base, 
retighten  the  bolts  until  the  run  is  over;  then  make  the  journal  bearing  smooth 
and  so  it  can  be  rotated  by  hand.  If  necessary,  turn  down,  smooth,  and 
repolish  the  journal  or  scrape  the  bearings  to  a  proper  fit. 

In  the  case  of  a  bent  or  sprung  shaft,  bend  it  by  carefully  springing  the 
shaft  or  turning  it  in  a  lathe. 

If  a  bearing  is  out  of  line,  loosen  the  foot  of  the  bearing  until  the  armature 
can  be  turned  freely  by  hand  with  the  belt  off,  being  careful  to  keep  the  arma- 
ture in  the  center  of  the  polar  space.  Ream  out  the  bolt  in  dowel-pin  holes 
and  fit  new  dowels  to  allow  the  new  position  to  be  retained  when  the  bolts  are 
drawn  up  tight.  If  the  shaft  must  be  raised  or  lowered,  pack  up  or  trim  down 
the  feet  of  the  bearing  to  allow  the  proper  setting. 

Heating  of  bearings  may  be  caused  by  end  pressure  of  the  pulley  hub  or  shaft 
collars  against  bearings.  The  foundation  should  be  level  and  the  armature 
should  have  a  free  end  motion.  If  there  is  no  end  motion,  turn  or  trim  off  the 
ends  of  the  bearings  or  hub  on  the  shaft  until  the  proper  end  motion  is  secured. 
Line  up  the  shaft  pulley  and  belt  so  that  no  end  thrust  is  maintained  on  the 
shaft  by  a  sidewise  pull  of  the  belt.  The  armature  should  have  free  end 
play  while  in  motion. 

If  the  heating  of  the  bearings  is  caused  by  too  great  a  load  or  strain  on  the 
belt,  reduce  the  load  so  that  the  belt  may  be  slackened  and  yet  not  slip;  avoid 
vertical  belts  if  possible.  Use  larger  pulleys,  wider  and  longer  belts,  run  slack 
on  top  to  increase  adhesion  and  pull  of  belt  without  excessive  tightening,  so  that 
a  full  load  may  be  carried.  Belts  should  be  tightened  just  enough  to  drive  a 
full  load  smoothly  without  that  vibrating  or  flapping  which  may  cause  the 
lamps  to  flicker. 

An  armature  out  of  center  in  polar  space  may  cause  hot  bearings.  The 
bearings  may  be  worn  out,  thereby  allowing  the  armature  to  move  out  of  the 
center  and  to  need  replacing.  Center  the  armature  in  the  polar  space  and 
adjust  the  bearings  to  a  new  position,  as  already  explained.  File  out  the  polar 
space  to  give  equal  clearance  all  around  or  spring  the  pole  pieces  away  from  the 
armature  and  secure  it  in  place;  this  will  be  a  difficult,  if  not  an  impossible, 
job  in  large  machines. 

NOISE 

If  the  armature  strikes  or  rubs  against  the  pole  pieces,  bend  or  press  down 
the  projecting  wires  and  secure  strongly  in  place  with  tie-bands  or  wire.  File 
out  the  pole  pieces  where  the  armature  strikes.  The  bearings  may  be  worn 


526  ELECTRICITY 

out,  thus  allowing  the  armature  to  move  out  of  the  center  and  may  need 
readjustment.  It  is  sometimes,  though  seldom,  necessary  to  file  out  the  polar 
space  to  give  equal  clearance  all  around,  or  to  spring  the  pole  pieces  away 
from  the  armature  and  to  secure  it  in  place.  This  is  a  difficult,  if  not  an 
impossible,  job  on  large  and  rigid  machines. 

Collars  or  shoulders  on  the  shaft  or  the  hub  or  web  of  the  pulley  may 
strike  or  rattle  against  the  bearings,  because  the  bearings  are  worn  out  and  too 
loose  New  .bearings  may  be  required  if  the  remedies  given  for  bearings  out 
of  line  and  for  loose  screws,  bolts,  or  connections  do  not  remove  the  trouble. 

If  the  noise  is  caused  by  loose  screws,  bolts,  or  connections,  tighten  them  all 
to  a  firm  bearing  and  keep  them  so  by  daily  attention.  The  jar  and  move- 
ment of  the  machine  tends  to  work  screwed  connections  loose  when  they  are 
not  held  by  check-nuts,  cotter  pins,  or  some  other  device  designed  for  that 

""^Singing  or  hissing  of  the  brushes  may  be  stopped  by  the  remedies  described 
for  brushes  not  properly  trimmed.  Sometimes,  it  may  be  necessary  to  apply 
a  little  mineral  oil,  preferably  vaseline,  or  a  piece  of  stearic-acid  candle  against 
the  commutator  and  then  wipe  it  off;  just  a  faint  trace  of  oil  or  grease  is  all  that 
is  necessary.  The  brushes  may  be  adjusted  in  the  holders  until  a  firm,  but 
gentle  pressure  free  from  any  vibration  is  secured.  The  trouble  may  be  due 
to  a  faulty  commutator,  the  remedies  for  which  have  already  been  given. 

Flapping  or  pounding  of  belt  joints  will  be  remedied  if  the  ends  of  the  belt 
are  properly  laced  or  joined  together,  or  an  endless  belt  used. 

If  belts  slip  from  overload,  use  larger  pulleys,  wider  and  longer  belts, 
and  run  with  the  slack  side  of  the  belt  on  top. 

To  stop  the  humming  of  armature  lugs,  or  teeth  as  they  pass  the  pole 
pieces,  slope  the  ends  of  the  pole  pieces,  in  order  that  the  armature  teeth  shall 
not  pass  the  edges  all  at  once.  Decrease  the  magnetism  of  the  field  or  increase 
the  magnetic  capacity  of  the  teeth. 

REGULATION 

Speed  Too  High. — Too  high  a  speed  may  cause  the  engine  to  fail  to  regulate 
with  a  varying  load,  in  which  case  adjust  the  governor  or  other  means  of  regu- 
lation. If  this  cannot  be  accomplished,  get  a  better  engine.  The  engine 
should  regulate  closely  with  proper  steam  supply  from  no  load  to  full  load. 

A  series  motor  may  run  too  fast  on  account  of  receiving  too  much  current 
for  the  load  that  it  carries,  and  hence  the  motor  runs  away.  In  the  case  of  a 
series  motor  on  a  constant-potential  circuit,  insert  a  resistance  in  series  with 
the  motor  in  order  to  cut  down  the  current;  or  use  a  proper  regulator  or  con- 
trolling switch,  or  change  to  automatic  speed  regulating  motor. 

The  regulator  may  not  be  properly  set,  the  proper  amount  of  current  may 
not  be  used,  or  the  motor  may  not  be  properly  proportioned  and,  therefore, 
may  fail  to  regulate  properly.  The  regulator  should  be  adjusted  to  control 
the  speed,  the  proper  current,  voltage,  and  rheostat  should  be  used  or  get  a 
motor  properly  designed  for  the  work. 

Speed  Too  Low. — It  may  be  necessary  to  drive  the  dynamo  with  a  better 
engine  that  .will  regulate  better  with  proper  steam  supply  from  no  load  to  full 
load.  The  motor  may  be  overloaded,  the  causes  and  remedies  for  which  have 
been  previously  given.  There  may  be  a  short  circuit  in  the  armature,  a  striking 
or  rubbing  of  the  armature  against  the  pole  pieces,  or  an  unusual  amount  of 
friction,  all  of  which  have  been  explained. 

MOTOR  STOPS,  FAILS  TO  START,  OR  RUNS  BACKWARDS  OR 
AGAINST  THE  BRUSHES 

The  stopping  of  a  motor  or  its  failure  to  start  may  be  due  to  no  load.  The 
stopping  may  also  be  due  to  the  motor's  being  greatly  overloaded.  In  this 
case  reduce  the  load  to  the  proper  amount  that  the  motor  is  rated  to  carry. 

Sometimes  the  stopping  is  caused  by  excessive  friction,  due  to  the  heating 
of  the  bearings,  the  cause  and  remedies  for  which  have  been  given.  Open 
the  switch  and  keep  it  open  and  the  arm  of  the  rheostat  on  the  off-position 
while  locating  and  eliminating  the  trouble;  then  close  the  switch  and  shift  the 
arm  gradually  to  the  on-position  to  see  if  everything  is  correct.  With  a  series 
motor  no  great  harm  will  result  from  the  motor  stopping  or  failing  to  start: 
.with  a  shunt  motor  on  a  constant-potential  circuit  the  armature  may  and 
probably  will  burn  out  or  the  fuse  will  blow. 

The  stopping  of  the  motor  may  be  due  to  the  circuit  being  open  on  account 
of  the  safety  fuse  being  melted,  a  broken  wire,  a  broken  connection,  the  brushes 
not  being  in  contact  with  the  commutator  or  brush  holder,  or  an  open  switch. 


ELECTRICITY  527 

In  any  case,  see  that  the  switch  is  in  good  order  and  makes  its  connections 
properly.  Then,  if  necessary,  open  the  switch,  locate  and  repair  the  trouble, 
and  replace.  A  melted  fuse  should  not  be  replaced  until  the  fault  is  corrected, 
for  otherwise  the  fuse  will  melt  again  when  the  motor  is  started  up.  If  the 
open  circuit  is  caused  by  a  fault  in  the  armature  or  with  the  brushes,  the 
remedy  has  already  been  given.  If  the  current  should  fail  or  be  shunted  off 
from  the  machine,  open  the  switch,  return  the  starting  lever  to  its  off-position, 
and  wait  until  the  current  is  again  supplied  to  the  line,  testing  from  time  to 
time  by  closing  the  switch  and  moving  the  starting  lever  to  close  the  circuit. 

When  the  trouble  is  due  to  a  short  circuit  of  the  field,  armature,  or  switch, 
test  for  and  repair  the  trouble  if  possible,  carefully  looking  over  the  insulation 
of  binding  posts  and  brush  holders  for  poor  insulation,  oil,  dirt,  or  copper  dust. 
Such  causes  and  remedies  are  given  more  fully  under  Armature  Faults  due  to 
short-circuited  coil. 

When  the  trouble  is  due  to  wrong  connections  through  the  motor,  connect 
up  the  motor  properly,  referring  to  a  correct  diagram  of  connections;  if  same 
is  not  to  be  had,  try  reversing  the  connections  to  brush  holders  or  make  other 
changes  until  the  correct  connections  are  secured  for  the  direction  of  rotation 
desired;  then  connect  up  permanently. 

FAILURE  OF  DYNAMO  TO  GENERATE 

Reversed  Residual  Magnetism. — The  dynamo  may  fail  to  generate  because 
the  residual  magnetism  is  reversed,  owing  to  reversed  current  through  field 
coils  due  to  earth's  magnetism,  proximity  of  another  dynamo,  or  too  weak 
residual  magnetism.  In  this  case,  a  current  should  be  sent  from  another 
dynamo  or  from  a  storage  or  primary  battery  through  the  field  coils  in  the 
proper  direction  to  correct  the  fault.  The  polarity  may  be  tested  by  holding 
a  compass  needle  as  near  as  convenient  to  the  center  of  each  pole  piece  and  the 
connections  of  any  or  all  of  the  field  coils  may  be  changed  until  the  proper 
polarity  is  obtained. 

When  the  reversed  residual  magnetism  is  caused  by  reversed  connections, 
connect  properly  for  the  direction  of  rotation  desired,  referring  to  proper 
diagram  of  connections  if  obtainable.  See  that  connections  for  series  coils 
(in  compound  dynamo)  are  properly  made  as  well  as  those  for  the  shunt  coil. 
Make  such  changes  in  connection  as  may  be  necessary  to  give  the  desired  and 
correct  rotation. 

If  the  brushes  are  not  in  their  right  position,  shift  them  until  evidence  of 
improvement  is  secured.  The  position  of  the  brushes  for  the  best  generation 
of  energy  should  be  clearly  understood  and  is  generally  at  or  near  the  neutral 
point,  as  has  already  been  stated. 

Short  Circuit  in  Machine. — When  the  failure  of  the  dynamo  is  due  to  a  short 
circuit  in  the  machine,  the  procedure  is  the  same  as  when  a  similar  fault  occurs 
in  the  motor. 

Short  Circuit  in  External  Circuits. — If  a  lamp  circuit  or  other  device  or  part 
of  a  line  is  short-circuited  or  grounded,  it  may  prevent  the  building  up  of  the 
shunt,  or  compound,  field  of  the  dynamo.  In  this  case,  look  for  and  remedy 
the  short  circuit  before  closing  the  switch.  This  fault,  also,  should  be  treated 
the  same  as  similar  faults  in  motors. 

Field  Coils  Opposed  to  One  Another. — If  some  of  the  field  coils  should  be 
opposed  to  one  another,  reverse  the  connections  of  one  or  more  of  them  and 
test  the  pole  pieces  with  a  compass.  Alternate  poles  should  show  opposite 
polarity.  If  the  pole  pieces  are  found  to  be  of  proper  polarity  or  are  so  con- 
nected as  to  give  the  proper  polarity,  and  if  the  dynamo  does  not  build  up, 
try  the  remedies  given  under  reversed  residual  magnetism  due  to  a  reversed 
current  through  the  field  coils,  earth's  magnetism,  proximity  of  another  dynamo 
or  to  too  weakened  residual  magnetism.  If  current  is  not  then  produced  in 
the  proper  direction,  reverse  field  connections  or  recharge  in  proper  direction. 

Open  Circuit. — When  the  failure  of  the  dynamo  to  operate  is  due  to  an 
open  circuit,  it  may  be  that  the  brushes  are  not  in  contact.  The  remedy  for 
this  fault  has  already  been  given. 

In  the  case  of  a  broken  or  melted  safety  fuse,  open  the  switch,  look  for  and 
repair  the  trouble  and  replace  the  fuse.  A  dead  short  circuit  should  blow  the 
fuse  and  a  new  fuse  should  not  be  put  in  until  this  fault  is  removed,  as  it  will 
simply  blow  the  fuse -again  when  the  switch  is  closed.  The  remedy  for  this 
trouble  is  obvious. 

If  the  external  circuit  is  open  or  not  properly  connected,  locate  the  trouble 
and  repair  it  while  the  dynamo  switch  is  open.  The  remedy  for  an  open 
circuit  in  the  armature  has  already  been  given. 


528  ELECTRICITY 

Overloaded  Dynamo. — If  the  dynamo  fails  to  generate  because  of  an  over- 
load, reduce  the  load.  After  the  dynamo  comes  up  to  full  voltage,  as  shown  by 
lamp  or  voltmeter,  close  external  circuits  in  succession,  watching  and  regulat- 
ing the  voltage.  If  the  load  consists  entirely,  or  partly,  of  incandescent 
lamps,  shut  off  some  of  the  lamps.  If  the  insufficient  voltage  generated  is  due 
to  too  weak  a  field,  gradually  turn  the  regulating  switch  to  cut  resistance 
out  of  the  field  rheostat  until  the  proper  voltage  is  secured. 

MISCELLANEOUS  TROUBLES 

Weak  Magnetic  Field. — A  weak  magnetic  field  may  be  due  to  a  broken 
circuit  in  the  field,  or  to  a  short  circuit  of  one  or  more  coils,  or  to  a  dynamo 
not  being  properly  wound,  or  without  having  the  proper  amount  of  iron.  If 
a  broken  circuit  is  outside  of  the  field  coils  where  it  is  possible  to  get  at  it,  it 
should  be  repaired.  If  the  break  is  inside  of  a  winding,  that  winding  will  have 
to  be  rewound.  If  the  machine  is  not  properly  wound  or  does  not  contain 
the  proper  amount  of  iron  there  is  no  remedy  except  to  rebuild  the  machine. 

Excessive  Current  in  Armature  Due  to  an  Overload. — An  overload  in  a 
dynamo  may  be  due  to  there  being  too  many  incandescent  lamps  on  the  circuit; 
or  to  a  ground  and  leak  from  a  short  circuit  on  the  line.  In  a  motor,  an  over- 
load may  be  due  to  excessive  voltage  on  a  constant-potential  circuit,  or  excessive 
amperage  on  a  constant-current  circuit;  it  may  also  be  due  to  friction  or  to  too 
great  a  load  on  the  pulley.  The  load  should  be  reduced  by  degrees  by  cutting 
out  a  number  of  incandescent  lamps  on  the  circuit,  or  by  removing  a  dead 
short  circuit.  A  dead  short  circuit  should  blow  the  safety  fuses  or  operate  the 
circuit-breakers.  The  machine  should  be  shut  down,  the  fault  located  and 
repaired,  and  a  new  fuse  put  in  or  the  circuit-breaker  restored  before  starting 
again;  fuse  should  not  be  inserted  until  the  fault  is  corrected,  as  it  is  very 
likely  to  blow  again  on  starting  up  the  machine.  A  motor  should  be  operated 
with  the  proper  amount  of  current  and  no  more,  and  a  rheostat  or  controlling 
switch  should  be  used  for  starting  it.  Trouble  due  to  friction  should  be 
remedied  by  eliminating  the  excessive  friction. 

Armature  Faults. — In  the  case  of  a  short-circuited  coil  in  the  armature, 
look  for  copper  dust,  solder,  or  other  metallic  particles  between  the  commu- 
tator bars.  See  that  the  clamping  rings  are  perfectly  insulated  from  the  com- 
mutator bars  and  that  carbonized  oil,  copper  dust,  or  dirt  is  not  causing  the 
short  circuit.  In  the  case  of  a  short  circuit  inside  the  armature,  remove  the 
armature  from  the  machine  and  remove  and  rewind  the  defective  coil;  this 
may  require  rewinding  the  entire  armature.  Examine  the  insulation  of  the 
brush  holders  for  the  fault;  dirt,  oil,  and  copper  dust  may  make  a  short  circuit 
from  the  brush  holders  to  the  rocker-arm  and  thus  short-circuit  the  machine. 

In  the  case  of  a  broken  circuit  in  the  armature,  bridge  the  break  temporarily 
by  staggering  the  brushes  until  the  machine  can  be  shut  down;  then  test  out  and 
repair.  This  is  only  a  temporary  makeshift  in  an  endeavor  to  stop  bad  start- 
ing before  the  dynamo  can  be  shut  down.  If  the  dynamo  can  be  shut  down, 
look  for  and  repair  the  broken  or  loose  connection  on  a  commutator  bar.  If 
a  coil  is  broken  inside,  rewinding  of  the  armature  is  the  only  sure  remedy, 
although  the  break  may  be  temporarily  bridged  by  hammering  the  disconnected 
bar  until  it  makes  contact  across  the  insulating  material  with  the  next  bar; 
this  remedy  is  of  doubtful  value,  and  if  done  the  bars  must  be  repaired  again 
when  the  fault  is  permanently  remedied.  Commutator  lugs  may  be  tempo- 
rarily soldered  together  with  or  without  a  piece  of  heavy  copper  wire  soldered 
to  both  bars,  thus  cutting  out  the  broken  coil.  Care  should  be  taken  not  to 
short-circuit  a  good  coil,  and  thus  cause  sparking. 

A  cross-connection  in  the  armature  may  have  the  same  effect  as  a  short 
circuit  and  is  to  be  treated  as  such.  Each  coil  should  show  a  complete  circuit 
without  being  crossed  with  any  other  coil. 

GENERAL  PRECAUTIONS 

Cleanliness  about  a  dynamo-electric  machine  is  imperative;  dirt,  oil,  or 
copper  dust  may  prove  sources  of  great  annoyance  or  damage.  Small  tubes, 
bolts,  or  pieces  of  iron  must  be  kept  away  from  the  dynamo,  as  the  magnetism 
may  draw  them  into  or  cause  them  to  fall  upon  the  rotating  armature  and 
ruin  it.  Hence,  loose  articles  of  any  kind  must  never  be  placed  upon  any 
portion  of  a  dynamo-electric  machine.  It  is  preferable  to  use  brass  or  copper 
oil  cans,  as  they  are  non-magnetic.  All  connections  should  be  clean  and 
firm.  All  screws  and  bolts  should  be  looked  over  daily  and,  if  necessary, 
tightened.  The  brushes  should  not  rest  on  the  commutator  when  a  dynamo 
is  idle. 


ELECTRICITY  529 


GENERAL  RULES  FOR  HANDLING  ELECTRICITY 

In  coal-mining  practice,  the  pressure,  voltage,  or  difference  of  potential 
in  or  on  any  circuit,  machine,  or  other  piece  of  equipment,  is  frequently  made 
a  basis  for  classification .  Low-pressure  circuits  are  those  in  which  the  difference 
of  potential  at  no -time  exceeds  250  to  300  volts;  in  medium-pressure  circuits, 
the  voltage  does  not  rise  above  550  to  650;  and  in  high-pressure  circuits,  the 
voltage  while  above  650  is  commonly  less  than  3,000.  Long-distance  trans- 
mission lines  operate  under  voltages  as  high  as  100,000  and  installations  at 
150,000  volts  are  contemplated.  However,  pressures  such  as  these  are  trans- 
formed in  a  special  transformer  house  outside  the  mine  into  low  or  medium 
voltage  before  being  conveyed  underground,  and,  so,  are  not  reckoned  with 
in  ordinary  mine  practice. 

No  voltage  higher  than  medium  (say,  550  volts)  should  be  used  anywhere 
in  any  mine  for  the  actual  operation  of  electrical  machinery,  and  nothing 
above  low  voltage  (say,  250  volts)  should  be  employed  at  the  face  for  operating 
coal-  or  rock-cutting  machinery. 

All  high-voltage  currents  should  be  carried  in  properly  insulated  cables, 
either  through  bore  holes  drilled  from  the  surface  or  along  passageways  upon 
which  men  do  not  travel,  to  a  transforming  station  where  they  should  be 
converted  to  low-  or  medium-pressure  currents  for  farther  conveyance  to  the 
point  of  application.  In  gaseous  mines,  high-voltage  cables  should  be  installed 
in  the  intake  airway  only,  and  high-voltage  motors  and  transformers  should  be 
installed  only  in  suitable  chambers  ventilated  by  a  current  of  intake  air  that 
has  not  passed  through  or  by  a  gaseous  district.  High-voltage  transformers 
should  have  a  normal  capacity  of  not  less  than  5  K.  W.,  and  high-voltage 
motors  should  have  a  normal  capacity  of  more  than  15-brake  H.  P. 

All  metallic  coverings  and  armoring  of  cables  (except  trailing  cables)  and 
the  frames  and  bedplates  of  generators,  transformers,  and  motors  other  than 
low-voltage  portable  motors,  should  be  properly  grounded,  as  should  be  the 
neutral  wire  of  three- wire  continuous-current  systems. 

When  handling  live  wires  or  when  making  repairs  to  the  live  parts  of 
machines,  a  person  should  wear  rubber  gloves  or  should  stand  upon  a  mat 
of  rubber  or  other  insulating  material.  Every  mine  should  have  a  special 
map  of  the  workings,  made  upon  a  sufficiently  large  scale  (not  less  than  200  ft. 
to  the  inch)  to  show  clearly  the  position  of  all  wires,  cables,  conductors,  trans- 
formers, trolley  lines,  switches,  lights,  and  all  fixed  machines  such  as  pumps, 
fans,  etc.  The  plan  should  indicate  the  size,  voltage,  etc.,  of  all  motors  and 
other  apparatus,  and  the  duty  performed  by  each.  In  addition,  the  map  should 
show  the  location  of  all  signal  and  telephone  wires,  bells,  telephones,  and  the 
like.  In  the  event  of  a  breakdown  or  in  event  of  any  portion  of  the  equipment 
becoming  alive,  the  current  should  be  shut  off,  the  trouble  located,  and  repairs 
made  at  once. 

All  single  switches,  circuit-breakers,  and  other  electric  instruments  should 
be  mounted  upon  insulating  bases  of  some  suitable  material.  Switchboards 
should  be  set  at  least  3  ft.  from  the  rib  if  the  current  is  medium  voltage,  and 
4  ft.  if  the  current  is  high  voltage;  they  should  be  accessible  on  all  sides  and 
combustible  material  should  not  be  used  near  them.  Insulating  floors  or 
mats  should  be  provided.  All  high-potential  feeder  circuits  with  a  capacity 
of  25  K.  W.  or  over,  should  have,  above  ground,  a  switch  on  each  pole,  and 
an  automatic  circuit-breaker  on  one  pole  of  direct-current  systems,  and  on 
two  poles  of  polyphase,  alternate-current  systems.  Ground-return  direct- 
current  circuits  should  have  a  switch  and  circuit-breaker  on  the  ungrounded 
side,  and  fuses  may  be  substituted  for  circuit-breakers  where  the  capacity  of 
the  line  is  25  K.  W.  or  less.  High-potential,  alternating,  feeder  circuits  should 
have,  at  the  surface,  on  each  pole  an  oil-break  switch  provided  with  an  auto- 
matic overload  trip.  All  circuits  should  have  an  ammeter.  Transformer 
rooms  should  be  fireproof,  should  be  provided  with  buckets  of  clean  dry  sand 
for  use  in  case  of  fire,  and  no  unauthorized  person  should  be  allowed  to  enter 
them.  Where  circuits  enter  or  leave  a  transformer,  they  should  be  protected 
by  circuit-breakers,  etc.,  as  on  the  surface. 

While  medium-  or  low-pressure  wires  leading  into  the  mine  may  be  bare, 
except  in  gaseous  sections  thereof,  high-pressure  wires  should  be  enclosed 
in  lead  or  other  armored  covers.  Underground  cables,  except  trailing  cables, 
should  be  supported  on  insulators  unless  provided  with  a  grounded  metallic 
covering.  The  conductors  connecting  lamp  and  power  supply  should  always 
be  insulated.  Lightning  arresters  should  be  provided  at  the  generating 

34 


530  ELECTRICITY 

station,  at  the  mine  mouth  if  this  is  500  ft.  from  the  station,  and  at  intervals 
of  not  more  than  1,000  ft.  if  this  distance  is  exceeded.  In  gaseous  mines 
or  through  gaseous  portions  of  a  mine,  the  potential  should  not  be  above 
medium  and  the  currents  should  be  brought  in  through  the  intake.  Each 
pole  at  the  junction  of  a  branch  and  main  circuit  should  have  a  switch  of 
not  less  than  100  amp.  capacity.  One  side  of  grounded  circuits  should  be 
carefully  insulated  from  the  earth.  Trolley  lines  should  be  placed  as  far  to 
one  side  of  the  entry  as  possible  and  should  be  supported  so  that  the  sag  between 
points  of  support  does  not  exceed  3  in.,  except  where  the  clear  height  of  the 
wire  above  the  rail  is  5  ft.  or  more  and  where,  the  increased  sag  thus  permissible, 
does  not  cause  the  trolley  in  passing  to  force  the  wire  upon  the  roof.  All 
wires,  except  telephone,  shot-firing,  and  signal  wires  should  be  on  the  same 
side  of  the  entry  as  the  trolley  wire.  Where  men  are  constantly  compelled 
to  work  or  pass  under  bare  power  wires  less  than  6£  ft.  above  the  top  of  the 
rail,  the  wires  should  be  set  in  channels  cut  in  the  roof  or  in  inverted  wooden 
troughs,  the  sides  of  which  are  not  less  than  5  in.  deep.  Branch  trolley  lines 
should  be  provided  with  some  device  by  which  the  current  may  be  shut  off 
from  them.  Track  rails  should  be  of  sufficient  size  to  provide  ample  capacity 
for  the  return  circuit,  should  be  bonded  rail  to  rail,  and  cross-bonded  at  intervals 
of  not  less  than  200  ft.,  and  should  be  frequently  bonded  to  any  air  or  water 
pipes  where  such  exist,  in  order  to  eliminate  difference  of  potential  between 
the  rails  and  pipes  and  to  prevent  electrolysis.  Lighting  wires  should  not  be 
wrapped,  or  tied  about  the  stems  or  studs  of  trolley  hangers,  but  should 
be  inserted  in  holes  drilled  therein,  held  in  place  by  a  setscrew,  and  should  be 
grounded  into  the  track  circuit.  Lighting  wires  should  be  strung  on  porcelain 
or  glass  insulators  and,  unless  protected  with  some  insulating  covering,  should 
be  strung  at  least  3  in.  apart.  All  joints  in  conductors  should  be  soldered,  if 
at  all  possible,  and  joints  in  insulated  wire  should  be  carefully  reinsulated. 
The  exposed  ends  of  cables,  where  they  enter  fittings,  should  be  protected,  so 
that  moisture  cannot  enter  the  cable  or  the  insulating  material  leak.  All 
holes  through  which  bare  wires  pass  through  metal  frames  or  into  boxes  or 
motor  casings,  should  be  bushed  with  insulating  material,  which  should  be  gas- 
proof where  necessary.  Extra  precautions  should  be  taken  to  see  that  power 
cables  in  shafts  are  highly  insulated  and  very  substantially  secured  in  place. 
If  a  cable  cannot  sustain  its  own  weight,  it  should  be  supported  at  intervals 
of  not  over  25  ft.  by  suitable  grips.  Hanging  cables  should  be  boxed  in,  but 
if  that  is  not  possible,  they  should  be  hung  clear  of  the  walls  so  that  they  may 
give  and  not  break  under  a  blow  from  falling  materials.  Cables  and  feed- 
wires  should  be  strung  so  as  to  clear  passing  cars  or  motors  by  at  least  12  in. 
and,  if  this  is  not  possible,  should  be  protected  by  guards.  Further,  unless 
metal-covered,  they  should  not  be  fixed  to  the  ribs  or  timbers  with  uninsulated 
fastenings;  and  while  repairs  are  being  made  in  the  entry  or  while  blasting  is 
going  on,  they  should  be  protected  from  injury  in  some  manner.  Trailing 
cables  should  be  protected  with  extra  strong  insulating  material,  should  be 
frequently  examined  for  defects,  and  if  these  are  found,  should  be  rejected 
until  the  proper  repairs  are  made.  Where  such  cables  are  divided  at  the 
motor,  the  split  should  be  as  short  as  possible,  and  they  should  be  securely 
clamped  to  the  frame  of  the  motor,  so  they  may  not  pull  out  from  the  con- 
nections. In  gaseous  portions  of  the  mine,  fixed,  flame-proof,  terminal  boxes 
with  a  switch  and  fuse  on  each  pole  of  the  circuit  should  be  provided  where 
trailing  cables  are  attached  to  the  power  lines.  The  switch  should  be  oper- 
atable  only  from  outside  the  box  when  it  is  closed,  and  should  be  so  arranged 
that  the  trailing  cables  cannot  be  detached  or  removed  when  the  switch  is 
closed. 

All  switches,  circuit-breakers,  and  fuses  should  have  incombustible  bases. 
Open-type  fuses  with  terminals  are  permissible  in  non-gaseous  parts  of  a 
mine,  but  where  gas  is  generated  they,  and  switches  and  circuit-breakers,  must 
be  inclosed  in  explosion-proof  casings  or  must  break  under  oil.  Puses  should 
be  marked  with  the  maximum  current  they  are  allowed  to  carry  and  should  be 
adjusted  and  replaced  only  by  a  competent  person.  Circuit-breakers  should 
trip  at  from  50  to  150%  of  their  rated  capacity,  and  should  be  provided  with 
an  indicator  showing  at  what  current  they  are  set  to  trip.  On  feeder  lines,  the 
circuit  breaker  should  trip  at  the  end  of  10  sec.  under  an  overload  of  50%. 
Except  on  signal  lines,  all  making  or  breaking  of  circuits  should  be  done  by 
means  of  switches,  which  should  be  so  arranged  that  they  cannot  be  closed  by 
gravity;  except  that  connections  between  gathering  locomotives  and  mining 
machines  and  the  trolley  line  may  be  made  by  means  of  hooks  or  similar 
devices. 


ELECTRICITY  531 

Stationary  motors  and  their  starting  resistance  should  have  a  fuse  on  one 
pole  or  circuit-breaking  device  where  direct  current  is  used,  and  on  both  poles 
where  alternating  current  is  employed,  and  should  be  provided  with  switches 
to  cut  off  the  power  entirely.  In  gaseous  parts  of  the  mine,  motors  should  be 
placed  in  a  room  ventilated  by  a  separate  split  of  intake  air,  or,  if  this  is  not 
possible,  all  current-carrying  parts,  starters,  connections,  terminals,  and  the 
like,  should  be  enclosed  in  non-inflammable  explosion-proof  casings,  which 
should  be  opened  only  by  authorized  persons  when  the  power  is  off.  Under- 
ground fan  motors,  not  provided  with  a  regular  attendant,  should  be  totally 
enclosed  unless  installed  in  a  special  room  lined  with  incombustible  material. 
In  gaseous  mines,  a  safety  lamp  should  be  provided  with  each  machine  and, 
on  the  first  indication  of  gas,  the  machine  should  be  stopped  and  the  current 
cut  off  at  the  nearest  switch  and  should  not  be  turned  on  until  the  place  has 
been  made  safe.  Enclosed  equipment  should  be  regularly  inspected  and  cleaned , 
motors  once  a  week  and  switches  once  a  month.  In  gaseous  mines,  a  coal- 
cutting  machine  should  not  be  operated  unless  the  absence  of  gas  has  been 
proved  by  the  use  of  a  safety  lamp,  the  operator  should  not  leave  the  machine 
while  it  is  in  use,  and  tests  for  gas  should  be  repeated  at  least  every  |  hr.  If 
gas  is  found,  the  machine  either  should  not  be  taken  to  the  face,  or  if  at  the 
face  the  current  should  be  at  once  cut  off  and  the  trailing  cable  disconnected 
from  the  power  wires.  A  machine  should  never  be  left  at  the  face  unattended 
unless  the  power  is  cut  off  from  the  trailing  cable.  If  arcing  outside  the 
machine  is  noticed  or  any  defect  is  discovered  in  it,  the  trailing  cables,  etc., 
the  power  should  be  cut  off  at  once  and  the  machine  put  out  of  commission. 

Electric  haulage  locomotives  should  not  have  a  higher  voltage  than  medium 
and  should  not  be  used  in  gaseous  mines  except  upon  an  intake  air-current  fresh 
from  the  outside.  Storage-battery  locomotives  are  permissible  in  gaseous 
mines  if  the  cells  and  other  electric  parts  are  enclosed  in  non-combustible 
explosion-proof  casings. 

Arc  lamps  should  be  of  the  enclosed  type  and  are  permissible  in  gaseous 
mines  under  the  same  conditions  as  electric  haulage  motors.  The  sockets  of 
incandescent  lamps  should  be  of  the  weather-proof  type,  the  exterior  of  which 
should  be  entirely  non-metallic.  Flexible  lamp-cord  connections  should  not 
be  used  except  in  the  case  of  portable  lamps  and.  then  only  when  the  lamp 
and  socket  are  enclosed  in  a  heavy  wire  cage,  which  is  attached  to  a  handle 
through  which  the  leading-in  wires  are  carried.  As  a  general  rule,  portable 
incandescent  lamps  of  the  ordinary  type  should  not  be  used  in  gaseous  portions 
of  the  mine,  and  in  other  parts  thereof  only  for  the  inspection  and  repair  of 
the  machinery.  Portable  incandescent  lamps,  of  the  battery  type,  that  have 
passed  the  requirements  of  the  Bureau  of  Mines  are  permissible  in  any  part 
of  any  mine.  Standard  incandescent  lamps  should  be  placed  so  that  they 
cannot  come  in  contact  with  combustible  material,  should  be  replaced  by 
competent  persons  after  having  tested  for  the  absence  of  gas,  and  in  gaseous 
portions  of  the  mine,  unless  ventilated  by  fresh  intake  air,  should  be  protected 
by  gas-tight  fittings  of  strong  glass.  If  the  lamps  are  of  220  volts  or  higher, 
not  over  8  c.  p.,  and  without  tips,  the  gas-tight  fittings  are  not  necessary. 

Electricity  from  grounded  circuits  should  not  be  used  for  firing  shots.  Only 
trained  men  should  be  allowed  to  handle  electric  shot-firing  apparatus.  Shot- 
firing  wires  or  cables  should  not  be  allowed  to  come  in  contact  with  light  or 
power  wires.  Electric  detonators  and  their  leads  should  be  of  an  approved 
type,  should  be  kept  in  a  dry  place  and  should  not  be  stored  with  other  explo- 
sives. Shot-firing  machines  should  be  enclosed  in  a  tight  case  inside  of  which 
all  contacts,  with  the  exception  of  the  binding  posts,  should  be  made.  The 
shot-firer  alone  should  connect  the  leads  to  the  battery  and  then  only  after  the 
shot  is  actually  and  completely  ready  for  firing,  and  all  persons  have  sought 
a  place  of  safety.  After  firing  a  shot,  the  leads  should  be  at  once  disconnected 
from  the  current.  If  the  shot  has  missed  fire,  the  firing  leads  should  likewise 
be  disconnected,  and  no  one  should  be  allowed  to  approach  the  face  until  at 
least  5  min.  thereafter. 

Care  should  be  taken  to  prevent  signal  and  telephone  wires  from  coming 
in  contact  with  power  or  other  wires,  whether  the  same  are  insulated  or  not. 
The  potential  used  for  signal  purposes  in  the  gaseous  parts  of  a  mine  should 
not  exceed  24  volts,  and  bare  wires  should  not  be  used  except  on  haulage  roads. 

The  electric  relighting  of  safety  lamps  should  be  done  in  a  special  room  not 
on  the  main  return  and  where  there  is  not  likely  to  be  an  accumulation  of  gas. 
The  relighting  apparatus  should  be  locked  so  that  it  cannot  be  handled  by 
unauthorized  persons,  and  all  lamps  should  be  carefully  examined  for  defects 
before  being  reissued. 


532  INTERNAL-COMBUSTION  ENGINES 

INTERNAL-COMBUSTION  ENGINES 


DEFINITIONS   AND  PRINCIPLES 

Internal-Combustion  Engines. — An  internal-combustion  engine  is  an  engine 
in  which  power  is  generated  by  burning  within  the  cylinder  a  mixture  of  air 
and  gas  or  air  and  alcohol,  kerosene,  gasoline,  or  other  liquid  fuel.  The  burning 
of  the  fuel  results  in  the  production  of  gases  of  high  temperature  and  pressure, 
which  act  directly  on  a  piston  that  moves  back  and  forth  in  a  cylinder  into 
which  the  air  and  fuel  are  admitted  and  from  which  the  burned  gases  are 
discharged  through  suitable  valves. 

Single-  and  Double-Acting  Engines. — Internal-combustion  engines  may  be 
single  or  double  acting.  Engines  in  which  gas  is  admitted  to  only  one  side  of 
the  piston  are  single  acting,  while  those  in  which  gas  is  admitted  to  each  end 
of  the  cylinder  alternately  and  is,  consequently,  burned  first  on  one  side  of  the 
piston  and  then  on  the  other,  are  double  acting.  All  haulage-motor  engines 
and  most  stationary  engines  in  which  gasoline  is  the  fuel  are  of  the  single- 
acting  type;  double-acting  engines  are  sometimes  used  where  gaseous  fuel  is 
available. 

Gasoline-Engine  Cycles. — As  applied  to  a  gasoline  engine,  the  term  cycle 
refers  to  the  operations,  or  events,  that  take  place  within  the  cylinder  from 
one  explosion  to  the  next,  and  by  means  of  which  the  fresh  charge  is  drawn  into 
the  combustion  chamber  and  exploded  and  the  exhaust  gases  expelled.  These 
events  always  occur  in  the  same  order  and  are  repeated  after  each  explosion. 
The  cycle  on  which  an  internal-combustion  engine  operates  is  one  of  the 
distinguishing  features  of  different  types. 

In  the  first  successful  gas  engine,  the  charge  drawn  into  the  cylinder  under 
atmospheric  pressure  during  part  of  the  outward -stroke  was  ignited  when  the 
piston  had  traversed  about  four-tenths  of  its  stroke;  the  sudden  rise  in  pressure 
due  to  the  explosion  of  the  gas  was  utilized  to  drive  the  piston  to  the  end  of 
its  stroke  and  work  was  performed  during  the  expansion  of  the  hot  gases. 
During  the  return  stroke,  the  burned  gases  were  driven  from  one  end  of  the 
cylinder  while  a  fresh  charge  was  drawn  in  and  ignited  at  the  other  end,  the 
engine  being  of  the  double-acting  type.  Because  of  the  extreme  wastefulness 
of  this  engine,  which  was  of  the  two-cycle  type,  a  French  scientist,  Beau  de 
Rochas,  in  1870,  proposed  a  new  cycle  of  operations.  This  cycle  was  adopted 
and  put  into  practical  use  by  Otto,  a  German,  who  built  his  first  compression 
engine  in  1876;  this  engine  is  known  by  his  name. 

The  Otto  cycle,  in  its  broad  and  strictly  scientific  meaning,  is  not  concerned 
with  the  method  of  getting  the  combustible  mixture  into  the  cylinder  nor  that 
of  expelling  the  hot  burned  gases.  The  steps  of  the  cycle  are  as  follows: 
Assume  that,  at  the  beginning  of  operations,  the  valves  are  closed,  that  the 
piston  is  at  the  position  farthest  out  toward  the  crank-shaft,  and  that  the 
cylinder  is  filled  with  a  combustible  mixture  at  atmospheric  pressure.  By 
forcing  the  piston  inwards  to  the  completion  of  the  inward  stroke,  the  charge 
will  be  compressed  into  the  compression  space,  or  combustion  space.  Now  by 
igniting  the  compressed  charge,  the  pressure  will  be  increased  still  more  by  the 
heat  of  combustion.  The  pressure  tends  to  drive  the  piston  outwards,  and  as 
soon  as  the  rotating  crank-shaft  has  made  the  angle  between  the  connecting- 
rod  and  crank  sufficiently  great,  the  pressure  of  the  hot  gases  against  the  piston 
face  will  drive  the  crank-shaft.  The  burned  gases  expand  to  fill  the  increasing 
volume  of  the  cylinder  as  the  piston  moves  outwards  and  the  pressure  decreases. 
At  the  completion  of  the  outward  stroke,  the  exhaust  valve  is  opened  and  the 
hot  burned  gases  escape  by  expansion  until  the  pressure  falls  to  that  of  the 
atmosphere.  This  completes  the  Otto  heat  cycle. 

The  expulsion  of  the  burned  gases  that  remain  in  the  cylinder  at  atmo- 
spheric pressure  and  the  taking  in  a  fresh  charge  of  combustible  mixture  is 
accomplished  in  two  distinct  ways,  which  are  the  foundation  for  the  com- 
mercial names,  four  cycle  and  two  cycle,  as  applied  to  gasoline  engines. 
le  Engines. — .' 


Four-Cycle  Engines. — A  four-cycle  engine  is  one  in  which  four  complete 
strokes  of  the  piston  are  required  to  complete  the  cycle.  In  this  engine  the 
burned  gases  remaining  in  the  cylinder  after  the  exhaust  valve  has  been  opened 
and  part  of  the  hot  gases  removed  by  expansion  are  expelled  in  part  by  a 


INTERNAL-COMBUSTION  ENGINES 


533 


separate  inward  stroke  of  the  piston,  and  a  fresh  charge  is  drawn  into  the 
cylinder  through  the  inlet  port  by  a  separate  outward  stroke.  Generally 
speaking,  one  event  occurs  during  each  of  the  four  strokes  of  this  cycle;  that  is, 
considering  the  stroke  by  which  the  charge  is  drawn  into  the  cylinder  as  the 
first  stroke,  the  mixture  is  compressed  during  the  second  stroke,  burned  during 
the  third  stroke,  and  the  exhaust  gases  are  expelled  during  the  fourth  stroke, 
after  which  the  conditions  are  the  same  as  at  first  and  the  cycle  is  complete. 
This  type  is  sometimes  known  as  the  four-stroke  Otto-cycle  engine,  and  is  in 
more  general  use  than  the  two-cycle  engine  as  it  is  much  more  economical 
in  fuel. 

Two-Cycle  Engines. — A  two-cycle  engine  is  one  in  which  only  two  strokes 
of  the  piston,  corresponding  to  one  revolution  of  the  crank-shaft,  are  required 
to  complete  the  cycle.  In  this  cycle  an  explosion  occurs  on  each  downward 
stroke  of  the  piston,  the  fresh  charge  being  admitted  and  the  exhaust  gases 
expelled  at  or  near  the  end  of  this  stroke.  Hence,  for  the  same  number  of 
revolutions  of  the  crank-shaft,  there  are  twice  as  many  explosions  in  the 
cylinder  of  a  two-cycle  engine  as  in  that  of  a  four-cycle  engine.  However,  this 
does  not  mean  that  the  power  developed  by  a  two-cycle  engine1  is  twice  as  great 
as  that  produced  by  a  four-cycle  engine  of  the  same  size  and  speed,  for,  on 
account  of  the  inefficient  scavenging,  or  cleaning,  of  the  cylinder  after  the 
explosion  and  the  lower  compression  pressure  in  the  two-cycle  engine,  the 


explosions  are  not  so  powerful  as  in  the  four-cycle  engine.  It  is  generally 
estimated  that  a  two-cycle  engine  of  a  certain  size  and  speed  will  develop 
about  1.65  times  as  much  power  as  a  four-cycle  engine  of  the  same  size  and 
speed.  This  type  is  sometimes  known  as  the  two-stroke  Otto-cycle  engine. 

Application  of  Four-Cycle  Principle. — In  the  four-cycle  engine,  the  first 
outward  stroke  is  the  suction  stroke,  the  gas  being  driven  into  the  cylinder  by 
the  pressure  of  the  atmosphere  or  other  pressure,  because  of  the  partial  vacuum 
produced  by  the  movement  of  the  piston.  This  stroke  fills  the  cylinder  with  a 
mixture  of  fuel  and  air  at  very  nearly  the  pressure  of  the  atmosphere.  On  the 
return  stroke  of  the  piston,  all  the  openings  leading  from  the  cylinder  are  closed 
and  the  mixture  is  compressed.  As  the  piston  nears  the  end  of  this  second 
stroke,  which  is  known  as  the  compression  stroke,  the  igniter,  or  device  by 
means  of  which  the  charge  is  fired,  is  operated  in  time  to  produce  full  ignition 
of  the  mixture  at  the  end  of  the  stroke.  The  pressure  rises  to  three  or  four 
times  that  due  to  compression,  and  drives  the  piston  forwards  on  its  next 
outward  stroke,  which  is  known  as  the  power,  or  expansion,  stroke.  Just  before 
this  stroke  is  completed,  or  as  it  is,  the  exhaust  valve  is  opened,  permitting  the 
burned  gas  and  uncombined  air  to  escape  to  the  atmosphere,  and  during  the 
following  inward  stroke  practically  all  of  this  waste  material  is  expelled;  this 
last  is  known  as  the  exhaust  stroke. 

Graphic  Representation  of  Four-Stroke  "Cycle. — The  four  strokes  of  the 
engine  and  the  corresponding  indicator  diagram  are  shown  in  Fig.  1.  Here, 


534  INTERNAL-COMBUSTION  ENGINES 

p  denotes  the  piston;  r  is  the  connecting-rod;  k.  the  crankpin;  q,  the  crank- 
shaft. In  the  indicator  diagram,  the  ordinates  or  vertical  distances  represent 
pressures,  and  the  abscissas  or  horizontal  distances  denote  the  distance  the 
piston  has  proceeded  on  its  stroke.  The  pressures  are  measured  from  the 
line  0V,  which  represents  the  pressure  of  the  atmosphere.  The  line  Ovbz  is  the 
suction  line,  and  the  line  bzcz  is  the  compression  line.  At  cz,  the  charge  is 
ignited,  czdz  is  the  explosion  line;  dzez,  the  expansion  line;  czfz,  combined  expan- 
sion and  exhaust;  and  fzwO  is  the  exhaust  line.  The  pressures  represented  by 
the  two  lines  »  and  w  are  slightly  exaggerated,  in  order  that  the  lines  may  be 
distinguished  from  the  atmospheric  line  0V,  which  they  follow  very  closely. 

In  the  suction  stroke,  the  crank-shaft  turns  in  the  direction  of  the  arrow 
and  the  piston  moves  from  the  line  ai  to  the  position  shown.  The  space 
between  the  end  of  the  cylinder,  when  at  the  line  ai,  and  the  cylinder  head  is 
called  the  clearance  space  or  the  combustion  chamber.  In  this  stroke,  the  inlet 
valve  is  open  and  the  mixed  air  and  gas  is  being  drawn  into  the  cylinder.  The 
pressure  within  the  cylinder  drops  slightly  below  the  atmosphere,  as  shown 
by  the  line  ».  The  valve  remains  open  until  the  piston  gets  to  the  right-hand 
end  of  its  stroke.  The  numbers  at  the  left  of  the  diagram  represent  the  pres- 
sures, and  those  at  the  bottom  the  volumes,  corresponding  to  the  cross-lines 
opposite  which  they  are  written. 

When  the  piston  starts  on  its  return  stroke,  the  inlet  valve  is  closed  and  the 
mixture  is  trapped  within  the  cylinder  and  compressed.  The  rise  of  pressure 
during  compression  is  shown  in  the  indicator  diagram  by  the  line  bzcz.  When 
the  compression  has  proceeded  to  cz,  a  spark  is  produced  by  the  igniter  and 
combustion  begins.  The  rise  of  pressure  from  cz  to  dz  is  therefore  due  to  the 
compression  and  the  combustion  of  the  gas,  but  the  maximum  pressure  is 
lessened  somewhat  by  expansion.  The  flame  spreads  rapidly,  and  during  the 
short  time  at  the  end  of  the  stroke  when  the  piston  is  practically  at  rest  the 
pressure  rises  to  dz.  This  stroke  is  called  the  compression  stroke. 

It  has  been  found  that  by  compressing  the  charge  before  igniting  it,  a 
greater  amount  of  power  can  be  obtained  from  a  given  quantity  of  fuel  than  by 
simply  burning  it  at  atmospheric  pressure.  In  other  words,  the  efficiency  of 
the  internal-combustion  engine  is  increased  by  compressing  the  charge  before 
igniting  it.  Compressing  the  charge  heats  it;  hence,  on  account  of  the  danger 
of  preigniting  the  charge  the  compression  pressure  is  limited  to  from  60  to  75  Ib. 
per  sq.  in.,  as  shown  by  a  pressure  gauge. 

.  In  the  expansion  stroke,  during  which  the  pressure  of  the  heated  gases  drives 
the  piston  toward  the  right,  the  pressure  falls  as  the  piston  moves  forwards, 
as  shown  by  the  drop  in  the  line  dzez.  When  the  expansion  stroke  has  been 
nearly  completed,  the  exhaust  valve  is  opened  and  from  ei  to  V  the  drop  of 
pressure  is  due  both  to  expansion  and  to  the  escape  of  the  gas  through  the 
exhaust  valve.  By  the  time  the  end  of  the  stroke  is  reached,  the  pressure  has 
fallen  very  nearly  to  that  of  the  atmosphere,  and  the  expanding  gas  has  done 
its  work. 

During  the  next  stroke,  the  piston  is  returning,  the  exhaust  valve  is  open, 
and  the  gases  are  driven  from  the  cylinder  to  prepare  it  for  the  reception  of  a 
new  charge.  There  is  a  small  rise  of  pressure  during  this  stroke,  due  to  the 
driving  of  the  gas  from  the  cylinder,  indicated  by  the  line  w .  At  the  end  of 
the  exhaust  stroke,  the  exhaust  valve  closes,  and  the  succeeding  outward 
stroke  begins  a  new  cycle  with  the  suction  of  a  fresh  charge  of  gas  and  air. 

The  series  of  operations  that  take  place  during  the  four-stroke  cycle  is  as 
follows: 

FIRST  REVOLUTION 

First  Stroke. — Outwards;  suction;  inlet  valve  open;  pressure  falls  below 
atmosphere. 

Second  Stroke. — Inwards;  compression;  both  valves  closed;  pressure  rises; 
ignition  before  end  of  stroke,  followed  by  explosion  and  rapid  rise  of  pressure. 
SECOND  REVOLUTION 

Third  Stroke. — Outwards;  expansion;  both  valves  closed;  pressure  falls; 
exhaust  valve  opens  near  end  of  stroke. 

Fourth  Stroke. — Inwards;  exhaust;  exhaust  valve  open;  pressure  rises  very 
little  above  that  of  the  atmosphere. 

Application  of  Two-Cycle  Principle.— Fig.  2  (a)  illustrates  the  operation 
of  a  typical  two-cycle  engine,  in  which  p  is  the  piston;  q,  the  crank-shaft; 
a,  the  crank;  k,  the  crankpin;  r,  the  connecting-rod;  e,  the  exhaust  port;  o,  the 
inlet,  or  transfer,  port;  b,  the  passage  leading  from  the  crank-chamber  to  the 
cylinder;  s,  the  inlet  valve;  d,  a  deflector  on  the  end  of  the  piston;  and  i,  the  part 
of  the  igniting  device  at  which  the  spark  is  produced.  The  diagram  of 


INTERNAL-COMBUSTION  ENGINES 


535 


pressures  in  the  cylinder  is  shown  in  (b),  while  the  diagram  for  the  pressures  in 
the  crank-case  is  shown  in  (c). 

The  difference  between  the  diagrams  of  this  engine  and  that  of  the  four- 
cycle engine  should  be  carefully  noted.  When  the  piston  is  moving  toward 
the  cylinder  head,  it  is  compressing  the  mixture  of  gas  and  air,  while  at  the 
same  time  it  is  drawing  a  new  charge  into  the  crank-case  through  the  valve  s. 
That  portion  of  the  diagrams  given  during  this  stroke  is  shown  by  full  lines. 
In  reality,  the  first  part  of  the  cycle  must  always  be  the  suction  into  the  crank- 
case  before  any  mixture  is  taken  into  the  cylinder.  The  line  Vfgh  is  identical 
with  the  compression  and  explosion  line  of  the  four-stroke  cycle  and  covers 
the  same  series  of  operations;  namely,  compression  to  /,  where  ignition  takes 
place,  increase  of  the  rate  at  which  the  pressure  rises  from  /  to  g,  and  the 
explosion  line  gh.  While  the  piston  is  compressing  the  charge  in  the  cylinder, 
the  crank-case  is  drawing  more  fuel  through  the  valve  s,  the  pressure  in  the 
crank-case  falling  below  the  atmosphere,  as  shown  by  the  line  v  below  O'V. 


360 
320 
28O 
24O 
200 
160 
120 
80 
4O 
O 

h 

\ 

\ 

\ 

^ 

(i/ 

-.^ 

X 

"• 

». 

^^ 

J 

-~~^. 

N 

J! 

123456789\K 

V 

> 

c 

c\ 

'  , 

, 

' 

\ 

, 

," 

I 

„ 

* 

.'' 

\ 

^ 

I 

—  2_  345     6_7^J 

»*^5^i( 

V 

It  should  be  noted  that  the  diagram  for  the  pressures  in  the  crank-case  have  a 
different  scale  of  pressures  from  the  scale  of  the  diagram  for  the  pressures  in 
the  cylinder. 

The  next  stroke  moves  the  piston  away  from  the  head  end,  making  the 
expansion  stroke  for  the  cylinder  and  the  compression  stroke  for  the  crank- 
case,  the  inlet  valve  5  being  closed.  Before  the  exhaust  port  e  is  uncovered, 
the  portion  of  the  indicator  diagram  from  h  to  j  for  the  cylinder  and  from  o' 
to  c'  for  the  crank-case  is  drawn. 

When  the  piston  is  very  near  the  end  of  the  outward  stroke,  both  the  inlet 
and  the  exhaust  ports  o  and  e  are  open;  the  exhaust  gases  escape  from  the 
exhaust  port  e  and  the  fresh  charge  enters  through  the  by-pass  b  and  port  o, 
and  is  thrown  by  means  of  the  deflecting  plate  d  toward  the  cylinder  head. 
The  momentum  of  the  column  of  exhaust  gas  as  it  leaves  the  cylinder  is  so 


536  INTERNAL-COMBUSTION  ENGINES 

great  that,  unless  there  is  considerable  resistance  in  the  exhaust  passage,  the 
pressure  falls  below  that  of  the  atmosphere,  as  shown  by  the  small  loop  w, 
and  is  raised  slightly,  as  shown  by  the  loop  y,  when  the  fresh  charge  enters  from 
the  crank-case.  If  the  engine  is  properly  proportioned,  none  of  the  new  mixture 
will  escape  at  the  exhaust  port  e,  as  it  will  be  closed  before  the  fresh  charge  has 
reached  it.  During  this  part  of  the  stroke,  the  pressure  in  the  crank-case 
rises  from  c'  to  c  and  then  drops  to  V,  when  the  transfer  port  is  opened.  The 
following  inward  stroke  compresses  the  new  mixture  in  the  cylinder  and  draws 
a  new  charge  into  the  crank-case,  thus  beginning  a  new  cycle. 

The  series  of  operations  taking  place  during  the  two-stroke  cycle  are  as 
follows: 

CYLINDER  CRANK-CASE 

FIRST  STROKE,  INWARDS 

Compression:  pressure  rises;  igni-  Suction:  inlet  valve  open;  pressure 

tion  near  end  of  stroke,  followed  by        falls  below  atmosphere, 
explosion  and  rapid  rise  of  pressure. 

SECOND  STROKE,  OUTWARDS 

Expansion:  pressure  falls;  exhaust  Compression:    pressure    rises    to 

followed  by  entrance  of  fresh  mixture  from  4  to  8  lb.;  charging  cylinder; 
from  crank-case.  pressure  falls  to  atmospheric  pressure. 


GAS-ENGINE  FUELS 

Gaseous  Fuels. — Of  the  gases  described  on  page  308  and  the  following 
pages,  those  generally  employed  for  power  purposes  are:  Natural  gas,  used  at 
and  within  piping  distance  (150  to  200  mi.)  of  the  wells  where  it  is  produced; 
water,  or  illuminating,  gas,  used  in  those  cities  having  gas  plants,  although  its 
application  is  limited  by  reason  of  its  relatively  high  pYice;  producer,  or  fuel, 
gas,  used  generally  at  iron  andsteel  works;  by-product  gas,  used  at  by-product 
coke  ovens,  which  are  usually  built  in  connection  with  steel  works  or  in  some 
large  city  where  there  is  a  market  for  the  coke  as  well  as  the  gas.  Gaseous  fuels 
are  suitable  for  use  in  stationary  engines  but  not  in  haulage  motors.  They  are 
rarely  used  in  internal-combustion  engines  at  coal  mines,  although  natural  gas, 
if  the  price  is  low  by  reason  of  the  wells  being  in  the  coal  fields,  is  sometimes 
used  instead  of  coal  under  the  boilers. 

Alcohol.— Of  the  two  kinds  of  alcohol,  methyl,  or  wood,  alcohol,  CHtO,  and 
grain,  or  ethyl,  alcohol,  CzHeO,  the  former  is  not  suited  for  use  in  internal- 
combustion  engines  as  it  apparently  liberates  acetic  acid,  which  corrodes  the 
cylinders  or  valves. 

Grain  alcohol  has  a  specific  gravity  of  .795,  or  64°  Baume.  It  is  obtained 
by  distillation  from  vegetable  substances  containing  sugar  or  starch,  such  as 
corn,  wheat,  rye,  or  other  grains,  potatoes,  molasses,  etc.  When  pure,  it 
absorbs  water  more  rapidly  than  it  loses  its  own  substance  by  evaporation. 
When  diluted  with  15%  of  water,  it  evaporates  as  if  a  single  liquid  and  not  a 
mixture. 

The  revenue  laws  of  most  countries  require  that  grain  alcohol  must  be 
denatured  or  rendered  unfit  for  the  manufacture  of  liquors  before  being  sold 
as  a  fuel,  by  the  addition  of  some  poisonous  or  harmful  ingredient  such  as 
wood  alcohol,  petroleum  distillates,  cotoring  matter,  or  the  like.  In  France, 
the  denaturing  is  accomplished  by  adding  to  26  gal.  of  grain  alcohol,  17  oz. 
ot  heavy  benzine,  and  10%  of  wood  alcohol.  The  alcohols  used  are  each  of 
0  strength  or  purity.  To  reduce  the  cost  of  the  mixture  below  38c.,  it  is 
generally  mixed  with  an  equal  volume  of  benzol  containing  85%  of  benzine. 
In  Germany  a  fuel  costing  from  15  to  17|c.  a  gallon  is  made  Jay  adding  to  the 
grain  alcohol  15%  of  benzol,  no  wood  alcohol  being  used 

Gasoline.— Gasoline  is  produced  by  the  distillation  of  petroleum,  being 
among  the  first  of  the  hydrocarbons  to  be  given  off  in  the  manufacture  of  kero- 
sene or  illuminating  oil.  Its  boiling  point  varies  from  158°  to  176°  F.,  its 
f?0em  SO^to^0  <66  t0  '67'  and  itS  density  according  to  the  Baume  scale 

Commercial  gasoline  is  not  a  simple  substance  but  a  mixture  of  lighter 
and  heavier  products.  It  is  rated  according  to  its  density  by  the  Baum6 
scale.  Owing  to  evaporation  and  other  causes,  the  density  of  the  gasoline  as 
actually  purchased  is  likely  to  be  somewhat  greater  than  its  nominal  rating 
and  may  test  as  low  as  68°.  The  vapor  of  gasoline  that  forms  over  the  liquid 


INTERNAL-COMBUSTION  ENGINES  537 

consists  chiefly  of  pentane,  C&Hu,  having  a  specific  gravity  of  .628;  but  the  liquid 
gasoline  consists  of  a  mixture  of  hexane  and  heptane,  the  composition  varying 
with  the  specific  gravity  of  the  gasoline. 

A  gasoline  with  a  specific  gravity  of  .683  and  a  boiling  point  of  154°  F.  has 
shown  the  following  composition  by  analysis:  hexane,  80%;  heptane,  18%; 
pentane,  2%.  The  chemical  composition  is  83.8%  carbon  and  16.2%  hydrogen  ; 
and  the  chemical  formula  is  41.86C6#i4  +  6.48C7#i6+C6fl]2.  This  formula  will 
aid  in  the  calculation  of  the  fuel  value. 

Commercial  gasoline  evaporates  very  readily  at  ordinary  temperatures,  but 
quite  slowly  in  cold  weather,  and  leaves  small  percentages  of  a  heavier  oil, 
which  evaporates  slowly  or  not  at  all.  The  vapor  tension  varies  considerably 
with  the  temperature,  but  at  60°  F.  the  vapor  of  commercial  gasoline  repre- 
sents about  130  volumes  of  the  liquid  and  sustains  a  water  pressure  of  from  6 
to  8  in.  An  explosive  mixture  of  gasoline  vapor  and  air  is  composed  of  the 
vapor  of  1  part  of  liquid  gasoline  to  from  8,000  to  10,000  parts  of  air  by  volume. 
The  volume  of  the  vapor  will  vary,  but  an  average  proportion  will  be  2.15  of 
gasoline  vapor  to  100  parts  of  air. 

Kerosene.  —  Kerosene,  or  illuminating  oil,  the  principal  product  of  the 
distillation  of  petroleum  and  sometimes  used  in  internal-combustion  engines, 
boils  at  302°  to  572°  F.,  has  a  specific  gravity  of  .753  to  .964,  and  a  density 
of  56°  to  32°  Baume. 

Commercial  kerosene  varies  in  specific  gravity  (at  59°  F.)  from  .760  to  .820. 
Exceptionally  light  kerosene,  such  as  the  Pennsylvania  light  oil,  has  a  specific 
gravity  below  .760.  The  boiling  point  of  kerosene  of  .760  specific  gravity  is 
302°  F.  and  of  kerosene  of  .820  specific  gravity  536°  F.  Kerosene  begins  to 
give  off  vapor  at  from  100°  to  120°  F.,  and  this  vapor  is  mainly  nonane, 


Liquid  kerosene  is  a  mixture  of  decane,  CioH&,  with  a  little  hexadecane, 
The  boiling  points  of  these  three  liquids  are  as  follows:  nonane,  CgHw,  277°  F.; 
decane  CioHis,  316°  F;  hexadecane,  C\sHu,  536°  F.  Average  kerosene  con- 
sists chiefly  of  decane.  For  the  chemical  action  that  takes  place  when  kerosene 
is  burned,  that  corresponding  to  the  combustion  of  decane  may  be  taken  with- 
out appreciable  error. 

Fuel,  or  Compound,  Oils.  —  Oils  that  are  lighter  than  about  70°  Baum6 
evaporate  so  rapidly  that  a  large  part  is  often  lost  before  they  reach  the  con- 
sumer. To  reduce  this  loss  on  the  part  of  the  light  oils  and  to  make  a  market 
for  the  less  salable  heavy  oils,  the  two  are  sometimes  mixed  and  offered  as  fuel, 
or  compound,  oil  or  by  some  trade  name.  These  mixtures  are  not  to  be  con- 
fused with  the  fuel  oil  produced  directly  from  wells  and  described  on  395  and 
the  following  pages,  which  is  crude  petroleum.  As  the  demand  for  the  diffi- 
cultly salable  heavy  oils  varies,  so  will  vary  the  composition  of  the  artificial 
fuel  oils  into  which  they  enter. 

Rating  of  Oil  and  Gasoline.  —  In  selecting  gasoline,  it  is  usually  sufficient 
to  know  its  density  by  Baum6's  scale,  this  being  the  rating  at  which  it  is  sold 
in  the  general  market.  For  instance,  "Gasoline  72  Baum6"  means  that  the 
density  of  the  gasoline  is  72°  of  Baum6's  hydrometer.  Kerosene  is  generally 
rated  by  its  flashing  point.  This  point  is  the  number  of  degrees  of 
temperature  to  which  it  must  be  heated  before  the  vapors  given  off 
from  the  surface  of  the  oil  will  take  fire  from  a  flame  held  over  the 
containing  vessel.  Thus,  oil  of  150°  test  is  oil  that  will  flash  or  take 
fire  when  heated  to  a  temperature  of  150°  F.  Kerosene,  at  ordinary 
temperatures,  should  extinguish  a  lighted  taper  when  the  taper  is 
plunged  into  it. 

Baume  Hydrometer.  —  The  Bauml  hydrometer  shown  in  the 
figure  consists  of  a  glass  tube,  near  the  bottom  of  which  are  two 
bulbs.  The  lower  and  smaller  bulb  is  loaded  with  mercury  or  shot, 
so  as  to  cause  the  instrument  to  remain  in  a  vertical  position  when 
placed  in  the  liquid  in  the  vessel  a.  The  upper  bulb  b  is  filled  with 
.air,  and  its  volume  is  such  that  the  whole  instrument  is  lighter  than 
an  equal  volume  of  water. 

The  point  to  which  the  hydrometer  sinks  when  placed  in  water 
is  usually  marked,  the  tube  being  graduated  above  and  below  in 
such  a  manner  that  the  specific  gravity  of  the  liquid  can  be  read 
directly.  It  is  customary  to  have  two  instruments:  one.  with  the 
zero  point  near  the  top  of  the  stem,  for  use  in  liquids  heavier  than 
water;  and  the  other  with  the  zero  point  near  the  bulb,  for  use  in  liquids 
lighter  than  water. 

Comparative  Value  of  Liquid  Fuels.  —  So  far  as  their  heating  value  per 
pound  goes,  there  is  not  mucn  to  choose  between  kerosene  and  gasoline,  each 


538 


INTERNAL-COMBUSTION  ENGINES 


READINGS 


QPQ 


QPQ 


20 
22 
24 
2(3 
28 
30 
32 
34 
30 


.9333 
.9210 
.9090 
.8974 


.8750 
.8641 
.8536 
.8433 


.8333 
.8235 
.8139 
.8045 
.7954 
.7865 
.7777 
.7692 
.7608 


.7526 
.7446 
.7368 
.7290 
.7216 
.7142 
.7106 
.7070 
.7035 


70 
71 
72 
73 
74 
75 

n 

77 
78 


.7000 
.6965 
.6931 
.6896 
.6863 
.6829 
.6796 
.6763 
.6730 


79 
80 
81 
82 
83 
84 
86 
88 
90 


.6666 
.6635 
.6604 
.6573 
.6542 
.6481 
.6422 
.6363 


developing  about  19,800  B.  T.  U.  per  Ib.  Kerosene,  however,  is  about  10% 
heavier,  so  that  1  gal.  of  kerosene  has  more  fuel  value  than  1  gal.  of  gasoline. 

As  compared  with  gasoline  as  a  fuel  for  internal-combustion  motors,  alcohol 
exhibits  several  striking  peculiarities.  First,  the  combustion  is  much  more 
likely  to  be  complete.  A  mixture  of  90°-alcohol  vapor  and  air  will  burn  com- 
pletely when  the  proportion  varies  from  1  of  the  vapor  with  10  of  air  to  1  of 
the  vapor  with  25  of  air,  thus  exhibiting  a  much  wider  range  of  proportions  for 
combustibility  than  is  the  case  with  gasoline.  As  the  combustion  is  complete, 
the  exhaust  is  practically  odorless,  consisting  only  of  water  vapor  and  carbon 
dioxide.  Second,  the  inflammability  of  an  alcohol  mixture  is  much  lower. 
This  is  due  partly  to  the  presence  of  water  in  the  alcohol,  which  is  vaporized 
with  the  alcohol  in  the  engine  and  must  be  converted  into  steam  at  the  expense 
of  the  combustion.  For  these  reasons,  the  compression  of  an  alcohol  mixture 
is  carried  far  above  that  permissible  with  a  gasoline  mixture,  without  danger 
of  spontaneous  ignition.  The  rapidity  of  combustion  of  alcohol  in  an  engine 
is  considerably  less  than  that  of  a  gasoline  mixture,  and  for  this  reason  the 
speed  of  alcohol  engines  must  be  somewhat  slow. 

With  an  engine  of  equal  size,  practically  the  same  horsepower  can  be 
obtained  when  adapted  to  burning  alcohol  as  when  adapted  to  burning  gaso- 
line. This  is  true  in  spite  of  the  fact  that  1  Ib.  of  alcohol  contains  considerably 
less  heat  energy  than  1  Ib.  of  gasoline,  and  it  is  explained  by  the  fact  that  1  Ib. 
of  alcohol  requires  much  less  air  for  its  complete  combustion  than  1  Ib.  of 
gasoline.  In  other  words,  a  larger  quantity  of  alcohol  than  of  gasoline  is 
required  to  make  1  cu.  ft.  of  explosive  mixture.  Approximately  speaking,  if 
there  is  no  surplus  air  in  either  case,  1  Ib.  of  gasoline  will  make  210  cu.  ft.  of 
explosive  mixture,  and  1  Ib.  of  alcohol  will  make  120  cu.  ft.  As  a  matter  of 
fact,  a  certain  percentage  of  additional  air  is  required,  both  for  the  most  rapid 
combustion,  and  for  the  necessary  economy  of  fuel.  So  far  as  can  be  judged, 
a  somewhat  greater  proportion  of  air  is  advantageous  with  alcohol;  but  it 
seems  to  be  clear  that  from  50  to  60%  more  alcohol  than  gasoline  by  weight 
is  required  to  obtain  the  same  power.  On  the  other  hand,  alcohol  is  about 
25%  heavier  than  gasoline,  so  that  1  Ib.  of  gasoline  has  1  \  times  the  volume 
of  1  Ib.  of  alcohol.  Consequently,  if  the  weight  of  alcohol  needed  for  a  given 
amount  of  work  is  50%  greater  than  the  weight  of  gasoline,  the  volume  of 
alcohol  required  will  be  only  one-fifth  greater,  or  in  the  proportion  of  1.5  to  1.25. 


TYPES  OF  INTERNAL-COMBUSTION  ENGINES 

Internal-Combustion  Engines  at  Mines. — Internal-combustion  engines,  so 
far  as  their  use  at  mines  is  concerned,  may  be  placed  in  one  of  three  general 
classes  or  groups;  stationary,  portable,  or  haulage-motor  engines. 

Those  of  the  first  class  are  permanently  attached  to  their  foundations  and 
comprise  hoisting  and  dynamo  engines,  engines  used  for  operating  station 
pumps,  etc.  They  may  be  horizontal  or  vertical,  may  have  one  or  more 
cylinders,  and  usually  run  at  a  speed  of  300  to  400  rev.  per  min.;  they  are, 


539 


540 


INTERNAL-COMBUSTION  ENGINES 


therefore,  relatively  large  and  heavy  for  the  amount  of  power  developed.  These 
engines  are  rarely  found  at  coal  mines  where  fuel  is  always  cheap  and  water 
for  boilers  usually  plentiful,  but  in  the  arid  regions,  where  both  fuel  and  water 
are  scarce,  they  are  in  extensive  and  satisfactory  use. 

Portable  engines,  which  may  be  moved  from  place  to  place,  are  quite 
commonly  used  in  and  around  coal  mines  for  operating  concrete  mixers,  small 
pumps  used  in  any  one  place  only  temporarily,  etc.  These  engines  are  hori- 
zontal or  vertical  and  usually  have  four  cylinders.  They  are  generally  designed 
so  that  their  speed  may  be  varied,  but  they  are  rated  at  the  maximum  power 
they  can  produce  at  their  highest  speed  of  from  1,000  to  1,800  rev.  per  min. 
They  are,  therefore,  lighter  than  stationary  engines  of  the  same  power. 

Haulage-motor,  or,  as 
they  are  commonly  called, 
gasoline-motor,  or  gasoline 
locomotive,  engines,  may 
be  horizontal  or  vertical. 
They  are  usually  of  the 
four-cylinder,  vertical  type, 
and  differ  but  slightly  from 
those  used  on  automobiles. 
Stationary  Gas  Engines. 
A  section  of  a  stationary 
gas  engine  is  shown  in 
Fig.  1.  The  valves  are  in 
the  cylinder  head,  which 
is  bolted  to  the  cylinder 
at  the  flange  a.  The  inlet 
valve  is  shown  at  b  and  the 
exhaust  valve  at  c.  When 
the  pressure  is  very  great, 
the  temperature  due  to 
compression  in  the  space  d 
may  be  sufficient  to  ignite 
the  mixture  of  gas  and  air. 
In  order  that  a  high  com- 
pression pressure  may  be 
used  without  igniting  the 
gas,  the  cylinder  head  is 
cooled  by  water  introduced 
at  e  through  the  pipe  /. 
The  water-cooled  projec- 
tion g  extends  into  the 
combustion  chamber  and 
cools  the  explosive  mixture 
of  air  and  gas.  The  water 
passes  from  the  cylinder 
head  to  the  water-jacket 
around  the  cylinder  through 
the  pipe  h  and  flows  to 
waste  through  the  pipe  ». 

Haulage-Motor  Gaso- 
line Engines.  —  One  of  the 
four  cylinders,  as  well  as 
the  necessary  mechanism 
of  a  gasoline  engine  suit- 
able for  use  on  haulage 
motors,  is  shown  in  Fig.  2. 
The  cylinder  is  a  and  the  cylinder  head  is  b.  The  piston  c  takes  the  place 
of  the  crosshead  and  therefore  carries  the  wrist-pin  d.  The  crank-shaft, 
crank,  crankpin,  and  connecting-rod,  are  lettered  e,f,fi,  and  g,  respect- 
ively. The  charge  enters  the  cylinder  through  the  passages  h  and  *,  which 
are  closed  by  the  conical  inlet  valve  j  on  the  yalve  seat  ji.  The  valve 
stem  k  is  pressed  downwards  through  the  guide  ci,  so  that  the  valve  is 
held  closed  by  the  spring  I,  except  when  the  valve  stem  is  pushed  up  by 
the  push  rod  m.  This  push  rod  is  lifted  by  the  cam  n  on  the  half-speed,  or  lay 
shaft  o,  and -is  held  in  position  by  the  guide  61.  The  letters  from  p  to  w  mark 
the  parts  on  the  exhaust  side  of  the  engine  corresponding  to  those  marked  by 
the  letters  h  to  o  on  the  inlet  side.  The  cup  shown  at  x  serves  the  double 


FIG.  2 


INTERNAL-COMBUSTION  ENGINES 


541 


purpose  of  priming  cup  and 
compression  relief  valve.  The 
spark  plug  is  shown  at  y  and 
the  water-jacket  for  cooling  the 
various  parts  of  the  engine  is 
at  z.  In  some  cases,  both 
valves  are  placed  on  one  side 
of  the  engine  and  are  operated 
by  cams  on  the  same  lay  shaft. 
The  four-cylinder  opposed 
engine  differs  from  the  vertical 
engine  only  in  the  arrangement 
of  the  cylinders.  The  shaft  a, 
Fig.  3,  has  four  cranks  b.  A 

cylinder  c  with  a  piston  d  and  connecting-rod  e  is  placed  opposite  each  crank. 
The  valves  and  operating  mechanism,  which  are  placed  above  the  cylinders, 
are  not  shown. 


CARBURETION  AND  IGNITION 

Carbureters  for  Constant-Speed  Engines.  —  When  liquid  fuel  is  used  in 
internal-combustion  engines,  it  must  be  reduced  to  a  vapor  or  fine  spray  before 
it  is  introduced  into  the  engine  cylinder.  The  device  by  which  this  is  done 
is  called  a  carbureter,  or  vaporizer,  one  form  of  which,  suitable  for  use  in  con- 
nection with  stationary  engines  running  at  very  nearly  constant  speed,  is 
shown  in  Fig.  1. 

The  carbureter  a  is  attached  to  the  side  of  the  inlet  pipe  &.  The  fuel  is 
pumped  to  the  carbureter  through  the  pipe  c  into  'the  reservoir  d  from  the 
side  of  which  the  nozzle  e  is  led  into  the  inlet  pipe  in  such  a  way  that  the  sur- 
face of  the  fuel  is  just  below  the  top  of  the  nozzle.  The  surplus  fuel  overflows 
from  d  and  returns  to  the  fuel-supply  tank  through  the  pipe  /.  The  supply 
of  fuel  may  be  regulated  by  the  needle  valve  g  and  may  be  shut  off  by  the  valve  h. 

When  the  piston  is  moving  out  on  the 
suction  stroke,  the  inlet  valve  i  is 
opened  and  air  is  drawn  in  through 
the  pipe  j  into  the  combustion  cham- 
ber k.  The  pipe  b  is  contracted  at  the 
level  of  the  nozzle  so  that  the  velocity 
of  the  passing  air  is  increased,  with 
the  result  that  some  of  the  oil  is  sucked 
up  from  the,  nozzle  and  enters  the 
cylinder  as  a  fine  spray  or  vapor 
mixed  with  the  proper  amount  of  air 
to  secure  its  complete  combustion. 

Carbureters  for  Variable  -  Speed 
Engines.  —  A  carbureter  suitable  for 
use  with  a  variable-speed  engine  is 
shown  in  Fig.  2.  In  it,  the  spray 
nozzle  a  and  the  tube  b  are  similar  to 
the  corresponding  parts  of  the  car- 
bureter just  described.  The  gasoline 
chamber  c  contains  a  cork  float  that 
controls  a  small  needle  valve  at  the 
right  through  which  the  gasoline  enters 
and  which  serves  to  maintain  the  fuel 
at  a  constant  level.  The  flow  of  gaso- 
line through  the  spray  nozzle  a  is 
regulated  by  the  needle  valve  d  and 
the  handle  e.  When  set,  this  valve 
may  be  locked  in  position  by  the 
screw  m.  The  main  air  inlet  is  at  / 
through  the  horn  g  and  the  pipe  lead- 
ing to  the  engine  is  connected  just 
above  the  throttle  valve  j. 

As  the  speed  of  the  engine  is  in- 
creased, the  proportion  of  gasoline  in  the  fuel  mixture  should  be  decreased. 
On  the  other  hand,  increased  speed  causes  the  air  to  flow  more  rapidly  around 


pIG 


542 


INTERNAL-COMBUSTION  ENGINES 


the  nozzle  a,  thus  taking  up  more  gasoline  and  enriching  the  fuel  mixture. 
To  reduce  the  proportion  of  gasoline  to  the  requirements  of  increased  speed, 
the  mixture  is  diluted  by  admitting  air  above  the  nozzle  through  auxiliary 
inlets  closed  by  bronze  balls  *.  When  a  certain  degree  of  suction  has  been 
reached,  one  or  more  of  these  balls  are  lifted  and  air  is  admitted  above  the 
nozzle  a,  thus  diluting  the  mixture.  The  balls  are  held  in  place  by  cages  k 
that  are  screwed  into  the  body  of  the  carbureter.  The  gasoline  chamber 

may  be  drained  by  the  cock  I. 

Make-and-Break  Ignition. — If 
the  ends  of  two  wires  forming  part 
of  an  electric  circuit  are  brought  in 
contact,  thereby  closing  the  circuit, 
and  then  quickly  separated,  a  bright 
spark  will  be  produced  as  the  con- 
tact is  broken.  This  phenomenon 
underlies  the  operative  principle 
of  what  is  known  as  the  make-and- 
break  system  of  ignition,  with  which 
it  is  necessary  first  to  complete  the 
electric  circuit  through  the  spark- 
producing  mechanism,  or  igniter, 
and  then  break  the  circuit  to  obtain 
a  spark  for  igniting  the  charge.  In 
stationary  gas-engine  practice,  the 
simplest  kind  of  igniter  uses  city 
lighting  current,  with  an  incandes- 
cent lamp  in  series,  in  order  to  pre- 
vent the  current  from  being  too 
strong,  and  consists  simply  of  a 
mechanical  device  for  making  and 
breaking  the  circuit  in  the  combus- 
tion chamber  at  the  proper  moment. 
Batteries  may  be  used  with  the 
make-and-break  system  of  ignition 
by  using  a  spark  coil. 

With  a  low-voltage  current, 
such  as  that  derived  from  a  primary 
battery,  a  spark  coil  must  be  em- 
ployed to  produce  the  necessary 
electric  tension  or  voltage  for  the 
spark.  When  a  battery  and  spark 
coil  are  employed,  the  abruptness 
of  the  break  between  the  contact 
point  serves  to  increase  the  inten- 
sity of  the  spark,  it  being  largely 
proportional  to  the  sharpness  of 
the  circuit  rupture.  Fig.  3  shows 
an  elementary  wiring  diagram  for  a 
primary  ignition  circuit,  with  the 
direction  of  the  current  indicated  by 
an  arrow.  When  the  timing  cam  a 
brings  the  points  b  and  c  into  con- 
tact, the  current  flows  from  the 
battery  d  through  the  switch  e 
(when  closed)-spark  coil /-insulated 
electrode  g-rocking  contact  finger  h- 
grounded  contacts  *,  back  to  the 
battery.  The  grounded  connec- 
tions i  may  be  made  to  the  frame 
of  the  machine,  or  any  other  convenient  metallic  return  may  be  used. 
^  Jump-Spark  Ignition. — The  mechanism  of  the  make-and-break  system  of 
ignition  requires  a  considerable  number  of  moving  parts  that  may  be  more 
or  less  objectionable.  What  is  known  as  the  jump-spark  system  of  ignition, 
in  which  the  primary  current  is  converted  by  an  induction  coil  into  a  secondary 
current  of  sufficiently  high  tension  to  cause  a  spark  to  jump  an  air  gap  may 
therefore  be  used.  With  this  system,  a  revolving  contact  timer  is  employed 
in  place  of  the  snap  cam.  As  there  are  no  other  moving  parts,  the  whole 
apparatus  is  extremely  simple. 


INTERNAL-COMBUSTION  ENGINES 


543 


In  Fig.  4  are  shown  the  essential  elements  of  a  jump-spark  system  of 
ignition.  Here  c  is  the  battery ;  b,  a  switch  for  opening  the  primary  circuit  when 
it  is  not  in  use;  and  c,  a  revolving  timer  turning  at  one-half  the  speed  of  the 
crank-shaft,  if  the  engine  is  of  the  four- 
cycle type.  The  timer  in  the  elemen- 
•  tary  apparatus  shown  consists  of  an 
insulating  ring  d,  mounted  on  the  shaft 
into  which  is  dovetailed  a  copper  or 
brass  segment  e  that  is  in  electric  con- 
nection, by  a  screw  or  otherwise,  with 
the  shaft/.  A  plate  g  is  mounted  loosely  ^s~i 
on  the  shaft,  so  that  it  does  not  turn  with  -~- 
it,  but  may  be  rocked  about  it  through  a  in~ 
suitable  arc,  say  45°.  Mounted  on  this  | 
plate,  and  insulated  from  it,  is  a  brush  h 
that  bears  against  the  insulating  ring 
and  makes  contact  with  the  metal 
segment  at  each  revolution  of  the  lat- 
ter. The  primary  winding  of  the  spark  f 
coil  is  represented  by  i,  andj  is  the 
ground  on  the  engine.  A  trembler  k  is  FIG.  3 
provided  so  that  the  current  may  be  rapidly  interrupted.  The  trembler  is 
for  the  purpose  both  of  interrupting  the  current  more  rapidly  than  could  be 
done  with  the  timer  and  to  produce  a  series  of  sparks  in  rapid  succession  instead 
of  only  a  single  spark. 

The  course  of  the  current  is  from  the  positive  pole  of  the  battery  to  the 
trembler-primary  winding  of  spark  coil-the  engine  frame  ./-contact  e-brush 
of  timer,  when  contact  is  made-switch  fc-negative  terminal  of  battery.  The 
negative  terminal  of  the  secondary  winding  of  the  coil  is  connected  to  the  bat- 
tery terminal  of  the  primary  winding,  and  the  positive  secondary  terminal  is 
connected  to  the  insulated  member  of  the  spark  device,  or  spark  plug,  from 
which,  after  jumping  over  the  gap  /,  the  current  returns  to  the  coil  by  way  of 
the  engine  frame  j  and  primary  winding.  When  the  circuit  is  closed  by  the 
timer,  a  stream  of  sparks  passes  between  the  spark  points  /.  For  use  with 
small,  highspeed  motors,  the  coil  vibrator  is  frequently  omitted,  and  a  snap  or 
vibrating  form  of  timer  is  used  that  gives  a  quick  break  but  only  one  spark. 


FIG.  4 

The  primary  winding  is  provided  with  a  condenser  m,  which  serves  the 
double  purpose  of  increasing  the  abruptness  of  the  circuit  rupture,  thereby 
increasing  the  intensity  of  the  secondary  spark,  and  of  absorbing  the  current 
that  otherwise  would  produce  a  hot  spark  at  the  trembler  contacts,  and  soon 


544  INTERNAL-COMBUSTION  ENGINES 

burn  them  out.  The  function  of  a  condenser  is  to  absorb  the  extra  current 
induced  in  the  primary  coil  at  the  moment  of  rupture.  Under  the  primary 
system  of  ignition,  it  is  precisely  this  extra  current  that  produces  the  useful 
spark  in  the  engine;  but  in  the  secondary  system,  this  extra  current  is  objection- 
able, because  it  dies  down  so  slowly  that  it  fails  to  induce  a  sufficiently  intense 
spark  in  the  secondary  coil. 

The  change  of  the  time  of  ignition  is  accomplished  for  different  speeds  by 
rocking  the  plate  g  to  the  right  or  left  by  means  of  the  rod  n,  so  that  contact 
is  made  by  the  timer  early  or  late  in  the  revolution  of  the  shaft. 

To  run  an  engine  at  varying  speeds,  it  is  necessary,  in  order  to  obtain  the 
best  results,  to  modify  the  time  of  ignition  to  suit  the  speed,  making  the  time 
earlier  for  high  than  for  low  speed.  It  is  also  necessary  to  modify  the  time  of 
ignition,  according  to  the  load  the  engine  is  carrying,  if  the  engine  is  regulated 
by  throttling.  In  other  words,  with  a  given  speed,  a  charge  will  burn  faster 
if  highly  compressed,  as  when  a  full  charge  is  taken,  than  if  only  slightly  com- 
pressed, as  it  may  be  if  the  charge  has  been  much  throttled.  For  these  reasons, 
a  great  many  engines  are  provided  with  means  for  varying  the  time  of  ignition. 

Requirements  of  Spark  Plugs.— The  spark  plugs  on  the  market  are  of  a 
variety  of  designs,  each  with  some  special  features  of  advantage  that  may  or 
may  not  be  possessed  by  others.  The  chief  requirements  of  a  good  spark  plug 
are  the  following: 

1.  Where  exposed  to  burning  gas  and  oil  vapors,  the  insulating  material 
of  porcelain  or  mica  between  the  central  electrode  or  stem,  which  is  connected 
to  the  positive  terminal  of  the  coil,  must  not  be  too  easily  coated  with  carbon 
deposit.     The  electric  resistance  of  any  gas  increases  considerably  as  the  gas 
is  compressed,  so  that,  although  the  current  may  jump  between  the  proper 
spark  points  when  the  plug  is  in  the  open  air,  the  resistance  between  these 
points  may  become  so  great  when  the  plug  is  in  the  cylinder  and  the  charge 
compressed,  that  the  current  will  take  an  easier  path  through  the  carbon  coat- 
ing on  the  porcelain.     Practically  the  same  thing  will  happen  if  the  porcelain 
is  cracked,  for  the  current  will  then  take  the  direct  route  through  the  crack 
rather  than  the  route  from  spark  point  to  spark  point  through  the  compressed 
gas.     The  leakage  through  the  carbon  deposit  must,  therefore,  be  made  as 
difficult  as  possible  by  giving  the  leaking  current  a  considerable  distance  to 
travel;  besides,  special  devices  are  sometimes  employed  to  prevent;  the  collec- 
tion of  carbon. 

2.  The  plug  must  be  easily  cleaned  of  whatever  carbon  may  be  deposited 
on  it.     It  must,  therefore,  be  taken  apart,  reassembled,  and  made  gas-tight 
easily;  besides,  the  packing  process  must  not  endanger  the  porcelain  more  than 
necessary. 

3.  The  plug  must  fit  the  standard  sizes  of  threaded  spark-plug  holes  and 
must  not  be  unduly  expensive  to  replace.     Among  the  sizes  most  used  is  the 
so-called  metric  size,  the  proportions  of  which  are  based  on  the  metric  system 
of  measurement.     Most  of  the  imported  spark  plugs  are  of  this  size,  which  is 
approximately  the  size  of  a  £-in.  pipe  tap,  but  they  are  not  tapered.     American 
spark  plugs  are  either  of  the  i-in.  or  the  f-in.  pipe  sizes.     The  pipe  sizes  are 
tapered  and  depend  for  tightness  on  the  plug  being  screwed  in  tightly.     This 
methpd  is  not  altogether  satisfactory,  as  the  thread  in  the  engine  wears  and 
permits  leakage,  which  causes  the  plug  to  heat.     Both  the  engine  and  plug 
tapers  are  liable  to  variations  that  may  make  one  plug  screw  well  into  its  hole 
while  another  catches  only  a  few  threads,  and  consequently  is  not  so  well  placed 
for  prompt  communication  of  flame  to  the  compressed  charge.     Plugs  that  are 
not  provided  with  tapered  threads  are  made  gas-tight  by  gaskets  of  asbestos 
covered  with  thin  copper  sheathing. 

It  is  desirable,  though  not  essential,  that  the  spark  points  should  be  of 
platinum,  because  they  do  not  then  burn  away  to  any  appreciable  extent. 
When  not  made  of  platinum,  they  are  often  made  of  a  special  alloy  of  steel 
and  nickel,  which  resists  oxidation  nearly  as  well  as  platinum.  The  air  gap 
between  the  spark-plug  points  should  not  exceed  3V  in.  nor  be  less  than  ^  in. ; 
the  best  size  is  about  midway  between  these  dimensions.  In  case  a  battery 
gives  out  and  there  is  no  other  at  hand,  the  engine  may  be  kept  going  for  a 
short  time  by  pinching  the  spark-plug  points  a  little  closer  together,  to  reduce 
the  resistance  offered  by  the  gap. 


INTERNAL-COMBUSTION  ENGINES  645 


OPERATION  OF  INTERNAL-COMBUSTION  ENGINES 

Engine  Starters. — Engines  of  less  than  40  H.  P.  are  usually  started  by 
turning  over  by  hand,  but  larger  engines  are  usually  provided  with  some  form 
of  starting  mechanism.  The  use  of  compressed  air  to  start  the  engine  is  prob- 
ably the  most  convenient.  Its  only  disadvantage  is  the  possibility  of  the  air 
supply  becoming  exhausted  by  leaks  in  the  tank  or  connections  or  through 
repeated  failures  to  start  the  engine.  This  disadvantage  is  of  course  increased 
if  the  air  compressor  is  operated  from  the  engine  itself  or  from  a  line  shaft 
operated  by  the  engine.  It  is  of  less  consequence  if  the  compressor  is  driven 
from  a  small  auxiliary  engine,  the  only  difficulty  in  that  case  being  the  delay 
caused  by  the  time  required  for  charging  the  air  tank. 

The  operation  of  compressed-air  starters  is  much  simplified  if  the  engine 
is  equipped  with  a  mechanically  driven  and  timed  valve  that  admits  the  air 
to  the  cylinder  during  what  is  usually  the  expansion  stroke  of  the  engine, 
and  allows  it  to  escape  during  the  regular  exhaust  stroke.  In  this  case,  all  the 
operator  has  to  do  is  to  open  the  cock  in  the  air  pipe  between  the  tank  and  the 
engine,  and  keep  it  open  until  the  engine  has  attained  a  fair  speed,  when  the 
air  connection  is  shut  off  and  the  fuel  supply  is  turned  on.  If  no  mechanically 
operated  timing  valve  for  compressed  air  is  provided,  the  cock  between  the  air 
tank  and  the  engine  must  be  opened  and  closed  by  hand,  at  proper  intervals; 
this  requires  skill  and  watchfulness  on  the  part  of  the  attendant,  since  the  cock 
must  be  closed  except  during  the  working  stroke  of  the  piston. 

A  very  effective  method,  employed  on  large  engines  especially,  is  to  admit 
air  during  every  forward  stroke  of  the  piston  and  expel  it  during  both  the 
compression  and  the  exhaust  strokes.  This  is  done  by  providing  auxiliary 
cams  that,  when  thrown  in  gear,  will  open  the  inlet  valve  during  the  suction 
and  expansion  strokes  and  the  exhaust  valve  during  the  compression  and 
exhaust  strokes.  After  the  engine  is  under  way,  the  cams  are  disengaged  and 
the  engine  is  run  in  the  regular  manner. 

In  order  that  the  engine  may  always  be  started  promptly,  the  attendant 
must  keep  the  air  compressor  and  storage  tank  in  good  working  order.  The 
compressor  requires  lubrication  at  regular  intervals,  and  the  air  valves  must 
be  kept  tight  to  insure  efficient  service.  The  pressure  in  the  tank  should  show 
no  perceptible  loss  over  night;  and  if  it  should  fall  to  any  great  extent,  the 
cause  of  the  leak  should  be  determined  and  the  proper  remedies  applied.  If 
the  leak  is  located  in  the  seams  or  rivets  of  the  tank,  they  must  be  calked  in 
the  usual  manner.  In  case  the  pipes  or  fittings  between  the  tank  and  the 
engine  are  not  tight,  they  must  be  screwed  up  or  defective  fittings  replaced 
with  perfect  ones. 

Starting  the  Engine. — The  following  rules  for  starting  and  stopping  gasoline 
engines  should  be  followed: 

1.  Attend  to  all  lubricators  and  oil  holes,  always  following  the  same  order. 

2.  Apply  a  few  drops  of  kerosene  to  the  valve  stems. 

3.  Open  the  gas-cock  back  of  the  rubber  bag  or  regulator,  or,  when  using 
gasoline,  open  the  cock  near  the  tank,  and  work  the  gasoline  pump  by  hand 
until  the  liquid  appears  in  the  valve  or  overflow  cup 

4.  See  that  the  electric  igniter  is  properly  connected,  turn  on  the  switch, 
and  see  that  the  spark  is  of  proper  intensity. 

5.  Turn  the  flywheel  until  the  engine  is  at  the  beginning  of  the  working 
stroke. 

6.  Open  the  fuel  cock  to  the  point  that  has  been  found  most  reliable  for 
starting. 

7.  Throw  the  relief  cam  in  gear  or  open  the  relief  cock. 

8.  If  a  compressed-air  or  some  other  self-starter  is  employed,  operate  the 
device.     If  no  starting  devices  are  used,  turn  the  flywheels  rapidly  until  the 
engine  starts. 

9.  Close  the  relief  valve  or  disengage  the  relief  cam  and  open  the  fuel  cock 
to  its  full  extent,  gradually,  as  the  speed  of  the  engine  increases. 

10.  Turn  on  the  cooling  water,  if  running  water  is  used,  or  see  that  the 
tank  is  full  and  the  cocks  open  if  the  tank  system  of  cooling  is  employed. 

11.  Throw  in  the  friction  clutch  or  shift  the  belt  to  the  tight  pulley  on  the 
line  shaft. 

Stopping  the  Engine. — 1.  Disengage  the  friction  clutch  or  shift  the  belt 
to  the  loose  pulley  on  the  line  shaft. 

2.     Close  the  gas-cock  near  the  rubber  bag  or  regulator  or  the  gasoline  cock 
near  the  storage  tank. 
35 


546  INTERNAL-COMBUSTION  ENGINES 

3.  Close  the  gas  or  gasoline  cock  on  the  engine. 

4.  Throw  off  the  switch  between  the  battery  and  the  engine,  or  turn  off 
the  burner  that  heats  the  tube. 

5.  Drain  the  water-jacket  by  closing  the  valve  in  the  supply  pipe  and 
opening  the  cock  that  connects  the  bottom  of  the  cylinder  to  the  drain  pipe. 
If  water  tanks  are  used,  close  the  cocks  in  the  water  pipe  and  open  the  drain 
cock. 

6.  Shut  off  all  sight-feed  lubricators. 

7.  Clean  the  engine  thoroughly,  wiping  off  any  oil  or  dust  that  may  have 
accumulated  on  the  engine. 

8.  See  that  the  engine  stops  in  a  position  where  the  exhaust  and  inlet 
valves  are  closed.     If  necessary,  turn  the  wheels  by  hand  until  this  position  is 
reached ;  it  will  protect  the  valve  seats  against  corrosion. 

Lubrication. — There  are  three  essential  properties  that  a  good  gas-engine 
cylinder  oil  must  possess. 

1.  It  must  have  as  high  a  fire-test  as  possible;  that  is,  the  temperature  at 
which  it  gives  off  inflammable  vapor  .should  be  as  high  as  possible.     In  the  best 
gas-engine  cylinder  oils,  this  temperature  will  be  from  500°  to  650°  F.,  which 
is  none  too  great  considering  the  temperatures  to  which  the  oil  is  subjected 
when  exposed  to  the  burning  charge  in  the  cylinder. 

2.  As  the  oil  is  vaporized  by  the  heat,  it  should  leave  as  little  residue  as 
possible.     Any  cylinder  oil  will  leave  some  carbon  deposit,  which  gradually 
accumulates  on  the  inner  walls  of  the  combustion  chamber  and  on  the  piston 
head  and  valves,  but  it  is  desirable  that  this  accumulation  should  be  prevented 
as  far  as  practicable.     If  it  becomes  thick,  especially  if  the  compression  is  high 
or  if  the  form  of  the  combustion  chamber  is  such  that  sharp  corners  are  exposed 
to  the  heat  of  the  flame,  particles  of  the  unburned  carbon  clinging  to  the  walls 
or  elsewhere  may  become  heated  to  such  a  degree  as  to  ignite  the  charge  spon- 
taneously before  compression  is  complete. 

3.  The  oil  should  have  a  fairly  high  viscosity;  that  is,  it  should  be  quite 
thick,  because  the  high  temperature  of  the  cylinder  will  cause  any  ordinary 
oil  t9  run  on  the  piston  much  like  water  and  lose  practically  all  its  lubricating 
qualities. 

It  is  often  advisable  to  use  a  higher  grade  of  oil  in  a  high-speed  engine  than 
is  necessary  in  a  low-speed  engine,  owing  to  the  greater  rapidity  of  the  explo- 
sions in  the  former  and  the  consequently  higher  internal  temperature.  As 
the  cylinder  head  of  a  high-speed  engine  is  frequently  cast  in  one  piece 
with  the  cylinder,  it  is  very  hard  to  get  at  the  combustion  chamber  to  scrape 
the  carbon  deposit  from  it,  and  consequently  it  is  well  to  use  an  oil  that 
leaves  as  little  deposit  as  possible. 

For  air-cooled  cylinders,  only  the  heaviest  oil  obtainable  and  with  the 
highest  possible  fire-test  should  be  used,  and  the  oil  tank  should  be  placed 
near  enough  to  the  cylinder  or  exhaust  pipe  to  insure  that  the  oil  will  not  refuse 
to  feed  in  cold  weather. 

For  ordinary  water-cooled  engines,  except  in  the  largest  sizes,  the  grade 
of  cylinder  oil  known  as  heavy  is  appropriate  for  summer  use.  In  weather  cold 
enough  to  cause  this  oil  to  stiffen,  the  next  lighter  grade,  or  medium,  may  be 
employed.  In  cold  weather,  if  the  medium  oil  does  not  feed  freely,  it  is  best 
to  use  a  special  oil  suitable  for  use  at  low  temperatures,  though  it  is  possible 
to  thin  the  regular  oil  with  kerosene  or  gasoline,  to  make  it  flow,  and  to  increase 
correspondingly  the  feed  off  the  oil  cup  or  mechanical  lubricator.  It  is  best  in 
every  case  to  purchase  oil  that  is  known  to  be  reliable.  Besides,  many  manu- 
facturers purchase  and  sell  oils  marked  with  their  own  labels,  which  they 
recommend  for  use  in  their  engines.  These  oils  may  always  be  used  with 
confidence  in  any  engine  of  about  the  same  character  as  that  for  which  they  are 
put  up. 

Should  it  be  found  impossible  to  obtain  oil  that  is  known  to  be  suitable, 
the  samples  available  may  be  tested  for  viscosity  by  putting  a  few  drops  of 
each  on  an  inclined  sheet  of  clean  metal  or  glass,  and  noting  the  relative  rapidity 
of  their  flow.  The  one  that  flows  most  rapidly  has  the  least  viscosity,  and  the 
one  that  flows  most  slowly  has  the  greatest  viscosity.  The  oils  may  be  tested 
roughly  for  flashing  point  and  for  the  carbon  residue  they  leave  by  putting  a 
little  on  a  sheet  of  iron  or  tin  plate,  and  heating  gradually  over  a  flame,  taking 
care  to  move  the  plate  over  the  flame  so  that  all  parts  of  it  are  evenly  heated. 
The  oils  will  become  less  viscous  and  will  run  on  the  plate,  and  for  this  reason 
two  samples  compared  at  the  same  time  should  not  be  placed  too  close  together. 
They  will  gradually  vaporize,  leaving  only  a  brownish  and  somewhat  thick 
residue,  which  should  be  as  small  in  amount  as  possible.  A  good,  heavy  oil 


INTERNAL-COMBUSTION  ENGINES  547 

will  vaporize  almost  completely,  but  will  retain  considerable  body  even  at 
temperatures  where  an  oil  of  low  fire-test  would  be  entirely  burned  away. 
Oils,  either  heavy  or  light,  that  leave  any  considerable  amount  of  black,  tarry 
residue  should  be  avoided. 

Although,  strictly  speaking,  cylinder  oil  needs  to  be  used  only  for  cylinder 
lubrication,  it  is  the  almost  universal  custom  to  use  the  same  oil  for  all  bearings 
of  the  motor.  This  simplifies  the  lubrication  and  removes  the  danger  of  making 
a  mistake  in  oiling  the  pistons.  Cylinder  oil  is  an  excellent  lubricant  for 
bearings  subjected  to  hard  service,  as  those  of  the  crankpins  and  crank-shaft. 
The  bearings  do  not  require  as  much  oil  as  the  pistons,  four  or  five  drops  a 
minute  usually  being  sufficient. 


ENGINE  TROUBLES  AND  REMEDIES 

Hot  Bearings. — The  causes  of  hot  bearings  and  the  remedies  therefor  are 
the  same  in  internal-combustion  as  in  steam  and  other  engines. 

Misfiring. — Either  total  or  partial  misfiring  may  be  due  to  any  of  the 
following  causes:  Circuit  not  closed;  weak  battery;  ignition  fouled  with  soot; 
wet  spark  points;  broken  spark  plug;  grounded  circuit,  usually  the  secondary; 
broken  wire  or  loose  connection;  trembler  out  of  adjustment;  igniter  spring 
weakened  or  broken;  rarely,  a  defective  spark  coil  or  condenser. 

Back  Firing. — The  cause  of  back  firing  is  in  most  cases  due  to  the  delayed 
combustion  of  a  weak  mixture  containing  an  insufficient  amount  of  fuel.  The 
result  of  such  a  mixture  is  a  weak  explosion  and  slow  burning,  so  that,  during 
the  entire  exhaust  stroke  and  even  at  the  beginning  of  the  sucti9n  stroke,  there 
is  a  flame  in  the  combustion  chamber.  The  fresh  charge  will  therefore  be 
ignited  by  the  flame  of  the  delayed  combustion  of  the  previous  charge;  and,  as 
the  inlet  valve  is  open  at  that  time  toward  the  air-supply  pipe  or  passage,  a 
loud  report  will  be  heard  in  the  air  vessel  or  in  the  space  under  the  engine  bed 
whence  the  air  is  taken.  The  remedy  for  this  condition  is  to  increase  the  fuel 
supply  until  the  explosions  become  of  normal  strength. 

Another  cause  of  back  firing  may  be  the  presence  of  an  incandescent  body 
in  the  combustion  chamber,  such  as  a  sharp  point  or  edge  of  metal,  a  projecting 
piece  of  asbestos  packing,  soot,  or  carbonized  oil,  and  similar  impurities  accumu- 
lating in  the  cylinder.  To  stop  back  firing  from  these  causes,  any  projections 
of  metal  or  other  material  should  be  removed  with  a  suitable  tool  and  the 
walls  of  the  combustion  chamber  made  as  smooth  as  possible,  or  the  cylinder 
should  be  cleared  of  any  soot  or  carbonized  oil  that  may  have  gathered  there. 

Failure  of  the  igniter  to  fire  all  charges  admitted  to  the  cylinder,  or  improper 
composition  of  the  mixture  resulting  in  the  same  way,  will  be  indicated  by  heavy 
reports  at  the  end  of  the  exhaust  pipe.  One  or  more  charges  may  in  this 
manner  be  forced  through  the  cylinder  into  the  exhaust  pipe,  and  the  first  hot 
exhaust  resulting  from  the  combustion  of  a  charge  will  fire  the  mixture  that 
has  accumulated  in  the  pipe. 

On  account  of  the  shorter  time  between  the  opening  of  the  exhaust  port  and 
the  admission  of  the  new  charge  in  a  two-cycle  engine,  there  is  much  greater 
liability  to  back  firing  in  an  engine  of  that  type  than  in  a  four-cycle  engine. 
In  a  four-cycle  engine,  back  firing  will  occur  only  when  the  inlet  valve  is  off 
its  seat;  hence,  back  firing  is  more  of  an  element  of  danger  in  four-cycle  than 
in  two-cycle  engines.  If  there  is  no  check-valve  in  the  carbureter  or  vaporizer, 
and  there  is  no  direct  opening  to  the  atmosphere,  the  column  of  flame  that  would 
be  blown  through  a  carbureter  or  auxiliary  air  supply  on  account  of  back 
firing  would  be  particularly  dangerous  because  accumulations  of  gasoline 
vapor  might  thereby  become  ignited. 

To  be  absolutely  safe,  a  four-cycle  engine  having  a  float-feed  carbureter 
not  supplied  with  a  check-valve  should  take  its  supply  of  air  from  some  high 
point  rather  than  from  a  point  near  the  base.  As  the  use  of  a  check-valve  in 
the  carbureter  would  materially  reduce  the  efficiency  of  the  engine,  it  is  rarely 
used.  If  a  float-feed  carbureter  is  used,  and  indications  point  to  imperfect 
carburization,  the  carbureter  should  be  examined  carefully.  If  the  float  leaks, 
so  that  the  height  of  gasoline  is  constantly  above  the  desired  level,  or  if  the 
float  does  not  cut  off  the  supply  where  it  should,  it  will  be  necessary  to  take 
the  carbureter  apart  to  ascertain  the  trouble. 

Explosions  in  the  muffler  and  exhaust  piping  are  usually  caused  by  the 
ignition  of  the  gas  accumulating  from  missed  explosions  due  to  weak  mixtures 
or  faulty  ignition.  They  are  not  usually  dangerous  unless  the  muffler  is  large 
and  is  weakened  by  rusting  inside  or  out. 


548  INTERNAL-COMBUSTION  ENGINES 

Explosions  in  the  carbureter  are  sometimes  caused  by  the  inlet  valve  stick- 
ing open  and  permitting  the  flame  to  communicate  from  the  spark.  More 
often  it  is  due  to  improper  mixture,  which  burns  so  slowly  that  flame  lingers 
in  the  cylinder  even  after  the  exhaust  stroke  is  completed  and  the  inlet  valve 
begins  to  open.  Either  a  weak  or  a  rich  mixture  will  produce  this  result, 
though  not  always  both  in  the  same  engine.  Carbureter  explosions  are  often 
attributed  to  the  exhaust  valve  closing  after  the  inlet  valve  opens,  or  to  simple 
leakage  of  the  inlet  valve;  but  these  are  seldom  the  real  causes. 

Preignition. — Premature  ignition,  or  preignition,  while  somewhat  similar  to 
back  firing  in  its  nature  and  origin,  manifests  itself  in  a  different  way  and  has 
a  different  effect  on  the  action  of  the  engine.  Premature  ignition,  as  usually 
understood,  is  the  firing  of  the  partly  compressed  mixture  before  the  time 
fixed  by  the  igniting  mechanism.  Its  causes  are  similar  to  those  that  result 
in  back  firing,  the  effect  being  different  in  that  the  charge  is  ignited  later  than 
when  back  firing  takes  place,  but  before  the  end  of  the  compression  stroke. 
Preignition  will  cause  the  engine  to  lose  power  on  account  of  the  maximum 
pressure  being  exerted  on  the  crank  before  it  reaches  the  inner  dead  center 
and  thus  haying  a  tendency  to  turn  it  in  the  wrong  direction. 

Besides  the  causes  cited  in  connection  with  back  firing,  preignition  may  be 
due  to  any  one  of  the  following  defects:  '  Insufficient  cooling  of  the  cylinder, 
due  either  to  shortage  of  cooling  water  or  to  the  fact  that  portions  of  the  water- 
jacket  become  filled  with  lime  deposits  or  impurities  contained  in  the  water, 
thus  interfering  with  proper  circulation;  compression  too  high  for  the  grade 
of  fuel  used;  imperfections  in  the  surfaces  of  the  piston  end  or  valve  heads 
exposed  to  the  combustion,  such  as  sandholes  or  similar  cavities  in  which  a 
small  portion  of  the  burning  charge  may  be  confined ;  electrodes  or  other  parts 
of  the  engine  exposed  to  the  burning  charge  too  light;  or  the  piston  head  or 
exhaust- valve  poppet  insufficiently  cooled  and  becoming  red  hot  while  the 
engine  is  running  under  a  fairly  heavy  load. 

Premature  ignition  manifests  itself  by  a  pounding  in  the  cylinder,  and,  if 
permitted  to  continue,  a  drop  in  speed,  finally  resulting  in  the  stopping  of  the 
engine.  It  will  also  put  an  excessive  amount  of  pressure  on  the  bearings, 
especially  the  connecting-rod  brasses,  and  cause  them  to  run  hot  even  when 
properly  lubricated.  After  a  shut-down  due  to  premature  ignition  and  a  short 
period  during  which  the  overheated  parts  are  allowed  to  cool,  it  is  possible  to 
start  again  and  run  until  the  conditions  of  load  will  again  cause  the  trouble. 

The  remedies  to  be  applied,  according  to  the  source  of  the  difficulty,  are 
as  follows:  Increase  the  water  supply  until  the  cooling  water  leaves  the 
cylinder  at  a  reasonable  temperature,  which  may  vary  with  the  fuel  used,  but 
which  should  never  be  over  180°  F.  Clean  the  water  space  and  ports  of  any 
dirt  or  deposit  so  as  to  insure  free  circulation  of  the  cooling  water.  Reduce 
the  compression  by  partly  throttling  the  air  and  fuel  supply.  Plug  any  sand- 
holes  or  blowholes  in  the  piston  or  valve  heads,  and  make  these  surfaces  per- 
fectly smooth.  Replace  electrodes  or  other  light  parts  with  some  capable 
of  absorbing  and  carrying  off  the  heat  without  becoming  red  hot.  If  necessary, 
arrange  for  cooling  the  piston  by  blowing  air  into  the  open  end  of  the  cylinder. 

If  the  head  of  the  exhaust  valve  becomes  too  hot,  it  is  a  sign  that  it  is  not 
heavy  enough,  and  it  should  be  replaced  by  one  with  a  head  of  sufficient  thick- 
ness to  carry  off  through  the  valve  stem  the  heat  imparted  to  it  by  the  combus- 
tion. If  a  small  particle  of  dirt  lodges  in  a  remote  portion  of  the  combustion 
chamber,  the  richer  part  of  the  charge  may  not  reach  it  until  the  piston  has 
traveled  over  a  considerable  portion  of  the  compression  stroke,  and  the  result- 
ing self -ignition  may  properly  be  called  preignition.  Every  part  of  the  com- 
bustion chamber  should  therefore  be  examined  and  all  dirt  removed. 

Carbureter  Troubles. — An  engine  may  work  improperly  because  the  car- 
bureter delivers  no  gasoline,  an  insufficient  amount  of  gasoline,  or  too  much 
gasoline  to  the  cylinders.  When  little  or  no  gasoline  reaches  the  cylinders, 
the  difficulty  may  be  caused  by:  A  failure  to  turn  on  the  supply  of  gasoline,  a 
clogged  feedpipe,  too  light  a  float,  failure  of  the  needle  valve  to  open  wide 
enough,  and  obstructed  nozzle.  Too  much  gasoline  in  the  carbureter  is  caused 
by  too  heavy  a  float  or  because  the  valve  does  not  close  tightly.  In  the  latter 
case,  the  valve  may  need  grinding  or  there  may  be  grit  between  it  and  its  seat. 

Compression  Troubles. — Either  partial  or  total  loss  of  compression  may 
be  due  to  any  of  the  following  causes:  The  valve  stem  may  stick  in  the  guide, 
in  which  case  it  should  be  washed  with  gasoline  or  kerosene  and  then  well 
oiled;  the  valve  stem  may  be  weak  or  broken;  the  cylinder  may  be  cracked;  the 
piston  ring  may  be  broken  or  turned  so  that  the  slots  are  in  line;  the  valve  may 
need  regnndmg;  water  may  leak  into  the  cylinder  through  a  bad  joint. 


PROSPECTING  549 


PROSPECTING 


OUTFIT  AND  METHODS 

The  prospector  should  have  a  general  knowledge  of  the  mineral-bearing 
strata,  and  should  know  from  the  nature  of  the  rocks  exposed  whether  to 
expect  to  find  coal  or  not.  _  He  should  also  possess  such  a  knowledge  of  the 
use  of  tools  as  will  enable  him  to  construct  simple  structures,  and  a  sufficient 
experience  in  blacksmithing  to  enable  him  to  sharpen  picks  and  drills,  or  to 
set  a  horseshoe,  if  necessary. 

Outfit  Necessary. — The  character  of  the  prospecting  being  carried  on  will 
have  considerable  effect  on  the  outfit  necessary,  which  should  always  be  as 
simple  as  possible.  In  general,  when  operating  in  a  settled  country,  the 
outfit  is  as  follows:  A  compass  and  clinometer  for  determining  the  dip  and 
strike  of  the  various  measures  encountered;  a  pick  and  shovel  for  excavating, 
and,  where  rock  is  liable  to  be  encountered,  a  set  of  drills,  hammer,  spoon 
for  cleaning  the  holes,  tamping  stick,  powder  and  fuse,  or  dynamite  fuse  and 
cap;  an  aneroid  barometer  for  determining  elevations,  and  a  small  hand  pick; 
the  latter  should  weigh  about  1|  lb.,  and  should  have  a  pick  on  one  end  and  a 
square-faced  hammer  on  the  other,  the  handle  being  from  12  to  14  in.  long. 

If  the  region  under  consideration  has  been  settled  for  some  time,  there 
will  probably  be  geological,  county,  railroad,  or  other  maps  available.  These 
may  not  be  accurate  as  to  detail,  but  will  be  of  great  assistance  in  the  work 
on  account  of  the  fact  that  they  give  the  course  of  the  railroads,  streams,  etc. 

When  operating  in  a  mountainous  region,  away  from  a  settled  country, 
the  following  materials,  in  addition  to  those  already  mentioned,  maybe  required: 
A  donkey  or  a  pony  packed  with  a  couple  of  heavy  blankets,  an  A  tent,  cook- 
ing utensils,  etc.;  a  supply  of  flour,  sugar,  bacon,  salt,  baking  powder,  and  coffee, 
sufficient  for  at  least  a  month.  It  is  also  well  to  take  some  fruit,  but  all  fruit 
containing  stones  or  pits  should  be  avoided,  as  they  are  only  dead  weight,  and 
every  pound  counts.  For  the  same  reason,  canned  goods  should  be  avoided, 
on  account  of  the  large  amount  of  water  they  contain.  A  healthy  man  will 
require  about  3  lb.  of  solid  food  per  day.  Many  prefer  to  vary  the  diet  by 
taking  rice,  corn  meal,  beans,  etc.,  in  place  of  a  portion  of  the  flour. 

Where  game  is  abundant,  a  shot-gun  or  rifle  will  be  found  useful  for  supply- 
ing fresh  meat.  In  regions  abounding  in  swamps  it  becomes  necessary  to 
operate  from  canoes,  or  to  take  men  for  porters  or  packers,  who  carry  the  outfit 
on  their  backs  or  heads.  These  men  will  carry  from  60  to  125  lb. 

Plan  of  Operations. — When  the  presence  of  coal  is  suspected  in  a  tract 
of  land,  a  thorough  examination  of  the  surface  and  a  study  of  the  exposed 
rocks,  in  place,  may  result  in  its  immediate  discovery,  or  in  positive  proof 
of  its  absence;  or  it  may  result  in  still  further  increasing  the  doubt  of,  or  the 
belief  that,  it  does  exist.  The  first  procedure  in  prospecting  a  tract  of  land 
is  to  traverse  it  thoroughly,  and  note  carefully  any  stains  or  traces  of  smut, 
and  all  outcrops  of  every  description;  and,  whenever  possible,  take  the  dip 
and  the  course  of  the  outcrop  with  a  pocket  compass.  Any  fossils  should  also 
be  carefully  noted,  to  assist  in  determining  the  geological  age  of  the  region. 
These  outcrops  are  frequently  more  readily  found  along  roads  or  streams  than 
any  other  place  on  the  tract.  In  traveling  along  the  streams,  the  prospector 
should  pay  particular  attention  to  its  bed  and  banks,  to  see  whether  there  are 
any  small  particles  of  coal  or  roof  slate  in  the  bed  of  the  stream,  or  any  stains 
or  smut  exposed  along  the  washed  banks.  If  small  pieces  of  coal  or  roof  slate 
are  found  in  the  stream,  a  search  up  it  and  its  tributaries  will  show  where  the 
outcrop  from  which  the  find  came  is  located.  When  the  ravines  and  valleys 
are  so  filled  with  wash  that  no  exposures  are  visible,  and  nothing  is  gained  by 
a  careful  examination  of  them,  the  prospector  must  rely  on  topographical 
features  to  guide  him. 

In  cases  where  there  are  no  outcrops  or  any  other  surface  indications,  it 
would  become  necessary  to  sink  shafts  or  test  pits,  or  to  proceed  by  drilling. 
The  absence  of  any  indication  of  coal  in  the  soil  may  not  prove  that  there  is 
not  an  outcrop  near  at  hand,  for  the  soil  is  frequently  brought  from  a  distance, 
and  bears  no  relation  to  the  material  underlying  it.  In  like  manner,  glacial 
soil  often  contains  debris  transported  from  seams  many  miles  away;  but  such 


550  PROSPECTING 

occurrences  can  usually  be  distinguished  by  the  general  character  of  the  asso- 
ciated wash  material. 

Frequently,  the  weathered  outcrop  of  a  seam  has  been  overturned  or 
dragged  back  upon  itself,  so  as  to  indicate  the  presence  of  a  very  thick  deposit. 
For  this  reason,  any  openings  made  to  determine  the  character  of  the  material 
should  be  continued  until  the  coal  is  of  a  firm  character,  and  both  floor  and 
roof  are  well  exposed.  Sometimes,  in  the  case  of  steeply  pitching  coal  beds, 
the  surface  may  be  overturned  for  a  considerable  depth,  so  that  it  is  difficult 
to  tell  which  is  the  roof  and  which  is  the  floor.  Usually,  if  Stigmaria?  are  found 
in  the  rocks  of  one  wall,  it  is  supposed  that  this  wall  is  the  floor  of  the  seam, 
while  if  Sigillariae,  fern  leaves,  etc.  are  found  in  the  wall  rock,  it  is  probably 
the  roof  of  the  deposit.  These  indications  are  not  positive  proof,  for  both  of 
these  fossils  may  occur  in  either  the  top  or  bottom  wall  of  a  coal  deposit,  though 
they  are  usually  found  in  the  positions  noted.  Coal  usually  occurs  in  unaltered 
deposits,  i.  e.,  in  rocks  that  have  not  undergone  metamorphism,  while  metals 
and  metallic  ores  usually  occur  in  rocks  that  have  undergone  more  or  less 
metamorphism.  This  change  may  have  been  accompanied  by  heat  and 
volcanic  disturbances  sufficient  to  render  the  rocks  thoroughly  crystalline,  or 
it  may  simply  have  been  the  converting  of  limestone  into  dolomite.  The 
prospector  for  coal  usually  avoids  regions  in  which  the  rocks  have  been  altered; 
but  it  should  be  remembered  that  a  basin  of  unaltered  stratified  rocks  con- 
taining coal  seams  may  be  found  in  the  very  midst  of  a  high  mountain  range 
and  surrounded  by  granitic  and  volcanic  rocks,  as  in  the  Rocky  Mountains. 

When  a  prospector  is  operating  in  any  particular  region,  it  is  best  to  study 
carefully  the  conditions  of  that  region  before  proceeding,  as  such  factors  as 
lack  of  rain,  frozen  ground,  etc.  may  have  played  an  important  part  in  deter- 
mining the  character  of  the  outcrop  and  surface  appearance  of  coal  deposits. 
Experience  obtained  in  one  region  is  frequently  very  misleading  when  applied 
in  another. 

COAL-BEARING  FORMATIONS 

Outcrops. — The  presence  of  the  outcrop  of  any  bed  may  often  be  located 
by  a  terrace  caused  by  the  difference  in  the  hardness  of  the  strata;  but  as  any 
soft  material  overlying  a  hard  material  will  form  a  terrace,  it  is  necessary  to 
have  some  means  of  distinguishing  a  coal  terrace  from  one  caused  by  worth' 
less  material.  Usually,  the  outcrop  of  a  coal  terrace  will  be  accompanied  by 
springs  carrying  a  greater  or  less  amount  of  iron  in  solution,  which  is 
deposited  as  ochery  films  upon  the  stones  and  vegetable  matter  over  which 
the  water  flows.  The  outcrops  of  beds  of  iron  or  other  ores  are  very  fre- 
quently marked  by  mineral  springs.  Sometimes  the  outcrop  of  a  bed  will 
be  characterized  by  a  marked  difference  in  the  vegetation,  as,  for  instance, 
the  outcrop  of  a  bed  of  phosphate  rock  by  a  luxuriant  line  of  vegetation,  the 
outcrop  of  a  mineral  bed  by  a  lack  of  vegetation,  the  outcrop  of  a  coal  bed 
contained  between  very  hard  rocks  by  more  luxuriant  vegetation  than  the 
surrounding  country,  etc.  Some  indication  as  to  the  dip  and  strike  of  the 
material  composing  the  bed  may  be  obtained  by  examining  the  terrace  and 
noting  the  deflections  from  a  straight  line  caused  by  the  changes  in  contour 
of  the  ground.  If  the  variation  occasioned  by  a  depression  is  toward  the  foot 
of  the  hill,  the  bed  dips  in  the  same  direction  with  the  slope  of  the  ground;  but 
if  the  deflection  is  toward  the  top  of  the  hill,  the  dip  is  the  reverse  from  the  slope 
of  the  ground,  or  into  the  hill.  After  any  terrace  or  indication  of  the  outcrop 
of  a  bed  has  been  discovered,  it  will  be  necessary  to  examine  the  outcrop  by 
means  of  shafts,  tunnels,  or  trenches.  The  position  of  such  openings  will 
depend  on  the  general  character  of  the  terrace.  If  the  dip  appears  to  be  with 
the  hill,  a  trench  should  be  started  below  the  terrace  and  continued  to  and  across 
it;  while  if  the  dip  appears  to  be  into  the  hill,  it  may  be  best  to  sink  a  shallow 
shaft  above  the  terrace. 

Formations  Likely  to  Contain  Coal.— No  coal  beds  of  importance  have  as  yet 
been  found  below  the  Carboniferous  period,  but  coal  may  be  looked  for  in  any 
stratified  or  sedimentary  rocks  that  were  formed  after  this  period,  although 
the  bulk  of  the  best  coal  has  been  found  in  the  Carboniferous  period.  As  a 
rule,  highly  metamorphic  regions  and  regions  composed  of  volcanic  or  igneous 
rocks  contain  no  coal.  An  examination  of  the  fossils  contained  in  the  rocks 
of  any  locality  will  usually  determine  whether  they  belong  to  a  period  below  or 
above  the  Carboniferous,  and  hence  whether  there  is  a  probability  of  the  forma- 
tions containing  coal.  On  account  of  this  fact,  the  prospector  should  familiar- 
ize himself  with  the  geological  periods,  and,  by  referring  to  any  elementary 


PROSPECTING 


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PROSPECTING 


Black  shale 
Limestone 
Shales  and  sandstone  (blue  stone) 
Black  shale 
Limestone 
Cherty  limestone 
Crystalline  limestone 
Shaly  sandstone 
Shaly  sandstone 
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slates,  phyllites,  iron  ores,  and 
jaspilites 

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PROSPECTING  553 

geology,  with  the  most  common  fossils  of  each.  The  rocks  most  common  in 
coal  measures  are  sandstones,  limestones,  shale,  conglomerates,  fireclays,  and, 
in  sonic  localities,  the  coal  deposits  are  frequently  associated  with  beds  of 
iron  ore. 

The  preceding  table  gives  the  names  of  the  various  geological  eras, 
periods,  epochs,  and  stages  as  they  occur  in  the  United  States,  together  with 
the  kinds  of  rocks  characterizing  each. 

Faults. — Frequently  a  seam  becomes  faulted  or  pinched  out  underground, 
and  it  is  necessary  to  continue  the  search  by  means  of  underground  prospect- 
ing. If  a  fault  or  dislocation  is  encountered,  the  manner  of  carrying  on  the 
search  will  depend  on  the  character  of  the  fault.  Where  sand  faults  or  wash- 
outs are  encountered,  the  drift  or  entry  should  be  driven  forwards  at  the 
angle  of  the  seam  until  the  continuation  of  the  formation  is  encountered,  when 
a  little  examination  of  the  rocks  will  indicate  whether  they  are  the  under- 
lying or  overlying  measures.  In  the  case  of  dislocations  or  throws,  the  con- 
tinuation of  the  seam  may  be  looked  for  by  Schmidt's  law  of  faults,  which  is 
as  follows:  Always  follow  the  direction  of  the  greatest  angle.  It  has  been  dis- 
covered that,  in  the  majority  of  cases,  the 
hanging- wall  portion  of  the  fault  has  moved 
down,  and  on  this  account  such  faults  are 
commonly  called  normal  faults.  For  in- 
stance, if  the  bed  ab,  of  the  accompany- 
ing figure,  were  being  worked  from  a  to- 
ward the  fault,  work  would  be  continued 
down  on  the  farther  side  of  the  fault  to- 
ward d,  until  the  continuation  of  the  bed 
toward  b  was  encountered.  In  like  man- 
ner, had  the  work  been  proceeding  from 
b,  the  exploration  would  have  been  carried 
up  in  the  direction  of  the  greatest  angle, 
and  the  continuation  toward  a  thus  dis- 
covered. A  reverse  fault  is  'one  in  which 
the  movement  has  been  in  the  opposite 
direction  to  a  normal  fault.  Especially  in  the  case  of  those  mines  where  the 
material  occurs  as  perpendicular  or  steeply  pitching  veins,  faults  are  liable  to 
displace  the  seam  both  horizontally  and  vertically,  in  which  case  it  may  be 
difficult  to  determine  the  direction  of  the  continuation  of  the  bed;  but  frequently 
pieces  of  coal  or  slate  are  dragged  into  the  fault,  and  these  serve  as  a  guide  to 
the  miner,  and  indicate  the  proper  direction  for  exploration.  Where  a  bed  or 
seam  is  faulted,  its  continuation  can  frequently  be  found  by  breaking  through 
into  the  measures  beyond,  when  an  examination  of  the  formation  will  indicate 
whether  the  rocks  are  those  that  usually  occur  above  or  below  the  desired  seam. 


EXPLORATION  BY  DRILLING  OR  BORE  HOLES 

Earth  Augers. — When  testing  for  coal  seams  that  occur  comparatively 
near  the  surface,  hand  augers  may  be  employed  to  great  advantage.  A  good 
form  of  hand  auger  consists  of  a  piece  of  flat  steel  or  iron,  with  a  steel  tip, 
twisted  into  a  spiral  about  1  ft.  long,  and  having  four  turns.  The  point  is 
split  and  the  tips  sharpened  and  turned  in  opposite  directions  and  dressed  to 
a  standard  width,  usually  2  in.  The  auger  is  attached  to  a  short  piece  of  1-in. 
pipe,  and  is  operated  by  joints  of  1-in.  pipe,  which  are  coupled  together  with 
common  pipe  couplings.  The  auger  is  turned  by  means  of  a  double-ended 
handle  having  an  eye  in  the  center  through  which  the  rod  passes. 

The  handle  is  secured  by  means  of  a  setscrew.  In  addition  to  the  auger 
it  is  well  to  have  a  straight-edged  chopping  bit  for  use  in  comparatively  hard 
seams.  This  may  be  made  from  a  piece  of  If-in.  octagon  steel,  with  a  2-in. 
cutting  edge.  The  upper  end  of  the  steel  is  welded  on  to  a  piece  of  pipe  similar 
to  that  carrying  the  auger.  When  the  chopping  bit  is  employed,  it  is  neces- 
sary to  have  a  heavy  sinking  bar,  which  may  be  made  from  a  piece  of  solid 
IJ-in.  iron  bar,  fitted  with  ordinary  1-in.  pipe  threads  on  the  ends.  Pros- 
pecting can  be  carried  on  to  a  depth  of  from  50  to  60  ft.  with  this  outfit.  The 
number  of  men  necessary  to  operate  the  rods  varies  from  two  to  four,  depending 
on  the  depth  of  the  hole  being  drilled.  When  more  than  30  ft.  of  rods  are  in 
use,  it  is  usually  necessary  to  have  a  scaffold  on  which  some  of  the  men  can 
stand  to  assist  in  withdrawing  the  rods.  When  withdrawing  the  rods,  to 
remove  the  dirt,  they  are  not  uncoupled  unless  over  40  ft.  of  rods  are  in  use 


554  PROSPECTING 

at  one  time,  and  sometimes  as  many  as  50  or  60  ft.  are  drawn  without 
uncoupling. 

Percussion  Drills. — Percussion,  or  churn,  drills  are  frequently  employed  in 
drilling  for  oil,  water,  or  gas,  and  were  formerly  much  used  in  searching  for 
coal  and  ores,  but,  owing  to  the  fact  that  they  all  reduce  the  material  passed 
through  to  small  pieces  or  mud,  and  so  do  not  produce  a  fair  sample,  and  to 
the  fact  that  they  can  only  drill  perpendicular  holes,  they  are  at  present  little 

used  in  prospecting  for  either  ore  or  coal. 
_  _TT  T  The  cost  and  rate  of  drilling  by  means  of  a 

COST  OF  WELL  DRILL-       percussion  or  churn  drill  varies  greatly,  being 
ING  affected  much  more  by  the  character  of  the 

strata  penetrated  than  is  the  case  with  the 
diamond  drill.     In  the  case  of  highly  inclined 


Size  of  Well 
Inches 


Cost  per          beds  of  varying  hardness,  the  holes  frequently 
Foot  run  out  of  line  and  become  so  crooked  that  the 

tools  wedge,  and  drilling  has  to  be  suspended. 


For  drilling  through  moderately  hard  forma- 
$1.50  tions,  usually  encountered  in  searching  for  gas 

or  water,  such  as  sandstones,  limestones,  slates, 

etc.,  the  accompanying  costs,  from  the  Ameri- 
5 . 00  can  Well  Works,  Aurora,  111.,  may  be  taken  per 
15  foot  for  wells  from  500  to  3,000  ft.  deep  for  the 
central  or  eastern  portion  of  the  United  States. 

This  cost  includes  the  placing  of  the  casing,  but 

not  the  casing  itself. 

When  drilling  wells  for  oil  or  gas  to  a  depth  of  approximately  1,000  ft., 
using  the  ordinary  American  rig  with  a  cable,  the  cost  is  sometimes  reduced 
to  as  little  as  65  c.  per  ft.  for  6-in.  or  8-in.  wells;  this  is  when  operating  in 
rather  soft  and  known  formations.  From  15  to  40  ft.  per  da.  of  24  hr.  is  usually 
considered  a  good  rate  of  drilling,  though  in  soft  materials  as  much  as  100  ft. 
may  be  drilled  in  a  single  day,  and  at  other  times,  when  very  hard  rock  is 
encountered,  it  is  impossible  to  make  more  than  from  1  to  2  ft.  per  da. 

Percussion  Core  Drill. — In  order  to  overcome  the  chief  objection  to  the 
use  of  percussion  drills  in  coal  prospecting  work,  an  attachment  is  now  provided 
which  can  be  used  in  connection  with  the  ordinary  oil-well  drilling  outfit  and 
by  means  of  which  a  core  of  a  coal  seam  may  be  recovered.  A  6-in.  hole  is 
sunk  with  the  ordinary  tools  until  the  vicinity  of  the  bed  to  be  cored  has  been 
reached.  The  tools  are  then  withdrawn,  the  bit  and  stem  are  removed,  leaving 
the  jars  and  rope  socket  attached  to  the  cable,  and  the  core  drill  is  attached 
to  the  jars.  This  drill  is  a  steel  pipe  about  14  ft.  long  provided  with  chisel- 
shaped  cutting  teeth,  and  within  which  is  placed  the  core-barrel.  The  hole 
is  carefully  cleaned  with  the  sand  pump  and  its  exact  depth  measured  and 
recorded.  This  core-drilling  attachment  is  lowered  carefully  into  the  hole 
until  it  rests  on  the  bottom  and  drilling  is  resumed  in  the  ordinary  way  at 
a  moderate  speed  but  with  a  stroke  of  from  15  to  18  in.  After  drilling  20  or 
30  in.  the  tools  are  withdrawn;  a  slight  jar  is  sometimes  necessary  to  break  the 
core  loose.  At  the  t9p  of  the  hole,  the  tools  are  swung  to  one  side,  the  core 
barrel  with  the  contained  core  removed  from  the  drill  and  another  core  barrel 
attached  if  a  longer  core  is  needed.  Drilling  operations  are  resumed  while 
the  core  is  being  removed  from  the  core  barrel  just  brought  up.  The  core 
barrels  are  9f  two  lengths,  the  shorter  ones  being  designed  for  use  in  hard 
formations  like  sand  rock,  limestone,  etc. 

Core  Drills. — What  are  known  as  core  drills  are  the  only  forms  that  have 
proved  successful  in  drilling  in  any  direction  through  hard,  soft,  or  variable 
material.  Even  with  core  drills,  many  difficulties  present  themselves  and 
demand  careful  study  in  adapting  the  form  of  apparatus  to  the  work  in  hand, 
and  in  rightly  interpreting  the  results  obtained  from  any  set  of  observations. 
Core  drills  are  of  two  main  types,  the  diamond  drill  and  the  calyx  drill. 
The  two  are  essentially  alike  in  consisting  of  a  cutting  bit  attached  to  the 
end  of  a  series  of  connected  rods  to  which  a  rotary  motion  is  applied  by  a 
steam,  electric,  compressed-air,  or  gasoline  motor.  In  the  diamond  drill,  the 
cutting  bit  consists  of  a  hard  steel  cylinder  in  the  bottom  rim  (both  inner  and 
outer  edges)  of  which  are  set  fragments  of  black  diamond  (bort,  or  carbonado) 
the  edges  of  which  slightly  project  beyond  the  metal  surface  of  the  bit.  Being 
the  hardest  substance  known,  upon  being  rotated,  the  diamonds  naturally 
cut  out  a  cylindrical  core  of  any  rock  penetrated. 

The  bit  of  the  calyx  drill  is  of  two  forms.  For  drilling  in  comparatively 
soft  rock,  it  consists  of  a  steel  cylinder  with  chisel-shaped  teeth  that  cut  and 


PROSPECTING  555 

scrape  away  the  rock.  For  drilling  in  harder  rock,  the  bit  is  without  teeth, 
being  merely  a  ring  of  metal  with  a  slot  in  the  side  through  which  chilled  steel 
shot  fed  into  the  bore  hole  above  find  their  way  so  that  they  may  be  rolled 
over  the  surface  of  the  rock  to  be  cut  as  the  bit  is"  rotated  in  the  hole.  While 
the  following  is  intended  primarily  to  guide  in  the  selection,  use,  etc.,  of  a 
diamond  drilling  machine,  it  is  also  applicable  to  the  calyx  drill. 

Selecting  the  Machine. — It  is  not  economy  to  employ  a  machine  of  large 
capacity  in  shallow  explorations,  as  the  large  machines  are  provided  with 
powerful  motors,  and  hence  do  not  work  economically  under  light  loads. 
When  a  large  machine  is  operating  small  rods  on  light  work,  the  driller  cannot 
tell  the  condition  of  the  bit,  or  properly  regulate  the  feed.  The  machine 
should  possess  a  motor  of  sufficient  capacity  to  carry  the  work  to  the  required 
depth,  but  where  much  drilling  is  to  be  done,  it  is  usually  best  to  have  two  or 
more  machines,  and  to  employ  the  small  ones  for  shallow  holes,  and  the  large 
ones  for  deep  holes. 

All  feed  mechanisms  employed  in  diamond  drilling  may  be  divided  into 
two  classes:  Those  that  are  an  inverse  function  of  the  hardness  of  the  material; 
this  class  includes  friction,  spring,  and  hydraulic  feeds.  Those  in  which  the 
feed  is  independent  of  the  material  being  cut,  as  in  the  case  of  the  positive 
gear-feed.  The  first  class  is  advantageous  when  drilling  through  variable 
measures  in  search  of  fairly  firm  material,  which  does  not  occur  in  very  thin 
beds  or  seams.  On  account  of  the  fact  that  this  class  of  feed  insures  the 
maximum  amount  of  advance  of  which  the  bit  is  capable  in  the  material  being 
cut,  the  danger  is  that  the  core  from  any  thin  soft  seam  may  be  ground  up 
and  washed  away,  without  any  indication  of  its  presence  having  been  given. 
The  second  class,  or  positive  gear-feed,  if  properly  operated,  requires  some- 
what greater  skill,  but  if  used  in  connection  with  a  thrust  register,  it  gives 
reliable  information  as  to  the  material  being  cut,  and  is  especially  useful  when 
prospecting  for  soft  deposits  of  very  valuable  material. 

Size  of  Tools. — The  size  of  tools  and  rods,  and  consequently  the  size  of  the 
core  extracted,  depends  on  the  depth  of  the  hole  and  the  character  of  the 
material  being  prospected.  When  operating  in  firm  measures,  such  as  anthra- 
cite, hard  rock,  etc.,  it  is  best  to  employ  a  rather  small  bit,  even  when  drilling 
up  to  700  ft.,  or  more,  in  depth.  For  such  work,  a  core  of  from  H  to  l^g  in.  is 
usually  extracted.  The  rate  of  drilling  with  a  small  outfit  is  very  much  greater 
than  with  a  large  one,  owing  to  the  fact  that  there  is  a  small  cutting  surface 
exposed,  and  the  rate  of  rotation  of  the  rods  can  be  much  greater.  When 
prospecting  for  soft  materials,  such  as  bituminous  coal,  valuable  soft  ores,  or 
for  disseminated  ores,  such  as  lead,  copper,  gold,  silver,  etc.,  it  is  best  to  employ 
a  larger  outfit  and  extract  a  core  2  or  3  in.  in  diameter,  and  sometimes  larger, 
even  though  a  comparatively  small  machine  is  used  to  operate  the  rods. 

Diamond-Drilling. — Drift  of  diamond-drill  holes,  or  the  divergence  from  the 
straight  line,  often  becomes  a  serious  matter.  This  trouble  may  be  minimized 
by  keeping  the  tools  about  the  bit  as  nearly  up  to  gauge  as  possible.  Core 
barrels,  with  spiral  water  grooves  about  them,  answer  this  purpose  very  well 
if  they  are  renewed  before  excessive  wear  has  taken  place. 

Surveying  of  diamond-drill  holes  may  be  carried  on  by  either  one  of  two 
methods,  depending  on  the  magnetic  conditions  of  the  district.  Where  there 
is  no  magnetic  disturbance,  the  system  developed  by  Mr.  E.  F.  MacGeorge, 
of  Australia,  may  be  employed.  This  consists  in  introducing  into  the  hole,  at 
various  points,  small  tubes  containing  melted  gelatine,  in  which  are  suspended 
magnetic  needles  and  small  plummets.  After  the  gelatine  has  hardened  the 
tubes  are  removed,  and  the  angles  between  the  center  line  of  the  tube,  the 
plummet,  and  the  needle  noted,  thus  furnishing  the  data  from  which  the  course 
of  the  hole  can  be  plotted.  This  method  gives  both  the  vertical  and  the 
horizontal  drift. 

Where  there  is  magnetic  disturbance  the  needle  cannot  be  used,  but  a  system 
brought  out  by  Mr.  G.  Nolten,  of  Germany ,  has  been  quite  extensively  employed. 
In  this  case,  tubes  partly  filled  with  hydrofluoric  acid  are  introduced  into  the 
hole,  at  various  points,  and  the  acid  allowed  to  etch  a  ring  on  the  inside  of  the 
tube.  After  the  acid  has  spent  itself  the  tubes  are  withdrawn,  and  by  bringing 
the  liquid  into  such  a  position  that  it  corresponds  with  the  ring  etched  on  the 
inside  of  the  tube,  the  angle  of  the  hole  at  the  point  examined  can  be  determined. 
This  method  gives  a  record  of  the  vertical  drift  of  the  hole  only. 

The  value  of  the  record  furnished  by  the  diamond  drill  depends  largely  on 
the  character  of  the  material  sought.  The  core  extracted  is  always  of  very 
small  volume  when  compared  with  the  large  mass  of  the  formation  prospected, 
and  hence  will  give  a  fair  average  sample  only  in  the  case  of  very  uniform 


556  PROSPECTING 

deposits.  The  value  of  the  diamond  drill  for  prospecting  may  be  stated  as 
follows:  More  dependence  can  be  placed  on  the  record  furnished  by  the  diamond 
drill  when  prospecting  for  materials  that  occur  in  large  bodies  of  uniform  com- 
position than  when  prospecting  for  materials  that  occur  in  small  bunches  or  irregu- 
lar seams.  To  the  first  class  belong  coal,  iron  ore,  low-grade  finely  disseminated 
gold  and  silver  ores,  many  deposits  of  copper,  lead,  zmc,  etc.,  as  well  as  salt, 
gypsum,  building  stone,  etc.  To  the  latter  class  belong  small  but  rich  bunches 
of  gold,  silver  mineral,  or  rich  streaks  of  gold  telluride. 

The  arrangement  of  holes  has  considerable  effect  upon  the  results  furnished. 
If  the  material  sought  lies  in  beds  or  seams  (as  coal),  the  dip  of  which  is  fairly 
well  known,  it  is  best  to  drill  a  series  of  holes  at  right  angles  to  the  formation. 
If  the  material  sought  occurs  in  irregular  bunches,  pockets,  or  lenses,  it  will 
be  necessary  to  drill  holes  at  two  or  more  angles,  so  as  to  divide  the  ground 
into  a  series  of  rectangles,  thus  rendering  it  practically  impossible  for  any  vein 
or  seam  of  commercial  importance  to  exist  without  being  discovered.  Where 
the  surface  of  the  ground  is  covered  with  drift  and  wash  material,  it  may  be 
best  to  sink  a  shaft  or  drill  pit  to  bed  rock,  and  locate  the  machine  on  bed  rock. 
After  this,  several  series  of  fan  holes  may  be  drilled  at  various  angles  from  the 
bottom  of  the  pit.  Owing  to  the  upward  drift  of  diamond-drill  holes,  the 
results  furnished  from  a  set  of  fan  holes  drilled  from  a  single  position  would 
make  a  flat  bed  appear  as  an  inverted  bowl,  or  the  top  of  a  hill.  On  this 
account,  it  is  best  to  drill  sets  of  fan  holes  from  two  or  more  locations,  so  that 
they  will  correct  one  another.  If  fan  holes  from  different  positions  intersect 
the  same  bed,  a  careful  examination  of  them  will  usually  furnish  a  check  on  the 
vertical  drift  of  the  holes. 

The  speed  and  cost  of  drilling  depend  on  the  hardness  and  character  of  the 
rock,  the  size  of  the  hole,  the  depth  of  the  hole,  and  the  height  of  the  derrick. 
Sedimentary  rocks,  such  as  sandstones,  slates,  and  limestones  are  generally 
more  rapidly  drilled  than  the  much  harder  and  unstratified  igneous  rocks,  and 
firm  rocks  than  those  that  cave  and  require  that  the  hole  be  cased.  Cores 
of  moderate  size,  say,  up  to  1£  to  2  in.  in  diameter  can  be  taken  out  more 
rapidly  and  hence  at  less  labor  cost  (the  chief  item  in  drilling)  than  larger  ones, 
and  answer  just  as  well  for  determining  the  nature  and  value  of  the  rocks 
passed  through.  The  deeper  the  hole,  the  more  costly  and  the  less  the  progress 
per  shift,  because  of  the  time  lost  in  pulling  the  drill  rods  and  removing  the 
cores.  With  deep  holes  the  labor  cost  is  materially  reduced  if  the  derrick  is 
sufficiently  high  to  permit  unscrewing  the  drill  rods  at  every  fourth  joint  while 
raising  them  for  the  purpose  of  extracting  the  core. 

The  actual  rate  of  drilling,  including  pulling  the  rods,  removing  the  cores, 
etc.,  is  dependent  on  the  depth  of  the  hole.  In  shallow  holes,  a  rate  of  2  ft. 
per  hr.  is  fair;  in  holes  of  moderate  depth,  say,  up  to  700  ft.,  a  rate  of  1  ft.  per 
hr.  should  be  secured. 

Prospecting  with  core  drills  is  usually  done  under  contract  at  an  agreed 
sum  per  foot,  which  is  determined  by  the  number  of  holes,  their  average  depth, 
size  of  core  extracted,  distance  apart  of  the  holes,  etc.  Contract  prices  for 
diamond  drilling  in  the  bituminous  coal  regions  range  from  $2  to  $2.75  per  foot 
for  extracting  cores  up  to  say,  H  in.,  where  the  holes  range  from  150  to  500  ft. 
in  depth  (averaging,  say,  250  ft.),  where  from  1,200  to  2,000  ft.  of  drilling  is 
required,  and  where  the  coal  and  water  are  furnished  the  contractor. 

Where  the  drill  is  owned  by  an  operating  coal  company,  the  cost  of  ordinary 
drilling  should  be  less  than  $1  per  ft.,  including  labor,  diamonds,  and  ordinary 
repairs. 

Calyx  Drilling. — The  calyx  drill  will  do  essentially  the  same  work  as  the  dia- 
mond drill,  except  that  it  will  rfot  cut  at  angles  of  over  45°  because  the  shot  will 
roll  to  and  remain  at  the  lower  side  of  the  hole,  and  even  this  pitch  is  too  flat 
for  really  satisfactory  work.  The  gain  in  the  use  of  the  calyx  over  the  diamond 
drill  consists  in  the  saving  in  cost  of  the  abrasive  material  used.  Black 
diamonds  are  now  quoted  as  high  as  $90  a  carat  for  the  larger  and  better  stones, 
so  that  a  single  bit  will  often  cost  from  $750  to  $2,000,  according  to  size.  There 
should  be  at  least  two  bits  in  stock,  so  that  one  may  always  be  in  condition 
for  use.  If  drilling  is  carried  on  a  long  distance  from  the  base  of  supplies, 
three,  four,  or  even  more  bits  must  be  available,  or  else  a  diamond -setter  must 
be  employed.  Setting  diamonds  is  highly  skilled  labor  and  is  paid  accordingly. 

When  the  material  is  so  soft  that  the  shot  wedge  or  press  into  it  the  bit  with 
teeth  is  to  be  preferred  to  the  shot  bit ,  the  latter  coming  in  use  when  the  rock  is 
firm  sandstone,  limestone,  and  the  like.  The  amount  of  shot  used  varies  with 
the  hardness  of  the  material  being  drilled.  Shale,  slate,  limestone,  and  ordi- 
nary sandstone  may  require  from  i  to  f  Ib.  of  shot  per  foot  of  hole.  Very 


PROSPECTING  557 

hard  sandstone,  granite,  quartz  conglomerate,  porphyry,  taconite,  and  jasper 
require  from  1£  to  4  Ib.  per  ft.  Another  material  sometimes  used  is  crushed 
steel,  variously  sold  under  such  names  as  "diamondite,"  "abrasite,"  etc.  While 
ordinarily  inferior  to  chilled  shot,  and  not  giving  such  satisfactory  results,  for 
comparatively  soft  formations  it  is  sometimes  better  than  shot. 

The  calyx  drill,  like  the  diamond  drill,  is  manufactured  to  be  operated  by 
hand  or  horsepower  for  use  in  boring  shallow  holes,  and  is  also  to  be  had  mounted 
on  a  wagon-luce  frame  with  attached  derrick  for  ease  in  transportation. 

Prospecting  for  Petroleum,  Natural  Gas,  and  Bitumen. — Among  the  surface 
indications  of  petroleum  and  bitumen  may  be  mentioned  white  leached  shales 
or  sandstones,  shales  burned  to  redness,  fumaroles,  mineral  springs,  and 
deposits  from  mineral  springs.  Also  natural  gas,  springs  of  petroleum  oil  and 
naphtha,  porous  rocks  saturated  with  bitumen,  cracks  in  shale,  and  other  rock 
partly  filled  with  bitumen.  Petroleum  is  never  found  in  any  quantity  in 
metamorphic  rocks,  but  always  in  sedimentary  deposits.  Bitumen  can  be  told 
from  coal,  vegetable  matter,  iron,  manganese,  and  other  minerals,  which  it 
sometimes  closely  resembles,  by  its  odor  and  taste,  also  by  the  fact  that  it  melts 
in  the  flame  of  a  match  or  candle,  giving  a  bituminous  odor.  (Iron  and  man- 
ganese do  not  fuse,  and  coal  and  vegetable  matter  burn  without  fusion.)  Bitu- 
men is  also  soluble  in  bisulphide  of  carbon,  chloroform,  and  turpentine,  usually 
giving  a  dark,  black,  or  brown  solution.  Frequently,  springs  or  ponds  have  an 
iridescent  coating  of  oil  upon  the  surface.  Sometimes  iron  compounds  give 
practically  the  same  appearance,  but  the  iron  coating  can  always  be  distin- 
guished from  the  oil  by  agitating  the  surface  of  the  water,  when  the  iron  coating 
will  break  up  like  a  crust  of  solid  material,  while  the  oil  will  behave  as  a  fluid, 
and  tend  to  remain  over  the  entire  surface  even  when  it  is  agitated. 

Frequently,  bubbles  of  gas  are  seen  ascending  from  the  bottoms  of  pools 
or  creeks.  These  may  be  composed  of  carbureted  hydrogen  or  natural  gas, 
which  is  a  good  indication  of  the  presence  of  petroleum  or  bitumen;  they  may 
be  composed  of  sulphureted  hydrogen  or  carbonic-acid  gas.  Carbureted  hydro- 
gen can  be  distinguished  by  the  fact  that  it  burns  with  a  yellow  luminous 
flame  whereas  sulphureted  hydrogen  burns  with  a  bluish  flame,  and  carbon 
dioxide  will  not  support  combustion,  but,  on  the  contrary,  is  a  product  of 
combustion.  When  carbureted  hydrogen  gas  is  discovered  ascending  from 
water,  the  bottom  of  which  is  not  covered  with  decaying  vegetation,  it  is 
almost  a  certain  sign  that  there  is  petroleum  or  bitumen  somewhere  in  the 
underlying  or  adjacent  formations.  If  natural  gas  or  bitumen  is  found  upon 
the  surface  of  shale,  it  is  probable  that  the  material  ascended  vertically  through 
cracks  in  these  rocks  from  porous  strata  below;  while  if  it  is  found  in  connection 
with  sandstones,  it  is  probable  that  the  material  was  derived  from  the  porous 
sandstone  itself.  This  is  especially  liable  to  be  true  if  the  sandstone  has  a 
steep  pitch. 

As  a  rule,  deposits  of  bitumen  or  petroleum  occur  in  porous  formations 
overlaid  by  impervious  strata,  such  as  shales,  slates,  etc.  Anticlines  are  more 
liable  to  contain  such  deposits,  though  they  are  not  absolutely  necessary  to 
retain  them,  as  at  times  portions  of  the  underlying  porous  strata  have  been 
rendered  impervious  by  deposits  of  calcium  salts,  silica,  etc.,  and  hence  the 
petroleum  or  bitumen  will  be  confined  to  the  porous  portions.  Natural  gas 
also  occurs  under  similar  conditions,  but  usually  in  anticlines  only. 

Construction  of  Geological  Maps  and  Cross-Sections. — After  the  surface 
examination  of  a  property  is  complete,  the  data  should  be  entered  on  the  best 
map  procurable,  or  a  map  constructed.  The  scale  depends  on  the  size  of  the 
property,  the  complexity  of  the  geological  formation,  the  value  of  the  property, 
and  the  material  to  be  mined  from  it.  The  amount  of  work  that  it  will  pay 
to  put  on  the  survey  will  depend  largely  on  the  value  of  the  property,  more 
detail  being  justified  in  the  case  of  high-grade  properties.  If  a  property  1 ,200  ft. 
X 3,000  ft.  (the  size  of  four  U.  S.  metal  mining  claims)  were  to  be  surveyed 
and  mapped  with  a  scale  of  1  in.  equal  to  100  ft.,  the  map  would  be  12  in, 
X30  in.  A  stratum  10ft.  wide  on  this  map  would  appear  as  ^g  in.  wide, 
which  is  about  the  smallest  division  that  could  be  shown  with  its  characteristic 
symbol;  for  greater  detail,  a  larger  scale,  or  larger  scaled  sheets  of  the  most 
important  portions  of  the  deposit,  will  be  necessary.  If  the  geologist  con- 
structs the  topographical  contour  map,  he  can  take  notes  on  the  geology  at 
the  same  time.  When  the  boundaries  of  the  property  are  being  surveyed, 
certain  points  should  be  established,  both  vertically  and  horizontally,  as 
stations  in  future'topographical  work.  If  the  map  is  on  government  surveyed 
fand,  the  government  lines  may  be  used  for  horizontal  locations,  but  it  will  be 
necessary  to  determine  the  elevation  of  the  different  points.  If  the  property 


558  PROSPECTING 

is  much  broken,  it  is  well  to  run  a  few  lines  of  levels  across  it,  to  establish 
points  from  which  to  continue  the  work.  This  work  is  usually  done  with  a 
Y  level  and  chain,  the  other  details  being  subsequently  filled  in  with  a  transit 
and  stadia;  the  levels  of  the  other  points  are  taken  by  using  the  transit  as  a 
level,  by  vertical  angles,  by  barometric 
observations,  or  by  means  of  a  hand  level. 
Where  lines  of  levels  are  run  across  the 
property  in  various  directions  it  is  best  to 
run  them  so  that  they  will  cross  the  strike 
of  the  strata  as  nearly  at  right  angles  as 
possible,  so  that  the  profile  thus  deter- 
mined may  be  used  in  constructing  a 
cross-section.  Sometimes,  for  preliminary 
work,  simply  a  sketch  map  is  all  that  may 
be  necessary.  All  of  the  outcrop  and  ex- 
posures, together  with  their  proper  dip, 
should  be  entered  on  the  map. 

To  Obtain  Dip  and  Strike  From  Bore- 
Hole  Records. — Before  the  results  obtained 
from  bore  holes  are  available  for  use  in 
map  construction,  the  dip  and  strike  of 
the  various  strata  must  be  ascertained. 
The  process,  in  the  case  of  stratified  rock, 
is  as  follows:  If  three  holes  were  drilled, 


FIG.  1 


as  at  A,  B,  and  C,  Fig.  1,  each  intersecting  a  given  bed,  the  strike  and  angle  of 
dip  of  the  bed  may  be  obtained  by  reducing  the  results  from  the  three  holes  to  a 
plane  passing  through  the  highest  point  of  intersection,  which  is  at  A.  The 
hole  B  intersected  the  bed  at  the  distance  Be,  and  C  at  the  distance  Cd  below 
the  point  A.  By  continuing  the  line  CB  indefinitely  and  erecting  two  lines  Be 
and  Cd  perpendicular  to  it,  each  representing  the  distance  from  the  horizontal 
plane  through  A  to  the  intersection  of  the  strata,  two  points  in  the  line  de  are 
obtained,  which  line  intersects  CB  produced  at  /;  /  is  one  point  in  the  line  of 
strike  through  A.  In  order  to  find  the  angle  of  dip,  the  perpendicular  Cg  is 
dropped  from  the  deepest  hole  C  upon  the  line  of  strike  A/.  The  distance  Ch, 
equal  to  Cd,  is  laid  off  at  right  angles  to  Cg,  when  the  angle  Cgh  gives  the 
maximum  dip.  The  results  obtained  from  bore  holes  may  thus  be  reduced 
to  such  form  that  the  dips  can  be  projected  on  the  surface  to  obtain  the  line  of 
outcrop  for  each  stratum.  Bore  holes  also  furnish  data  for  constructing 
underground  curves  in  cross-sections  of  stratified  rocks. 

Having  recorded  on  the  map  all  exposures,  whether  surface  or  those  obtained 
from  underground  work,  draw  the  line  of  strike  and  the  outcrops.  Also  con- 
struct a  cross-section.  If  the  seam  is  perpendicular,  the  outcrop  will  be  a 
straight  course  across  the  map.  If  the  bed  is  horizontal,  the  outcrop  will 
correspond  with  a  contour  line.  For  beds  dipping  at  -any  other  angle,  results 
between  these  limits  will  be 
obtained.  % 

If  the  property  being  ex-  f- 
amined  is  cut  by  synclines  or 
anticlines,  the  dips  will  not 
all  be  in  the  same  direction, 
and  if  there  is  a  dip  along  the 
axis  of  the  synclines  or  anti- 
clines, the  construction  of  the 
map  will  be  considerably  com-  ' 
plicated.  Fig.  2  represents  a 
plan  or  map  on  which  there  is 
an  axis  xy  toward  which  the 

strata  dip   from   both    sides.  \  / 

Outcrops  are  indicated  at 
A,  B,  C,  A'  and  B',  each  hav- 
ing a  dip  in  the  direction  of  the  V 
arrow.  The  lines  mn,  op,  and  pIG  2 
qr  are  contours.  If  the  cross- 
section  were  constructed  on  the  line  FG,  perpendicular  to  the  axis  xy,  the  various 
beds  or  deposits  would  be  cut  at  such  an  angle  as  to  show  a  thickness  in  the 
cross-section  greater  than  that  which  actually  exists.  In  order  to  show 
the  actual- thickness  for  each  seam,  the  cross-section  must  be  taken  along  the 
line  perpeandictalar  to  the  strike  of  the  strata,  which,  in  the  present  case,  is 


PROSPECTING 


559 


along  the  line  IHK.  In  other  words,  the  cross-section  must  be  constructed 
in  two  parts.  Where  a  general  sketch  is  all  that  is  necessary,  a  single  cross- 
section  with  notes  correcting  the  thickness  of  the  seams  may  answer. 

In  order  to  construct  the  cross-section  IHK,  the  outcrops-  A,  B,  C,  A', 
and  B'  must  be  projected  to  the  points  a,  b,  c,  a',  and  b',  this  projection  being 
along  their  contours.  If  the  points  on  the  line  of  the  intended  cross-section 
were  not  upon  the  contour,  it  would  be  necessary  to  project  them  on  the  plane 
of  the  cross-section,  as  shown  in  the  figure,  and  then  from  the  dip  of  the  strata 
and  the  difference  in  elevation  to  obtain  a  corrected  point  along  the  line  IHK. 
The  cross-section  is  constructed  as 
shown  in  Fig.  3,  each  seam  having 
its  actual  thickness  as  shown  at  the 
outcrop.  If  the  upper  surface  of 
the  cross-section  is  not  a  true  profile 
of  the  surface,  and  the  points  are  not 
projected  in  the  plane  on  the  cross- 
section,  on  this  cross-section,  ac- 
cording to  their  dips,  there  is  con- 
siderable danger  of  exaggerating 
their  thickness  one  way  or  the  other. 

On  mine  maps,  the  supposed 
course  of  the  beds  should  be  sketched 
in,  subject  to  revision,  as  more 
data  are  brought  out  by  later 
development  work.  Even  in  the 
case  of  stratified  rocks,  it  is  diffi- 


FIG.  3 


cult  to  form  a  definite  idea  as  to  the  underground  conditions  from  surface 
indications,  and,  in  the  case  of  metamorphic  or  crystalline  rocks,  it  is  abso- 
lutely necessary  to  determine  the  underground  conditions  by  drilling,  or  actual 
development  work.  If  the  property  being  examined  is  liable  to  become  a  large 
and  valuable  mining  property,  the  original  survey  should  be  tied  to  monuments 
or  natural  landmarks,  so  that  it  can  be  checked  by  future  observations,  and 
these  monuments  or  landmarks  should  become  the  basis  of  future  and  more 
careful  mining  surveys. 

Some  of  the  advantages  of  a  careful  geological  examination  of  a  property 
are  that  other  materials  of  economic  value  would  probably  be  discovered 
if  any  should  exist  on  the  porperty:  also,  such  an  examination  of  the 
property  gives  information  as  to  the  drainage  system  of  the  country  that 
nray  be  of  great  advantage  in  laying  out  the  mine,  and  future  exploration  by 
drilling  or  sinking  can  be  done  to  better  advantage  after  a  careful  surface 
examination. 

Sampling  and  Estimating  the  Amount  of  Mineral  Available. — In  many 
cases,  it  is  necessary  to  do  some  development  or  exploration  work  before  fair 
average  samples  can  be  obtained.  The  samples  as  taken  should  fairly  represent 
the  coal  as  it  will  be  extracted.  Such  slate  as  would  be  sold  with  the  coal 
should  be  included  in  the  sample.  When  sampling  any  property  it  is  well  to 
divide  the  seam  up  into  blocks,  and  sample  each  one  separately.  The  samples 
may  then  be  analyzed  and  an  average  obtained  later,  or  the  different  samples 
may  be  mixed  and  an  average  analysis  obtained.  The  amount  of  material 
broken  for  sample  may  vary  from  a  few  pounds  to  several  tons.  Large  samples 
may  be  reduced  by  shoveling  (that  is,  taking  a  proportionate  number  of  shovel- 
fuls for  the  sample,  as  every  third  or  fourth  shovelful).  After  the  sample  has 
been  partly  reduced,  the  operation  may  be  carried  on  by  quartering,  which 
may  be  described  as  follows: 

The  coal  is  shoveled  into  a  conical  pile  by  throwing  each  shovelful  on 
to  the  apex  of  the  cone.  After  this,  the  cone  may  be  reduced  by  scraping  it 
down  with  a  shovel,  passing  slowly  around  it.  If  the  amount  of  material  is 
small,  a  flat  plate  may  be  introduced  into  the  cone,  and  the  pile  flattened 
by  revolving  the  plate.  The  pile  is  then  divided  into  quarters  by  drawing 
lines  across  it.  After  this,  two  alternate  quarters  are  scraped  out  and  shoveled 
away,  and  the  other  two  quarters  are  left  as  the  sample.  The  process  may 
be  repeated  until  the  block  has  been  sufficiently  reduced.  In  shoveling  away 
the  discarded  portions,  care  should  be  taken  to  see  that  the  fine  dust  under 
them  is  brushed  away  also,  as  it  often  contains  much  of  the  impurity  in  the 
seams  and  its  not  being  included  might  unduly  increase  the  quality  of  the 
resulting  sample.  If  the  property  being  examined  is  a  mine  in  active  opera- 
tion, samples  may  be  taken  from  the  working  faces,  and  also  from  cars,  loading 
chutes,  etc.  Usually,  the  samples  from  the  face  are  kept  separate  from  those 


560  PROSPECTING 

from  the  cars  and  loading  chutes,  the  latter  being  intended  as  a  check  on  the 
former. 

The  human  factor  always  plays  a  large  part  in  the  value  of  a  sample  as 
finally  selected,  and  hence  it  should  be  taken  by  a  man  who  has  had  con- 
siderable experience  in  this  class  of  work.  For  this  reason,  it  is  best  to  employ 
a  mining  engineer.  One  not  accustomed  to  sampling  very  rarely  undervalues 
a  property,  owing  to  the  fact  that  it  seems  to  be  human  nature  to  pick  up  a 
pure  piece  of  coal,  rather  than  the  worthless  bone  or  slate. 

If  a  seam  is  penetrated  by  a  number  oi  bore  holes,  or  by  workings  extended 
over  a  considerable  area,  it  is  fair  to  estimate  that  the  material  will  run  prac- 
tically as  exposed  for  a  considerable  area;  but  especially  in  the  case  of  bitu- 
minous coal,  it  is  a  comparatively  easy  matter  to  form  some  estimate  as  to  the 
amount  of  material  available.  The  tonnage  of  coal  seams  per  1  in.  and  1  ft. 
of  thickness  is  given  in  the  section  upon  weights  of  materials,  etc. 


1.  SITUATION  AND! 
SURROUNDINGS  | 


2.  TOPOGRAPHY 


1.  Name 


DIAGRAM  FOR  REPORTING  ON  COAL  LANDS 

The  following  diagram  will  be  useful  as  a  guide  in  making  out.  .a  report  on 
a  coal  mining  property: 

"  1.  Location,  if  on  surveyed  land 

2.  Nearest  town  or  village 

3.  Mineral  district 

.  4.  County,  state,  or  territory 

(.  2.  Distance  and  direction  from  one  or  more  points 
'  1  .  Hills  or  mountains 

2.  Character  of  surface,  vegetation,  and  timber 

3.  Streams  and  water  supply 

4.  Elevations 

1.  Stratified 

Crystalline 
.  Igneous 
Anticlines  or  synclines 

1.  Number 

2.  Strike 


1.  Structure 


3.  GEOLOGY- 


1.  Rocks 

2.  Axes 


{I: 

\3. 


3.  Faults 


4.  Dikes 


Horses 


2.  Geological  period 


3.  Dip 

4.  Throw 

1.  Number 

2.  Strike 

ip 

illi 

Throw 

Number  and  size 
Location 
Material 


3.  Di 

4.  Filng 


3.  Coal  beds 


(I: 


|  1.  Reported 


4.  Quality  of  coal,  spec- 
imens, appearance  in 
mine,  in  cars 


Number     I  2.  Measured    fl.  Reported 
Thickness  I  3.  Average       <  2.  According      to 
[  4.  Uniformity  [      measurement 

1.  Color,  external,  powder 

2.  Luster 

3.  Clearness  from  clay  or  sand,  shale 

4.  Sulphur 

5.  Resin 

6.  Firmness,  size  of  lumps,  air  slaking 

7.  Cleavage  or  fiber 
.8.  Coking 

9.  Color  of  ashes 

10.  Use:  Gas,  steam,  domestic,  forge, 
metallurgy,  coking 

11.  Analyses 


PROSPECTING 
DIAGRAM  FOR  REPORTING  ON  COAL  LANDS— (Continued) 


561 


4.  MINING 


1.  History 


2.  Mine 


1.  Dates  of  opening,  abandoning,  reopening,  num- 
ber of  mines  and  names 

2.  Ownership 

3.  Superintendence 

1.  Shaft,  slope,  or  tunnel 

{1.  Total  depth 
2.  Depth  below  water  level 
3.  Number  of  levels 
4.  Extent  of  levels 

3.  Water  pumps,  size  and  kind,  water  cars,  number 
and  size,  natural  drainage 

4.  Ventilation,    natural,     furnace,    fan    (force    or 
exhaust),  sufficient  or  insufficient 

o.  Lighting,  system  used 

6.  Powder,  kind  and  grade  used 

7.  Explosive  or  noxious  gases 

8.  Coal-cutting  machines  and  power  drills 

'1.  Room  and  pillar:  (a)  single  entry, 
(6)  double  entry,  (c)  three  or  more 

9.  Mode  of  I       entries 

working   |  2.  Longwall:    (a)    advancing,    (b)    re- 
treating 
3.   Modifications  of  (1)  and  (2) 


10.  Rooms,  p 


lars,  dimensions,  and  general  plan 


3.  Sections 


5.  MAPS  AND  DRAWINGS 


G.  COKE  OVENS  •< 


11.  Timbering 

12.  Roof,  or  hanging  wall,  strong  or  weak,  air  slakes 
or  not 

13.  Floor,  or  foot-wall,  hard  or  soft,  creeps  or  not 

14.  Roads,  rails,  and  cars 

II.  Mules 
2.  Electricity 
3.  Compressed  air 
4.  Wire  rope 
5.  Chain 
6.  Locomotive 
16.  System  of  hoisting;  Cage,  skip,  cars. 

1.  Of  the  whole  region 

2.  Of  the  underground  workings 

'1.  Cross 

2.  Longitudinal 

fl.  General 

3.  Columnar  {2.  Coal   bed    or    other 

I      deposit 

4.  Buildings,  works,  or  machinery 
'1.  Scale 
2.  North  line,  magnetic  variation 

o.  Explanation  <{  £  gate^ 

5.  Can  buy,  take,  borrow,  or  have 
copied 

1.  History,  ownership,  etc. 

2.  Number 

3.  Character  of  ovens 

4.  Dimensions 

5.  Construction,  materials,  etc. 

f  1.  Charge,  quantity,  etc. 

6.  Operations  <  2.  Working 

13. 

7.  Repairs 

8.  Quality  of  product  (analyses,  if  any) 

9.  Disposition  of  by-products 

(1.  Construction 
2.  Condition 
3.  Capacity 
4.  Water  supply  and  consumption 
5.  Quality  of  product 


Discharging,  quenching 


36 


562  PROSPECTING 

DIAGRAM  FOR  REPORTING  ON  COAL  LANDS—  (Continued) 


7.  DISPOSITION 
OF  PRODUCT 


1.  Shipped 


t 

•K 


As  mined  to 

As  coke  | ; 

Distance 
Roads 


jobber 

Blast  furnace 
Trade  or  jobber 


8.  STATISTICS 


2.  Shipment,  3>  Rail,oads 
1.4.  Navigation 
f  1.  Capacity,  maximum  and  minimum 

1.  Productions  fl.  Daily.weekly,  or  monthly,  in  tons 

1 2.  ActuaK  2.  Yearly,  in  tons 

1 3.  Average 
1.  Whole  number  of  workers 

2.  Labor  {  2.  Number  of  workers  in  each  class 

3.  Number  of  horses  or  mules 

1.  Timber 

2.  Tools 

3.  Fuel 

4.  Oil 

5.  Powder 

i    p«™  Jfi    T    *fl.  Day,  different  classes 

Orl2.  Contract  or  piece,  yard  or  ton 

7.  Carriage 

8.  Local  sales  of  product 

(1.  Machinery 
2.  Buildings 
3.  Roads,  tracks,  etc. 
4.  Rolling  stock 
5.  Supplies 
{1.  Boilers 
2.  Waterwheels 
3.  Air  compressors 
4!  Steam  and  gas  engines 
5.  Electric  plants 

( 1.  Power  for 
1.  Smith's 
shop 


9.  SURFACE  PLANT 


2.  Shops 


3.  Powder  houses 

4.  Offices 


5.  Dry  or  change  houses 

6.  Storehouses 


2.  Number  of  forges 

3.  Steam  hammers 

4.  Other  tools 

{1.  Power  for 
2.  Saws 
I!  otSfmachines 
5.  Benches  and  vises 

1.  Power 

2.  Lathes 

3.  Planers 

4.  Shapers 

5.  Drill  presses 

6.  Other  tools 

7.  Benches  and  vises 


3.  Machine 
shop 


7.  Boarding  and  dwelling  houses 

8.  Stables 

9.  Shaft  houses 

10.  Tipples 

11.  Pockets  or  slack  bins 

12.  Company  store 

13.  Timber  yard  and  plant  for  preparing  timber 


14.  Water 


1.  City  or  com- 
mercial 


2.  Company 
service 


1.  Quality  of  water 

2.  Sufficient  or  insufficient 

3.  Pressure 

1.  Quality  of  water 

2.  Sufficient  or  insufficient 

3.  Gravity  system 

fl.  Direct 

4.  Pumping  <  2.  Reservoir 
system     I  or  stand  pipe 


OPENING  A  MINE 
DIAGRAM  FOR  REPORTING  ON  COAL  LANDS—  (Co  nlinued) 


563 


'15.  Lighting 


Character 


Origin 


f  1 .  Commercial  plant 
\2.  Company  plant 


I  3.  Sufficient  or  insufficient 
f  1.  Steam  engines 


16.  Hoisting  or  wind-  1  J  ^1  oJgas^ne'engines 

ing  plant                  |  ^  Electric  motors 

1  5.  Water  motors 

1.  Gauge 

2.  Total  length 

1.  Railroad- 

3.  Size  of  cars 
4.  Number  of  cars 

17.  Surface  trans- 

5. Power  used 
6.  Number  of  motors 

portation 

1.  Character   and   sur- 

2.  Wagon 
roads 

face  of 
2.  Length 
3.  Number   of   wagons 

and  teams 

10.  MISCELLANEOUS 


11.  CONCLUSIONS  < 


Gross 


1.  Yearly  income,  last  year,  or  for  any  year-j  ^    Net 

2.  Average  cost  per  ton  of  material 

f  1 .  Quality  of  coal  or  coke 
I  2.  A 


3.  Merits   of 
property 


4.  Advice 


5.  Local  considerations 


Amount  of  coal/ 1.  Gross 
\       in  sight  1 2.  Net 

1 3.  Value  of  coal  in  sight 
2.  Value  of  plants  and  works 

.  Continue  present  system 

Change  system  to 

2.  Disposition  f  1.  Ship  as  mined 
Coke  and  ship 

1.  Troubles 

2.  Labor 

3.  Supplies 

4.  Climate 

5.  Shipment  facilities 

6.  Markets 


. 

1     \/t-   •„„        /!• 

1.  Mining        (2. 

2.  Disposition  fl. 
of  product  \  2. 


OPENING  A  MINE 


GENERAL  AND  FINANCIAL  CONSIDERATIONS 

Usually  the  kind  of  opening  through  which  the  coal  underlying  a  tract  of 
land  must  be  extracted  is  not  a  matter  of  choice  but  is  fixed  by  the  distance 
of  the  seam  above  or  below  the  surface  at  the  point  where  the  plant  must  of 
necessity  be  built.  If  the  seam  outcrops  near  the  selected  site,  the  coal  will  be 
opened  by  a  drift  if  the  measures  are  horizontal  or  nearly  so,  or  by  a  slope 
driven  down  the  dip  if  the  bed  is  inclined.  If  the  coal  does  not  outcrop,  it 
must  be  opened  by  a  vertical  shaft,  although,  if  the  distance  to  the  seam  does 
not  exceed,  say,  50  to  100  ft.,  the  mine  may  be  opened  by  a  rock  slope;  that 
is,  by  an  inclined  passageway  driven  downwards  through  the  rock  to  intersect 
the  seam. 

In  mountainous  districts,  the  outcrop  of  a  steeply  pitching  seam  may  be 
inaccessible  by  reason  of  its  great  elevation  above  the  valley.  In  such  a  case, 
the  mine  may  be  opened  by  a  rock  tunnel  driven  from  some  point  at  the  proper 
elevation  in  the  valley  across  the  inclined  measures  until  the  seam  is  met. 
In  rare  instances,  the  seam,  while  not  outcropping  within  the  limits  of  the 
property,  lies  but  a  short  distance  beneath  the  surface,  and  may  be  worked 
by  stripping  as  explained  under  Methods  of  Working, 


564  OPENING  A  MINE 

Relation  Between  Investment  and  Cost  of  Production. — Where  a  choice  is 
possible,  the  relative  cost  of  opening  and  equipping  the  mine  by  each  type  of 
opening  (drift,  slope,  and  shaft)  must  be  considered  in  connection  with  the 
cost  of  operating  through  each  before  a  selection  can  be  made.  If  the  capital 
is  to  be  had,  an  increased  investment  is  often  warranted  by  a  lower  cost  of 
production  made  possible  through  its  use.  The  increased  cost  of  driving  and 
equipping  one  kind  of  opening  as  compared  with  another  can  usually  be  deter- 
mined within  fairly  close  limits,  but  it  requires  the  skill  and  judgment  acquired 
through  long  experience  to  be  able  to  estimate,  even  approximately,  in  advance 
of  actual  developments  how  much  more  it  will  cost  per  ton  to  extract  coal  under 
one  set  of  conditions  than  under  another.  The  general  method  of  making 
these  calculations  is  shown  in  the  following: 

EXAMPLE.— --There  are  2,000,000  T.  of  coal  in  a  property  that  it  is  proposed 
to  extract  in  10  yr.  at  the  average  rate  of  200,000  T.  per  yr.  A  shaft  costing 
$50,000  to  sink  and  equip  will  effect  an  estimated  saving  of  5.25  c.  per  T.  in 
the  cost  of  production  over  a  slope  costing  $20,000.  If  the  money  to  open  the 
property  must  be  repaid  in  ten  annual  instalments  with  interest  at  6%,  which 
opening  should  be  selected  and  what  is  the  gain  by  so  doing? 

SOLUTION. — In  the  case  of  the  shaft,  there  will  be  due  at  the  end  of  the  first 
year  interest  on  the  entire  loan  or  $3,000  and  one- tenth  of  the  principal  or 
$5,000,  a  total  of  $8,000;  at  the  end  of  the  second  year  there  will  be  due  inter- 
est on  $45,000  or  $2,700  and  one-tenth  of  the  remaining  capital,  a  total  of 
$7,700;  and  similarly  each  year  thereafter  until  the  end  of  the  tenth  year 
when  the  last  payment  of  $5,300  for  both  principal  and  interest  will  be  due. 
During  the  life  of  the  mine  there  will  have  been  paid  out  for  principal  and 
interest,  the  sum  of  $66,500,  or  an  average  of  66,500^2,000,000  =  3.325  c.  per 
T.  of  coal  produced. 

In  the  same  way  it  may  be  shown  that  the  total  cost  for  principal  and  inter- 
est for  sinking  and  equipping  a  slope  will  be  $26,600,  or  at  the  rate  of  1.33  c. 
per  T. 

So  far  as  the  investment  alone  is  concerned,  the  slope  is  the  cheaper  to 
the  extent  of  3.325—1.33  =  1.995  c.  per  T.,  or  very  nearly  $40,000  during  the 
life  of  the  property.  On  the  other  hand,  mining  through  a  shaft  means  a  reduc- 
tion in  the  cost  of  production  of  5.25  c.  per  T.  Hence,  a  net  saving  of  5.25 
-1.995  =  3.255  c.  per  T.,  or  a  total  saving  of  .3255X2,000,000  =  $65,100  will 
be  effected  by  sinking,  equipping,  and  using  a  shaft. 

Relative  Cost  of  Different  Types  of  Opening. — As  drifts  and  slopes  are 
driven  through  much  softer  material  (coal),  they  are  much  less  costly  than 
shafts,  which  are  sunk  through  rock;  and,  further,  the  returns  from  the  coal 
extracted  from  them  to  some  extent  offset  the  cost  of  driving.  Owing  to  the 
greater  difficulty  of  handling  materials  on  a  pitch,  to  the  added  cost  of  pump- 
ing water,  etc.,  slopes  are  more  expensive  to  drive  than  drifts.  Furthermore, 
the  cost  of  the  massive  head-frames,  powerful  pumps  and  hoisting  engines, 
etc.,  comnwnly  required  at  shafts,  and  to  but  a  slightly  less  extent  at  slopes, 
adds  materially  to  the  capital  invested  in  equipment  over  that  necessary  for 
a  drift.  Therefore,  from  the  standpoint  of  capital  required,  the  choice  of  open- 
ing will  be  in  the  order,  drift,  slope,  shaft. 

Cost  of  Production  as  Affected  by  Type  of  Opening. — That  type  of  opening 
is  to  be  preferred  which  permits  of  the  lowest  cost  of  production  for  the  same 
investment  of  capital.  In  the  case  of  flat  seams,  the  cost  of  production  is 
materially  less  in  a  mine  opened  by  a  drift  than  in  one  opened  by  a  slope  or  a 
shaft.  This  is  largely  due  to  the  fact  that  in  the  latter  cases,  the  delivery  of 
the  coal  to  the  tipple  is  made  in  two  stages;  first,  hauling  it  to  the  foot  of  the 
slope  or  shaft;  second,  hoisting  it  to  the  surface.  In  drift  mines,  the  coal  is 
hauled  directly  to  the  tipple  in  one  operation  and  hoisting  costs  are  thus  saved. 
Furthermore,  in  drift  mines  the  cost  of  pumping  is  usually  negligible  and  that 
of  handling  men  and  supplies  is  a  minimum.  Flat  seams  are  sometimes  opened 
by  a  rock  slope,  but  no  reduction  in  operating  costs  is  effected  thereby  unless 
the  slope  is  short  and  the  pitch  such  that  long  trips  can  be  hauled  and  the  men 
can  walk  to  and  from  their  work. 

Whether  a  pitching  seam  is  more  cheaply  operated  through  a  slope  driven 
from  the  outcrop  on  the  coal  or  through  a  vertical  shaft  intersecting  the  seam 
at  some  depth  below  the  crop  cannot  be  determined  without  a  careful  study  of 
all  the  factors  concerned  in  the  particular  case.  If  the  slope  is  comparatively 
flat  it  is  to  be  preferred  to  a  shaft,  but  if  the  pitch  is  so  great  that  the  mine  cars 
must  be  hoisted  on  a  slope  carriage  or  is  so  very  steep  that  the  coal  must  be 
lumped  at  the  foot  of  the  slope  into  a  gunboat  or  skip,  a  shaft  is  more  cheaply 


OPENING  A  MINE  565 

In  general,  the  cost  of  production  through  the  three  types  of  opening  is  in 
the  same  relative  order  as  the  cost  of  making  openings;  namely,  drift,  slope, 
and  shaft,  although,  in  the  case  of  highly  inclined  slopes,  the  order  will  be, 
drift,  shaft,  and  slope.  

LOCATION  OF  SURFACE  PLANT 

While  every  endeavor  should  be  made  to  locate  the  mine  opening  and 
screening  plant  so  that  each  may  be  operated  with  the  greatest  efficiency  and 
economy,  this  is  not  always  possible.  Usually,  the  surface  plant  must  be 
located  to  meet  certain  natural,  business,  or  financial  conditions,  and  the  loca- 
tion of  the  mine  opening  is  subordinated  to  the  absolute  necessity  of  prepar- 
ing the  coal  in  such  a  way  that  it  is  marketable.  When  locating  the  surface 
plant  the  following  points  have  to  be  considered: 

Grades. — The  track  grade  should  be  such  that  the  railroad  cars  will  drop 
by  gravity  from  one  end  of  the  siding  to  the  other.  Opinions  differ  as  to 
the  most  desirable  grades,  but  1.5  to  2%  from  the  end  of  the  tail-track  to  the 
tipple  is  ample  for  the  empties;  and  for  loading  under  the  tipple  and  thence  to 
the  end  of  the  loaded  track,  1.25%  gives  excellent  results.  Sometimes  grades 
of  3%  and  more  are  met  above  a  tipple,  but  such  slopes  are  very  dangerous, 
owing  to  the  liability  of  a  string  of  empties  running  down  into  the  cars  being 
loaded.  When  the  grades  are  so  flat  that  the  cars  will  not  run  except  when 
pinch  bars  are  used,  it  will  prove  profitable  to  install  some  kind  of  car  haul 
or  car-spotting  device  operated  by  steam  power. 

Length  and  Number  of  Sidings. — The  length  of  the  sidings  necessary  for 
the  storage  of  empty  and  loaded  railroad  cars  will  depend  on  the  daily  output 
of  the  mine  and  the  number  of  sizes  of  coal  shipped.  The  output  of  the  mine 
depends  on  the  ability  of  the  company  to  sell  the  coal  at  a  profit,  and  this, 
in  a  great  measure,  hinges  on  the  quality  of  the  product.  A  high-grade  fuel, 
even  at  a  high  price,  is  more  salable  and  is  in  steadier  demand  than  a  poor  one. 

There  must  be  as  much  storage  room  for  loaded  cars  below  the  tipple  as 
there  is  for  the  storage  of  empty  cars  above  it.  If  the  coal  is  loaded  in  steel 
hoppers  of  100,000  Ib.  (50  T.)  capacity,  averaging  40  ft.  in  length  there  will 
be  required  for  each  1,000  T.  of  daily  capacity  (1 ,000 -i- 50)  X  40  =  800  ft.  of 
siding.  To  allow  for  switches  and  for  cars  of  less  capacity,  it  is  better  to  assume 
1,000  ft.  of  siding  for  each  1,000  T.  of  daily  output.  For  a  single-track  tipple, 
that  is,  one  under  which  there  is  but  one  loading  track  and  hence  shipping 
mine-run  coal  only,  there  will  thus  be  required  2,000  ft.  of  siding  for  each 
1,000  T.  of  output.  In  the  case  of  two-  and  three-track  tipples  (those  load- 
ing two  or  three  sizes  of  coal)  if  there  is  2,000  ft.  from  the  point  of  switch  on 
the  main  line  above  the  tipple  to  the  corresponding  point  below  it,  there  will 
be  car-storage  room  for  more  than  1,000  T.  capacity.  This  is  because  the 
second  loading  track  will  have,  say,  1,500  ft.,  and  the  third,  say,  1,000  ft.  of 
available  storage  room,  half  above  and  half  below  the  tipple.  Owing  to 
uncertainties  and  irregularities  in  train  service,  it  is  highly  advisable  to 
provide  storage  room  for  2  da.  car  supply. 

The  width  of  bottom  land  required  for  the  siding  depends  on  the  number 
of  sizes  of  coal  shipped.  It  is  possible,  but  unusual,  to  ship  but  one  size,  that 
is,  mine  run  or  the  unscreened  output  as  mined.  If  the  supply  train  pushes 
the  empties  above  the  tipple,  they  may  be  dropped  down  and  loaded  upon  the 
same  track.  This  will  require  about  16  ft.  in  width^for  the  roadbed  and  ditches. 
Commonly,  the  empties  are  placed  by  the  switch'engine  at  the  upper  end  of 
the  mine  branch  railroad  (or  are  dropped  on  the  main  line  if  the  mine  is  situated 
thereon),  and  pass  by  gravity  on  to  the  mine  siding  or  loading  track,  and  down 
it  to  the  tipple.  The  two  tracks  are  commonly  laid  with  their  center  lines  13  ft. 
apart,  which  requires  a  grade  from  26  to  28  ft.  wide,  depending  on  the  size  of 
the  side  ditches.  At  the  tipple,  and  for  a  few  hundred  feet  above  and  below 
it  where  the  cars  are  being  handled  during  loading,  the  tracks  should  be  laid 
with  not  less  than  15  ft.  between  center  lines ;  and  if  fast  passenger  traffic  is 
passing  on  the  main  line,  this  distance  should  be  18  to  20  ft.,  unless  a  high  fence 
is  built  between  the  mine  and  railroad  tracks.  This  will  require  a  bottom 
width  of  from  28  to  35  ft.  For  each  additional  size  of  coal  shipped  one  track 
and  15  ft.  of  width  should  be  allowed.  Thus,  if  three  sizes  are  made  and  the 
supply  and  first  loading  track  require  30  ft.  of  width,  there  will  be  needed  a 
total  of  30+ 15+ 15  =  60  ft.  for  the  three  loading  and  one  supply  track.  While 
this  width  may  be  reduced  in  a  tipple  of  steel  construction,  which  spans  the 
tracks  and  does  not  require  bents  between  them,  it  is  not  advisable  to  reduce 
the  distance  between  the  supply  and  first  loading  tracks. 


566  OPENING  A  MINE 

Mining  Plant. — The  space  required  for  the  mining  plant,  including  in  that 
term  the  tipple,  boiler,  and  power  house,  car  and  repair  shops,  stable,  sup- 
ply house,  fan,  etc.,  will  vary  from  a  few  hundred  square  feet  at  a  small  mine 
to  several  acres  at  a  large  one.  The  tipple  must  be  located  with  respect  to  the 
tracks  as  explained.  The  fan  is  always  and  the  car  and  repair  shops  and  the 
stable  are  commonly  placed  near  the  mine  mouth.  The  supply  house  is  better 
placed  near  the  tracks  for  ease  in  unloading  supplies.  If  electric  power  is  used 
and  the  boiler  and  power  plant  are  placed  near  the  tipple,  cheap  slack  may  be 
used  for  fuel,  and  the  necessary  power  for  running  the  fan,  shop  machinery, 
haulage  motors,  etc.,  may  be  cheaply  conveyed  to  the  mine  at  any  reasonable 
distance.  If  compressed  air  is  used  for  coal  cutting  and  haulage,  the  air  com- 
pressor may  be  placed  at  the  mine  mouth  and  operated  by  electricity  generated 
at  a  distance.  If  room  for  the  boiler  and  power  plant  is  not  to  be  had  at  the 
tipple,  they  must  be  located  near  the  mine  mouth,  must  use  mine-run  coal  for 
fuel,  and  the  power  for  operating  the  machinery  must  be  transmitted  to  the 
tipple.  For  ease  in  supervision,  the  various  units  of  the  plant  should  be  near 
to  one  another. 

Mining  Village. — As  it  is  easier  to  hold  and  secure  men  if  their  homes 
are  near  their  work,  it  is  advisable  to  place  the  mining  town  (village,  camp,  or 
settlement)  near  the  mine  mouth,  as  this  location  will  suit  practically  all 
the  workers  except,  perhaps,  the  tipple  hands.  The  space  required  for  the 
town  varies  according  to  the  number  of  men  required  to  produce  the  desired 
tonnage,  and  this  will  depend  on  the  thickness  of  the  seam,  its  relative  hard- 
ness, use  or  non-use  of  coal-cutting  machinery,  etc.  Probably  it  is  a  fair  esti- 
mate to  assume  that  housing  must  be  provided  for  from  150  to  200  families  for 
each  1,000  T.  of  daily  output.  In  addition,  space  must  be  provided  for  a  store, 
a  schoolhouse,  several  churches,  a  hall  for  assemblies,  etc.  It  is  now  cus- 
tomary to  provide  playgrounds  for  the  children  and  baseball  fields  and  swim- 
ming pools,  etc.,  for  the  men.  Each  house  should  be  placed  on  a  lot  50X 150  ft., 
that  there  may  be  room  for  a  kitchen  garden  in  the  rear.  If  i  A.  can  be  given 
each  house  it  is  better,  and  the  saving  in  insurance  by  having  the  houses  farther 
apart  is  an  item  of  importance.  Two  hundred  houses,  each  on  a  lot  50 X 150  ft., 
can  be  built  on  50  A.,  assuming  the  streets  and  alleys  to  take  half  as  much 
space  as  the  building  lots.  To  the  50  A.  must  be  added  from  10  to  25  A.  for 
stores,  churches,  schools,  playgrounds,  etc.  Space  for  the  village  is  easily 
obtainable  in  level  country,  but  in  mountainous  districts  the  houses  are  too 
commonly  perched  along  the  hillsides  in  an  unsightly  fashion.  In  this  case, 
it  is  advisable  to  secure  the  services  of  a  competent  landscape  architect  to 
secure  the  best  and  most  artistic  arrangement  of  the  houses  with  respect  to  the 
irregularities  of  the  surface.  It  is  greater  economy  to  pump  water,  haul  sup- 
plies, etc.,  to  a  well-situated  town,  than  to  consider  only  the  first  cost  and  place 
the  town  in  an  undesirable  location  near  a  stream  or  the  railroad  tracks. 

Coke  Ovens. — If  the  coal,  either  as  mine  run  or  as  slack,  is  coked  on  the 
property,  more  room  is  required  than  if  it  is  all  shipped  to  market,  except  in 
the  unusual  case  where  there  are  four  or  five  loading  tracks  under  the  tipple. 
The  space  required  for  the  ovens  will  depend  on  the  tonnage  of  coke  desired, 
whether  the  ovens  are  built  in  bank  (single  row)  or  in  block  (double  row  placed 
back  to  back) ,  and  on  the  width  of  yard  required  in  front  of  the  ovens  to  store 
the  coke  before  it  is  loaded  into  cars.  A  beehive  oven  may  be  counted  upon 
to  yield  an  average  of  2  to  2.5  T.  of  coke  daily,  depending  on  the  size  of  the 
oven,  kind  of  coal  charged,  etc.  An  output  of  500  T.  per  day  will,  therefore, 
require  200  to  250  ovens.  The  distance  apart,  center  to  center,  of  the  ovens 
will  be  equal  to  the  diameter  of  the  oven  plus  twice  the  thickness  of  the  lining 
brick,  or  2X9  =  18  in.,  plus  from  4  to  6  in.  between  ovens  in  which  clay  is 
tamped.  The  spacing  for  ovens  12  ft.  6  in.  in  inside  diameter  (a  common  size) 
will  thence  be  12  ft.  6  in.  +  l  ft.  6  in.  +  (say)  6  in.  =  14  ft.  6  in.  Allowing  5  ft. 
for  the  two  end  walls,  the  200  to  250  ovens  required  for  an  output  of  500  T. 
will  be  either  200X14.5+5  =  2,905  ft.  or  250X14.5+5  =  3,625  ft.  if  built  in 
bank,  and  one-half  these  lengths  if  built  in  block.  The  capacity  of  the  rail- 
road cars  into  which  coke  is  loaded  varies  greatly.  It  is  difficult  to  get  the  full 
30  T.  into  box  cars  of  60,000  Ib.  capacity,  but  special  coke  racks,  as  they  are 
called,  will  hold  50  T.  Thus  it  will  require  ten  to  twenty  cars,  depending  on 
their  kind,  to  hold  the  assumed  500  T.  of  coke.  If  750  ft.  of  clear  trackage, 
or,  say,  1,000  ft.  to  allow  for  switches,  clearance,  etc.,  is  allowed  both  above 
and  below  the  ovens,  there  will  be  ample  room  to  hold  the  smallest  cars  used 
in  the  coke  business.  Thus,  including  the  storage  tracks,  a  bank  of  200  to 
250  ovens  will  be,  say,  4,900  to  5,600  ft.  long.  If  built  in  block  about  1,000  ft. 
in  total  length  will  be  saved. 


OPENING  A  MINE  567 

The  12.5-ft.  bank  oven  has  a  width  of  practically  16  ft.  from  the  side  hill 
against  which  it  is  built  to  the  front,  or  mortar  wall.  The  width  of  the  coke 
yard  in  front  of  the  ovens  varies  from  as  little  as  10  ft.,  in  cases  where  the  coke 
is  loaded  out  promptly,  to  as  much  as  30  ft.  where,  owing  to  uncertain  market 
conditions,  the  coke  must  be  piled  on  the  yards  pending  sale.  Further,  there 
must  be  added,  say,  14  ft.  for  the  track  upon  which  the  cars  are  loaded.  Hence, 
a  row  of  bank  ovens,  exclusive  of  the  space  required  for  the  supply  track,  will 
have  a  width  of  from  16+10+14  =  40  ft.  to  16+30+14  =  60  ft. 

The  same  sized  oven  arranged  in  block  will  require  a  width  of  about  33  ft. 
from  the  face  of  one  front  wall  to  the  other.  The  two  yards  will  vary  between 
2X10  =  20  ft.  and  2X30  =  60  ft.  in  width,  and  the  two  loading  tracks  will 
require  2  X 14  =  28  ft.  Thus,  a  block  of  beehive  ovens  of  standard  size  will  be 
81  to  121  ft.  wide,  exclusive  of  the  supply  track. 

It  is  well  to  have  the  tipple  or  coal  bins  at  the  upper  end  of  the  ovens, 
particularly  if  the  grade  is  steep,  so  that  the  charging  larry  may  run  or  may  be 
assisted  in  running  by  gravity.  This  is  not  so  important  if  mechanical  haulage 
is  used. 

LOCATION  OF  MINE  OPENING 

In  level  countries,  it  is  almost  always  possible  to  so  locate  the  mine  with 
respect  to  the  surface  plant,  that  both  mining  and  outside  costs  are  a  minimum. 
In  hilly  countries,  however,  the  site  of  the  surface  plant  is  determined  by  the 
conditions  just  discussed,  and  the  place  for  the  mine  opening  may  have  to  be 
decided  by  striking  a  balance  between  an  increased  or  decreased  cost  of  pro- 
duction on  the  one  hand  and  a  decreased  or  increased  capital  charge  (interest 
and  sinking  fund)  on  the  other. 

When  locating  the  mine  opening,  the  following  points  should  be  consid- 
ered: The  opening  should  be  at  the  lowest  point  of  the  seam;  that  gravity 
may  assist  both  the  underground  haulage  and  drainage;  haulage  is  almost 
always  cheaper  underground  than  on  the  surface  and  particularly  so  where 
the  winters  are  severe  and  the  fall  and  spring  wet;  the  mine  opening  should  be 
as  near  as  possible  to  the  tipple,  as  the  concentration  of  the  plant  at  one  point 
tends  to  efficient  management,  and  objectionable  surface  haulage  is  avoided. 

Flat  Seams. — A  flat  seam  is  commonly  understood  to  be  one  in  which 
the  dip  does  not  exceed  50  to  150  ft.  to  the  mile,  or,  say,  1  to  3%;  in  all  cases 
such  a  seam  should  be  opened  at  the  tipple  by  the  necessary  drift  or  shaft. 
It  is  desirable  to  have  the  dip  of  the  seam  in  favor  of  the  haulage,  but  if  it  is 
not,  the  more  advantageous  location  of  the  opening  and  the  saving  in  surface 
haulage  more  than  offsets  the  small  increased  cost  for  power  in  hauling  up  such 
slight  grades.  If  the  seam  outcrops,  an  endeavor  should  be  made  to  open  it  at 
tipple  height.  By  tipple  height  is  meant  the  distance  between  the  rail  on  which 
the  mine  cars  stand  on  the  tipple  and  the  rail  on  which  the  railroad  cars  are 
loaded.  This  distance  varies  according  to  the  number  of  sizes  of  coal  shipped. 
If  mine-run  coal  only  is  loaded,  this  height  need  not  exceed  16  to  18  ft.  If 
three,  four,  or  more  sizes  are  loaded  the  height  will  be  30  or  32  ft.,  or  even  more, 
in  order  that  the  proper  pitch  may  be  given  the  screens  over  which  the  coal 
is  sized.  For  modern  tipples,  a  fair  height  is  32  ft.  It  will  be  understood  that 
the  outcrop  of  the  seam  is  assumed  to  be  at  some  elevation  above  the  tipple 

Klatform  in  order  that  gravity  may  assist  the  movement  of  the  loaded  mine  cars 
rom  the  drift  mouth  to  the  dump.  This  elevation  will  be  at  the  rate  of  1  to 
1.5  ft.  per  100  ft.  of  distance.  Thus,  a  drift  mouth  35  ft.  above  the  railroad 
and  300  ft.  from  the  dump  will  afford  a  tipple  height  of  35—  (300  X  .01)  =32  ft. 
if  the  down-grade  from  the  mine  is  1%.  If  the  coal  is  not  shipped  but  is  coked 
at  the  plant,  the  mine  cars  may  be  run  from  an  opening  60  to  75  ft.  above  the 
valley  directly  to  bins  into  which  they  are  dumped,  the  coal  being  drawn  out 
below  into  larries  and  conveyed  to  the  ovens.  If  the  coal  outcrops  at  more  than 
tipple  height,  say,  at  an  elevation  of  100  or  200  ft.,  or  more,  it  is  commonly 
lowered  on  a  self-acting  or  gravity  incline.  In  other  cases,  the  coal  is  dumped 
at  the  mine  mouth  into  a  retarding  conveyer  and  carried  in  a  continuous  stream 
to  the  tipple,  or  the  loaded  cars  are  dropped  to  the  tipple  by  a  chain  haul.  In 
the  Pocahontas  region  of  West  Virginia,  in  order  to  provide  storage  room  for 
coal  that  the  mine  may  be  kept  in  operation  while  waiting  for  railroad  cars  to 
load  the  output,  as  well  as  to  secure  height  for  the  slack  bins,  which  are  built  in 
as  an  integral  part  of  the  tipple,  it  is  customary  to  make  the  tipple  height  60  ft. 
or  more,  even  in  those  cases  where  the  mine  cars  are  dropped  down  on  a  self- 
acting  incline.  This  permits  of  a  very  long  chute  in  which  may  be  stored 
enough  coal  to  fill  three,  four,  or  even  more  railroad  cars. 


568  OPENING  A  MINE 

Seams  of  Moderate  Dip.— Where  the  pitch  of  the  seam  does  not  exceed, 
say  30°  if  the  opening  can  be  placed  at  the  tipple,  it  is  probably  the  better 
plan  to  open  the  property  by  a  slope  driven  directly  down  the  dip.  The  seam 
may  then  be  developed  by  a  series  of  levels  driven  both  to  the  right  and  left 
on  grades  favorable  to  haulage,  and  the  mine  cars  may  be  run  directly  from 
these  levels  to  and  up  the  slope.  If  a  seam  of  this  pitch  is  opened  by  a  shaft, 
it  will  be  necessary  to  lower  all  the  coal  produced  on  each  level  to  the  mam  level 
driven  from  the  shaft  bottom.  While  this  lowering  is  commonly  done  on  self- 
acting  inclines  at  no  expense  for  power,  the  machinery  and  track  are  costly  to 
maintain  and  there  must  be  several  attendants  for  each  incline.  If  the  seam 
lays  in  the  form  of  a  syncline,  whether  it  is  better  opened  by  one  or  more  slopes 
driven  down  from  the  outcrop  or  by  a  shaft  tapping  the  basin  at  its  lowest 
point  should  be  made  the  subject  of  a  careful  calculation  by  these  methods. 

Seams  of  High  Dip.— Where  the  dip  of  the  seam  is  so  great  that  the  coal 
must  be  dumped  into  gunboats,  much  fine  coal  is  made  through  this  extra 
handling  While  this  is  not  objectionable  where  the  entire  output  is  coked  or 
even  in  those  cases  where  the  slack  alone  is  so  treated,  it  is  a  source  of  loss  at 
those  mines  where  a  large  percentage  of  lump  coal  is  desirable.  In  the  latter 
case  the  cost  of  production  is  less  and  the  coal  will  reach  the  surface  in  better 
shape  if  the  seam  is  opened  from  a  vertical  shaft  by  rock  tunnels  driven  there- 
from at  regular  intervals,  as  the  underground  haulage  is  less  and  the  mine  cars 
are  loaded  directly  on  to  the  shaft  cages.  As  before,  the  best  method  for  open- 
ing is  to  be  decided  after  striking  a  balance  between  increased  capital  account 
and  decreased  cost  of  production  and  higher  selling  price  because  of  the  larger 
percentage  of  lump  coal. 

Method  of  Working. — As  the  system  ad9pted  for  actually  extracting  the 
coal  may  have  some  effect  upon  the  location  and  method  of  opening  the 
mine,  the  section  entitled  Method  of  Working  should  be  consulted  in  connection 
herewith.  

DRIFTS 

The  size  of  a  drift  depends  on  the  output  desired,  the  size  of  the  mine  cars 
to  be  used,  the  character  of  the  haulage,  the  thickness  and  character  of  the 
coal  seam,  and  the  character  of  the  top  and  bottom  rock.  The  height  of  the 
drift  should  not  exceed  the  thickness  of  the  seam,  unless  absolutely  necessary, 
in  order  to  avoid  the  expense  of  brushing  (taking  down)  the  roof  or  lifting 
(taking  up)  the  floor.  There  should  be  at  least  6  ft.,  and  better,  6  ft.  6  in., 
from  the  top  of  the  track  tie  to  the  roof  or  to  the  bottom  of  the  timbers  used 
for  supporting  the  roof,  so  that  the  men  who  are  employed  at  the  mine  mouth 
in  handling  the  cars  can  walk  without  stooping. 

The  width  of  the  drift  depends  on  the  purpose  for  which  it  is  employed.  If 
used  solely  for  a  manway,  a  width  of  6  ft.  is  ample.  If  used  solely  as  an  intake 
airway,  the  drift  should  be  as  wide  as  economically  possible,  in  order  to  reduce 
the  friction  and  the  velocity  of  the  air  and  the  power  required  to  move  it. 
Common  widths  for  intake  airways  are  8  and  10  ft.  When  the  drift  is  used  for 
haulage,  about  the  least  width  that  can  be  used  when  any  allowance  is  made 
for  the  safe  passage  of  men  is  8  ft.,  and  10  ft.  is  much  better  in  view  of  the  fact 
that  the  average  haulageway  is  also  an  airway  in  which  the  mine  cars  form  a 
serious  obstruction  to  the  ventilation,  even  if  the  opening  is  of  good  size. 

When  the  drifts  are  used  for  haulage,  it  is  a  question  whether  the  empty 
and  loaded  trips  should  run  upon  parallel  tracks  or  whether  each  should  have  its 
separate  opening.  A  two-track  opening  will  have  to  be  16  to  20  ft.  in  width, 
and  if  the  roof  is  at  all  poor  the  cost  of  timbering  will  be  excessive.  For  this 
reason,  and  to  prevent  accidents  to  the  employes  from  trips  passing  in  opposite 
directions,  many  operators  prefer  distinct  openings  for  the  in-going  and  out- 
going traffic.  In  any  case,  posts  (props)  are  to  be  avoided  between  tracks. 

The  grade  of  a  drift  is  determined  by  the  dip  of  the  seam,  but  the  perfect 
grade  is  one  on  which  the  pull  required  to  return  the  empty  car  to  the  face  is 
exactly  equal  to  that  needed  to  bring  out  the  loaded  car.  A  grade  of  from  1  to 
1.5%  in  favor  of  the  loads  gives  excellent  results,  but  less  will  do  if  the  track 
is  well  kept  up  and  the  car  wheels  are  provided  with  roller  or  ball  bearings  to 
reduce  friction. 

A  gutter  or  ditch  is  commonly  dug  along  one  rib,  and  is  lined  with  tile  or 
concrete  or  has  a  wooden  trough  laid  in  it  if  the  bottom  is  soft  and  apt  to  erode. 
If  the  drift  is  being  driven  down  hill,  the  water  can  be  siphoned  out  for  some 
time,  after  which  a  small  steam,  compressed-air,  or  electric  pump  must  be 
used  for  the  purpose. 


OPENING  A  MINE 


569 


In  beginning  a  drift,  an  open  cut  is  first  started  in  the  hillside.  Its  width 
at  the  face  should  be  somewhat  wider  than  the  drift  itself,  and  the  two  wings, 
or  side  walls,  should  diverge  outwards  so  that  the  floor  plan  has  somewhat  the 
shape  of  a  truncated  V.  This  open  cut  should  be  continued  until  rock  firm 
enough  to  be  supported  by  timber  is  encountered,  when  a  substantial  set  of 
timbers  should  be  placed.  These  may  be  replaced  after  the  drift  is  sufficiently 


advanced  by  steel  beams  or  by  masonry  or  concrete.     When  the  coal  is  reached, 
ordinary  mining  operations  begin. 

In  order  to  prevent  the  hillside  from  washing  into  the  cut  and  blocking  the 
tracks  at  the  drift  mouth,  the  loose  material  above  the  opening  as  well  as  that 
forming  the  roof  and  sides  is  frequently  held  in  place  by  masonry  or  concrete 
walls,  arches,  etc.  Some  of  the  forms  employed  are  shown  in  the  accompany- 
ing illustration. 


TUNNELS 

TUNNELS  THROUGH  LOOSE  GROUND 

Unless  the  outcrop  of  the  seam  is  plainly  exposed,  it  is  well  to  put  down  a 
number  of  churn-drill  holes  along  the  supposed  place  of  outcrop  and  at  an  eleva- 
tion above  that  of  the  roof  of  the  coal.  These  holes  will  determine  the  char- 
acter of  the  covering  immediately  over  the  seam.  If  the  roof  rock  is  found  in 
place  but  a  short  distance  back  of  the  toe  of  the  crop,  the  drift.may  be  begun 
by  an  open  cut  as  just  explained.  If,  however,  the  outcrop  is  covered  with  a 
layer  of  wash  or  drift,  25  or  50  ft.,  or  more,  in  thickness,  it  is  not  generally 
possible  (owing  to  the  running  of  the  sides,  etc.)  to  proceed  with  an  open  cut. 
Instead,  some  one  of  the  methods  for  tunneling  through  loose  ground  must  be 
employed.  These  methods  have  been  very  completely  developed  in  connec- 
tion with  railroad  and  underwater  tunnels.  Among  the  numerous  processes 
are  forepoling,  wedging,  the  pneumatic  process,  the  freezing  process,  and  the 
use  of  metallic  shields;  the  last  three  are  described  under  the'  heading  Shafts. 

Forepoling. — Forepoling  is  used  when  driving  through  loose  ground  both 
at  the  outcrop  of  the  seam,  and  underground  where  the  coal  seam  is  replaced 
by  the  clay,  sand,  and  gravel  of  an  old  river  bed.  The  process  consists  in 
driving  sharpened  pieces  of  narrow  plank,  or  lagging,  into  the  roof  at  a  very 
slight  pitch.  The  lagging  rests  on  the  collar  of  one  timber  set  and  is  held 
firmly  by  having  its  end  underneath  the  next  timber  toward  the  outside. 


570 


OPENING  A  MINE 


In  the  cut,  a  are  the  posts  of  sets  of  timbers,  b  the  caps,  and  e  the  top  bridg- 
ing. The  front  ends  of  the  spiles  g  from  any  given  set  rest  on  the  bridging  of  the 

next  advanced  set,  and  the  spiles 
for  advancing  the  work  are  driven 
between  the  bridging  and  the  set, 
as  shown.  To  force  the  spiles 
into  the  ground,  so  as  to  provide 
room  for  the  placing  of  the  next 
set,  tail-pieces  *  are  placed  behind 
the  back  end  of  the  spiles  as  they 
are  being  driven.  After  the  spiles 
have  been  driven  forwards  the 
desired  amount,  another  set  is 
p]acedf  the  tail-pieces  knocked 
out,  and  the  front  end  of  the  spiles  allowed  to  settle  against  the  bridging 
of  a  new  set.  Where  the  face  is  composed  of  extremely  bad  material,  it  may 
be  necessary  to  hold  it  in  place  with  breast  boards  k  held  in  place  by  props  I 
that  rest  against  the  forward  timber  set.  In  a  similar  manner  the  side  lagging  h 
is  placed  in  position.  When  breast  boards  are  used,  it  is  generally  necessary  to 
employ  foot  and  collar  braces  between  the  sets,  so  as  to  transfer  the  pressure 
of  the  breast  back  through  several  sets. 

To  start  the  forepoling  at  the  mouth  of  the  drift,  several  sets  of  timbers  are 
set  up  and  long  lagging  driven  over  them  into  the  earth  beyond.  By  bal- 
ancing the  pressure  of  the  earth  on  the  points  of  the  lagging  with  a  weight  of 
stone  or  timber  on  the  outside  end,  they  are  held  up  and  enough  earth  removed 
to  allow  another  set  being  placed  to  support^the  lagging  nearer  the  tunnel  face. 
While  practicable  in  rather  loose  ground,  this  method  is  not  available  in  mate- 
rial containing  boulders,  and  is  dangerous  when  used  in  quicksand. 

Wedging. — It  has  sometimes  been  possible  to  drive  through  quicksand 
by  using,  in  combination  with  forepoling,  a  number  of  wedges  as  shown  in 
the  accompanying  illustration.  Here,  a  are  the  posts  of  regular  timber  sets; 
b,  the  side  planking;  c,  the  spiling  driven,  as  in  forepoling,  to  support  the  top; 
d,  the  wedges;  e,  the  tailing  pieces;  /,  the  floor;  g,  the  bridging  pieces;  and  h, 
the  cap  pieces.  The  set  of  timber  shown  below  e  is  only  placed  temporarily, 
and  is  removed  after  the  spile  c  is  driven  forwards. 

The  wedges  d  are  driven  into  the  face  by  means  of  a  ram  made  of  a  piece 
of  timber  swung  from  the  roof.  They  simply  crowd  the  material  away  from 


in  front  of  the  excavation;  if  the  pressure  becomes  so  great  that  they  can  be 
driven  no  farther,  a  few  auger  holes  are  bored  into  the  face  to  relieve  the  pres- 
sure by  allowing  some  of  the  material  to  flow  into  the  drift.  Wedges  are 


OPENING  A  MINE 


571 


driven  into  the  floor  with  a  mallet  as  fast  as  those  in  the  face  advance,  and  are 
ultimately  covered  with  a  plank  floor. 

TUNNELS  THROUGH  ROCK 

Tunnels  through  rock,  commonly  called  rock  tunnels,-  are  used  in  coal- 
mining operations  to  open  a  steeply  pitching  seam  that  extends  upwards  in 
the  hills  a  considerable  distance  above  drainage,  by  driving  across  the  measures 
to  the  coal  from  some  convenient  elevation  near  the  surface  plant.  They 
are  also  much  used  in  mines  where  the  strata  are  contorted,  as  in  the  anthra- 
cite regions  of  Pennsylvania,  to  connect  two  pitching  and  parallel  seams,  and 
to  drive  through  anticlines  or  synclines  in  those  cases  where  following  the  con- 
tour of  the  seam  would  result  in  the  gangway  being  either  too  crooked  or  too 
steep  for  successful  haulage. 

The  conditions  governing  the  location,  size,  etc.,  of  rock  tunnels  used  to 
develop  a  property  are  the  same  as  in  the  case  of  drifts.  If  the  surface  is  firm , 
the  tunnel  may  be  started  by  an  open  cut;  if  it  is  not,  forepoling  or  wedging 
must  be  resorted  to.  Underground  tunnels,  used  to  connect  adjacent  seams, 
etc.,  are  usually  made  as  small  as  is  consistent  with  safety  as  they  are  used 
mainly  for  haulage. 

Arrangement  of  Drill  Holes. — In  driving  rock  tunnels,  the  chief  item  of 
cost,  under  ordinary  circumstances,  is  that  of  drilling.  Where  machine  drills 


are  used,  there  will  be  more  or  less  time  consumed  in  shifting  machines,  for 
which  reason  it  is  deemed  advisable,  wherever  headings  are  large  enough,  to 
use  two  machines  and  if  possible  on  one  column  or  bar.  This  is  frequently 
also  the  case  in  shaft  sinking.  The  machines  should  be  so  placed  that  the  holes 
may  be  drilled  methodically,  so  as  to  economize  in  powder  and  time. 

In  tunnel  driving  and  in  shaft  sinking,  there  is  always  one  free  face,  and  in 
order  to  obtain  two  free  faces  it  is  necessary  to  first  take  out  a  cone  or  wedge 
of  rock  from  the  center  or  side  of  the  heading.  Holes  put  in  for  this  purpose 
are  termed  key  holes,  or  cut  holes,  and  are  fired  simultaneously,  in  order  to  obtain 
the  best  effect  of  the  powder  and  to  save  time. 

In  making  key  holes,  the  size  of  the  heading  and  the  hardness  of  the  rock 
are  to  be  considered.  In  soft  rock,  key  holes  in  the  bottom  may  be  the  best. 
In  harder  rock,  the  key  holes  may  be  arranged  in  circular  form  to  take  out  a 
cone.  The  outer  holes  are  then  arranged  more  or  less  concentrically  with  the 
center  cut  holes,  or  more  frequently  the  key  holes  are  arranged  in  straight 
lines  from  top  to  bottom  of  the  face  so  as  to  take  out  a  wedge-shaped  center 
cut.  _  The  enlarging  holes  are  similarly  arranged  in  straight  lines  parallel  to 
the  lines  of  key  holes. 

American  and  European  Practice. — -It  is  customary  in  some  European 
countries  to  place  the  breaking-in  holes  so  that  they  will  not  meet,  in  order 


572 


OPENING  A  MINE 


that  there  may  be  a  wide  end  to  the  cavity  broken  out  by  them;  American 
practice  however,  is  to  make  them  meet  so  that  the  increased  quantity  of 
powder  that  may  be  inserted  will  have  more  effect.  European  practice  is  gen- 
erally to  use  short  holes;  that  is,  one-half  the  width  of  the  heading,  while  Amer- 
ican practice  is  to  make  the  holes  about  as  deep  as  the  heading  is  high.  While 
the  two  systems  call  for  about  the  same  number  of  feet  of  drill  hole,  there  must 
necessarily  be  considerable  saving  in  time  where  drills  are  not  changed  as  often 
as  is  required  in  European  practice. 

The  American  system  is  probably  the  better  where  labor  is  expensive, 
since  it  permits  of  quicker  advance  and  keeps  the  shifts  up  to  their  work  in 
better  shape.  It  requires,  however,  more  explosive,  and  is  therefore  best 
adapted  for  countries  where  explosives  are  cheaper  than  labor. 

Conical  Center  Cut.— Fig.  1  (a)  shows  a  rock  heading  6  ft.  by  7  ft.  in 
medium-hard  homogeneous  rock.  The  key  holes  1  are  put  in  at  an  angle  so 
that  the  bottom  of  the  holes  will  meet  at  a  depth  of  about  6  ft.  from  the  face; 
view  (b)  shows  a  section  of  (a).  Where  drill  holes  meet  in  this  manner,  they 
form  a  chamber  in  which  the  powder  can  be  placed  in  larger  quantities  and  be 
more  effective  than  in  single  drill  holes.  The  direction  of  the  second  rows  of 
holes  is  shown  at  2,  and  the  third  row  at  3.  The  holes  are  all  drilled  in  one  shift, 
and  the  blasting  done  and  the  broken  rock  removed  by  the  following  shift, 
It  is  customary  to  charge  and  blast  the  holes  by  rounds,  1  being  first  fired. 


f\             y 

3                   3 

3 

9                     2 

:,3                       1 

3^, 

j€r^oc_,J 

y 

?     J     2 

3^  = 

444 

4 

*?                 n               fl 

y 

FIG.  2 

and  as  soon  as  rock  is  cleared  from  this  the  enlarging  holes  &  may  be  charged. 
It  is  sometimes  customary  to  fire  holes  2  and  3  together,  but  it  is  better  to 
fire  2  and  remove  the  dirt,  and  lastly  S,  as  that  gives  a  larger  free  surface  to 
work  on.  There  must  be  a  wait,  after  each  round  is  fired,  for  the  air  to  change, 
but  with  an  air  hose  the  foul  air  can  be  driven  out  quickly,  and  while  the  rock 
is  being  removed  the  next  round  may  be  charged.  The  number  8  round  is 
known  as  the  squaring-up  round,  and  while  the  holes  are  placed  a  short  dis- 
tance from  the  roof  and  floor  they  are  kept,  as  nearly  as  is  possible,  parallel 
with  the  side  walls.  That  they  are  not  put  in  exactly  horizontal  is  due  to  the 
inability  of  the  drill  runner  to  place  the  machine  nearer  the  walls.  The  num- 
ber and  position  of  the  drill  holes  for  enlarging  will  depend  on  the  size  of  the 
heading  and  the  explosive  used. 

In  some  cases,  the  bottom  holes  S  are  fired  after  the  upper  holes  S,  as  by 
that  operation  the  debris  is  moved  forwards  making  the  work  of  the  shovelers 
easier. 

Fig.  2  (a)  and  (6)  shows  another  arrangement  where  the  rock  is  hard.  The 
key  holes  1  m  this  case  are  four  in  number  and  outside  of  them  are  four  enlarg- 
ing holes  2.  It  might  be  possible  to  load  and  fire  holes  S  and  4  together,  but 
as  the  latter  are  in  tension  and  the  number  S  holes  are  assisted  somewhat  by- 
gravity,  better  results  will  probably  be  obtained  by  firing  number  4  holes  last. 


OPENING  A  MINE 


573 


It  is  to  be  understood  that  what  has 
been  stated  is  not  always  the  proper 
way  to  place  holes;  much  depends  on 
the  force  of  the  explosive,  the  hard- 
ness of  the  rock,  and  the  evenness  of 
its  texture.  The  miner  must  be 
guided  largely  by  experience  and 
common  sense,  in  finding  exactly  the 
best  position.  To  drill  extra  hand 
holes  for  squaring  up  a  heading  is 
unsatisfactory  and  expensive,  conse- 
quently, the  key  holes  that  furnish 
two  free  faces  are  the  particular  ones 
to  be  watched.  Key  holes  should  be 
placed  as  far  apart  as  experiments 
show  it  to  be  necessary  to  give  the 
best  results,  and  when  that  distance 
has  been  found,  it  should  not  be  varied. 
The  Billy  White  Cut. — Three  holes 
1,  2,  and  3,  Fig.  3,  are  drilled  straight 
into  the  breast,  exactly  in  a  line  with 
one  another,  at  a  distance  of  5  in., 
center  to  center,  thus  making  the  dis-  £ 
tance  over  all  12  in.,  assuming  the  | 
holes  are  each  2  in.  in  diameter.  An-  '  _, 

other  hole  4  is  drilled  7  in.  to  the  right  * IG-  8 

of  the  first  three  holes  and  in  a  horizontal  line  with  hole  2.     Hole  5  is  drilled 
12  in.  to  the  left  of  hole  2  and  in  the  same  line  as  hole  4.     These  five  holes 


complete  the  drilling  of  the  cut. 
5ust  enough  to  hold  water. 


FIG.  4  (d) 

All  are  put  in  horizontally  or  looking  down 


574 


OPENING  A  MINE 


The  success  of  this  cut  lies  mainly  in  drilling  the  holes  in  planes  with  one 
another  and  in  shooting  them  in  the  proper  rotation.  Four  of  them  are  loaded 
in  the  usual  manner,  care  being  taken  to  cut  the  several  fuses  of  slightly  vari- 
able length  so  that  the  holes  will  go  off  in  the  following  order;  viz.,  1,  3,  4, 
and  5.  Hole  2  is  drilled  merely  to  provide 
space  for  hole  1  to  break  to,  and  is  never  loaded. 
Each  shot  creates  more  clear  face  for  the  fol- 
lowing shot.  After  holes  1  and  8  have  gone, 
the  chamber  is  about  12  in.  vertically  by  5  in. 
horizontally  and  somewhat  oval  in.  section. 
After  all  the  holes  have  been  shot,  there  is 
produced  a  chamber  about  12  in.  by  21  in.,  as 
shown  in  the  illustration. 

The  cut  breaks  as  big  at  the  bottom  as  at  the 
collar,  and  to  a  depth  of  at  least  6  ft.     The  full 
bore  of  the  tunnel  is  obtained  by  the  usual 
placing  of  holes  that  will  break  to  this  initial  cut. 
Square-Cut  Drilling  and  Blasting. — A  center 
cut  is  taken  out  the  full  height  of  the  face  and 
all  subsequent  holes  are  drilled  in  lines  parallel 
T,       _  with  the  side  of  the  heading.     Fig.  4  (a),  (b), 

(c),  and  (d)  illustrates  the  square-cut  method 

driven  according  to  the  European  practice  in  blasting;  that  is,  the  holes  are 
not  more  than  one-half  the  width  of  the  heading  in  depth.  View  (a)  shows 
the  face  of  the  heading;  (b)  and  (c)  are  horizontal  sections,  and  (d)  is  a 
vertical  section. 

Two  or  four  drills  can  be  used  to  advantage  in  drilling  the  holes  for  the 
square-cut  system.  With  strong  hard  rock,  the  diameter  of  the  holes  will  be 
about  If  in.  at  the  bottom,  but  the  four  holes  1,  2,  3,  4  will  be  somewhat  shal- 
lower than  the  others.  It  will  also  be  noticed  that  there  are  only  three  upwardly 
inclined  or  dry  holes  to  be  bored  in  this  arrangement,  as  compared  with  four 
in  the  center-cut  systems,  Figs.  1  and  2.  As  the  drill  holes  are  always  slightly 
conical  (because  each  succeeding  drill  is  of  smaller  diameter  than  the  preceding) , 
the  four  shallower  holes  will  be  nearly,  if  not  quite,  li  in.  in  diameter  at  the 
bottom.  The  entering  wedge,  Fig.  4  (b),  is  best  removed  in  two  stages:  First, 
the  part  e  g  h  by  the  breaking-in  shots  1,  2,  8,  and  4,  and  then  the  part  e  f  h 
by  the  breaking-in  shots  5,  6,  7,  and  8.  The  order  of  firing  the  shots  is  as  fol- 
lows: First  volley,  1,  2,8,  and  4,  simultaneously;  second  volley,  5,  6,  7,  and  8, 
simultaneously:  third  volley,  9,  10,  11,  and  12,  either  simultaneously  or 
consecutively;  fourth  volley,  18t  14,  15,  and  16,  either  simultaneously  or  con- 
secutively; fifth  volley,  17,  18,  19,  20,  21,  and  22,  either  simultaneously  or 
consecutively.  The  effect  is  practically  the  same  whether  the  enlarging  shot 
holes  are  fired  simultaneously  or  consecutively,  on  account  of  the  fact  that 
they  are  top  far  apart  to  assist  each  other,  but  to  save  time  simultaneous 
firing  is  advisable. 

Side    Cut    in 
Heading. — Some- 
times   there    is     a 
natural    parting  at  Y/ 
one  side  of  the  head-  ' 
ing,    as    when    the  V 
heading  is  following  '/ 
a  vein  of  ore,  or  a  '/ 
slip  in  the  rock.   In  y 
such     a    case,    the 
side  cut  offers  very  '/ 
important      adyan    y 
tages  and  especially  '/ 
when  only  one  rock 
drill    is    employed    £? 

S'ofSMeS 
to  make  an  advance 
of  3  ft.  6  in.  in  a 
heading  by  means  of  a  side  cut.  The  order  of  firing  would  be  as  follows: 
First  volley,  1  and  2,  simultaneously;  second  volley,  3,  4,  and  5,  consecu- 
tively; third  volley,  6,  7,  and  8,  consecutively;  fourth  volley,  9,  10,  and  11, 
consecutively. 


40 

OA 

so 

OB 

CO 

oc 

DO 

OD 

£0       0 

oE 

FIG.  6 


OPENING  A  MINE  575 

Special  Arrangement  for  Throwing  Broken  Rock  from  Face. — Of  course, 
no  general  rules  can  be  laid  down  for  drilling  holes  under  all  circumstances, 
as  the  rock  may  vary  from  point  to  point  in  the  same  drift  or  heading,  and  the 
seams  or  joints  will  always  have  an  effect  on  the  results.  Fig.  6  illustrates 
a  set  of  holes  drilled  in  the  face  of  a  heading,  which  brings  out  another  princi- 
ple. In  this  case,  the  holes  are  fared  in  the  order  of  their  numbers,  the  holes  E 
being  fired  last.  It  will  be  noticed  that  there  has  been  an  extra  hole  placed 
at  the  bottom,  and  these  bottom  holes  are  sometimes  overcharged  in  order 
that  the  last  shot  may  have  a  tendency  to  throw  the  broken  rock  away  from 
the  face.  If  the  order  had  been  reversed,  and  the  upper  shots  fired  last,  the 
broken  rock  would  be  piled  against  the  face  of  the  heading  in  the  very  place 
where  the  drill  would  have  to  be  set  up  for  the  next  operation,  and  much  valua- 
ble time  would  be  lost  in  throwing  back  the  broken  material  before  the 
machine  could  be  set  up.  

SLOPES 

A  slope  resembles  a  tunnel,  a  drift,  or  a  shaft,  depending  on  its  inclination. 
A  flat  slope  is  treated,  -as  to  its  size,  method  of  driving,  timbering,  etc.,  essen- 
tially as  a  drift  or  tunnel,  while  a  steep  slope  is  treated  like  a  shaft.  Blasting 
in  a  slope  is  more  difficult  than  in  either  a  shaft  or  a  tunnel,  as  the  rock  is  said 
to  bind,  owing  to  the  inclination  of  the  strata;  and,  in  general,  it  may  be  said 
that  more  holes  and  more  powder  are  required  for  a  slope  than  for  either  a 
tunnel  or  a  shaft  of  equal  size.  The  amount  of  increase  in  the  width  of  the 
slope  pillars  as  the  slope  descends  depends  on  the  degree  of  pitch  of  the  slope, 
which  determines  the  thickness  of  cover  above  the  slope. 

The  removal  of  the  material  excavated  from  a  slope  is  more  difficult  than 
in  drifting  or  tunneling,  and  this  difficulty  increases  with  the  inclination  of  the 
slope.  When  starting  a  steep  slope,  as  when  starting  a  shaft,  the  material  is 
removed  by  the  use  of  a  windlass  for  drawing  the  car  up  the  slope,  or  a  small 
portable  hoisting  engine  may  be  set  up  when  the  slope  has  been  sunk  but  a  few 
yards. 

The  drainage  of  a  slope  is  accomplished  by  pumps  located  at  or  near  the 
foot,  small  sinking  pumps  placed  on  trucks  being  generally  used.  In  order 
not  to  be  obliged  to  move  a  large  pump  too  often  while  sinking,  inspirators, 
which  are  easily  moved  as  the  work  advances,  are  sometimes  used  at  the  slope 
bottom  to  throw  the  water  up  to  the  pump  station. 

The  timbering  of  a  slope  differs  from  that  of  a  drift  or  tunnel  in  the  man- 
ner of  setting  the  posts,  which,  in  a  slope,  are  underset  or  made  to  lean  up  the 
pitch  from  the  normal  position  in  the  seam,  or  from  a  position  perpendicular 
to  the  plane  of  stratification.  The  amount  the  post  is  underset  and  the  man- 
ner of  undersetting  vary  with  the  inclination  of  the  seam. 

Safety  Appliances. — The  necessity  of  safety  appliances  increases  with  the 
inclination  of  the  slope.  Refuge,  or  shelter,  holes  for  the  safety  of  the  men 
engaged  in  the  slope  should  be  made  in  the  sides;  in  some  states,  they  are 
required  by  law,  owing  to  the  liability  to  accident  to  men  by  being  caught  and 
squeezed  between  the  rib  and  a  trip  of  cars,  or  by  the  breaking  of  the  hoisting 
rope  or  car  couplings,  or  the  possibility  of  cars  descending  the  incline  before 
being  attached  to  the  rope. 

Safety  blocks  are  necessary  at  the  knuckle  or  the  head  of  all  inclines,  and  in 
some  states  are  required  by  law.  They  consist  of  pieces  of  heavy  timber  so 
arranged  as  to  prevent  cars  descending  the  incline  before  all  is  ready  and  the 
signal  given.  They  may  be  operated  at  the  knuckle,  by  the  topman,  or  head- 
man, or  from  the  engine  room.  The  block  is-  so  arranged,  by  means  of  a  spring 
pole,  weight,  or  spring,  that  the  ascending  cars  will  pass  it  without  difficulty, 
but  it  will  automatically  return  to  its  place  when  the  car  has  passed.  At  some 
slopes,  safety  blocks  are  arranged  at  regular  intervals  along  the  incline,  for 
the  purpose  of  preventing  the  descent  of  the  car  or  cars  if  the  hoisting  rope 
should  break. 

A  derailing  switch  is  sometimes  employed  either  instead  of  or  in  conjunction 
with  a  safety  block.  This  is  an  automatic  spring-pole  switch  similar  to  the 
switch  used  for  turnouts  in  mine  haulage,  and  permits  the  ascending  cars  to 
pass  on  the  main  track,  but  a  descending  car  will  be  switched  off  on  a  side 
track.  The  derailing  switch,  like  the  safety  block,  may  be  operated  from  the 
knuckle  or  from  the  engine  room,  as  desired. 

The  safety  dog  is  a  heavy  trailing  bar  attached  or  coupled  to  the  drawbar 
at  the  rear  of  the  ascending  car  or  trip  of  cars,  and  allowed  to  drag  along  the 
track  as  the  car  proceeds  up  the  incline.  The  lower  end,  which  drags  on  the 


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578  OPENING  A  MINE 

ground  may  be  either  pointed  or  split.  If  the  hoisting  rope  breaks,  the  weight 
of  the  car  on  the  incline  forces  the  dog  into  the  floor,  and  the  cars  are  either 
stopped  or  derailed. 


SHAFTS 

INTRODUCTION 

Form  of  Shaft.  —  A  shaft  may  be  circular,  elliptic,  polygonal,  or  rectangular. 
The  first  three  forms  are  better  adapted  to  withstand  pressure  than  the  rect- 
angular, but  they  are  more  difficult  to  timber,  and  there  is  always  a  consider- 
able area  of  the  cross-section  that  is  not  available  for  hoisting.  Such  shafts 
are  usually  lined  with  brick,  masonry,  concrete,  or  metal  instead  of  timber 
and  are  preferred  in  many  European  countries.  The  practice  of  lining  shafts 
with  concrete  is  growing  rapidly  and  many  of  these  have  their  sides  and  ends 
made  as  arcs  of  circles,  so  as  to  present  an  arch  to  the  side  and  end  pressures; 
the  approximate  section  of  the  shaft  is  then  elliptic.  Rectangular  shafts  are 
either  oblong  or  square,  the  former  being  the  usual  form  for  a  hoisting  shaft, 
while  the  latter  is  often  used  for  a  small  prospect  shaft,  or  for  a  second  open- 
ing to  be  used  as  an  escape  shaft  or  an  air-shaft.  Rectangular  shafts  are 
usually  not  lined  with  masonry  on  account  of  the  danger  of  the  walls  bulging 
from  the  pressure  of  the  strata  behind  them,  although  a  number  of  rect- 
angular shafts  have  been  lined  with  concrete;  timber  of  sufficient  size  is  gen- 
erally used  for  the  lining  in  these  shafts,  and  when  bulging  takes  place,  any  of 
these  timbers  can  be  taken  out  and  replaced  by  others  after  the  trouble  has 
been  removed. 

Compartments.  —  A  shaft  is  usually  divided  into  two  or  more  compartments, 
either  by  buntons  or  cross-timbers  placed  one  above  another  and  spaced  from 
6  to  8  ft.  apart,  or  by  solid  partitions  formed  of  3-in.  or  4-in.  planking.  If 
there  are  but  two  compartments,  both  of  them  may  be  hoistways  or  one  may  be 
a  hoistway  and  the  other  a  pumpway  and  ladderway.  If  there  are  three  com- 
partments, two  of  them  are  hoistways,  and  the  third,  and  smaller,  compart- 
ment, which  is  at  the  end  of  the  shaft,  is  used  for  a  manway  and  pumpway 
and  for  carrying  steam  or  compressed-air  pipes  or  electric  wires  into  the 
mine. 

Size  of  Shafts.  —  The  size  of  a  shaft  depends  on  the  use  for  which  it  is 
intended  and  is  determined  by  the  hoisting,  drainage,  and  ventilating  condi- 
tions at  the  given  mine.  Nothing  is  saved  in  sinking  a  shaft  of  too  small 
dimensions,  for  the  work  of  excavation  is  more  easily  accomplished  in  a  large 
shaft,  while  the  serious  annoyance  and  limitations  of  a  small  shaft,  and  the 
great  expense  of  enlarging  a  shaft  already  sunk,  warrant  a  shaft  of  generous 
size.  A  tight  shaft  is  one  in  which  there  is  but  little  space  between  the  curb- 
ing and  the  edge  of  the  cage.  In  such  a  shaft,  the  cage  acts  like  the  piston  of 
an  air  pump,  moving  the  doors  in  the  mine,  and  causing  a  general  disarrange- 
ment of  ventilation.  In  such  a  shaft,  also,  a  very  small  amount  of  ice  will 
interfere  with  hoisting.  Shafts  for  coal  mines  vary  in  size  from  5  ft.XlO  ft. 
to  12  ft.X54  ft.  inside  the  timbers.  Shafts  at  metal  mines  vary  in  size 
from  5  ft.X5  ft.  to  15  ft.X25  ft.  The  table  on  page  576  gives  interesting 
data  about  some  of  the  leading  American  shafts.  The  size  of  a  hoisting  shaft 
is  determined  by  the  output  of  material  required,  the  depth  of  the  shaft,  the 
speed  of  hoisting,  the  size  of  the  mine  car,  and  the  number  of  cars  hoisted 
at  one  time. 

Width  of  Shaft.  —  The  width  of  the  shaft  depends  on  the  size  of  the  car  to 
be  hoisted.  The  length  of  the  box  of  a  mine  car  is  determined  by  the  formula 


in  which  /«=  inside  length,  in  feet; 

c  =  capacity,  in  cubic  feet; 

6  =  average  breadth,  in  feet; 

d  =  depth,  in  feet,  including  the  topping. 

To  the  inside  length  of  the  car  calculated  by  this  formula,  must  be  added 
the  thickness  of  the  end  planks,  each  end  being  from  1  to  2  in.  thick,  and  the 
length  of  the  bumpers  at  each  end  of  the  car,  from  4  to  10  in.,  according  to  the 
style  of  car  used,  in  order  to  obtain  the  length  of  car,  out  to  out  of  bumpers. 
To  this  must  be  added  6  to  8  in.  for  clearance  between  each  end  of  the  car  and 


OPENING  A  MINE 


579 


the  cage,  and  6  to  9  in.  more  for  clearance  between  each  end  of  the  cage  and 
the  shaft  timbers,  to  obtain  the  width  of  the  shaft  in  the  clear. 

Cars,  for  use  in  coal  mines,  vary  from  4  to  6  ft.  in  width,  from  5  to  10  ft. 
in  length,  and  from  2  to  5  ft.  in  height.  Their  capacities  vary  from  1,000  to 
8,000  Ib.  and  their  weight  from  500  to  4,000  Ib. 

EXAMPLE.  —  Find  the  width  of  a  shaft  required  for  hoisting  an  output  of 
1,200  T.  of  bituminous  coal  per  day  of  8  hr.  from  a  depth  of  500  ft.;  the  seam 
is  5  ft.  6  in.  thick,  and  has  a  good  roof  and  floor;  the  specific  gravity  of  the  coal 
is  1.3. 

SOLUTION.—  Allowing  5%  for  delays,  the  net  time  of  hoisting  is  .95  X  (8X  60) 
=  456  min.  ;  the  output  is 

1'2004^2'00°^s>y.  5.263  Ib.  per  min. 

The  speed  of  hoisting  in  a  shaft  500  ft.  deep  varies  from  25  to  40  ft.  per  sec. 
Assuming  25  ft.  per  sec.,  the  time  of  hoisting  one  trip  is  500^-25  =  20  sec. 
Assuming  10  sec.  for  the  time  of  caging  and  uncaging,  the  total  time  for  each 
hoist  is  20+  10  =  30  sec.  Then  60  sec.  -J-  30  =  2  hoists  per  min.,  and  if  one  car  is 
hoisted  at  a  time,  the  weight  of  material  per  hoist  is  5,263-^-2  =  2,632  Ib.  of  coal. 

The  weight  of  bituminous  coal  having  a  specific  gravity  of  1.3  varies  from 
45  to  50  Ib.  per  cu.  ft.,  when  broken  (loose).  For  the  ordinary  mine  run, 
assume  48  Ib.  per  cu.  ft.;  then  the  capacity  of  a  car  is  2,  632-7-48  =  about 
55  cu.  ft. 

Assuming  that  the  depth  of  coal  on  the  car,  including  topping,  is  30  in. 
(2J  ft.)  and  the  inside  width  40  in.  (3|  ft.),  then  the  inside  length  is 


Adding,  to  the  inside  length,  4  in.  for  the  ends  of  the  car  and  12  in.  for  bump- 
ers, the  total  length  of  car  will  be  8  ft.  Then  adding  3  in.  clearance,  between 
each  end  of  the  car,  and  the  cage 
and  9  in.  at  each  end  for  shaft 
clearance,  the  required  width  of 
the  shaft  is  10  ft.  in  the  clear. 

Length  of  Shaft.—  The 
length  of  the  shaft  must  ordin- 
arily be  such  as  to  provide  for 
two  hoistways,  and  a  pumpway 
or  man  way.  The  width  of 
each  hoisting  compartment 
should  be  such  as  to  give  at 
least  6  in.  of  clearance  between 
the  greatest  width  of  the  car, 
out  to  out,  and  the  guides.  Al- 
lowance must  be  made  also  for 
the  width  9f  buntons  separating 
the  two  hoistways,  the  thickness 
of  the  guides,  and  the  width  of 
buntons  separating  the  hoisting 
compartment  from  the  pump- 
way.  According  to  the  size  and 
depth  of  the  shaft  and  the  char- 
acter of  the  strata,  the  thickness 
of  the  buntons  will  vary  from  4 
to  12  in.  The  size  of  the  guides 
often  employed  in  hoisting  shafts  is  4  in.X4  in.,  and  the  guides  are  commonly 
spiked  to  the  buntons. 

In  Fig.  1,  the  width  of  the  car  is  shown  as  40  in.,  out  to  out,  while  the  clear 
width  between  the  guides  in  each  hoistway  is  4'  ft.  10  in.,  giving  a  clearance  of 
9  in.  on  each  side  of  the  car.  The  size  of  the  guides  is  4  in.  X  4  in.,  making 
the  total  width  of  each  hoistway  5  ft.  6  in.  The  buntons  shown  in  the  figure 
are  6  in.  wide  and  the  pumpway  5  ft.  wide,  making  the  total.length  of  the  shaft, 
in  the  clear,  17  ft.  The  width  of  the  hoistway  also  depends  on  the  number 
and  size  of  cars  hoisted  at  one  time,  and  whether  two  cars  are  placed  side  by 
side  on  the  cage,  or  one  above  the  other  on  a  double-deck  cage. 

Fig.  2  shows  the  cross-section  of  a  shaft  where  two  cars  are  hoisted  side  by 
side  on  the  cage.  The  entire  length  of  the  shaft  in  the  clear,  including  hoist- 
ways  and  pumpways,  is  28  ft.,  giving  two  hoistways  each  9  ft.  10  in.  in  the  clear, 
between  guides,  and  a  pumpway  5  ft.  in  the  clear.  The  guides  are  each  4  in. 


580 


OPENING  A  MINE 


and  the  buntons  6  in.  wide;  the  width  of  the  cars  is  46  in.,  giving  a  clearance 
of  8  in.  on  each  side,  and  10  in.  between  the  cars.     This  is  a  very  large  shaft, 


FIG.  2 

being  capable  of  accommodating  an  output  of  between  3,000  and  4,000  T. 
per  da. 

SINKING  TOOLS  AND  APPLIANCES 

Buckets. — The  buckets  used  for  hoisting  the  material  excavated  in  shaft 
sinking  are  usually  made  of  boiler  iron  or  steel,  weigh  from  150  to  500  Ib.  and 
hold  from  2.5  to  14  cu.  ft.  or  more.  The  bucket  C,  Fig.  1,  is  commonly  swung 
between  handles  or  bails  b,  which  are  attached  to  the  hoisting  rope  by  a 
special  hook  provided  with  a  clip  or  extra  link  and  pin  for  securing  the  hook 
fastening  while  the  bucket  is  being  dumped;  or  two  hooks  with  the  points 
facing  and  closed  by  a  drop  link  g  passing  over  their  necks  may  be  used.  In 
the  common  form,  the  bail  is  attached  to  a  point  below  the  center  of  gravity 
of  the  bucket  so  that  the  tendency  of  the  bucket  is  to  turn  over  and  empty 
itself.  These  buckets  are  easily  dumped  but  have  been  the  cause  of  many 
fatal  accidents  through  overturning  while  hoisting  men  and  material.  A 
bucket  is  often  made  by  sawing  off  an  oil  barrel  just  above  the  second  hoop  from 
the  top,  and  riveting  to  the  lower  part  substantial  eyes  for  securing  the  bail. 
Buckets  with  drop  bottoms  are  sometimes  used  instead  of  the  form  described, 

and  while  a  greater  speed  in  re- 
moving material  is  claimed  for 
them,  they  are  dangerous  on  ac- 
count of  premature  opening  of  the 
bottom  and  sinkers  should  not  be 
allowed  to  ride  on  them. 

Bucket  Guides. — When  the 
shaft  is  deep,  the  bucket  has  a  ten- 
dency to  twist  or  spin.  This  may 
be  overcome  by  the  use  of  guides 
and  some  form  of  sinking  yoke. 
The  guide  ropes,  which  may  be 
made  from  old  but  unkinked 
hoisting  ropes  c,  Fig.  1,  are  either 
coiled  on  a  drum  and  lowered  as  the 
sinking  proceeds,  or  are  hung  from 
timbers  across  the  top  of  the  shaft. 
Large  weights  are  attached  to  the 
lower  end  to  keep  them  steady. 
The  hoisting  rope  passes  through  a 
hole  in  the  center  of  the  rider 
(monkey,  or  jockey)  d,  which  is  an 
iron  frame  consisting  of  two  legs 
joined  together  by  a  cross-bar,  and 
encircling  the  two  rope  guides 
loosely  at  the  four  points  d.  At 
the  bottom  of  the  shaft  timbers  stop-blocks  hold  the  rider  while  the  bucket 
goes  to  the  bottom  of  the  shaft,  thus  keeping  the  rider  and  the  guide  ropes 
out  of  the  way  of  the  sinkers.  As  the  bucket  is  hoisted,  the  rope  socket  picks 
up  the  rider  when  it  is  reached. 


OPENING  A  MINE  581 

In  some  cases  wooden,  instead  of  rope,  guides  are  used  and  the  bucket  is 
provided  with  a  yoke.  This  consists  of  two  wooden  uprights  carrying  the  guide 
shoes  and  two  crosspieces  holding  the  uprights  together.  In  each  crosspiece 
is  a  ferrule  through  which  the  rope  passes,  the  bottom  one  being  conical  to 
receive  the  rope  socket.  At  the  bottom  of  the  timbering,  blocks  are  bolted 
to  each  guide  to  prevent  the  yoke  passing  below  the  timbers,  while  the  bucket 
passes  down  to  the  bottom  of  the  shaft.  In  using  wooden  guides  and  yokes 
(crossheads),  the  former  must  be  parallel  and  have  smooth  joints  to  prevent 
the  yokes  from  hanging  while  the  bucket  continues  to  descend.  Should  the 
yoke  stick  and  subsequently  be  jarred  loose  and  fall  upon  the  bucket  a  serious 
accident  may  follow. 

Dumping  Buckets. — The  bucket  may  be  dumped  automatically  by  placing 
a  catch  hook  so  that  it  engages  one  side  of  the  bucket  rim  and  tips  it  as  the 
hoisting  is  continued,  dumping  the  material  either  into  a  car  or  chute.  Dump- 
ing the  bucket  while  over  the  shaft  is  dangerous,  as  small  stones  may  fall  down 
the  shaft  through  the  hole  provided  for  the  rope  in  the  shaft  covering.  It  also 
throws  a  considerable  strain  on  the  head-frame,  hoisting  gear,  and  rope;  and 
if  an  accident  occurs  to  the  hoisting  rope  while  dumping,  the  bucket  and  its 
load  may  fall  on  the  shaft  cover  with  sufficient  force  to  break  through  and  fall 
to  the  bottom.  A  better  arrangement  is  to  swing  the  bucket  clear  of  the  shaft 
by  means  of  a  short  snatch  rope-that  hangs  from  a  point  in  the  top  of  the  head- 
frame  and  at  one  side  of  the  shaft  opening.  The  hook  is  quickly  put  into 
the  bail  of  the  bucket  as  it  comes  up,  and  when  slack  is  given  by  the 
engineer,  the  bucket  is  swung  clear  of  the  shaft  and  dumped  or  transferred 
to  a  car. 

Several  buckets  are  often  used  for  hoisting  material,  and  as  soon  as  the 
bucket  has  passed  through  the  shaft  opening,  a  larry  or  truck  running  on  a 
broad  track  that  spans  the  shaft  opening  is  pushed  underneath  it,  the  bucket 
is  lowered  on  to  the  larry,  the  hooks  are  snapped,  and  an  empty  bucket  attached 
in  its  stead.  The  larry  is  then  moved  to  one  side  and  the  empty  bucket  low- 
ered into  the  shaft. 

Engines  and  Boilers. — When  sinking  small  and  shallow  shafts,  an  ordi- 
nary contractor's  hoist  is  commonly  used  in  which  an  upright  boiler  is  mounted 
on  the  same  bedplate  as  a  small  hoisting  engine.  For  larger  and  deeper  shafts 
the  engine  and  boiler  are  in  separate  units.  The  former  is  usually  placed  on  a 
temporary  foundation  of  heavy  timbers  and  should  be  powerful  enough  to 
pick  up  the  bucket  at  the  bottom  at  any  time  without  getting  stuck  on  the  cen- 
ter or  having  to  run  back  for  slack.  The  boiler  is  usually  of  the  locomotive 
type.  In  some  cases  the  permanent  boiler  and  hoisting-engine  plant  are 
installed  at  the  outset,  and  used  to  hoist  the  material  while  shaft  sinking. 

Sinking  Head  Frame. — The  sinking  head-frame  is  generally  designed  for 
temporary  use  only,  though  when  an  air-shaft  or  escape  shaft  is  supplied  with 
cages  or  a  bucket  for  hoisting,  the  sinking  tower,  or  head-frame,  may  be  left 
in  place  after  the  shaft  has  been  sunk.  It  is  usually  built  of  8"X8"  or  10"  X 12" 
pine  timbers  that  are  mortised  and  cross-braced,  or  tied,  with  heavy  iron  rods. 
Fig.  2  shows  an  unusual  form  of  frame  that  was  used  in  sinking  one  of  the  largest 
shafts  ever  sunk;  it  was  12  ft.  X  54  ft.  in  cross-section. 

Sinking  frames  are  sometimes  built  of  2%"X2?"  angle  iron;  in  some  cases, 
these  are  cheaper  than  those  made  of  timber,  as  they  are  put  together  with 
bolts  and  rivets,  which  can  be  easily  removed  with  less  damage  to  the  parts 
than  in  the  case  of  a  timber  frame  put  together  with  mortise  and  tenon.  Rail- 
road rails  are  laid  across  the  shorter  dimension  of  the  shaft  mouth  midway 
of  its  length  for  a  larry  track. 

A  single  sheave  from  6  to  8  ft.  in  diameter  rests  on  the  tower,  usually  at  a 
height  of  from  20  to  30  ft.  above  the  ground,  so  that  the  bucket  will  hang  in 
the  center  of  the  shorter  dimension  of  the  shaft.  Instead  of  using  a  head- 
frame,  a  derrick  is  frequently  used,  at  least  until  after  the  shaft  has  been  sunk 
through  the  surface  wash. 

In  order  that  the  work  of  sinking  may  not  interfere  with  the  progress  of 
the  permanent  work  about  and  over  the  shaft,  such  as  the  erection  of  the  main 
tower,  or  head-frame,  and  the  building  of  the  foundations  for  the  permanent 
hoisting  engine,  buildings,  etc.,  the  temporary  hoisting  engine  should  be  located 
at  one  end  of  the  shaft  (at  the  end  opposite  the  man  way  if  possible) .  The  man- 
way  is  divided  from  the  hoisting  compartments  by  a  close  partition  of  heavy 
timber.  The  buntons  separating  the  two  hoistways  are  put  in  later,  or  when 
the  sinking  is  completed.  The  head-frame  is  set  on  the  cross-sills,  just  inside 
the  main  sills,  so  as  not  to  interfere  with  the  erection  of  the  outer  posts  of  the 
permanent  head-frame.  By  this  arrangement,  the  hoisting  of  the  excavated 


582  OPENING  A  MINE 

material  may  continue  uninterruptedly  while  the  permanent  head-frame  and 
buildings  are  being  erected. 

The  waste  material  hoisted  out  of  the  shaft  is  dumped  about  the  shaft 
frame  and  about  the  foundations  of  the  permanent  machinery  and  a  level  sur- 
face is  thus  gradually  built  up.  If  the  ground  slopes  away  rapidly  from  the 
shaft,  it  may  be  necessary  to  build  a  trestle  for  the  larry  track.  A  smaller 
car  is  sometimes  placed  on  a  larger  truck  and  run  out  on  a  trestle  at  right  angles 
to  the  main  dumping  trestle. 

Shaft  Coverings. — In  order  to  prevent  material  falling  into  the  shaft,  the 
top  should  be  covered  with  3-in.  or  4-in.  plank,  excepting  the  portion  that  must 


PIG.  2 

be  left  open  for  the  passage  of  the  hoisting  bucket.  This  opening  may  be  simply 
covered  by  the  larry,  but  it  is  better  to  have  a  pair  of  doors  meeting  in  the 
middle  and  closing  down  flat,  or  as  shown  in  Fig.  3.  In  the  raised  position , 
they  rest  on  a  triangular  boxing  at  each  end  and  may  be  so  arranged  that  the 
ascending  bucket  will  open  the  doors  for  its  own  passage,  while  they  are  closed 
by  means  of  weights  not  shown;  or  the  doors  may  be  opened  and  closed  by  the 
levers  shown  in  the  figure.  The  balance  weights  should  not  hang  inside  the 
shaft  as  is  sometimes  done,  for  if  the  ropes  break  they  will  drop  to  the  bottom. 
When  the  doors  are  closed,  the  hoisting  rope  passes  through  a  small  hole  cut 
in  the  two  edges  of  the  doors. 


OPENING  A  MINE 


Ventilation  and  Lighting.  —  An  air-shaft  of  boards  erected  over  the  man- 
way  at  the  surface  serves  the  double  purpose  of  protecting  the  manway  and 
ventilating  the  shaft  by  means  of  a  * 
natural  air-current.  The  partition  | 
separating  the  manway  from  the  ' 
hoistway  should  be  kept  close  to 
the  bottom  of  the  shaft.  If  this 
does  not  produce  a  sufficient  cur- 
rent  of  air,  a  steam  jet  or  small 
blower,  such  as  is  used  in  a  black- 
smith's forge,  may  be  employed. 
Where  rock  drills  driven  by  com- 
pressed air  are  used  in  sinking, 
their  exhaust  will  commonly  pro- 
vide an  ample  supply  of  pure  air. 
fir 


In  some  cases  a  fire  of  wood  or 
coal  suspended  in  a  bucket  in 
the  shaft,  and  known  as  a  fire- 
basket,  is  used  to  produce  the  cir- 
culation. 

For  general  illumination  at  the 
shaft  bottom,  incandescent  electric 
lamps  protected  by  metal  baskets, 
are  to  be  preferred.  They  do  not 
foul  the  air  like  oil  lamps  and  may 
be  drawn  up  out  of  the  way  while 
blasting.  For  individual  use,  portable  electric  or  acetylene  lamps  are  to  be 
preferred  to  those  using  oil. 

SINKING  THROUGH  FIRM  GROUND* 

Preliminary  Operations.  —  Where  the  seam  is  flat,  the  long  side  of  the  shaft 
should  be  made  parallel  to  the  loading  tracks  so  that  the  chutes  may  be  at 
right  angles  thereto.  If  the  seam  is  inclined,  the  long  side  of  the  shaft  should 
be,  as  nearly  as  possible,  parallel  to  the  line  of  dip  of  the  coal;  in  which  case 
curved  loading  chutes  will  be  necessary  unless  the  lay  of  the  ground  permits 
the  tracks  to  be  shifted  into  parallelism  with  the  longer  side  of  the  shaft. 

The  shaft  is  staked  out  by  driving  eight  stakes  in  line  with  the  ends  and 
sides  of  the  shaft  and  outside  the  area  likely  to  be  disturbed  by  the  sinking 
operations  as  shown  in  the  cut.  The  lines  formed  by  the  side  stakes  are  at  a 
distance  apart  equal  to  the  \\idth  of  the  shaft,  and  the  distance  between  the 
lines  joining  the  end  stakes-is  equal  to  the  length  of  the  shaft.  Cords  stretched 
between  the  stakes  will,  at  their  intersections,  determine  the  four  corners  1,  2, 
S,  4,  of  the  shaft. 

Shallow  trenches  are  dug  on  each  end  line  and  in  them  are  laid  the  end- 
or  cross-sills,  which  extend  6  to  8  ft.  outside  the  shaft  line  on  each  side.  Similar 
side  or  main  sills  are  laid  across  the  end  sills  and  extend  4  or  5  ft.  beyond 
each  end  line.  The  sills  are  of  carefully  selected  12"X12"  or  12"X16"  oak. 
They  are  fastened  together  where  they  cross  one  another  by  square  boxings 
\  in.  to  2  in.  deep,  through  which  a  heavy  drift  pin  is  passed.  This  framing  is 
called  a  shaft  template  and  its  inner  sides  define  the  dimensions  of  the  shaft  in 
the  clear.  In  order  to  prevent  surface  water 
running  into  the  shaft  these  sills  are  fre- 
quently supported  on  blocking  with  clay 
packed  beneath  and  around  them. 

Sinking  Through  Earth  and  Loose  Rock. 
When  the  material  overlying  the  coal 
measures  is  composed  of  ordinary  earth  and 
loose  rock  free  from  water,  the  excavation 


iuuac   lu^ft.   iitc   iiyuj    wcitci,    nic   GA^CI  v  a  tnjn       »  ^ 

to   solid   rock  is   carried  on  by  means  of    Q t2 

ordinary  long-handled  shovels.  After  a 
depth  of  8  or  10  ft.  is  reached,  the  earth 
must  be  thrown  upon  a  staging  whence  a  i  ^f 

second  gang  of  shovelers  throw  it  to  the 

surface.     The  excavation  is  made   larger  than  the  inside  dimension  by  an 
amount  2  or  3  in.  more  than  the  thickness  of  the  lining.     Thus,  if  the  final 
size  of  the  shaft  is,  say,  10  ft.  X  26  ft.,  and  the  lining  is  1  ft.  thick,  the  ex- 
treme dimensions  of  the  excavation  will  be,  say,  12  ft.  4  in.  X  28  ft.  4  in. 
*  See  section  on  Timbering  for  methods  of  supporting  excavations. 


584 


OPENING  A  MINE 


Plumb-lines  are  suspended  in  each  corner  of  the  shaft  as  a  guide  for  the 
sinkers.  These  may  be  hung  from  a  triangular-shaped  piece  of  plank  nailed 
in  the  corners  of  the  template  or  from  an  iron  plate  screwed  upon  the  surface 
thereof.  In  either  case  the  supporting  device  is  perforated  with  a  small  hole 
to  receive  the  plumb-line,  which  hangs  4  to  6  in.  from  the  face  of  the  shaft 

The  lining  is  commonly  built  up  from  the  bottom  as  sinking  progresses, 
the  space  behind  being  filled  in  with  fine  material  to  distribute  the  pressure 
evenly  over  the  lining.  In  wet  ground,  the  space  behind  the  lining  is  rammed 
with  clay  to  prevent  the  inflow  of  silt  or  fine  sand  between  the  timbers.  The 
work  of  sinking  and  placing  the  lining  is  carried  on  alternately,  the  lining, 
except  when  sinking  through  rock,  being  kept  close  to  the  bottom,  say,  within 
6  to  8  ft.  at  the  most. 

Sinking  Through  Rock. — As  soon  as  the  strata  become  hard  or  firm  enough 
to  hold  the  explosive  charge,  powder  is  employed  and  churn,  hand,  or  machine 
drills  are  used,  the  type  of  drill  depending  on  the  character  of  the  rock.  In 
soft  rock,  a  churn  drill  is  used  and  a  light  lifting  shot  is  employed  to  dislodge 
the  material  from  its  bed.  This  material  is  afterwards  broken  by  wedges  and 
hammers  or  sledges.  For  this  class  of  work,  a  slow  large-grained  powder  is 
required.  A  quick  powder  exploded  in  soft  material  will  find  vent  by  a  single 


FIG.  1 


FIG.  2 


rupture  of  the  strata  without  exerting  the  lifting  force  on  a  great  mass  of  mate- 
rial, as  is  done  when  a  slower  powder  is  used.  If,  however,  the  strata  are  full 
of  seams  and  cracks,  a  small  charge  of  a  quick  powder  is  used,  since  such  rock 
will  not  confine  the  explosive  force  sufficiently  to  do  effective  work  when  a  slow 
powder  is  used.  In  hard  rock,  dynamite  is  used,  and  power  drills,  operated 
by  compressed  air  or  steam  and  usually  mounted  on  shaft  bars,  are  employed. 
The  general  position  of  the  holes  and  their  depth  are  about  the  same  as 
described  under  Tunneling.  The  first  shots  in  a  level  floor  should  be  inclined 
at  a  fairly  sharp  angle  with  the  floor,  and  are  usually  central  in  the  shaft.  These 
holes  are  often  called  sumping  hole.s;  their  purpose  is  to  start  the  excavation 
by  blowing  out  a  wedge-shaped  piece  of  rock  from  the  center  of  the  floor. 
The  holes  are  generally  arranged  in  series,  or  rows,  on  each  side  of  the  center 
and  across  the  width  of  the  shaft,  and- are  spaced  an  equal  distance  from  one 
another.  The  general  position  of  these  holes  is  illustrated  in  Fig.  1,  which 
also  shows  the  position  of  the  shaft  bar  on  which  the  drills  were  mounted. 
The  dimensions  given  are  those  that  were  employed  in  the  sinking  of  a  shaft 
m  a  white  crystalline  limestone.  In  this  shaft,  at  first,  only  6-ft.  cuts  were 
made,  a  single  series  of  shots  excavating  the  material  to  this  depth.  The  depth 
of  cut,  however,  was  afterwards  greatly  increased  by  boring  the  side  holes 


OPENING  A  MINE 


585 


deeper,  as  shown  in  Fig.  2,  until  the  cuts  averaged  11  ft.,  six  successive  cuts 
excavating  the  shaft  a  depth  of  66  ft. 

Fig.  3  illustrates  the  sinking  of  a  6'X  18'  shaft  in  limestone  of  varying  hard- 
ness.    The  position  of  the  shaft  bar  on  which  the  drills  were  mounted  is  shown 
at  a,  ci,  at,  b,  b\,  bt.     The  two  center  rows  of 
holes  1,  or  the  sumping  holes,  were  drilled 
first,  and  each  hole  filled  with  from  five  to  seven 
f-lb.  sticks  of  giant  powder  or  dynamite,  con- 
taining 50%  of  nitroglycerine.     The  depth  of 
the  holes  varied  from  3$  to  6  ft.     Beginning 
at  the  center,  the  successive  rows  of  holes, 
marked  1,  2,  3,  and  4,  respectively,  on  both 
sides  of  the  shaft,  were  drilled,  charged,  and 
fired  in  pairs,  the  material  being  loaded  and 
hoisted  between  each  operation.    The  end  holes 
required  but 
mite  apiece;  m«-  ^,. 
used  from  50  to  60 

vated  the  material  to  a  depth  averaging  from 
3i  to  6  ft.  The  average  quantity  of  40%  and 
50%  dynamite  used  in  this  material  was  12  Ib. 
per  ft.  of  depth,  or  3  Ib.  of  dynamite  per  cubic 
yard  of  excavation.  The  sinking  was  carried 
on  by  three  shifts  of  four  men  each,  and  the 
record  of  the  sinking  showed  a  depth  of  100  ft. 
in  30  working  da.,  or  an  average  of  3?  ft.  per  da. 

Long-Hole,  or  Continuous-Hole,  Method. 
As  in  sinking  in  rock,  much  time  is  ordinarily 
lost  in  drilling;  and  as  machine  drills  cannot 
work  close  to  the  sides,  ends,  or  corners  of  the 
shaft,  the  continuous-hole  method  is  some- 
times used.  By  this  method,  a  number  of 
diamond-drill  holes  are  put  down  at  definite 
distances  apart,  and  from  100  to  300  ft.  deep, 
over  the  area  where  the  shaft  is  to  be  sunk. 


FIG.  3 


They  are  arranged  in  rows,  from  3  to  4  ft.  apart,  with  the  outside  rows  close 
to  the  sides  and  ends  of  the  shaft,  so  that  they  will  nearly  square  it  up  and  save 
much  digging  and  trimming.  They  are  then  filled  with  sand  or  water,  pref- 
erably the  former.  The  sinkers  prepare  for  the  work  of  blasting  by  remov- 
ing 3  to  4  ft.  of  sand  from  the  holes  and  filling  this  space  with  explosives, 
which  are  tamped  and  fired. 

Fig.  4  shows  how  the  holes  are  arranged.  The  holes  marked  a  are  first 
cleaned  and  fired  to  give  a  loose  end  to  the  holes  b  on  the  outside,  which  are 
next  cleaned  out  and  fired.  This  work  is  continued  until  the  bottom  of  the 
hole  drilled  by  the  diamond  drill  is  reached,  when  another  series  of  long  holes 
is  drilled. 

This  method  probably  originated  from  one  that  is  sometimes  used  in  the 
coal  fields  of  the  Central  Basin.  Shafts  are  sunk  about  the  diamond-drill  hole 
that  has  been  used  in  prospecting,  and  from  which  the  casing  has  been  with- 
drawn, or  is  drawn  as  the  sinking  proceeds.  The  sinkers  charge  a  section  of 
the  hole,  using  a  false  bottom,  and  blow  out  a  center  cut. 

— ,  When  shafts  are  sunk  to  workings  al- 
*  ready  opened,  a  diamond-drill  or  churn-drill 
hole  is  sometimes  put  down  into  the  open 
works  below,  and  this  hole  is  kept  open  during 
sinking,  thereby  avoiding  all  hoisting  of  water. 
A  long  chain  is  used  to  clean  out  the  hole 
when  it  becomes  stopped  up. 

Both  this  plan  and  the  long-hole  plan  are 
apt  to  cause  crooked  shafts,  on  account  of  the 

[•&__ •.& •& •*__.?*.    divergence  of  the  drill  hole  from  the  vertical. 

"FIG  4  The  advantages  of  the  long-hole  system  are 

that  sinkers  need  not  wait  while  holes   are 

being  drilled;  and  blasting  can  be  done  as  soon  as  debris  from  shots  is  removed. 
The  method  is  said  to  be  very  much  quicker  than  the  ordinary  practice  of 
using  power  drills  driven  by  air  or  steam,  but  is  more  expensive. 

Timbering  is  usually  not  required  for  securing  the  sides  of  the  excavation 
when  sinking  in  hard  rock.  Cross-buntons  to  support  the  cage  guides,  pipes, 


*  •  * 


•<*         »a         •<» 


586  OPENING  A  MINE 

wires,  etc.,  are  set  in  hitches  in  the  face  of  the  rock,  and  are  spaced  6  or  8  ft. 
apart.  They  are  carefully  lined  and  placed  vertically  over  each  other  and  then 
tightly  wedged.  When  sinking  through  soft  shale  or  loose  crumbling  rock,  a 
greater  amount  of  timber  is  needed  for  securing  the  sides.  The  sides  are 
trimmed  with  the  pick;  and  when  the  material  is  dry,  a  close-fitting  lining  of 
3-in.  or  4-in.  planking  is  sufficient,  the  thickness  of  the  planking  increasing 
with  the  depth  of  the  excavation.  In  wet  material,  4-in.  timber  should  be 
used  at  the  surface,  6-in.  at  100  ft.,  and  8-in.  at  200  ft. 

Sinking  in  Swelling  Ground. — Clay  or  marl  that  swells  when  brought  in 
contact  with  air  and  water  is  difficult  to  excavate  and  support.  There  is  no 
power  that  can  prevent  this  swelling;  it  will  burst  any  timber  or  break  any 
frame  that  can  be  put  in.  When  sinking  a  shaft  or  a  slope  under  such  condi- 
tions, the  strata  should  be  excavated  for  a  certain  depth  back  of  the  lining  so 
as  to  give  a  good  clearance  between  the  formation  and  the  lining  all  around 
the  shaft.  This  space  should  be  so  arranged  that  a  man  can  enter  it  and  clear 
it  from  time  to  time  as  may  be  required.  Drainage  should  be  provided  by 
cutting,  in  the  hard  pan  or  floor  underlying  such  strata,  a  ditch  connected  by 
a  pipe  with  the  sump  at  the  foot  of  the  shaft.  A  good  circulation  of  air  should 
be  made  to  travel  around  the  space  thus  excavated  so  as  to  keep  the  clay  as 
dry  as  possible. 

The  method  of  sinking  through  such  ground  does  _not  differ  materially 
from  that  used  in  other  loose  ground  or  rock,  but  the  timbering  of  the  exca- 
vation is  of  great  importance. 

SINKING  THROUGH  RUNNING  GROUND* 

Draining  the  Ground. — Where  beds  of  quicksand  or  loose  water-bearing 
sand  or  gravel  are  supposed  to  occur,  the  ground  should  be  thoroughly  drilled 
before  sinking  operations  are  begun,  and  in  localities  where  such  deposits  may 
be  expected  there  should  be  kept  on  hand  an  ample  supply  of  the  materials 
required  during  sinking.  Timber  of  different  sizes  should  be  framed  and 
ready  for  instant  use,  and  pumps  and  piping  of  the  proper  kind  and  capacity 
should  be  on  hand.  Eight  or  ten  pointed  pipes,  with  perforated  ends,  are 
sometimes  driven  into  the  sand  6  or  8  ft.  apart  and  connected  at  their  upper 
ends  to  a  suitable  pump.  In  some  cases,  a  few  hours'  pumping  draws  off  the 
water  and  the  boiling  sand  settles  and  solidifies  so  that  it  may  be  removed  with 
a  shovel.  Water  can  sometimes  be  drained  from  the  soft  ground  within  the 
area  of  the  shaft  into  wells  or  small  temporary  shafts  sunk  adjacent  to  the  larger 
shafts,  thus  leaving  the  sand  within  the  shaft  area  compact  and  easily 
removable  by  shoveling. 

When  the  watery  sand  is  thus  drained,  there  is  a  considerable  decrease  in 
volume  of  the  material  surrounding  the  sides  of  the  shaft;  the  shaft  lining  is 
thus  frequently  robbed  of  all  supporting  material  for  a  considerable  distance 
up  the  shaft  and  begins  to  separate  and  sag,  while  the  shaft  may  be  swung 
out  of  line.  This  decrease  in  volume,  or  displacement  of  the  strata,  due  to  the 
draining  off  of  the  water,  may  be  carried  to  such  an  extent  that  the  surface 
of  the  ground  will  sink  several  feet  over  a  large  area  surrounding  the  shaft. 
In  removing  the  water,  a  large  amount  of  sand  is  also  removed;  the  effect  of  its 
removal  is  often  not  appreciated  until  too  late.  The  sand  contained  in  the 
water  will  often  cut  out  the  pump  linings  in  a  short  time,  and  render  the  pump 
useless;  but  if  a  layer  of  straw  or  other  light  material  is  thrown  into  the  shaft, 
it  will  form  a  mesh  by  which  the  sand  will  be  largely  filtered  from  the  water. 

The  methods  to  be  adopted  when  sinking  through  such  material  are  par- 
ticularly methods  of  timbering,  or  supporting,  the  sides  of  the  excavation; 
and  the  excavation  must  be  kept  timbered  close  to  the  bottom  of  the  shaft. 
There  are,  however,  certain  methods  of  sinking  that  are  particularly  applicable 
to  such  ground,  as  follows:  piling,  forepoling,  the  use  of  shoes,  the  pneumatic 
process,  and  the  freezing  process. 

Piling. — A  bed  of  quicksand  or  other  soft  material  lying  near  the  surface 
is  often  best  treated  by  piling.  If  the  bed  is  shallow,  it  may  be  sufficient  to 
drive  a  single  set  of  piles  all  around  the  site  of  the  proposed  shaft.  Where 
thicker  beds  of  quicksand  occur,  it  may  be  necessary  to  drive  several  series  of 
piles,  each  successive  series  being  driven  inside  the  former  after  the  material 
has  been  excavated  to  a  point  near  the  bottom  of  the  first  piles  driven.  The 
second  set  of  piles  having  been  driven,  the  material  within  these  is  excavated 
to  a  point  near  the  bottom  of  the  piles,  and,  if  necessary,  a  third  set  of  piles 
is  driven  within  the  second.  This  method  is  illustrated  in  Fig.  1. 

*See  section  on  Timbering  for  methods  of  supporting  excavations. 


OPENING  A  MINE 


587 


After  driving,  the  first  set  of  piles  a  should  be  strengthened  by  timber  frames 
or  timber  sets  at  their  top  and  half-way  of  their  length,  as  the  material  is  exca- 
vated from  the  space  they  en- 
close. It  is  important  that 
these  frames  should  be  set 
promptly  and  braced  by  cross- 
bun  tons;  they  are  supported 
by  punch  blocks  e.  As  will 
appear  from  the  figure,  it  will 
be  necessary  to  set  the  first 
sets  of  piles  back  a  sufficient 
distance  from  the  shaft  to  allow 
for  the  decreased  size  of  the 
excavation  when  each  series 
of  piles  is  driven.  This  dis- 
tance is  easily  calculated  when 
the  depth  of  the  sand  beds  is 
known  (and  this  is  given  by 
the  bore  or  drill  hole  t  made 
beforehand). 

In  some  cases,  the  soil  at 
the  surface  may  be  firm  for  a 
considerable  depth,  but  under- 
laid by  a  flowing  bed  of  quick- 
sand. In  this  case,  the  excava- 


tion of  the  overlying  soil  may 


FIG.  1 

be  done  in  the  usual  manner,  and  after  this  is  lined  or  curbed  the  piles  may 
be  driven  from  the  foot  of  the  excavation  in  the  same  manner  as  from  the  sur- 
face. In  this  system  of  sinking  through  watery  strata,  the  permanent  shaft 
lining  is  built  up  as  soon  as  the  rock  is  reached.  The  space  between  the 
shaft  lining  and  the  piles  is  then  filled  with  clay,  where  this  can  be  obtained, 
or  the  timbers  are  backed  with  a  sufficient  thickness  of  cement,  and  this,  in 
turn,  with  the  material  excavated. 

Forepoling. — Fig.  2  shows  a  method  of  forepoling  for  sinking  through 
quicksand,  very  similar  to  the  method  of  forepoling  described  under  Tunneling. 
Strong  timber  sets  j  are  framed  to  the  sides  of  the  shaft.  As  each  set  is  put  in, 
it  is  suspended  from  the  timbers  a  above  by  the  light  strips,  or  lath,  /,  while 
the  punch  blocks  b  are  set  between  the  frames  to  hold  them  apart.  Two-inch 
planks  with  the  ends  sharpened  are  used  for  the  spiles  k,  and  are  driven  down- 
wards in  an  inclined  position  behind  the  lower  timber  set.  Before  driving 

the  spiles,  the  tail-pieces  c  are 
spiked  to  the  lining  just  above 
the  lower  timber  frame;  the 
spiles  are  then  driven  as  the 
excavation  advances  until  their 
tops  reach  this  tail-piece.  An- 
other set  of  timbers  is  then 
placed  in  position  at  the  floor 
and  tied  to  the  timbers  above, 
and  the  same  operation  re- 
peated, driving  the  spiles  and 
excavating  the  material  as 
rapidly  as  possible.  This  proc- 
ess of  forepoling  may  be  carried 
on  at  any  depth  below  the  sur- 
face where  the  strength  of  the 
timbers  will  resist  the  pressure 
of  the  sand. 

Where  the  sand  is  thicker 
and  is  found  at  a  greater  depth 
below  the  surface,  the  spiles 
are  driven  in  at  a  flatter  angle, 
che  timber  frames  are  placed 
•pir  2  somewhat  closer  and  no  tail- 

piece is  employed,  the  tops  of 

the  spiles  bearing  against  the  timber  above  instead  of  against  the  tail-piece. 

Fig.  3  illustrates  the  use  of  breast  boards  where  the  bottom  has  a  tendency 

to  rise  and  fill  the  shaft  and  must  be  planked  to  keep  it  down.     The  material 


688 


OPENING  A  MINE 


is  removed  a  little  at  a  time.     A  sump  is  carried  ahead  of  the  regular  exca- 
vation by  driving  short  piles  and  putting  in  a  small  frame. 

Another  method  of  forepoling  requires  the  use  of  interlocking  channel  bars, 
as  in  Fig.  4.     The  shaft  is  started  2  ft.  larger  each  way  than  the  size  desired, 

and  sunk  in  the  ordinary  manner 
vl;  to  the  sand;  thus,  an  8' XI 6'  shaft 
•;;  must  be  started  as  10  ft.  X  18  ft. 
"i  The  lining  forming  the  sides  is 
i-:  composed  of  alternate  channels  a 
;•;  and  b.  The  channels  a  have  Z 
•/.  bars  c  riveted  to  them,  which  en- 
Xy  gage  and  interlock  the  edges  of  the 
';•:  channels.  The  channels  b  have 
•£•  angle  irons  d  riveted  to  them,  thus 
;'s  forming  grooves  in  which  the  sides 
V;  of  the  channels  a  run.  The  cor- 
£  ners  of  the  shaft  lining  are  made  of 
•v  three  angles  e  riveted  together,  as 
;•$  shown,  which  interlock  with  the 
,-f  side  and  end  channels  a  by  means 
:';'  of  the  Z  bar  riveted  to  a.  Heavier 
sections  can  be  used,  which  would 
make  the  thickness  of  the  metal 
about  \  in.  When  sand  is  reached,  these  channels  are  set  plumb  in  a  solid 
frame  inside  of  the  shaft  lining,  and  are  driven  vertically  downwards 
through  the  sand  to  the  solid  material,  if  possible,  before  any  sand  is 
excavated.  No  one  channel  should  be  driven  more  than  2  ft.  ahead  of 
the  rest.  A  perfect  fitting  anvil,  or  clinker,  is  used  to  protect  the  head  of 
the  channel  bar  while  driving.  Channels  12  ft.  long  are  readily  driven  their 
entire  length  into  the  sand.  The  sheathing  can  be  driven  to  varying  depths 
by  feeding  in  pieces  from  the  top,  thus  driving  the  preceding  one  down,  in  the 
same  manner  that  a  follower  is  used  when  driving  piling.  The  individual 
members,  engaging  and  interlocking,  slide  on  one  another  so  that  one  can  be 
driven  at  a  time,  and  thus  afford  an  opportunity  to  drive  channels  all  around  a 
boulder,  should  one  be  encountered.  The  channels  interlock  nearly  water- 
tight, and,  by  cementing  above  and  below  them,  the  water  may  practically 
be  shut  off.  The  channels  take  up  about  5  in.,  while  6  in.  should  be  allowed 
for  timber.  The  price  of  this  sheathing  or  lining  is  about  $2.50  per  sq.  ft., 
iin.  ft.  for  an  8'X16'  shaft.  The  channels  are  either  left  as  a  per- 


FIG.  3 


or  $120  per  lin 

manent  lining  or  they  may  be  drawn  after  a  timber  lining  has  been  laid. 

are  cheaper  than  steel  shoes  or  drums. 


They 


FIG.  4 


Shoes  for  Shaft  Sinking. — The  shoe  consists  of  a  wooden  or  metal  frame 
of  the  same  size  and  shape  as  the  shaft.  Attached  to  its  bottom  is  a  beveled 
steel  cutter  that  will  sink  easily  through  soft  ground.  While  the  shoe  is 
usually  open  at  both  top  and  bottom,  the  top  is  sometimes  closed  with  heavy 


OPENING  A  MINE 


589 


$  Sheer  iron  Lap 


Boiler  P/ate  a/larounct 


steel  plates  in  order  to  resist  the  pressure  of  the  sand  from  the  shaft  bottom. 

The  upper  part  of  the  shoe  is  outside  the  shaft  lining  from  12  to  16  in.,  and 

the  lower  part  is  usually  divided  into  compartments  by  braces. 
In  principle,  the  plan 

of  sinking  by  a  shoe  is 

similar  to  the  method  of 

tunneling  in  soft  ground 

with  the  use  of  an  advance 

shield,  except  that  shaft 

shoes    in    America    are 

usually     rectangular     in 

shape,  while  the  shield  in 

tunnel   driving  is    cylin- 

drical.     As   the   material 

is  excavated  from  beneath 

the  shoe,  the  shoe  drops 

by  its  own  weight  or  on 

account   of  pressure   ap- 

clied  to  its  upper  surface 

by  weights  laid  on  it  or 

by  means  of  jacks,  gener- 
ally the  latter,  thus  wall- 
ing back  the  sand,  while 

the  lining  is  being  put  in 

place.  Only  enough  ma- 
terial is  excavated  from 

underneath  the  shoe  and 

it  is  moved  just  far  enough 

ahead  to  permit  the  plac-  ,,        _ 

ing  of  one  set  of  timbers 

at  a  time;  if  planks  are  used  for  the  shaft  lining,  they  are  put  in  flatwise.     The 

shoe  should  descend  uniformly  at  all  points,  and  should  be  carefully  leveled 

before  the  timber  is  placed. 

The  steel  shoe  shown  in  Fig.  5  is  made  of  f-in.  steel  boiler  plate  braced  as 

shown,  has  a  height  of  30  in.  under  the  shaft  timbers,  and  a  sheet-iron  lap 
_     a  n     ~  18  in.  deep  extending  outside 

of  the  timbers.  Fig.  6  shows 
it  in  position  at  the  bottom  of 
the  shaft,  as  well  as  the  manner 
of  supporting  it  and  controlling 
its  descent.  Four  hooks,  or 
claws,  are  provided,  which  may 
be  screwed  into  the  lower  coup- 
lings, Fig.  7.  To  each  of  these 
hooks  is  fastened  a  strong  chain 
attached  to  the  frame  of  the 
shoe;  by  this  means,  the  down- 
'••;  ward  progress  of  the  shoe  is  con- 
x  trolled,  and  there  is  less  liability 
of  its  becoming  wedged  and 
thrown  out  of  line. 

One  of  the  disadvantages  of 
using  the  shoe  is  the  fact  that 
it  is  apt  to  be  stopped  by  boul- 
ders,  clay  seams,  or  other  ob- 
structions,  one  part  remaining 
stationary  while  the  other  goes 
down,  thus  throwing  the  shoe 
out  of  level  and  wedging  it  so 
tightly  that  it  cannot  be  moved, 
and  causing  the  shaft  to  be 
thrown  out  of  line  and  perhaps 
abandoned.  By  means  of  the 
chains  shown  in  Fig.  6,  this 
difficulty  is  partly  overcome, 


FIG.  6 


as  by  their  use  the  shoe  can  be  held  stationary  until  the  obstruction  is 
removed.  The  chain  may  also  be  slacked  at  any  time  to  allow  the  shoe  to 
move. 


590  OPENING  A  MINE 

The  cross-beams  of  the  shoe  frame  furnish  also  a  good  support  for  the  planks 
that  are  used  in  the  shaft  lining.  As  the  shoe  is  lowered  2  in.,  or  the  thickness 
of  a  plank,  the  latter  is  slipped  in  place  and  spiked  upwards  from  beneath, 
40-penny  nails  being  used  for  this  purpose. 

The  shoe  is  sometimes  forced  downwards  by  the  weight  of  the  lining,  if 
this  rests  directly  on  top  of  the  shoe  instead  of  hanging  from  the  top  of  the  shaft. 
The  lining  is  then  built  from  the  surface  by  adding  set  on  set,  the  increasing 
weight  gradually  forcing  the  shoe  through  the  soft  material. 

Owing  to  the  flowing  character  of  the  material  being  sunk  through  there 
is  a  tendency  on  the  part  of  the  shaft  lining  to  settle  and  draw  apart  and  for 
the  shaft  itself  to  be  thrown  out  of  a  vertical  line.  This  is  due  to  the  running 
into  the  bottom  of  the  shaft  of  a  large  amount  of  the  loose  material  from  the 
sides,  or  the  removal  of  the  water  in  the  sand  by  pumping  or  drainage,  as 
explained.  To  remedy  this,  the  lining  is  often  hung  from  a  strong  frame  at 
the  surface  or  at  some  point  in  the  shaft  where  a  firm  foundation  can  be 

Fig.  6  illustrates  the  hanging  of  the  lining  from  a  frame  or  built-up  beam 
at  the  surface,  by  steel  rods  coupled  to  each  other  in  lengths  of  10  ft.,  and  sup- 
porting at  each  coupling  a  cross-bunton  on  which  rests  the  intervening  lining. 
The  rods  may  be  of  any  convenient  length  until  the  sand  is  reached,  when 
their  length  should  be  about  10  ft.  The  size  of  the  rods  may  vary  from  1J  to 
2i  in  according  to  the  depth  from  the  surface,  the  size  decreasing  as  the  depth 
from  the  surface  increases.  The  lower  end  of  each  section  of  the  rods  is  passed 
through  a  hole  in  a  cross-bunton  b,  Fig.  7,  and 
an  iron  bearing  plate,  or  washer,  a  is  placed  over 
the  end  of  the  rod  underneath  the  bunton.  A 
screw  coupling  c  is  then  fitted  to  the  end  of  the 
rod  and  screwed  in  place.  This  coupling  fur- 
nishes the  support  for  the  next  section  of  rod 
below,  which  is  not,  however,  put  in  position 
until  the  excavation  has  reached  the  point  where 
another  cross-bunton  is  required.  Until  this 
time,  the  timbers  of  the  shaft  lining  are  sup- 
ported by  strips  of  lath  nailed  to  their  face,  or 
by  being  spiked  together  from  underneath  when 
flat  planks  are  used. 

In  some  cases,  instead  of  the  built-up  beam 
shown  in  Fig.  6,  the  rods  are  supported  from 
^  a  wooden  truss  fashioned  after  the  style  of  an 

p.       7  ordinary  highway  bridge.     In  other  cases,  the 

rods  are  supported  from  heavy  railroad  rails, 
steel  I  beams,  or  girders.  The  supporting  frame  should  extend  outwards 
beyond  the  shaft  to  solid  ground  so  as  not  to  be  affected  by  shifting  sands, 
and  should  be  strong  enough  to  support  the  weight  of  the  sinking  head-frame 
and  sheaves,  if  necessary.  These  frames  are  commonly  built  of  12"X12"  to 
16"X16"  white  oak. 

Pneumatic  Process. — The  pneumatic  process  used  for  sinking  shafts  is 
commonly  known  as  the  Triger  method  after  its  inventor,  and  is  an  adapta- 
tion of  the  caisson  method  used  in  building  bridge  piers  or  driving  tunnels 
through  mud,  as  beneath  a  river.  In  this  method,  a  cylinder  of  cast  iron, 
made  by  successively  adding  one  ring  to  another  at  the  surface,  is  made  to 
gradually  sink  into  the  loose  ground,  either  by  its  own  weight,  by  weights  piled 
on  top  of  the  cylinder,  or  by  means  of  pressure  applied  through  jacks.  In 
order  to  keep  out  the  water  from  surrounding  strata,  compressed  air  is  led  into 
a  closed  chamber  at  the  bottom  of  the  iron  cylinder,  the  pressure  of  the  air 
being  kept  just  sufficient  to  prevent  an  inflow  of  water  and  loose  sand.  This 
chamber  forms  the  working  space  in  which  the  material  is  excavated;  above  it, 
and  connected  to  it  by  suitable  trap  doors,  is  another  closed  space,  known  as 
an  air  lock.  This  air  lock,  by  means  of  trap  doors  above  and  below,  gives 
a  means  of  communication  between  the  working  chamber  and  the  surface.  A 
person  enters  it  through  the  upper  trap  door;  after  closing  this  door  he  allows 
the  compressed  air  from  the  working  chamber  to  enter,  by  means  of  suitable 
valves,  until  the  air  has  reached  the  same  pressure  as  that  in  the  working 
chamber  or  caisson;  the  lower  trap  door,  which  leads  to  the  caisson,  is  then 
opened  and  he  descends  into  the  working  chamber.  In  order  to  leave  the 
caisson,  the  opposite  procedure  is  adopted. 

The  excavated  material  can  either  be  removed  through  the  air  lock,  or  it 
can  be  blown  out  through  a  pipe  by  means  of  air  pressure  after  being  mixed 


OPENING  A  MINE  591 

with  water.  If  only  a  few  boulders  are  found  during  the  sinking,  they  are  car- 
ried down  in  the  caisson  and  are  hoisted  out  after  solid  material  has  been 
reached  and  the  roof  of  the  caisson  cut  away.  If  many  boulders  are  encoun- 
tered, they  must  be  blasted  and  the  pieces  hoisted  out  through  the  air  lock. 
In  some  cases,  the  metal  casing  on  top  of  the  caisson  forms  a  sufficient  lining 
for  the  shaft;  in  other  cases,  it  is  necessary  to  build  a  lining  of  timber  or  metal 
in'side  of  this  casing. 

Freezing  Processes. — In  the  freezing  process,  a  sufficient  thickness  of  the 
fluid  material  is  frozen  to  form  a  substantial  wall  around  the  shaft  so  as  to  per- 
mit the  excavation  of  the  material  encased  within  its  area.  Surrounding  the 
shaft,  a  series  of  holes  from  6  to  10  in.  in  diameter,  is  bored  through  the  sand 
bed  and  cased  with  ordinary  well  casing;  or  if  the  sand  is  very  fluid  the  casing 
may  be  driven  through  the  sand.  These  holes  if  bored  from  the  surface  are 
usually  vertical,  but  if  bored  from  a  point  in  the  shaft  a  few  feet  above  the  bed 
of  sand,  they  are  inclined.  They  are  not  more  than  3  or  4  ft.  apart,  in  order 
to  insure  the  thorough  freezing  of  the  sand  between  them.  Inside  these  casing 
tubes,  smaller  ones,  usually  about  4  in.  in  diameter  and  closed  at  the  bottom, 
are  let  down  to  the  solid  stratum,  and  the  outer  temporary  casings  withdrawn. 
The  4-in.  tubes  are  closed  at  the  top  with  metal  cap  pieces,  and  each  contains 
a  1-in.  tube  that  extends  almost  to  the  bottom.  The  1-in.  and  the  4-in.  tubes 
are  connected  at  the  surface  to  circular  mains,  each  vertical  tube  being  fitted 
with  a  screw-down  stop-valve  so  that  it  can  be  cut  off  from  the  main. 

There  are  two  freezing  processes  distinguished  by  the  character  of  the 
freezing  medium.  The  Pcetsch  system  uses  a  brine  composed  of  a  solution  of 
calcium  chloride  (or  magnesium  chloride)  passed  through  a  cooling  machine 
on  the  surface,  where  its  temperature  is  reduced  to  about  8°  F.  below  zero. 
The  solution  of  chloride  of  calcium  is  pumped  through  the  smaller  tube  to  the 
bottom  of  the  hole,  and  then  rises  through  the  larger  tube  to  the  surface. 
In  this  process,  the  material  is  frozen  first  and  hardest  at  the  bottom  where  the 
greatest  pressure  is.  Since  this  freezing  mixture  is  much  heavier  than  water, 
the  pressure  inside  the  pipes  is  greater  than  that  outside,  so  that  there  is  a 
tendency  to  burst  the  tube  conveying  the  freezing  solution,  thus  allowing  it  to 
escape  into  the  sand  outside  and  rendering  it  incapable  of  being  frozen. 

In  the  Gobert  system  anhydrous  ammonia  is  sent  down  the  inner  tube  (which 
is  then  usually  made  of  copper)  and  allowed  to  vaporize  in  the  tubes,  thus  freez- 
ing the  ground  directly  instead  of  allowing  it  to  cool  a  mixture  that  freezes 
the  ground  indirectly,  as  in  the  Pcetsch  process.  The  ammonia  gas  is  drawn 
off  by  a  pump  and  reliquefied  by  compression  and  used  over  again.  As  the 
pressure  is  less  inside  than  outside  the  tubes,  if  a  leak  occurs  in  the  tube  any 
water  entering  will  be  immediately  frozen  and  the  leak  thus  stopped. 

The  pipes  may  be  driven  well  outside  of  the  intended  shaft  area  and  a  wall 
of  earth  frozen  around  the  shaft,  the  central  portion  or  shaft  area  being  removed 
before  it  is  frozen.  In  most  cases,  however,  the  ground  has  to  be  frozen  solid 
and  then  blasted  as  though  it  were  rock. 

Cementation  Process. — Cement  injection  is  now  replacing  the  various 
freezing  processes  for  the  sinking  of  shafts  in  water-bearing  ground.  The  proc- 
ess appears  to  have  been  developed  in  the  chalky  formation  of  Northwestern 
France,  but  is  suited  for  any  fissured  water-bearing  rocks,  although  not  for 
soft  running  ground  such  as  quicksand.  It  consists  of  a  number  of  bore  holes 
sunk  at  equal  intervals  in  the  form  of  a  ring  surrounding  the  proposed  site  of 
the  shaft.  Cement  and  water,  injected  through  these  bore  holes  by  means  of 
a  force  pump,  find  their  way  into  all  the  cavities  and  crevices  of  the  ground  sur- 
rounding each  hole,  in  which  the  cement  sets.  As  the  cement  from  one  hole 
penetrates  the  rocks  surrounding  it,  that  coming  from  the  adjoining  hole  is 
encountered  and  a  cemented,  water-tight  wall  is  formed  around  the  proposed 
shaft.  In  France,  the  cost  of  sinking  by  this  process  is  found  to  be  about  one- 
third  that  of  the  Pcetsch  system. 

The  sizes  of  the  holes  through  which  the  cement  is  forced  vary  from  as 
much  as  12  in.  down  to  as  low  as  3  in.  The  larger  holes  are  commonly  sunk 
with  an  ordinary  oil-well  drilling  outfit,  but  the  smaller  ones  are  put  down 
with  a  diamond  drill.  The  pressure  under  which  the  cement  is  forced  into  the 
ground  varies  from  800  to  1,200  Ib.  per  sq.  in.  The  holes  are  drilled  to  a  depth 
of  from  10  to  20  ft.,  and  the  cement  injected.  After  it  has  set  about  30  hr. 
the  holes  are  drilled  out,  and  sinking  resumed.  When  solid  non-water  bear- 
ing rock  is  reached,  cementation  is  discontinued.  While  sinking,  the  various 
drill  holes  are  watched  for  signs  of  escaping  water;  if  such  is  noted,  cement  solu- 
tion is  again  injected  into  the  holes.  In  some  cases  as  an  additional  precau- 
tion, holes  are  drilled  horizontally  as  the  various  water-bearing  horizons  are 


OPENING  A  MINE 


encountered,  and  cement  injected.     The  open  spaces  behind  the  permanent 
shaft  lining  are  also  filled  with  cement  in  the  same  way. 

OTHER  METHODS  OF  SHAFT  SINKING 

The  Kind-Chaudron  system  is  applicable  only  to  the  sinking  of  circular 
shafts,  and  has  been  extensively  used  in  Europe  for  sinking  through  strata 
with  heavy  feeders  of  water  that  prevent  the  use  of  ordinary  methods.  The 
excavation  is  carried  down  to  water  level  by  the  ordinary  methods  ot  sinking, 
and  the  shaft  is  lined  to  this  point  with  timber  or  masonry.  Boring  is  then 
commenced  by  means  of  a  large  trepan  sus- 
pended in  the  shaft.  The  diameter  of  the 
excavation  to  water  level  must  be  suffi- 
cient to  allow  for  the  thickness  of  the  wall- 
ing or  timbering,  so  that  the  latter  will  not 
interfere  with  the  use  of  the  trepan  for 
sinking  below  this  level.  The  excavation 
is  effected  in  two  or  more  successive  opera- 
tions. The  first  trepan  used  cuts  a  hole  in 
the  center  of  the  shaft  from  4  to  5  ft.  in 
diameter;  this  is  called  the  guide  pit  and  is 
kept  at  least  35  ft.  in  advance  of  the 
second  cut,  which  is  made  by  enlarging 
the  guide  pit  by  means  of  a  special  trepan. 
During  the  entire  boring,  the  water  is  allowed 
to  accumulate  in  the  hole,  which  often 
stands  full,  and  the  boring  is  done  under- 
neath the  water. 

The  first  trepan,  or  cutting  tool,  Fig.  1, 
consists  of  a  horizontal  wrought-iron  bar  T 
having  steel  teeth  B  attached  below.  The 
action  of  the  cutting  tool  is  the  same  as 
that  of  a  churn  drill.  The  trepan  is  sus- 
pended in  the  shaft  by  means  of  heavy 
iron  rods  attached  to  a  large  walking  beam 
at  the  surface,  and  the  weight  is  partly 
balanced  by  a  counterpoise  at  the  other 
end  of  the  beam.  An  engine  operates  the 
beam,  raising  the  rod  a  height  varying  from 
10  to  20  in.  and  dropping  it  to  the  bottom. 
To  avoid  the  shock  caused  by  a  cutting 
tool  of  such  great  weight,  a  slide  bar  similar 
to  the  jars  in  the  American  rope  method  of 
drilling  is  used.  The  trepan  is  turned  by 
men  who  stand  on  a  platform  built  above 
the  level  of  the  water  in  the  shaft.  When 
making  this  first  cut,  the  hole  is  cleared  by 
means  of  a  sheet-iron  sand  pump  about 
6  ft.  long,  which  is  raised  and  lowered  by 
the  trepan  rods. 

The  second  cut  is  an  enlargement  of 
the  first  and  is  made  with  a  trepan  that 
usually  weighs  from  36,000  to  50,000  Ib. 
It  is  quite  similar  to  the  first  trepan,  being 
formed  of  a  wrought-iron  bar  having  teeth 
attached  to  that  portion  of  its  length  that 
exceeds  the  diameter  of  the  guide  pit.  It 
is  guided  by  means  of  a  cradle,  or  iron  bar. 
that  fits  closely  within  the  excavation  made 
by  the  smaller  trepan.  The  teeth  on  the 
large  trepan  are  "so  set  that  they  cut  the 


FIG.  1 


bottom  of  the  annular  portion  surrounding  the  guide-bore  pit  into  a  sloping 
surface,  so  as  to  allow  the  fragments  and  cuttings  to  roll  into  the  smaller  shaft, 
where  they  are  caught  in  a  sheet-iron  bucket  previously  lowered  to  the  bottom 
of  the  guide-bore  pit.  Sometimes  scrapers,  which  drag  around  after  the  trepan 
and  sweep  the  material  down  the  incline  and  into  the  bucket,  are  provided. 
The  excavation  having  been  made  of  the  required  size  in  two  or  more  successive 
operations,  the  shaft  is  lined  with  iron  tubbing,  which  is  built  in  sections  4$  or 
5  ft.  high  and  added  at  the  top  as  the  whole  is  lowered  from  the  surface. 


OPENING  A  MINE 


593 


s  bored  the  desired  diameter  at  one  operation  by 


To  assist  in  lowering  the  great  weight  of  the  steel  tubbing,  it  is  provided 
with  a  water-tight  bottom  in  which  is  a  nozzle  having  a  stop-cock  by  which 
a  sufficient  amount  of  water 
can  be  let  into  the  tubbing 
to  sink  it  gradually.  The 
tubbing  is  thus  floated  in 
the  shaft  until  it  finally 
rests  on  the  solid  bed  leveled 
to  receiye  it.  A  special 
moss  packing  below  the  tub- 
bing makes  a  watertight 
joint  when  the  water  is 
pumped  out. 

The  Lippman  system 
differs  from  the  Kind- 
Chaudron  in  that  the  shaft 

using  the  cutting  tool  shown  in  Fig.  2.     The  tools  are  made  and  the  cutting 
teeth  secured  in  a  manner  similar  to  that  employed  in  the  Kind-Chaudron  system. 

ENLARGING  AND  DEEPENING  SHAFTS 

Enlarging  Shafts. — Shafts  may  be  enlarged  by  extending  one  end  or  one 
side  of  the  shaft,  for  then  timbering  already  in  place  is  made  use  of,  the  aline- 
ment  of  the  shaft  is  maintained,  excavating  is  done  easily,  and  less  readjust- 
ment of  hoisting  sheaves,  stops,  etc., 
is  necessary.  In  order  not  to  inter- 
fere with  the  hoisting  of  coal,  the 
widening  operations  are  commonly 
carried  on  at  night. 

A  method  used  for  doing  the  work 
is  shown  in  Fig.  1.  Cleats  a  are 
nailed  on  the  old  lining  and  buntons 
b  placed  on  them  across  the  shaft; 
on  these  is  laid  a  temporary  platform 
on  which  the  men  work.  The  enlarg- 
ing is  begun  on  the  surface  and  car- 
ried downwards,  a  section  about  8  ft. 
high  being  taken  out  from  each  plat- 
form. The  drillers  work  on  the  rock 
bench  cd  and  load  the  waste  directly 


into    cars    on    the   regular      ostng 
cage.     The  end  ef  is  timbered  and 


ef  is 
inking 


hoisti 
red  a 

backed  as  in  sinking  a  new  shaft. 
The  timber  joints  at  the  corners  g  and 
h  are  left  undisturbed.  Each  alter- 
nate side  timber  is  taken  out  for  part 
of  its  length  and  a  new  timber  dove- 
tailed in  between  it  and  the  timbers 
above  and  below,  the  parts  being 
joined  by  a  feather-edge  joint.  The 
dotted  lines  show  the  original  posi- 
tion of  the  partitions  and  linings. 
These  cannot  be  moved  if  mining 
operations  are  being  carried  on  until 
the  widening  is  completed  for  the 
depth  of  the  shaft. 

If  both  the  length  and  breadth 
of  the  shaft  are  to  be  increased, 
mining  operations  must  be  suspended 
as  the  shaft  will  .have  to  be  entirely 
relined.  Shafts  have  been  enlarged 
and  retimbered  by  filling  them  to  the 
surface  with  cinders  and  ashes.  The 
retimbering  or  enlarging  begins  at  the 

pIG   -t  surface,  and  the  method,  while 

costly,  is  often  cheaper  in  the  end 

than  endeavoring  to  use  one  or  more  sides  or  ends  of  the  old  shaft. 

Deepening  Shafts.  —  First   Method.  —  A  false  bottom  of  heavy  timbers  is 

provided  in  the  sump  as  a  resting  place  for  the  cage,  and  sinking  is  begun  on 
38 


594 


OPENING  A  MINE 


the  bottom  of  the  sump.  When  the  new  seam  is  reached,  a  new  sump  is  made, 
new  guides  are  extended  from  the  bottom  upwards  to  meet  the  old  guides, 
the  false  bottom  is  removed,  and  the  cage  ropes  spliced,  or  new  ones  of  sufficient 
length  to  allow  the  cages  to  hoist  from  the  lower  seam  substituted  for  the  old 
ropes.  This  method  is  often  used  where  material  is  being  hoisted  during  the 
day  and  sinking  done  at  night.  A  small  sinking  cage  is  slung  under  the  regu- 
lar cage  or  a  bucket  is  used  instead,  the  material  being  hoisted  to  the  old  shaft- 
bottom  level  and  there  taken  back  into  the  old  workings  and  gobbed.  The 
disadvantages  of  this  method  are  that  all  the  water  from  the  old  sump  drains 
through  the  false  bottom  and  down  on  the  sinkers  at  their  work,  and  there  is 
always  danger  of  materials  falling  down  the  shaft  on  the  sinkers. 

Second  Method. — At  a  short  distance  from  the  shaft  bottom  and  on  a  pas- 
sageway that  is  not  much  used,  a  steep  slope  ab,  Fig.  2,  or  small  shaft  is  sunk, 
the  depth  of  sinking  depending  on  the  amount  of  rock  necessary  to  be  left  as  a 
support  under  the  old  sump  while  the  deepening  proceeds.  At  the  foot  of  the 
slope  a  level  heading  be  is  first  driven  to  the  opposite  face  of  the  shaft;  the  roof 
of  this  heading  is  strongly  timbered  by  setting  the  collars  in  hitches  cut  in  the 
sides,  before  the  work  of  excavating  the  shaft  below  is  commenced.  When  this 
is  done,  the  excavation  is  begun  and  carried  down  in  exact  line  with  the  shaft 
above,  the  material  being  removed  by  a  hoisting  bucket,  operated  by  a  wind- 
lass or  temporary  hoisting  engine  lo- 
cated at  some  point  near  the  head  of 
the  slope.  The  further  operation  of 
sinking,  timbering,  etc.,  is  the  same 
as  that  previously  described.  When 
the  sinking  is  complete  and  the  shaft 
timbered,  the  main  sump  s  is  drained 
and  the  two  shafts  connected  by  dri- 
ving downwards  from  the  bottom  of 
the  sump,  or  upwards  from  below 
from  a  strong  temporary  staging 
erected  at  c. 

Third  Method. — Fig.  3  shows  the 
method  of  deepening  a  shaft  while  the 
upper  part  is  in  use,  by  opening  only 
that  portion  of  the  shaft  area  not  un- 
der the  hoistway  for  a  distance  of  12 
to  15  ft.,  and  then  widening  it  out  the 
entire  size  of  the  main  shaft.  This 
leaves  a  roof  of  rock  (pentice)  that 
shields  the  men.  When  another  lift 
has  been  sunk,  the  pentice  is  cut  away 
and  another  started  for  the  next  drop. 
The  hoisting  is  done  by  an  under- 
ground engine  or  by  a  bucket  and 
windlass. 

The  main  hoisting  engine  may  be 
used  by  setting  out  one  of  the  cages  and 


FIG.  2 


passing  the  hoisting  rope  through  a  hole  drilled  through  the  pentice  and  attach- 
ing it  to  the  sinking  cage. 

Upraising. — Shafts  are  sometimes  driven  from  the  bottom  upwards  as 
when  two  parallel  seams  are  to  be  worked  through  the  same  opening.  From 
the  labor  standpoint  the  process  is  much  cheaper,  as  there  is  no  hoisting  to  do. 
The  material  extracted  is  generally  stowed  in  the  old  workings  below,  but  some- 
times when  room  is  not  available  it  is  sent  to  the  surface.  Before  commencing 
to  drive  upwards,  a  careful  survey  is  made:to  establish  the  four  corners  of  the 
shaft  in  the  mine  immediately  under  the  surface  location.  Four  iron  pins  are 
driven  in  the  bottom  to  mark  these  corners.  If  necessary,  posts  or  timber 
cribs  are  set  to  secure  the  roof  around  the  place  before  blasting  is  begun.  When 
the  excavation  has  proceeded  upwards  8  or  10  ft.  in  the  roof,  the  bottom  is 
cleaned  up,  the  pins  located,  and  the  shaft  tested  for  alinement  by  hanging 
plumb-bobs  in  each  of  the  four  corners.  Timbering  is  then  begun  by  first 
setting  a  heavy  square  frame/,  Fig.  4,  in  the  roof,  resting  on  substantial  posts 
a£d  sills,  as  shown  in  the  figure.  The  inside  measurements  of  the  frame  must 
correspond  to  the  size  of  the  shaft  in  the  clear  when  timbered.  This  frame  is 
exactly  located  by  means  of  the  plumb-bobs  hanging  over  the  four  points  pre- 
viously established,  and  is  then  firmly  wedged  in  place.  The  timbering  of  the 
shaft  is  built  up  on  this  frame  after  the  ordinary  manner  of  shaft  timbering. 


OPENING  A  MINE 


595 


The  timbering  is  carried  as  close  to  the  roof  as  practicable,  and  a  partition  is 
carried  up  dividing  the  shaft  into  two  compartments.  This  partition  may  later 
be  used  in  the  opera- 
tion of  the  shaft  as  one  i 
of  the  permanent  par- 
titions, and  should  be 
located  accordingly. 

A  heavy  bulkhead 
is  now  constructed  at 
the  bottom  of  the  shaft, 
and  a  chute  arranged 
under  the  larger  com- 
partment h,  by  which 
the  loose  material  ex- 
cavated above  and 
thrown  into  this  com- 
partment may  be 
drawn  and  loaded  as 
required.  To  control 
the  descent  of  the  loose 
material  in  this  com- 
partment, a  door  is 
arranged  at  the  foot 
of  the  chute.  The 
compartment  m  serves 
the  .double  purpose  of 
a  manway  and  air 
shaft,  and  for  this  pur- 
pose it  is  divided  by  a 
temporary  partition. 
A  ladder  is  constructed 
in  the  manway,  by 
which  the  workmen 
travel  up  and  down. 

In  the  operation  of 
upraising,  the  workmen 
ascend  the  manway  by 


the   ladder  and  stand    ""**' 
on  a  temporary  plat- 
form, or  on  the  loose  material  that  is  allowed  to  fill  the  compartment  h.     The 
material  is  drawn  from  this  compartment  only  as  is  required  to  furnish  good 

standing  room  at  the  face.  In  up- 
raising, the  ventilation  of  the  shaft  is 
always  more  or  less  difficult,  owing  to 
the  tendency  of  the  smoke  and  hot  bad 
air  to  remain  at  the  top.  The  air  com- 
partment may  be  connected,  by  a  box, 
to  the  main  air-course  while  the  man- 
way is  open  to  the  return,  or  vice 
versa;  by  this  means,  a  fair  current  of 
air  may  be  maintained  at  the  top  of  the 
shaft  or  upraise.  At  times,  a  small 
blower  is  used  to  blow  the  air  into  the 
face.  When  compressed  air  is  used  to 
operate  the  drills,  there  will  be  air 
sufficient  for  the  ventilation  of  the  up- 
raise without  making  other  provisions. 
The  timbers  required  must  be  taken  up 
the  manway  or  the  air  compartment. 
When  blasting,  the  manway  and  air 
compartments  are  covered  with  heavy 
planks,  to  avoid  the  material  loosened 
by  the  blast  falling  down  the  shaft. 

Of  these  methods  of  deepening 
shafts,  those  shown  in  Figs.  2  and  3 
are  generally  employed,  because  it  is 


FIG.  4 


unusual  to  have  a  lower  seam  open  in  advance  of  development;  a  condition 
that  is  assumed  to  exist  when  the  method  shown  in  Fig.  4  is  used. 


596 


OPENING  A  MINE 


FIG.  1 


SHAFT  DRAINAGE  AND  PUMPING 

Surface  water  is  kept  put  of  tho-  shaft  by  banking  around  the  shaft  sills 
the  clay  and  other  material  taken  out  during  sinking.  The  water  pumped 
or  hoisted  from  the  shaft  is  carried  away  in  tight  wooden  troughs  that  lead  in  the 
direction  in  which  the  surface  dips,  and  extend  far  enough  from  the  shaft  to 
prevent  the  water  from  returning.  Water  within  a  comparatively  short  dis- 
tance from  the  surface  can  be  drained  from 
the  shaft  by  sinking  a  well  or  small  shaft 
adjacent  to  the  main  shaft.  During  the 
sinking,  a  hole,  or  sump,  is  excavated  at 
one  end  or  in  the  center  of  the  shaft  some- 
what in  advance  of  the  general  work.  The 
water  is  either  bailed  out  of  this  hole  and 
hoisted  in  buckets,  or  a  sinking  pump  of 
special  form  is  employed.  These  pumps 
may  be  hung  by  hooks  from  the  timbering, 
at  any  point  or  simply  hung  by  ropes,  and 
may  be  hoisted  and  lowered  as  desired. 
Instead  of  a  special  sinking  pump,  a  small  horizontal  pump  of  ordinary  pattern 
is  often  set  up  on  a  temporary  staging,  which  is  moved  downwards  as  the 
work  advances.  Either  of  these  pumps  is  connected  with  the  steam  and 
water  pipes  in  the  manway  by  short  lengths  of  wire-wound  rubber  hose. 

Water  Rings. — To  draw  away  the  water  made  by  the  shaft,  a  notch  is  cut 
in  the  rock  as  shown  in  Fig.  1,  or  if  the  shaft  is  timbered  water  rings,  or  curb 
rings,  are  built  in  the  lining  as  shown  in  Fig.  2.  These  catch  the  water  run- 
ning down  the  lining  and  conduct  it  to  the  corner  of  the  shaft,  from  whence^ 
a  pipe  leads  it  to  the  sump  at  the  bottom  9r  to  a  lodgement  or  a  coffer  dam. 

Coffer  Dams. — A  coffer  dam  is  a  section  of  solid  lining  designed  to  dam 
back  water  coming  from  a  bed  of  water-bearing  rock.  Sufficient  material  is 
excavated  from  the  water-bearing  bed  to  allow  a  good  cement  backing  to  be 
inserted  behind  the  shaft  timbers.  This  excavation  should  be  carried  a  short 
distance  into  the  overlying  and  underlying  impervious  rock  so  as  to  form  a 
water-tight  joint.  The  space  behind  the  timbers  is  filled  with  concrete  either 
at  the  time  they  are  placed  or  later  through  an  opening  left  in  them.  The 
timber  is  often  made  much  stronger  and  heavier  at  this  point. 

Lodgements,  or  Basins. — Lodgements,  or  basins,  are  openings  from  6  to 
8  ft.  high,  equal  in  width  to  the  shaft,  and  driven,  usually,  from  the  end  thereof. 
As  they  extend  from  50  to  60  ft.  back  from  the  shaft  they 
hold  large  quantities  of  water,  which  may  be  pumped  thence 
to  the  surface  instead  of  from  the  sump  at  the  shaft  bot- 
tom, thus  effecting  a  large  saying  in  power.  They  are 
commonly  floored  and  lined  with  cement  to  prevent  the 
water  reaching  lower  levels  through  cracks  in  the  rock. 
The  mouth  of  the  lodgement  is  closed  with  a  timber,  or 
concrete,  dam,  in  which  an  opening  large  enough  to  admit 
a  man  is  left.  In  the  case  of  basins,  no  dam  is  necessary  as 
it  is  made  by  excavating  the  floor  of  the  lodgement  to  a 
sufficient  depth  to  hold  the  water. 

Sump. — The  shaft  is  carried  far  enough  below  the  cage 
landing  at  the  bottom  to  provide  a  catch  basin,  or  sump, 
large  enough  to  hold  the  water  draining  into  it  from  the 
shaft  and  workings  during  24  hr.  The  depth  of  the  sump 
will  be  the  height  to  which  the  suction  end  of  the  pump 
can  draw  water,  say,  25  ft.  at  sea  level.  Where  the  mine  _ 

makes  much  water,  the  area  of  the  shaft  is  not  sufficient  to  * IG-  • 

afford  the  required  capacity,  and  the  sump  must  either  be  extended  at  one  end 
or  a  second  sump,  draining  into  the  first,  must  be  provided. 


SLOPE  AND  SHAFT  BOTTOMS 

SLOPE  BOTTOMS 

At  the  foot  of  a  slope,  or  at  the  landing  at  any  lift,  the  entry  is  widened  out 
to  accommodate  at  least  two  tracks — one  for  the  empty  and  the  other  for 
loaded  cars.  The  empty  track  should  be  on  the  upper  side  of  the  entry,  or 
that  side  nearer  the  floor  of  the  seam,  and  the  loaded  track  on  that  side  of 
the  entry  nearer  the  roof  of  the  seam. 


OPENING  A  MINE 


597 


Fig.  1  shows  an  arrangement  of  tracks  often  used.     At  a  distance  of  40  or 

50  ft.  above  the  entry,  the  slope  is  widened  out  to  accommodate  the  branch 

leading  into  the  entry  loaded  track.     This  branch  descends  with  a  gradually 

lessening  inclination  un- 
til nearly  at  the  level  of 

the  entry  it  turns  into 

the  main  loaded  track. 

A  short  distance  above 

the    entry    and    below 

the  switch  b   a  hinged 

bridge  d  is  placed, 

which,    when    lowered, 

forms   a  connecting 

platform  or  bridge   by 

which  the  empty   cars 

are  taken  off  the  slope. 

The  empty  track  e  is 

about  6  ft.  higher  than 

the  loaded  track  /,  and 

is  carried  over  it  on  a 

trestle. 

The  figure  shows  the 

plan  A  and  profile  B  as 

arranged    for    a    single 

slope,  or  one  side  only 

of  a  slope  taking  coal  from  both  sides.     When  coal  is  to  be  hoisted  from 

this  landing,  the  bridge  is  closed,  the  empty  cars  lowered  in  the  slope  run  off 

over  the  bridge,  the  cars  unhooked  from  the  rope,  and  the  hook  and  chain 

thrown  down  to  the  track  below  on 
which  the  loaded  cars  are  standing;  the 
loaded  cars  are  then  attached  to  the 
rope  and  hauled  to  the  main  track  on 
the  slope  and  hoisted.  This  plan  can 
only  be  economically  employed  in  a 
seam  of  moderate  thickness  that  will 
not  require  the  taking  down  of  a  large 
amount  of  the  top.  The  cars  can  be 
handled  on  the  landing  by  gravity. 

Fig.  2  shows  an  excellent  method 
of  laying  switches  in  either  thick  or 
thin  seams  where  the  pitch  does  not 
exceed  20°.  When  there  is  only  one 
track  in  the  slope  and  coal  is  to  be 


B 


FIG.  1 


FIG.  2 


hoisted  from  both  sides,  the  same  arrangement  is  used  on  each  side;  but  to 
avoid  complications,  such  as  crossings,  etc.,  it  is  better  to  locate  one  of  the 
switches  on  the  main  track  farther  down  the  slope,  as  indicated  by  the  dotted 
lines.  The  empty  track  e  joins 
the  loaded  track  /  before  it 
reaches  the  slope  track  s. 

Fig.  3  shows  a  plan  A  and 
profile  B  ot  a  switch  used  at 
the  bottom  of  a  slope.  The 
figure  shows  one  side  only  of 
the  slope,  the  other  side  be- 
ing similar.  At  the  switch  a 
there  is  a  pair  of  spring  latches 
set  for  the  empty  track  e  and 
which  causes  the  empty  cars 
coming  down  the  slope  to 
take  this  track.  The  empty 
cars  pull  the  rope  in  to  where 
it  can  be  attached  to  the  loaded 
cars,  which  are  standing  near 
the  slope  on  the  road  /. 

Fig.  4  shows  a  cross-section 
of  the  slope  landing  shown  in 


FIG.  3 


Fig.  3  when  the  empty  track  e  is  higher  than  the  loaded  track  /,  so  that  both 
the  loaded  and  empty  cars  can  be  handled  by  gravity. 


598 


OPENING  A  MINE 


When  the  pitch  of  the  slope  is  so  steep  that  the  coal  or  ore  falls  out  of  the 

cars  during  hoisting,  a  gunboat  is  used  or  the  cars  are  raised  on  a  slope  car- 
riage— in  either  case,  the  arrangement 
of  the  tracks  at  lift  landings  is  entirely 
different.  With  either  a  gunboat  or  a 
slope  carriage,  the  arrangement  of 
tracks  on  the  slope  is  the  same;  but,  in 
the  former  case,  a  connection  between 
the  slope  and  empty  tracks  is  often  ad- 
visable. When  a  gunboat  is  used,  the 
empty  tracks  run  direct  to  the  slope, 
and  a  tipple,  or  dump,  is  placed  on 
each  side  to  dump  the  mine  cars  over 
the  gunboat;  but  when  the  cars  are 
raised  on  a  slope  carriage,  the  gang- 
way tracks  run  direct  (at  right  angles) 
to  the  slope,  to  carry  the  car  to  the 
cage  or  carriage.  The  floor  of  the  cage 
is  horizontal,  and  has  a  track  on  it 
that  fits  on  the  end  of  the  entry  track 
when  the-  carriage  is  at  the  bottom, 
and  this  track  is  arranged  with  stops 
similar  to  those  on  cages  used  in 
shafts. 
Another  common  arrangement  ot  tracks  at  the  bottom  of  a  slope  is  shown 

in  Fig.  5.     A  branch  is  made  by  widening  the  slope  out  near  the  bottom,  and 

this,  being  a  few  feet  higher  than  the  main  track,  is  used  to  run  off  the  empties 

by  gravity.     The  loaded  cars  run  in  by  gravity  around  the  curve  to  the  foot 

of  the  slope  in  position  to  be  attached  to  the  rope. 

In  ascending,  the  loaded  car  forces  its  way  through  the  switch,  or  the  switch 

may  be  set  by  a  lever  located  at  the  foot  of  the 

slope.     When  the  empty  car  descends,  it  runs  in 

on  the  branch,  where  the  chain  is  unhooked  and 

thrown  over  in  front  of  the  loaded  car,  and  runs 

around  the  curve  into  the  entry  by  gravity. 

It  will  be  observed  that  in  this  plan  the  loaded 

car  and,  consequently,  the  bottom  men,  stand  on 

the  track  in  line  with  the  slope,  and  are  in  danger 

from  any  objects  falling  down  the  slope,  or  from 

the  breakage  of  the  rope  or  couplings;  but  this 

can  be  obviated  by  making  the  bottom  on  the 

curve.     The  illustration  shows  only  one  side  of  the 

slope;  the  other  side  is,  of  course,  similar. 


FlG.  4 


FIG.  5 


pw«    MFBB  MOU*    WB  la,   Ul    U0WUVU    vMlliildl  . 

Ail  these  plans  necessitate  the  location  of  that  part  of  the  entry  near  the 
slope,  in  the  upper  benches  of  the  coal  or  near  the  top  rock.  The  gangway 
is  then  curved  gently  around  toward  the  floor,  so  that,  when  it  has  been  driven 
far  enough  to  leave  a  sufficiently  thick  pillar,  the  bottom  bench  is  reached 
arid  the  entry  is  then  driven  along  the  bottom  rock. 

A  very  different  bottom  arrangement  is  shown  by  Fig.  6,  which  also  rep- 
resents a  plan  frequently  adopted  on  surface  planes. 
The  two  slope  tracks  are  merged  into  one  a  short  dis- 
tance from  the  bottom  of  the  slope,  and  on  the  oppo- 
site sides  of  the  bottom  two  tracks  curve  around  into 
) LATCH  S£7  the  entry  on  opposite  sides  of  the  slope.  As  these 
Br  CAR  branches  curve  into  the  main  entry  tracks,  a  switch 
sends  off  a  side  track  for  the  empty  cars.  The  switch 
on  the  slope  is  either  set  by  the  car — and  this  can  be 
done  because  the  next  loaded  goes  up  on  the  same  side 
on  which  the  last  empty  descended— or  by  a  lever 
located  at  the  bottom. 

It  will  at  once  be  seen  that  in  this  plan  np  oppor- 

.   The 


FIG. 


tunity  is  afforded  of  handling  the  cars  by  gravity 
curved  branches  are  made  nearly  level,  and  the  mo- 
mentum of  the  descending  car,  if  quickly  detached, 
is  often  sufficient  to  carry  it  partly  or  wholly  around  the  curve,  even  against  a 
slight  adverse  grade.  The  disadvantage  of  having  the  bottom  in  direct  line 
with  the  slope  (where  there  is  danger  from  breakage  and  falling  material) 
also  obtains  in  this  plan. 


OPENING  A  MINE 


599 


In  the  plan  shown  by  Fig.  7,  the  grades  may  be  so  arranged  that  the  cars 
can  be  entirely  handled  by  gravity.  The  latches  on  the  main-slope  track  may 
be  closed  automatically  by  a  spring  or  weight,  the  loaded  car  running  through 
them  in  its  ascent  on  the  slope,  or  both  sets  may  be 
operated  by  a  single  lever  at  the  bottom.  The  switch 
at  the  upper  end  of  the  central  track  (loaded)  is 
set  by  a  hand  lever.  All  three  sets  may  be  linked 
together,  so  that  they  can  all  be  properly  set  by  a 
single  lever.  Reference  to  Fig.  5  will  show  that 
this  is  only  a  modification  of  that  method.  It 
requires  space  at  the  bottom  for  only  three  tracks, 
while  Fig.  7  requires  width  to  accommodate  four 
tracks,  and  is  objectionable  because  it  is  more  com- 
plicated. The  extra  set  of  latches  at  the  top  of  the 
central  track,  and  the  curvature  of  both  main  tracks 
into  this  central  one,  must  inevitably  cause  much 
trouble  and  delay  from  cars  jumping  the  track  at 
this  point. 

The  plan  shown  in  Fig.  8  is  open  to  many  of  the  objections  pertaining  to 
some  of  those  already  described,  and  which  need  not  be  reiterated  here.  It 
can  only  be  employed  in  thick  seams,  or  in  seams  of  moderate  thickness  lying 
at  a  slight  angle  or  dip.  v 

In  planning  the  arrangement  of  tracks  on  a  slope,  it  is  advisable  to  place 
as  few  switches  as  possible  on  the  slope  itself,  to  keep  the  main  track  unbroken, 
to  make  the  tracks  as  straight  as  possible,  to  have  nothing  standing  at  the 
bottom  in  direct  line  with  the  slope  tracks,  and  to  arrange  the  tracks  so  that 
cars  are  handled  by  gravity. 

The  arrangement  of  tracks  near  the  top  of  the  slope,  and  on  the  surface 
is  often  very  similar  to  the  bottom  arrangements,  as  already  described;  but 
as  all  loaded  cars  (except  rock  and  slate  cars,  which  are  run  off  on  a  separate 
switch)  are  to  be  sent  off  on  one  track,  and  all  the 
empties  come  in  on  the  same  track  to  the  head  of 
the  slope,  and  as  there  is  usually  abundance  of 
room  for  tracks  and  sidings,  these  top  arrangements 
are,  in  a  measure,  much  more  easily  designed.  In 
some  instances,  the  two  main-slope  tracks  run  into 
a  single  track  near  the  head  of  the  slope — a  plan 
somewhat  similar  to  the  bottom  arrangement  shown 
in  Fig.  6 — and  the  cars  are  then  brought  to  the  sur- 
face on  one  track,  which,  after  passing  the  knuckle, 
bifurcates  into  a  loaded  and  empty  track.  A  similar 
arrangement  is  frequently  adopted  at  slopes  on  which 
a  carriage  or  gunboat  is  used.  When  the  two  main- 
slope  tracks  are  continued  up  over  the  knuckle  to  the 
surface — the  most  common  and  best  plan — the  arrange- 
ment of  tracks  and  switches  may  be  planned  entirely 
with  a  view  to  the  quickest  and  most  economical 
method  of  handling  the  cars. 

Vertical  Curves. — The  vertical  curves  at  the  knuckle 
and  bottom  of  a  slope  or  plane  should  have  a  suffi- 
ciently large  radius,  so  that  when  passing  over  them  the  car  will  rest  on  the 
rail  with  both  front  and  back  wheels.  The  wheel  base  of  the  car  must  be 
considered  in  adopting  the  radius  for  these  curves,  for  if  the  curve  is  of  too 
short  a  radius,  there  is  danger  of  the  car  jumping  the  track  every  time  it 
passes  over  the  curve. 

SHAFT  BOTTOMS 

When  coal  is  received  on  one  side  of  the  shaft  only,  an  arrangement  of  tracks 
such  as  shown  in  Fig.  1  is  often  adopted,  by  which  the  empty  car,  when  bumped 
from  the  cage  s  by  the  loaded  car,  descends  a  short,  sharp  grade  to  b,  and  then 
by  its  own  momentum  ascends  a  short  grade  c  called  a  kick-back  and  return- 
ing by  gravity  passes  through  a  spring  latch  at  b,  by  which  it  is  automatically 
switched  and  passes  around  the  shaft  by  the  track  g  that  connects  with  the 
empty  track,  which  is  from  2  to  3  ft.  lower  than  the  level  of  the  loaded  track. 
At  times,  the  track  leading  around  the  shaft  passes  through  a  cross-over  to 
an  air-course  or  parallel  entry  occupied  by  the  empty  track,  instead  of  return- 
ing to  the  main  shaft  bottom  where  the  loaded  track  is  located.  Sometimes, 
the  loaded  track  is  in  line  with  the  center  of  the  shaft,  instead  of  as  shown  in 
the  figure,  the  switch  allowing  the  cars  to  pass  to  either  cage,  as  desired. 


FIG.  8 


600 


OPENING  A  MINE 


Where  there  is  not  room  back  of  the  shaft  for  the  length  of  track  shown  in 
the  cut  and  where  power  is  available,  the  empty  tracks  are  brought  together 


FIG.  1 

as  soon  after  leaving  the  cageway  as  possible.  At  the  point  of  the  spring  latches 
is  the  foot  of  a  power-djriven  chain  haul,  which  hoists  the  empty  cars  to  a  suf- 
ficient elevation  for  them  to  run  back  by  gravity  along  the  line  bd  to  a  con- 
nection with  the  main  entry  track.  The  height  through  which  the  empties 

are  hoisted  will  vary  from  4  to 
8  ft.  or  more,  and  depends  on 
the  length  and  grade  of  the  sid- 
ing bd.  A  profile,  of  the  ar- 
rangement is  shown  in  Fig.  2. 
in  which  s  is  the  shaft,  d  the 
switch  connecting  the  empty 


t  2 


and  loaded  tracks  on  the  main  road,  and  b  the  switch  back  of  the  shaft  between 
the  car  haul  track  and  empty  car  siding  bd. 

When  loads  are  caged  from  both  sides  of  the  shaft,  the  bottom  arrange- 
ments are  as  shown  in  Fig.  3,  or  some  modification  thereof.     The  grades  should 


Air  Shaf, 


Air  Course 


Empty  Trad 
Level 


IS. 


Loaded 
Track 


ILoaaea  trac 
'*'G'a« 


FIG.  3 

be  so  arranged  that  from  the  inside  latches  of  the  crossings  the  empty  track 
has  a   slight  down-grade  from   the  shaft,   and   the  loaded  track   a   slight 


OPENING  A  MINE  601 

down-grade  toward  it.  The  crossings  and  the  short  straight  piece  of  road 
close  to  the  shaft  should  be  level. 

As  it  is  often  necessary  to  move  cars  from  one  side  of  the  shaft  to  the  other 
without  stopping  the  hoisting,  a  narrow  branch  road  connecting  the  tracks 
on  opposite  sides  of  the  shaft  should  be  cut  through  the  shaft  pillar,  similar 
to  that  shown  in  bgd.  Fig.  1. 

Other  shaft-bottom  arrangements  will  be  found  in  the  section  on  Timber- 

GENERAL  BOTTOM  DETAILS 

In  arranging  tracks  for  shaft  bottoms,  at  tops  and  bottoms  of  slopes,  on 
coal  bins,  for  mechanical-haulage  landings,  at  foot  of  slopes  or  shafts,  or  in 
the  body  of  the  mine,  it  is  customary  to  provide  double  tracks  of  sufficient 
length  to  hold  the  requisite  number  of  cars  for  economically  operating  the 
plant  and  with  sufficient  distance  from  center  to  center  of  tracks,  and 
from  centers  of  tracks  to  sides  of  entries,  to  easily  pass  around  the  cars  where 
it  may  be  necessary,  either  in  handling  them,  or  in  lubricating  the  wheels. 
For  cars  with  a  capacity  of  from  1$  to  2  T.,  it  generally  requires  an  entry  to 
be  about  15  to  17  ft.  wide  in  the  clear  for  ordinary  landings  in  the  body  of  the 
mine,  while  at  shaft  bottoms  the  necessary  width  may  attain  17  to  18  ft.  in 
the  clear,  owing  largely  to  location  and  local  requirements.  The  curved  cross: 
overs  connecting  the  tracks  at  shaft  bottoms  should  be  designed  with  radii 
of  as  great  length  as  can  be  introduced,  thereby  giving  an  easy  running  track. 
They  should  not  be  less  than  from  20  to  50  ft.  on  center  lines  for  ordinary 
gauge  of  tracks,  i.  e.,  36  to  44  in. 

On  landings  constructed  in  the  body  of  the  mine  for  the  reception  of  empty 
and  full  cars  handled  by  mechanical  haulage  from  shaft  or  slope,  and  from  this 
point  transported  by  animal  power  to  the  various  working  places  in  the  mine, 
a  grade  of  about  1%  in  favor  of  the  loaded  cars  to  be  handled  by  the  stock 
will  be  found  quite  an  assistance  in  delivering  the  cars  to  the  haulage.  The 
frogs  and  switches  for  these  landings,  as  well  as  those  required  at  the  shaft  or 
slope,  should  be  formed  of  regular  track  rails,  and  can  generally  be  arranged 
to  be  thrown  by  a  spring  or  a  conveniently  located  hand  lever,  as  has  been 
described,  instead  of  being  kicked  to  position,  as  was  the  custom  at  one  time. 

Besides  these  usual  arrangements  of  shaft-bottom  landings,  at  many 
plants  the  natural  grades  of  the  entries  can  be  taken  advantage  of  in  design- 
ing convenient  and  economical  methods  for  handling  the  mine  cars.  For 
instance,  where  the  coal  is  to  be  hauled  from  the  dip  workings  of  a  mine  by 
some  form  of  mechanical  haulage,  and  a  summit  can  conveniently  be  arranged 
for  in  the  track  on  the  same  side  of  the  hoisting  shaft,  at  the  proper  distance 
therefrom,  to  accommodate  the  requisite  number  of  loaded  cars  to  be  hauled, 
thus  allowing  them  to  run  by  gravity  over,  say,  a  1%  grade  to  the  shaft,  sev- 
eral empty-track  arrangements  can  be  made.  The  most  simple  form  is  to  have 
the  empty  cars  descend  a  short  grade  of  from  4%  to  5%  when  pushed  from  the 
cage  by  the  succeeding  full  one.  The  momentum  thus  secured  is  quite  suf- 
ficient to  carry  the  car  up  an  opposing  grade  of  about  1.5%.  It  again  descends 
on  the  same  track,  and  passing  through  an  automatic  switch,  continues  to  the 
empty-car  siding.  From  this  latter  point  it  is  handled  by  the  regular  haulage 
machinery,  and  in  its  route  passes  around  the  shaft  through  an  _entry  especially 
prepared  for  this  arrangement.  A  shaft  bottom  so  constructed  is  very  economi- 
cal to  operate,  requiring  but  few  men  to  handle  the  cars. 

Occasionally,  it  becomes  more  expedient  to  have  a  separate  short  haulage 
to  draw  the  empty  cars  to  the  main  haulage  when  it  cannot  be  easily  arranged 
to  construct  a  complete  gravity  landing.  Several  other  modifications  of  such 
a  general  design  can  be  made.  All  the  different  devices,  however,  depend 
largely  on  the  local  requirements  of  the  particular  mine  under  consideration. 

When  endless-rope  haulage  is  employed,  it  is  generally  found  to  be  most 
convenient  to  have  the  landings  for  full  and  empty  cars  in  the  body  of  the  mine 
reached  by  switches  off  of  the  main-haulage  track,  the  cars  coming  on  and 
leaving  the  main  track  at  slight  knuckles  introduced  in  the  track,  in  order 
to  allow  a  place  for  the  passing  of  the  rope,  which  then  moves  along  through 
a  short  cut  or  channel  through  the  switch  rails.  The  flanges  of  the  cars  pass 
over  the  rope  in  this  manner  without  any  injury  to  it. 

Mine  Stables. — In  the  location  of  the  mine  stable,  the  following  points 
should  be  considered:  The  prompt  rescue  of  the  mules  in  case  of  accident;  the 
ventilation  of  the  stable  by  a  separate  split  of  fresh  air  without  contaminat- 
ing the  air-current  passing  into  the  mine;  the  handling  of  the  daily  stable  refuse 
and  feed  to  and  from  the  surface;  water  supply;  distance  from  the  stable  to 
the  working  face.  The  stable  is  generally  located  near  the  bottom  of  the  shaft 


602  OPENING  A  MINE 

especially  during  the  early  development  of  the  mine;  though  sometimes  later, 
and  after  the  workings  have  become  extensive,  the  stable  may  be  moved  to 
some  convenient  second  opening  or  air-shaft  where  the  mules  will  be  closer 
to  the  working  face  and  can  still  be  rescued  promptly  and  fed  and  cared  Tor 
economically.  One  arrangement  is  shown  in  the  accompanying  figure. 

Usually  no  door  is  required  at  the  entrance  to  the  stable,  but  a  regulatpr 
is  placed  at  its  rear  end  to  control  the  supply  of  air  entering  from  the  main 

As  a  protection  from  fire,  the  posts  for  supporting  the  roof,  as  well  as  the 
partitions  between  the  stalls,  the  doors,  etc.,  are  made  of  sheet  iron.  Very 
frequently,  the  walls  and  floors  are  coated  with  cement,  which  material,  but 
with  a  wooden  lining,  is  also  often  used  in  the  construction  of  the  feeding 
troughs.  Stalls  are  commonly  built  so  that  there  will  be  a  passageway  2  to 
3  ft.  wide  between  the  heads  of  the  mules  and  the  ribs.  Commonly  a  track 
is  laid  back  of  the  mules  so  that  all  manure,  straw  used  for  bedding,  and.  other 
stable  litter  may  be  loaded  into  a  mine  car  and  sent  to  the  surface  each  day. 
Wherever  possible,  underground  stables  should  be  provided  with  incandescent 
lights  hung  in  metal  wire  baskets. 

The  question  of  water  supply  for  the  stables  is  sometimes  a  troublesome 
one.  Where  the  mules  cannot  drink  the  mine  water,  as  is  usually  the  case, 
a  supply  of  water  must  be  piped  to  the  stable  from  the  surface.  It  is  impor- 
tant to  maintain  a  bar  or  chain  at  the  entrance  of  the  stable  to  prevent  mules 
that  get  loose  from  wandering  into  other  parts  of  the  mine;  the  instinct  of 
the  mule  will  almost  invariably  lead  him  to  the  sump  where  he  may  be  drowned. 


Pump  Room. — The  pump  room  frequently  is  located  near  the  foot  of  the 
pump  way  of  the  main  hoisting  shaft.  The  use  of  a  compartment  of  the  hoist- 
ing shaft  for  pumping,  however,  often  proves  a  serious  inconvenience  in  the 
operation  of  the  mine,  owing  to  the  exhaust  steam  filling  the  shaft  and  shaft 
bottom  so  as  to  interfere  with  the  work  of  hoisting.  With  the  pump  room 
located  in  the  shaft  pillar  between  the  downcast  or  air-shaft  and  the  main  hoist- 
ing shaft,  this  trouble  is  avoided. 

It  frequently  happens  that  owing  to  the  varying  grades  in  the  seam  it  is 
impracticable  to  drain  all  the  mine  workings  to  a  sump  at  the  shaft  bottom. 
In  such  cases,  a  sump  is  often  located  at  some  c9nvenient  low  point  in  the  work- 
ings, and  the  pump  room  is  then  located  at  this  point,  and  the  water  pumped 
to  the  surface  through  bore  holes  drilled  for  this  purpose.  The  steam  supply- 
ing the  pump  is  likewise  conducted  in  pipes  from  the  boilers  at  the  surface 
to  the  pump  in  the  mine  through  a  bore  hole. 

Engine  Room. — The  engine  for  rope  haulage  is  often  located  at  some  point 
in  the  mine,  and  where  steam  is  used  for  power  it  may  be  taken  down  the  shaft 
and  along  the  entry  to  the  engine  room,  or  down  a  bore  hole  that  opens  into 
the  mine  near  the  engine  room.  The  engine  may  exhaust  into  a  pipe  leading 
up  the  shaft,  or  bore  holes  for  this  purpose  may  be  sunk  from  the  surface  at  the 
point  where  the  engine  is  located.  The  engine  room  is  an  opening  made  in 
the  shaft  pillar  or,  if  away  from  the  shaft,  in  the  entry  pillar,  which  is  then 
made  larger  to  provide  for  the  room.  The  roof  over  the  engine  room  is  well 
secured  by  solid  timbers,  or  by  steel  I  beams  supported  on  brick  or  concrete 
walls  at  the  sides  of  the  room.  The  engine  should  be  placed  so  that  the  pull 
of  the  rope  will  be  as  direct  as  possible. 

Lamp  Stations. — In  a  very  gaseous  mine  where  none  but  safety  lamps  are 
used  in  the  workings,  the  lamp  room  or  lamp  station  is  generally  located  at 
the  surface.  In  many  gaseous  mines,  however,  safety  lamps  are  restricted 
to  a  portion  of  the  workings  only  and  naked  lights  are  used  in  the  other 


OPENING  A  MINE  603 

portions  ot  the  mine.  In  such  cases,  lamp  stations  are  frequently  provided 
at  some  point  on  the  main  intake  of  the  mine  near  the  mouth  of  the  entries 
or  headings  leading  to  these  workings.  Similar  lamp  stations,  called  relight- 
ing stations,  are  likewise  often  provided  at  different  points  on  the  main  intake 
wherever  safety  lamps  are  used,  where  lights  that  have  been  extinguished 
may  be  relighted.  A  lamp  station  is  a  simple  opening  made  in  rib  or  pillar 
coal  on  the  intake  airway,  where  a  strong  current  of  pure  air  is  passing,  and 
where  safety  lamps  may  be  kept  or  relighted  when  extinguished. 

Shanties. — The  various  other  shanties  used  in  the  operation  of  the  mine, 
such  as  the  mine-boss  shanty,  tool  shanty,  oil  house,  etc.,  as  well  as  the  wash 
rooms  and  hospital  rooms,  are  simple  openings  made  in  the  shaft  or  entry 
pillar,  the  size  and  arrangement  depending  on  their  use.  Many  mines  now  have 
wash  rooms  and  hospital  rooms  at  the  shaft  bottom,  supplied  with  steam  and 
water  pipes,  for  the  convenience  of  the  men  and  for  the  care  of  the  injured. 
The  walls  of  these  rooms,  as  also  those  of  the  mine-boss  shanty,  are  often 
cemented  and  whitewashed,  and  the  floors  are  also  cemented  so  that  they  can 
be  kept  clean  and  comfortable.  Tool  shanties  are  often  located  at  convenient 
points  for  the  distribution  of  the  tools  to  the  company  men,  and  sometimes 
there  are  blacksmith  shops  in  the  mine  for  the  sharpening  of  the  tools,  though 
this  is  generally  done  at  the  surface. 

Manway  About  the  Shaft. — A  small  manway  should  encircle  at  least  one 
end  of  every  hoisting  shaft.  This  manway  is  sometimes  made  by  enlarging 
the  shaft  excavation  by  widening  on  the  rib,  but  this  is  not  a  good  plan.  At 
other  times,  a  narrow  heading  or  passageway  is  driven  in  the  solid  coal  from 
one  side  of  the  shaft  to  the  other.  A  manway  in  the  shaft  pillar  is  objected  to 
by  some  as  endangering  the  shaft  pillar,  but  allowance  can  be  made  for  it  in 
laying  out  the  size  of  the  shaft  pillar,  and  it  can  be  well  timbered,  if  necessary, 
so  as  to  run  no  risk  of  weakening  the  strata  near  the  shaft.  No  hoisting  shaft 
should  be  operated  without  such  a  manway,  in  order  to  avoid  the  risk  to  which 
the  eager  is  exposed  if  obliged  to  pass  under  the  moving  cages. 

SURFACE  TRACKS  FOR  SLOPES  AND  SHAFTS 

The  arrangement  of  the  tracks  on  the  surface  naturally  differs  at  every 
mine,  owing  to  the  different  existing  conditions.  All  surface  roads  should  be 
so  arranged  that  the  loaded  cars  can  be  moved  with  the  least  possible  power, 
always  looking  out  for  the  return  of  the  empties  with  as  little  expenditure  of 
power  as  possible.  To  secure  the  running  of  the  loaded  cars  from  the  mouth 
of  the  shaft  or  slope  by  gravity,  a  slight  grade  is  necessary,  the  amount  of  which 
depends  on  the  friction  of  the  cars,  which  varies  greatly.  Care  should  be  taken 
that  an  excessive  grade  is  not  constructed,  or  there  will  be  trouble  in  return- 
ing the  empties  from  the  dump  to  the  head  of  the  shaft  or  slope. 

The  tracks  connecting  the  top  of  the  shaft  and  the  tipple  may  be  very 
short,  or  of  considerable  length,  depending  on  the  conditions  at  each  mine. 
Usually  from  20  to  60  ft.  will  be  sufficient,  although  no  definite  rule  can  be 
given  for  this. 

There  are  two  general  arrangements  of  tracks  about  the  head  of  a  shaft: 
First,  where  the  loaded  cars  are  removed  from  the  cage  and  the  empty  cars 
placed  upon  it  from  the  same  side  of  the  shaft;  second,  where  the  loaded  cars 
are  removed  from  one  side  of  the  shaft  and  the  empty  cars  returned  to  the 
cages  from  the  opposite  side  of  the  shaft. 

In  either  case  there  are  usually  several  empty  cars  on  the  platform  ready 
to  be  put  on  the  cages  when  the  loaded  cars  have  been  removed. 

Where  the  conditions  are  such  that  the  loaded  cars  can  be  run  by  gravity 
to  the  dump,  a  good  plan  is  to  have  a  short  incline,  equipped  with  an  endless 
chain,  in  the  empty  track.  The  empty  cars  can  be  run  to  the  foot  of  this, 
hoisted  by  machinery  to  the  top,  and  thus  gain  height  enough  to  run  them 
back  to  the  shaft  or  slope  by  gravity. 

At  the  Philadelphia  and  Reading  Coal  and  Iron  Co.'s  Ellangowan  colliery, 
where  the  tipple  at  the  head  of  the  breaker  is  above  the  level  of  the  head  of 
the  shaft,  the  following  plan  is  used:  The  loaded  cars  are  taken  off  the  east 
side  of  the  cages,  and  run  by  gravity  to  the  foot  of  the  incline  where  the  axles 
of  the  car  are  grasped  by  hooks  on  an  endless  chain  and  the  car  pulled  up  to 
the  tipple.  After  being  dumped,  the  car  is  run  back  from  the  tipple  to  the 
head  of  the  incline,  and  is  carried  to  the  foot  of  the  empty  track  of  the  incline 
by  an  endless  chain.  The  foot  of  the  empty  track  is  several  feet  higher  than 
that  of  the  loaded  track,  and  the  cars  are  run  by  gravity  around  to  the  west 
side  of  the  cages,  and  are  put  on  from  that  side.  The  empty  cars,  as  they  run 
on  the  cage,  have  momentum  enough  to  start  the  loaded  car  off  the  cage  and 


604  METHODS  OF  WORKING 

on  toward  the  foot  of  the  incline.  There  are  a  number  of  hooks  attached  to 
both  the  empty  and  loaded  chain  on  the  incline,  and  there  are  often  several 
loaded  and  several  empty  cars  on  different  parts  of  the  plane  at  once.  This 
arrangement  permits  of  the  hoisting  of  from  700  to  800  cars  per  day  out  of  a 
shaft  110  yd.  deep,  with  single-deck  cages. 

Another  excellent  arrangement  for  handling  coal  on  the  surface  is  the 
invention  of  Mr.  Robert  Ramsey,  and  has  been  adopted  by  the  H.  C.  Frick 
Coke  Co.  and  a  number  of  other  prominent  operators.  A  description  of 
this  arrangement  as  applied  at  the  H.  C.  Frick  Coke  Cp.'s  standard  shaft 
is  as  follows:  The  landing  of  the  shaft  is  made  slightly  higher  than  the  level 
of  the  tipple,  which  is  north  of  the  shaft.  South  of  the  shaft  is  located  a 
double  steam  ram,  one  ram  being  directly  in  line  with  the  track  on  each  cage. 
Directly  in  front  of  the  rams  is  a  transfer  truck,  worked  east  and  west  by 
wire  rope.  The  loaded  car  on  the  cage  is  run  by  gravity  to  the  tipple,  where 
it  is  dumped  by  means  of  a  nicely  balanced  dumping  arrangement.  As  soon 
as  it  is  empty  it  rights  itself  and  runs  by  gravity  alongside  the  shaft  to  the  trans- 
fer truck,  which  carries  it  up  a  grade  to  a  point  directly  in  line  with  the  cage 
that  is  at  the  landing,  and  one  of  the  steam  rams  pushes  it  on  the  cage,  and  at 
the  same  time  starts  the  loaded  car  off  toward  the  tipple.  This  second  loaded 
car  is  then  returned  by  the  same  means  to  the  opposite  cage.  The  whole 
mechanism  is  operated  by  one  man,  by  means  of  conveniently  arranged  levers, 
each  of  which  is  automatically  locked,  except  when  the  proper  time  to  use  it 
arrives.  It  is  therefore  impossible  for  the  topman  to  work  the  wrong  lever 
and  put  an  empty  car  into  the  wrong  compartment  of  the  shaft.  Besides 
the  one  man  at  the  levers,  there  is  but  one  other  man  employed  at  the  tipple, 
and  his  work  is  solely  to  look  after  the  cars  when  dumping.  All  switches  are 
worked  automatically,  and  the  average  hoisting  at  this  shaft  is  at  the  rate 
of  3  cars  per  minute.  The  shaft  is  about  250  ft.  deep,  and  single-deck  cages  are 
used. 

The  Lehigh  and  Wilkes-Barre  Coal  Co.  has  a  system  in  use  at  a  number 
of  collieries  that  has  also  proved  very  effective.  In  this  system  the  loaded 
cars  are  run  by  gravity  from  the  cage  to  the  dump,  and  the  empties  are  hauled 
from  the  dump  back  to  a  transfer  truck  by  a  system  of  endless-rope  haulage. 
The  transfer  truck  carries  the  car  to  a  point  opposite  the  back  of  the  cage. 
The  empty  car  runs  by  gravity  to  the  cage,  and  its  momentum  starts  the  loaded 
car  on  the  cage  on  its  way  to  the  dump.  This  system  necessitates  the  employ- 
ment of  more  topmen,  but  is  a  very  good  one.  At  the  Nottingham  shaft, 
which  is  475  ft.  from  landing  to  landing,  from  140  to  150  cars  per  hour  are 
hoisted  on  single-deck  cages. 


METHODS  OF  OPEN  WORK 

No  definite  rules  can  be  given  for  the  selection  of  a  method  of  mining  that 
will  cover  all  the  conditions  that  may  exist  at  any  given  mine.  The  system 
finally  selected  is  that  which  will  yield  the  maximum  percentage  of  coal  in  the 
best  marketable  condition  at  the  minimum  of  cost  and  danger. 

All  methods  of  working  may  be  grouped  under  one  of  two  heads  or  classes, 
viz.,  open  work,  or  closed  work. 

Open  work  applies  to  the  mining  of  those  deposits  that  are  either  so  thick 
or  lie  so  near  the  surface  that  the  material  overlying  them  may  be  removed 
and  the  coal  quarried  out  at  a  profit. 

The  advantages  of  this  system  are  that  all  the  coal  may  be  extracted  with- 
out any  loss  in  pillars  or  through  squeezes,  and  in  the  lumpiest  condition; 
no  timber  is  required;  unprofitable  underground  workings  do  not  have  to  be 
kept  open  and  in  repair;  when  required,  a  simple  hoisting  plant  is  used;  there 
is  less  danger  to  the  workmen  from  falls  of  roof  and  from  blasting;  there  is 
practically  no  danger  from  fire;  artificial  lights  are  not  required;  mining  can 
be  done  more  economically,  as  larger  faces  are  open,  larger  blasts  can  be  used, 
and  the  amount  of  work  accomplished  per  miner  is  greater,  and  better  super- 
intendence can  be  had;  the  health  of  the  men  is  usually  much  better  when 
working  in  the  open;  and,  under  proper  conditions,  the  output  can  be  increased 
almost  indefinitely. 

The  chief  disadvantage  of  open  work  is  the  possible  reduction  in  output 
during  the  winter  months  owing  to  snow,  the  exposure  of  the  men  to  the 
weather,  etc.  Further  trouble  may  arise  from  flooding  during  the  rainy 
season,  and,  unless  the  seam  lies  parallel  to  the  surface,  the  cost  of  remov- 
ing the  over-burden  soon  becomes  excessive. 


METHODS  OF  WORKING  605 

The  removal  of  the  overburden  is  known  as  stripping,  and  may  be  carried 
on  with  or  without  the  use  of  excavating  machinery.  When  machinery  is 
not  used,  the  covering  is  removed  with  pick  and  shovel  when  it  is  earth,  and 
by  hand  drilling  and  blasting  when  it  is  rock.  This  is  the  original  method  of 
stripping,  probably  first  applied  in  the  United  States  to  the  thick  deposits 
of  the  anthracite  region  of  Pennsylvania,  and  is  limited  in  its  application  to 
those  seams  that  are  either  very  near  the  surface  or  are  abnormally  thick. 
Experience  has  shown  that  it  will  pay  to  remove,  without  the  aid  of  machinery, 
1  ft.  in  thickness  of  overburden  for  each  foot  in  thickness  ot  the  underlying 
coal.  Thus  a  seam  6  ft.  thick  will  permit  of  the  profitable  removal  of  6  ft.  of 
cover,  and  one  25  ft.  thick  of  25  ft.,  possibly  35  ft.,  of  cover.  Mines  of  this 
class  are  known  as  strippings  in  Pennsylvania,  and  as  strip-pits  in  the  middle 
West. 

Steam-Shovel  Mines. — Steam-shovel  mines  are  the  result  of  the  applica- 
tion of  the  familiar  railroad  contractor's  steam  shovel  to  stripping.  Under 
favorable  conditions,  there  is  probably  no  cheaper  method  of  mining.  It  is 
extensively  used  in  the  neighborhood  of  Park  City,  Utah,  in  metal  mining 
and  on  the  iron  ranges  of  the  Lake  Superior  region,  where  an  output  of  2,000  T. 
of  ore  per  da.  for  a  steam  shovel  and  one  locomotive  has  been  reached. 

The  cost  of  removing  97,854  yd.  of  material  from  over  a  seam  of  anthra- 
cite (Pa.)  was  $1  a  yd.  of  material  stripped  and  $.516  per  T.  of  coal  obtained. 
The  average  depth  of  the  stripping  was  75  ft.,  and  about  two- thirds  of  the 
material  removed  was  rock.  Recent  contracts  in  the  same  region  have  been 
let  for  as  low  as  25  c.  a  yd.  for  rock  and  5  c.  a  yd.  for  earth.  Where  conditions 
are  very  favorable  and  a  shovel  of  large  size  can  be  kept  steadily  employed, 
even  lower  average  costs  per  yard  (shale  rock  and  dirt  combined)  may  be  had. 
The  volume,  in  cubic  yards,  of  overburden  removed  per  long  ton  of  coal 
extracted  in  recent  Pennsylvania  practice  is  3.3,  3.8,  3.5,  3.6,  and  3.0  to  1. 
In  one  extreme  case,  5.4  cu.  yd.,  and  in  another  but  1.8  cu.  yd.  of  overburden 
were  removed  per  long  ton  of  coal  extracted. 

In  the  Kansas  field,  where  the  surface  is  level  and  the  seams  horizontal, 
shovels  of  the  largest  size  are  employed  to  remove  the  covering  to  an  average 
depth  of  17  ft.  (6  ft.  to  24  ft.)  from  a  seam  that  is  but  little  more  than  36  in. 
thick.  The  upper  6  ft.  of  cover  is  dirt,  the  second  6  ft.  is  soft  shale  or  soapstone, 
underlying  which  is  blue  shale  to  the  top  of  the  coal  bed.  Where  the  seam  has 
about  20  ft.  of  cover,  the  average  steam  shovel  will,  if  employed  pretty  con- 
stantly, strip  12  to  15  A.  a  yr.  at  a  cost  of  from  5  to  6  c.  per  cu.  yd.  The  wage 
scale  on  an  8-hr,  basis,  is  very  close  to  $2.50,  varying  from  $1.95  for  water- 
boys  to  $3.05  for  blacksmiths.  Most  of  the  workers  receive  $2.52  to  $2.62 
per  da. 

Near  Danville,  Illinois,  where  the  conditions  are  very  similar  to  those  in 
Kansas,  38  to  40  ft.  of  overburden,  of  which  16  to  24  ft.  is  shale,  is  profitably 
removed  from  a  coal  seam  8  ft.  thick.  This  is  a  fair  general  average  for  the 
district,  although  a  ratio  of  6  to  1  has  been  had. 

The  disposal  of  the  overburden  is  frequently  a  matter  of  difficulty,  par- 
ticularly when  it  is  thick.  If  it  has  to  be  transported  to  any  great  distance, 
the  cost  thereof  may  be  prohibitory.  If  much  water  or  sand  occurs  in  the  cover 
the  cost  of  stripping  is  likewise  increased.  Strippings  liable  to  overflow  from 
flooded  rivers  are  costly  to  operate  and  the  workings  should  be  protected  by 
dams  built  of  the  overburden. 

After  the  surface  covering  has  been  removed,  a  track  is  usually  laid  along 
the  face  of  the  stripping  on  the  bottom  of  the  workings,  and  the  coal,  after 
being  blasted,  is  loaded  into  railroad  cars  by  the  steam  shovel  if  it  is  shipped 
as  mine  run  or  into  smaller  cars  for  transportation  to  the  tipple  if  it  must  be 
screened  into  sizes. 


METHODS  OF  WORKING 


METHODS  OF  CLOSED  WORK 


INTRODUCTORY 

By  closed  work  is  meant  the  mining  and  removal  of  the  coal  without  the 
previous  removal  of  the  overburden.  In  general,  the  word  mine  is  used  to 
define  a  series  of  underground  workings,  and  the  words  stripping,  strip-pit, 
open-cut,  open-pit,  and  the  like,  to  what  are  more  properly  coal  quarries  of 
the  nature  just  described. 

No  definite  rules  can  be  given  for  the  selection  of  a  method  of  mining  that 
will  cover  all  the  conditions  that  may  exist  at  any  given  mine.  The  system 
finally  selected  will  be  that  which  will  result  in  the  production  of  the  maximum 
amount  of  coal  per  acre  in  the  best  marketable  condition  and  at  the  minimum 
cost  of  extraction  with  the  least  danger  to  the  workers. 

General  Considerations. — Some  of  the  items  to  be  considered  in  selecting 
a  method  of  working  are  the  thickness  of  the  seam  and  the  amount,  location, 
and  nature  of  its  impurities;  the  use  to  which  the  coal  is  to  be  put;  the 
character  of  the  roof  and  floor;  the  amount  of  cover  over  the  seam;  the  dip 
of  the  coal;  the  nature  and  direction  of  the  cleat  or  cleavage  of  the  seam;  the 
character  of  the  labor  to  be  employed;  the  presence  or  absence  of  gas,  etc. 

1.  Roof  Pressure. — Of  these  items,  the  roof  pressure  is  the  most  impor- 
tant, and  a  number  of  other  causes  are  directly  affected  by  it.     The  weight  of 
the  overlying  cover  will  give  a  maximum  roof  pressure,  but  this  may  be  so 
variously  modified  that  the  determination  of  the  actual  pressure  is  practically 
impossible,  and  estimates  of  this  pressure  must  be  based  largely  on  practical 
experience;  hence,  rules  for  its  calculation  are  of  comparatively  little  value. 
One  very  essential  point,  however,  must  be  borne  in  mind,  i.  e.,  that  the  direc- 
tion of  pressure  is  perpendicular  to  the  bedding  plane. 

2.  Strength  and  Character  of  Roof  and  Floor. — The  strength  of  roof  refers 
to  the  power  of  being  self-supporting  over  smaller  or  larger  areas.     A  strong 
roof  permits  larger  openings,  but  increases  the  load  on  the  pillars,  thereby 
necessitating  larger  pillars.     A  weak  roof  requires  smaller  openings,  and  per- 
mits smaller  pillars  when  the  floor  is  good.     A  strong  roof  may  yield  and  settle 
gradually,  giving  good  conditions  for  longwall  work,  or  it  may  be  hard  and 
brittle,  and  difficult  to  manage. 

The  character  of  floor  influences  largely  the  size  of  pillars.  A  soft  bottom 
requires  large  pillars  and  narrow  openings,  especially  when  the  roof  is  strong. 

3.  Texture  of  Coal  and  Inclination  and  Thickness  of  Seam. — Soft,  friable 
coal  requires  large  pillars,  while  a  hard,  compact  coal  requires  only  small 
pillars.    The  inclination  and  thickness  of  the  deposit  increase  the  size  of  pillars 
required,  and   also  influence   the  haulage,   drainage,   timbering,   method   of 
working,  arrangement  of  breasts,  etc. 

4.  Presence  of  Gas. — The  presence  of  gas  in  the  seam  or  in  the  enclosing 
strata  affects  the  system  of  working,  as  ample  air  passages  must  be  provided, 
and  provision  must  frequently  be  -made  for  ventilating  separately  the  different 
sections  of  the  mine.     Where  the  gas  pressure  is  strong,  and  outbursts  are  of 
frequent  occurrence,  narrow  openings  are  necessitated  that  render  the  working 
safe  until  the  gas  has  escaped. 

5.  Use  to  Which  Coal  is  Put. — If  the  coal  is  destined  to  be  coked,  a  method 
of  mining  is  to  be  preferred  which  results  in  the  production  of  the  largest  pos- 
sible amount  of  slack;  whereas,  if  the  coal  is  screened  into  sizes  in  the  ordinary 
way,  choice  should  be  given  to  that  system  which  results  in  the  largest  amount 
of  lump  coal. 

When  the  longwall  method  is  used,  it  is  particularly  important  to  have  a 
constant  market  for  the  output,  such  as  obtains  if  the  mine  is  shipping  fuel 
coal  to  a  railroad  at  a  fixed  tonnage  per  day,  as  a  few  days'  idleness  may  cause 
serious  trouble  at  the  face,  even  in  temporarily  closing  it  if  the  pressure  is 
great. 

6.  Character  of  Labor. — While,  in  the  room-and-pillar  system  of  mining,  the 
temporary  or  even  long-continued  stoppage  of  work  in  a  portion  or  all  of  the 
working  places,  does  not  commonly  have  other  effect  than  reducing  the  out- 
put and,  consequently,  the  profits,  under  the  longwall  system  the  shutting 
down  even  for  a  few  days  of  a  comparatively  few  working  places  may  cause 


METHODS  OF  WORKING  607 

serious  trouble  in  handling  the  pressure  at  the  face.  Hence  the  necessity, 
under  the  longwall  system,  of  having  not  only  a  steady  car  supply  as  explained, 
but  also  steady  men  who  will  not  lay  off  for  one  trivial  excuse  or  another. 

General  Systems  of  Mining. — For  purposes  of  classification  the  various 
systems  of  mining  coal  fall  into  one  of  two  groups,  as  follows: 

1.  Systems  in  which  the  tract  to  be  exploited  is  first  penetrated  by  a  series 
of  two  or  more  relatively  narrow  (8  to  10  ft.)  entries  (headings  or  gangways) 
from  some  of  which  entries  are  (usually)  turned  relatively  wide  (15  to  30  ft.) 
rooms  (breasts  or  chambers)  which  are  separated  the  one  from  the  other  by 
pillars  of  coal,  and  in  which  rooms  the  bulk  of  the  output  of  the  mine  is  obtained. 
This  group  may  be  further  subdivided  into  the  room-and-pillar,  pillar-and-stall, 
and  panel  methods. 

2.  Systems  in  which  entries  are  not  driven,  but  in  which  all  the  coal  is 
extracted  in  one  operation  from  a  continuous  face,  the  roof  being  allowed  to 
fall  or  cave  as  fast  as  the  coal  is  removed,  haulage  roads  being  maintained 
through  the  caved  area  by  means  of  walls  of  stone  built  along  their  sides.     The 
longwall  system,  largely  used  abroad,  and  but  to  a  slight  extent  in  the  United 
States  where  the  vast  bulk  of  the  coal  is  mined  by  the  room-and-pillar  method, 
is  the  single  example  of  this  second  group. 

The  consideration  of  any  system  of  mining  requires  a  discussion  of  the  fol- 
lowing subjects:  The  system  of  mining  as  a  whole,  including  the  direction  of 
driving  the  entries  and  rooms,  the  number  and  grade  of  the  former,  etc.;  meth- 
ods of  supporting  the  roof  and  sides  of  excavations,  see  Timbering;  methods 
and  appliances  for  removing  water  from  the  workings,  see  Hydraulics;  methods 
of  bringing  down  the  coal  at  the  working  face,  see  Explosives  and  Blasting; 
methods  of  transporting  the  coal  from  the  face  to  the  tipple,  see  Haulage  and 
Hoisting;  methods  of  supplying  the  working  places  with  a  current  of  fresh  air 
from  the  surface,  see  Ventilation. 


ROOM-AND-PILLAR  SYSTEMS  OF  MINING 

PRELIMINARY  CONSIDERATIONS 

In  the  room-and-pillar  system  of  mining,  the  tract  to  be  worked  is  divided 
into  small  districts,  or  blocks,  by  main  entries  and  cross-entries  intersecting 
one  another  at  right  angles  or  nearly  so.  The  coal  in  each  block  is  mined  by 
turning  off  from  the  cross-entries  a  number  of  rooms. 

That  part  of  the  coal  which  is  left  between  the  individual  rooms  and  entries 
is  called  a  pillar,  and  the  pillars  are  pierced  at  more  or  less  regular  intervals 
by  cross-cuts  or  break-throughs  in  part  for  the  purposes  of  haulage,  but  most 
largely  to  provide  a  passage  for  the  air-currents  that  a  better  ventilation  of  the 
working  faces  may  be  secured.  The  removal  of  the  coal  in  driving  the  entries 
and  rooms  is  called  the  first  working,  or  more  rarely  the  advance  working  or 
working  on  the  advance. 

Unless  it  is  necessary  to  leave  in  the  pillars  to  support  the  surface  per- 
manently they  are  commonly  removed  as  soon  as  the  rooms,  either  in  part  or 
all  those  turned  from  a  single  cross-entry,  have  been  driven  their  full  length; 
and  unless  the  pillars  can  be  removed  the  room-and-pillar  system  of  mining 
is  very  wasteful  of  coal,  as  from  30  to  50%  of  the  total  amount  must  be  left 
in  the  mine.  The  removal  of  the  pillars  is  variously  known  as  second  working, 
working  on  the  retreat,  robbing,  drawing-back  the  pillars,  pillar  working,  pillar  4 
drawing,  pulling  pillars,  etc.  Fig.  1  shows  a  mine  laid  out  on  the  double- 
entry  room-and-pillar  system  of  mining. 

Number  of  Entries. — The  haulageways  in  a  bituminous  mine  are  known 
as  entries  or  headings  and  in  an  anthracite  mine  as  gangways.  There  are  sev- 
eral methods  of  arranging  these  passageways,  known  as  single-entry,  double- 
entry,  triple-entry,  etc. 

The  multiple-entry  systems  are  expensive  to  drive,  and  the  greater  the  num- 
ber of  entries  the  greater  the  expense,  and  are  only  used  by  companies  with 
ample  capital,  large  acreage  of  undeveloped  coal,  and  a  large  and  regular 
market. 

In  the  single-entry  system,  now  used  but  very  rarely  if  at  all,  a  single  entry 
is  driven  ahead  and  rooms  are  turned  from  one  or  both  sides  of  it.  This  entry, 
which  is  also  the  main  haulage  road,  acts  as  an  intake,  the  air  being  conducted 
along  it  to  the  last  room,  up  which  it  passes  to  the  break-through  and  back 
along  the  working  faces  to  the  first  room  and  thence  by  a  small  air-course  to 
the  upcast.  The  circulation  of  air  is  liable,  in  this  method,  to  be  cut  off  at  any 


60S  METHODS  OF  WORKING 

time  by  a  fall  of  roof  in  the  rooms,  and  the  mine  must  be  closed  until  the  ven- 

*  fThe^double-entry  system  of  mining,  illustrated  in  Fig.  1,  may  be  considered 
the  standard  of  American  practice.  The  main  entries  are  driven  from  the  shaft 
bottom  or  from  the  drift  mouth,  and  from  these  the  cross-  or  butt-entries  are 
driven  usually  at  right  angles.  The  rooms  may  be  turned  directly  off  these 


FIG.  1 

cross-entries,  or  other  entries  may  be  driven  at  right  angles  to  the  cross-entries, 
and  the  rooms  turned  off  them. 

The  advantages  of  the  double-entry  system  are  that  in  case  of  accident 
on  one  entry  the  other  is  available  for  escape,  a  fall  of  roof  in  one  of  the  rooms 
does  not  obstruct  the  circulation  in  other  portions  of  the  mine,  one  or  more 
of  the  pairs  of  cross-entries  may  be  closed  for  any  reason  without  in  any  way 
affecting  other  parts  of  the  mine,  and  the  entries  may  be  driven  ahead  of  room 
turning,  as  far  as  desired,  for  the  purpose  of  prospecting  the  seam  or  to  pro- 
vide for  a  large  number  of  extra  working  places  that  the  output  may  be  increased 
in  event  of  a  sudden  demand. 


METHODS  OF  WORKING 


In  the  triple-entry  system,  the  center  one  of  the  three  parallel  entries  is 
usually  made  the  intake  and  t%  main  haulage  road  for  the  mine,  while  the 
two  side  entries  are  made  the  return  air-courses  for  their  respective  sides  of  the 
workings.  Overcasts  are  usually  built  at  the  mouth  of  the  center  entry  of 
each  set  of  cross-entries  to  conduct  the  return  current  over  the  haulage  road. 
Although  this  system  requires  a  greater  outlay  because  of  the  extra  price  paid 
for  narrow  work,  it  is  often  absolutely  necessary  in  the  working  of.  a  gaseous 
seam,  to  which  it  is  particularly  adapted.  It  is  also  used  where  it  is  not  pos- 
sible to  drive  a  single  entry  of  sufficient  width  for  a  double-track  haulage  road 
pr  where  single  or  double  entries  of  sufficient  area  to  give  the  required  quantity 
of  air  cannot  be  driven  or  economically  maintained  on  account  of  poor  roof  or 
creep.  Sometimes  this  system  is  applied  to  the  main  entries  only,  the  cross- 
entries  being  driven  double,  as  shown  in  Fig.  2. 

In  the  four-  or  quadruple-entry  system  of  mining,  four  parallel  entries  are 
driven.  In  this  case,  each  side  of  the  mine  usually  has  its  own  intake  (one 
of  the  center  entries)  and  return  (one  of  the  outer  entries) .  The  center  entries 
are  the  haulage  roads,  or  one  may  be  used  for  haulage  and  the  other  as  a  man- 
way  or  traveling  road  for  the  men.  Where  high-speed  endless-rope  haulage 
is  employed,  this  system  is  well  adapted,  the  loads  coming  from  the  mine  along 
one  of  the  center  entries  and  the  empties  entering  it  along  the  other.  In  some 
cases  the  center  entries 
are  not  connected  by 
breakthroughs,  the 
right-hand  and  left- 
hand  pairs  of  entries 
being  used  as  the  intake 
and  return,  respective- 
ly, of  corresponding 
sides  of  the  mine.  This 
is  equivalent  to  operat- 
ing two  distinct  mines 
through  the  same  main 
opening. 

The  five-  or  quin- 
tuple-entry system  is  the 
same  as  the  preceding 
with  the  addition  of 
one  more  entry,  which 
is  used  as  a  manway. 

Size  of  Entries. 
The  size  of  an  entry  de- 
pends on  its  use,  as  well 
as  on  the  thickness  of 
the  seam  and  the  na- 
ture of  the  roof  and 
floor.  The  cost  of  main- 
taining wide  roadways  under  a  bad  roof  or  where  the  floor  has  a  tendency  to 
heave  or  where  the  coal  is  frail,  often  prevents  their  use  and  necessitates  nar- 
rower openings.  The  thickness  of  the  seam  also  affects  the  width  of  the  road- 
ways for  a  given  output  of  coal,  by  reducing  the  height  of  .~~l  *-"..'£  thin  seams, 
and  requiring  a  greater  width  of  car,  and  consequently  greater  j£dth  of  road- 
way for  the  same  capacity  or  output.  The  amount  of  the  daily  output  of 
coal  is  also  a  factor  determining  to  a  large  extent  the  size  of  the  haulage  roads 
required.  In  a  coal  seam  6  ft.  thick,  with  a  good  roof,  and  when  the  coal  is 
clean  and  does  not  yield  much  gobbing  material,  the  width  of  a  single-track 
entry  is  generally  from  8  to  10  ft.  As  the  amount  of  material  to  be  gobbed 
increases,  the  width  is  increased,  if  the  roof  will  permit;  but  occasionally  entries 
are  driven  only  6  ft.  wide  owing  to  poor  roof.  The  general  practice  is,  however, 
to  drive  entries  as  wide  as  the  roof  conditions  will  permit  so  as  to  avoid 
yardage  as  much  as  possible.  In  thin  seams,  where  the  roof  must  be  taken 
down  or  the  bottom  lifted  to  provide  headroom  on  the  haulage  roads,  an  entry 
is  often  driven  12  or  14  ft.  wide  where  the  conditions  with  respect  to  the  roof 
and  coal  will  permit.  By  this  means,  the  cost  of  driving  is  paid  by  the  coal 
taken  out,  there  is  no  charge  for  yardage,  and  room  is  provided  for  stowing 
the  waste  material  taken  down  from  the  roof.  This  waste  is  built  along  the 
side  of  the  road  as  a  pack  wall,  or  building,  as  it  is  called.  Fig.  3  shows  a 
cross-section  of  an  entry  where  the  roof  has  been  taken  down  to  afford  head- 
room and  the  waste  built  up  at  the  side  of  the  road. 


FIG.  2 


610 


METHODS  OF  WORKING 


A  common,  but  bad,  practice  is  to  make  the  haulage  road,  which  is  the 
intake,  of  a  good  height  for  passage  of  car£  by  Dipping  down  the  roof,  but  leaving 
the  return  airway  of  the  height  of  the  seam.  Thus,  if  both  entries  are  driven 
10  ft.  wide,  and  the  roof  in  the  intake  is  taken  down  to  give  a  height  of  6  ft. 
while  the  height  of  the  return  is  that  of  the  coal,  or,  say,  4  ft.,  the  one  entry 
has  an  area  of  60  sq.  ft.  and  the  other  one  of  40  sq.  ft.,  the  disadvantages  of 
which  from  the  standpoint  of  proper  ventilation  are  obvious.  The  return  air- 
way should  have,  at  least,  the  same  area  as  the  intake. 

Where  practicable,  the  airways  should  be  made  in  the  form  of  a  square 
instead  of  a  parallelogram  of  the  same  area.  Thus  a  square  entrv  10  ft.  by 
10  ft.  in  dimensions  has  an  area  of  100  sq.  ft.  and  a  perimeter  of  40  ft.;  whereas, 
an  entry  5  ft.  by  20  ft.  in  size  while  having  the  same  area  has  a  perimeter  of 
100  ft.,  and  the  friction  of  the  air  in  passing  through  and  the  power  required 
to  produce  ventilation  is  much  greater  than  in  the  square  entry. 

Break-throughs  between  entries  are  usually  made  about  the  same  width 
as  the  entry  and  at  a  distance  apart  determined  by  law  Or  by  the  gaseous  con- 
dition of  the  coal. 

Distance  Between  Entries. — The  distance  between  the  center  lines  of  the 
main  entries  is  commonly  made  from  30  to  60  ft.,  which  provides  for  a  pillar 
from  20  to  50  ft.  in  thickness  if  the  entries  are  10  ft.  wide  as  is  usually  the  case. 
While  the  pillars  are  made  as  thin  as  possible  to  reduce  the  cost  of  narrow  work 
in  driving  break-throughs,  they  must  be  sufficiently  strong  to  withstand  the 
effects  of  the  pressure  brought  upon  them  by  drawing  the  room  and  entry 
pillars  on  the  cross-headings.  Furthermore,  as  the  main-entry  pillars  must 
last  through  the  lifetime  of  the  mine,  they  must  be  larger  and  stronger  than 
those  between  the  cross-entries,  which  are  frequently  pulled  as  soon  as  the  rooms 
on  them  are  worked  out.  The  cross-entry  pillars,  which  do  not  have  to  stand 

so  long,  are  frequently  made  20  ft. 
thick,  indicating  a  spacing  of  the 
center  lines  of  30  ft.  when  the  en- 
tries are  10  ft.  wide. 

The  distance  between  the  cen- 
ter lines  of  the  room  entry  of  one 
pair  of  cross-entries  and  the  return 
air-course  of  the  next  parallel 
pair  of  cross-entries  is  equal  to 
the  width  of  one  entry  plus  the 
length  of  the  room  plus  the  thick- 
ness of  the  pillar  left  between  the 
faces  of  the  rooms  driven  from  the 


FIG.  3 


one  entry  and  the  return  air-course  of  the  next  entry. 

Direction  of  Entries  in  Flat  Seams. — The  direction  of  the  main  entries  is 
determined  by  the  shape  of  the  property,  the  direction  of  the  cleavage  of  the 
coal,  etc.  If  the  property  is  long  and  narrow,  it  effects  an  economy  in  haul- 
age if  the  main  entries  are  driven  as  near  as  possible  and  parallel  to  one  of  the 
longer  sides  so  that  all  the  cross-  or  room-entries  may  be  on  the  same  side  of 
the  haulage  road.  If  the  property  is  square,  the  main  entries  are  commonly 
driven  to  divide  the  tract  into  two  as  nearly  equal  parts  as  possible,  with  room 
entries  of  the  same  length  on  each  side  of  the  main  road.  If  the  property  is 
short  and  wid«?m  order  to  avoid  excessive  length  of  the  cross-entries,  two  sets 
of  main  entries  may  be  driven,  which  diverge  toward  opposite  sides  of  the 
mine  at  a  point  a  short  distance  inbye  the  drift  mouth  or  the  foot  of  the  shaft 
or  slope. 

The  influence  of  the  direction  of  the  cleavage  of  the  coal  upon  that  of  the 
workings  is  more  particularly  noted  under  the  head  of  Laying  off  Rooms, 
but  it  should  be  noted  here  that  it  is  advisable  to  drive  the  headings  parallel 
to  one  of  the  vertical  cleavages  and  usually  to  the  face.  It  is  not  unusual  to 
demand  an  extra  price  per  ton  for  mining  coal  in  entries  driven  across  the  cleav- 
age in  those  districts  where  this  feature  is  pronounced.  In  such  cases,  it  is  a 
question  for_  calculation  whether  the  saving  in  haulage,  etc.,  by  having  the 
headings  divide  the  property  on  the  lines  just  explained  will  offset  the  increased 
cost  of  driving  them  across  the  cleavage;  assuming  that  the  cleavage  and  prop- 
erty lines  are  not  parallel. 

So-called  flat  seams  usually  have  a  more  or  less  decided  dip,  often  rising 
to  3%,  in  one  direction  or  another.  Where  possible,  the  main  roads  are  driven 
either  directly  up  or  directly  down  the  dip,  so  that  the  cross-entries  on  which 
the  coal  is  produced  may  be  level,  and  the  haulage  on  a  pitch  is  confined  to 
that  on  the  main  entries. 


METHODS  OP  WORKING  611 

If  the  property  lies  in  a  syncline,  it  is  advisable  to  lay  out  the  main  roads 
in  the  basin,  rather  than  across  it,  that  the  coal  from  the  rooms  may  run  down 
hill  toward  them. 

Direction  of  Entries  in  Inclined  Seams. — In  pitching  seams,  the  main  roads 
are  almost  always  driven  either  directly  up  or  directly  down  hill,  regardless  of 
the  direction  of  cleavage,  etc.  If  the  dip  is  not  very  marked,  the  main  roads 
are  frequently  called  dip  headings  or  rise  headings  as  may  be,  but  when  the  dip 
is  pronounced  they  are  commonly  referred  to  as  the  slope,  main  slope,  hoisting 
slope,  etc. 

The  cross-entries  are  driven  to  the  right  and  left  (either  or  both)  of  the 
slope,  approximately  on  the  strike  of  the  seam,  but  with  an  up-grade  of  1  to  2% 
to  favor  the  haulage  of  the  loaded  cars,  to  insure  drainage,  etc. 

If  it  is  desired  to  drive  the  cross-entries  on  any  given  grade,  the  direction 
of  the  cross-entry  may  be  found  from  the  formula 

tan  x         z 

sm  A  =  - = , 

tan  y     tan  y 

in  which          A  =  angle  between  cross-entry  and  strike  of  seam; 

*  =  pitch  of  cross-entry,  in  degrees; 

y  =  pitch  of  seam,  in  degrees; 

2  =  percentage  of  grade  of  cross-entry  =  tan  x. 

EXAMPLE. — A  slope  pitches  15°  in  the  direction  N  25°  30'  E;  what  are 
the  bearings  of  the  right  and  left  cross-entries  if  driven  with  a  rising  grade  of  1%? 

SOLUTION.— Substituting,  sin  A  =.-?—  =  ~^^  =  .03732,  whence  A  =  2°  8'. 

tan  y     tan  15° 

The  strike  has  a  bearing  of  S  64°  30'  E  on  the  right  of  the  slope  and  one  of 
N  64°  30'  W  on  the  left.  The  bearing  of  the  right-hand  cross-entry  will  be 
64°  30'-2°  8'  =  S  62°  22'  E,  and  of  the  left-hand  entry,  64°  30'+ 2°  8'  =  N  66° 
38' W. 

Alinement  and  Grade  of  Entries. — As  far  as  possible,  the  entries  should 
be  straight  and  of  uniform  grade  in  order  to  reduce  the  friction  and  wear  and 
tear  on  the  rolling  stock,  tracks,  etc.,  to  lessen  the  amount  of  coal  shaken 
from  the  cars,  which  is  subsequently  ground  into  explosive  dust,  to  diminish 
the  number  of  accidents  due  to  cars  jumping  the  track,  and  to  decrease  the 
amount  of  power  required  for  haulage. 

Natural  conditions  are  usually  such  in  American  mines  that  it  is  easily 
possible  to  secure  straight  tracks,  although  to  produce  a  uniform  grade  it  may 
be  necessary  to  fill  in  swamps  and  cut  down  hills  by  shooting  down  the  roof  in 
the  bottom  of  the  dips  and  by  taking  up  the  floor  at  the  top  of  a  local  rise. 
This  grading  is  commonly  confined  to  the  main  haulage  road,  which  must 
usually  last  throughout  the  life  of  the  mine,  the  cross-entries  being  allowed 
to  follow  the  convolutions  of  the  seam  but  with  a  slight  upward  grade. 

Sharp  angles  are  to  be  avoided  on  all  entries,  whether  used  for  haulage  or 
for  air-courses,  by  substituting  curves  for  angles  or  by  means  of  diagonal  roads 
or  cut-offs. 

In  flat  seams,  the  grades  depend  on  the  slight  inclination  of  the  seam  that 
may  exist.  On  the  main  haulage  roads,  the  grade  is  the  same  as  the  pitch  of 
the  seam;  and  on  cross-entries  it  is  just  sufficient  for  haulage  and  drainage  pur- 
poses, say,  with  a  rise  toward  the  face  of  1  to  1.5%.  Uniform  grades,  on  main 
roads,  are  commonly  secured  by  brushing  the  roof  and  lifting  the  floor  as 
explained;  and  on  cross-entries,  by  following  the  strike  of  the  seam,  although 
the  alinement  thus  secured  may  not  be  the  best.  In  inclined  seams,  any 
desired  grade  can  usually  be  obtained  by  altering  the  direction  of  the  cross- 
entry,  as  described  before. 

Rooms  in  General. — Rooms  are  commonly  turned  off  one  side  on  an  entry 
at  a  predetermined  distance  apart,  the  distance  between  the  center  lines  of 
adjacent  rooms  being  equal  to  the  width  of  the  room  added  to  the  thickness 
of  the  pillar  between  the  rooms.  They  are  usually  opened  by  driving  a  nar- 
row neck  of  about  the  width  of  the  entry  for  a  distance  of  10  to  30  ft.,  depend- 
ing on  the  roof  pressure,  after  which  the  place  is  -widened  out  more  or  less  rap- 
idly on  one  or  both  sides  to  full  room  width,  which  may  be  from  15  to  30  ft. 
or  more,  probably  -  averaging  24  ft.  in  American  mines.  If  the  rooms  are 
inclined  to  the  entry,  the  necks  must  be  longer  than  if  they  are  at  right  'angles 
to  it,  in  order  to  furnish  a  sufficiently  solid  entry  pillar.  Room  necks  should 
not  be  driven  any  wider  than  need  be  and  the  seam  should  be  undercut  or 
sheared  before  blasting,  that  the  minimum  amount  of  powder  may  be  required 
to  bring  down  the  coal,  thus  preventing  shattering  and  consequent  weakening 
of  the  entry  pillar. 


612  METHODS  OF  WORKING 

The  tracks  are  generally  laid  along  the  straight  rib  (opposite  to  the  gob 
side,  or  that  side  on  which  the  room  is  widened)  and  at  such  a  distance  from  it 
that  there  may  be  safe  clearance  for  the  miner  between  the  side  of  a  car  and 
the  rib.  Sometimes  the  track  is  laid  up  the  center  of  the  room,  in  order  to 
shorten  the  distance  the  coal  has  to  be  shoveled  into  the  car  at  the  face,  in 
which  case  the  room  is  commonly  widened  on  both  sides.  In  the  case  of  very 
wide  rooms,  a  track  is  sometimes  laid  up  along  each  side.  These  tracks  join 
at  the  neck  of  the  room,  that  there,  may  be  but  one  room  switch  on  the  entry. 
Unless  the  mouth  of  the  room  is  very  wide  the  corner  of  the  pillar  on  the  entry 
and  on  the  gob-side  of  the  room  is  commonly  rounded  or  beveled  off  to  per- 
mit of  a  less  abrupt  curve  on  the  track  entering  the  place.  Where  necessary, 
the  roof  is  supported  over  the  track  and  at  the  face  by  props  or  props  and  caps 
(cross-bars).  Any  roof  rock  that  falls  and  refuse  from  the  seam  are  stowed 
on  the  wide  side  of  the  room;  whence  the  term,  gob  side.  The  practice  of 
throwing  the  fine  coal  resulting  from  mining  (slack  or  bug-dust)  into  the  gob 
cannot  be  too  strongly  condemned,  as  it  will  serve  to  furnish  fuel  for  the  propo- 
gation  of  a  dust  explosion. 

The  distance  between  centers  of  parallel  and  adjacent  rooms  as  well  as 
the  width  of  the  room  and  the  thickness  of  the  separating  pillar,  depend  on  the 
character  of  the  roof,  coal,  and  floor,  and  on  the  thickness  of  the  coal  and  the 
amount  of  cover  over  it.  No  general  rule  for  properly  proportioning  the  width 
of  room  to  the  thickness  of  the  pillar  can  be  given,  but  points  for  consideration 
are  given  under  the  head  of  Timbering.  The  distances  between  the  centers 
vary  from  33  ft.  to  80  ft.  under  different  conditions.  With  40-ft.  centers, 
the  pillars  are  usually  12  to  16  ft.  wide,  and  the  rooms  28  to  24  ft.  wide.  When 
the  centers  are  farther  apart  than  40  ft.,  the  pillars  are  often  20  to  30  ft.  wide. 
Narrow  rooms,  about  12  ft.  wide,  are  often  driven  and  wide  pillars  of  60  to 
70  ft.  left  between.  The  greater  part  of  the  coal  is  then  got  out  by  drawing 
_  m  ^^^^^^^^^^^^^«  back  these  wide  pillars,  as  explained  later.  When 
HHH^I  the  room  centers  are  40  ft.  or  more  apart,  if  the 
1,1  I  •  coal  is  soft  the  pillars  are  wide  and  the  rooms 

^H  narrow,  but  if  the  coal  is  hard  the  rooms  are  wide 

•  and  the  pillars  narrow,  provided  that  the  roof 

•  •  ••  ^  •  •  ^  ^1  and  door  conditions  will  permit.     The  ratio  be- 

•  •  •§  •  ••  •  •  tween  the  width  of  the  room  and  width  of  pillar 
_  _  m.^^^m.^m^^m^'^f  m  general  decreases  with  an  increase  in  depth 

•  below  the  surface.     When  an  undue  proportion 

|l,J^HHH^^Hj^HI|  °f  coal  is  mined  in  the  first  working,  creeps  are 
•  brought  on,  with  all  [the  accompanying  evils  of 
II  |  crushed  coal,  dilapidation  of  roadways  and  air- 

ways, extra  cost  for  labor  and  material  in  repair- 
* IG>  4  ing  damages,  and  diminished  production. 

The  length  of  the  rooms  is  governed  by  the  distance  decided  on  between 
entries.  It  is  usual  to  make  them  from  150  to  300  ft.  long,  the  former  being 
preferable  in  thin  beds  and  the  latter  in  thick  and  steep  pitching  beds  in  order 
to  avoid  the  expense  of  narrow  work  and  cross-entry  rails.  The  length  of  the 
rooms  is  also  somewhat  governed  by  the  distance  to  whioh  the  coal  can  be 
economically  hauled  from  the  face  to  the  entry,  and  by  the  gas  present  in  the 
coal. 

The  distance  apart  of  break-throughs  depends  on  the  amount  of  gas  given 
off  by  the  coal,  on  local  practice,  and  on  the  mine  laws  of  the  state.  Owing  to 
the  tendency  of  heated  air,  gas,  etc.,  to  accumulate  at  the  face,  rooms  driven 
to  the  rise  require  the  distance  between  break-throughs  to  be  less  than  if  the 
rooms  are  flat,  while  rooms  driven  to  the  dip  require  break-throughs  at  less 
frequent  intervals  than  flat  ones.  Break-throughs  should  have  the  same  cross- 
section  as  the  other  airways  in  the  mine  and  should  be  turned  and  driven  with 
as  much  care.  Break-throughs  between  adjoining  rooms  should  be  driven 
in  line  so  that  the  series  of  openings  through  the  pillars  formed  by  them  can  be 
used  for  haulage  purposes  when  necessary. 

Double  Rooms. — When  it  is  necessary  to  have  a  greater  length  of  face  than 
is  afforded  by  a  single  room,  double  rooms,  as  illustrated  in  Fig.  4,  may  be 
driven.  These  rooms  are  connected  to  the  entry  by  two  necks  and  have  two 
straight  ribs  with  a  track  along  each.  Refuse  is  stored  between  the  tracks, 
and  where  enough  material  is  to  be  had,  pack  walls  are  built  along  the  track 
so  as  to  form  two  roadways  leading  to  the  face.  The  pillars  are  also  wider 
than  in  the  case  of  single  rooms. 

For  the  purposes  of  ventilation  in  gaseous  seams,  or  as  a  protection  against 
squeeze,  to  which  a  bed  of  coal  may  be  especially  liable,  or  for  the  purpose  of 


METHODS  OF  WORKING 


613 


starting  a  long  face  for  machine  working,  rooms  are  sometimes  turned  off  of 
an  entry  as  already  described,  but  are  opened  into  each  other  by  the  removal 
of  the  pillar  in  the 
first  working,  thus 
forming  a  contin- 
uous breast,  as 
shown  in  Fig.  5. 

Rooms  With 
Extra  Entry  Pillars. 
Where  there  is  ex- 
cessive weight  on 
the  entry  pillars,  it 
is  necessary ,  in  order 
to  keep  open  the 
entries,  that  these 
pillars  be  very  large, 
or  that  a  special  pil- 
lar be  left  to  protect 
the  entry  used  as  a 
haulage  road,  while  FIG.  5 

the     rooms    are 
opened  out  from  a  parallel  entry  or  cross-cut. 

Fig.  6  shows  a  method  used  at  Danville,  Illinois,  where  the  coal  is  under- 
laid by  a  soft  bottom,  but  has  a  strong  cover.  The  weight  of  the  coyer  would 
tend  to  force  the  pillars  into  the  bottom  and  thus  close  up  the  entries.  This 
is  prevented  by  leaving  the  extra  pillar  e.  The  main  entries  a  are  driven  and 
timbered  for  a  double  track;  the  cross-entries  b  are  driven  10  ft.  wide  and  the 
first  room  neck  c  is  turned  10  ft.  wide  and  driven  up  15  ft.  and  then  widened 
out  on  one  side  to  a  full  width  of  30  ft.  A  cross-cut  d  is  driven  20  ft.  wide  and 
two  more  rooms  are  turned  off  this  cross-cut,  as  shown;  the  fourth  room  is 
turned  directly  off  the  cross-entry,  widened  out  on  the  right,  and  a  cross-cut 
turned  to  the  right  as  before  and  two  more  rooms  are  turned  off  this  cross- 
cut, etc.  The  large  entry  coal  pillars  e,  40  ft.  X 125  ft.  in  size,  keep  the  weight 
off  the  cross-entries;  and  by  making  a  rather  thin  pillar  between  the  rooms, 

the  weight  is  thrown 
on  the  face  and  made 
to  assist  in  the  mining. 
In  the  second  work- 
ing, these  large  pillars 
can  be  taken  out,  as 
well  as  the  stumps  /, 
the  room  pillars  g,  and 
the  pillars  h  between 
the  entries. 

Fig.  7  shows  an- 
other method  of  turn- 
ing off  the  rooms  in 
order  to  give  additional 
support  to  the  entries. 

^^_^_^^^^_  ^^^^^^^^^^^  ^^  Large  pillars  a  are  left 
^^^•VJY^^^I  ^^^••^^HHi  I  aDOVe  tne  entry  b,  and 
^BHHBHH  !'••  from  each  neck  c 

a  ,      t  ^|  turned  off  the  entry  b 

mm  mmm  •••       •  •••  •••  ••  two  roads  are  driven, 

•  ^Bl  ^BB         •  ^Hl  ^Bfl  ^pj  one  along  each  side  of 
B       li       V        I    ^    ^B    ^  the   room    Pillars    e. 

v  •••-.-••-•  B  •  B  I  /  I  This  plan  has  been 
2  —  _ — ~—  —  S^  I  successfully  used  in  a 
B  I  B  B  B  B  I  bed  of  hard  coal  with 

•  •        •       B|        B|       V       I  a  strong  bottom  and  a 

^  thick,  strong  roof. 

Inclination  of 
Rooms  to  the  Entry. 
The  direction  in  which 
rooms  are  driven  with  respect  to  the  entries  off  which  they  are  turned  depends  on 
the  inclination  of  the  bed,  the  cleat  of  the  coal,  and  the  nature  of  the  overlying 
rock.  When  possible,  the  rooms  are  usually  driven  at  a  right  angle  to  the  entry. 
If  the  bed  is  flat,  the  rooms  may  be  turned  both  to  the  right  and  to  the  left  of 


614 


METHODS  OF  WORKING 


the  cross-entries,  and  in  such  a  seam,  and  where  the  entries  are  driven  in  pairs, 
a  series  of  rooms  is  often  driven  off  each  entry  of  the  pair.  If  the  bed  is  inclined 
to  any  extent,  the  rooms  are  turned  only  to  the  rise  of  the  higher  entry,  the 
other  entry  of  the  pair  being  used  as  an  air-course.  Rooms  are  usually  not 

turned  to  the  dip  if  much  water  will 
accumulate  at  the  face.  Where  there 
is  not  much  water  to  collect  at  the  face, 
the  rooms  may  be  turned  to  the  dip 
on  a  pitch  as  high  as  6°,  although,  if 
the  loaded  car  must  be  hauled  out  by  a 
mule,  the  dip  of  the  room  toward  the  face 
should  preferably  not  exceed  3°  to  4°. 
If  the  loaded  cars  are  pushed  out  of  the 
rooms  by  hand,  the  road  should  dip 
from  the  face  toward  the  entry,  or  should 
at  least  be  level.  A  car  can  be  con- 
trolled by  spragging  when  pushed  by 
hand  until  the  inclination  of  the  track 
is  about  6°;  that  is,  until  the  grade  is 
about  10%. 

As  it  is  not  usually  practicable  to 
haul  empty  cars  up  a  grade  of  more  than 
6°  to  8°,  if  the  pitch  of  the  bed  is  greater 
than  this  but  less  than  about  12°,  a 
suitable  grade  for  haulage  may  be  secured 
in  the  rooms  by  driving  the  rooms  at  an 

•p,  r  »  angle  to  the  entry,  as  shown  in  Fig.  8. 

The  method  of  working  an  inclined  room 

does  not  differ  from  that  used  where  the  room  is  at  right  angles  to  the 
entry.  The  angle  that  the  room  makes  with  the  entry  should  not  be  less 
than  30°  or  the  entry  pillar  will  not  have  the  required  strength,  unless  it  is 
left  very  large.  Where  rooms  are  driven  at  an  angle  to  the  entry,  the  coal 
between  the  first  room  and  the  slope  or  main  entry,  as  the  case  may  be,  is 
worked  out  by  means  of  cross-rooms  b 
driven  off  from  the  first  room  a  as 
shown.  When  the  inclination  of  the 
bed  is  above  10°  to  12°,  the  rooms  are 
usually  turned  at  right  angles  to  the 
entry  and  the  coal  conveyed  from  the 
face  to  the  entry  and  there  emptied 
into  the  mine  car. 

Rooms  driven  to  the  dip  are  also 
sometimes  driven  at  an  angle  to  the 
entry  where  the  inclination  of  the  seam 
exceeds  3°  and  where  mule  haulage  is 
used  in  the  rooms. 

The  angle  that  a  room  should  make 
with  the  entry  in  order  to  obtain  a 
given  grade  of  track  in  a  seam  having 
a  given  inclination  is  found  by  the  method  described  under  Direction  of 
Entries  in  Inclined  Seams,  but  placing  A  =  angle  between  room  and  cross-entry. 
Direction  of  Rooms  as  Determined  by  Cleat. — In  most  coal  seams  there 
are  vertical  cleavages,  called  cleats,  which  cross  the  seam  in  two  directions 

about  at  right  angles  to  each  other. 
The  face  cleats  are  the  longer  and  usually 
the  more  pronounced,  while  the  end 
or  butt  cleats  are  the  shorter  and  more 
irregular.  The  cleat  of  the  coal  some- 
times determines  the  direction  in  which 
the  room  should  be  driven,  since  the 
coal  may  break  more  easily  on  one 
cleat  than  another  and  thus  produce  a 
larger  amount  of  coal  for  a  given 
amount  of  undercutting.  Fig.  9  shows 
rooms  driven  at  various  angles  to  the 
cleat  and  the  name  by  which  each  is  designated. 

In  driving  face  on,  the  room  is  driven  so  that  the  face  is  parallel  to  the  face 
cleats,  which  are  represented  by  the  longer  white  lines,  while  the  end  cleats 


FIG.  8 


FIG.  9 


METHODS  OF  WORKING 


615 


DISTANCE  FROM  CENTER  TO   CENTER  OF  ROOMS  OR    BREASTS 
MEASURED  ON  ENTRY  OR  GANGWAY 


&: 

Width  of  Room  +  Thickness  of  Pillar,  in  Feet 

Q)        M     H. 

20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

** 

Distance  Measured  on  Entry,  in  Feet 

90 

20.0 

25.0 

30.0 

35.0 

40.0 

45.0 

50.0 

55.0 

60.0 

65.0 

70.0 

75.0 

85 

20.0 

25.1 

30.1 

35.1 

40.2 

45.2 

50.1 

55.2 

60.2 

65.3 

70.3 

75.3 

80 

20.3 

25.4 

30.5 

35.5 

40.6 

45.7 

50.8 

55.8 

60.9 

66.0 

71.1 

76.2 

75 

20.7 

25.9 

31.1 

36.2 

41.4 

46.6 

51.8 

56.9 

62.1 

67.3 

72.5 

77.7 

70 

21.3 

26.6 

31.9 

37.2 

42.6 

47.9 

53.2 

58.5 

63.9 

69.2 

74.5 

79.8 

65 

22.1 

27.6 

33.1 

38.6 

44.1 

49.6 

55.2 

60.7 

66.2 

71.7 

77.2 

82.8 

60 

23.1 

28.9 

34.6 

40.4 

46.2 

52.0 

57.7 

63.5 

69.3 

75.1 

80.8 

86.6 

55 

24.4 

30.5 

36.6 

42.7 

48.8 

54.9 

61.0 

67.1 

73.3 

79.4 

85.5 

91.6 

50 

26.1 

32.6 

39.2 

45.7 

52.2 

58.7 

65.3 

71.8 

78.3 

84.9 

91.4 

97.9 

45 

28.3 

35.4 

*42.4 

49.5 

56.6 

63.6 

70.7 

77.8 

84.9 

91.9 

99,0 

106.1 

40 

31.1 

38.9 

46.7 

54.5 

62.2 

70.0 

77.8 

85.6 

93.3 

101.1 

109.0 

116.7 

35 

34.9 

43.6 

52.3 

61.0 

69.7 

78.5 

87.2 

95.9 

104.6 

113.4 

122.1 

130.8 

30 

40.0 

50.0 

60.0 

70.0 

80.0 

90.0 

100.0 

110.0 

120.0 

130.0 

140.0 

150.0 

25 

47.3 

59.2 

71.0 

82.8 

94.6 

106.5 

118.3 

130.1 

142.0 

153.8 

165.6 

177.5 

20 

58.5 

73.1 

87.7 

102.3 

117.0 

131.6 

146.2 

160.8 

175.5 

190.1 

204.7 

219.3 

15 

77.3 

96.6 

115.9 

135.2 

154.5 

173.9 

193.2 

212.5 

231.9 

251.2 

270.5 

289.8 

10 

115.2 

144.0 

172.8 

201.6 

230.4 

259.2 

287.9 

316.7 

345.5 

374.3 

403.1 

432.0 

5 

229.5 

286.9 

344.2 

401.6 

459.0 

516.3 

573.7 

631.1 

688.4 

745.8 

803.2 

860.5 

are  shown  by  the  shorter  ones.  This  is  the  general  direction  of  driving  rqotns 
and  is  adopted  where  conditions  permit.  Fig.  1  shows  that  in  the  prevailing 
American  practice  the  rooms  are  parallel  to  the  main  entries;  hence  main 
entries  are  face  entries  and  cross-entries  are  driven  parallel  to  the  ends  of  the 
coal  and  are  end-entries,  although  far  more  commonly  called  butt-entries. 
Face  on  is  adopted  where  the  face  cleats  are  not  as  free  or  as  numerous  as  the 
end  cleats.  Coal  worked  in  this  way  breaks  well,  and  the  yield  is  perhaps 
larger  for  the  same  amount  of  undercutting  than  by  any  of  the  other  methods, 
producing  also  a  greater  proportion  of  lump  coal. 

In  working  long  horn,  the  opening  is  driven  so  that  the  face  makes  an 
angle  less  than  45°  with  the  face  cleats  of  the  coal;  the  coal  breaks  in  long  slabs 
or  wedge-shaped  masses,  giving  rise  to  the  name  long  horn.  A  face  driven  this 
way  does  not  require  the  same  amount  of  cutting;  and  if  slightly  inclined  grip 
shots  are  used,  good-sized  lump  coal  is  produced.  If  the  coal  works  too  freely 
face  on,  by  this  method  support  is  given  the  ends  of  the  coal  while  being 
undercut. 

In  working  half  on,  the  rooms  are  driven  at  an  angle  of  45°  with  the  cleats 
of  the  coal.  The  method  is  adapted  to  coals  that  break  about  equally  well  on 
the  face  and  the  end  cleats. 

In  working  short  horn,  the  face  of  the  room  makes  an  angle  between  45° 
and  0°  with  the  face  cleats.  The  method  is  adapted  to  the  working  of  coal 
where  the  end  cleats  are  so  pronounced  as  to  require  the  additional  support 
given  to  the  coal  by  this  method  when  mining  or  undercutting.  It  bears  the 
same  relation  to  end-on  work  that  long  horn  bears  to  face-on. 

In  working  end  on,  the  face  of  the  room  is  at  right  angles  to  the  face  cleats, 
and,  consequently,  parallel  to  the  end  or  butt  cleats.  This  method,  and  short 
horn,  are  adapted  to  the  working  of  coals  under  strong  roof  pressure.  In  gen- 
eral, the  size  of  the  coal  and  the  yield  are  not  as  great  as  in  face  on  or  long  horn. 

As  the  face  cleats  are  quite  pronounced  when  rooms  are  driven  end  on, 
wide  pillars  are  generally  used. 

Where  there  is  much  occluded  gas  at  high  pressure,  the  direction  of  the  work- 
ing face  with  respect  to  the  face  cleats  of  the  coal  is  important,  as  a  breast 
driven  face  on  affords  little  or  no  opportunity  for  the  escape  of  this  gas,  except 


616  METHODS  OF  WORKING 

as  it  finds  vent  in  violent  outbursts.  On  the  other  hand,  if  this  coal  is  worked 
end  on,  the  face  cleats  are  cut  across  and  exposed  and  the  gas  escapes  gradually 
and  quietly.  The  method  by  short  horn  or  half  on,  may  be  found  to  give  good 
results  in  such  a  case,  as  the  pressure  of  the  gas  is  then  made  to  do  effective 
work  in  assisting  to  break  down  the  coal. 

Direction  of  Rooms  as  Determined  by  Slips  in  the  Roof.— A  roof  slip  is  a 
line  of  weakness  that  was  at  some  time  a  line  of  fracture  in  the  rock  and 
which  may  or  may  not  have  been  filled  subsequently,  by  infiltration,  with 
clay  or  other  matter.  Roof  slips  frequently  occur  in  parallel  lines  in  the 
rocks  overlying  coal  seams;  if  this  is  the  case,  there  is  great  danger  from 
roof  falls  if  the  room  face  is  parallel  to  the  direction  of  the  slips,  for  the 
miner  cannot  see  the  slip  until  too  late  to  prevent  accident  by  the  falling  of 
the  slate  or  the  sudden  breaking  down  of  the  coal.  By  driving  the  room  at 
an  angle  across  the  slips,  not  only  is  sufficient  support  given  to  the  roof  to 
prevent  its  breaking  suddenly,  but  the  presence  of  the  slip  is  readily  observed. 

When  the  face  is  at  right  angles  to  the  direction  of  the  slips,  there  is  not 
the  same  danger  at  the  face  as  when  the  face  is  parallel  to  the  slip,  because  the 
roof  is  better  supported  by  the  coal.  The  chief  danger  occurs  when  drawing 
back  the  pillars,  for  as  the  slips  are  parallel  to  the  line  of  the  pillars,  a  large 
fall  may  occur  suddenly  at  any  time  by  an  unexpected  cross-break.  In  any 
case,  when  driving  under  such  roof,  a  larger  amount  of  good  timber  is  required. 

WORKING  FLAT  SEAMS 

The  general  arrangement  of  a  mine  worked  on  the«double-entry  system 
according  to  the  common  American  practice  is  shown  in  Fig.  1.  The  reasons 
for  the  direction,  dimensions,  etc.,  of  the  entries  and  rooms  have  been  given 
in  previous  paragraphs.  The  general  method  is,  of  course,  slightly  changed 
locally  to  meet  prevailing  conditions,  some  of  the  modifications  being  given 
here  under  the  names  of  the  mining  districts  in  which  they  are  used. 

Pittsburg  Region. — The  coal  is  worked  with  double  entries,  with  cut- 
throughs  between  for  air,  and  on  face  and  butt  entries  are  about  9  ft.  wide, 
and  the  rooms  21  ft.  wide  and  about  250  ft.  long;  narrow  (or  neck)  part  of  room, 
21  ft.  long  by  9  ft.  wide;  room  pillars,  15  to  20  ft.  wide,  depending  on  depth 
of  strata  over  the  coal,  which  is  from  a  few  feet  to  several  hundred  feet.  The 
mining  is  done  largely  by  machines  of  various  types.  Coal  is  hard,  of  course, 
and,  in  many  places,  the  roof  immediately  over  the  coal  is  also  quite  hard. 
There  are  about  4  ft.  of  alternate  layers  of  hard  slate  and  coal  above  the  coal 
seam.  Rooms  are  mined  from  lower  end  of  butt  as  fast  as  butt  is  driven, 
the  ribs  being  drawn  as  mining  progresses.  As  the  coal  is  harder  than  in  the 
Connellsville  region,  thickness  of  coal  pillar  between  parallel  entries  is  some- 
what less. 

Clearfield  Region. — The  butt  and  face  are  not  strongly  marked  in  the  B 
or  Miller  seam,  the  one  chiefly  worked  in  this  region.  Where  possible,  these 
cleavages  are  followed  in  laying  out  the  workings,  but  the  rule  is  to  drive  to 
the  greatest  rise  or  dip  and  run  headings  at  right  angles  to  the  right  and  left, 
regardless  of  anything  else.  The  main  dip  or  rise  heading  is  usually  driven 
straight,  and  is  raised  out  of  swamps  or  cut  down  through  rolls — very  com- 
mon here — unless  they  are  too  pronounced,  when  the  heading  is  curved  around 
them.  The  same  is  true  of  room  headings,  except  that  they  are  more  usually 
crooked,  not  being  graded  except  over  very  minor  disturbances. 

As  the  B  seam  rarely  runs  over  4  ft.  in  thickness,  and  is  worked  as  low  as 
2  ft.  8  in.,  in  the  haulage  headings  the  roof  is  taken  down  to  give  5  ft.  to  5  ft. 
2  in.  above  the  rail,  or  5  ft.  8  in.  to  5  ft.  10  in.  in  the  clear.  Where  the  result- 
ing rock  is  taken  outside,  the  headings  are  driven  10  ft.  wide  with  24  ft.  of 
pillar,  roof  taken  down  in  haulage  heading  but  not  in  the  air-course.  Where 
the  rock  is  gobbed  underground,  the  haulage  heading  is  18  to  24  ft.  wide,  air- 
course  10  ft.,  pillar  24  ft.,  and  roof  taken  down  in  haulage  heading  only.  The 
thinner  the  coal,  the  wider  the  heading.  It  is  more  economical  to  haul  the  rock 
to  daylight.  The  bottom  generally  consists  of  3  ft.  to  5  ft.  of  hard  fireclay, 
frequently  carrying  sulphur  balls. 

In  numerous  places,  the  sand  rock  is  immediately  over  the  coal,  but  in 
most  cases  there  is  from  3  to  5  ft.  of  slate  before  the  sand  rock  is  reached. 
Room  headings  are  driven  280  ft.  apart,  haul  rock  to  daylight,  heading  10  ft. 
wide  with>24  ft.  pillar  to  10  ft.  air-course,  in  which  roof  is  left  up.  A  15  ft.  to 
25  ft.  chain  pillar  is  left  between  air-course  and  faces  of  rooms  from  the  lower 
heading,  every  fourth  to  eighth  of  which  is  driven  through  to  the  air-course 
to  shorten  the  travel  of  the  air.  The  rooms  are  therefore  180  to  200  ft.  long, 
and  the  men  push  the  cars  to  the  face,  an  important  item  in  this  thin  coal. 


METHODS  OF  WORKING  617 

Rooms  are  21  ft.  wide  with  a  15  ft.  pillar,  and  a  15  ft.  chain  pillar  is  left 
between  the  first  room  on  any  room  heading  and  the  main  heading,  and  roof 
is  not  taken  down  in  rooms.  Main-heading  track  is  usually  30-lb.  iron,  room 
heading,  12  lb.,  and  2"X  1"  strap  iron  set  on  edge  is  used  in  the  rooms  in  low 
coal.  Mine  cars  hold  from  600  to  800  lb.  in  low  seams,  and  1,500  to  2,000  lb. 
in  the  so-called  thick  seams;  i.  e.,  3  ft.  8  in.  to  4  ft.  thick. 

Reynoldsville  Region. — The  measures  are  very  regular,  and  the  method 
employed  is  the  typical  one  shown  in  Fig.  1.  The  average  thickness  of  the  prin- 
cipal seam  is  6$  ft.  and  the  pitch  is  3°  to  4°.  The  coal  is  hard  and  firm,  and 
contains  no  gas;  the  cover  is  light,  and  on  top  of  the  coal  there  are  3  or  4  ft. 
of  bony  coal;  the  bottom  is  fireclay.  Drift  openings  and  the  double-entry 
system  are  used.  Both  main  and  cross-entries  are  10  ft.  wide,  with  a  24-ft. 
pillar  between.  The  cross-entries  are  600  ft.  apart,  and  a  24-ft.  chain  pillar 
is  left  along  the  main  headings.  The  rooms  are  about  24  ft.  wide  and  open 
inbye,  the  necks  being  9  ft.  wide  and  18  ft.  long.  The  pillars  are  from  18  to 
30  ft.  thick. 

West  Virginia  Region. — The  general  plan  of  working  the  Pittsburg  coal 
in  the  northern  part  of  West  Virginia  is  as  follows:  The  coal  measures  vary 
from  7  to  8  ft.  in  thickness,  and  have  a  covering  varying  from  50  to  500  ft. 
The  coal  does  not  dip  at  any  place  over  5%.  In  most  places  the  coal  is  prac- 
tically level,  or  has  just  sufficient  dip  to  afford  drainage.  The  usual  method 
of  exploitation  is  to  advance  two  parallel  headings,  30  ft.  apart,  on  the  face  of 
the  coal.  At  intervals  of  500  to  600  ft.,  cross-headings  are  turned  to  right  and 
left,  and  from  these  headings  rooms  are  turned  off.  These  cross-headings  are 
driven  in  pairs  about  20  or  30  ft.  apart.  Between  the  main  headings  and  the 
first  room  is  left  a  block  of  coal  about  100  ft.  wide,  and  on  the  cross-headings 
there  is  often  left  a  barrier  pillar  of  100  ft.  after  every  tenth  room. 

The  headings  are  driven  from  8  to  12  ft.  wide,  and  the  rooms  are  made 
24  ft.  wide  and  250  to  300  ft.  long.  A  pillar  is  left  between  the  rooms  about 
15  to  20  ft.  wide.  These  pillars  are  withdrawn  as  soon  as  the  panel  of  rooms 
has  been  finished.  The  rooms  are  driven  in  from  the  entry  about  10  ft.  wide 
for  a  distance  of  20  ft.,  and  then  the  room  is  increased  in  width  on  one  side. 
The  track  usually  follows  near  the  rib  of  the  room.  Cross-cuts  on  the  mam 
and  cross-headings  are  made  every  75  to  100  ft.,  and  in  rooms  about'  every 
100  ft.  for  ventilation. 

The  double-heading  system  of  mining  and  ventilation  is  in  vogue.  Over- 
casts are  largely  used,  but  a  great  many  doors  are  used  in  some  of  the  mines. 
Rooms  are  worked  in  both  directions.  This  is  the  general  practice  when  the 
grades  are  slight.  When  the  coal  dips  over  1%,  the  rooms  are  driven  in  one 
direction  only.  In  this  case,  the  rooms  are  made  longer,  as  much  as  350  ft. 
It  is  the  custom  then  to  break  about  every  third  room  into  the  cross-heading 
above  (a  practice  ill  advised).  The  floor  of  this  bed  of  coal,  being  composed 
of  shale  and  fireclay,  often  heaves,  especially  when  it  is  made  wet.  Some  trouble 
is  at  times  experienced  by  having  the  floor  heave  by  reason  of  the  pillars  being 
too  small  for  the  weight  they  support. 

The  dimensions  of  rooms  and  pillars  given  are  for  a  mine  (with  covering 
300  to  500  ft.  thick)  having  a  fairly  good  and  strong  roof.  Where  roof,  bot- 
tom, and  thickness  of  cover  change,  these  dimensions  are  altered  to  suit  the 
requirements.  The  main-heading  pillars  may  be  reduced  to  30  or  40  ft.; 
the  rooms  may  be  made  15  ft.  wide  with  12  ft.  pillars,  and  no  barrier  pillars 
may  be  left  on  the  cross-headings. 

The  foregoing  plan  is  very  much  followed  in  other  parts  of  the  state;  at 
least  an  attempt  is  made  to  do  so,  but  local  disturbances  often  require  changes 
in  the  plan.  This  plan  is  followed  on  some  parts  of  New  River,  and  also  in 
the  Flat  Top  field. 

George's  Creek  District,  Md. — Fig.  10  shows  the  method  used  in  the 
George's  Creek  field,  Maryland.  The  coal  shows  no  indication  of  cleats,  and 
the  butts  and  headings  can  be  driven  in  any  direction.  The  main  heading  is 
driven  to  secure  a  light  grade  for  hauling  toward  the  mouth.  Cross-headings 
making  an  angle  of  35°  to  40°  are  usually  driven  directly  to  the  rise,  and  of  the 
dimensions  shown.  Pillars  are  drawn  as  soon  as  the  rooms  are  completed, 
being  attacked  on  the  ends  and  from  the  rooms  on  either  side,  the  coal  being 
shoveled  to  the  mine  car  on  a  track  in  the  room.  Very  wide  pillars  are  split. 
No  effort  is  made  to  hold  up  the  overlying  strata,  and  the  entire  bed  is  removed 
as  rapidly  as  possible.  An  extraction  of  85%  of  the  bed  is  considered  good 
work.  A  section  of  the  seam  is  as  follows:  Roof  coal,  10  in.;  coal,  7  ft.; 
slate,  i  in.;  coal,  10  in.;  slate,  \  in.;  coal,  10  in.;  fireclay;  slate.  The  top  bench 
is  bony  and  frequently  left  in  place  to  prevent  disintegration  of  the  roof  by  the 


618 


METHODS  OF  WORKING 


air  Above  this  coal  is  from  8  to  10  ft.  of  rashings,  consisting  of  alternating 
thin  beds  of  coal  and  shale,  that  is  very  brittle,  and  requires  considerable 
timber  to  keep  it  in  place. 

Blossburg  Coal  Region,  Pa. — Coal  is  generally  mined  trom  emits,  but  in  a 
few  cases  by  slopes.  Fig.  11  shows  the  general  method  adopted;  the  breasts 
are  run  at  right  angles  to  the  slips;  the  breast  pillars  are  split  by  a  center  head- 
ing and  taken  out  as  soon  as  the  breasts  are  finished.  The  gangway  pillars 


FIG.  10 

are  taken  out  retreating  from  the  crop  or  boundaries  of  the  property.  The 
general  average  of  the  coal  seams  is  not  over  3^  ft.,  accompanied  by  fireclay 
and  some  iron  ore.  The  dip  of  the  veins  is  about  3%. 

Indiana  Coal  Mining. — Fig.  12  shows  the  double-entry  room-and-pillar 
methods  as  used  in  Indiana.  The  entries  are  generally  6  ft.  high,  8  ft.  broad, 
the  minimum  height  required  by  law  being  4  ft.  6  in.  The  rooms  are  from 
21  to  40  ft.  in  width.  The  mines  are  generally  shallow.  The  rooms  are  shown 
as  widened  on  both  ribs,  but  a  more  usual  method  in  this  locality  is  to  widen 
the  room  on  the  inbye  rib,  leaving  one  straight  rib  for  the  protection  of  the 
road  in  the  room. 

Iowa  Coal  Mining.— The  coal  lies  at  a  depth  of  200  ft.  below  the  surface,  and 
is  geologically  similar  to  that  of  the  Missouri  and  Illinois  fields.  It  lies  in 
lenticular  basins  extending  northwest  and  southeast  and  outcropping  in  the 
larger  river  beds.  The  seams  are  practically  level,  non-gaseous,  and  gen- 
erally underlaid  by  fireclay  and  overlaid  by  a  succession  of  shales,  sandstones, 


FIG.  11 


Mouth  N°3  Drift 


and  limestones,  which  are  generally  of  a  yielding  nature,  giving  a  strong, 
good  roof  for  mining.  There  are  three  distinct  seams,  the  lower  one,  which 
varies  from  4  to  7  ft.  in  thickness,  being  the  only  one  worked.  The  coal  is  a 
hard,  brittle,  bituminous  that  shoots  with  difficulty,  but  is  excellent  for  steam 
and  domestic  uses.  About  Centerville,  the  coal  has  a  distinct  cleat,  but  else- 
where in  the  state  this  is  lacking. 

The  entry  pillars  along  the  main  roads  are  6  to  8  yd.  thick,  for  the  cross- 
entries  5  to  6  yd.,  and  for  the  rooms  3  to  5  yd.  Room  pillars  are  drawn  in 
when  approaching  a  cross-cut.  Both  room-and-pillar  and  longwall  methods 


METHODS  OF  WORKING  619 

are  in  use,  with  modifications  of  each.  In  the  room-and-pillar  method,  the 
double-entry  system  is  almost  invariably  used  in  the  larger  mines.  Rooms  are 
driven  off  each  entry  of  each  pair  of  cross-entries  at  distances  of  30  to  40  ft., 
center  to  center;  the  rooms  are  8  to  10  yd.  in  width,  and  pillars  3  to  4  yd.  The 
rooms  are  narrow  for  a  distance  of  3  yd.,  and  then  widened  inbye  at  an  angle 
of  45°  to  their  full  width.  They  vary  from  50  to  100  yd.  in  length,  and  the 
road  is  carried  along  the  straight  rib. 

When  double  rooms  are  driven,  the  mouths  of  the  rooms  are  40  to  50  ft. 
apart,  and  they  are  driven  narrow  from  the  entry  a  distance  of  4  or  5  yd.  A 
cross-cut  is  then  made  connecting  them,  and  a  breast  16  yd.  wide  is  driven 
up  50  to  60  yd.  The  pillar  between  each  pair  of  rooms  is  12  to  15  yd. 

In  pillar-and-stall  work,  the  stalls  are  usually  turned  off  narrow  and  widened 
inside,  the  pillar  varying  from  5  to  8  yd.  The  stalls  are  30  to  40  yd.  in  length, 
and  the  pillars  are  drawn  back.  When  the  stalls  are  driven  in  pairs,  the 
pillar  8  to  10  yd.  in  width  is  carried  between  them. 

Steep  Rooms. — Where  the  pitch  is  so  great  that  mules  cannot  haul  the  car 
to  the  face  for  loading,  a  windlass  may  be  used  for  the  purpose,  the  handle 
of  which  is  turned  by  the  miner.  If  electric  haulage  is  used,  the  motor  may 
be  blocked  on  the  rails  near  the  mouth  of  the  room,  and  its  cable  reel  or  a  special 
drum  used  to  wind  up  a  rope  running  over  the  necessary  sheaves  (pulleys) 
at  the  mouth  and  face  of  the  room,  which  rope,  attached  to  the  end  of  the  car, 


FIG.  12 

hauls  it  up  to  the  face.  In  other  cases,  self-acting  inclines  are  used,  in  which 
the  weight  of  the  descending  loaded  car  pulls  the  empty  car  to  the  face.  This 
arrangement  requires  a  double  track  in  the  room.  Where  roof  conditions 
permit  of  only  a  single  track,  another  pair  of  lighter  rails  may  be  laid  between 
those  of  the  regular  room  track  and  upon  these  a  carriage  with  a  counterweight 
will  run.  This  counterweight  is  so  adjusted  that  while  the  loaded  car  in  descend- 
ing will  raise  it  to  the  face,  its  weight  in  descending  will  pull  the  empty  car 
to  the  face. 

Usually,  a  grade  at  which  mules  may  pull  the  cars  to  the  face  is  secured 
by  inclining  the  rooms  to  the  entry,  the  direction  being  determined  by  the 
formula  given  before.  If  the  rooms  are  inclined  and  equipped  with  some 
one  of  the  mechanical  appliances  just  described,  coal  may  be  loaded  at  the 
face  on  much  steeper  pitches  than  would  otherwise  be  the  case. 

WORKING  PITCHING  SEAMS 

Difficulties  in  Mining  on  a  Pitch. — A  soft  friable  coal  when  mined  on  a 
steep  pitch  has  a  tendency  to  run;  that  is,  without  any  mining,  it  breaks  freely 
from  the  face  of  the  breast  and  then  slides  down  the  pitch.  Sometimes  little 
or  no  work  need  be  done  in  the  breast  after  the  chute  has  been  widened  out 
to  form  the  breast,  as  sufficient  coal  thus  breaks  from  the  face  from  time  to 
time  to  keep  the  breast  full  as  the  coal  is  drawn  out  through  the  loading  chute; 
the  coal  continues  to  run  until  the  breast  breaks  through  into  the  upper  gang- 
way. The  uncertainty  that  necessarily  exists  in  regard  to  the  flow  of  the  coal 


620  METHODS  OF  WORKING 

renders  this  method  unreliable,  although  it  is  often  adopted  from  neces- 
sity. One  objection  to  this  method  is  that  the  running  of  the  coal  cannot  be 
controlled,  and  the  widths  of  the  breast  and  pillars  cannot  be  maintained; 
the  breast  is  often  increased  in  width  and  much  or  all  of  the  pillar  coal  runs 
out  at  the  chutes,  while  at  other  times  the  width  of  the  breast  gradually 
decreases  and  ultimately  the  coal  stops  running.  The  miner  must  then  go 
up  into  the  breast  and  start  the  coal  to  running  again  by  widening  out  the 
breast,  or  by  placing  one  or  more  small  shots  in  the  coal;  this  is  a  dangerous 
operation,  as  the  coal  may  come  with  a  rush. 

The  coal  on  a  steep  pitch  may  not  run  sufficiently  to  do  away  with  mining, 
but  it  may  be  so  free  as  to  require  particular  support  at  the  face  to  prevent  the 
coal  from  running  sufficiently  to  injure  the  miners.  The  working  of  free  coal 
on  a  heavy  pitch  requires  skilled  labor;  and  as  gas  usually  issues  from  such  coal 
in  large  quantities,  safety  lamps  must  often  be  used,  thus  increasing  the  danger 
from  falls  on  account  of  insufficient  light.  The  props  used  under  these  con- 
ditions should  not  be  less  than  6  in.  in  diameter  and  should  be  very  firmly  set. 
If  the  roof  is  strong  and  firm,  these  props  may  be  taken  out  and  moved  for- 
wards as  required,  thus  saving  labor  and  material. 

In  working  coal  by  the  battery  method,  the  coal  will  sometimes  become 
clogged  and  form  an  arch,  which  supports  all  the  coal  above  the  arch  and  allows 
the  breast  below  to  become  empty  as  the  coal  is  gradually  drawn  out  through 
the  loading  chute.  This  condition  is  dangerous  to  the  men  working  on  top 
of  the  coal  near  the  face,  for  if  the  arch  suddenly  gives  away  they  may  be  car- 
ried down  and  buried  in  the  coal.  Such  a  slide  is  also  apt  to  be  very  disastrous 
to  the  battery  and  the  sides  of  the  chute.  To  break  down  such  an  arch,  an 
opening  may  be  made  in  the  side  of  the  chute  and  the  coal  started  to  running 
by  means  of  bars.  Occasionally  a  small  stick  of  dynamite  is  put  under  the 
coal  and  the  arch  loosened  in  this  way.  When  this  is  done,  an  opening  should 
be  made  from  the  side,  and  the  miner  should  not,  as  he  sometimes  does,  climb 
up  the  chute  and  after  setting  off  his  fuse  trust  to  getting  out  before  the  coal 
begins  to  slide,  as  this  is  extremely  dangerous. 

After  the  face  has  been  blasted  down,  lumps'of  coal  will  sometimes  lodge 
in  the  manways  alongside  the  chute  and  these  must  be  similarly  dislodged  by 
means  of  bars  or  with  dynamite.  In  returning  to  the  face  after  a  blast  has 
been  fired,  the  miner  and  his  laborer  should  be  exceedingly  careful  that  the 
loose  coal  does  not  roll  down  the  manway  on  them,  and  should  also  use  great 
care  to  see  that  all  loose  coal  in  the  face  is  barred  down  before  they  again 
begin  work. 

Working  Thick  and  Gaseous  Seams  That  Run. — In  large  seams,  when  the 
coal  is  soft  and  shelly  or  slippery,  lies  at  an  angle  of  more  than  50°,  and 
generates  large  quantities  of  firedamp,  a  source  of  danger  is  the  sudden  lib- 
eration of  gas  should  a  breast  run.  To  meet  these  conditions,  the  air-eourse 
may  be  driven  above  the  entry  or  gangway  and  used  as  a  return,  the  fan  being 
attached  as  an  exhaust,  and  the  working  rooms  or  breasts  ventilated  in  pairs. 
The  inside  manway  of  one  of  a  pair  of  breasts  is  connected  with  the  gangway  for 
the  intake,  and  the  outside  manway  of  the  other  breast  with  the  return  airway, 
giving  each  pair  of  breasts  a  separate  split  of  the  current.  In  collieries  where 
this  system  of  working  is  followed,  the  coal  is  soft.  A  new  breast  is  worked  up 
a  few  yards,  but  as  soon  as  it  is  opened  out,  the  coal  runs  freely  and  the  man- 
ways are  pushed  up  on  each  side  as  rapidly  as  possible,  to  keep  up  with  the 
face.  Two  miners,  one  on  either  side,  sometimes  finish  a  breast  without  being 
able  to  cross  to  each  other.  The  work  is  done  exclusively  with  safety  lamps, 
and  when  a  breast  runs  the  gas  is  liberated  in  such  quantities  that  it  fre- 
quently fills  breasts  from  the  top  to  the  airway  before  the  men  can  get  down 
the  manway  on  the  return  side.  When  the  gas  reaches  the  cross-hole,  it 
passes  into  the  return  airway  without  reaching  any  part  where  men  are  work- 
ing. Should  a  run  of  coal  block  a  breast  by  closing  the  manway,  it  affects  the 
current  of  one  pair  of  breasts  alone.  As  the  gangway  is  the  intake,  leakage  at 
the  batteries  passes  into  the  breasts,  as  the  cross-holes  are  above  their  level 
and  the  gas  is  thus  kept  above  the  starter  when  at  the  draw-hole.  The  gang- 
way, chutes,  and  airway  are  supplied  by  wooden  pipes,  which  connect  with  a 
door  behind  the  inside  chute.  If  a  breast  runs  up  to  the  surface,  it  does  not 
affect  the  return  airway,  as  it  is  in  the  solid. 

Among  the  disadvantages  urged  against  this  system  of  working  are  the 
following: 

It  increases  the  friction,  as  the  air  must  pass  in  the  airway  all  the  distance 
from  the  breast  to  the  fan,  the  area  of  the  airway  being  small  in  comparison 
to  the  gangway  or  intake. 


METHODS  OF  WORKING  621 

As  the  faces  of  the  breasts  are  so  much  higher  than  the  return  airway,  the 
lighter  gas  must  be  forced  down  into  the  return  against  the  buoyant  power  of 
its  smaller  specific  gravity. 

The  reduction  of  friction  obtained  by  splitting  is  neutralized  by  each  split 
running  up  one  small  man  way  and  down  another;  the  advantage  of  running 
through  several  pillar  headings  and  thus  securing  a  shorter  course  being  lost. 
This  can  be  partly  obviated  by  ventilating  the  breasts  in  groups,  but  the  dangers 
avoided  in  splitting  are  increased. 

Blackdamp,  which  accumulates  in  the  empty  or  partly  empty  breasts, 
works  its  way  down  and  mixes  with  the  intake  current,  as  there  is  no  return 
current  in  the  breast  strong  enough  to  carry  it  away,  the  return  being  closed 
in  the  airway. 

All  things  considered,  when  the  seam  is  soft  and  has  a  pitch  of  40°  and 
upwards,  and  emits  large  quantities  of  gas  in  sudden  outbursts,  as  in  running 
breasts,  this  system  is  the  best  that  can  be  adopted. 

Working  Thick  Non-Gaseous  Seams. — The  reverse  of  the  system  just 
described  is  followed  at  some  collieries  where  the  coal  is  hard  and  but  little  gas 
is  encountered.  The  airway  is  driven  over  the  gangway  or  against  the  top, 
the  fan  being  used  to  force  the  air  inward  to  the  end  of  the  airway.  The  air  is 
distributed  as  it  returns,  being  held  up  at  intervals  by  distributing  doors  placed 
along  the  gangway. 

Among  the  advantages  claimed  for  this  plan  are  the  following: 

As  the  pressure  is  outwards,  it  forces  smoke  and  gas  out  at  any  openings 
that  may  exist  from  crop-hole  falls  or  other  causes. 

The  warm  air  from  the  interior  of  the  mine  returning  up  the  hoisting  slope 
or  shaft  prevents  it  from  freezing. 

As  the  current  is  carried  from  the  fan  to  the  end  of  each  lift  without  passing 
through  working  places,  the  opening  of  doors  as  cars  are  passing,  etc.  does  not 
interfere  with  the  current. 

If  a  locomotive  is  used,  the  smoke  and  gases  generated  by  it  are  carried 
away  from  the  men  toward  the  bottom.  Locomotives  are  generally  used  only 
from  the  main  turnout  to  the  bottom. 

An  objection  to  this  system  is  that  the  gangway,  as  the  return,  is  apt  to  be 
smoky.  Starters  and  loaders  are  forced  to  work  in  more  or  less  smoke,  and 
even  the  mules  work  to  disadvantage,  while  if  gas  is  given  off,  it  is  passed  out 
over  the  lights  of  those  working  in  the  gangway. 

However,  in  places  where  there  is  but  little  gas,  and  airways  of  large  area 
can  be  driven,  this  plan  works  very  satisfactorily,  and  some  of  the  best  ven- 
tilated collieries  are  worked  upon  it. 

An  objection  advanced  by  some  against  forcing  fans  is  that  they  increase 
the  pressure,  thus  damming  the  gas  back  in  the  strata.  In  case  the  speed  of 
the  fan  is  slacked  off,  the  accumulated  gas  may  respond  to  the  lessened  pres- 
sure and  spring  out  in  large  volumes  from  its  pent-up  state.  This  argument, 
however,  works  both  ways.  An  exhaust  fan  running  at  a  given  speed  is  taking 
off  pressure,  and  if  anything  occurs  to  block  the  intake,  the  pressure  is  dimin- 
ished, and  the  gas  responds  to  the  decrease  on  the  same  principle. 

Working  Small  Seams  Laying  From  Horizontal  to  10°. — Two  gangways 
may  be  driven,  the  lower  or  main  gangway  being  the  intake.  Branch  gang- 
ways should  then  be  driven  diagonally  or  at  a  slant,  with  a  panel  or  group  of 
working  places  on  each  slant  gangway.  Large  headings  should  connect  the 
panels.  In  this  system,  the  air  is  carried  directly  to  the  face  of  the  gangway 
and  up  into  the  breasts,  returning  back  through  the  working  places.  The  intake 
and  return  are  separated  by  a  solid  pillar,  the  only  openings  being  the  slant 
gangways  on  which  are  the  panels.  The  advantages  of  this  plan  are: 

The  main  gangway  is  solid,  with  the  exception  of  the  small  cross-holes 
connecting  with  the  gangway  above;  these  furnish  air  to  the  gangway  and 
are  small  and  easily  kept  tight.  These  stoppings  should  be  built  of  brick, 
and  made  strong  enough  to  withstand  concussion. 

A  full  trip  of  wagons  can  be  loaded  and  coupled  in  each  panel  or  section 
without  interfering  with,  or  detaining  the  traffic  on,  the  main  road;  one  trip 
can  be  loaded  while  another  is  run  out  to  the  main  gangway  for  transporta- 
tion to  the  bottom. 

The  only  break  in  the  intake  current  is  when  a  trip  is  taken  out  from,  or 
returns  to,  a  panel;  this  can  be  partly  provided  against  by  double  doors,  set 
far  enough  apart  to  permit  one  to  close  after  the  trip  before  the  other  is  opened. 
This  distance  can  be  secured  by  opening  the  first  three  breasts  on  a  back 
switch  above  the  road  through  the  gangway  pillar,  or  by  running  each  branch 
over  the  other  far  enough  to  obtain  the  distance  for  the  double  doors. 


622 


METHODS  OF  WORKING 


If  it  is  not  desired  to  carry  the  whole  volume  of  air  to  the  end  of  the  air- 
way, a  split  can  be  made  at  each  branch  road.  These  will  act  as  unequal 
splits  in  reducing  friction,  and,  although  not  theoretically  correct,  are  prefer- 
able to  dragging  the  whole  current  the  full  length  of  the  workings. 

The  objections  urged  to  this  plan  are  that  it  involves  too  much  expense 
in  the  large  amount  of  narrow  work  at  high  prices  necessary  to  open  out  a 
colliery,  that  it  necessitates  a  double  track  the  whole  length  of  the  lift,  and 
that  the  grade  ascends  into  each  panel  or  section.  But  the  latter  criticism 
falls,  because  the  loss  of  power  hauling  the  empty  wagons  up  a  slight  grade 
is  more  than  made  up  by  the  loaded  wagons  running  down  while  the  mules 
are  away  pulling  a  trip  into  another  panel  or  section. 

For  a  large  colliery  this  is  without  doubt  the  best  and  cheapest  system. 
Working  Small  Seams  Laying  at  More  Than  10°.  —  In  small  seams  lying 
at  an  angle  of  more  than  10°,  and  too  small  to  permit  an  airway  over  the  chutes, 
it  is  more  difficult  to  maintain  ventilation.  If  air  holes  are  put  through  every 
few  breasts,  and  a  fresh  start  obtained  by  closing  the  back  holes,  or  if  an  open- 
ing can  be  gotten  through  to  the  last  lift  as  often  as  the  current  becomes  weak, 
an  adequate  amount  of  air  can  be  maintained,  because  the  lift  worked  can  be 

used  as  the  intake, 
and  the  abandoned 
lift  above  as  the  re- 
turn. To  ventilate 
fresh  ground,  the 
filling  of  the  chutes 
with  coal  will  have 
to  be  depended  on, 
or  a  brattice  must 
be  carried  along  the 
gangway.  This  can 
be  done  for  a  lim- 
ited distance  only, 
as  a  brattice  leaks 
too  much  air.  As 
a  rule,  collieries 
worked  on  this  plan 
are  run  along  until 
the  smoke  accumu- 
lates and  the  venti- 
lation becomes 
poor;  then  a  new 
hole  is  run  through 
and  the  brattice  re- 
moved and  used  as 
before  for  the  next 
section.  This  oper- 
ation  is  repeated 


13 


until  the  lift  is  worked  out.  Sometimes,  to  make  the  chutes  tight,  canvas 
covers  are  put  on  the  draw  holes,  but  as  they  are  usually  left  to  the  loaders  to 
adjust,  they  are  often  very  imperfectly  applied.  Then,  as  the  coal  is  fre- 
quently very  large,  the  air  will  leak  through  the  batteries. 

This  plan  works  very  satisfactorily  if  the  openings  are  made  at  short  inter- 
vals, say,  as  frequent  as  every  fifth  breast,  but  the  distance  is  usually  much 
greater  to  save  expense.  As  the  power  of  the  current  decreases  as  the  distance 
between  the  air  holes  is  increased,  good  ventilation  is  entirely  a  question  of  how 
often  a  cut-off  is  obtained. 

An  effective  ventilation  could  be  maintained  in  a  small  seam  at  a  heavy 
angle  by  working  with  short  lifts,  say  two  lifts  of  50  yd.  instead  of  one  of  100  yd., 
as  at  present.  The  gangways  should  be  frequently  connected,  and  one  used 
as  an  intake  and  the  other  as  a  return.  This  would  necessitate  driving  two 
gangways  where  one  is  now  made  to  do,  but  the  additional  expense  would  be 
made  up  in  the  greater  proportion  of  coal  won. 

Buggy  Breasts.  —  For  inclinations  between  10°and  18°,  that  is,'  after  mule 
haulage  becomes  impossible  and  until  the  coal  will  slide  in  chutes,  buggies 
are  often  used.  Fig.  13  shows  a  buggy  breast  m  plan  (a)  and  section  (&).  Coal 
is  loaded  into  a  small  car  or  buggy  c,  which  runs  to  the  lower  end  of  the  breast 
and  there  delivers  the  coal  upon  a  platform  I,  from  which  it  is  loaded  into  the 
mine  car.  The  refuse  from  the  seam  is  used  in  building  up  the  track,  and  if 
there  is  not  sufficient  refuse  for  this,  a  timber  trestle  is  used. 


METHODS  OF  WORKING 


623 


Another  form  of  buggy  breast  is  shown  in  Fig.  14.  Here  the  coal  is 
dumped  directly  into  the  mine  car  from  the  buggy.  If  the  breast  pitches 
less  than  6°,  the  buggy  can  be  pushed  to  the  face  by  hand,  but  in  rooms  of 
a  greater  pitch,  a  windlass  is  permanently  fastened  to  timbers  at  the  bottom 
of  the  breast,  while  the  pulleys  at  the  face  are  temporarily  attached  to  the 
props  by  chains,  so  that  they  can  be  advanced  as  the  face  advances.  The 
rope  used  is  from  £  in.  to  f  in.  in  diameter,  and  any  form  of  ordinary  hori- 
zontal windlass  can  be  used.  With  the  windlass  properly  geared,  one  man 
can  easily  haul  a  buggy  to  the  face  of  a  breast  in  a  few  minutes'  time.  The 
buggy  runs  upon  20-lb.  T  rails  spiked  with  2\"Xl"  spikes  upon  2"X4"  hem- 
lock studding  sawed  into  lengths  of  14  ft. 

Chutes.  —  A  chute  is  a  narrow  inclined  passage  down  which  the  coal  slides 
by  gravity,  or  is  pushed.  When  the  pitch  of  the  chute  is  between  15°  and  30°, 
sheet  iron  is  laid  in  it  to  furnish  a  good  sliding  surface  for  the  coal.  When  the 
inclination  is  less  than  20°,  it  is  generally  necessary  to  push  the  coal  down  the 
chute,  as  it  does  not  then  slide  readily  even  on  sheet  iron.  When  the  inclina- 
tion of  the  chute  exceeds  30°,  coal  will  slide  readily  on  a  rock  bottom  without 


FIG.  14 


the  use  of  sheet  iron.  The  use  of  chutes  is  therefore  limited  to  seams  whose 
inclination  is  greater  than  15°,  that  is,  to  what  are  generally  called  steep  seams. 

When  the  inclination  of  the  seam  is  less  than  30°  to  -35°,  a  single  chute  is 
usually  placed  in  the  center  of  the  room.  The  chute  ends  in  a  platform  pro- 
jecting into  the  entry,  and  from  this  platform  the  coal  can  be  readily  loaded  into 
the  mine  car.  The  refuse  made  in  mining  is  thrown  on  either  side  of  the  chute; 
and,  if  the  pillars  are  to  be  robbed,  this  refuse  should  be  kept  as  near  to  the 
center  of  the  room  as  possible.  Two  chutes  are  sometimes  employed,  one  along 
each  rib,  but  as  the  cost  of  the  second  chute  is  considerable,  it  is  not  generally 
used  unless  it  is  required  for  purposes  of  ventilation. 

Fig.  15  shows  an  inclined  room  with  a  sheet-iron  chute  a  in  the  center. 
As  the  coal  is  mined  at  the  face  b,  it  is  shoveled  into  the  chute  and  slides  by 
gravity  to  the  platform  c,  from  which  it  is  shoveled  into  the  mine  cars  on  the 
track  d.  Rows  of  props  e  are  frequently  stood  alongside  the  chute  to  keep  up 


624 


METHODS  OF  WORKING 


the  roof  above  it,  and  the  gob  is  stored  between  the  posts  and  the  rib  in  the 
spaces  /.     The  chute  also  acts  as  a  manway,  and  by  means  of  the  props  the 


FIG.  15 

miners  are  able  to  work  their  way  up  and  down  the  room.  The  top  coal  g 
is  left  up  to  help  keep  up  the  roof  and  may  be  taken  down  after  the  room  has 
been  driven  to  its  full  length  or  it  may  be  left  in 
place. 

When  the  bed  inclines  at  a  greater  angle  than 
about  35°,  it  is  necessary  to  provide  a  staging  or 
platform  of  some  kind  on  which  the  workmen  can 
stand  in  mining  the  coal.  A  staging  of  timbers 
may  be  built  and  advanced  as  the  face  advances, 
but  this  is  an  expensive  method,  and  it  is  gener- 
ally better  to  allow  the  room  to  fill  up  with  the 
broken  coal,  keeping  the  level  of  this  broken  coal 
just  near  enough  to  the  face  to  provide  a  stand- 
ing place  for  the  workmen.  The  coal  is  supported 
at  the  bottom  of  the  room  by  a  bulkhead  of  heavy 
timber  known  as  a  battery,  and  the  method  of 
working  is  known  as  working  on  battery.  Only 
enough  coal  is  taken  out  through  a  chute  at  the 
bottom  of  the  room  to  take  off  the  excess  of  coal 
that  cannot  be  thus  stored  in  the  room  owing  to 
the  fact  that  the  broken  coal  occupies  about  75% 
more  space  than  the  same  coal  in  the  solid. 

Single-Chute  Rooms. — Fig.  16  illustrates  the 
general  form  of  a  single-chute  room.  The  coal  a 
is  stored  in  the  center  and  a  manway  b  is  con- 
structed up  each  side  with  props  and  planking  for 
the  purpose  of  ventilation  and  to  afford  access  to 
the  face  for  the  workmen.  Cross-cuts  c  are  made 
by  driving  through  the  pillar  separating  adjacent 
rooms.  At  the  point  where  the  room  neck  widens 
to  full  room  width,  a  battery  is  constructed  to  hold 
FIG.  16  back  the  coal  in  the  chute.  This  is  composed  of 


METHODS  OF  WORKING 


625 


FIG.  17 


FIG.  18 


strong  posts  d  set  in  the  roof  and  floor  of  the  seam  as  a  support  for  the  cross- 
timbers  e\  a  small  opening  /,  known  as  the  loading  chute,  is  left  at  the  center 
of  the  battery  and  through  this  the  coal  is  drawn  as  required.  The  man- 
ways  b  are  connected  with  the  room  neck  by  a  small  opening  in  the  battery, 
through  which  workmen 
pass  in  going  to  and  from 
work.  This  opening  as 
covered  by  a  curtain  so  is 
to  maintain  the  air-current 
along  the  face. 

When  the  coal  is  drawn 
put  through  a  central  load- 
ing chute,  the  movement 
takes,  place  principally  in 
the  coal  lying  near  the  cen- 
ter of  the  breast.  If  the 
roof  is  poor,  the  movement 
of  the  coal  will  not  in  this  _ 
way  cause  it  to  fall  and  mix  with  the  coal;  and  if  the  floor  is  soft  the  props 
protecting  the  chute,  and  which  are  stepped  into  the  floor,  are  not  so  liable 
to  be  unseated,  closing  the  manway  and  blocking  the  ventilation.  The  sur- 
plus coal  is  sometimes  thrown  down  the  manways,  instead  of  being  drawn  out 
at  the  bottom  of  the  breast  through  a  loading  chute,  leaving  the  loose  coal 
in  the  center  of  the  breast  undisturbed  until  the  limit  is  reached. 

Double  Chute  Rooms. — Fig.  17  shows  the  arrangement  of  an  inclined 
room  in  which  the  weight  of  the  loose  coal  is  supported  mainly  by  a  pillar  of 
coal  left  along  the  entry.  The  coal  is  drawn  out  of  the  room  by  two  loading 
chutes,  one  at  each  side  of  this  pillar,  and  the  workmen  gain  access  to  the  man- 
ways along  the  room  ribs  through  short  manways  driven  through  the  entry 
pillars.  Fig.  18  shows  a  similar  arrangement  to  that  shown  in  Fig.  17  except 
that  the  sides  of  the  loading  chutes  are  in  line  with  the  sides  of  the  chute  in  the 
room,  the  manways  are  straight,  and  the  loading  chute  and  manway  are  in 
the  same  opening  in  the  coal.  This  method  has  an  advantage  over  that  shown 
in  Fig.  17,  as  it  requires  less  cutting  of  the  entry  pillars. 

An  advantage  of  supporting  the  coal  by  a  pillar  at  the  bottom  of  the  room, 
as  shown  in  Fig.  24,  is  that  there  is  less  likelihood  of  a  break  occurring  in  the 
batteries,  which  would  throw  all  of  the  coal  on  the  gangway  or  airway,  and  thus 
close  off  these  passages  and  interfere  both  with  haulage  and  ventilation. 

If  the  coal  seam  is  mixed  with  rock  that  can  be  readily  separated  from  the  coal 
underground,  this  separation  may  be  made  on  the  platform  /,  Fig.  19  (a), 
the  rock  being  left  in  the  center  of  the  room  instead  of  the  coal,  as  was  illus- 


(«)      *  (*») 

FIG.  19 

trated  in  Figs.  16,  17,  and  18.  The  coal  is  then  thrown  down  the  chutes  c 
and  loaded  into  cars  on  the  entry  g.  Fig.  19  (b)  is  a  section  through  the  room 
shown  in  (a)  on  the  line  bdeh.  This  method  is  also  used  where  the  coal  is  very 
gaseous  and  where  it  is  not  well,  therefore,  to  keep  broken  coal  stored  in  the 
40 


626 


METHODS  OF  WORKING 


room.  The  air-current  passes  through  the  airway  a  and  up  the  chute  c  to  the 
face.  This  method  is  not  adapted  to  very  thick  seams,  as  it  is  impracticable 
to  build  the  necessary  platforms  in  such  seams. 

The  accompanying  table  gives  approximate  inclinations  of  the  seam  when 
the  several  methods  just  described  are  employed.  These  inclinations  may  be 
varied  by  local  conditions. 

METHOD  SUITABLE  FOR  USE  IN  INCLINED  SEAMS 


Method 


Cars  lowered  by  hand,  or  drawn  by  mule  or  motor, 
rooms  on  full  pitch < 

Cars  lowered  by  hand,  or  drawn  by  mule  or  motor, 
rooms  at  angle  with  pitch 

Cars  lowered  by  windlass,  rooms  on  full  pitch 

Self-acting  incline  or  jig  road .'  ^v^; 

Buggy  system,  thick  seams -.•.«?.£•. 

Sheet-iron  chutes 

Natural  chutes  with  battery 


Inclination  of  Seam 
Degrees 


0-6 

5-12 

5-10 

5-30 
10-18 
15-30 
30  upwards 


The  manways  in  steeply  inclined  rooms  are  constructed  in  two  general 
ways.  In  a  seam  that  is  not  over  6  to  8  ft.  thick,  the  method  shown  in  Fig.  20 
may  be  used.  The  posts  a  are  set  as  shown  and  lined  with  plank;  this  par- 
tition forms  the  sides  of  the  chute  b  and  leaves  a  manway  c  between  the  chute 
and  the  rib. 

In  thick  seams,  inclined  posts  called  jugulars  a,  Fig.  21,  are  used.  These 
are  set  in  hitches  cut  in  the  floor  and  the  rib,  so  as  to  form  a  triangular  pas- 
sageway or  manway  b.  The  jugulars  are  lined  with  plank  to  form  the  sides 
of  the  center  chute  c,  which  is  filled  with  loose  coal  or  refuse. 

As  a  general  rule,  in  inclined  seams  as  in  flat  seams,  the  rooms  are  driven 
up  to  within  a  short  distance  of  the  entry  above,  a  chain  pillar  being  left 
between  the  ends  of  the  rooms  and  this  entry;  the  width  of  this  pillar  varies 
with  the  character  of  the  roof,  floor,  and  coal,  depth  of  cover,  and  inclination 
of  the  seam.  To  secure  better  ventilation,  an  occasional  room  is  often  holed 
through  this  pillar  into  the  entry  above;  and  where  the  coal  has  been  worked 


FIG.  20 


FIG.  21 


out  from  the  chambers  above,  and  there  is  no  water  to  interfere  with  the  lower 
workings,  many  or  all  of  the  rooms  are  thus  driven  through  to  the  upper  entry. 
The  chain  pillar  is  sometimes  drawn  back  with  the  other  pillars.  The  distance 
between  the  successive  lifts  or  entries  varies  with  the  conditions,  but  is  usually 
about  the  same  or  slightly  less  than  the  distance  between  entries  in  flat  work- 
ings under  the  same  conditions. 

Battery  Breasts. — The  methods  of  working  by  single  and  double  chutes 
and  batteries  are  adaptations  of  similar  methods  originally  applied  in  connec- 
tion with  anthracite  mining.  Many  modifications  of  these  simple  methods  are 
used  in  order  to  meet  the  requirements  of  different  pitches  and  different  thick- 
nesses of  coal.  The  following  are  the  most  important  of  these  modifications: 

Fig.  22  shows  an  elevation  (a)  and  cross-section  (fc)  of  a  breast  in  a  thick 
seam  pitching  about  60°.  The  seam  is  16  ft.  thick  with  several  thin  slate  part- 
ings; the  roof  and  floor  are  good,  and  the  coal  hard  and  firm.  The  gangway  g  is 
driven  on  the  strike  of  the  seam,  near  the  bottom  of  the  coal  and  with  sufficient 


METHODS  OF  WORKING 


627 


grade  to  insure  drainage.  A  small  airway  h  is  driven  just  below  the  top 
bench  of  coal,  and  is  connected  with  the  gangway  by  occasional  openings  not 
shown.  This  airway  is  often  called  a  monkey  gangway,  or  simply  a  monkey. 


FIG.  22 


(&) 


A  narrow  opening,  called  a  chute,  is  opened  off  the  gangway  and  driven  up 
on  the  floor  of  the  seam  a  distance  of  about  5  yd.,  and  at  this  point  it  is  widened 
out  gradually  on  both  ribs,  until  the  full  width  of  the  breast,  5  to  8  yd.,  is 
reached.  A  timbered  chute  c  conveys  the  coal  into  the  car  on  the  gangway  g. 
A  battery  of  timber  b  is  constructed  at  the  point  where  the  breast  is  widened 
out  by  setting  double  posts  on  each  side  of  the  center  and  close  to  the  ribs; 


these  posts  are  firmly  set  in  holes  cut  in  the  floor  and  the  roof,  and  cross-tim- 
bers are  then  placed  behind  them,  leaving  only  a  small  opening  for  the  coal 
to  pass  through.  A  manway  w  is  constructed  up  each  side  of  the  chute,  by 


628 


METHODS  Of  WORKING 


placing  about  30  in.  from  each  rib  a  line  of  posts  which  are  firmly  set  in  holes 
cut  in  the  roof  and  floor  and  lined  with  plank  to  form  the  sides  of  the  chute. 
An  opening  r  in  the  battery  connects  each  manway  with  the  chute  c  and  also 
affords  access  to  the  face  of  the  breast.  Cross-cuts  a  are  driven  between 
adjoining  breasts  at  points  up  the  pitch.  The  breast  is  kept  full  of  loose  coal, 
on  which  the  miner  stands  as  he  works  at  the  face. 

Fig.  23  represents  in  elevation  (a)  and  cross-section  (6)  breasts  driven  to 
the  full  pitch  of  a  thick  seam  whose  inclination  is  about  60°.  The  gangway  g 
is  driven  on  the  strike  and  in  the  top  of  the  seam  while  the  airway  c  is  above 
the  gangway  and  in  the  top  coal. 

The  breasts  are  opened  by  a  narrow  opening  9  ft.X6  ft.  driven  up  the  pitch 
for  a  distance  of  18  to  24  ft.,  this  neck  being  gradually  widened  out  to  the  proper 
breast  width,  as  shown.  The  section  is  taken  on  the  lines  Ik  and  ij,  and  the 
elevation  is  made  on  the  line  pq,  and  does  not  show,  therefore,  the  headings  c 
and  d  shown  in  (b).  In  the  middle  of  the  pillar  between  the  loading  chutes, 
a  small  manway  m  is  driven  up  a  few  yards,  and  then  branches  s  are  turned 
off  in  both  directions  until  intersection  is  made  with  the  breasts  on  each  side. 
From  these  points  the  manways  w  are  carried  up  on  each  side  of  the  breast  along 
the  rib  as  shown.  A  narrow  manway  n  is  usually  made  by  planking  off  a  por- 


(ft) 


FIG.  24 


tion^of  the  opening  so  that  the  loaders  may  have  free  access  to  the  battery  at 
all  times. 

A  small  airway  d  is  driven  from  airway  c  to  the  manway  m,  but  cross-cuts 
between  the  airway  and  gangway  are  also  necessary  where  much  gas  is  given 
off  during  the  working.  The  air-current  passes  along  the  gangway  g  and  returns 
along  the  faces  of  the  breasts.  The  small  airways  d  and  c  are  not  used  when 
the  breast  is  working,  but  if  any  accident  in  a  breast  manway  ID  blocks  the  ven- 
tilation, the  air  can  be  conveyed  around  the  breast,  through  the  airways  d 
and  c  by  simply  removing  stoppings.  This  plan  is  especially  adapted  to 
working  thick  steeply  inclined  seams  of  soft  gaseous  coal. 

_  When  the  pitch  of  the  bed  is  less  than  about  50°,  the  gangway  g  is  usually 
m  the  bottom  coal,  but  for  a  greater  inclination  it  is  in  the  top  coal,  so  that 
the  flpw-of  the  coal  may  be  more  easily  controlled. 

Fig.  24  shows  a  method  in  which  a  loading  chute  c  is  arranged  on  each  side 
of  the  breast  and  a  supporting  pillar  of  solid  coal  is  left  in  the  mouth  of  each 
breast;  the  batteries  b  are  built  near  the  upper  side  of  this  pillar.  The  gang- 
wayg  and  the  airway  h  above  it  are  driven  in  the  top  coal.  The  loading  chutes  c 
are  driven  up  from  the  gangway  and  across  the  full  width  of  the  seam  at  such 
an  angle  that  the  coal  can  be  easily  controlled  in  the  chute.  When  the  chutes  c 
reach  the  floor  of  the  seam,  they  are  widened  out  to  breast  width  and  at  the 
same  time  the  coal  face  is  opened  up  to  the  top  of  the  seam  in  a  more  or  less 
vertical  line,  as  shown  in  the  cross-section  (6).  The  manways  m  are  driven 


METHODS  OF  WORKING 


629 


through  the  gangway  pillar  between  the  breasts  and  are  divided  into  two  parts, 
as  was  described  in  connection  with  Fig.  23,  a  manway  n  extending  up  each 
side  of  the  breast.  The  advantage  of  the  method  illustrated  in  Figs.  23  and  24 
over  that  shown  in  Fig.  22  is  that  the  man  ways  and 
the  coal  chutes  are  kept  apart  and  there  is  therefore 
usually  free  access  to  the  face  at  all  times,  even 
should  there  be  a  break  in  the  coal  chute. 

By  driving  the  gangway  near  the  roof,  as  shown 
in  Fig.  24,  where  the  pitch  is  heavy  the  loading  chute 
c  is  more  easily  controlled,  and  the  gangway  is  also 
less  likely  to  be  injured  by  a  squeeze.  The  disad- 
vantage of  the  method  is  the  extra  expense  incurred 
in  driving  long  chutes. 

Fig.  25  is  a  sectional  view  of  a  thick  seam  of  coal 
standing  vertically  and  mined  by  room  and  pillar. 
The  gangway  or  level  g  is  connected  with  the  air- 
way h  by  the  passages  c,  d,  and  e.  The  battery  b 
is  at  the  inner  end  of  the  chute  c  and  near  the  foot 
of  the  vertical  manway  m,  in  which  a  ladder  is  placed. 
The  passages  d  and  e  are  for  the  purpose  of  ventila- 
tion; they  also  serve  as  man  ways  to  connect  the  gang- 
way g  with  the  foot  of  the  vertical  manway  m. 

Fig.  26  is  a  section  through  what  is  called  a  back 
breast  p  in  thick  anthracite  seams.  The  regular 
breast  b  having  been  mined  out,  the  coal  over  the 
main  gangway  g  and  monkey  gangway  k  is  worked  „  '__ 

by  opening  a  breast  p  off  the  monkey  gangway  or 

off  another  gangway  driven  especially  for  the  purpose  of  getting  out  this  coal, 
and  driven  so  that  the  coal  may  slide  through  chutes  to  the  cars.  Such  a 
mode  of  working  may  enable  a  large  proportion  of  the  gangway  stumps  to  be 
removed,  which  would  be  entirely  lost  otherwise. 

Working  Contiguous  Seams. — Coal  seams  that  are  approximately  parallel 
and  are  close  together  are  said  to  be  contiguous.  The  following  points  must  be 
carefully  considered  in  the  working  of  contiguous  seams:  Thickness  and  char- 
acter of  the  rock  separating  them;  thickness  of  the  seams;  nature  of  the  roof, 
floor,  and  coal  of  each  seam;  inclination  of  the  strata;  and  general  depth  below 
the  surface.  The  thickness  of  strata  separating  contiguous  seams  varies  from 
a  fraction  of  an  inch  to  several  feet.  When  this  thickness  does  not  exceed  2  or 

3  ft.,  the  separating  rock  is 
called  a  parting  and  all  the 
coal  and  rock  are  then  usually 
taken  out  at  the  same  time 
as  one  face  of  coal,  or  the  face 
in  the  lower  seam  is  kept  a 
few  yards  in  advance  of  that 
above.  The  waste  material 
forming  the  parting  is  not 
removed  in  either  case,  but 
simply  left  where  it  falls, 
except  on  the  roads,  as  the 
handling  of  so  large  an 
amount  of  waste  would  ren- 
der the  econ9mical  working 
of  the  coal  impossible.  At 
other  times,  the  openings  are 
first  driven  in  the'  lower 
seam,  and  when  these  reach 
the  limit  of  the  workings  the 
tracks  in  the  rooms  are  taken 
up  and  the  rock  or  slate 
parting  is  allowed  to  fall  or 
is  blasted  down.  The  upper 
coal  is  then  taken  down. 
When  the  thickness  of  the 


FIG.  26 


intervening  rocks  is  greater,  contiguous  seams  may  be  worked  either  by  what 
are  called  rock  chutes  or  by  cross-tunnels.  Fig.  27  shows  a  section  of  two  seams, 
separated  by  a  few  yards  of  rock.  Chutes  from  4Jto  7  ft.  high  and  7  to  12  ft. 
wide  are  driven  in  the  rock  from  the  gangway  or  level  g  to  the  level  /  in  the  seam 


630 


METHODS  OF  WORKING 


above,  at  such  an  angle  that  the  coal  will  gravitate  from  the  upper  seam  into 

the  gangway  g.     The  working,  otherwise,  is  similar  to  that  previously  described. 

Rock-chute  mining  contemplates  the  following  sequence  of  operation: 

1.  The  opening  of  all  gangways 
and  airways   in  the  lower   seam,  to 
develop  coal  as  yet  untouched  in  a 
thick  seam  lying  a  few  feet  above  it. 

2.  Developing  the  thick  bed  by 
a  regular  series  of  rock  chutes  driven 
from  the  gangway  below;    workings 
being  opened  out  from  the  chutes — as 
in   ordinary   pillar-and-breast   work- 
ing— the  panel  system  or  some  other 
plan  may  be  found  better  than  pillar- 
and-breast  workings. 

3.  Driving    the    breast    to    the 
limit  of  the  lift  and  robbing  out  the 
pillars  from  a  group  of  breasts  as  soon 
as  possible,  even  if  a  localized  crush 
is  induced. 

4.  After  one  group  of  breasts  is 
taken  out  and  the  roof  has  settled, 

pIG>  27  opening  a  second  series  of  chutes  for 

the  recovery  of  coal  from  any  large 
pillars  that  were  not  taken  out  when  the  crush  closed  the  workings. 

5.  While  the  work  of  recovering  the  pillar  coal  is  in  progress,  a  second 
group  of  breasts  may  be  worked,  and  the  process  continued  until  all  the  area 
to  be  worked  from  that  gangway  has  been  exhausted.     The  same  process  is 
employed  in  opening  lower  lifts. 

6.  When  all  the  upper  bed  of  coal  has  been  exhausted,  the  lower  seam 
may  be  worked  by  the  ordinary  method.     Workings  in  this  seam  may  be 
carried  on  simultaneously  with  the  upper  bed,  but  to  avoid  the  possibility 
of  a  squeeze  destroying  these  workings,  very  large  pillars  must  be  left.     After 
exhausting  the  upper  seam,  these  pillars  may  be  advantageously  worked  by 
opening  one  or  two  breasts  in  the  center  of  each,  and  when  these  are  worked 
to  the  upper  limit,  attacking  the  thin  rib  on  each  side,  commencing  at  the  top 
and  drawing  back. 

When  the  roof  of  the  lower  bed  is  good,  the  cost  of  timbering  and  keeping 
open  the  gangways  and  airways  will  ^^ 
be  considerably  less  than  if  these  were 
driven  in  the  upper  seam,  and  this  dif- 
ference, in  some  cases,  may  be  sufficient 
to  pay  for  driving  all  the  rock  chutes. 

There  are  three  undetermined 
points  in  this  connection,  viz.:  (1) 
The  maximum  distance  between  the 
two  beds,  or  the  length  of  rock  chute 
that  can  be  driven  with  satisfactory 
financial  results.  (2)  The  maximum 
dip  on  which  such  workings  can  be  suc- 
cessfully opened.  (3)  The  maximum 
thickness  of  the  upper  and  also  of  the 
lower  seam,  which  will  yield  results 
warranting  the  additional  outlay  when 
rock  chutes  are  of  considerable  length. 

Fig.  28  shows  how  one  or  more 
seams  are  worked  by  connecting  them 
by  a  stone  drift,  or  tunnel,  driven  hori- 
zontally across  the  measures,  through 
which  the  coal  from  the  adjacent  seams 
is  taken  to  the  haulagewa'y  leading  to 
the  landing  at  the  foot  of  the  slope  or 
shaft.  Tunnels  are  sometimes  driven 
horizontally  through  the  measures  from 


FIG.  28 


the  surface,  so  as  to  cut  one  or  more  seams  above  water  level. 

The  lower  seam  of  coal  is  worked  from  a  gangway  or  level  I,  connected 
by  a  tunnel,  or  stone  drift  /,  to  the  level  or  gangway  g,  in  the  thick  seam.  The 
stone  drift  may  be  extended  right  and  left  to  open  seams  above  and  below  the 


METHODS  OF  WORKING  631 

thick  seam.  This  tunnel,  or  stone  drift,  is  never  driven  under  a  breast  in  the 
upper  seam,  but  directly  under  the  middle  of  the  pillar. 

In  the  upper  and  thicker  seam,  when  the  coal  is  very  hard,  a  breast  b  is 
worked  to  the  limit  and  the  loose  coal  nearly  all  run  out  through  the  chute  s 
into  the  gangway  g.  The  monkey  gangway  m  is  driven  near  the  top  as  a 
return  airway,  and  is  connected  to  the  upper  end  of  the  chute  s  by  a  level 
heading  «,  and  to  the  main  gangway  g  by  a  heading  v.  These  headings  are 
driven  for  the  purpose  of  ventilation  and  to  provide  access  to  the  battery  in 
case  the  chute  5  should  be  closed.  In  the  lower  seam,  the  breast  is  still  being 
worked  upwards  in  the  ordinary  way. 

New  Castle,  Colorado,  Method. — The  following  method  is  used  at  New 
Castle,  Colorado,  for  highly  inclined  bituminous  seams.  The  coals  mined  are 
only  fairly  hard,  contain  considerable  gas,  and  make  much  waste  in  mining. 
Fig.  29  shows  the  method  used  for  extracting  the  thicker  vein  to  its  full  width 
of  45  ft.,  and  the  E  seam  18  ft.  thick,  excepting  that  left  for  pillars.  Rooms 
and  pillars  are  laid  out  under  each  other  in  the  two  seams  whenever  practi- 
cable. Entries  are  along  the  foot-wall;  30  ft.  up  the  pitch  is  an  air-course. 
Rooms  and  breasts  are  laid  out  as  shown  in  Figs.  17  and  18.  In  the  thick  vein, 
the  manways  go  through  the  entry  pillars  to  the  air-course  and  thence  along  the 


FIG.  29 

ribs  each  side  of  the  room,  one  manway  to  tne  main  entry  serving  for  two 
double  rooms.  A  lower  bench  of  6  ft.  is  first  mined  the  full  length  of  the  rooms, 
120  ft.,  side  manways  being  protected  by  vertical  or  leaning  props,  bordered 
with  3-in.  planks  outside,  and  the  chute  or  battery  is  then  put  in.  At  the  top 
the  rooms  are  connected  by  cross-cuts,  and,  occasionally,  intermediate  cross- 
cuts are  required.  The  room  is  kept  full  of  loose  coal,  only  sufficient  being 
drawn  to  keep  the  working  floor  at  the  proper  height  for  the  mining.  When 
driven  to  the  limit  and  with  cross-cuts  connected,  the  coal  is  all  drawn  out  at 
the  chutes,  which  have  receptacles  for  rock  and  waste  at  their  sides,  to  be 
picked  out  by  the  loaders.  The  next  operation  is  to  drive  across  the  seam  at 
the  air-course  until  the  hanging  wall  is  reached,  manways,  called  back  man- 
ways, being  maintained  as  before.  A  triangular  section  of  coal  is  mined  off, 
as  shown  in  Fig.  17,  and  the  room  filled  with  loose  coal.  The  full  thickness 
of  the  seam  is  now  taken  off,  shots  being  first  placed  at  SS,  coal  being  drawn 
out  at  the  bottom  as  required.  In  robbing  a  pillar,  the  manways  are  moved 
back  into  the  pillar  each  side  10  ft.  or  so,  by  mining  on  the  lower  bench  as  before, 
and  holes  are  drilled  into  the  roof  with  long  drills,  which  bring  down  as  much  of 
the  overhanging  part  as  can  be  reached. 

Alabama  Methods. — Fig.  30  shows  the  common  methods  used  in  working 
the  Alabama  coals.     The  seams  now  working  vary  from  .2  to  6  ft.  thick,  and 


632  METHODS  OF  WORKING 

they  pitch  from  2°  to  40°.  Where  the  seams  are  thin,  the  coal  is  hard,  and 
pillars  of  about  20  to  30  ft.  are  used  to  support  the  roof.  The  thick  seams  are 
soft  and  easily  broken,  and  much  larger  pillars  are  left.  The  character  of  bot- 
tom and  top  varies;  fireclay  bottom  and  slate  roof  are  usually  found  with  the 
thick  seams,  and  hard  bottom  and  sandstone  roof  with  the  thin  seams.  The 
general  plan  of  laying  out  the  mine  is  to  drive  the  slope  straight  with  the  pitch 
of  the  seam;  this  is  usually  on  the  butts  of  the  coal.  A  single-track  slope  is 
8  ft.  wide,  and  a  double-track  slope  16  ft.  Cross-headings  are  driven  or  turned 
from  the  slope  water  level  every  300  ft.;  air-courses  are  driven  parallel  on  either 
side  of  the  slope.  Where  an  8  ft.  slope  is  driven,  30  ft.  of  pillar  is  left  between 
the  slope  and  airway,  and  for  a  16  ft.  slope,  40  ft.  of  pillar.  The  size  of  pillar, 
however,  depends  largely  on  the  character  of  the  roof  and  thickness  and 
strength  of  coal.  On  the  lower  side  of  the  heading,  pillars  from  20  to  60  ft. 
are  left  on  the  entry  before  turning  the  first  room.  The  rooms  are  worked 
across  the  pitch  on  an  angle  of  about  5°  on  the  rail,  as  shown  in  A ,  when  the 
coal  does  not  pitch  greater  than  20°;  where  the  pitch  is  greater,  chutes  are 


PIG.  30 

worked  and  the  rooms  are  driven  straight  up  the  pitch  B.  In  a  few  cases 
where  the  pitch  is  not  greater  than  15°,  double  rooms  are  worked  with  two 
roadways  in  each  room,  as  shown  in  C.  A  rope  with  two  pulleys  is  used,  and 
each  track  keeps  the  rib  side  of  the  room,  the  loaded  car  pulling  up  the  empty 
on  the  opposite  side  of  the  room;  distance  between  room  centers,  about  42  ft. 
Where  single  rooms  are  worked,  the  room  is  driven  narrow  (8  ft.  wide)  for 
•j i  j  en  connectlons  are  made  with  the  room  outside  of  it;  the  room  is  then 
widened  out  to  about  25  ft.,  sloping  gradually  until  this  width  is  attained; 
pillars  of  from  10  to  20  ft.  thick  are  left  between  the  rooms,  and  cross-cuts  for 
ventilation  are  made  about  every  50  ft.;  every  third  or  fourth  room  is  driven 
through  to  the  entry  above;  pillars  are  then  drawn  back  to  the  entry  stumps 
or  pillars.  The  average  cover  over  the  coal  now  working  is  from  100  to  600  ft 
Air-courses  usually  have  an  area  of  30  ft.,  and  sufficient  coal  is  taken  out  to 
give  this  area,  the  roof  and  bottom  being  left. 

Tesla,  California,  Method.— The  Tesla,  California,  method  is  shown  in 
*ig.  31.     The  coal  seam  averages  7  ft.  of  clear  coal,  and  pitches  60°.     This 


METHODS  OF  WORKING 


633 


system  was  adopted  in  a  portion  of  the  mine  to  get  coal  rapidly;  for,  at  this 
point,  a  short-grained,  slate  cap  rock  came  in  over  the  coal,  making  it  difficult 
to  keep  props  in  place.  The  floor  is  a  close  blue  slate  and  has  a  decided  heaving 
tendency.  The  roof  is  an  excellent  sandstone.  There  is  a  small  but  trouble- 
some amount  of  gas.  Two  double  chutes  are  driven  up  the  pitch  at  a  distance 
of  36  ft.  apart,  connected  every  40  ft.  by  cross-cuts.  One  side  of  each  chute  is 
used  for  a  coal  chute  and  the  other  for  a  manway  and  air-course.  At  a  distance 
of  12  yd.  apart  small  gangways  are  driven  parallel  with  the  main  mine  gang- 
ways. These  are  continued  from  each  chute  a  distance  of  300  ft.,  if  the  con- 
ditions warrant  it.  The  top  line  is  then  attacked  from  the  back  end  and  the 
coal  is  worked  on  the  cleavage  planes;  the  breast,  or  room,  therefore  consists 
of  a  12-yd.  face,  including  the  drift  or  gangway  through  which  the  coal  is  car- 
ried to  the  chutes;  a  rib  of  coal  (2  or  3  ft.)  is  left  between  the  breasts  to  keep  the 
rock  from  falling  on  the  breast  below.  Thus  in  each  breast  the  miners  have  a 
working  face  of  about  15  or  16  yd.,  and  as  the  coal  is  directed  to  the  car  by  a  light 
chute,  moved  along  as  the  face  advances,  the  coal  is  delivered  into  the  cars  at 
small  cost,  and  but  little  loss  results  from  the  falling  coal,  as  a  minimum  of 
handling  is  thus  obtained.  Immediately  above  each  gangway,  and  starting 
from  these  main  chutes,  an  angle  chute  is  driven  at  about  45°,  connecting  with 
a  part  as  the  gangway  chutes  (30  ft)  ,  at  an  angle  of  35°,  and  cross-cuts  are  driven 
the  breast  gangway  above  it,  and  into  these  chutes  the  coal  from  that  breast 


Manway  fc/f/r  Course 


FIG.  31 

is  delivered,  runs  into  the  main  chute,  and  from  it  is  loaded  into  the  mine  cars 
in  the  main  gangway.  These  angle  chutes  serve  as  a  means  of  keeping  the 
main  chute  full,  and  at  the  same  time  give  each  breast  an  opportunity  to 
send  out  coal  continuously.  They  also  serve  the  purpose  primarily  intended, 
of  saving  the  coal  from  breakage,  by  giving  it  a  more  gradual  descent  into  the 
full  chute.  The  breast  gangways  are  driven  5  ft.  wide.  No  timbers  are  needed 
in  these  gangways,  as  they  are  driven  in  the  coal,  except  on  the  foot-wall  or  floor 
side,  which,  as  before  stated,  is  a  firm  sandstone.  It  is  found  safest  to  leave 
a  rib  of  coal  on  the  top  of  the  breast  2  or  3  ft.  thick,  until  the  working  face 
has  passed  on  12  or  15  ft.,  when  this  rib  is  cut  out  and  thus  all  the  coal  extracted, 
the  roof  caving  behind  and  filling  in  the  opening.  As  cross-cuts  are  driven 
every  36  ft.,  ventilation  is  kept  along  the  working  faces,  and  a  safe  and  effec- 
tual means  of  securing  all  the  coal  in  the  seam  is  thus  attained. 

Fig.  32  shows  another  system  used  in  No.  7  vein  at  the  same  place.  The 
seam  averages  7  ft.  of  coal.  The  roof  is  shelly  and  breaks  quickly,  hence  the 
coal  must  be  mined  rapidly. 

In  this  system  the  gangway  chutes  are  driven  at  right  angles  with  the  strike 
of  the  seam,  40  ft.  up  the  pitch;  a  cross-cut  5  ft.X6  ft.  is  then  driven  parallel 
with  the  gangway.  From  this  cross-cut,  chutes  are  driven  at  same  distance 
every  40  ft.  between  chutes,  for  ventilation.  After  a  panel  of  five  or  more 
chutes  is  driven  up  the  required  distance,  work  is  commenced  on  the  upper 


634 


METHODS  OF  WORKING 


outside  pillar  and  the  pillars  on  that  line  are  drawn  and  the  next  line  is  attacked , 
and  this  is  continued  until  the  panel  or  block  is  worked  down  to  the  cross- 
cut over  the  gangway.  About  every  80  ft.  in  this  level  it  is  found  advantageous 


° QSeam 


anaway 


-Fie.  32 

to  build  a  row  of  cogs  parallel  with  the  strike  of  the  seam  as  the  pillars  are 
drawn.  This  serves  to  save  the  crushing  of  the  pillars,  and  prevents  any  acci- 
dents from  falls,  qf  rock.  But  few  timbers  are  required  by  this  system. 


PILLAR-AND-STALL  SYSTEMS  OF  MINING 

The  pillar-and-stall  system,  also  known  as  post-and-stall,  board-and-pillar, 
or  stoop-and-room,  is  a  modification  of  the  general  room-and-pillar  method  in 

which  the  openings,  usually  called 
stalls  or  rooms  in  America,  are  narrow, 
rarely  exceeding  4  or  5  yd.  in  width. 
The  pillars  are  at  least  as  wide  and 
usually  wider  than  the  stalls.  In  the 
single-stall  system,  the  stalls  are  turned 
narrow  off  the  entry  as  shown  in  Fig.  1 
(a),  and  widened  inside  as  described  in 
room-and-pillar  work.  In  the  double- 
stall  system,  shown  in  (6),  the  openings 
are  wider,  and  are  similar  in  every 
respect  to  double  rooms,  except  that 
the  pillars  separating  the  double  stalls 
are  generally  wider  in  proportion  to  the 
width  of  the  stalls  than  are  the  pillars 
separating  rooms.  In  double-stall 
work,  the  openings  are  often  12  or  15  yd. 
,  the  roof  being  supported  on 


•p 
riG' 


in  width 

good  pack  walls  in  the  center  of  the 

stall;  the  pillars  often  reach  a  width  of  30  yd.  The  pillar-and-stall  system  is 
adapted  to  weak  roof  and  floor,  to  strong  roof  and  soft  bottom,  to  soft,  brittle 
coal,  and  in  general  to  conditions  requiring  ample  support  of  the  roof;  the 
system  is  particularly  useful  in  deep  seams  where  the  roof  pressure  is  great. 


METHODS  OF  WORKING 


635 


Connellsville  Region. — Fig.  2  shows  the  common  method  used  in  the  Con- 
nellsville,  Pennsylvania,  region.  The  average  dip  is  about  5%.  The  face 
and  butt  headings  are  driven,  respectively,  at  right  angles  to  each  other  on 
the  face  and  the  butt  of  the  coal.  The  face  headings  leave  the  main  butts 
about  1,000  ft.  apart,  while  from  these  face  headings,  and  400  ft.  apart,  sec- 
ondary butts  are  driven,  and  again  from  these  butts  on  the  face  of  the  coal  the 
rooms  or  wide  workings  are  excavated  to  a  length  of  300  ft.,  this  having  proved 
the  most  convenient  length  for  economical  working.  Room  pillars  have  a 
thickness  of  30  to  40  ft.,  while  the  rooms  are  12  ft.  in  width  and  are  spaced 
42  to  52  ft.  between  centers,  depending  on  depth  of  strata  over  the  coal.  The 
headings  are  8  ft.  wide,  and  in  all  main  butts  and  faces  the  distance  between 
centers  of  parallel  headings  is  60  ft.,  leaving  a  solid  rib  of  52  ft.  A  solid  rib 
of  60  ft.  is  also  left  on  the  side  of  each  main  heading.  The  average  thickness 


FIG.  2 

of  cover  at  the  Leith  mine,  which  is  here  described  and  which  may  be  con- 
sidered as  a  type  of  the  region,  is  250  ft.,  the  overlying  measures  being  alter- 
nate layers  of  soft  shale  and  coal  for  4  ft.  The  bottom  is  an  18-in.  layer  of  hard 
fireclay  and  slate.  These  floor  and  roof  materials  are  soft,  and  are  easily  dis- 
integrated by  air  and  water.  At  some  mines,  cover  will  reach  as  much  as 
700  ft.,  and  the  dip  of  5%  (as  at  Leith)  is  much  heavier  at  some  points  on  east- 
ern outcrop,  and  will  run  as  high  as  12%,  flattening  off  as  the  synclinal  line 
of  the  basin  is  reached,  until  it  is  almost  level.  In  some  localities,  the  material 
below  coal  is  hard  limestone,  requiring  blasting  to  remove  it,  and  at  other 
places  the  roof  slates  are  much  more  solid  than  at  Leith,  and  not  readily  dis- 
integrated. The  method  of  drawing  ribs  is  one  of  the  advantages  of  the  sys- 
tem, since  it  is  harder  to  do  successfully  in  a  soft  coal  like  the  Connellsville 
than  in  hard  coal.  The  coal  itself  is  firm.  When  necessary  to  protect  the 
top  or  bottom,  4  to  6  in.  of  coal  is  left  covering  the  soft  material. 


636  METHODS  OF  WORKING 

The  method  just  given  is  often  applied  to  a  whole  series  of  butts  (4  or  5) 
at  once  instead  of  to  butt  by  butt,  as  shown  in  Fig.  2.  In  this  case,  work 
is  started  at  the  upper  end  of  the  uppermost  butt  and  progresses,  as  shown, 
but,  after  cutting  across  the  butt  heading  from  which  the  rooms  are  driven, 
the  butt  heading  itself  and  the  upper  rooms  from  the  second  butt,  or  that 
just  before,  are  likewise  drawn  back  by  continuous  slices  being  removed  from 
the  rooms  of  the  upper  butt,  and  on  across  the  next  lower  butt,  etc.,  all  on  an 
angle  to  the  butts,  and  so  continued  as  the  operations  progress,  until  another 
butt  is  reached,  etc.,  thus  gradually  making  a  longer  and  longer  line  of  frac- 
ture, which  is  only  limited  by  the  number  of  butts  it  is  desired  to  include  at 
one  time  in  the  section  thus  mined.  This  works  very  nicely  and  makes  long 


Breasf  to  Surface  Holes  fo  putdbwn  Timber  - 


FIG.  3 

even  lines  of  fracture,  the  steps  of  the  face  of  the  workings  (in  the  rib  drawing) 
being  about  30  ft.  ahead  of  one  another. 

J.  L.  Williams  Method.— The  J.  L.  Williams  method  of  working  anthracite. 
Fig.  3,  was  applied  successfully  by  the  originator  at  the  Richards  mine, 
Mt.  Camel,  Pennsylvania,  and  by  it  90%  of  the  available  coal  is  said  to  have 
been  obtained.  The  method  is  a  pillar-and-stall  method  with  the  following  dis- 
tinguishing points:  (1)  Timbering  the  gob  with  props  set  not  more  than  6  ft. 
apart,  to  keep  up  the  roof  during  the  extraction  of  the  pillars.  (2)  Making 
holes  from  the  crop,  for  the  delivery  of  timber  into  the  workings.  (3)  Remov- 
ing the  pillars  in  shorter  lifts  than  is  possible  when  the  roof  is  supported  with 
culm  pillars.  (4)  Keeping  the  gob  open  with  timber  for  dumping  the  fallen 
rock,  that  would  have  to  be  sent  to  the  surface  if  the  breasts  were  flushed. 

Both  the  floor  and  the  roof  of  the  mine  were  weak,  so  that  it  was  not 
possible  to  make  either  the  breasts  or  the  pillars  wide.  In  some  cases,  the 
floor  consisted  of  3  ft.  of  clod,  and  to  prevent  its  lifting  and  sliding,  every 


METHODS  OF  WORKING 


637 


alternate  prop  was  put  through  the  clod  and  its  foot  set  in  the  slate  beneath, 
while  the  other  props  were  set  on  pieces  of  2-in.  plank  2  ft.  in  length  to  keep 
down  the  bottom.  A  small  gangway  X  is  driven  to  take  out  the  chain  pillar, 
and  Y  is  a  small  gangway  for  taking  in  timber. 


PANEL  SYSTEM  OF  MINING 

In  the  panel  system,  the  coal  area  is  first  blocked  out  by  pairs  of  entries 
driven  at  right  angles  to  one  another  if  possible.  As  soon  as  the  panel  has  been 
thus  blocked  out,  the  removal  of  the  coal  within  the  panel  is  begun  by  driving 
openings  a,  Fig.  1,  from  the  cross-entries.  These  openings  are  connected  by 
a  cross-heading  b,  a  suitable  pillar  being  left  between  b  and  the  cross-entry. 
Rooms,  or  stalls  c  are  then  opened  off  the  heading  b  and  driven  almost  the  full 
length  of  the  panel,  only  leaving  suitable  chain  pillars  d  for  the  protection'  of 
the  main  and  cross-headings  enclosing  the  panel.  After  the  rooms,  or  stalls, 
have  been  driven  their  full  length,  the  pillars  separating  the  stalls  are  drawn 
back,  allowing  the  roof  to  fall  as  shown.  The  Connellsville  method  described 
under  the  heading  Pillar- 
and-Stall  Systems  of  Min- 
ing, while  closely  resem- 
bling the  Scotch  and  En- 
glish pillar-and-stall 
method,  may  be  considered 
a  modification  of  the  panel 
system. 

When  a  panel  is  worked 
out,  in  order  to  close  off  the 
whole  panel  it  is  usually 
necessary  only  to  put  stop- 
pings in  the  mouths  of  the 
openings  a.  A  pipe  is  put 
through  each  stopping  with 
a  valve  in  the  pipe  on  the 
outside  of  the  stopping. 
As  firedamp  is  often  given 
off  in  the  panel  after  it  is 
worked  out,  these  valves 
should  be  opened  at  regu- 
lar intervals  and  the  issu- 
ing air  tested  for  firedamp 
with  a  safety  lamp  held  a 
few  inches  from  the  mouth 
of  the  pipe,  so  that  any 
escaping  gas  can  mix  with 
the  fresh  air.  If  gas  is 
found,  the  valve  is  left  open 
and  the  gas  allowed  to  escape  and  should  be  led  into  the  return;  it  is 
sometimes  lighted  at  the  pipe  and  allowed  to  burn  off,  but  this  is  danger- 
ous, for  the  flame  may  travel  back  through  the  pipe  and  explode  the  gas  in  the 
panel.  A  second  pipe  on  which  is  a  pressure  gauge  is  sometimes  placed  in  the 
stopping  to  test  the  pressure  of  gas  behind  the  stopping,  particularly  when  the 
gob  is  on  fire  and  generating  gases.  If  there  is  much  pressure  of  gas  behind 
the  stoppings,  the  pipe  through  the  stoppings  should  be  left  open  when  the  men 
are  not  in  the  mine.  In  some  cases,  the  pipe  through  the  stopping  is  con- 
nected with  a  pipe  laid  along  the  entries  and  leading  into  the  return  air-current. 

The  term  panel  system  is  rather  loosely  applied  in  the  United  States  to 
any  system  of  mining  in  which  the  mine  is  divided  into  a  series  of  blocks  in 
which  blocks  the  pillars  are  drawn  and  that  section  of  the  mine  sealed  off 
while  operations  are  being  carried  on  in  adjacent  blocks.  Thus,  a  tract  devel- 
oped by  a  series  of  parallel  cross-  or  butt-entries,  say,  350  to  500  ft.  apart,  is 
often  spoken  of  as  being  worked  on  the  panel  system  when  the  respective  butt 
entries  are  not  connected  and  the  room  workings  from  one  pair  of  entries  are 
not  driven  through  to  the  next  parallel  entry,  the  pillars  being  drawn  as  soon 
as  the  rooms  and  the  entries  reach  their  limit  of  length,  or  the  coal  between 
pairs  of  the  parallel  entries  may  even  be  worked  by  the  longwall  method. 

Col.  Brown's  Method. — Fig.  2  shows  a  panel  system  devised  by  Col.  D.  P. 
Brown,  of  Lost  Creek,  Pennsylvania,  which  gives  good  results  in  thick  seams 


FIG.  1 


638 


METHODS  OF  WORKING 


pitching  from  15°  to  45°,  where  the  top  is  brittle,  the  coal  free,  and  the  mine 
gaseous.  Rooms  or  breasts  are  turned  off  the  gangway  in  pairs,  at  intervals 
of  about  60  yd.  The  breasts  are  about  8  yd.  wide,  and  the  pillar  between, 
which  is  about  5  yd.  wide,  is  drawn  back  as  soon  as  the  breasts  reach  the  airway 
near  the  level  above.  In  the  middle  of  each  large  pillar  between  the  several 
pairs  of  breasts,  chutes  about  4  yd.  wide  are  driven  from  the  gangway  up  to 
the  airway  above.  These  are  provided  with  a  traveling  way  on  one  side, 
giving  the  miners  free  access  to  -the  workings.  Small  headings  are  driven  in 
the  bottom  bench  of  coal,  at  right  angles  to  these  chutes,  and  about  10  or 
20  yd.  apart.  These  headings  are  continued  on  either  side  of  the  chutes  until 
they  intersect  the  breasts.  When  the  chute  and  headings  are  finished,  the  work 
of  getting  the  coal  in  the  panel  is  begun  by  going  to  the  end  of  the  upper- 
most heading  and  widening  it  out  on  the  rise  side  until  the  airway  above  is 
reached  and  a  working  face  oblique  to  the  heading  is  formed.  This  face  is 
then  drawn  back  to  the  chute  in  the  middle  of  the  panel.  After  the  work- 
ing face  in  the  uppermost  section  has  been  drawn  back  some  10  or  12  yd., 
work  in  the  next  section  below  is  begun,  and  so  on  down  to  the  gangway, 
working  the  various  sections  in  the  descending  order.  Both  sides  of  the  pil- 
lar are  worked  similarly  and  at  the  same  time  toward  the  chute. 

Small  cars,  or  buggies,  are  used  to  convey  the  coal  from  the  working  faces 
along  the  headings  to  the  chute,  where  it  is  run  down  to  the  gangway  below 


FIG.  2 

and  loaded  into  the  regular  mine  cars.  This  system  affords  a  great  degree  of 
safety  to  the  workmen,  because  whenever  any  signs  of  a  fall  of  roof  or  coal 
occur,  the  men  can  reach  the  heading  in  a  very  few  seconds  and  be  perfectly 
safe.  A  great  deal  of  narrow  work  must  be  done  before  any  great  quantity 
of  coal  can  be  produced.  The  breasts  are  driven  in  pairs  and  at  intervals, 
to  get  a  fair  quantity  of  coal  while  the  narrow  work  is  being  done,  and  they 
are  not  an  essential  part  of  the  system.  It  is  claimed  that  the  facility  and 
cheapness  with  which  the  coal  can  be  mined,  handled,  and  cleaned  in  the  mine 
more  than  counterbalance  the  extra  expense  for  the  narrow  work. 

The  advantages  of  the  panel  system  are:  A  more  complete  control  of  the 
ventilating  current  is  possible,  and  the  ventilation  in  any  panel  may  be  altered 
as  circumstances  may  require;  the  powder  smoke  from  each  panel  goes  directly 
into  the  return  air-current  and  does  not  go  throughout  the  mine;  an  explosion 
or  a  fire  occurring  in  one  panel  is  usually  confined  to  that  panel;  creeps  or 
squeezes  are  of  rare  occurrence,  and  are  confined  to  the  panel  in  which^they 
occur;  the  output  of  coal  is  better  regulated  and  more  reliable.  The  dis- 
advantage of  the  system  is  the  expense  of  entry  driving,  and  the  delayed  extrac- 
tion of  the  coal  within  the  panel  until  the  driving  of  the  main  and  cross-head- 
ings has  been  completed.  

MINING  AND  BLASTING  COAL 

SHOOTING  OFF  THE  SOLID 

Coal  may  be  broken  down  at  the  working  face  by  blasting  from  the  solid; 
by  blasting  after  having  undercut  or  sheared  the  seam;  and  by  a  combination 
of  the  methods. 

The  term  solid  shooting,  or  shooting  off  the  solid,  is  used  to  describe  a  method 
of  working  in  which  the  coal  is  blasted  from  a  solid  face  without  previous 


METHODS  OF  WORKING 


639 


shearing  or  undercutting.  It  is  practically  the  only  method  used  in  mining 
anthracite,  and  is  also  much  used  in  bituminous  mining.  The  chief  labor  in 
the  production  of  coal  by  this  method  is  the  drilling  of  the  holes  for  the  powder 
and  the  loading  of  the  coal  into  mine  cars.  The  holes  are  drilled  with  a 
churn  drill  or  with  a  rotary  drill  worked  either  by  hand  or  by  electric  or 
compressed-air  power. 

The  location  of  the  holes,  the  d.epth  to  which  they  must  be  drilled,  and 
their  direction  depend  on  the  nature  of  the  coal.  If  the  coal  is  compact  and 
without  cleat,  as  is  the  case  with  anthracite,  the  holes  are  placed  as  they  would 
be  for  a  rock  face  worked  under  similar  conditions.  If  the  coal  has  a  cleat, 
advantage  must  be  taken  of  this  to  produce  the  maximum  effect  of  the  shot 
and  to  prevent  the  shot  seaming  out.  The  best  method  of  blasting  a  par- 
ticular coal  can  only  be  learned  by  experience. 

Drill  holes  must  be  so  placed  that  the  explosion  of  the  charges  will  increase 
the  number  of  free  faces  (loose  or  open  ends)  exposed  to  the  action  of  subse- 
quent blasts  and  thus  reduce  the  amount  of  powder  otherwise  necessary  to 
bring  down  the  coal. 


FIG.  1 

Fig.  1  shows  a  common  method  of  placing  the  shots  in  shooting  off  the  solid 
used  both  for  rooms  and  wide  entries,  where  the  coal  is  5  to  7  ft.  thick  and  is 
strong  and  close-grained  and  without  cleats  or  partings  which  need  be  con- 
sidered in  the  blasting.  When  firing  with  squib  or  fuse,  the  holes  are  exploded 
singly  or  in  the  numbered  order,  except  1  and  2,  which  must  be  fired  simul- 
taneously. When  firing  with  electric  detonators,  the  shots  are  fired  in  pairs; 
first  1  and  2\  then  3  and  4;  and,  lastly,  5  and  6,  The  mutual  reinforcing 
action  of  two  charges  when  fired  together  is  very  noticeable  in  the  case  of 
holes  pitching  toward  one  another  as  1  and  2,  which  may  be  placed  much 
farther  apart  and  will  break  down  much  more  coal  when  fired  together  than 
when  fired  singly.  Shots  1  and  2  are  sometimes  called  breaking,  or  busting, 
shots,  as  they  break  out  the  center  and  thus  give  loose  ends  for  the  shots  3  and 
4,  which  should  take  out  the  greater  part  of  the  coal.  The  shots  5  and  6  are 
placed  about  10  in.  from  the  ribs  and  are  intended  mainly  to  straighten  the 
ribs;  they  are  often  inclined  toward  the  rib.  A  cut  from  4^  to  6  ft.  deep 
across  the  face  should  be  taken  out  by  such  a  round  of  holes. 

If  any  shot  does  not  blow  out  the  entire  face  from  top  to  bottom,  it  is  neces- 
sary to  mine  out  the  bottom  or  top  coal  that  is  left  in  order  to  square  up  the 
face  in  preparation  for  the  next  round  of  shots.  Occasionally,  a  short  hole, 


640 


METHODS  OF  WORKING 


or  plug  shot,  is  used  to  do  this,  but  such  a  shot  results  in  small  coal,  and  a  pick 
should  preferably  be  used.     The  miner  should  aim  to  keep  the  center  slightly 

ahead  of  the 
sides  in  order  to 
have  free  faces 
for  the  side 
shots.  The  only 
difference  in  the 
application  of 
this  method  of 
placing  the 
shots  for  a  room 
or  entry  is  that 
the  shots  are 
closer  together 
in  the  case  of 
an  entry. 


(a) 


(c) 


FIG.  2 

When  shooting  fairly  hard  bituminous  coals,  especially  where  the  coal  breaks 
in  wedge-shaped  pieces,  the  holes  should  be  inclined  at  a  small  angle  with  the 
face  of  the  coal.  Shots  inclined  to  the  face  of  the  coal  are  called  grip  shots, 
and  the  shot  is  said  to  be  gripped  more  or  less  according  as  it  makes  a  greater 
or  less  angle  with  the  face.  _  When  a  shot  is  gripped 
too  strongly,  and  the  charge  is  located  too  deep  on  the 
solid,  the  force  of  the  blast  will  be _ insufficient  for  the 
strength  of  the  coal  and  may  result  in  a  blown-out  shot. 

If  the  center  of  the  coal  seam  is  soft  or  if  it  contains 
a  parting,  shots  placed  near  the  center,  as  shown  in 
Fig.  1,  may  only  tear  out  a  gap,  leaving  the  top  and 
bottom  intact.  Under  such  conditions,  it  is  necessary 
to  place  the  shots  so  as  to  blast  off  the  top  and  bot- 
tom alternately,  as  is  shown  in  Fig.  2  (a),  (b),  and  (c). 
The  holes  are  placed  across  the  face  about  as  shown  in 
Fig.  1,  but  are  inclined  at  a  much  greater  angle  with 
the  horizontal.  In  Fig.  2  (a),  the  coal  face  is  shown 
vertical  and  the  first  round  of  drill  holes  is  intended  to 
take  off  the  lower  part  of  the  face;  the  holes  are  run 
from  a  little  below  the  center  of  the  coal  as  shown  at  1 , 
and,  excepting  the  buster  and  rib  shots,  the  holes  are 
drilled  diagonally  across  the  face  of  the  room  and  down- 
wards, so  that  the  charge  of  powder  is  placed  across 
the  strong  portion  of  the  coal  to  be  displaced.  This 
round  of  shots  will  throw  out  the  bottom  coal  and 
leave  the  coal  face  standing  with  the  top  overhanging 
as  shown  in  (b).  The  next  round  of  holes  2  is  run  up- 
wards and  diagonally  across  the  room  to  take  off  the 
upper  bench  of  coal.  The  third  round  3,  shown  in  (c) , 
will  be  run  downwards,  and  by  thus  alternately  inclin- 
ing the  rounds  upwards  and  downwards  the  face  is 
advanced. 

If  the  face  is  kept  straight  and  center  or  buster 
shots  must  be  used  in  connection  with  each  round,  an 
excessive  use  of  powder  is  necessary  and  a  larger 
amount  of  small  coal  is  made  than  where  an  irregular 
face  is  carried,  with  the  center  in  advance  of  the  sides, 
or  with  either  side  in  advance  of  the  center.  An  ir- 
regular face  provides  a  free  side  for  the  shots  and  allows 
the  holes  to  be  placed  to  greater  advantage  than  where 
the  face  is  kept  straight.  Fig.  3  shows  a  method  of 
blasting  off  the  solid  that  is  applicable  either  to  rooms 
or  to  wide  entries  under  conditions  similar  to  those 
given  in  connection  with  the  method  illustrated  in 
Fig.  1.  The  coal  is  assumed  to  be  from  5  to  7  ft. 
thick,  strong,  and  close  grained,  and  without  partings  >*» 

or  cleats  that  interfere  with  or  assist  in  the  blasting,  _, 

and  is  under  a  strong  roof.     Fig.  3  (a)  and  (b)  shows 

the  location  of  the  holes  in  the  first  round.  These  holes  are  placed  about  midway 
of  the  face  vertically ;  they  are  inclined  to  the  face  about  as  shown  in  (a)  and  to  the 
horizontal  about  as  shown  in  view  (b).  Shot  1  is  a  buster  shot,  which  takes 


METHODS  OF  WORKING 


641 


out  a  piece  dbc\  shot  2  is  placed  about  10  in.  from  the  rib  to  straighten  the  rib; 
shot  3  takes  out  the  greater  part  of  the  center  coal,  while  4  and  5  act  simi- 
larly to  1  and  2.  After  the  straight  face  has  thus  been  broken,  the  location 
of  the  subsequent  shots  is  largely  a  matter  of  judgment,  as  so  much  depends 
on  the  conditions.  No  definite  rules  can  be  given,  except  that  in  solid  coal  the 
direction  of  the  hole  should  be  parallel  to  a  free  face  if  possible,  though  even 
this  general  rule  will  be  greatly  modified  by  cleats,  partings,  etc. 

Fig.  4  shows  approximately  the  appearance  of  the  face  after  the  shots 
shown  in  Fig.  3  have  been  fired.  If  there  was  a  cleavage  to  the  coal,  a  shot 
placed  about  as  shown  might  blow  out  the  piece  of  coal  within  the  dotted  line 
and  thus  provide  two  free  faces  with  respect  to  which  side  shots  could  then  be 
placed.  If  there  was  no  cleavage  and  the  coal  was  hard  and  solid,  the  shot 
would  be  placed  nearer  the  previous  shot  4- 

Precautions  in  Solid  Shooting. — Where  a  single  center  shot,  which  is  also 
known  as  the  opening  shot,  such  as  is  shown  by  the  treble  dotted  line  in  Fig.  4, 
is  employed  to  make  an  additional  free  face,  its  angle  of  grip  and  its  length 
should  bear  such  a  relation  to  the  strength  of  the  coal  that  not  to  exceed  2  Ib. 
of  black  powder  (provided  permissible  powder  is  not  used)  will  be  required 
to  bring  the  coal.  This  is  commonly  accomplished  in  coals  where  there  are 
no  marked  cleats  by  limiting  the  angle  between  the  straight  face  and  the  hole 
to  35°,  in  which  case  a  5-ft.  hole,  which  is  of  the  maximum  allowable  length, 
would  have  a  line  of  least  resistance  2  ft.  10  in. 
long  to  work  against.  Where  the  cleats  are 
favorable,  the  angle  of  grip  may  be  as  much  as, 
but -should  never  be  greater  than,  45°. 

Gripping  shots  (see  under  Explosives) 
should  not  be  permitted,  as  they  are  very  apt 
to  blow  out,  or  to  blow  off  the  heel,  leaving  the 
toe  in  place,  in  which  case  a  portion  of  the 
powder  may  burn  in  the  air.  On  the  other 
hand,  holes  should  not  be  so  pitched  as  to  give 
them  too  thin  a  toe  as  the  shot  may  blow  out 
at  the  back  leaving  the  heel  standing. 

Shots  that  are  all  dead  (as  would  be  6  in 
Fig.  3  if  fired  alone)  or  are  partly  dead,  should 
be  prohibited.  No  shots  should  be  drilled 
directly  into  the  face  and  no  shot  should  be 
drilled  to  such  a  depth  that  any  portion  of  the 
charge  is  beyond  the  point  where  a  perpendicu- 
lar dropped  from  the  drill  hole  will  not  cut  a 
free  face. 

As  a  rule,  shot  holes  should  be  parallel  to 
a  free  face,  as  shown  in  Fig.  4,  and  should 
pitch  a  few  degrees  from  the  horizontal  so  as  to 
cut  across  the  bedding  planes.  It  is  advisable  -p,  , 

to  incline  the  holes  slightly  in  the  direction  of 

the  length  of  the  room,  so  that  they  may  cut  across  the  vertical  cleavage 
planes.  Shots  should  not  be  placed  in  soft  streaks  of  coal,  or  shale,  or  mother 
coal,  as  they  may  blow  out  along  these  lines  of  weakness. 

Shots  should  be  well  balanced  with  toe  and  heel  of  equal  width,  which  should 
never  be  more  than  5  ft.  in  any  case  and  never  greater  than  the  thickness  of  the 
seam  when  less  than  5  ft.  A  hole  5  ft.  long,  working  against  a  toe  and  heel 
each  4  ft.  wide,  will  give  excellent  results  in  seams  4  ft.  thick  and  over. 

Straight  holes  of  uniform  diameter  give  better  results  than  crooked  ones, 
and  generally  short  holes  are  to  be  preferred  to  long  ones.  To  ensure  the  holes 
being  of  a  uniform  size  best  adapted  to  the  coal,  the  drills  should  be  frequently 
tested. 

Shots  that  cannot  do  their  work  when  fired  separately  but  depend  for  their 
successful  action  on  the  results  accomplished  by  another  shot  or  shots  fired  at 
the  same  time,  and  which  are,  consequently,  known  as  dependent  (or  follow) 
shots,  should  not  be  permitted  and  are  prohibited  by  law  in  some  states.  In 
Fig.  1,  while  shots  1  and  2  are  strictly  dependent  shots,  since  either  one  fired 
alone  would  blow  out,  yet  with  proper  judgment  they  may  be  safely  used  if 
fired  at  the  same  instant  with  an  electric  battery.  The  holes  S  and  4  are  in 
every  sense  dependent  as  they  are  dead  unless  a  free  face  has  been  made  by 
firing  1  and  2.  Similarly,  5  and  6  are  dependent  on  the  successful"  firing  of  S 
and  4-  If  fuse  or  squibs  are  used,  S  and  4  may  explode  a  few  seconds  before 
the  others,  resulting  in  blown-out  shots,  to  be  followed  by  the  detonation  of  1 

41 


642  METHODS  OF  WORKING 

and  2  simultaneously  which  will  do  their  work,  the  final  explosion  of  5  and  6 
resulting  in  blown-out  shots.  The  reason  for  the  failure  to  explode  at  the  same 
instant  is  due  to  the  impossibility  of  securing  either  squibs  or  fuse  that  will 
burn  at  exactly  the  same  rate.  In  electric  firing  with  a  blasting  machine,  holes  1 
and  2  may  be  fired  first,  and  then,  after  the  smoke  and  dust  have  cleared  away, 
S  and  4  and  5  and  6  in  separate  pairs.  If  delay-action  detonators  are  used, 
all  the  holes  may  be  fired  in  sequence  in  pairs  by  a  single  application  of  the  cur- 
rent by  using  no-delay  caps  in  1  and  2,  first-delay  caps  in  3  and  4,  and  second- 
delay  caps  in  5  and  6.  However,  one  of  the  strongest  arguments  against  solid 
shooting  is  that  it  is  so  entirely  impossible  to  place  the  second  of  a  series  of  drill 
holes  until  the  results  accomplished  by  the  detonation  of  the  first  hole  have  been 
studied.  Good  practice,  then,  demands,  that  the  center  shot  or  shots  (as  1 
and  2,  Fig.  1)  be  fired  first,  and  that  the  other  shots  be  placed  where  needed 
after  the  face  has  been  examined. 

Objections  to  Solid  Shooting. — The  objections  to  solid  shooting  are  two- 
fold: It  increases  the  percentage  of  slack  coal  produced  and  is  dangerous 
to  the  men  and  mine,  particularly  where  inexperienced  or  careless  workers 
using  black  powder,  are  allowed  to  drill,  charge,  and  fire  their  own  shots,  when, 
where,  and  how  they  please. 

From  an  economic  standpoint,  the  objection  to  solid  shooting  is  that  the 
usual  employment  of  excessive  charges  of  powder  in  poorly  placed  holes  always 
leads  to  the  production  of  an  excessive  amount  of  slack.  While  this  may  be 
an  advantage  where  the  coal  is  coked,  for  ordinary  commercial  use  the  coal 
must  be  lumpy  and  as  free  from  slack  as  possible. 

The  same  causes  that  tend  to  produce  an  excessive  amount  of  fine  coal, 
also  tend  to  the  production  of  blown-out  shots,  and  these,  in  turn,  have  been 
the  cause  of  many  mine  explosions.  These  dangers  are  largely  reduced  if  per- 
missible powders  are  used  and  particularly  so  if  shot  firers  and  electric  blasting 
are  employed.  They  are  reduced  to  the  minimum  if,  in  addition,  the  coal  is 
undercut  before  blasting. 

If  the  duties  of  the  shot  firer  are  limited  to  firing  the  holes  that  have  been 
previously  drilled,  charged,  and  otherwise  prepared  by  the  miner,  the  pos- 
sibility of  damage  to  property  is  not  reduced,  and  the  danger  to  life  is  merely 
transferred  from  the  miner  to  the  shot  firer.  Under  these  conditions  the  shot 
firer  is  killed  in  event  of  accident  and  not  all  the  underground  workers. 

A  distinct  advance  toward  safety  is  made  if  the  shot  firers  charge  as  well 
as  blast  the  holes  previously  drilled  by  the  miner,  and  are  required  to  refuse 
to  fire  any  and  all  holes  that  are  improperly  placed.  In  theory,  the  method  is 
perfect,  but  leads  to  many  accidents  in  practice,  as  the  shot  firers,  through 
mistaken  friendship  for  the  miner,  often  fire  shots  their  better  judgment  must 
condemn. 

The  highest  degree  of  safety  is  attained  by  employing  an  inspector  who 
is  independent  of  the  miners  to  oversee  the  placing  and  drilling  of  all  shot 
holes.  The  inspector  not  only  instructs  the  miner  where  to  place  the  holes 
but  determines  their  pitch,  depth,  and  the  amount  of  charge  as  well.  Before 
the  miner  leaves  his  place,  the  inspector  examines  it,  and  compels  the  drilling  of 
other  holes  in  place  of  those  drilled  contrary  to  his  previously  issued  instructions. 
The  inspector  commonly  places  a  marker  or  flag  (a  piece  of  paper)  in  the  mouth 
of  each  hole  to  be  fired,  the  charging  and  blasting  being  left  to  the  shot  firers. 

Notwithstanding  all  precautions  taken  by  inspecting  the  holes  as  described, 
the  fatality  rate  among  shot  firers  is  needlessly  high  by  reason  of  the  failure 
of  many  of  them  to  blast  the  holes  properly.  Having  a  certain  number  of  holes 
to  charge  and  fire  in  order  to  complete  their  shift,  the  work  is  commonly  done 
in  from  one-half  to  one-third  the  time  that  should  be  devoted  to  it;  and  this 
leads  to  carelessness  in  charging,  in  going  back  on  delayed  shots,  and  has  led 
to  serious  mine  explosions  through  blown-out  shots  igniting  the  dust  thrown 
into  suspension  through  rapid  firing.  To  protect  the  shot  firers  against  them- 
selves has  arisen  the  custom  of  firing  all  the  shots  at  one  time  by  means  of  a 
current  of  electricity  applied  from  some  point  outside  the  mine,  and  after  all 
the  men  have  left  the  workings.  This  practice  is  not  without  danger  to  the 
mine,  through  its  possible  wrecking  by  a  dust  explosion  caused  by  the  detona- 
tion at  a  single  instant  of  many  hundred  pounds  of  high  explosives  in  an  atmos- 
phere charged  with  dust. 

BLASTING  AFTER  UNDERCUTTING 

The  object  of  mining  or  undermining  the  seam  of  coal  previous  to  blasting 
is  to  secure  the  advantages  of  an  additional  free  face.  The  mining  may  be 
made  in  the  bottom  of  the  seam  or  in  the  fireclay  underlying  it  (undercutting), 


METHODS  OF  WORKING 


643 


in  a  band  or  layer  of  shale  or  clay  near  the  middle  of  the  seam,  or  near  the  roof 
(topcutting)  and  may  be  done  by  a  pick  or  by  machinery.  The  depth  of  the 
undercut  in  seams  up  to  6  ft.  or  8  ft.  in  thickness  is  commonly  equal  to  the 
thickness  of  the  seam  where  machinery  is  used,  but  is  not  usually  much  over 
4  J  ft.  where  the  work  is  done  with  a  pick.  Where  the  cut  is  made  with  a  chain 
machine,  it  has  a  uniform  height  from  front  to  back  of  from  4  in.  to  6  in.  When 
made  with  a  punching  machine  or  with  a  pick,  the  height  of  the  cut  decreases 
from  14  in.  to  18  in.  at  the  front  to  4  in.  to  6  in.  at  the  back. 

The  proper  placing  of  the  shot  holes  in  a  face  that  has  been  mined  is  a 
simple  matter  compared  to  the  same  work  in  solid  shooting.  The  precautions 
previously  given  concerning  the  drilling  of  gripping,  dead,  and  unbalanced 
shots,  and  charging  with  the  proper  amount  of  explosive  must  be  heeded. 
As  a  rule,  the  depth  of  any  hole  should  be  about  6  in.  less  than  the  depth  of  the 
mining,  and  to  secure  this  relationship  between  depth  of  mining  and  length  o, 
shot  hole,  it  is  a  common  practice  where  the  coal  is  undercut  to  a  depth  of, 
say,  7  ft.,  to  make  the  drills  furnished  the  miner  of  a  maximum  length  of  6  ft. 
to  6  ft.  6  in. 

In  entries  and  in  rooms  not  over  20  ft.  wide  where  the  coal  is  6  ft.  to  8  ft. 
thick,  three  shots  placed  as  1,  2,  and  3,  in  Fig.  1,  should  serve  to  bring  down 
the  coal.  Where  the  place  is 


FIG.  1 


more  than,  say,  2£  times  as 
wide  as  the  coal  is  thick,  in- 
stead of  a  single  center  or  burst- 
ing shot  1,  two  may  be  used,  as 
A  and  B.  The  bursting  shots, 
where  the  seam  has  been  un- 
dercut to  a  depth  of  6  or  7  ft 
are  commonly  but  from  4  to 
5  ft.  in  length  and  are  usually 
given  a  pitch  of  from  5°  to  10° 
downwards.  In  some  cases,  1 
may  advantageously  be  placed  nearer  the  roof  in  the  same  horizontal  line 
with  2  and  S,  but  is  usually  placed  about  as  shown  at  two-thirds  the  height 
of  the  seam  from  the  floor,  and  will  break  out  a  piece  of  coal  with  a  cross- 
section  approximately  GlH.  When  two  holes  A  and  B  are  used  and  the  place 
is  not  too  wide,  the  coal  broken  will  be  about  on  the  line  EABF.  The  holes  2 
and  8  are  placed  from  10  in.  to  15  in.  from  the  rib  and  so  far  below  the  roof 
that  when  diilled  with  an  upward  pitch  of  from  5°  to  10°,  their  points  will 
just  clear  the  roof  slate. 

In  some  tough,  tenacious  coals,  when  undercut  by  chain  machines  and 
blasted  with  the  comparatively  slow-acting  black  powder,  there  is  a  tendency 
on  the  part  of  the  coal  to  sit  down  on  the  undercut  because  its  height  is  so 
small  that,  in  falling,  the  coal  does  not  gather 
sufficient  impetus  to  roll  forwards  away  from  the 
face.  In  this  case,  the  front  part  of  the  mining 
must  be  snubbed  to  a  height  of  18  in.  to  24  in.  either 
with  a  pick  or  by  placing  a  series  of  snubbing,  or 
pop  shots,  as  AB,  Fig.  2,  in  a  row  along  the  face. 
These  shots  require  a  very  small  amount  of  pow- 
der, are  not  usually  more  than  2  ft.  deep  and 
serve  to  break  out  a  wedge-shaped  piece  of  coal 
appioximately  along  the  lines  A  BCD.  If  the 
r=  coal  thus  brought  down  is  loaded  out  of  the  way, 
"~  there  will  be  ample  room  provided  for  the  free 
fall  of  the  rest  of  the  seam. 

When  shots  are  fired  by  blasting  machine  or 
battery,  shot  1  is  fired  first  and  the  coal  loaded  out  into  cars.  When  two 
bursting  shots  A  and  B  are  necessary,  they  are  fired  simultaneously,  and ,  as 
before,  the  place  cleaned  up.  Shots  2  and  3  may  then  be  fired  together. 
Whet  firing  from  a  point  on  the  surface  is  practised,  the  three  shots  are 
detonated  at  the  one  time,  but  good  practice  seems  to  indicate  that  no-delay 
caps  should  be  used  in  1  (or  in  A  and  E),  and  first-delay  or  even  second-delay 
caps  in  2  and  3. 

COMBINED  UNDERCUTTING  AND  SOLID  SHOOTING 

A  method  sometimes  followed,  which  reduces  the  amount  of  undercutting 
in  rooms,  is  shown  in  plan  in  the  accompanying  illustration.  Here,  the  face  be 
with  a  width  of  from  8  ft.  to  10  ft.  is  driven  some  6  to  10  ft.  in  advance  of  the 


FIG. 


644  METHODS  OF  WORKING 

rest  of  the  room.  Only  the  narrow  face  be  is  undercut  and  is  shot  down  with 
the  customary  three  holes.  After  the  coal  thus  made  is  loaded  out,  two  or 
at  the  most  three  light  shots  serve  to  bring  the  coal  bounded  by  the  faces  cd 
and  de.  The  method  is  adaptable  to  pick  mining,  but  where  machines  are  used 
it  would  be  much  better  to  carry  a  straight  face  and  undercut  the  room  for  the 
_____  full  width. 

gMMMH^  A  method  of  mining  formerly  employed  to  some 

extent  is  known  as  following  the  crack,  and  consists  in 

^^^^^^_      shearing  to  a  depth  of  2  ft.,  and  firing  a  shot,  called  a 

HHHB     snubber,  placed  close  to  the  side  of  the  cut,  the  hole 

<f  I     being  drilled  3  ft.  deep,  thereby  locating  the  charge  1  ft. 

I     on   the   solid.     The  firing  of  the  snubber  cracks  or 

H    crevices  the  seam  along  the  rib.      After  the  firing  of 

/         the  snubber,  successive  back  shots  are  fired  between 

these  and  the  rib  at  the  far  side  of  the  face,  the  coal 

being  removed  after  the  firing  of  each  shot.  The  next  shear  or  side  cut  is 
made  at  the  place  where  the  snubber,  drilled  1  ft.  on  the  solid,  has  cracked 
the  coal.  The  dangers  incident  to  the  use  of  this  method  are  apparent. 

UNDERCUTTING  IN  LONGWALL 

In  longwall  work,  the  weight  of  the  roof  is  made  to  act  upon  the  face  so  as 
to  materially  assist  the  breaking  down  of  the  coal.  Usually  a  succession  of 
shallow  cuts  6  or  8  in.  deep  is  made  across  the  entire  face  of  the  coal,  thereby 
giving  the  roof  pressure  time  to  act  on  the  face  of  the  cut,  the  coal  at  the  back 
being  thus  crushed  and  rendered  more  easy  to  mine.  If,  however,  the  roof 
pressure  is  excessive  or  is  allowed  to  act  on  the  face  for  too  long  a  time,  the 
crushed  mining  dirt  is  compacted  and  the  undercutting  made  more  difficult. 

By  machinery,  the  coal  is  undercut  to  the  full  depth  in  one  cut.  When 
the  old-style,  chain-breast  machines  are  employed,  the  cockermegs,  or  cockers, 
are  placed  before  the  undercutting  is  started,  and  are  removed  and  reset  in 
turn  as  the  machine  advances.  With  the  present,  self-propelling,  longwall 
machine,  which  can  make  a  continuous  cut  of  any  length  without  resetting, 
the  sprags  are  placed  immediately  behind  the  machine  as  fast  as  it  pulls  itself 
along  the  face.  As  these  machines  require  5  ft.  or  less  of  space  between  the 
face  and  the  gob,  they  do  not  interfere  with  the  timbering,  gob,  pack  walls,  etc. 

MACHINE  MINING 

The  commercial  use  of  coal-mining  machines  may  be  said  to  date  from  the 
year  1891  when  the  545  machines  in  use  undercut  6,211,732  T.  of  coal,  or  6.66% 
of  the  entire  output  for  the  year,  and  at  an  annual  rate  of  11,398  T.  per  machine. 
In  1910,  13,254  machines  undercut  174,012,293  short  T.  of  coal,  or  41.7%  of 
the  output,  showing  an  annual  capacity  of  13,127  T.  each.  In  1910,  the 
machines  in  use  comprised  6,716  of  the  pick  or  puncher  type,  5,973  of  the  qjiain- 
breast  type,  518  longwall  machines,  and  47  of  the  shortwall  type.  It  will  be 
noted  that  the  puncher  machines  formed  more  than  one-half  of  the  entire  num- 
ber used. 

A  universal  mining  machine  has  not  yet  been  brought  out,  and  one  of  the 
principal  reasons  for  the  failure  of  mining  machines  in  a  number  of  instances 
has  been  the  attempt  to  use  a  machine  under  conditions  to  which  it  was  not 
adapted.  _  When  a  mining  machine  is  designed  and  built  to  suit  the  conditions 
under  which  it  is  to  be  operated,  it  is  safe  to  say  that  there  are  but  few  mines 
in  which  they  cannot  be  successfully  utilized.  They  are  of  particular  advan- 
tage where  there  is  a  long  working  face  and  where  the  coal  is  over  3  ft.  in  thick- 
ness. Low  seams  require  more  undercutting  for  a  given  output  than  high 
seams.  As  a  rule  it  has  not  been  found  economical  to  use  machines  in  seams 
pitching  over  12°  to  15°,  though  pick  machines  have  been  used  in  mines  having 
an  inclination  of  23°,  the  difficulty  being  not  so  much  in  the  cutting  as  in  moving 
the  machine  from  place  to  place. 

There  are  two  general  types  of  mining  machines:  Pick,  or  puncher, 
machines  in  which  a  steel  pick  attached  to  the  end  of  a  piston  rod  is  given  a 
reciprocating  motion  by  means  of  compressed  air;  the  action  of  the  machine 
simulating  that  of  a  miner  with  a  hand  pick.  Cutter,  or  chain,  machines  in 
which  a  series  of  teeth  attached  to  a  chain  (usually)  or  to  a  disk  or  bar  moved 
by  an  electric  or  compressed-air  motor,  scrape  away  the  coal. 

Pick  Machines. — Pick  machines  may  be  divided  into  several  classes  accord- 
ing to  their  mounting.  The  ordinary  type  is  mounted  upon  low  wheels  and  is 
especially  adapted  for  undercutting  a  straight  face.  For  making  a  vertical 
sheer,  the  machine  is  mounted  upon  much  larger  wheels  and  is  provided  with 


METHODS  OF  WORKING  645 

longer  bits.  Pick  machines  mounted  upon  wheels  are  not  adapted  to  under- 
cutting seams  where  the  pitch  is  more  than  10°  because  of  the  difficulty  of 
keeping  the  machine  up  to  the  face.  For  pitches  up  to  40°,  the  machine  is 
mounted  on  a  post  that  is  firmly  wedged  in  the  roof  and  floor,  constituting 
what  is  commonly  known  as  a  post  puncher,  although  the  various  manufac- 
turers have  their  distinctive  names.  While  the  post  puncher  is  able  to  work 
at  practically  any  angle  of  pitch,  in  seams  inclined  at  more  than  40°  shoot- 
ing is  generally  done  off  the  solid,  the  difficulty  of  moving  weights  of  any 
kind  on  such  steep  slopes  prohibiting  the  use  of  machinery.  The  post  puncher 
is  adapted  for  shearing  or  for  undercutting  in  a  horizontal  line  at  any  dis- 
tance above  the  floor.  One  of  the  objections  made  to  punchers,  that  they  cut 
put  too  much  coal  or  the  cut  is  too  high,  making  an  excessive  amount  of  slack, 
is  overcome  by  the  use  of  these  machines,  which  will  cut  nearly  as  close  to  the 
floor  as  a  chain  cutter. 

Punching  machines  directly  operated  by  electricity  have  not  met  with 
success,  but  a  punching  machine  in  which  the  electric  current  operates  a  small 
air  compressor,  which  in  turn  supplies  the  power  for  operating  the  pick  are 
well  and  favorably  known.  In  the  Pneumelectric  puncher,  the  motor  and  air- 
compressing  mechanism  are  all  in  the  one  machine,  which  may  be  mounted 
upon  wheels  in  the  ordinary  way  or  upon  a  post.  In  mines  intending  to  use 
electric  motors  for  haulage  or  in  mines  already  wired,  this  machine  will  save 
the  cost  of  special  compressed-air  piping. 

The  advantages  claimed  for  pick  machines  are  that  they  are  able  to  cut 
around  sulphur  balls  or  other  obstructions  in  the  seam  and  are  particularly 
suitable  in  places  having  rolls  in  the  floor;  that  the  exhaust  air  helps  the 
ventilation,  particularly  in  tight  places;  that  there  is  no  danger  of  igniting 
either  gas  or  dust  from  short  circuits  of  the  electric  arc;  that  they  can  be 
pointed  at  any  horizontal  angle  and  so  can  cut  around  and  between  posts 
which  may  be  set  close  to  the  face;  that  they  require  less  skilled  labor  than 
chain  machines;  and  that  they  may  be  used  for  working  pillars  on  which  there 
is  a  squeeze,  as  they  are  light  and  can  be  easily  handled  and  readily  removed. 

Chain  Machines. — Chain  machines  consist  of  a  low  metal  bed  frame  upon 
which  is  mounted  a  motor  that  rotates  a  chain  to  which  suitable  cutting  teeth 
are  attached.  To  operate  chain  machines  to  the  best  advantage,  the  coal 
should  be  comparatively  free  from  pyrites.  They  also  require  more  room  than 
pick  machines,  and  a  space  from  12  to  15  ft.  in  width  is  necessary  along  the 
face  to  work  them  to  advantage.  These  machines  have  proved  failures  in  some 
mines  on  account  of  the  incessant  jarring  of  the  roof  by  the  rear  jack.  Chain- 
cutter  machines  cannot  be  used  to  undercut  coal  when  a  squeeze  is  upon  it. 
Coal  seams  that  are  comparatively  level  and  free  from  pyrites  and  have  a  com- 
paratively good  roof  can  undoubtedly  be  more  satisfactorily  and  economically 
cut  with  chain-cutter  machines  than  with  any  other  type. 

The  average  height  of  cut  is  4|  to  5  in.,  and  at  this  height,  the  chain-cutter 
machine  makes  only  about  60%  as  much  small  coal  as  a  pick  machine.  This 
is  not  always  an  advantage,  as  it  does  not  always  allow  sufficient  height  for 
the  coal  to  fall  down  after  the  cut  is  made.  In  a  3^-ft.  seam,  three  men  are 
required  to  handle  the  machine  to  advantage. 

Chain  machines  may  be  operated  either  by  compressed  air  or  electric  motor 
and  both  are  very  extensively  used.  The  original  form  of  chain  machine,  after 
making  its  undercut,  has  to  be  moyed  across  the  face  the  width  of  a  cut  before 
another  cutting  can  be  made.  This  takes  considerable  time  and  in  low  seams, 
especially,  involves  much  hard  labor.  To  overcome  these  difficulties,  what  are 
known  as  short-wall  machines  are  extensively  used.  These  machines  are  set 
up  in  the  same  general  way  as  the  older  type,  but  after  making  the  first  or 
sumping  cut  at  one  side  of  the  face,  instead  of  withdrawing  the  cutter  and  jack- 
ing the  machine  into  a  new  position  for  another  cut,  the  whole  machine  pulls 
itself  across  the  face  by  means  of  a  chain  or  wire  rope  attached  to  the  opposite 
rib,  cutting  as  it  goes. 

When  a  dirt  or  slate  parting  exists  in  the  seam  at  such  a  distance  above  the 
floor  that  the  bed  is  divided  into  two  more  or  less  nearly  equal  parts,  it  often 
is  a  material  economy  and  leads  to  the  production  of  clean  coal  if  the  cutting 
is  done  in  the  parting.  When  post  punchers  are  used,  this  is  easily  done  by 
raising  or  lowering  the  puncher  on  its  supporting  post,  but  cannot  generally 
be  done  with  chain  machines  unless  they  were  supported  upon  a  cribbing  of 
logs,  the  building  of  which  requires  much  time.  The  recently  introduced 
turret  coal  cutter  permits  the  undercutting  of  the  seam  by  a  chain  machine  at 
any  height  from  2  ft.  to  5  ft.  from  the  floor.  The  machine  consists  of  a  self- 
propelling  truck  with  the  necessary  cable-reel  to  attach  to  the  power  line  in 


646  METHODS  OF  WORKING 

the  entry.  The  cutting  machine  is  mounted  on  a  turntable  carrying  lour 
heavy  standards  on  which  the  machine  is  moved  up  and  down  to  the  desired 
height.  After  moving  itself  to  the  face  of  the  working  place,  the  machine  is 
anchored,  the  cutter  raised  to  the  proper  height,  and  the  machine  turned  on 
the  turret  towards  the  right-hand  rib  and  locked  in  position  at  an  angle  of  about 
15°  with  the  track.  After  the  cut  is  made  on  this  setting,  the  cutter  is  swung 
across  the  face,  cutting  as  it  moves,  until  its  angle  with  the  room  is  about  20° 
to  the  left.  The  cutter  is  withdrawn,  completing  the  left-rib  cut,  is  swung 
parallel  to  the  track,  and  is  ready  for  moving  to  the  next  place.  One  advantage 
of  this  machine  is  that  the  entire  cut  may  be  made  without  removing  it  from 
the  truck. 

Capacity  of  Coal  Cutting  Machines. — So  much  depends  on  local  conditions 
that  it  is  almost  impossible  to  give  specific  data  or  rates  of  working  and  costs 
of  operating  cutting  machines,  but  the  following  figures  are  fair  working  approxi- 
mations. In  the  case  of  chain  machines,  the  amount  of  undercutting  that 
can  be  done  in  a  given  time  depends  on  the  ability  of  the  men  running  it,  the 
character  of  the  coal,  and  the  presence  of  faults  and  impurities  and  other 
obstructions  and  hindrances  to  the  work_  of  cutting.  Under  favorable  con- 
ditions, one  machine  operated  by  two  men  is  recorded  as  having  made  104  cuts, 
each  6  ft.  deep,  in  10  hr.,  these  cuts  being  made  in  rooms  and  entries.  This  is 
exceptional  cutting  and  much  higher  than  the  average.  It  is  fair  to  say  that  a 
machine  making  from  36  to  45  cuts,  6  ft.  deep,  in  10  hr.,  is  doing  good  work. 
An  average  of  40  cuts,  42  in.  wide,  will  represent  140  lin.  ft.  of  face,  which 
for  coal  6  ft.  in  height  will  make  approximately  140  T.  of  coal  per  shift  of  10  hr. 
Under  unfavorable  conditions,  the  result  will  not  run  nearly  so  high.  There 
are  cases  where,  with  the  chain  breast  machine,  the  undercutting  of  one  room 
per  shift  of  10  hr.  is  considered  good  work.  The  capacity  of  the  machine  or 
the  number  of  runs  it  will  make  differs  in  every  locality  and  seam,  and  experi- 
ence in  the  use  of  machines  in  a  given  locality  is  by  far  the  best  guide  when  the 
capacity  of  the  machine  is  to  be  considered.  The  time  it  takes  for  a  machine 
to  make  a  cut  is  generally  but  a  small  part  of  the  total  time  consumed  in  its 
operation,  unless  unfavorable  conditions  exist,  as  the  time  for  moving  and  reset- 
ting the  machines  greatly  exceeds  the  time  of  cutting.  In  cutting  clean  coal, 
a  machine  should  make  a  cut  its  full  depth  in  4  J  min.,  and  1  min.  more  will  be 
required  to  withdraw  the  machine;  the  rest  of  the  time  is  consumed  in  loading 
and  unloading,  moving  and  setting  the  machine  in  place  ready  for  another  cut, 
besides  such  delays  as  waiting  to  have  rooms  cleaned  for  operation,  waiting 
for  driver,  and  many  small  accidents  that  are  liable  to  occur  at  any  time. 
In  the  use  of  longwall  machines,  a  record  has  been  made  of  500  lin.  ft.  of  coal, 
cut  6  ft.  deep,  in  10  hr.  This  is  an  unusual  record,  as  a  longwall  machine 
under  ordinary  conditions  will  not  average  more  than  400  lin.  ft.  In  a  seam 
4  ft.  thick,  a  length  of  400  ft.,  cut  6  ft.  deep,  makes  approximately  280  T.  of 
coal,  which  would  be  the  average  output  of  a  machine  per  shift  of  10  hr.; 
but  under  unfavorable  conditions  the  output  will,  of  course,  be  much  less. 

In  the  case  of  pick  machines,  a  fair  average  of  cutting  for  any  one  machine 
working  in  rooms  would  be  100  lin.  ft.  per  da.  of  10  hr.,  making  a  cutting  6  ft. 
deep.  This  in  a  seam  6  ft.  thick  makes  about  100  T.  of  coal,  which  is  the  aver- 
age output  of  a  machine  per  day  of  10  hr.  The  amount  of  coal  that  a  loader 
can  shoot  down  and  load  in  a  day  varies,  of  course,  with  the  thickness  of  the 
seam  and  the  character  of  the  coal,  but  an  average  for  a  day  of  10  hr.  is  12  to 
15  T.  In  longwall  work,  as  no  changing  of  places  is  required,  a  fair  average 
is  150  lin.  ft.,  6  ft.  deep,  per  da.,  making  about  150  T.  per  machine  per  da. 
The  capacity  of  a  pick  machine  for  shearing  depends  largely  on  the  height  of 
the  coal  sheared.  Working  in  coal  of  average  height,  eight  cuts,  sheared  6  ft. 
deep,  in  10  hr.  is  considered  fair  work. 

Longwall  Machines. — Longwall  machines  are  of  two  main  types:  (1)  Disk 
and  cutter-bar  machines;  (2)  modified  forms  of  chain  machines.  In  the  disk 
machine,  a  series  of  bits  or  cutters  are  inserted  in  the  periphery  of  a  cutter 
wheel  or  disk  to  which  a  horizontal  rotary  motion  is  imparted.  The  machine 
impels  itself  across  a  longwall  face  by  means  of  a  rope  fixed  at  any  convenient 
distance  as  in  the  shortwall  machine.  In  the  cutter-bar  machine,  the  cutting 
is  d^ne  by  means  of  teeth  set  in  a  shaft  about  2  in.  in  diameter  set  at  right 
angles  to  the  machine.  The  teeth  are  arranged  so  that  one-fourth  of  them 
cut  and  three-fourths  of  them  break  the  coal  as  the  bar  advances  horizontally 
along  the  face.  Lateral  motion  is  secured  by  the  use  of  a  pair  of  rails  laid  along 
the  face.  One  of  these  rails  is  notched  and  the  other  is  plain.  The  machine 
is  propelled  by  means  of  a  toothed  wheel  meshing  into  the  notches  of  the 
notched  rail, 


METHODS  OF  WORKING 


647 


Longwall  machines  of  the  second  class  generally  consist  of  a  cutter  arm  of 
any  desired  length,  depending  on  the  depth  of  undercut  needed.  Around 
the  necessary  sprocket  wheels  on  this  arm  is  passed  a  chain  bearing  cutting 
teeth,  the  chain  being  given  motion  by  a  compressed  air  or  electric  motor  of 
the  type  used  for  ordinary  chain  machines. 

Heading  Machines. — In  the  Stanley  header,  shown  in  the  accompanying 
figure,  the  driving  and  the  feeding  mechanisms  are  placed  on  a  massive  frame  a 
that  is  mounted  on  wheels.  When  the  machine  is  in  place  ready  to  commence 
work,  it  is  held  fast  by  the  top  jacks  b  and  the  side  jacks  c.  At  the  end  of  the 
main  shaft  s,  an  auger  drill  e  is  placed  for  the  purpose  of  steadying  the  cutter 
frame  while  the  machine  is  working.-  The  cutter  frame  consists  of  a  large 
revolving  cross-head  h  carrying  two  arms  /  in  the  ends  of  which  the  cutters 
or  bits  are  set.  The  driving  mechanism  is  so  constructed  that  different  rates 
of  speed  of  the  cutter  frame  can  be  produced  as  desired  for  a  given  rate  of  feed 
advance,  on  coals  of  varying  hardness.  As  the  main  shaft  rotates,  it  advances, 
turning  the  cutter  frame.  The  bits  cut  out  an  annular  groove  from  3  to  85  in. 
wide,  forming  a  C9mplete  cylinder  of  coal  as  deep  as  the  arms  /.  When  this 
is  done,  the  machine  is  run  back  and  the  coal  is  taken  down  and  loaded  up. 
The  machine  is  again  set  in  place  and  another  cylinder  is  cut  out. 

The  cuttings  are  forced  to  the  front  of  the  annular  groove  by  the  scrapers 
on  the  arms  /,  and  from  here  they  are  raked  to  one  side  of  the  machine  by  a 
helper  whenever  the  revolving  arms  are  not  in  the  way.  Lumps  of  coal  that 


fall  from  the  face  are  also  drawn  to  the  side  by  the  helper,  and  finally  loaded 
into  a  car.  In  many  of  these  machines,  however,  the  cuttings  and  the  coal 
that  falls  while  the  machine  is  working  are  taken  from  the  face  by  a  friction 
worm  and  loaded  into  a  mine  car  by  means  of  a  conveyer  or  elevator. 

The  principal  use  of  this  machine  is  for  entry  driving,  where  the  work  must 
be  pushed  rapidly.  It  is  especially  advantageous  for  prospecting  a  piece  of 
coal,  as  an  entry  can  be  driven  a  long  distance  as  a  single  entry,  and  with  no 
other  ventilation  than  that  caused  by  the  air  used  by  the  machine. 

The  Stanley  header  can  cut  out  a  cylinder  of  bituminous  coal  4  ft.  in  diam- 
eter and  5  ft.  in  length  in  15  min.,  and  after  making  the  necessary  allowance 
for  removals,  a  rate  of  advance  equal  to  75  ft.  per  shift  of  10  hr.  is  accomplished. 
Where  it  is  necessary  to  drive  wide  entries,  two  machines  may  be  worked  side 
by  side,  thus  driving  two  parallel  entries  that  nearly  intersect  each  other. 
The  thin  pillar  left  between  them  can  easily  be  cut  out  with  a  pick.  If  the 
coal  could  be  removed  as  quickly  as  the  cutting  is  done,  the  machine  could 
advance  an  entry  12  ft.  wide  25  ft.  in  10  hr.  The  entries  thus  cut  can  be 
widened  out  to  the  desired  height  and  width  by  the  use  of  the  pick.  Impurities, 
such  as  sulphur  balls,  existing  in  coal  hamper  the  use  of  the  Stanley  header, 
and  when  they  are  present  its  progress  cannot  be  as  rapid  as  in  coal  favorable 
to  mining.  An  average  cost  per  linear  foot  of  entry  for  a  cylindrical  cut  alone 
should  not  exceed  25  c. 


648 


METHODS  OF  WORKING 


Machine  Mining  in  Anthracite  Mines.— Owing  to  the  exhaustion  of  the 
thicker  seams  and  the  rapidly  increasing  cost  of  mining  the  thinner  seams, 
the  anthracite  operators  in  northeastern  Pennsylvania  have  begun  to  use 
undercutting  machines  of  the  ordinary  bituminous-coal  mine  type.  The 
method  of  using  the  machines  differs  in  no  way  from  that  employed  in  the 
soft-coal  fields,  although  numerous  ingenious  expedients  have  been  adopted 


pitch  and  can  be  used  on  pitches  of 
these  pitching  places,  after  the  sumping  cut  is  made,  an  iron  rail  is  placed  back 
of  the  machine  and  parallel  to  the  face  of  the  room.  This  rail,  which  is  held 
in  place  by  jacks,  holds  the  machine  up  to  the  face  and  along  it  the  machine 
slides  to  the  end  of  the  cut.  The  rail  is,  of  course,  moved  up  after  each  cut 
is  made  and  the  coal  shot  down.  The  machine  has  the  necessary  power  to  pull 
itself  up  to  the  face  and  to  make  the  sumping  cut  at  the  same  time. 


DRAWING  PILLARS 

The  work  of  drawing  back,  or  robbing,  that  is,  removing  the  pillars  left  in 
the  first  working,  should  be  commenced  as  soon  as  the  rooms  are  worked  up 
their  full  length,  whenever  this  is  possible.  If  this  is  delayed,  and  the  open- 
ings left  to  stand  for  any  length  of  time,  the  roof  will  settle  heavily  on  the  pil- 
lars and  there  will  be  danger  of  crushing  them  and  thus  losing  the  coal.  Fig.  1 
shows  the  way  of  drawing  the  pillars  in  rooms  turned  off  one  side  of  a  single  pair 
of  entries  where  the  drawing  begins  next  to  the  main  entries  and  progresses  inbye. 

The  drawing  of  the  pillars  has  been  completed  in  rooms  1,2,  3,  and  4,  down 
to  the  entry  pillars  a,  which  are  left  and  these  rooms  are  closed;  the  work  on 
pillars  5,  6,  and  7  is  in  progress;  rooms  8  and  9  have  reached  the  limit,  and  the 


FIG.  1 

work  on  the  pillar  separating  rooms  8  and  9  will  now  begin.  The  rooms  inside 
of  number  9  have  not  been  completed,  and  the  last  room  on  this  pair  of  entries 
has  just  been  turned.  After  the  cross-entries  b  and  c  have  been  completed 
and  all  of  the  rooms  off  them  completed  and  the  pillars  between  the  rooms 
drawn,  the  pillars  between  the  entries  b  and  c  and  the  stumps  a  will  be  drawn 
back  to  the  main  entries  d.  It  is  advantageous  to  carry  on  the  pillar  drawing 
systematically  and  to  keep  the  ends  of  the  pillars  in  a  line  to  avoid  excessive 
pressure  being  brought  on  a  single  pillar  by  the  drawing  of  the  pillars  on  either 
side  of  it.  Unless  the  ends  of  the  pillars  are  kept  in  line,  there  is  also  increased 
danger  from  falls,  and  the  work  of  drawing  timber  is  made  more  difficult. 
If  rooms  are  driven  toward  each  other  from  adjoining  cross-entries,  a  pillar 
should  be  left  between  the  ends  of  the  rooms  and  removed  when  the  pillars 
between  the  rooms  are  taken  out. 


METHODS  OF  WORKING 


649 


Fig.  2,  page  635,  shows  the  reverse  method  of  drawing  the  ribs,  that  is, 
from  the  inby  end  of  the  entries  or  headings  toward  the  haulage  roads.  The 
cross-headings  are  driven  in  pairs  off  the  main  headings,  and  off  of  one  of  these 
cross-headings  other  headings  called  butt  headings,  are  driven.  These  butt 
headings  divide  the  mine  into  panels  and  they  are  driven  their  full  length, 
but  so  as  to  leave  a  chain  pillar  c  between  the  end  of  the  butt  headings  and  the 
next  pair  of  cross-headings.  The  rooms  are  then  started  from  the  inbye  end 
of  the  butt  headings,  and  as  soon  as  the  first  or  inbye  room  has  been  driven 
up  to  its  full  length,  leaving  a  chain  pillar  between  it  and  the  next  pair  of  butt 
headings,  the  pillars  are  drawn,  as  shown.  As  soon  as  the  pillars  have  been 
drawn  back  to  the  butt  headings,  the  pillars  between  the  butt  headings,  and  the 


lit 

imi 


••ii 


FIG.  2 

chain  pillar  between  the  lower  butt  heading  and  the  next  lower  tier  of  rooms 
are  drawn  back  as  shown.  The  advantage  of  this  method  over  that  illustrated 
in  Fig.  1  is  that  both  the  room  pillars  and  the  entry  pillars  are  drawn  back 
in  one  operation,  instead  of  the  room  pillars  being  first  drawn  and  the  entry 
pillars  and  stumps  drawn  subsequently.  A  greater  portion  of  the  total  amount 
"  of  coal  is  probably  obtained  in  this  manner  when  it  is  possible  to  carry  it  out. 
The  method  of  drawing  back  the  pillars  illustrated  in  Fig.  2  is  similar  to 
that  just  described,  but  it  is  extended  over  a  much  larger  area.  The  cross- 
headings  a  are  driven  to  the  boundary  of  the  property  before  the  robbing  is 
begun;  from  these  headings  the  butt  headings  b  are  driven,  and  off  these 


650 


METHODS  OF  WORKING 


narrow  rooms,  as  shown.     The  pillars  over  the  entire  length  of  the  property 
are  then  brought  back  at  one  time. 

Work  of  Drawing. — When  the  work  of  drawing  the  pillar  is  to  begin,  a 
cut-through  is  driven  from  the  face  of  each  room  to  the  face  of  the  room  adjoin- 
ing so  as  to  give  a  free  face  across  the  end  of  the  pillar.  There  are  a  number 
of  ways  of  attacking  the  pillar,  the  choice  of  a  method  being  determined  by 

local  conditions  and 
custom. 

Fig.  3  illustrates 
one  way  of  drawing 
back  pillars  separ- 
ating wide  rooms 
in  which  there  is  a 
track  along  each  rib 
of  the  pillar.  The 
work  of  drawing 

<-'CWA  T ¥ck  the  5iUar?  is 

4$£v&39r.j 


FIG.  3 


shown  as  having 
just  begun,  the  pil- 
lars having  been  cut 
through  at  the  face, 

and  the  first  shots  having  removed  the  coal  at  each  corner  of  the  pillar. 
The  second  holes  a  will  remove  the  remainder  of  the  first  slice  across 
the  pillar  and  the  holes  b  the  first  cut  of  the  second  slice.  The  coal  is  thus 
removed  in  steps.  A  row  of  props  c  keeps  up  the  roof  along  the  face  of  the  pil- 
lar. As  the  pillar  is  drawn  back  a  sufficient  distance,  a  second  row  of  props 
similar  to  that  shown  at  c  is  stood  across  the  face  of  the  pillar,  parallel  to  the 
first  row  c,  which  is  then  withdrawn.  In  pillar  drawing,  the  back  timber 
should  be  drawn  only  so  fast  as  to  throw  a  proper  weight  on  the  pillar.  If  this 
weight  is  excessive,  the  end  of  the  pillar  is  crushed.  An  excessive  weight  is 
also  thrown  on  the  pillars  by  leaving  too  much  timber  standing.  Just  how 
much  timber  to  use  can  be  determined  only  by  experience.  If  the  pillar  is 
very  wide,  a  slice  or  skip  may  be  taken  off  it  from  the  entry  to  the  face  before 
the  pillar  is  cut  across  at  the  face. 

When  the  pillars  have  been  drawn  back  to  the  entry  stump  at  the  mouth  of 
the  room,  where  the  room  begins  to  narrow  toward  the  neck,  care  should  be 
taken  to  break  the  roof,  if  necessary,  back 
to  the  entry  pillar  or  stump.  With  a  hard 
roof,  it  may  be  necessary  to  place  one  or 
two  shots  in  the  roof  at  this  point.  By 
this  means  the  entry  pillars  are  relieved 
of  excessive  pressure  due  to  the  settlement 
in  the  abandoned  rooms,  which  have  been 
closed  by  the  drawing  of  the  pillars. 

Fig.  4  shows  other  methods  very  com- 
monly used  for  drawing  pillars  in  both 
flat  and  inclined  seams,  known  as  splitting 
a  pillar.  In  the  method  shown  in  (a) ,  the 
opening  b  is  driven  up  the  center  of  the 
pillar  as  wide  as  the  strength  of  the  roof 
will  permit  without  crushing  the  pillars 
left  between  this  opening  and  the  rooms. 
Each  of  these  small  side  pillars  is  then 
drawn  back  in  slices  by  a  method  similar 
to  that  shown  in  Fig.  3.  In  Fig.  4  (b),  the 
pillar  is  shown  divided  into  a  number  of 
small  pillars  by  cross-cuts  c.  Each  of 
these  small  pillars  is  then  divided  lengthwise  as  shown  at  d.  In  (c),  the 
pillar  is  divided  up  its  full  length  by  a  narrow  place  e.  This  narrow 
place  and  the  break-throughs  /  divide  the  original  pillars  into  a  number  of 
small  pillars  g.  These  small  pillars  are  next  broken  up  by  other  cross-cuts 
h,  leaving  still  smaller  pillars,  and  these  are  then  taken  out  by  shots,  as 
shown. 

Fig.  5  shows  some  of  the  methods  used  in  robbing  the  pillars  in  steep  pitch- 
ing, thick  beds  of  anthracite.  To  get  the  coal  out  of  the  pillar  at  the  left  of  A , 
a  skip  is  taken  off  the  side,  as  shown.  Successive  skips  are  thus  taken  off  until 
the  whole  is  removed,  the  miner  keeping  the  manway  open  to  the  heading 
below  as  a  means  of  retreat.  The  pillar  between  A  and  B  is  very  similarly 


METHODS  OF  WORKING  651 

worked.  To  remove  that  between  B  and  C,  a  narrow  chute  or  heading  is 
driven  up  the  middle,  and  cross-cuts  put  to  the  right  and  left  a  few  yards  from 
the  upper  end.  Shots  are  placed  in  the  four  blocks  of  coal  thus  formed,  as 
shown,  and  they  are  fired  simultaneously  by  battery.  This  operation  is 
repeated  in  each  descending  portion 
unless  the  pillar  begins  to  run.  A 
pillar  from  which  the  coal  has  started 
to  run  is  shown  to  the  right  of  C. 

Delayed  Pillar  Drawing. — The 
work  of  drawing  pillars  between  the 
rooms  is  sometimes  preferably  delayed 
until  the  entries  have  been  driven  to 
the  boundary  and  the  rooms  also 
worked  up  to  that  point,  when  the 
work  of  drawing  pillars  will  be  com- 
menced at  the  boundary  and  proceed 
uniformly  toward  the  mine  opening.  FIG.  5 

This  may  be  necessary  in  the  working 

of  two  beds  separated  by  only  a  few  feet  of  solid  strata  where  a  number  of 
overlying  beds  are  worked;  or  in  certain  cases  where  the  bed  is  overlaid  by 
water-bearing  strata,  and  where  the  breaking  of  the_roof  rock  would  result  in 
the  flooding  of  the  mine. 

When  this  method  is  used,  a  constantly  increasing  extent  of  airways  and 
roadways  must  be  kept  open  and  in  repair,  until  the  robbing  begins,  while  the 
difficulties  of  ventilation  are  also  increased.  Again,  the  pillars  first  formed 
are  last  removed  and  there  may  be  a  loss  from  depreciation  of  the  pillar  coal 
due  to  weathering  and  also  from  the  crushing  of  the  pillars,  unless  much  larger 
pillars  are  left  than  are  required  when  the  pillars  are  drawn  as  soon  as  the  rooms 
are  finished.  With  fairly  thick  and  very  soft  coals,  the  rapid  working  up  of 
the  rooms  and  equally  quick  drawing  of  the  ribs  as  soon  as  the  rooms  are  driven 
their  full  distance,  is  essential  to  economical  working;  for  delay  in  extracting 
ribs  and  pillars  in  such  circumstances  results  in  their  getting  crushed  and  the 
coal  lost  or  largely  ground  to  slack. 

Precautions  in  Pillar  Drawing. — When  two  or  more  overlying  seams  are 
worked  simultaneously,  the  pillars  in  the  lower  seam  should  not  be  removed 
until  the  upper  seams  have  been  worked  out  and  the  pillars  drawn. 

It  is  not  generally  advisable  to  attempt  to  draw  the  pillars  in  a  limited  area 
surrounded  by  a  district  in  which  the  pillars  are  not  drawn,  particularly  under 
a  hard  roof,  as  an  excessive  weight  will  then  be  thrown  on  the  pillars  left  stand- 
ing and  a  disturbance  set  up  that  may  extend  a  long  distance  from  the  imme- 
diate district  from  which  the  pillars  are  removed. 

In  very  gaseous  mines,  the  pillars  are  sometimes  not  taken  put  until  the 
workings  have  reached  a  considerable  distance  from  the  shaft,  in  order  that 
there  may  not  be  accumulations  of  gas  in  the  gob  and  waste  near  the  shaft, 
since  it  is  often  more  difficult  to  prevent  gas  accumulations  in  robbed  workings 
than  when  the  pillars  are  left  standing.  If  the  coal  is  tender,  the  removal  of 
the  pillars  should  be  delayed  if  the  roof  will  not  fall  readily,  because  if  they  are 
taken  out,  excessive  pressure  may  be  brought  on  the  entry  pillars.  In  the  case 
of  bad  roof,  the  pillars  should  be  taken  out  as  soon  as  possible,  not  only  for 
economy,  but  also  because,  when  the  roof  is  bad  and  falls  freely  as  the  pillars 
are  drawn,  the  d6bris  soon  sustains  the  superincumbent  pressure  and  relieves 
the  weight  on  the  pillars  next  to  the  entries.  Early  drawing  of  pillars  also  con- 
centrates the  working  district,  and,  excepting  in  a  gaseous  mine,  reduces  the 
area  to  be  ventilated. 

With  a  strong  roof  that  does  not  break  readily  when  the  pillars  are  removed, 
great  care  must  be  taken  that  the  removal  of  the  room  pillars  does  not  bring 
sufficient  weight  on  the  entry  pillars  to  crush  them.  A  weak  roof  falls  freely 
and  soon  fills  up  the  gobs,  thus  partly  sustaining  the  pressure  from  the  roof 
and  relieving  somewhat  the  weight  on  the  pillars  along  the  side  and  main 
roads,  due  to  the  layers  of  rock  immediately  above  the  coal. 

If  the  roof  has  fallen  in  the  rooms  before  the  work  of  drawing  begins,  the 
strata  above  the  pillar  can  usually  be  kept  up  comparatively  easily  by  props 
about  the  working  face,  without  great  danger  to  the  miner,  but  where  the  roof 
remains  over  the  rooms,  excessive  pressure  is  often  thereby  thrown  on  the  pil- 
lars and  the  work  of  drawing  is  very  dangerous  and  treacherous;  under  such 
circumstances,  the  whole  pillar  can  rarely  be  removed,  as  it  will  usually  crush 
before  it  can  be  taken  out. 

In  drawing  pillars,  their  ends  should  be  kept  in  a  straight  line,  for  if  they 


652 


METHODS  OF  WORKING 


are  not,  some  pillars  are  subjected  to  greater  pressure  than  others,  valuable 
coal  is  lost,  and  the  work  is  materially  interfered  with. 

Especial  attention  should  be  paid  to  the  effect  of  the  removal  of  the  pillars 
on  the  surface  and  the  overlying  strata,  particularly  if  the  latter  are  water- 
bearing or  contain  running  materials,  such  as  quicksand. 

The  work  of  drawing  pillars  is  particularly  dangerous  where  faults  or  slips 
are  frequent  in  the  roof,  or  top  coal  is  to  be  taken  down,  or  where  pot  bottoms, 
sink  holes,  boulders,  etc.  are  of  frequent  occurrence  in  the  roof,  or  where  the 
workings  underlie  or  approach  buried  valleys  or  extensive  beds  of  quicksand. 

Where  the  pillars  are  crushed  and  creviced,  blown-out  shots  are  liable  to 
occur  in  their  working.  Undermining,  in  pillar  work,  should  be  done  with 
caution.  Pillar  coal  can  sometimes  be  undermined  with  machines,  but  the 
practice  is  not  general  and  hand  work  is  usually  depended  on.  Small  stumps, 
or  portions  of  pillars  should  not  be  left  scattered  through  the  gob,  as  they 
interfere  with  the  uniform  breaking  of  the  top. 

The  conditions  at  different  mines  are  so  varied  that  no  general  rule  can  be 
laid  down  to  suit  all.  There  is  probably  no  more  dangerous  work  in  mining 
than  pillar  drawing  and  the  method  adopted  depends  largely  on  local  conditions 
and  on  the  experience  of  the  miner. 


LONGWALL  SYSTEM  OF  MINING 

SYSTEMS  OF  LONGWALL 

In  the  longwall  system  of  mining,  the  coal  is  taken  out  in  a  single  oper- 
ation, the  face  of  the  workings  advancing  in  an  unbroken  line  or  wall;  no  pil- 
lars of  coal  are  left  to  support  the -roof  which  is  allowed  to  fall  and  settle  behind 
the  miners  as  the  workings  advance.  The  accompanying  illustration  shows 
the  general  system  of  longwall  followed  in  the  United  States.  From  the  shaft, 
or  point  from  which  the  workings  are  opened  out,  a  number  of  roads  are  kept 

open  for  haulage  pur- 
poses to  the  working 
face,  as  shown.  Roads 
a,  d,  e,  h  and  *  are 
called  main  roads,  or 
main  entries,  as  they  are 
kept  open  permanently. 
The  roads  d  and  e  are 
sometimes  called  diag- 
onal main  roads,  or 
main  diagonal  roads,  as 
they  cut  diagonally  ac- 
ross the  workings  be- 
tween the  straight  roads 
a  and  h  and  a  and  i. 
Each  of  the  broken 
straight  lines  represents 
a  temporary  road  from 
the  face  to  the  nearest 
haulage  road.  The  dis- 
tance between  any  two 
of  these  broken  lines 
constitutes  a  working 
place,  or  a  room.  The 
crossroads  b,  c,  f,  g,  j,  k 
are  driven  off  the  main 
roads  usually  at  an  angle 
of  about  45°,  and  their  purpose  is  to  cut  of?  the  working  rooms  from  time  to 
time  so  that  haulage  distances  may  be  reduced.  The  distance  between  cross- 
entries,  or  the  limiting  lengths,  of  the  rooms  is  determined  by  the  time  it  is 
possible  to  keep  the  temporary  roads  from  the  face  to  the  main  or  cross-roads 
open. 

The  waste  material  from  the  seam,  roof,  or  floor,  is  built  in  the  form  of 
pack  walls  along  each  side  of  the  roadways  and  in  the  spaces  between,  from 
which  the  coal  has  been  taken  out.  The  pack  walls,  or  packs,  lining  the  road- 
ways, are  called  road  packs,  and  those  between  the  roads  gob  packs. 


METHODS  OF  WORKING  653 

There  are  two  general  systems  of  longwall:  longwall  advancing  and  long- 
wall  retreating.  In  longwall  advancing,  the  face  is  started  from  the  foot  of  the 
shaft  or  from  the  inner  side  of  the  shaft  pillar  and  advances  toward  the  boun- 
dary of  the  property.  As  the  haulage  roads  under  this  system  are  maintained 
by  pack  walls,  it  is  often  called  the  gob-road  system.  This  is  the  method  widely 
favored  in  those  parts  of  the  United  States  where  longwall  is  used,  as  by 
means  of  it  the  mine  is  rapidly  opened  up  and  early  returns  are  secured  upon 
the  capital  invested.  There  is  no  expense  for  narrow  work,  and  a  minimum 
amount  of  timber  is  required. 

In  longwall  retreating,  narrow  entries  are  driven  through  the  solid  coal  to 
the  boundary  of  the  property  and  the  longwall  face  is  started  at  that  point, 
the  coal  being  taken  out  completely  as  the  face  is  brought  back  toward  the 
shaft.  This  is  probably  the  better  system  of  the  two,  provided  the  demand 
for  coal  and  the  capital  available  are  such  th<*t  the  time  may  be  taken  to  drive 
the  entries.  For  fragile  roof  and  soft  coal,  or  a  soft  bottom,  the  method  has 
many  advantages,  particularly  for  working  seams  lying  at  a  great  depth,  as 
there  is  practically  no  expense  for  the  maintenance  of  the  haulage  roads  and 
the  mined-out  area  is  abandoned  as  soon  as  the  coal  is  removed.  The  ventila- 
tion of  the  face  is  also  more  efficient  and  less  expensive. 

CONSIDERATIONS  AFFECTING  THE  ADOPTION  OF  LONGWALL 

The  points  that  must  be  considered  before  adopting  the  longwall  method 
of  mining  coal,  in  preference  to  the  room-and-pillar  method,  are  as  follows: 
The  roof  strata  overlying  the  seam;  depth  of  cover;  nature,  thickness,  and  incli- 
nation of  the  seam;  nature  of  the  floor  or  underlying  strata;  quantity  of  stow- 
age or  waste  in  the  seam  or  contiguous  strata;  surface  damage  and  the  presence 
of  water  or  gas  in  the  seam  or  contiguous  strata;  supply  of  timber;  labor  con- 
ditions; and  the  transportation  and  marketing  of  the  product. 

Roof  Pressure. — Although  the  longwall  method  is  most  successfully 
employed  when  the  seam  lies  at  a  considerable  depth  below  the  surface,  yet 
it  has  been  successfully  adopted  under  favorable  roof  strata  where  the  depth 
of  coyer  did  not  exceed  80  ft.  The  ideal  roof  in  longwall  is  composed  of  tough, 
elastic,  and  pliable  strata,  that  yield  gradually  by  bending  when  the  coal  is 
removed,  thereby  causing  a  uniform  settlement  over  the  area  mined  and  throw- 
ing a  sufficient  weight,  or  roof  pressure,  on  the  coal  face  to  break  the  coal  when 
the  same  has  been  mined  or  undercut. 

The  roof  pressure  depends  on  the  depth  and  character  of  the  cover  or  mate- 
rial overlying  the  seam.  In  the  longwall  method  of  mining,  the  weight  of  the 
strata  overlying  the  seam  is  made  to  settle  on  the  waste  material  or  the  pack 
walls  that  are  built  as  the  coal  is  removed,  hence  there  is  practically  no  limit 
of  depth  beyond  which  it  cannot  be  worked. 

In  the  room-and-pillar  system,  there  is  a  practical  limit  to  the  width  of 
opening  that  can  be  safely  and  economically  kept  open,  and  to  the  width 
of  pillar  that  can  be  left  to  support  the  increasing  roof  pressure  without 
crushing.  These  widths  of  opening  and  pillar  determine  the  depth  of  the 
workings  that  can  be  mined  by  this  method.  As  the  width  of  pillar  increases, 
the  expense  of  driving  the  necessary  cross-cuts  increases,  and  the  percentage  of 
coal  obtained  in  the  first  working  is  decreased.  The  limiting  depth  is  not 
absolute,  but  will  vary  according  to  conditions,  and  as  this  depth  is  approached, 
pillar  mining  becomes  more  and  more  difficult  and  expensive.  On  this  account, 
the  longwall  system  is  generally  better  adapted  to  the  working  of  very  deep 
seams  than  the  room-and-pillar  method. 

Nature  of  Coal  Seam. — Longwall  is  best  adapted  to  a  strong,  tough  coal 
that  can  be  undercut  to  a  moderate  depth  without  breaking,  and  to  seams  of 
uniform  and  moderate  thickness  lying  flat  or  nearly  flat.  Irregularities  in  the 
seam,  such  as  sudden  thickenings  or  thinnings,  the  presence  of  large  masses 
of  iron  pyrites,  black  bat,  etc.,  are  unfavorable  to  the  adoption  of  longwall, 
but  in  the  room-and-pillar  system  can  usually  be  cut  through  or  around.  In 
steep  inclinations  of  the  seam,  longwall  is  not  as  successful  as  in  flat  seams, 
owing  to  the  weight  being  drawn  from  the  working  face. 

Waste. — In  the  longwall  method,  there  is  usually  ample  space  for  the 
storage  underground  of  all  waste  rock,  so  that  the  expense  and  delay  due  to  the 
haulage  and  hoisting  of  such  rock  is  avoided.  It  is  not  always  possible  to 
avoid  this  expense  and  delay  in  room-and-pillar  work.  .If  there  is  not  suf- 
ficient waste  as  the  result  of  mining  the  coal  by  longwall,  this  method  cannot 
be  adopted  to  advantage  unless  it  is  practicable  to  bring  material  for  the  pack 
walls  into  the  mine  from  the  surface.  This  objection  to  the  method  is  very  apt 


654  METHODS  OF  WORKING 

to  apply  in  the  case  of  thick  seams  where  a  large  quantity  of  waste  or  gob  is 
required  for  the  packs. 

For  the  working  of  a  thin  seam,  on  the  other  hand,  longwall  is  particularly 
advantageous;  for  it  is  often  absolutely  essential  for  the  successful  working 
of  a  seam  that  all  the  coal  be  f  ecovered,  and  that  the  expense  for  timber  and 
maintenance  of  roadways  be  reduced  to  a  minimum.  This  can  often  best  be 
secured  by  the  longwall  method.  Where  plenty  of  waste  material  is  present, 
there  is  little  probability  of  a  creep  or  squeeze  in  longwall  work,  except  with  a 
very  soft  bottom-. 

Surface  Damage,  Water,  Gas,  Etc.— In  longwall  W9rking,  damage  to  the 
surface  is  not  as  liable  to  occur,  nor  is  it  as  great,  as  in  the  room-and-pillar 
system  of  mining,  the  subsidence  of  the  surface,  owing  to  the  removal  of  the 
coal,  being  more  gradual  and  uniform  in  longwall,  and  seldom  producing  the 
large  breaks  and  caving  in  of  the  surface  that  are  so  common  in  room-and-pillar 
work.  Consequently,  the  inflow  of  surface  water  is  less  in  longwall  work  than 
in  the  room-and-pillar  system. 

The  presence  of  gas  in  a  seam  is  unfavorable  to  longwall  work,  for  while 
the  ventilation  of  the  working  face  is  as  good,  or  better,  in  this  system  than  in 
room-and-pillar  work,  it  is  less  easily  controlled,  and  a  large  quantity  of  gas 
liberated  in  one  portion  of  the  mine  is  not  as  easily  confined  to  that  portion 
of  the  mine  in  extended  longwall  work  as  in  some  forms  of  room-and-pillar 
work,  unless  some  of  the  panel  adaptations  of  longwall  are  used.  In  general, 
in  longwall  work,  gas  issuing  at  one  point  of  the  face  is  carried  along  the_entire 
working  face. 

Timber  Supply. — Where  timber  is  scarce  or  expensive,  longwall  is  par- 
ticularly advantageous,  owing  to  the  small  amount  of  timber  required.  In 
longwall,  much  more  of  the  timber  can  generally  be  used  again  and  again  than 
in  room-and-pillar  work,  the  props  being  drawn  and  set  forwards  as  the  face 
advances.  On  the  other  hand,  in  room-and-pillar  work,  a  more  abundant 
supply  of  timber  is  usually  necessary,  as  the  timbers  cannot  generally  be  used 
again. 

Labor  and  Trade  Conditions. — The  longwall  miner  is  a  more  highly  skilled 
artisan  than  one  who  works  in  mines  operated  on  the  room-and-pillar  system, 
and  must  be  a  steady,  regular  worker.  If  absent  a  day  his  place  falls  behind, 
making  his  work  harder  and  his  output  less  because  of  the  excessive  amount 
of  slack  that  is  likely  to  result  from  excessive  roof  pressure  where  the  face 
falls  behind.  Longwall  work  is  not  adapted  to  conditions  where  regularity 
of  output  is  not  certain,  owing  to  the  frequent  occurrence  of  strikes,  to  the 
scarcity  of  labor,  or  where  market  conditions  are  irregular  or  transportation 
facilities  uncertain  and  liable  at  any  time  to  cause  an  enforced  idleness  of  the 
mine.  Long  seasons  of  idleness  are  not  favorable  to  longwall  work. 

The  chief  advantages  claimed  for  the  longwall  method  of  mining  coal  are 
as  follows:  Complete  removal  of  the  coal  at  a  minimum  expense,  requiring 
a  smaller  capital;  an  earlier  development  on  an  extended  scale  is  afforded  than 
by  any  other  method  of  mining,  bringing  earlier  returns  on  the  capital  invested ; 
the  output  of  the  coal  is  more  uniform  and  of  a  better  marketable  size,  yield- 
ing a  better  price;  fewer  roadways  are  required  to  be  maintained  for  the  same 
face  of  coal;  there  is  no  yardage  for  entry  driving;  less  timber  is  required  on  the 
roadways  and  at  the  face;  better  ventilation  of  the  working  face  is  secured  at 
less  expense,  a  minimum  quantity  of  air  being  required,  and  fewer  doors,  stop- 
pings, and  overcasts  are  necessary;  there  is  less  liability  to  accident  from  falls 
of  roof,  and  there  are  no  pillars  to  be  drawn;  less  damage  results  to  the  sur- 
face in  this  method;  the  amount  of  surface  water  in  the  workings  is  gener- 
ally less. 

The  disadvantages  of  the  longwall  method  are  as  follows:  To  obtain  the 
best  results  by  this  method,  experienced  longwall  miners  are  required,  or  those 
familiar  with  the  work,  and  ordinary  labor  cannot  be  used  to  the  same  advan- 
tage as  is  often  done  in  room-and-pillar  work ;  where  a  large  amount  of  gas  is 
present,  the  ventilation  of  a  portion  of  the  mine  cannot  be  controlled  or  the 
section  sealed  off  as  in  room-and-pillar  work,  where  a  panel  system  of  working 
is  adopted;  a  large  amount  of  labor  must  be  expended  in  the  building  of  pack 
walls;  this,  however,  is  accomplished  by  cheap  labor;  the  method  is  not  practi- 
cable where  periods  of  enforced  idleness  are  liable  to  occur  from  any  cause 
whatsoever;  when  the  coal  field  is  disturbed  by  faults,  it  is  difficult  or  impossible 
to  maintain  a  continuous  tongwall  face.  When  the  seam  is  thick  and  the  roof 
hard,  it  is  difficult  to  obtain  sufficient  packing  material. 


METHODS  OF  WORKING 
LONGWALL  WORKING  IN  FLAT  SEAMS 


665 


Scotch,  pr  Illinois,  Plan. — The  system  of  longwall  mining  extensively  used 
in  the  interior  coal  basin  of  the  United  States  is  illustrated  in  Fig.  1,  and  is  a 
modification  of  the  Scotch,  or  45°  system  of  longwall,  in  that  the  diagonal  roads 
make  an  angle  of  60°  instead  of  45°  with  the  main  roads.  A  main  entry  a  for 
single  track  is  driven  from  the  hoisting  shaft  H  through  the  shaft  pillar,  which 
is  left  large  enough  to  protect  all  buildings  on  the  surface  and  to  contain  the 
air-shaft  or  escapement  shaft  A  and  the  stables,  which  are  placed  as  shown. 
At  the  edge  of  the  shaft  pillar,  entries  b  are  driven  at  right  angles  to  the  main 
entries.  Diagonal  roads  c  are  then  driven  at  an  angle  of  60°  with  the  main 
road  b  and  300  ft.  apart.  After  the  work  has  progressed  a  certain  distance, 
every  other  cross-road  is  discontinued  and  coal  is  hauled  out  through  the  remain- 


FIG.  1 


ing  roads;  after  the  work  has  progressed  still  farther,  the  center  cross-road 
only  is  used  for  hauling  the  coal  out  of  each  quarter  of  the  mine,  the  coal  being 
taken  to  this  road  through  the  rooms  or  along  the  face.  The  permanent  haul- 
age roads  are  shown  in  the  plan  with  packs. 

The  main  haulage  roads  are  made  6  ft.  high  above  the  rails  and  10  ft.  wide; 
the  cross-roads  c  are  8  ft.  wide.  Pack  walls  not  less  than  4  ft.  thick,  and  well 
built  of  strong  slate,  are  erected  along  all  main  roads.  In  the  first  brushing 
along  the  roads,  the  miner  takes  down  18  in.  to  2  ft.  of  slate  for  pack  walls; 
and  in  the  second  brushing,  the  company  men  secure  the  roof  and  take  down 
slate  to  make  the  roof  6  ft.  above  the  rail.  Heavy  cross-bars  and  legs  are  used 
to  support  the  roof  after  the  final  brushing  on  the  main  entries.  The  legs  are 
given  1  ft.  pitch  in  6  ft.  Permanent  timbers  or  doors  cannot  be  set  until  the 
roof  has  settled  and  no  permanent  timbers  can  be  put  in  for  a  distance  of  200 
to  300  ft.  back  from  the  face.  When  turning  off  the  roads  c  from  the  main 
roads,  an  angle  crib  of  some  soft  wood  is  put  in  so  that  it  will  give  to  the  weight. 
Each  room  or  working  face  is  about  30  ft.  wide,  and  as  the  circle  of  the  working 


656 


METHODS  OF  WORKING 


face  increases  in  size,  the  mine  manager  measures  along  the  face  and  locates 
a  new  room,  giving  each  two  men  about  30  ft.  of  face  to  work  in.  When  the 
mine  is  first  opened  out,  if  water  is  present,  a  gutter  is  made  in  the  entry  around 
the  shaft  pillar  below  the  coal  and  covered  with  railroad  ties. 

The  air  is  first  split  at  the  bottom  of  the  downcast  shaft  H  and  again  at  the 
face  of  the  main  road  a  on  each  side  of  the  mine,  thus  giving  each  quarter  of 
the  mine  a  fresh  current  of  air,  a  canvas  door  being  used  in  each  ross-road  c 
to  direct  the  air  along  the  working  faces. 

Rectangular  Longwall. — Fig.  2  shows  a  rectangular,  or  square,  longwall 
method,  which,  in  some  sections,  is  taking  the  place  of  the  diagonal  method 
just  described.  The  entries  and  rooms  are  turned  off  at  an  angle  of  90° 
instead  of  at  60°,  as  in  Pig.  1.  A  pillar  is  left  about  the  shaft  and  work 
begun  in  much  the  same  way  as  in  the  Scotch  plan.  The  room  necks  a  are 
made  10  ft.  wide  and  are  driven  in  from  the  haulageway  18  ft.  The  coal 
pillars  &  are  left  in  to  protect  the  haulageways  at  the  ends  of  the  shaft  pillar. 


FIG.  2 


The  caging  is  done  on  one  side  of  the  shaft,  empties  are  run  to  the  bumping 
post  shown  and  mules  or  motors  pass  through  the  smail  passages  c  called  boll 
holes  to  the  empties.  The  distance  between  the  cross-entries  is  100  ft.  The 
main  entry  is  single-  tracked,  and  partings,  or  pass-bys,  are  made  every  1,000  ft. 
by  going  into  the  mouth  of  one  of  the  entries,  passing  up  the  first  room  to  the 
next  cross-entry,  and  then  out  to  the  main  entry  again.  After  the  work  has 
been  opened  to  a  certain  extent,  each  alternate  cross-entry  is  abandoned  and 
later  more  of  the  cross-entries  are  abandoned,  leaving  only  an  occasional  cross- 
entry  for  haulage  purposes,  thus  decreasing  the  expense  for  maintaining 
haulageways.  The  last  room  on  an  entry  is  always  kept  open  between  cross- 
entries  as  a  means  of  bringing  coal  from  one  entry  to  another. 

An  objection  to  the  square  system  is  the  longer  haulage  roads  required  than 
in  the  diagonal  system. 


METHODS  OF  WORKING 


657 


LONGWALL  WORKING  IN  PITCHING  SEAMS 

True  longwall  in  which  the  face  advances  in  a  more  or  less  circular  form 
cannot  be  applied  to  pitching  seams,  as  the  face  cannot  be  carried  down  hill 
because  the  packs  would  fall  upon  the  miner.  The  general  method  of  open- 
ing pitching  seams  is  strikingly  similar  to  that  used  in  the  room-and-pillar 
method.  A  pair  of  slopes  is  carried  to  the  dip  and  to  the  right  and  left  of  them 
are  turned  pairs  of  levels.  The  coal  between  the  pairs  of  levels  is  worked  up 
hill  on  the  longwall  advancing  system,  the  pillars  between  the  pair  of  upper 
levels  being  taken  out  when  the  longwall  face  from  the  lower  level  reaches 
them.  A  barrier  pillar  is  left  throughout  the  life  of  the  mine  on  each  side  of  the 
slope,  and  these  barrier  pillars  are  extracted  after  the  property  is  otherwise 
worked  out. 

As  the  movement  of  the  loose  coal  down  steep  pitches  would  probably 
injure  men  working  at  a  lower  point  on  the  same  face,  longwall  faces  in  pitch- 
ing seams  are  frequently  laid  out  in  steps.  This  step  arrangement  of  the  face 
is  not  used  unless  the  pitch  is  so  steep  as  to  render  it  necessary  as  it  increases 
the  amount  of  small  coal,  does  not  permit  of  systematic  regulation  of  the  weight 


FIG.  1 

over  the  entire  face,  and  makes  it  more  difficult  to  insure  regularity  of  working 
and  of  advance  in  adjoining  places. 

A  longwall  face  is  usually  advanced  across  the  pitch  in  order  to  regulate 
the  roof  pressure  on  the  coal;  to  decrease  the  grade  on  the  roads;  lessen  the 
inclination  of  the  face  and  thus  reduce  the  danger  in  the  work  of  mining  while 
making  the  coal  more  easily  handled  at  the  face.  Breaks  and  slips  in  the  roof 
as  well  as  the  cleavage  of  the  coal  often  require  that  the  line  of  face  should  make 
an  angle  with  the  strike  of  the  seam  in  order  to  give  a  better  support  to  the  roof 
at  the  face.  . 

One  of  the  chief  difficulties  in  working  longwall  in  pitching  seams  is  the 
tendency  of  the  roof  to  slip  and  sink  back  from  the  face,  thus  taking  the  pres- 
suie  from  the  coal.  For  flat  working  it  is  comparatively  easy  to  control  the 
traveling  weight  on  the  coal;  but  as  the  inclination  increases,  there  is  consider- 
able difficulty  in  preventing  the  broken  roof  masses  from  falling  away  from  the 
coal  in  the  direction  of  the  dip,  and  then  either  sinking  in  front  of  the  line  of 
face,  or,  if  they  wedge  and  jam  too  tightly,  they  may  bring  an  excessive  pres- 
sure on  the  coal  face  and  crush  it.  In  inclined  seams,  it  is  very  much  more  diffi- 
cult to  maintain  the  roads  than  in  level  seams,  owing  to  the  tendency  of 

42 


658 


METHODS  OF  WORKING 


materials  to  slide  down  hill;  for  this  reason,  the  principal  level  haulage  roads 
are  frequently  protected  on  one  or  both  sides  by  pillars  of  solid  coal. 

Longwall  on  Low  Inclination. — In  Fig.  1  is  shown  a  longwall  face  on  the 
advancing  system,  in  which  the  gob  roads  are  built  across  the  pitch  on  a  suit- 
able grade  for  handling  the  cars  by  mule  or  by  hand.  This  method  can  be 
employed  in  seams  having  an  inclination  varying  from  about  5°  to  15°, 


FIG.  2 

Fig.  2  shows  a  pair  of  levels,  the  upper  for  haulage  and  the  lower  for  drain- 
age purposes.  The  levels  are  driven  on  the  strike  of  a  seam,  and  the  long-wall 
face  is  arranged  at  a  small  angle  with  the  line  of  strike.  The  coal  is  lowered 
from  the  face  to  the  levels  by  the  self-acting  inclines  i,  which  are  provided  with 
safety  holes,  or  manholes,  o  near  the  face.  A  slant  road  a  is  driven  from  the 
haulage  road  to  the  lower,  or  drainage,  level  on  such  an  angle  that  the  coal 
may  be  drawn  out  of  this  level  by  a  mule. 

Longwall  When  Inclination  is  Less  Than  40°. — Thin  seams  of  coal  having 
an  inclination  of  about  40°,  or  less,  are  worked  in  Great  Britain,  France,  and 
Belgium,  by  driving  levels  or  lifts  on  the  strike  of  the  seam  in  each  direction 
to  .the  right  and  left  of  a  main  slope  or  incline.  Both  the  advancing  and  the 
retreating  methods  are  used.  When  the  retreating  method  is  used,  the  levels 
are  driven  to  their  limit  or  boundary,  and  the  longwall  face  started  at  this  point. 
In  the  advancing  method,  the  longwall  face  is  started  at  the  slope,  after  leav- 
ing a  sufficient  pillar  of  solid  coal  for  its  protection.  In  either  case,  the  upper 
rib  of  the  level  is  marked  off  in  sections,  the  length  of  which  depends  on  the 
conditions  for  getting  the  coal  to  the  roads.  This  length  varies  from  a  few 

yards,  15  or  20,  up  to  60  or 
100.  Fig.  3  represents  the 
general  plan  where  the  ad- 
vancing method  is  used. 

The  coal  is  attacked  by 
the  usual  longwall  methods 
of  undercutting  and  sprag- 
ging  the  face  in  each  sec- 
tion. In  this  system,  the 
longwall  face  advances 
directly  up  the  pitch  or  on 
the  face  cleats  of  the  coal. 
The  face  in  each  section 
has  one  fast  end  that  must 
be  sheared.  Each  section 
is  kept  from  3  to  5  yd.  in 
The  work  in  the  first  section  started,  a 


FIG.  3 


advance  of  the  section  next  inby.      

being  the  most  advanced,  has  two  fast  ends  and  is  the  most  difficult.  The  waste 
of  the  seam  is  stowed  in  the  space  between  the  roads  b  maintained  by  solid 
pack  walls  and  placed  in  the  center  of  each  section,  so  as  to  provide  a  minimum 
distance  the  coal  must  be  handled  at  the  face.  The  pack  walls  are  started  at 
the  level  by  building  substantial  cribs  that  are  supported  against  slipping  by 
timbers  set  in  foot-holes  cut  in  the  roof  and  floor.  The  road  from  the  face  to 
the  level  is  sometimes  called  a  jig  road. 


METHODS  OF  WORKING 


659 


The  coal  is  lowered  from  the  face  to  the  level  by  buggies  operated  by  a  wind- 
lass located  either  at  the  top  or  the  bottom  of  the  incline;  when  located  at  the 
bottom  of  the  incline,  the  position  of  the  windlass  is  permanent.  The  rope 
by  which  the  buggy  is  raised  and  lowered  passes  over  a  block,  or  pulley,  that 


FIG.  4 


s  attached  by  a  rope  or  chain  to  a  timber  at  the  head  of  the  incline.  Instead 
of  the  windlass,  a  form  of  wheel  is  often  used  for  lowering  and  raising  the  buggy 
by  hand.  The  rope  is  given  a  couple  of  turns  around  the  wheel,  the  slack  end 
being  held  in  one  hand,  while  the  brake  band  is  applied  with  the  other  hand 
by  means  of  a  lever  to  control  the  movement  of  the  buggy  or  car  down  the 
incline.  The  buggies  are  emptied  into  cars  along  the  level  and  the  coal  carried 
to  the  slope  or  shaft  and  hoisted  to  the  surface. 

It  is  possible  to  shorten  the  jig  roads  from  the  face  to  the  main  haulage 
road  from  time  to  time.  This  may  be  done  as  slwwn  in  Fig.  4,  by  building 
cqunterlevels  a  in  the  waste  or  gob  parallel  to  the  main  level  b  either  connecting 
with  one  of  the  jig  roads  c,  which  is  kept  open  and  operated  as  a  main  jig,  or 
else  these  counterlevels  may  run  to  a  landing  on  the  main  incline  or  slope. 

Longwall  When  Inclination  is 
From  30°  to  60°.— The  method 
shown  in  Fig.  5  may  be  used  for  a 
seam  pitching  from  10°  to  60°,  but 
it  is  particularly  adapted  to  seams 
pitching  from  30°  to  60°  and  where  the 
roof  and  floor  are  good  and  the  roof 
pressure  is  moderate.  In  this  method, 
owing  to  the  steeper  inclination  or  to 
the  fact  that  the  coal  works  better, 
the  working  face  is  advanced  on  the 
ends  of  the  coal  or  parallel  to  the 
strike  of  the  seam.  The  working 
face  is  broken  into  steps,  or  sections, 
usually  about  20  yd.  long,  each  sec- 
tion being  kept  from  5  to  8  yd.  in  ad- 
vance of  that  above  it  to  protect  the 
miner  from  the  falling  coal  in  the  up- 
per sections.  In  each  section,  there 
are  several  miners,  usually  three  or 
four  for  a  face  20  yd.  long,  and  each 
miner  stands  on  a  temporary  plat- 
form, or  on  planks  laid  on  props 
securely  set  in  foot-holes  cut  in  the 
roof  and  floor  of  the  seam,  or  else 
stands  on  a  gob  built  up  from  below. 
The  platforms  also  serve  to  protect  the  miners  working  in  the  lower  portions  of 
each  section,  from  the  falling  coal  above  them.  Level  roads  are  built  in  the 
waste  or  gob  at  the  foot  of  each  section.  The  coal  is  sheared  at  the  upper  end 
of  each  section  and  after  being  undercut  it  falls  to  the  road  at  the  bottom  of  the 
section  where  it  accumulates  and  is  loaded  in  cars  or  buggies  and  transported 


FIG.  5 


660  METHODS  OF  WORKING 

directly  to  the  slope  or  to  a  jig  road,  or  main  incline  a,  down  which  it  is  taken 
to  the  level  b,  and  then  to  the  slope  c.  The  lowest  section  of  longwall  face  is 
started  on  the  inby  rib  of  the  level  b,  the  face  extending  a  short  distance  below 
the  level.  A  sufficient  amount  of  coal  is  taken  out  on  the  lower  side  of  the  level 
to  bring  the  breaks  in  the  roof  over  the  gob  packs  below  the  roadway.  In 
deciding  what  breadth  of  coal  should  be  worked  on  the  lower  side  of  the^  level, 
it  is  necessary  to  be  guided  largely  by  the  direction  of  the  first  breaks  in  the 
roof,  both  on  the  rise  side  and  the  dip  side  of  the  opening-out  places.  It  is 
generally  found  that  the  direction  of  these  first  breaks  varies  considerably  from 
the  direction  of  the  main  break. 

When  the  first  section  has  advanced  over  5  or  8  yd.,  the  next  section  above 
is  started,  and  a  second  level  built  in  the  gob.  In  this  manner,  the  upper  sec- 
tions are  started  consecutively  one  after  another.  As  the  face  advances,  the 
length  of  the  level  roads  increases;  so  to  avoid  the  unnecessary  expense  of  main- 
taining these  roads,  they  are  cut  off,  from  time  to  time,  by  an  incline  driven 
on  the  full  pitch  of  the  seam.  It  is  often  necessary  to  cut  off  these  inclined 
planes  by  a  counterlevel  driven  on  the  strike  of  the  seam  between  the  main 


FIG.  6 

levels,  or  built  in  the  waste  or  gob  as  the  face  advances.  When  the  method  is 
used  for  comparatively  flat  seams,  an  inclined  road  is  maintained  at  an  angle 
with  the  main  level  instead  of  perpendicular  to  it,  as  shown. 

The  nature  of  the  roof,  floor,  and  coal  at  times  necessitates  greater  pro- 
tection against  squeeze  or  creep  than  is  afforded  in  the  method  just  described. 
In  this  case,  a  pair  of  entries,  a  and  b.  Fig.  6,  are  driven  on  the  strike  of  the  seam 
from  the  main  slope  or  incline  c  and  roads,  or  chutes,  d  turned  off  these  levels 
at  regular  intervals  and  on  the  full  pitch  of  the  seam.  A  pillar  of  coal  from  10 
to  15  yd.  thick  is  left  for  the  protection  of  the  level  a  before  opening  out  the 
longwall  face  on  these  rise  roads.  As  shown  in  the  figure,  the  face  is  opened 
to  the  right  and  left  of  each  road  d,  cross-roads  e  being  maintained  in  the  gob. 
The  faces  in  each  section,  or  lift,  are  advanced  until  they  hole  into  each  other, 
when  the  lift  is  abandoned,  the  cross-road  being  often  filled  with  waste  from 
other  parts  of  the  mine. 

Where  the  roof  is  particularly  frail  or  the  bottom  soft,  especially  with  a 
heavy  roof  pressure,  the  method  just  described  may  be  modified  as  follows: 
As  before,  the  inclined  roads,  or  chutes,  d  are  driven  at  regular  intervals  on 


METHODS  OF  WORKING 


661 


the  full  pitch  of  the  seam,  Fig.  7,  and  cross-levels  e  are  then  driven  to  the  right 
and  left  of  each  chute  until  they  hole  into  each  other.  At  this  point,  the  pil- 
lars separating  the  cross-levels  are  holed  through  on  the  pitch  of  the  seam 
and  the  coal  drawn  back  by  longwall  retreating.  In  both  of  the  methods 
shown  in  Figs.  6  and  7,  the  coal  is  lowered  down  jig  roads  or  inclines  from 
the  levels  to  the  entry,  whence  it  is  taken  to  the  main  hoisting  slope  or  shaft. 


FIG.  7 

Longwall  in  Steeply  Inclined  Seams. — The  work  in  steeply  inclined  seams, 
as  shown  in  Fig.  8,  is  similar  to  that  described  in  connection  with  Figs.  5  and  6; 
but  the  length  of  each  section  of  the  face  is  only  about  6  ft.;  one  miner  works 
in  each  section.  The  coal  is  worked  on  end,  the  face  being  advanced  in  a  direc- 
tion parallel  to  the  strike  of  the  seam.  Small  shafts,  or  chutes,  to  carry  the  coal 
to  the  entry  are  built  in  the  waste  on  the  full  pitch  of  the  seam,  one  chute  being 
built  to  three  sections  of  the  face.  They  are  similar  to  the  chute  used  in  work- 
ing steep  seams  by  the  room-and-pillar  method,  except  that  they  are  built  in 
the  waste  instead  of  being  driven  in  the  coal.  These  chutes  are  kept  full  of 
coal,  which  is  drawn  as  desired  by  opening  a  gate  at  the  bottom.  The  miner 


FIG.  8 

stands  on  the  gob,  on  planks,  or  on  a  temporary  platform  reaching  from  the 
gob  to  the  face  of  the  coal.  In  the  three  methods  illustrated  in  Figs.  6,  7,  and  8, 
the  risk  or  danger  from  falling  coal  increases  with  the  inclination  of  the  seam. 

SPECIAL  FORMS  OF  LONGWALL  WORKING 

Longwall  in  Panels. — With  the  ordinary  longwall  method,  the  mine  can- 
not be  divided  easily  into  separate  districts,  as  it  is  often  desirable  to  do  in 
working  gaseous  seams.  In  order  to  adapt  longwall  to  the  working  of  such 


METHODS  OF  WORKING 


Beams,  it  is  necessary  to  restrict  the  length  of  continuous  working  face  by  divid- 
ing the  mine  into  panels  and  carrying  a  longwall  face  in  each  panel,  as  shown 

in  Fig.  1.  Several 
rooms,  or  chambers, 
are  turned  off  of  a 
pair  of  entries  and 
are  connected  at 
the  inside  of  the 
entry  pillar  by  being 
holed  into  each 
other.  They  are 
then  driven  up  as  a 
single  breast  by 
longwall  advancing. 
The  breast,  how- 
ever, has  two  fast 
ends,  one  on  each 
side  of  the  panel, 
pIG.  i  which  must  be 

sheared  as  the  face 

is  advanced.  Each  panel  has  a  separate  ventilating  current  and  may  be 
stopped  off  in  case  of  a  fire  or  a  squeeze  without  interfering  with  the  rest 
of  the  mine.  The  methods  of  working  inclined  seams  previously  described 
are  practically  panel  methods. 

The  modified  longwall  system  followed  at  Vintondale,  Pa,,  is  shown  in 
Fig.  2.  The  pitch  of  the  seam  is  8%,  or  about  4^°,  and  the  coal  is  about 
3  ft.  8  in.  thick,  the  roof  being  blue  slate,  and  the  floor  a  hard  fireclay.  The 
cover  is  a  fairly  hard  sandstone,  174  ft.  thick.  The  main  entry  a,  is  driven 
directly  up  the  pitch  and  centrally  in  the  coal  field,  bisecting  itbetween  the 
outcrops.  This  main  entry  is  paralleled  by  two  airways  b  as  shown,  one  on 
each  side  for  the  purpose  of  ventilating  each  side  independently.  On  the 
right  side  of  the  figure,  at  c,  is  shown  one  method  of  laying  out  the  faces  par- 
allel to  the  dip.  At  the  end  of  the  cross-entry  d,  an  ordinary  room  is  turned 
up  the  pitch  and  driven  practically  parallel  to  the  main  heading  to  a  connec- 
tion with  the  next  pair  of  cross-entries  inby,  as  shown  at  e.  The  outby  rib 
of  this  wide  room  forms  the  longwall  face,  which  is  worked  back  toward  the 
main  entry.  Empty  mine  cars  are  taken  to  the  faces  on  the  lower  road  of  the 


FIG.  2 

inner  cross-headings  /  and  hauled  along  the  face  c,  where  they  are  loaded  and 
hauled  out  on  the  upper  road  of  the  lower  cross-headings  d  to  the  main  heading. 


METHODS  OF  WORKING 


663 


On  the  left  of  the  diagram  at  g,  is  shown  the  method  of  laying  out  faces  so 
that  they  are  90°  with  the  line  of  pitch,  so  that  the  full  influence  of  any  roof 
pressure  due  to  the  pitch  is  exerted  fully  on  the  gob.  In  this  case,  the  empty 
mine  cars  are  taken  into  the  lower  road  of  the  upper  pair  of  cross-entries  h, 
dropped  through  the  room  i,  which  connects  the  pair  of  cross-entries,  then  to 
the  face  g  along  which  they  are  loaded,  thence  dropped  through  a  gob  road- 
way j  to  the  upper  road  of  the  lower  pair  of  cross-entries  k.  The  gob  road- 
way j  has  solid  coal  for  one  of  its  ribs,  and  is  maintained  by  means  of  a  sub- 
stantial timber  crib,  built  as  the  face  progresses.  On  the  left  of  the  diagram, 
the  faces  advance  directly  up  hill. 

Longwall  in  Thick  Seams.  —  A  thick  seam  of  coal  is  usually  worked  in  sev- 
eral benches  of  moderate  thickness.  The  longwall  method  i»  variously  modified 
to  suit  the  conditions,  but  the  plan  generally  adopted,  and  which  has  given 
the  best  results  in  France,  Bohemia,  and  other  countries  where  such  seams  are 
worked,  both  with  respect  to  the  safety  of  the  working  and  the  percentage  of 
coal  obtained  from  the  seam,  is  that  of  close  packing,  or  completely  filling  with 
waste  the  space  from  which  the  coal  is  taken.  Sufficient  waste  is  not  pro- 
duced, ordinarily,  in  the  working  of  the  seam,  and  waste  material  is  brought 
from  the  surface  to  fill  in  this  space. 


In  the  working  of  flat  seams  by  this  method,  a  longwall  face  is  carried  for- 
wards in  each  bench  of  the  coal,  the  face  in  each  bench  being  kept  from  80  to 
100  yd.  in  advance  of  that  in  the  bench  next  above.  Fig.  3  shows  the  general 
plan  and  cross-section  of  the  workings  at  the  face  of  a  thick  flat  seam,  the  seam 
being  divided,  as  shown,  into  three  benches.  The  first  mining  is  done  in  the 
lowest  bench,  in  which  the  parallel  main  roads  ab  and  en  are  driven  and  con- 
nected by  the  cross-roads  c.  The  roads  o  that  lead  to  the  face  are  protected 
by  packs,  and  correspond  to  the  temporary  roads,  or  working  places  in  the  gen- 
eral longwall  method.  Above  the  cross-roads  c  and  from  80  to  100  yd.  back 
from  their  faces  are  the  cross-roads  c'  in  the  second  bench.  Above  the  cross- 
roads c'  and  from  80  to  100  yd.  back  from  their^faces  are  the  cross-roads  c" 
in  the  third  bench.  As  the  temporary  roads  o  in  the  lower  bench  attain  a 
length  equal  to  the  advance  between  the  cross-roads  c,  they  are  cut  off  by  a 
new  cross-road  in  the  lowest  bench  of  the  seam.  At  the  same  time,  the  corre- 
sponding temporary  roads  o  in  each  of  the  benches  above  and  which  are  in  the 


664  METHODS  OF  WORKING 

same  line  with  the  roads  o  in  the  lowest  bench  reach  their  limits.  The  roof  of 
the  cross-roads  c  in  the  lowest  bench  is  then  ripped  or  taken  down  and  the  road 
is  packed  with  waste  on  which  a  new  cross-road  c'  is  laid  in  the  bench  above. 
In  like  manner,  the  roof  of  each  cross-road  c'  in  the  second  bench  is  taken  down, 
and  the  old  road  is  packed  with  waste  on  which  the  new  cross-road  is  laid  in 
the  bench  above,  as  before.  The  main  roads  on  each  side  are  treated  in  the 
same  manner,  the  road  being  graded  from  the  cross-road  in  the  lower  bench 
to  the  cross-road  in  the  upper  bench,  as  indicated  in  the  cross-section  by  the 
dotted  line  across  the 'gob  and  marked  road.  This  inclined  road  advances 
with  the  work  in  each  bench. 

Longwall  in  Inclined  Thick  Seams. — In  the  working  of  inclined  thick 
seams,  when  the  in«lination  of  the  seam  is  moderate,  the  method  just  described 
may  be  used  for  the  removal  of  the  coal.  In  steeper  inclinations,  a  slope  road 
is  driven  in  the  lower  bench  of  the  coal  on  the  floor  of  the  seam,  and  gangways, 
or  levels,  are  driven  to  the  right  and  left  in  the  seam  from  this  slope.  Cross- 
drifts  are  then  driven  from  these  gangways  across  the  seam  to  the  roof  rock, 
at  intervals  varying  from  16  to  20  yd.  At  the  roof,  they  are  holed  across  from 
one  to  the  other,  and  the  coal  drawn  back,  on  the  retreating  method,  in  hori- 
zontal slices  from  5  to  6  ft.  in  thickness.  The  face  is  also  broken  into  steps 
between  the  cross-drifts,  and  as  each  slice  of  coal  is  taken  out,  it  is  often  neces- 
sary to  fill  in  the  space  with  waste. 

Longwall  in  Contiguous  Seams. — In  the  application  of  longwall  •  to  con- 
tiguous seams,  the  methods  of  work  at  the  face  do  not  differ  from  those  already 
described.  Seams  have  been  worked  in  England  as  one  seam  when  separated 
by  a  slate  parting  7  ft.  in  thickness.  In  this  particular  case,  the  lower  seam 
was  7  ft.,  and  the  upper  seam  2  ft.,  in  thickness.  A  general  method  for  work- 


PIG.  4 

ing  contiguous  seams  is  shown  in  Fig.  4,  which  is  a  cross-section  of  the  working 
face.  The  lower  seam  a  is  worked  first,  the  slate  parting  b  being  supported 
on  three  rows  of  props  c,  d,  e  set  parallel  to  the  face.  By  the  withdrawal  of 
the  rear  row  of  props  e,  the  slate  parting  falls  or  is  wedged  down.  The  work 
of  taking  down  the  upper  seam  /  then  follows.  The  slate  parting,  as  it  falls, 
is  broken  up  and  leveled  off,  thus  forming  a  convenient  flat  g  at  the  top  of  the 
incline  *'.  Thereof  above  the  incline  is  supported  by  pack  walls  j. 

When  contiguous  seams  are  worked  separately  by  the  longwall  method, 
either  by  driving  cross-tunnels  between  the  different  seams,  or  by  separate 
slopes  or  inclines,  the  longwall  face  in  an  overlying  seam  should  generally  be 
kept  in  advance  of  that  in  a  lower  one,  as  the  working  of  an  underlying  seam 
by  longwall  will  usually  result  in  the  crushing  and  crevicing  of  overlying  seams 
to  a  certain  extent. 

DETAILS  OF  LONGWALL  WORKING 

T  S.**1*?118  kongwall. — There  are  two  methods  of  starting  longwall  workings, 
in  the  first,  the  work  of  extraction  begins  at  the  shaft  itself,  the  coal  being 
taken  out  all  around  and  its  place  filled  with  solid  packs,  leaving  only  space 
for  the  roadways.  In  the  second  method,  a  pillar  of  solid  coal  is  left  to  sup- 
tort  the  shaft,  cut  only  by  the  roadways.  The  longwall  work  is  then  started 
uniformly  all  around  this  pillar.  Great  care  is  needed  in  building  the  first  pack 


METHODS  OF  WORKING  665 

walls  around  the  shaft  pillar,  to  see  that  they  are  solidly  built  and  well  rammed, 
in  order  to  break  the  roof  over  the  coal.  The  system  will  not  work  rightly, 
however,  until  the  breast  has  been  advanced  some  distance  from  the  pillar, 
so  as  to  secure  the  benefit  from  the  weighting  action  of  the  roof  upon  the  coal 
face.  The  mining  will  be  more  difficult  in  the  start,  and  in  some  exceptional 
cases  it  may  even  be  necessary  to  place  some  light  shots;  this,  however,  should 
be  avoided,  if  possible. 

Roadways. — The  general  plan  of  laying  out  the  roads  is  shown  on  pages  652 , 
655,  and  656.  The  temporary  roads  connect  the  working  places,  or  rooms,  with 
the  cross-roads,  but  as  they  are  cut  off  from  time  to  time  by  other  cross-roads 
they  are  not  protected  by  as  substantial  pack  walls  as  the  other  roads.  The 
length  of  the  temporary  roads  may  be  different  for  each  section  of  the  mine, 
and  must  be  determined  in  each  case  as  the  work  progresses.  A  cross-road  is 
started  off  the  main  road  whenever  the  temporary  road  gives  signs  of  closing. 
It  will  thus  be  seen  that  the  distance  between  cross-roads,  measured  on  the 
main  entries,  may  not  be  a  uniform  distance  for  the  different  sections  of  the 
mine,  and  may  even  vary  in  the  same  section.  Again,  owing  to  a  creep  or 
crush  closing  some  rooms,  it  may  be  necessary  to  turn  a  short  stub  road  directly 
across  the  heads  of  such  rooms  or  working  places,  the  old  roads  in  this  case  being 
gobbed  tightly  to  counteract  the  effect  of  the  squeeze.  The  distance  between 
the  temporary  roads  is  decided  mainly  by  the  possibility  of  taking  the  cars 
along  the  face,  which,  in  turn,  depends  on  the  clear  width  it  is  possible  to  keep 
open  between  the  face  of  the  coal  and  packs.  When  it  can  be  done,  roadways 
are  laid  along  the  face  and  protected  by  timbers.  At  the  junction  of  the  track 
along  the  face  with  the  track  running  into  the  room,  a  turntable  consisting 
of  an  iron  plate  that  allows  the  car  to  be  turned  is  sometimes  used.  This  track 
may  be  made  of  oak  mine  rails  spiked  to  cross-ties,  or  of  light  iron  rails,  held 
together  by  spreaders  of  £"X1£"  strap  iron. 

If  the  mine  car  cannot  be  taken  along  the  face  and  there  is  a  hard,  smooth 
bottom,  the  coal  is  often  loaded  on  a  sled,  or  buggy,  which  is  dragged  along 
the  face  to  the  head  of  the  temporary  road,  where  it  is  loaded  into  a  car.  The 
distance  between  the  temporary  roads  will  then  depend  on  the  distance  to 
which  the  coal  can  be  thus  conveniently  carried,  but  is  usually  from  40  to  60  yd., 
though  it  has  reached  100  yd.  in  exceptional  cases. 

When  it  is  necessary  to  shovel  the  coal  to  the  road  head  where  it  is  loaded 
or  to  wheel  it  in  barrows  along  the  face,  the  roads  are  made  from  15  to  20  yd 
apart,  center  to  center. 

In  some  mines  a  motor-driven  conveyer  laid  along  the  face  is  used  to  carry 
the  coal  to  one  of  the  roads  where  it  is  loaded  into  mine  cars.  The  conveyer 
is  usually  of  the  trough  type,  is  moved  forwards  bodily  as  the  face  is  advanced, 
and  works  well  where  the  face  is  reasonably  straight. 

Control  of  Roof  Pressure. — The  removal  of  the  coal  and  the  slow  advance 
of  the  working  face  is  followed  by  a  slow,  but  irresistible,  downward  move- 
ment of  the  cover  or  overburden,  known  as  settlement.  The  immediate  effect 
of  this  is  to  produce  breaks  in  the  roof  strata  over  the  area  from  which  the  coal 
has  been  taken,  more  or  less  parallel  to  the  working  face,  and,  consequently 
at  right  angles  to  the  line  of  advance.  The  effect  of  removing  the  coal  is  to 
divide  the  overburden  into  two  portions: 

1.  An  underweight  of  broken  material  from  10  to  40  ft.  thick  which  may 
be  likened  to  heavy  falls  of  the  rocks  immediately  overlying  the  seam  in  room- 
and-pillar  work.     The  weight  of  this  broken  material  is  small,  compared  with 
the  overweight,  and  it  may  be  temporarily  supported  by  the  timbers  and  by 
the  face  of  the  coal  and  the  packs.     By  the  withdrawal  of  the  timber  next  the 
packs,  the  weight  is  thrown,  or  settles,  forwards  on  the  coal  and  breaks  it. 
The  amount  of  the  underweight  thrown  on  the  coal  face  is  controlled,  as  far 
as  possible,  by  the  posts  set  parallel  to  the  face.     The  amount  of  timber,  num- 
ber of  rows,  and  the  distances  apart  of  the  rows  and  of  the  timbers  in  each  row 
depend  on  the  conditions  at  the  face.     For  given  conditions  of  roof  and  floor, 
more  weight  is  thrown  on  the  face  of  the  coal  by  decreasing  the  amount  of 
timber,  while  increasing  the  timber  decreases  the  weight  on  the  coal.     With 
a  hard  roof  and  floor,  the  posts  should  be  set  on  some  soft  material,  or  be  pro- 
vided with  a  thick  soft  cap  that  will  yield  and  allow  the  post  to  take  the  weight 
gradually,  or  the  post  is  sometimes  tapered  at  the  end  for  the  same  purpose. 

2.  An  overweight  due  to  the  weight  of  the  rocks  from  the_  top  of  that  por- 
tion of  them  causing  the  underweight  to  the  surface,  and  which  is  practically 
equal  to  the  weight  of  the  entire  overburden.     It  is  irresistible  and  its  effect 
is  to  compress  the  pack  walls  and  gob  into  spaces  between  the  walls  until  the 
resistance  offered  to  the  weight  is  practically  equal  to  that  of  the  coal  that  has 


666  METHODS  OF  WORKING 

been  removed.  The  amount  of  settlement  due  to  this  overweight  is  regulated 
mainly  by  the  proportion  of  pack  walls  to  the  entire  area  from  which  the  coal 
has  been  removed  and  by  the  manner  of  building  these  pack  wails. 

The  aim  in  longwall  work  is  to  so  control  the  roof  pressure  that  it  may  be 
just  sufficient  to  break  the  coal  from  the  face  and  yet  not  crush  it.  When  this 
pressure  can  be  controlled,  it  is  done  by  means  of  the  number  and  size  of  the 
pack  walls,  by  rows  of  props  placed  parallel  to  the  face,  and  by  varying  the  open 
space  left  along  the  face  between  the  coal  and  the  pack  walls.  Experience 
under  the  given  conditions  alone  determines  in  just  what  way  and  to  what 
extent  this  control  may  be  secured.  The  pack  walls  provide  for  a  gradual 
and  uniform  settlement  of  the  roof  over  the  entire  area  from  which  the  coal  has 
been  removed.  They  relieve  the  timbers  at  the  face  of  a  great  part  of  the  weight 
they  would  otherwise  have  to  carry  and  permit  the  weight  on  the  coal  face  to 
be  regulated  largely  by  means  of  timbers  so  that  the  coal  may  be  properly 
broken  and  not  crushed. 

Excessive  weight  on  the  face  of  the  coal  is  shown  by  increased  hardness  of 
the  under  clay  and  the  increased  difficulty  of  undercutting  in  it,  and  also  by 
the  crushing  and  nipping  of  the  coal.  This  excessive  weight  may  be  due  to  too 
small  packs  and  too  little  timbering,  or  to  the  attempt  to  carry  too  wide  an 
area  between  the  packs  and  the  face.  The  remedy  is  to  increase  the  amount 
of  timber  and  the  size  or  number  of  packs,  or  to  decrease  the  distance  between 
the  face  and  the  packs. 

Too  small  a  weight  on  the  face  of  the  coal  is  evidenced  by  the  slow  break- 
ing of  the  coal.  This  may  be  due  to  too  large  a  proportion  of  packs,  to  too  many 
timbers,  or  to  too  narrow  a  space  between  the  face  of  the  coal  and  the  packs. 
The  remedy  is  to  decrease  the  proportion  of  packs  or  the  amount  of  timber, 
or  to  increase  the  open  width  at  the  face. 

Building  Pack  Walls  and  Stowing. — Pack  walls  should  be  built  ,  large 
enough  at  first  and  kept  well  up  to  the  face,  to  prevent  the  weight  coming  upon 
the  timber  and  also  to  permit  the  roof  to  settle  rapidly  when  the  timber  is 
taken  out  of  the  face.  Often  the  roof  will  not  stand  this  second  movement 
without  breaking,  and  possibly  closing  in  the  entire  face.  The  face  should 
therefore  be  kept  in  shape,  and  just  as  soon  as  there  is  room  for  a  prop  or  chock, 
it  should  be  put  in  immediately,  and  the  pack  walls  likewise  should  be  extended 
after  each  cut  or  web  is  loaded  out. 

As  a  general  thing,  the  pack  walls  in  the  gob  are  not  so  wide  as  the  road- 
side ones,  particularly  when  the  seam  produces  enQugh  waste  material  to  stow 
the  marches,  cundies,  or  gobs,  between  these  pack  walls.  Usually  about  50% 
of  the  cubic  contents  of  the  solid  seam  taken  out  will  stow  the  spaces  between 
the  pack  walls  in  thick  pitching  seams,  where  the  entire  gob  must  be  completely 
filled  or  nearly  so.  No  waste  material,  except  such  as  will  hasten  spontaneous 
combustion,  should  be  taken  out  of  the  mine  to  the  surface. 

Timbering  a  Longwall  Face. — The  method  of 
timbering  the  working  face  depends  on  the  nature 
of  the  roof,  floor,  coal,  etc.  The  action  of  the  roof 
on  the  coal  face  is  regulated  almost  entirely  by 
timber;  consequently,  when  the  coal  is  of  such  a 
nature  as  to  require  little  weight  to  make  it  mine 
easily,  the  roof  must  be  timbered  with  rows  of 
chocks  and,  if  necessary,  a  few  props. 

The  ends  of  all  stone  packs  nearest  the  face  of 
the  coal  should  be  in  line,  and  the  ends  of  these 
pack  walls  should  form  a  line  parallel  to  the  face  of  the  coal.  Timbers  set  at 
equal  distances  and  in  line  along  a  longwall  face  are  much  more  efficient  in  sup- 
porting the  roof  than  irregularly  set  timbers.  The  accompanying  figure  shows 
the  proper  way  of  locating  the  pack  walls  and  the  face  timber. 


EXPLOSIVES  AND  BLASTING 


667 


EXPLOSIVES  AND  BLASTING 


CLASSIFICATION  OF  EXPLOSIVES 

The  characteristics  of  a  good  blasting  explosive  are:  (1)  Sufficient  stability 
or  difficulty  of  detonating  by  mechanical  shock,  and  strength;  (2)  convenience 
in  form  and  safety  in  handling;  (3)  absence  of  injurious  effects  upon  the  user. 

Explosives  are  of  two  general  classes:  low  explosives,  or  those  discharged 
by  fire,  and  high  explosives,  or  those  that  require  a  detonator. 

Low  Explosives. — Ordinary  gunpowder  and  black,  or  blasting,  powder 
are  low  explosives.  Blasting  powder  consists  of  73  parts  of  Chili  saltpeter 
([nitrate  of  soda,  NaNOa),  16  parts  of  charcoal,  and  11  parts  of  sulphur.  Blast- 
ing powder  is  graded  according  to  the  size  of  the  grains  passing  through  and 
over  various  sizes  of  round  holes  in  sieves.  In  low  explosives,  the  force  of 
shattering  effect  is  produced  by  the  rapid  combination  of  the  oxygen  of  the 
saltpeter  with  the  carbon  of  the  charcoal;  the  sulphur  is  added  merely  to  make 
the  mixture  more  easily  ignitable. 

SIZES  OF  GRAINS  OF  BLACK  BLASTING  POWDER 


Trade  Name 

Through 

Over 

CCC 
CC 
C 
F 
FF 
FFF 
FFFF 

I 

if 

High  Explosives. — High  explosives,  which  are  very  commonly  called 
dynamites  regardless  of  their  composition,  usually  consist  of  a  base  or  absorbent 
known  as  dope,  which  may  or  may  not  be  an  aid  to  the  explosive,  and  an  explo- 
sive proper.  If  the  active  agent  is  a  liquid,  as  it  is  in  the  case  of  true  dynamites, 
the  dope  is  added  to  hold  or  absorb  the  explosive;  if  the  active  agent  is  a  solid, 
the  base  is  added  to  reduce  the  temperature  of  the  gaseous  products  of  com- 
bustion or  to  shorten  the  length  of  the  flame  produced  by  their  burning,  and, 
in  general,  to  render  their  use  safer.  The  high  explosives  generally  derive 
their  names  from  those  of  their  active  principle. 

Nitroglycerin  is  prepared  by  slowly  running  glycerin  into  a  mixture  of  con- 
centrated nitric  and  sulphuric  acids,  the  bath  being  stirred  and  kept  cool  dur- 
ing the  process  of  mixing.  It  is  a  dense,  oily  liquid,  white  when  pure  but  of  a 
yellowish  cast  as  found  on  the  market.  It  is  very  poisonous,  not  only  when 
taken  through  the  mouth  but  also  through  the  inhalation  of  its  fumes,  pro- 
ducing violent  headaches  which,  however,  tend  to  diminish  in  intensity  after 
repeated  exposures.  Nitroglycerin  may  freeze  after  some  exposure  to  a  tem- 
perature of  52°  F.  It  explodes  when  confined  at  360°  F.  It  takes  fire  at 
306°  F.  and,  if  unconfined,  usually  burns  harmlessly  unless  in  large  quantities, 
so  that  a  part  of  it,  before  coming  in  contact  with  the  air,  becomes  heated  to  the 
exploding  point. 

Picric  acid,  which  forms  the  basis  of  many  explosives,  is  made  by  treating 
carbolic  acid  (derived  from  coal  tar)  with  concentrated  nitric  acid. 

Ammonium  nitrate  is  a  salt  similar  to  sodium  and  potassium  nitrate  and  is 
largely  used  in  the  manufacture  of  a  class  of  explosives  known  as  ammonium 
(or  ammonia')  nitrate  powders,  ammonia  dynamite,  etc.  It  has  been  used  in 
the  United  States  for  nearly  30  yr.  in  the  manufacture  of  some  dynamites, 
taking  the  place  of  sodium  nitrate  over  which  it  has  the  advantage  that  upon 
exploding  it  goes  completely  into  gases.  It  is  also  largely  used  here  and  abroad 
in  the  making  of  the  so-called  permissible,  or  permitted,  powder  for  use  in  gaseous 
and  dusty  coal  mines,  for  the  reason  that  upon  exploding  it  forms  large  amounts 
of  water,  and  this  lowers  the  temperature  of  all  the  products  of  combustion. 


EXPLOSIVES  AND  BLASTING 


EXPLOSIVES  FOR  ROCK  WORK 

Explosives  for  rock  work  in  mining  are  all  of  the  high-explosive  type.  The 
original  form  is  dynamite,  which  consists  of  a  base,  usually  wood  pulp,  with 
which  the  explosive  or  explosives  are  mixed. 

Straight  Nitroglycerin  Dynamite. — By  a  straight  dynamite  is  meant  one 
that  contains  no  other  high  explosive  than  nitroglycerin.  Straight  dynamites 
are  graded  according  to  the  percentage  of  nitroglycerin  they  contain  and  their 
strength  is  made  the  basis  of  comparing  the  strengths  of  dynamites  of  other 
types.  Thus,  a  40%-ammonia  dynamite  means  a  dynamite  that  has  the  same 
strength  as  a  40%  straight  nitroglycerin  dynamite.  The  Un  ted  States  Bureau 
of  Mines  has  given  the  subject  of  explosives  considerable  study,  and  in  this  con- 
nection the  results  of  its  investigations  are  freely  used.  The  compositions 
of  straight  nitroglycerin  dynamites  are  given  in  the  accompanying  table. 

COMPOSITIONS   OF   STRAIGHT   NITROGLYCERIN   DYNAMITES   OF 
VARIOUS  STRENGTHS 


Ingredients 

15% 

20% 

25% 

30% 

35% 

40% 

45% 

50% 

55% 

60% 

Nitroglycerin                  .    . 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

Combustible  material*  .  .  . 
Sodium  nitrate     

20 
64 

19 
60 

18 
56 

17 
52 

16 

48 

15 

44 

14 
40 

14 
35 

15 

29 

16 
23 

Calcium    or    magnesium 
carbonate  

1 

1 

1 

1 

1 

1 

1 

1 

1 

*Consisting  of  wood  pulp,  flour,  and  sulphur  for  grades  below  40%;  wood 
pulp  only  for  other  grades. 

The  straight  nitroglycerin  dynamites,  as  a  class,  develop  greater  disruptive 
or  shattering  force  than  any  of  the  other  commercial  types  of  explosives,  and  for 
this  reason  they  should  be  used,  whenever  the  conditions  permit,  for  producing 
shattering  effects  or  for  blasting  very  tough  or  hard  materials. 

Slow,  or  Low-Freezing,  Dynamites. — The  accompanying  table  shows 
typical  compositions  of  low-freezing  dynamites.  The  slow,  or  low-freezing, 
dynamites  have  the  advantage  of  not  freezing  until  exposed  for  a  considerable 
time  to  a  temperature  of  35°  F.  or  less,  but,  like  all  nitroglycerin  explosives, 
after  they  become  frozen  they  must  be  thawed  before  used  in  order  to  insure 
the  most  effective  results. 


COMPOSITIONS  OF  LOW-FREEZING  DYNAMITES  OF  VARIOUS 
STRENGTHS 


A 

4 

fc?M 

>4 

of 

4 

4 

Ingredients 

o  c 

"3  g 

O  C 

1C  § 

|?c 

CO   (H 

CO  £ 

^    IH 

o  S 

w 

to 

to 

w 

to 

w 

to 

Nitroglycerin 

23 

26 

30 

34 

38 

41 

45 

Nitrosubstitution  compounds  .... 

7 

9 

10 

11 

12 

14 

15 

Combustible  material* 

17 

16 

15 

14 

14 

15 

16 

Sodium  nitrate"  

52 

48 

44 

40 

35 

29 

23 

Calcium  or  magnesium  carbonate  . 

1 

1 

1 

1 

1 

1 

Composition  similar  to  that  in  the  straight  nitroglycerin  dynamites. 

Ammonia  Dynamites. — The  ammonia  dynamites,  compared  with  the  other 
dynamites,  have  the  disadvantage  of  taking  up  moisture  very  readily,  because 
ammonium  nitrate  is  deliquescent,  and  care  should  be  observed  when  they  are 
stored  or  used  m  wet  places.  The  following  table  shows  typical  compositions 
of  ammonia  dynamites; 


EXPLOSIVES  AND  BLASTING 

COMPOSITIONS  OF  AMMONIA  DYNAMITES  OF  VARIOUS 
STRENGTHS 


669 


Ingredients 

30% 

strength 

35% 

strength 

40% 

strength 

50% 

strength 

60% 

strength 

Nitroglycerin  
Ammonium  nitrate  .... 
Sodium  nitrate  
Combustible  material*. 
Calcium    carbonate    or 
zinc  oxide 

15 
15 
51 

18 

1 

20 
15 

48 
16 

1 

22 
20 
42 
15 

1 

27 
25 
36 
11 

1 

35 
30 
24 
10 

1 

Composition  similar  to  that  in  the  straight  nitroglycerin  dynamites  of  the 
grades  below  40%. 

Gelatin  Dynamites. — The  gelatin  dynamites  have  been  used  to  a  large 
extent  in  wet  blasting,  as  in  the  removal  of  obstacles  to  navigation  and  in  deep 
workings,  and  as  a  general  rule  are  best  suited  for  these  purposes.  In  the 
manufacture  of  these  dynamites,  the  nitroglycerin  is  gelatinized  by  the  addi- 
tion of  a  small  percentage  of  nitrocellulose.  The  jelly-like  mass  thus  formed 

COMPOSITIONS  OF  GELATIN  DYNAMITES  OF  VARIOUS 
STRENGTHS 


Ingredients 

og 

CO    (H 
M 

^§ 

10  g 

coj; 
to 

f"o 
§ 

"w 

^1 

§£ 
V 

£?& 

s§ 

In 

4 
§l 

4 
gl 

Nitroglycerin  

23.0 

28.0 

33.0 

42.0 

46.0 

50.0 

60.0 

Nitrocellulose     

0.7 

0.9 

1.0 

1.5 

1.7 

1  9 

2  4 

Sodium  nitrate  

62.3 

58.1 

52.0 

45.5 

42.3 

38.1 

29.6 

Combustible  material         .    .    . 

13.0 

12.0 

13.0 

10.0 

9.0 

9  0 

70 

Calcium  carbonate  

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

is  impervious  to  water  and  is  of  high  density  and  plasticity.  For  these  reasons, 
it  is  generally  preferred  for  tunneling  in  hard  rock.  By  the  addition  of  dif- 
ferent percentages  of  suitable  absorbents  the  various  grades  of  these  dynamites 
are  made. 

The  compositions  of  gelatin  dynamites  generally  offered  for  sale  in  this 
country  are  given  in  the  accompanying  table.     The  combustible  material 

ANALYSES  OF  HIGH  EXPLOSIVES 


Constituent 

40% 
Strength 
Low- 
Freezing 
Dynamite 

40% 
Straight 
Nitro- 
glycerin 
Dynamite 

40% 
Strength 
Ammonia 
Dynamite 

40% 
Strength 
Gelatin 
Dynamite 

1  13 

.97 

.88 

1.47 

Nitroglycerin  
Nitrocellulose  
Ammonium  nitrate  

27.56 
10.13 

39.19 

21.60 
18.86 

30.70 
.88 

Sodium  nitrate  

51.54 
8.52 

49.53 
9.77 

46.04 
5.45 

54.27 
8.58 

4.85 

3.08 

.88 

1.02 

Calcium  carbonate  

1.12 

.54 

1.44 

670 


EXPLOSIVES  AND  BLASTING 


6  &' 


qqqqqqqqqqq 


qqqqqqqqqqq 


1C  iO         1C         O 

8      &     3     ^ 


in  the  60  and  70%  strength 
gelatin  dynamite  is  wood 
pulp.  Sulphur,  flour,  wood 
pulp,  and  sometimes  resin 
are  used  in  other  grades. 
Some  manufacturers  replace 
a  small  percentage  of  the  ni- 
trpglycerin  in  these  explosives 
with  an  equal  amount  of  am- 
monium nitrate.  Ammonia- 
gelatin  dynamites  have  some- 
what the  same  advantages 
over  straight  gelatin  dyna- 
mites that  ammonia  dyna- 
mites have  over  straight  dy- 
namites, except  that  they 
are  no  slower  in  velocity  of 
detonation,  but  in  certain 
classes  of  work  the  fumes  are 
less  objectionable. 

Comparative  Analyses. 
The  analyses  on  page  669 
show  the  composition  of  the 
four  classes  of  high  explosives, 
each  being  rated  as  a  40% 
dynamite.  It  will  be  noted 
that  the  only  one  of  these 
analyses  showing«an  approxi- 
mate content  of  40%  of  nitro- 
glycerin  is  the  straight  dyna- 
mite in  the  second  column, 
which  is  the  basis  of  com- 
parison. 

Products  of  Combustion. 
The  analyses  of  mine  air  taken 
at  West  Winfield,  Pa.,  while 
blasting  operations  were  be- 
ing carried  on  in  the  usual 
way  are  given  in  the  accom- 
panying table.  They  are  of 
interest  in  showing  that  where 
the  ventilation  is  good,  the 
contamination  of  mine  air  by 
the  products  of  combustion 
of  high  explosives  is  very 
slight,  even  in  the  case  of 
straight  dynamites  which 
yield  a  large  amount  of  CO. 

Dynamite  is  frequently 
condemned  for  producing  in- 
jurious fumes,  when,  as  a 
matter  of  fact,  these  fumes 
were  made  by  the  partial 
burning  of  the  dynamite  be- 
fore its  explosion,  the  dyna- 
mite having  been  lighted  by 
the  fuse  before  the  fare  reached 
the  cap.  An  experienced  per- 
son can  readily  distinguish 
between  the  fumes  produced 
by  burning  dynamite,  and 
those  produced  by  detonation. 
Comparative  Strength  of 
Explosives.  —  The  following 
table  gives  the^  relative 
strengths  of  the  different  high 
explosives  as  determined  from 
an  extended  series  of  tests 


EXPLOSIVES  AND  BLASTING 


671 


by  the  Bureau  of  Mines.  In  all  cases  40%  straight  nitroglycerin  dyna- 
mite has  been  taken  as  the  standard  with  a  value  of  100%.  The  relative 
disruptive  and  propulsive  effects  here  tabulated  are  shown  graphically  in  the 
accompanying  figure.  Disruptive  effect  indicated  represents  averages  of 
energies  developed  in  the  Trauzl  lead-block,  small  lead  block,  and  rate-of- 
detonation  tests;  propulsive  effect  indicated  represents  averages  of  ballistic- 
pendulum  and  pressure-gage  tests.  _  The  figures  given  in  this  table  are  fairly 
consistent  with  general  practice,  and  it  is  believed  that  the  classification  will  serve 

RESULTS    OF   TESTS   TO   DETERMINE   POTENTIAL   ENERGY   AND 
DISRUPTIVE  AND  PROPULSIVE  EFFECTS  OF  EXPLOSIVES 


Class  and  Grade 

Percentage 
Strength 
Represent- 

Average 
Percentage 
Strength 
Represent- 

Average 
Percentage 
Strength 
Represent- 

Potential 
Energy 

ing^ 
Disruptive 
Effect 

Propulsive 
Effect 

30%  straight  nitroglycerin  dynamite  .  . 
40%  straight  nitroglycerin  dynamite.  . 
50%  straight  nitroglycerin  dynamite  .  . 
60%  straight  nitroglycerin  dynamite.  . 
60%  strength  low-freezing  dynamite  .  . 

93.1 
100.0 
111.0 
104.0 
60.2 

84.1 
100.0 
109.2 
119.8 
93.5 

96.8 
100.0 
107.4 
114.9 
91.2 

40%  strength  ammonia  dynamite  

101.8 

67.9 

99.1 

40%  strength  gelatin  dynamite  

105.7 

78.4 

95.8 

5%  granulated  nitroglycerin  powder.  .  . 

67.6 

21.6 

53.3 

Black  blasting  powder  

71.6 

6.8 

58.6 

as  a  useful  guide  for  comparing  the  practical  value  of  explosives.  It  is  worthy 
of  note  that  the  potential  energy  of  40%  strength  ammonia  dynamite  and  of 
40%  strength  gelatin  dynamite  (that  is,  the  theoretical  maximum  work  that 
these  explosives  can  accomplish)  is  higher  than  that  of  40%  straight  nitro- 
glycerin dynamite,  but  that  the  disruptive  and  propulsive  effects,  which 
represent  the  useful  work  done  as  shown  by  actual  tests,  are  less  than  those 
of  40%  dynamite.  While  it  is  true  that  straight  dynamites  possess  greater 


EXPLOSIVE 


ENERGY 


Disruptive  Effect, 
Per  Cent. 


Propulsive  Effect, 
Per  Cent. 


20  30  40  50 60 70 80 flOWOIlO 


Black  powder  (FFF) 

5%  granulated  powder.  .  . 
40%  ammonia  dynamite .  . 

40%  gelatin  dynamite 

30%  nitroglycerin  dynamite 
60%  low-freezing  dynamite 
40%  nitroglycerin  dynamite 
50%  nitroglycerin  dynamite 
60%  nitroglycerin  dynamite 

shattering  effect  than  other  standard  types  of  explosives  they  are  being  rapidly 
displaced  by  the  ammonia  and  gelatine  explosives  on  account  of  the  greater 
safety  in  handling  characteristic  of  the  latter.  In  hard,  brittle  rock,  especially 
in  chambered  holes,  the  straight  dynamites  are  more  effective  than  the  slower 
acting  ones,  but  in  softer  rocks  like  sandstone,  calcite,  marl,  etc.,  explosives  of 


672  EXPLOSIVES  AND  BLASTING 

the  gelatin  and  ammonia  types  are  very  much  more  effective.  Ordinary  black 
blasting  powder  has  only  about  one-third  of  the  disruptive  effect  of  granulated 
nitroglycerin  powder. 

EXPLOSIVES  FOR  COAL  MINES 

As  the  object  in  practically  all  coal  mines  is  to  obtain  as  large  a  proportion 
of  lump  coal  as  possible,  the  quick-acting,  powerful,  high  explosives  are  not 
well  adapted  to  use.  In  their  stead,  the  slower  acting  low  explosives  are  greatly 
to  be  preferred.  These  coal  mine  explosives  are  of  two  general  kinds:  Black 
powder  and  the  so-called  permissible  powders. 

Black  powder  is  an  excellent  explosive,  but,  unfortunately,  is  not  always 
safe  for  coal  mine  use.  Unless  skilfully  handled,  its  long  flame  is  practically 
certain  to  ignite  dust  or  methane  when  more  than  a  small  amount  of  these  is 
present  in  the  workings. 

Permissible,  or  permitted,  explosives  have  come  into  use  in  the  United  States 
within  the  past  few  years,  although  they  have  has  been  used  in  Europe  for 
a  much  longer  time.  The  original  terms,  flameless  explosive  and  safety  explosive 
have  been  dropped  for  the  ones  given,  as  none  of  them  is  absolutely  flameless 
or  absolutely  safe. 

In  the  United  States,  it  is  a  function  of  the  Bureau  of  Mines  to  determine 
by  tests  what  explosives  are  relatively  safe  under  the  dangerous  conditions  of 
gas  and  dust  prevailing  in  coal  mines. 

In  determining  this,  the  following  rules  are  observed:  The  charge  of 
explosive  to  be  fired  in  tests  1  and  2  shall  be  equal  in  deflective  power  to  $  Ib. 
(227  grams)  of  40%  nitroglycerin  dynamite  of  the  composition  given  on 
page  669.  Each  charge  shall  be  fired  with  an  electric  detonator,  which  will 
completely  explode  the  charge,  as  recommended  by  the  manufacturer.  In 
order  that  the  dust  used  in  tests  2  and  3  may  be  of  the  same  quality,  it  is 
always  taken  from  the  same  mine,  ground  to  the  same  fineness,  and  used  while 
still  fresh. 

If  a  powder  passes  the  three  following  tests  made  in  the  explosion  gallery 
of  the  Bureau's  testing  station,  at  Pittsburg,  Pa.,  it  may  be  placed  upon  the 
list  of  permissible  explosives. 

Test  1. — Ten  shots  each  with  the  charge  described,  in  its  original  wrapper, 
shall  be  fired,  each  tamped  with  1  Ib.*  of  clay  stemming,  at  a  gallery  temperature 
of  77°  F.,  into  a'  mixture  of  gas  and  air  containing  8%  of  gas  (methane  and 
ethane).  An  explosive  is  considered  to  have  passed  the  test  if  no  one  of  the 
ten  shots  ignites  this  mixture. 

Test  2. — Ten  shots  each  with  the  charge  described,  in  its  original  wrapper, 
shall  be  fired,  each  tamped  with  1  Ib.*  of  clay  stemming,  at  a  gallery  temperature 
of  77°  P.,  into  40  Ib.  of  bituminous-coal  dust,  20  Ib.  of  which  is  to  be  distributed 
uniformly  on  a  wooden  bench  placed  in  front  of  the  cannon  and  20  Ib.  placed 
on  side  shelves  in  sections  4,  5,  and  6.  An  explosive  is  considered  to  have 
passed  the  test  if  no  one  of  the  ten  shots  ignites  this  mixture. 

Test  3. — Five  shots  each  with  1$  Ib.  charge,  in  its  original  wrapper,  shall 
be  fired  without  stemming,  at  a  gallery  temperature  of  77°  F.,  into  a  mixture 
of  gas  and  air  containing  4%  of  gas  (methane  and  ethane)  and  20  Ib.  of  bitumi- 
nous-coal dust,  18  Ib.  of  which  is  to  be  placed  on  shelves  along  the  sides  of 
the  first  20  ft.  of  the  gallery  and  2  Ib.  to  be  so  placed  that  it  will  be  stirred  up 
by  an  air-current  in  such  manner  that  all  or  part  of  it  will  be  suspended  in  the 
first  division  of  the  gallery.  An  explosive  is  considered  to  have  passed  the  test 
if  no  one  of  the  five  shots  ignites  this  mixture. 

Classes  of  Permissible  Explosives. — The  following  is  the  classification 
of  permissible  explosives  made  by  the  Bureau  of  Mines: 

Class  1.  Ammonium-Nitrate  Explosives. — To  Class  1  belong  all  the  explo- 
sives in  which  the  characteristic  material  is  ammonium  nitrate.  The  class  is 
divided  into  two  subclasses.  Subclass  a  includes  every  ammonium-nitrate 
explosive  that  contains  a  sensitizer  that  is  itself  an  explosive.  _  _  Subclass  b 
includes  every  ammonium-nitrate  explosive  that  contains  a  sensitizer  that  is 
not  in  itself  an  explosive.  When  fresh,  these  explosives,  if  properly  detonated, 
have  the  advantage  of  producing  only  small  quantities  of  poisonous  and 
inflammable  gases,  and  are  adapted  for  mines  that  are  not  unusually  wet,  and 
also  for  mines  and  working  places  that  are  not  well  ventilated. 

Class  2.  Hydrated  Explosives. — To  Class  2  belong  all  explosives  in  which 
salts  containing  water  of  crystallization  are  the  characteristic  materials.  The 

*Two  Ib.  of  clay  stemming  is  used  with  slow-burning  explosives. 


EXPLOSIVES  AND  BLASTING  673 

explosives  of  this  class  are  somewhat  similar  in  composition  to  the  ordinary 
low-grade  dynamites,  except  that  one  or  more  salts  containing  water  of  crystal- 
lization are  added  to  reduce  the  flame  temperature.  They  are  easily  detonated, 
produce  only  small  quantities  of  poisonous  gases,  and  most  of  them  can  be  used 
successfully  in  damp  working  places. 

Class  3.  Organic  Nitrate  Explosives. — To  Class  3  belong  all  the  explosives 
in  which  the  characteristic  material  is  an  organic  nitrate  other  than  nitro- 
glycerin. The  permissible  explosives  listed  under  class  3  are  nitrostarch 
explosives.  They  produce  small  quantities  of  poisonous  gases  on  detonation. 

Class  4-  Nitroglycerin  Explosives. — To  Class  4  belong  all  the  explosives 
in  which  the  characteristic  material  is  nitroglycerin.  These  explosives  contain 
free  water  or  an  excess  of  carbon,  which  is  added  to  reduce  the  flame  tempera- 
ture. A  few  explosives  of  this  class  contain  salts  that  reduce  the  strength 
and  shattering  effect  of  the  explosives  on  detonation.  The  nitroglycerin  explo- 
sives have  the  advantages  of  detonating  easily  and  of  not  being  readily  affected 
by  moisture.  On  detonation  some  of  them  produce  poisonous  and  inflammable 
gases  equal  in  quantity  to  those  produced  by  black  blasting  powder,  and  for 
this  reason  they  should  not  be  used  in  mines  or  working  places  that  are  not 
well  ventilated. 

CARE  OF  EXPLOSIVES 

Storing  Explosives. — Dynamite  cartridges  should  always  be  laid  on  the 
side  and  not  stood  on  end,  for  in  the  latter  position  the  nitroglycerin  may  ooze 
out  from  the  dope  and  collect  in  the  bottom  of  the  cartridge.  Dynamite  should 
never  be  kept  for  any  length  of  time  (as  in  storage  magazines)  at  a  temperature 
greater  than  75°  F.  It  should  be  stored  in  a  dry  place  having  a  reasonably 
uniform  temperature.  Magazines  should  be  heated  by  means  of  hot-water 
or  exhaust-steam  pipes,  never  by  a  stove  or  live-steam  pipes.  There  should, 
preferably,  be  two  powder  houses  or  magazines  at  a  mine.  The  main  maga- 
zine, holding  the  stock  of  explosive  on  hand,  should  be  built  sufficiently  far  from 
the  plant  or  with  some  natural  obstruction  (such  as  a  hill)  between  it  and  the 
plant  that  its  accidental  explosion  may  not  injure  the  miners'  village  or  the 
surface  equipment.  This  magazine  is  commonly  under  the  direct  supervision 
of  some  one  of  the  higher  officials  and  is  usually  opened  only  to  receive  sup- 
plies in  carload  lots  direct  from  the  manufacturer  and  to  withdraw  the  daily 
amount  required  by  the  men.  Near  the  mine  mouth  is  a  smaller  magazine, 
commonly  called  the  powder  house,  to  which  the  day's  supply  is  taken  from 
the  main  magazine,  and  where  it  is  handed  out  to  the  men  individually.  All 
main  magazines  should  be  proof  against  high-power  rifle  bullets  fired  at  short 
range.  Storing  explosives  in  large  quantities  in  a  mine  is  a  bad  and  dangerous 
practice  and  in  most  states  is  prohibited  by  law. 

The  effect  of  storing  fuse  for  several  days  at  temperatures  much  above  or 
below  the  normal  is  to  greatly  retard  its  rate  of  burning;  commonly  to  the 
extent  of  50%  or  more.  It  follows  that  fuse  should  not  be  stored  in  too  warm 
a  place  as  over  boilers  and  steam  pipes  in  winter,  or  in  a  tin  box  exposed  to  the 
direct  rays  of  the  sun  in  summer,  nor  should  it  be  left  in  an  unheated  tool 
house  when  the  temperature  is  much  below  the  freezing  point.  Fuse  is 
extremely  difficult  to  dry  out  after  wetting,  and,  as  a  general  rule,  fuse  that 
has  been  stored  in  damp  places  or  has  in  any  way  become  wet  should  not  be 
used  in  mining. 

Thawing  Dynamite. — Dynamite  freezes  at  about  45°  F.,  and  when  solidly 
frozen  it  is  exploded  with  difficulty,  and  if  it  is  exploded  the  detonation  is 
only  partial.  It  is  dangerous  to  cut,  break,  or  ram  a  frozen  dynamite  cart- 
ridge, as  the  frozen  nitroglycerin  crystals  may  explode.  No  attempt  should 
be  made  to  explode  dynamite  that  has  been  frozen  until  it  has  been  thoroughly 
thawed  and  is  soft  and  plastic ;  many  accidents  occur  through  failure  to  observe 
this  precaution.  If  incomplete  detonation  occurs,  unexploded  powder  is  often 
found  in  the  holes  or  in  the  material  blown  down  by  the  shot. 

In  cold  weather,  the  cartridges  should  not  be  taken  to  the  place  where  they 
are  to  be  used  until  all  the  holes  are  ready  to  be  loaded,  and  all  cartridges 
should  be  soft  and  warm  when  charged  into  the  holes.  Dynamite  that  has  been 
chilled,  but  not  frozen,  looses  a  large  part  of  its  efficiency.  Many  instances 
are  on  record  in  which  some  of  the  holes  of  a  blast  were  loaded  with  warm, 
and  others  with  frozen,  or  partially  frozen,  dynamite;  the  dynamite  that  had 
been  warmed  exploded  and  that  which  was  frozen  did  not,  and  miners  have 
subsequently  been  killed  or  injured  by  drilling  into  these  misshots. 

43 


674  EXPLOSIVES  AND  BLASTING 

When  thawing  dynamite,  it  is  necessary  to  use  caution  to  keep  the  tempera- 
ture from  rising  very  high,  as  each  degree  rise  is  that  much  nearer  the  danger 
limit  where  extreme  sensitiveness  to  shock  prevails.  The  thawing  of  dynamite 
by  placing  it  in  a  tight  box  surrounded  by  manure  is  a  good  method  if  the 
manure  is  fresh  so  that  it  is  giving  off  heat.  Dynamite  should  never  be  thawed 
before  an  open  fire,  on  a  shovel,  in  a  tin  can,  or  in  an  oven,  for,  while  dynamite 
will  very  frequently  burn  in  the  open  and  when  unconfined,  it  very  often 
explodes.  Also,  it  should  never  be  thawed  by  immersion  in  hot  water  as  that 
has  a  tendency  to  leach  out  the  nitroglycerin  and  make  it  dangerous.  The 
common  practice  of  thawing  dynamite  cartridges  by  passing  them  through 
an  oven  or  over  a  lighted  candle  is  very  dangerous. 

When  dynamite  is  being  used  on  a  large  scale  during  the  winter,  it  is  well 
to  provide  a  special  thawing  room,  in  which  1  or  2  days'  supply  can  be  kept 
ready  for  use.  The  room  need  not  be  of  great  size,  say  12  ft.X16  ft.  The 
powder  needed  for  the  day's  consumption  can  be  carried  in  during  the  after- 
noon and  left  over  night,  the  boxes  simply  being  opened  or  the  explosive  taken 
out  and  put  on  shelves,  the  procedure  depending  on  the  time  available.  A 
thermometer  should  be  consulted  to  insure  that  the  temperature  does  not  rise 
above  85°  and  is  preferably  kept  between  75°  and  80°  F.  If  a  brick  or  stone 
vault  is  made  below  the  surface  and  tightly  roofed  over  and  banked  with  earth, 
dynamite  may  be  kept  in  it  all  winter  without  freezing. 

For  handling  smaller  quantities  of  frozen  dynamite,  special  thawing  kettles 
are  used  to  advantage.  One  device  consists  of  a  metal  can  having  tubes  that 
pass  through  it.  The  tubes  are  surrounded  by  water,  and  the  whole  so  arranged 
that  a  miner's  lamp  or  candle  may  be  placed  underneath  the  can  to  keep  the 
water  warm.  When  in  use,  the  tubes  are  filled  with  sticks  of  dynamite,  the 
space  surrounding  them  is  filled  with  water,  and  the  cover  slipped  over  so 
that  the  cartridges  cannot  fall  out  of  the  tubes.  A  lamp  or  candle  placed 
under  the  can  will  soon  heat  the  water  sufficiently  to  thaw  out  the  cartridges. 
These  thawers,  being  portable,  are  very  convenient  and,  filled  with  hot  water, 
will  keep  dynamite  in  good  condition  for  some  time  without  being  artificially 
heated.  It  is,  however,  of  great  importance  that  the  water -receptacle  should 
always  contain  water,  otherwise  an  explosion  may  occur.  A  double  thawing 
kettle  commonly  used  consists  of  an  outer  kettle  standing  on  legs  and  an 
inner  kettle,  which  is  held  up  by  a  bead  around  the  edge,  in  which  the  cartridges 
are  placed. 

Handling  Explosives. — While  the  dangerous  practice  still  prevails  to  some 
extent  of  daily  opening  the  main  magazine  and  there  handing  out  to  the  men 
all  the  explosives  they  may  demand,  this  method  has  been  very  largely  super- 
seded by  the  much  safer  plan  of  taking  the  estimated  total  daily  mine  con- 
sumption to  the  small  powder  house  near  the  opening  where  only  enough  for 
the  day's  work  is  given  each  miner.  The  amount  of  explosive  is  charged  to  the 
men  either  from  entries  made  by  the  person  in  charge  of  the  powder  house 
or  from  written  orders  or  receipts  given  by  the  men  themselves.  At  some 
mines,  the  men  purchase  in  advance  several  dollars'  worth  of  so-called  powder 
checks,  which  are  pieces  of  metal  stamped  with  a  number  of  value  (12J  c., 
25  c.,  50  c.,  etc.)  and  which  may  be  exchanged  at  the  powder  house  for  explo- 
sives and  other  blasting  supplies.  After  the  men  have  taken  their  require- 
ments, the  explosive  remaining  is  commonly  returned  to  the  main  magazine, 
although  this  may  not  be  done  until  late  in  the  afternoon  for  fear  it  may  be 
needed. 

The  amount  of  explosive  that  a  miner  may  have  in  his  possession  or  carry 
into  the  mine  at  one  time  is  commonly  regulated  by  law.  In  rare  instances 
there  is  no  limit  placed  upon  this  amount,  although  a  miner  will  seldom  carry 
in  more  than  a  single  keg  of  25  Ib.  Where  there  is  a  limit,  a  keg  is  purchased, 
but  is  kept  in  the  magazine,  and  from  it  the  miner  draws  his  daily  allowance  of 
from  5  to  10  Ib.,  which  he  carries  to  his  working  place  in  a  metal  canister, 
preferably  of  copper.  Where  permissible  powders  are  used,  a  day's  supply 
should  not  exceed  5  Ib.,  as  this  amount  of  powder  exploded  in  properly  placed 
holes  will,  in  a  seam  of  average  thickness  and  when  undercut  as  it  should 
be,  bring  down  all  the  coal  a  man  can  load  out  on  one  shift. 

t  It  is  a  dangerous  practice  to  carry  large  metal  cans  of  black  powder  into  the 
mine  upon  the  shoulder  or  in  mine  cars  where  electric  wires  charged  with  current 
are  strung  along  the  roadway.  Cars  in  which  powder  is  being  transported 
should  be  hauled  by  mules  when  the  current  is  shut  off  the  wires.  At  the 
working  face,  the  powder  can  should  be  stored  in  a  wooden  box  separate  from 
the  caps  and  fuse.  The  box  should  be  kept  locked  when  not  in  use  and  should 
be  placed  some  100  ft.  from  the  face  and  25  ft,  from  the  track  if  this  is  possible. 


EXPLOSIVES  AND  BLASTING  675 

Where  shot-firers  are  employed  who  charge  the  holes,  the  mine  is  commonly 
divided  into  a  series  of  districts  of  a  size  that  two  men  can  charge  and  fire  all 
the  holes  therein  in  a  reasonable  time.  The  explosives  estimated  to  be  enough 
for  the  various  districts  are  placed  in  separate  boxes  at  the  main  magazine, 
conveyed  to  the  nearest  point  to  where  they  are  to  be  used  in  a  car  hauled  by  a 
mule,  and  are  there  unloaded  by  the  district  shot-firer  and  his  helper. 

Precautions  When  Handling  Coal-Mining  Explosives. — The  Bureau  of 
Mines  suggests  that  the  following  precautions  should  be  observed  in  handling 
black  powder: 

Never  open  a  metal  keg  of  powder  with  a  pick  or  metal  object;  use  the 
opening  provided  by  the  manufacturer  of  the  keg. 

Never  make  up  charges  or  handle  cartridges  or  powder  with  an  open  light 
on  the  head;  place  the  light  at  least  5  ft.  away  on  the  return-air  side  so  that 
sparks  from  it  will  not  fall  into  the  powder. 

Never  allow  powder  or  other  explosive  to  remain  exposed;  keep  it  in  a  well- 
locked  box  at  least  100  ft.  from  the  working  face  and  in  an  unfrequented  place. 

Never  go  nearer  than  5  ft.  to  a  powder  box  or  powder  when  wearing  an  open 
light  or  when  smoking. 

Never  use  coal  slack  or  coal  spalls  for  stemming;  it  is  dangerous.  Use 
moistened  clay,  wet  wood  pulp,  or  other  noninflammable  material;  even  wet 
coal  slack  may,  under  some  circumstances,  cause  an  explosion. 

Never  withdraw  a  shot  that  has  missed  fire;  drill  a  fresh  hole  at  least  2  ft. 
from  it  but  parallel  to  the  old  hole  and  fire  this  new  hole.  After  the  shot  a 
careful  search  should  be  made  for  the  unexploded  charge  to  prevent  its  being 
struck  by  a  pick  and  perhaps  causing  an  explosion. 

Never  fire  the  hole  the  second  time;  if  the  first  charge  proves  useless  powder 
and  labor  are  wasted  in  loading  the  hole  a  second  time.  Moreover,  the  first 
shot  often  cracks  the  coal  so  much  that  the  second  shot  has  a  chance  to  blow 
out  of  the  cracks,  and  thus  a  blown-out  shot  may  result. 

Never  use  iron  or  steel  tampers  or  needles;  have  at  least  6  in.  of  hard-drawn 
copper  on  the  tamping  end  of  the  bar  or,  better  still,  use  a  hardwood  tamping 
stick.  The  needle  should  be  made  entirely  of  hard-drawn  copper. 

Never  tamp  shots  with  an  iron  or  steel  scraper  and  do  not  push  a  cartridge 
into  the  drill  hole  with  the  scraper;  the  scraper  rod  should  be  tipped  with  at 
least  6  in.  of  brass  or  copper  on  the  scraping  end. 

Never  allow  the  point  of  the  coal  auger  to  become  dull  or  to  become  of  less 
than  the  standard  gauge,  so  that  a  drill  hole  may  be  made  with  it  into  which 
the  cartridge  may  always  be  pushed  freely. 

Never  drill  a  hole  past  the  loose  end,  chance,  or  cutting  in  solid  shooting; 
if  the  coal  has  been  undercut,  do  not  drill  beyond  the  undercutting.  It  is  better 
to  stop  at  least  6  in.  short  of  the  solid  coal. 

Never  bore  gripping  holes ;  keep  the  holes  parallel  to  the  ribs  or  as  nearly  so 
as  possible.  Use  the  side  gear  on  the  machine  if  you  can  when  boring  a  hole. 

Never  guess  at  the  quantity  of  powder  to  be  used;  always  measure  it.  This 
course  is  cheaper  and  better  than  guessing.  Use  cartridges  rather  than  loose 
powder  and  make  them  of  cartridge  paper.  Don't  use  newspaper  for  cart- 
ridge making. 

Never  place  black  blasting  powder  in  the  same  drill  hole  with  dynamite 
or  a  permissible  explosive. 

Never  use  short  fuse;  always  have  the  fuse  long  enough  to  stick  out  at 
least  2  in.  from  the  mouth  of  the  drill  hole.  When  the  short  fuse  is  lit  any 
gas  in  the  hole  may  be  ignited,  and  this  may  result  in  a  premature  blast. 

Never  bite  a  piece  of  the  match  off  the  squib,  nor  oil  it  to  make  it  burn 
faster. 

Never  use  sulphur  and  gas  squibs  at  the  same  working  face. 

Never  light  two  or  more  shots  at  the  same  time. 

Never  fire  shots  in  adjoining  working  faces  at  the  same  time. 

Never  return  to  a  shot  that  has  failed  to  explode  until  at  least  10  min.  after 
lighting  it,  if  squibs  were  used,  or  12  hr.  after  lighting  if  fuse  was  used.  When 
shots  are  fired  electrically  be  sure  that  all  wires  are  disconnected  from  the 
battery,  and  wait  at  least  5  min.  before  returning  to  the  face. 

Never  fire  a  rib  or  butt  shot  before  a  center  or  busting  shot  is  fired;  the 
opening  shots  should  be  fired  first,  in  order  to  give  the  succeeding  shots  a  chance 
to  do  their  work. 

Never  drill  a  hole  near  the  remaining  portion  of  a  former  shot,  nor  near 
cracks  and  fissures  made  by  previous  shots,  because  there  is  great  danger  of 
the  powder  gases  on  explosion  flying  out  of  the  loose  coal  or  the  cracks  and 
igniting  gas  or  dust  in  the  mine  air. 


676  EXPLOSIVES  AND  BLASTING 

Never  use  squibs  or  any  kind  of  fuse,  except  electric  fuse,  in  mines  that 
make  inflammable  gases. 

Never  fire  a  shot  without  making  sure  that  the  coal  dust  near  by  is  well 
wet  down. 

Never  light  a  dependent  shot  at  the  same  time  as  another  shot,  and  never 
fire  a  dependent  shot  until  the  first  shot  has  broken  properly. 

Never  fire  a  split  shot;  that  is,  never  fire  a  hole  that  has  been  drilled  into  a 
mass  of  coal,  cracked  and  shattered  by  a  previous  shot  that  failed  to  dislodge 
the  coal. 

The  following  additional  precautions  are  to  be  observed  in  handling  per- 
missible explosives: 

Never  take  more  than  1  da.  supply  of  permissible  explosives  into  the  mine 
at  one  time. 

Never  leave  permissible  explosives  in  the  mine  over  night. 

Never  purchase  permissible  explosives  not  suited  to  the  coal  bed. 

Never  use  weak  detonators. 

Never  fire  a  charge  until  it  has  been  completely  and  carefully  tamped. 

Never  put  black  blasting  powder  and  permissible  explosives  together  in 
the  same  drill  hole. 

Never  break  the  covering  of  a  cartridge  of  a  permissible  explosive  until 
ready  to  charge. 

Never  expect  permissible  explosives  to  yield  entirely  satisfactory  results 
when  coal  is  blasted  off  the  solid. 

Never  expect  the  first  blast  with  permissible  explosives  in  a  newly  opened 
coal  bed  to  be  satisfactory.  Several  trials  are  often  required  before  satis- 
factory results  are  obtained. 

Never  forget  that  permissible  explosives  are  different  from  dynamite  and 
entirely  unlike  black  blasting  powder. 

Never  use  fuse  to  fire  permissible  explosives  when  it  is  possible  to  use 
electric  firing. 

FIRING  EXPLOSIVES 

MEANS  OF  FIRING  LOW  EXPLOSIVES 

Ordinary  black  blasting  powder  may  be  ignited  by  means  of  squibs,  fuse, 
and  electric  squibs.  High  explosives,  including  permissible  powders,  are  fired 
with  fuse  and  caps,  or,  preferably,  by  means  of  electricity,  and  by  means  of  an 
electric  detonator;  in  the  latter  case  the  current  is  derived  either  from  a  battery 
or  from  a  dynamo.  Fuse  and  caps  are  commonly  employed  for  firing  single 
holes,  and  electric  firing  is  used  where  several  holes  are  fired  at  once,  or  in  a 
volley,  although  portable  electric  blasting  machines  (formerly  called  batteries) 
are  to  be  preferred  even  for  firing  single  holes. 

Squibs. — A  squib  (sometimes  known  as  a  match,  reed,  rush,  spire,  etc.) 
consists  of  a  small  paper  tube  that  is  filled  with  quick-burning  powder  and 
has  a  slow  match  attached  at  one  end.  The  burning  of  the  slow  match  gives 
the  miner  time  to  get  to  a  place  of  safety  between  the  time  that  he  lights  the 
match  and  the  time  that  the  flame  reaches  the  quick  powder.  When  the 
quick  powder  is  ignited  by  the  burning  match,  the  squib  shoots  like  a  rocket 
through  the  hole  that  has  been  left  in  the  tamping  by  the  withdrawal  of  the 
needle  into  the  blasting  powder.  Two  kinds  of  squibs  are  in  general  use, 
gas  squibs  and  sulphur  squibs.  In  the  gas  squib,  the  match  end  is  impregnated 
with  a  composition  that  does  not  flame  when  burning  but  glows  throughout 
its  length,  and,  for  this  reason,  is  supposed  to  be  safe  in  an  explosive  mixture 
of  methane  and  air.  In  the  sulphur  squib,  the  match  end  is  dipped  in  sulphur 
and  burns  with  a  flame  and  somewhat  faster  than  a  gas  squib.  Since,  in  the 
rocket-like  action  that  is  necessary  to  propel  the  squib  into  the  charge,  large 
volumes  of  sparks  are  given  off,  neither  type  of  squib  can  be  safe  in  explosive 
atmospheres. 

Fuse. — Fuse,  sometimes  called  safely  fuse  or  Bickford's  fuse,  from  its 
inventor,  consists  essentially  of  a  central  core  of  fine-grained  gunpowder 
wrapped  about  by  threads  of  hemp,  jute,  or  cotton.  These  threads  are  wound 
in  two  sets,  the  inner  being  known  as  the  spinning  threads  and  the  outer  as 
the  counter-threads  or,  simply^  countering.  In  single-tape  fuse,  the  threads 
are  wound  with  tape  and  then  coated  with  tar  and  covered  with  fuller's  earth 
or  powdered  talp  to  prevent  sticking.  Double-tape  fuse  is  single-tape  fuse 
wound  with  a  second  layer  of  tape,  which  is  also  tarred  and  powdered.  Cotton 
or  hemp  fuse,  not  tape  wound,  is  made,  but  is  only  suitable  for  use  in  absolutely 


EXPLOSIVES  AND  BLASTING  677 

dry  places  and  in  hot  climates.  In  cold  countries,  fuse  covered  with  tar  is  apt 
to  crack  and  thus  become  wet  and  misfire,  while  in  hot  countries  it  becomes 
sticky  and  unfit  for  use.  For  these  reasons  special  fuses  are  manufactured 
for  use  in  either  arctic  or  tropical  regions.  For  use  under  water,  gutta-percha 
covered  fuse  has  been  made. 

According  to  the  work  in  which  it  is  intended  to  be  used,  fuse  may  be 
divided  into  four  classes.  Fuse  of  the  first  class  is  suitable  for  dry  work  such 
as  stump  blasting  and  quarrying;  it  is  usually  untaped  hemp  and  cotton  fuse. 
Fuse  of  the  second  class  is  intended  for  damp  work,  as  in  coal  mining,  or.  in 
surface  work  where  mud,  rain,  or  dampness  is  encountered;  it  is  commonly  of 
the  single  tape  variety.  Fuse  of  the  third  class  is  suitable  for  very  wet  work, 
such  as  tunneling,  shaft-sinking,  etc.  Fuse  of  the  fourth  class  is  designed  for 
submarine  work;  double- tape,  triple-tape,  gutta-percha,  and  taped  double- 
countered  fuse  belong  to  these  classes.  Owing  to  the  large  amount  of  car- 
bonaceous material  in  the  wrappings  of  fuse,  the  gases  produced  by  its  burning 
contain  a  large  proportion  of  carbon  monoxide,  CO.  Where  numerous  coils 
of  fuse  have  caught  fire  and  burned,. as  has  happened  in  magazines  and  in  the 
rooms  of  poorly  ventilated  mines,  the  gases  evolved  have  been  found  to  be 
particularly  suffocating  and  poisonous. 

The  rate  of  burning  of  the  better  grades  of  American  fuse  has  been  deter- 
mined by  the  Bureau  of  Mines  to  be  very  nearly  30  sec,  per  ft.  of  length,  with 
a  variation  of  some  10%  either  way. 

Electric  Squibs. — F9r  use  with  black  blasting  powder  only,  electric  squibs 
are  made.  They  are  similar  to  electric  blasting  caps  in  appearance,  but  the 
cap  is  made  of  paper  instead  of  copper  and  the  charge  does  not  detonate  but 
shoots  out  a  small  flame.  They  are  made  with  iron  wires  4,  5,  6,  or  8  ft.  long, 
and  with  copper  wires  of  the  same  lengths  as  well  as  10  and  12  ft.  The  wires 
are  insulated  and  the  space  between  them  in  the  squib  is  bridged  with  fine 
platinum  .wire,  which  glows  when  the  electric  current  is  applied  and  furnishes 
enough  heat  to  ignite  the  powder.  They  are  designed  to  ignite  the  powder  at 
the  center  of  the  charge,  something  that  is  obviously  impossible  with  the 
ordinary  paper  squib. 

MEANS  OF  FIRING  HIGH  EXPLOSIVES 

Fuse  and  Caps. — Dynamite  and  other  detonating  explosives,  including 
permissible  powders,  may  be  fired  by  means  of  detonators  or  caps,  but  are  best 
exploded  by  means  of  electric  detonators  of  the  strength  prescribed  for  each 
one.  Caps,  blasting  caps,  detonators,  or  exploders,  as  they  are  variously  called, 
consist  of  copper  capsules,  about  as  thick  as  an  ordinary  lead  pencil,  that  are 
commonly  charged  with  dry  mercury  fulminate  or  with  a  mixture  of  dry  mer- 
cury fulminate  and  potassium  chlorate  that  is  compressed  in  the  bottom  of 
the  capsule,  filling  it  to  about  one-third  its  length.  Several  grades  of  these 
detonators  are  on  the  market,  and  they  are  differently  designated  by  different 
manufacturers.  A  strong  detonator  is  essential  to  securing  the  perfect  explo- 
sion of  permissible  powders,  etc.,  and  for  this  purpose  those  of  No.  6  strength, 
containing  15.4  gr.  of  charge,  are  recommended.  Fulminate  of  mercury  is 
extremely  sensitive  to  heat,  friction,  and  blows,  and  for  these  reasons  blasting 
caps  should  be  handled  with  as  much  care  as  dynamite,  or  a  violent  explosion 
may  result. 

The  following  precautions  are  recommended  in  handling  them: 

Never  attempt  to  pick  out  any  of  the  composition. 

Do  not  drop  caps  or  strike  them  with  anything  hard. 

Do  not  step  upon  caps  or  place  them  where  they  may  be  stepped  upon. 

When  crimping  caps  on  to  the  fuse,  take  care  not  to  squeeze  the  fulminate, 
and  never  crimp  with  the  teeth. 

Caps  should  be  stored  in  a  dry  place  and  in  a  separate  building  from  any 
other  explosives. 

Caps  should  not  be  carried  into  the  mine  with  other  explosives,  or  placed 
near  other  explosives  except 
in  a  bore  hole. 

Electric  Detonators. 
To  overcome  the  dangers 
incident  to  the  use  of  fuse 
and  squibs,  electric  deto- 
nators (also  called  electric  blasting  caps)  have  been  devised.  These  are 
simply  ordinary  detonators  that  have  been  fitted  with  the  means  of  firing 
them  with  the  electric  current.  This  is  done,  as  shown  in  the  accom- 
panying figure,  by  inserting  within  the  caps  two  copper  wires  d,  joined 


678  EXPLOSIVES  AND  BLASTING 

at  the  inner  ends  by  an  extremely  fine  platinum  or  other  high-resistance 
wire  e,  which  becomes  heated  until  it  glows  when  an  electric  current  is  passed 
through  it.  This  wire,  known  as  the  bridge,  is  set  within  the  fulminate  b, 
above  which  is  placed  a  composition  /  designed  to  hold  the  wires  more  firmly 
in  place.  The  space  above  is  filled  and  closed  by  means  of  a  plug  of  sulphur 
or  other  waterproof  composition  which  is  poured  in  while  soft  and  which  is 
held  in  place  by  means  of  the  corrugation  a,  in  the  shell  of  the  cap.  The  copper 
wires  c  beyond  the  cap  are  called  legs  or  wires  and  are  insulated,  and  come  in 
lengths  of  4  ft.  increasing  by  2  ft.  to  30  ft.  For  firing  charges  of  permissible 
powder  or  high  explosives,  the  detonator  used  should  be  at  least  a  No.  6  (double 
strength)  with  15.4  gr.  of  fulminate.  The  precautions  to  be  used  in  handling 
blasting  caps  apply  with  equal  force  to  electric  detonators.  Heavy  jars  are 
particularly  to  be  avoided  as  they  may  break  the  delicate  bridge  wire;  and 
when  this  is  broken  the  detonator  is  worthless.  The  wires  must  not  be  bent 
sharply  or  forcibly  separated  at  the  point  where  they  enter  the  copper  cap, 
as  this  may  break  or  loosen  the  filling  material  and  permit  water  to  enter  and 
damage  the  charge. 

Delay-Action  Detonators. — In  some  kinds  of  blasting,  particularly  in  tunnel 
work  and  shaft  sinking,  it  is  necessary  to  blast  the  holes  in  sets  or  rounds,  and 
it  is  a  saving  in  time  and  adds  to  the  safety  of  the  operations  if  it  will  not  be 
necessary  for  the  men  to  return  to  the  face,  after  the  first  round  has  been  fired, 
in  order  to  light  the  fuses  in  the  second  and  subsequent  rounds.  This  firing 
of  the  holes  in  sequence,  or  rounds,  when  fuse  is  used  is  accomplished  by  cut- 
ting the  fuse  to  different  lengths  (assuming  that  it  all  has  the  same  rate  of 
burning  per  foot)  and  lighting  all  the  holes  as  nearly  as  may  be  at  the  same 
time;  the  holes  exploding  in  the  order  of  the  length  of  the  fuse  used.  When 
electric  firing  is  employed,  the  same  result  is  accomplished  with  one  application 
of  the  electric  current  by  means  of  what  are  known  as  no-delay,  first-delay,  and 
second-delay,  electric  blasting  caps.  No-delay  caps  detonate  at  the  instant  the 
electric  current  passes  through  them.  The  first-  and  second-delay  caps  contain 
a  slow-burning  substance,  which  is  ignited  by  the  electric  spark  and  which, 
after  burning  a  short  time,  ignites  the  detonating  composition  below  it.  It  is 
impossible  from  a  commercial  standpoint,  to  make  the  rate  of  burning  of  this 
slow-burning  composition  absolutely  uniform  and,  consequently,  delay-action 
detonators  in  the  same  circuit  may  not  all  explode  at  exactly  the  same  instant. 
On  the  other  hand,  there  is  always  a  distinct  time  interval  between  the  explo- 
sion of  the  no-delay  caps  and  the  quickest  of  the  first-delay,  and  between  the 
slowest  of  the  first-delay  and  the  quickest  of  the  second-delay.  These  delay- 
action  detonators  are  commonly  made  in  the  No.  6,  or  double  strength,  grade 
only.  .  :  m.  :[: 

CHARGING  AND  FIRING  EXPLOSIVES  WITH  SQUIBS  OR  WITH  CAP 
AND  FUSE 

Charging  Black  Powder  and  Firing  With  Squib. — Black  powder  (blasting 
powder)  is  used  in  paper  cases  or  cartridges,  which  are  made  and  filled  by  the 
miner  at  the  face  and  which  are  of  slightly  less  diameter  than  the  drill  holes, 
in  the  bottom  of  which  they  are  placed.  If  the  hole  is  dry,  these  cartridges 
may  be  tamped  hard  enough  to  break  the  cartridge  paper  so  that  the  powder 
will  pack  closely  and  fill  all  spaces,  for  the  closer  the  powder  is  packed  in  the 
hole  the  greater  will  be  the  effect  produced  by  the  blast.  In  putting  paper 
cartridges  into  holes,  care  should  be  taken  not  to  break  the  paper  until  the 
bottom  of  the  hole  is  reached.  In  case  the  hole  is  in  seamy  rock,  a  ball  of  clay 
is  first  put  in  the  hole  and  then  a  clay  bar  driven  into  it,  to  spread  it  out  and 
fill  all  crevices.  If  these  crevices  are  not  filled,  the  gases  due  to  the  explosion 
escape  through  them  and  much  of  the  force  of  the  explosive  is  lost.  The  clay 
bar  is  a  good  hickory  or  oak  stick  with  a  slightly  pointed  iron  shoe  at  one  end, 
or  is  an  iron  bar  pointed  at  one  end  with  an  eye  at  the  other  for  removal  from 
the  hole.  To  make  the  hole  round,  after  using  the  clay  bar,  an  auger  may  be 
turned  in  the  hole  and  the  surplus  clay  removed.  Should  the  hole  be  wet, 
the  same  method  of  claying  is  followed,  but  the  cartridges  are  well  coated  with 
miners  soap  and  not  tamped  so  hard  as  to  break  them. 

The  needle,  which  is  a  copper  rod  about  i  in.  in  diameter  pointed  at  one 
end  and  provided  with  a  handle  at  the  other,  is  run  into  the  cartridge,  and  about 
it  the  tamping  is  rammed  in  by  means  of  a  tamping  bar,  which  has  a  groove 
through  the  head  to  accommodate  the  needle.  The  tamping  bar  is  commonly 
of  iron  with  a  copper  head  of  a  diameter  a  little  less  than  that  of  the  drill  hole. 
Where  cartridges  are  not  used  and  powder  is  charged  in  bulk,  the  tamping  bar 
is  made  entirely  of  copper,  since  if  iron  comes  in  contact  with  rock  or  pyrites 


EXPLOSIVES  AND  BLASTING 


679 


it  is  apt  to  strike  a  spark  and  cause  a  premature  explosion  if  loose  powder  is 
sticking  to  the  sides  of  the  hole.  The  danger  from  the  use  of  metal  tamping 
bars  has  been  recognized  in  some  states  and  their  employment  wisely  pro- 
hibited by  law.  The  tamping  or  stemming  is  put  in  and  tamped  little  by 
little,  being  rammed  hard  to  keep  the  needle  hole  open  when  the  needle  is 
removed. 

In  anthracite  mines,  the  blasting  barrel  is  often  used  instead  of  the  needle, 
as  tamping  fine  enough  to  pack  is  not  obtainable  unless  the  miner  pounds  up 
slate  and  coal.  The  blasting  barrel  is  a  steel  or  wrought-iron  tube  of  about 
\  in.  inside  diameter;  one  end  is  inserted  in  the  cartridge  ^and  the  squib  is  fired, 
through  it  to  the  powder.  The  rammer  fits  over  the  blasting  barrel  in  the  same* 
way  as  over  the  needle.  The  blasting  barrel  is  valuable  where  the  tamping 
is  damp  or  the  hole  slightly  wet,  but  after  each  shot  is  fired  it  has  to  be  recovered 
and  if  used  again  must  be  straightened. 

The  squib  is  inserted  in  the  needle  hole  or  blasting  barrel  with  the  match 
end  outwards  and  after  igniting  the  extreme  end  of  the  match  with  his  lamp, 
the  miner  hastens  to  a  place  of  safety.  The  practice  of  biting  or  breaking  off 
the  end  of  a  squib,  or  unrolling  it,  or  dipping  it  in  oil  in  order  to  hasten  its 
burning  is  extremely  dangerous  and  is  almost  sure  to  result  in  a  premature 
explosion. 

Firing  Black  Powder  With  Fuse  and  Cap. — After  cutting  off,  with  a  sharp 
knife,  1  or  2  in.  of  the  fuse  in  order  that  the  portion  about  to  be  used  is  dry  and 
in  good  condition,  the  detonator  (cap)  is  slipped  over  the  end  and  is  crimped 
tightly  in  place  by  a  form  of  pliers  or 
pincers  known  as  a  crimper.  The  cap 
should  never  be  crimped  on  the  fuse 
with  the  teeth  as  an  explosion  may 
result,  and  the  cap  contains  enough 
fulminate  to  blow  off  a  man's  head. 
When  placing  the  cap  in  the  cartridge, 
there  is  great  diversity  of  opinion  as  to 
which  of  the  many  ways  used  is  the 
best.  Fig.  1  shows  a  very  common 
method  in  which  the  cap  is  placed  in 
the  top  of  the  cartridge  and  in  the 
center  with  only  about  two-thirds  of 
the  cap  embedded  in  the  material  of 

the  cartridge.  This  is  done  to  avoid  the  danger  of  its  igniting  the  explosive 
and  thus  causing  deflagration  of  the  cartridge  in  place  of  detonation.  An 
objection  to  a  cap  placed  in  the  center  of  the  cartridge  is  that  the  fuse  is 
very  apt  to  be  bent  and  injured  in  the  tamping,  while  it  also  interferes  with 
the  tamping. 

Instead  of  placing  the  cap  in  the  center  of 
the  end  of  the  cartridge  and  tying  the  end  of 
the  paper  wrapper  about  the  fuse,  an  inclined 
hole  is  made  in  the  end  of  the  cartridge,  as 
shown  in  Fig.  2,  and  the  cap  placed  deep  down 
in  the  charge.  Instead  of  inserting  the  cap 
through  the  end  of  the  cartridge,  many  manu- 
facturers of  explosives  strongly  recommend 
placing  it  in  a  hole  in  the  side,  as  shown  in 
Fig.  3.  The  fuse  is  tied  in  two  places,  a  half 
hitch  being  taken  around  it. 

A  common,  but  bad,  practice  among  miners 
is  to  make  a  hole  in  the  side  of  a  cartridge, 
place  the  cap  and  fuse  in  it,  and  bend  back 
the  fuse,  as  shown  in  Fig.  4  in  order  to  prevent 
the  cap  being  pulled  out.  The  sharp  bend  in 
the  fuse  is  sometimes  sufficient  to  cause  a  break 
in  the  train  of  powder,  resulting  in  a  misfire. 

If  the  length  of  the  cap  is  greater  than  the 
diameter  of  the  cartridge  and  it  is  stuck  through 
FIG.  2         FIG.  3  FIG.  4      the  side   either  diagonally  -or  straight  across, 

there  is  danger  of  its  being  jammed  against  the 

side  of  the  hole  when  tamping,  and  thus  cause  a  premature  explosion.  Care 
must  be  taken  to  insure  that  that  portion  of  the  cap  which  contains  the  fulmi- 
nate is  entirely  within  the  charge;  otherwise,  the  detonation  of  the  explosive 
will  be  imperfect. 


680 


EXPLOSIVES  AND  BLASTING 


When  tamping  holes  to  be  fired  with  fuse,  hard  bits  of  rock  or  slate  mixed 
with  the  stemming  may  cut  the  fuse  and  cause  a  misfire,  or  the  fuse  may  be 
kinked  by  a  hump  in  the  hole  and  thus  cause  either  a  misfire  or  a  delayed  shot. 
In  order  to  use  fuse  with  entire  safety,  it  should  be  long  enough  and  should 
be  run  through  a  blasting  barrel.  In  gaseous  mines,  it  is  extremely  important 
that  the  fuse  extend  beyond  the  end  of  the  hole,  for  if  it  does  not,  when  such  a 
fuse  is  lighted  any  gas  in  the  untamped  part  of  the  drill  hole  is  certain  to  be  set 
on  fire  at  the  same  time  and  a  premature  explosion  will  follow. 

If  the  work  is  wet,  waterproof  fuse  should  be  used,  the  end  of  which  should 
be  protected  by  applying  bar  soap,  pitch,  or  tallow  around  the  edge  of  the  cap 
where  the  fuse  enters  it. 

Charging  and  Firing  Dynamite  With  Cap  and  Fuse. — Blasting  powder  is 
commonly  charged  into  the  drill  hole  in  one  large  cartridge,  whereas  dynamite 
and  other  high  explosives,  including  permissible  powders,  are  charged  as  a  num- 
ber of  single  and  much  smaller  cartridges.  When  loading  a  hole  with  explosives 
of  the  latter  type,  the  cartridges  are  placed  in  one  after  another  and  pressed, 
not  rammed,  into  place  with  a  wooden  bar.  If  the  cartridges  at  hand  are 
less  than  the  required  size,  the  paper  coverings  may  be  split  open  with  a  knife 
and  the  explosive  forced  to  fill  the  hole  with  the  aid  of  the  tamping  bar.  It  is 
very  important,  if  the  full  effect  of  the  explosive  is  to  be  obtained,  that  the  part 
of  the  hole  in  which  the  charge  is  located  is  completely  filled,  and  that  no  air 
spaces  are  left  between  the  charge  and  the  walls  of  the  hole. 

The  cartridge  containing  the  cap  is  called  the  primer,  and  while  it  is  usually 
the  last  or  next  to  the  last  cartridge  to  be  placed  in  the  hole,  it  may  be  placed 
in  the  middle  of,  or  even  at  the  bottom  of  the  charge,  with  the  idea  of  insuring 
a  more  thorough  explosion.  This  is  theoretically  correct,  as  the  explosion  acts 
equally  in  all  directions,  but  while  there  may  be  some  reason  for  firing  a  charge 
with  black  powder  in  this  manner,  there  is  no  good  reason  for  such  practice 
when  firing  dynamite,  except  when  firing  holes  consecutively,  for  the  explosion 
of  dynamite  is  so  quick  that  there  is  no  appreciable  difference  in  the  result, 
whether  the  cap  is  placed  in  the  top  or  in  the  middle  of  the  charge.  There  is, 
however,  a  decided  objection  to  placing  the  cap  in  the  middle  or  bottom  of  the 
charge  when  using  common  fuse,  as  there  is  a  chance  that  the  fuse  will  set  fire 
to  the  dynamite  and  cause  not  only  a  loss  of  dynamite,  but  a  premature  explo- 
sion, which  cannot  be  as  thorough  as  if  detonated  by  the  cap.  The  primed 
cartridge  is  pressed  down  until  it  rests  on 
those  already  placed,  and,  after  the  car- 
tridges are  all  pressed  into  place,  the 
tamping  is  pressed  lightly  on  the  charge, 
care  being  taken  not  to  explode  the  primer. 
Fig.  5  (a)  shows  a  hole  with  the  primer 
placed  in  the  center  of  the  charge  and  in 
which  there  is  no  bend  in  the  fuse,  a  theo- 
retical arrangement  seldom  found  in  prac- 
tice. View  (b)  shows  a  common  method 
of  placing  a  charge  with  the  primer  on  top 
and  the  cap  placed  in  the  side  of  the  cart- 
ridge as  illustrated  in  Fig.  3. 

Precautions  When  Tamping  Explosives. 
Before  any  shots  are  fired  in  a  bituminous 
coal  mine,  the  dust  made  by  the  augers 
should  be  scraped  from  the  shot  holes  and, 
with  the  bug  dust  made  by  mining  ma- 
chines, should  be  loaded  into  tight  cars  and 
hauled  outside.  This  is  to  prevent  the  pos- 
sibility of  a  dust  explosion  either  in  the 
hole  or  in  the  bug  dust  immediately  at  the 
face.  As  the  loading  out  of  the  dust  throws 
considerable  of  the  finest,  and  consequently 
most  dangerous,  particles  into  the  air,  some  time,  say  £  hr.,  should  elapse  after 
this  loading  out  is  done  before  shots  are  fired.  In  very  dusty  mines,  the  face 
should  be  wet  down  with  a  hose  or  a  liberal  application  of  shale  dust  made 
before  shots  are  fired.  The  material  used  for  tamping  should  be  of  fine  and  uni- 
form grain  that  it  may  be  packed  tightly  and  should  not  contain  any  substances, 
such  as  grains  of  quartz,  pyrites,  etc.,  that  may  strike  fire  while  being  rammed 
home.  The  depth  of  the  stemming  should  be  at  least  one-half  that  of  the  .drill 
hole,  and  it  should  completely  fill  the  hole  from  the  explosive  to  the  mouth. 
Under  no  circumstances  whatsoever  should  slack  or  bug  dust  from  bituminous 


pIG   5 


EXPLOSIVES  AND  BLASTING 


681 


coal  be  used  for  tamping.  Moist  clay  or  brick  dust  sufficiently  moistened  to 
make  it  adhere  form  the  best  of  tamping  materials.  Suitable  stemming 
may  be  had  by  grinding  and  screening  clay  or  shale  rock,  by  digging  it  from ' 
a  bank  on  the  surface,  or  from  the  fireclay  floor  of  the  seam.  The  stemming 
is  usually  distributed  in  quantity  by  the  company  men  after  working  hours, 
being  left  in  a  pile  at  the  mouth  of  each  entry  or,  more  rarely,  at  the  mouth 
of  each  room.  For  use,  the  miner  makes  the  material  into  cartridges  of  the 
same  diameter  as  those  containing  powder  but  only  about  10  in.  long.  Where 
shot  firers  do  the  charging,  the  miner  commonly  makes  and  leaves  at  the  face 
beneath  each  shot  hole  a  sufficient  number  of  these  dobe,  or  dummy,  cartridges 
to  supply  the  tamping.  Holes  of  large  diameter  require  a  proportionally  greater 
length  of  tamping  than  smaller  holes.  The  tamping  should  be  rammed  solid, 
in  order  to  diminish  the  risk  of  a  blown-out  shot  and  to  confine  the  powder 
tightly,  that  it  may  do  its  full  work. 

High  explosives  of  the  nitroglycerin  type,  which  develop  their  full  power 
instantaneously,  usually  require  less  tamping  than  powder,  although  the  best 
results  from  their  use  are  obtained  by  thorough  tamping.  The  experiments  of 
the  Bureau  of  Mines  prove  that  in  the  case  of  high  explosives  when  the  weight 
of  the  tamping  is  about  that  of  the  charge,  the  efficiency  or  work  done  by 
them  is  increased  from  60  to  nearly  80%,  depending  on  the  kind  of  stemming 
and  the  way  it  is  used.  While  in  deep  downward-pitching  holes,  water  makes 
a  fair  tamping,  fine  sand,  clay,  etc.,  are  preferable  and  are  generally  used. 
The  first  5  or  6  in.  above  the  charge  is  filled  in  carefully  so  as  not  to  displace 
the  cap  and  primer;  and  then  with  a  wooden  rammer  the  balance  of  the 
stemming  is  packed  in  as  solidly  as  possible,  ramming  with  the  hand  alone, 
and  not  using  any  form  of  hammer. 

FIRING  EXPLOSIVES  BY  ELECTRICITY 

Charging  for  Electric  Firing. — Figs.  1  and  2  illustrate  the  method  of  placing 
an  electric  exploder,  or  cap,  in  a  cartridge  of  dynamite.  The  cap  a  is  placed 
either  in  the  bottom  or  at  the  side  of  the  cartridge,  the  hole  to  receive  it  having 
been  made  with  a  sharp  stick  or  lead  pencil.  The  best  practice  is  to  place 
the  detonator  so  that  it  points  to  the  bulk  of  the  charge. 
After  this  is  accomplished,  the  blasting  wires  b  are  tied 
firmly  to  the  cartridge,  as  illustrated  at  c.  In  firing 
dynamite  by  means  of  electricity,  there  is  no  danger 
of  the  wires  setting  fire  to  the  powder,  and  hence  the 
exploder  can  be  placed  well  down  in  the  cartridge. 
Sometimes,  when  a  long  charge  in  a  very  deep  hole  is 
to  be  fired,  two  or  more  electric  exploders  are  used  in 
the  same  charge,  one  cartridge  containing  an  exploder 
being  placed  near  the  bottom  of  the  hole  and  another 
at  the  top.  The  method  of  loading  holes  for  firing  by 
electricity  is  the  same  as  that  described  for  firing  with 
fuses.  As  much  care  as  possible  should  be  taken  to 
prevent  the  leading  wires  from  coming  in  contact  with 
the  damp  earth,  also  that  in  tamping  the  hole  the  wires 
do  not  become  broken,  or  the  covering  materially 
injured,  and  that  the  wires  are  not  brought  into  con-  _^_ 
tact  with  each  other  or  with  the  damp  ground.  _  _  _, 

Many  miners  have  a  bad  practice  of  putting  the  cap  * IG-  * 
of  an  electric  exploder  in  obliquely  and  bending  the  wire  over  and  securing  the 
cap  by  a  half  hitch  of  the  wire,  as  shown  in  Fig.  3,  or,  to  make  it  worse,  by 
two  half  hitches.  So  much  force  is  used  in  making  the  half  hitch  that  there 
is  danger  of  a  short-circuit  being  formed,  or  the  sulphur  filling  in  the  electric 
cap  may  be  broken,  sometimes  disarranging  the  wires  in  the  cap  and  even 
breaking  the  fine  platinum  wire  or  bridge.  In  any  event,  the  cement  is  so  broken 
as  to  leave  free  passage  into  the  cap  of  any  water  that  may  be  contained  in 
the  hole.  The  platinum  bridge  of  an  electric  cap  is  very  small  and  delicate 
in  order  to  be  heated  red  hot  by  the  very  small  current  of  electricity  that  is 
used  to  fire  the  cap,  and  any  unusual  strain  on  the  wires  may  break  the  bridge, 
thus  breaking  the  circuit  and  causing  a  failure  of  the  shot.  Furthermore, 
sharp  bending  of  the  copper  wires  may  damage  the  insulation,  very  likely 
leaving  bare  wires  touching,  causing  a  short  circuit  and  a  failure  of  that  par- 
ticular cap.  The  bared  wires,  even  if  they  do  not  touch,  offer  an  opportunity 
for  a  short  circuit  through  any  moisture  present,  which  will  rob  that  particu- 
lar cap  of  part  of  the  current  of  electricity,  while  the  next  cap  might  get  the 
full  current.  The  result  will  be  that  the  first  cap  will  miss  fire. 


682 


EXPLOSIVES  AND  BLASTING 


Shot  Firing  With  the  Electric  Blasting  Machine.— <)ne  method  of  electric 
blasting,  as  used  in  America,  depends  on  the  generation  of  a  current  of  elec- 
tricity by  means  of  a  small  electric  machine,  which 
is  really  a  small  dynamo,  the  armature  of  which 
is  made  to  revolve  rapidly  between  the  poles  of  the 
field  magnets  by  means  of  a  crank  or  by  a  ratchet. 
The  machine,  commonly,  but  incorrectly,  called  a 
battery,  is  shown  in  Fig.  4.  It  consists  of  a  field 
magnet  a  and  an  armature  b  that  revolves  between 
the  poles  of  the  field  magnet.  The  loose  pinion 
c  (the  teeth  of  which  engage  the  rack  bar  d)  is 
arranged  with  a  clutch,  so  that  as  the  rack  bar 
descends  the  pinion  causes  the  armature  b  to 
rotate  and  generate  a  current.  During  the  down- 
ward stroke  of  the  rack  bar,  the  connections  are 
such  that  the  current  flows  inside  the  machine 
without  affecting  the  outside  circuit.  The  current 
increases  in  strength  until  the  rack  bar  strikes  the 
spring  e,  which  changes  the  connections  so  as  to 
send  the  full  strength  of  the  current  into  the  out- 
side circuit  and  through  the  caps  for  firing  the 
blasts.  When  more  than  one  shot  is  fired  at  a  time 
by  means  of  a  blasting  machine  the  holes  should 
be  connected  in  series.  Blasting  machines  are  also 
called  push-down  machines  and  are  rated  by  the 
number  of  electric  detonators  they  can  explode,  as 
4-hole  machines,  50-hole  machines,  etc. 

Connecting  Wires. — To  connect  the  ends  of  two 
wires,  scrape  off  the  insulation  for  about  2  in.  from 
each  end  and  scrape  the  wires  clean  and  bright. 
Then  twist  the  ends  together,  as  shown  in  Fig.  5. 


FIG.  4 


FIG.  5 


It  is  very  important,  to  prevent  misfires,  that  all  connections  are  clean  and 
well  made,  as  one  bad  connection  may  cause  all  the  holes  to  misfire. 

Connecting  Up  and  Firing  the  Blasts. — After  the  holes  have  been  loaded, 
the  fuse  wires  are  left  projecting  from  the  holes,  and  are  joined  by  connecting 
wires  in  such  a  manner  as  to  leave  one  free  wire  at  each  end  of  the  series  to  be 
fired,  as  at  b,  Fig.  6,  the  fuse  wires  a  leading  downwards  to  the  charges  to  be  fired. 
After  all  is  in  readiness,  the 
leading  wires  are  connected  to 
the  loose  ends  b,  and  when 
every  one  has  left  the  vicinity 
of  the  blast,  the  other  ends  of 
the  lead  wires  or  cables  are 
attached  to  the  blasting  ma- 
chine. Some  blasting  machines 
are  provided  with  three 
screws  on  the  outside,  to  which  leading  wires  are  attached.  When  only  a 
small  number  of  blasts  are  to  be  fired,  one  of  the  lead  wires  is  attached  to  the 
middle  screw  and  the  other  to  the  outside  as  illustrated  in  Fig.  6.  When  a 
large  number  of  blasts  are  to  be  fired  the  lead  wires  are  arranged  as  shown 
in  Fig.  7,  a  being  one  series  of  charged  holes,  and  b  another.  The  wires  on  the 
outside  are  attached  to  the  ends  of  the  entire  series,  as  in  the  previous  case, 

while  the  wire  from  the  central  screw 
is  attached  to  the  center  of  the  series 
of  connecting  wires  as  at  c.  By  this 
arrangement,  a  large  number  of  blasts 
can  be  fired  with  a  single  battery  and 
the  size  of  the  lead  wires  very  much 
reduced.  The  firing  is  accomplished 
by  lifting  the  handle  of  the  machine  to 
its  full  height,  and  pushing  it  down- 
wards with  full  force,  until  the  rack 
attached  to  the  handle  reaches'  the 
bottom  of  the  box  and  sends  the  cur- 
rent through  the  caps  in  the  holes.  When  firing  a  hole  by  means  of  a  blasting 
machine,  the  handle,  or  rack  bar,  should  never  be  churned  up  and  down,  but 
should  simply  be  given  one  vigorous  stroke,  as  directed.  Most  blasting 
machines  are  made  to  fire  with  a  downward  stroke,  but  some  fire  with  an 


FIG.  6 


EXPLOSIVES  AND  BLASTING  683 

upward  stroke  of  the  handle.  A  machine  should  always  be  kept  clean  and  never 
abused  and  played  with.  Its  strength  should  be  tested  from  time  to  time  by 
means  of  a  test  lamp  or  rheostat.  Test  galvanometers  are  used  to  ascertain 
if  any  breaks  exist  in  the  circuit  and  the  caps. 

In  Europe,  another  form  of  electric  blasting  machine  is  used.  These 
magneto  machines  consist  essentially  of  an  armature  revolving  between  the 
poles  of  a  set  of  permanent  magnets,  are  not  unlike  the  American  blasting 
machine  in  appearance,  and  are  used  in  very  much  the  same  way. 


FIG.  7 

Firing  With  Dry  Batteries. — Firing  charges  of  explosives  by  means  of  ordi- 
nary dry  cells  has  been  prohibited  in  foreign  countries,  because  premature 
firing  of  detonators,  and  sometimes  of  the  charge,  has  been  caused  by  the 
wires  coming  in  contact  with  the  poles  of  the  batteries.  Safety-contact  dry- 
cell  batteries  have  lately  been  introduced  in  the  United  States  and  abroad. 
They  are  made  with  a  spring-key  contact,  or  with  two  safety-spring  contact 
buttons,  which  are  the  poles  of  the  battery.  The  two  leading  wires  are  laid 
on  the  buttons,  which  are  at  the  same  time  pushed  downwards.  When  the 
pressure  of  the  thumbs  is  released  the  contact  is  broken.  If  the  wires  of  a 
detonator  accidentally  come  into  contact  with  the  poles  of  the  battery,  the 
current  cannot  be  discharged  unless  both  poles  are  pushed  downwards.  As 
these  dry-cell  batteries  are  cheap  and  easily  portable  in  comparison  with  the 
blasting  machine,  they  have  become  quite  popular,  but  those  without  safety 
contacts  have  been  the  means  of  numerous  fatal  accidents  through  premature 
explosions  due  to  the  unintentional  coming  in  contact  of  the  wires  with  the 
binding  posts  before  the  men  had  left  the  face,  or  when  carried  in  sacks  with 
the  explosives  and  detonators  through  a  contact  made  between  the  battery 
and  the  detonator  wires  resulting  in  an  explosion. 

Small  devices  such  as  these  can  be  used  to  fire  only  a  few  shots  in  one  circuit, 
as  those  in  a  single  room.  The  number  of  shots  to  be  fired  and  the  length  of 
the  leading  wires  and  other  conductors  must  be  known,  so  that  a  battery  of 
sufficient  capacity  may  be  selected.  The  strength  of  the  battery  may  be  tested 
by  passing  the  current  through  a  small  electric  lamp  of  known  capacity  and 
noting  the  brightness  of  the  light  given  by  the  lamp.  Or  the  battery  current 
may  be  passed  through  a  testing  circuit  whose  resistance  is  equal  to  that  of  the 
circuit  to  be  fired  and  which  has  in  it  one  electric  detonator,  which  must  be  put 
in  a  safe  place.  If  the  battery  fires  this  detonator,  it  is  strong  enough  and  is 
in  good  condition. 

Precautions  When  Firing  With  the  Electric  Blasting  Machine. — To  insure 
success  when  firing  blasts  by  electricity,  the  following  points  should  be  observed: 

1.  The  machine  wires  and  primers  should  be  suitable  to  each  other;  two 
kinds  of  primers  must  not  be  used  in  the  same  blast. 

2.  The  blasting  machine  should  be  of  sufficient  power  to  fire  all  the  caps 
or  primers  connected  at  one  time;  a  blasting  machine  must  not  be  loaded  to 
its  full  limit. 

3.  The  electric  caps  or  primers  should  be  kept  in  a  dry  place,  and  every- 
thing kept  as  clean  as  possible. 

4.  All  the  joints  at  connections  and  points  of  contact  of  the  wires  should 
be  well  made  so  that  the  wires  cannot  separate,  and  the  surfaces  should  be 
clean;  the  joints  in  one  wire  must  not  touch  those  in  another,  and  bare  joints 
must  not  touch  the  ground. 

5.  The  wires  must  not  be  kinked  or  twisted^so  as  to  cut  the  insulation 
during  the  process  of  tamping.     If  the  insulation  is  cut,  the  fuse  is  useless  for 
wet  ground  or  a  wet  hole  and  should  be  laid  to  one  side. 

6.  The  operator's  hands  should  not  touch  the  terminals  of  the  blasting 
machine  when  firing. 


684  EXPLOSIVES  AND  BLASTING 

7.  The  blasting  machine  should  not  be  connected  to  the  leading  wire  or 
cable  until  every  one  is  in  safety. 

8.  The  wire  connections  should  be  bound  with  insulating  tape  in  damp 
places  to  avoid  leakage  and  short-circuiting  of  the  current. 

9.  Before  firing  the  blast,  the  circuit  should  be  tested  by  a  galvanometer 
to  insure  that  there  is  no  break  or  short-circuit. 

Firing  From.  Dynamo  — Instead  of  obtaining  the  necessary  current  to  fire 
the  blasts  from  a  blasting  machine  or  a  dry -cell  battery,  it  is  a  very  common 
practice  to  derive  it  from  the  dynamo  used  in  the  power  plant  of  the  mine. 
While,  in  most  cases,  the  current  is  carried  into  the  mine  upon  special  wires 
known  as  the  firing  circuit,  the  practice  prevails  to  some  extent  of  connecting 
up  to  and  firing  the  shots  by  the  trolley,  or  haulage,  wires.  The  latter  practice 
is  extremely  dangerous  and  is  commonly  prohibited  by  law  because  the  power 
on  the  trolley  wires  is  always  much  more  than  is  required  to  fire  the  shots. 
There  is,  consequently,  a  certainty  of  arcing  and  a  probable  fusing  of  the  lead 
wire  on  account  of  its  small  size  and  high  resistance. 

In  some  cases  the  shots,  either  those  in  a  single  room  or  those  in  all  the  rooms 
in  a  district,  are  exploded  from  a  firing  station  or  from  a  number  of  firing 
stations  within  the  mine;  in  other  cases,  the  shots  are  fired  as  a  whole  from  a 
firing  cabin  on  the  surface  after  all  the  men  have  been  withdrawn  from  the 


Feed  line  from  Sub 

Pilot  Lamp"!1 
Trolley  from  Sub  Station-' 

Wire  to  shot 


fT^         A  Hlot  Lamp 

ition-"         J 

Trolley  and  shot  wire  to  mine) 


workings.  Fig.  8  shows  the  system  in  use  at  the  mines  of  the  Stag  Canon  Fuel 
Company,  Dawson,  N.  Mex.  As  the  men  enter  the  mine  they  are  required 
to  deposit  a  metal  check  at  the  shot-firing  house  outside,  near  the  entrance. 
These  checks  are  placed  on  a  check-board  and  returned  to  the  men  as  they 
come  from  the  mine.  A  record  of  the  working  place  of  each  check  number  is 
kept  in  the  shot-firing  house,  and  in  case  any  check  is  uncalled  for,  the  shot 
firer  makes  a  search  for  the  man  until  he  is  found.  No  shots  are  fired  until  it 
is  known  positively  that  no  one  is  in  the  mine.  The  method  of  placing  the 
shots  is  shown  in  Fig.  8.  To  insure  safety  against  accidental  discharge  of  the 
shots  by  electricity,  there  are  two  or  more  locked  switch  boxes  in  each  mine, 
with  throw-off  switches,  one  at  the  mouth  of  the  mine  and  at  one  or  more 
stations  inside  the  mine.  After  inspecting  the  inside  connections  with  the  shots 
to  be  fired,  the  shot  firer  en  route  from  the  mine  makes  connection  at  each  of 
the  switches  mentioned.  He  then  goes  to  the  shot-firing  cabin  to  turn  on  the 
electric  current,  but  before  doing  so  he  turns  on  an  electric  signal  light  in  a 
red  globe,  to  warn  all  persons  to  remain  away  from  the  vicinity  of  the  mouth 
of  the  mine;  so  that  should  an  explosion  occur  within  the  mine,  no  one  outside 
could  be  injured  by  flying  debris.  In  connection  with  this  system  of  shot 
firing,  the  company's  rules  provide  that  the  undercutting  must  extend  at  least 
6  in.  beyond  the  back  of  the  shot  holes;  that  all  shot  holes  must  be  at 
least  2$  ft.  deep;  that  all  dust  must  be  removed  from  the  shot  holes  before 
they  are  charged;  that  no  more  than  five  sticks  of  powder  (which,  at  some 
mines,  is  in  excess  of  the  safe  limit)  shall  be  used  in  any  one  hole;  that  stand- 
ing holes,  or  parts  thereof,  must  not  be  recharged  ;that  holes  in  tight  corners 
must  be  at  least  1  ft.  from  the  rib  at  the  back  end  of  the  hole;  and  that,  in 
solid  faces,  shot  holes  must  not  be  more  than  6  ft.  apart  horizontally,  and  that 
not  less  than  two  such  holes  shall  be  fired. 


EXPLOSIVES  AND  BLASTING  685 

All  shot-firing  wires  should  be  well  insulated.  The  size  of  wire  used  is 
commonly  No.  6  on  the  principal  line  along  the  main  entry;  from  a  No.  8  to  a 
No.  12  on  the  cross-,  butt-,  or  side  entries,  depending  on  their  length;  and  a 
No.  14  for  the  room  connections.  The  connections  between  the  cross-entry 
lines  and  the  main  line  and  between  the  rooms  and  cross-entry  lines  are  made 
in  parallel  so  that  the  failure  of  the  shots  to  explode  on  a  cross-entry  or  in  any 
room  or  rooms  on  a  cross-entry,  will  not  prevent  the  detonation  of  any  others. 
When  two  or  more  shots  are  to  be  fired  in  the  same  room,  they  are  connected 
in  series.  The  connecting  up  of  the  shots  should  proceed  outwards  from  the 
working  faces  to  the  mine  mouth;  that  is,  the  detonator  wires  should  first 
be  connected  to  the  room  wires;  then  the  room  wires  to  the  cross-entry  wires; 
and,  finally,  the  cross-entry  wires  to  those  on  the  main  entry.  The  room 
connections  are  usually  permanent,  unless  it  is  desired  to  fire  shots  singly  from 
the  room  mouth,  but  the  connections  on  the  main  entry  with  the  cross-entry 
circuits  and  at  the  foot  of  the  shaft  are  made  by  switches.  These  switches 
are  contained  in  locked  boxes,  the  head  shot  firer  alone  being  trusted  with 
the  keys. 

When  preparing  for  blasting,  all  the  holes  in  all  the  rooms  on  No.  1  entry 
are  first  connected  to  their  respective  room  firing  circuits,  then  all  the  holes 
in  all  the  rooms  on  No.  2  entry  are  connected,  and  so  on  until  those  on  the 
innermost  entry  are  connected.  On  the  way  out  from  the  last  entry,  the  shot 
firer  opens  the  boxes  and  throws  in  the  switches  at  the  mouth  of  each  room 
entry.  At  the  foot  of  the  shaft,  or  at  the  drift  mouth,  the  final  switch  con- 
necting the  mine  and  firing  circuits  is  thrown  in.  The  current  from  the  dynamo 
is  then  applied.  After  the  shots  have  been  fired,  the  shot  firer  returns  to  the 
mine,  opening  the  various  switches  and  relocking  the  boxes  on  the  way.  At 
the  working  places,  an  examination  is  made  for  fire,  the  room  wires  are  placed 
out  of  the  way  of  the  loaders,  and  are  disconnected  from  any  detonators  that 
may  have  failed  to  explode;  the  mine  foreman  being  subsequently  notified 
of  the  location  of  any  misfires.  During  the  day  the  entire  shot-firing  system 
is  overhauled,  defective  insulations,  etc.,  are  repaired,  and  everything  made 
ready  for  the  work  of  the  following  shift. 

Firing  Single  Shots  From  the  Surface  — From  time  to  time  various  devices 
have  been  introduced  to  reduce  or  overcome  the  danger  of  a  coal-dust  explosion 
due  to  the  detonation  in  a  single  blast  of  the  very  large  amount  of  high  explo- 
sives (often  over  1,000  Ib.)  required  in  large  mines.  The  logical  procedure  is 
to  have  a  separate  circuit  from  each  working  place  to  the  firing  cabin,  but  the 
cost  of  installing  and  maintaining  the  400  or  more  wires  necessary  for  this 
purpose  in  a  mine  of  even  moderate  size,  is  prohibitory.  The  mine  may  be 
divided  into  two,  three,  or  four,  districts  with  the  same  number  of  firing  circuits 
and  four,  six,  or  eight  sets  of  wires,  but  beyond  this  subdivision  it  is  not 
usually  economically  possible  to  go.  In  a  recent  device,  what  are  known  as 
sparker  boxes  are  introduced  in  the  firing  circuit  at  the  mouth  of  each  room. 
The  main-line  wires  A  enter  the  box  in  the  usual  way  but  are  separate  from 
the  wires  B  connecting  one  box  with  another.  The  room  wires  C  are  also 
distinct  from  either  pair  of  wires  A  or  B.  By  pushing  a  button,  the  room 
wires  C  are  placed  in  circuit  with  the  entry  wires  A,  the  wires  B  to  the  next 
box  remaining  dead.  The  application  of  the  current  at  the  surface  detonates 
the  holes  in  the  room  and  at  the  same  time  releases  the  button  so  that  the 
wires  A  and  B  become  in  circuit.  A  second  application  of  the  current  fires 
the  shots  in  the  second  room  and  arranges  the  mechanism  in  the  sparker  box 
at  its  mouth  so  that  the  current  may  pass  to  the  third  box,  and  similarly 
throughout  the  mine.  .  The  failure  of  the  shots  in  any  room  to  detonate  does 
not  interfere  with  the  current  passing  from  one  box  to  another.  According 
to  the  statements  of  a  Western  operator,  this  device  has  proved  successful 
at  his  mine. 

SUBSTITUTES  FOR  BLASTING  IN  DRY  AND  DUSTY 
MINES 

Before  the  introduction  of  permissible  powders  and  the  adoption  of  the 
various  safety  measures  used  in  connection  therewith,  numerous  substitutes 
for  powder  and  divers  means  of  bringing  down  coal  without  blasting  were 
tried  from  time  to  time  and  with  more  or  less  success. 

Wedging  Down  Coal  — The  plan  of  wedging  down  coal  has  been  employed 
until  quite  recently  and  has  its  uses  even  at  present.  The  seam  is  undercut 
in  the  usual  way,  and  a  series  of  drill  holes  but  a  short  distance  apart  are  placed 


686  EXPLOSIVES  AND  BLASTING 

in  a  horizontal  row  near  the  roof  in  thin  seams  or  between  the  roof  and  the 
floor  in  thick  ones.  If  the  seam  has  a  pronounced,  bedding  plane,  an  inter- 
stratified  layer  of  slate,  or  another  line  of  weakness  along  which  it  splits  readily, 
the  holes  should  be  drilled  in  it.  Wedges,  placed  in  the  holes  and  driven 
home  by  blows  of  a  sledge  will  bring  down  the  coal  in  large  lumps.  Other 
things  being  equal,  the  nearer  the  drill  holes  to  one  another,  the  easier  is  the 
coal  brought  down.  If  the  coal  is  thin,  hard,  and  blocky  and  adheres  strongly 
to  the  roof,  wedges  will  not  work  well,  as  the  coal  will  break  off  short  and  but 
1  in.  or  so  in  depth  of  the  face  will  be  removed  at  each  application  of  the  wedges. 
If  the  coal  is  soft,  the  wedge  will  be  driven  in  flush  with  the  face  and  will  merely 
enlarge  the  size  of  the  drill  hole  without  bringing  down  any  part  of  the  seam. 
Seams  having  a  tendency  to  split  horizontally  along  a  bedding,  or  other  plane, 
are  best  adapted  to  wedging. 

The  wedges  used  are  of  various  types.  The  common  form  is,  of  course, 
the  ordinary  single-piece  wedge.  The  device  known  as  plug  and  feathers, 
familiar  to  quarry  men,  has  been  largely  used.  This  consists  of  two  narrow 
triangular  pieces  of  iron  (the  feathers)  placed  on  opposite  sides  of  the  hole, 
between  which  a  long  wedge  (the  plug)  is  driven  by  blows  of  a  sledge.  As  both 
the  feathers  and  plug  are  tapered,  the  force  of  the  blow  is  multiplied.  To  still 
further  increase  the  force  of  the  blow,  multiple  wedges  have  been  used.  They 
are  essentially  the  same  as  the  device  just  described,  but  there  are  four  instead 
of  two  tapering  feathers  between  which  the  plug  is  driven  as  before.  In  a 
special  form  of  wedging  machine,  the  plug  and  feathers  are  introduced  in  the 
back  of  the  hole,  the  plug  being  drawn  forwards  by  a  combination  of  a  screw 
and  a  lever.  In  a  similar  machine,  in  order  to  reduce  the  friction  of  two  plane 
wedges  sliding  upon  one  another,  the  plug  is  made  to  run  upon  roller  bearings 
between  double  feathers,  and  is  drawn  forwards  from  the  back  of  the  hole  by 
the  action  of  a  screw  and  nut,  driven  by  a  ratchet  and  pawl. 

In  a  French  device  used  in  rock  work,  a  series  of  holes  are  drilled  in  a  group 
in  the  face.  The  drill  bit  is  replaced  with  a  hammer  head,  which  by  compressed 
air  drives  in  the  plugs  inserted  between  the  feathers  in  the  holes,  breaking 
down  and  splitting  up  the  rock. 

Hydraulic  Cartridge. — The  hydraulic  cartridge  has  been  in  use  in  many 
foreign  mines  for  several  years  past,  is  absolutely  safe  in  any  atmosphere,  and 
is  remarkable  for  the  large  proportion  of  lump  coal  produced  in  comparison 
with  blasting,  but  does  not  appear  to  be  adaptable  to  breaking  down  all  kinds 
of  coal.  The  cartridge  itself  is  a  forged-steel  cylinder  of  varying  length  and 
diameter,  and  having  eight  duplex  rams  or  pistons  arranged  in  a  row,  along 
one  side.  The  size  most  generally  in  use  is  21  in.  long  and  3  in.  in  diameter, 
and  the  expansion  of  the  duplex  piston  is  2J  in.,  giving  a  pressure  of  60  T. 
The  larger  sizes  are  used  only  in  very  narrow-entry  work  or  in  extremely 
thick  coal.  The  action  of  the  pistons  is  simultaneous,  the  pressure  being 
applied  through  the  longitudinal  passage  in  the  steel  cylinder  at  the  back  of 
the  pistons.  A  liner  of  sheet  iron,  <fa  in.  to  J  in.  thick,  1J  in.  wide,  and  22  in. 
long,  is  usually  introduced  in  the  lower  side  of  the  hole,  to  present  a  uniform 
bearing  surface  for  the  pistons  and  to  prevent  their  sinking  into  the  coal. 

In  the  original  machine  the  pressure  was  produced  by  the  operation  of  a 
lever  pump,  but  in  the  present  type  a  powerful  screw  pump  is  used  to  compress 
the  water  and  expand  the  pistons.  The  coal  having  been  undercut  and  the 
holes  drilled  as  near  the  roof  as  possible,  and  parallel  to  it,  the  cartridge,  shown 


FIG.  1 
33*1  IM 

in  Fig.  1,  is  inserted  in  the  hole,  the  pistons  being  telescoped  and  contained 
within  the  body  of  the  cartridge.  The  small  handle  attached  to  the  pump 
plunger  is  then  slowly  drawn  in  and  out  a  few  strokes  until  the  cartridge  is 
filled  with  water  from  the  small  reservoir,  which  is  connected  by  a  reinforced- 
rubber  tube,  and  pressure  is  reached,  the  quantity  of  water  thus  used  being 
about  1  i  pt.  The  valves  then  being  closed ,  the  screw  is  operated  by  the  handles 
and  the  compression  rapidly  increased.  As  the  pistons  are  forced  out  the  coal 


EXPLOSIVES  AND  BLASTING  687 

begins  to  work  and  crack,  and  as  the  maximum  expansion  is  approached,  it 
falls  in  large  lumps  rarely  exceeding  one-man  size.  The  release  valve  is  then 
opened,  the  water  returns  to  the  reservoir,  and  the  pistons  are  pushed  back 
ready  for  the  next  hole.  The  pipe  connecting  the  pump  and  cartridge  is  made 
in  any  required  length  suitable  to  the  depth  of  the  hole,  which  is  usually  about 
6  in.  less  than  that  of  the  undercut.  The  number  of  holes  necessary  depends 
on  the  thickness  of  the  seam,  the  nature  of  the  coal,  the  partings,  if  any,  and  the 
adhesion  of  the  roof  rock;  but  in  general  it  averages  one  hole  for  every  10  ft.  of 
face  in  room-and-pillar  work,  and  one  hole  for  every  30  ft.  of  face  in  longwall 
work.  The  length  of  time  necessary  to  bring  down  one  hole  varies  with  the 
location,  breaking-in  shots  requiring  from  10  to  15  min.,  and  free-end  shots 
from  3  to  5  min.  In  an  English  mine  where  38,263  thrusts  were  made  in  12  mo. , 
the  average  cost  of  breaking  down  the  coal  was  2&  mills  per  ton.  A  pressure 
of  3  T.  per  sq.  in.  is  usually  required  in  seams  up  to  4  ft.  thick,  and  this  gives 
a  total  pressure  of  60,  90,  and  150  T.,  respectively,  on  the  three  sizes  of  cart- 
ridges made. 

Lime  Cartridges. — The  expansion  of  quicklime  under  the  action 
of  water  has  been  used  to  some  extent  abroad  as  a  substitute  for  pow- 
der in  fiery  mines.  Ordinary  limestone  is  calcined;  that  is,  has  the 
carbon  dioxide  driven  off  by  burning  in  kilns,  and  is  ground  to  a  fine 
powder.  The  powder  is  compressed  hydraulically  into"  a  cartridge 
having  a  groove  running  down  its  side.  The  cartridge  is  about  5  in. 
long  and  2$  in.  in  diameter,  is  wrapped  in  paper,  and  is  kept  in  an  air- 
tight box.  The  seam  is  undercut  and  the  holes  drilled  in  the  cus- 
tomary way.  A  perforated  iron  tube,  $  in.  in  diameter  and  having  a 
small  external  chan  nelon  the  upper  side,  is  inserted  for  the  full  length  &- 
of  the  hole.  Several  cartridges  are  placed  in  each  hole,  the  grooves 
in  them  fitting  around  the  pipe,  and  the  rest  of  the  hole  is  tamped 
with  clay.  Water  is  forced  into  the  tube  by  means  of  a  small  hand 
pump,  and  the  water  acting  on  the  lime  greatly  expands  its  bulk, 
forcing  down  the  coal.  The  process  can  be  used  only  for  certain  classes 
of  coal,  and  much  care  must  be  taken  to  keep  the  cartridges  dry. 

Water  Cartridge. — The  water  cartridge  is  not  a  substitute  for  ex- 
plosives, but  is  a  means  of  using  them  in  a  less  dangerous  manner 
than  as  ordinarily  employed.  A  cartridge  of  high  explosive  is  placed 
in  a  skeleton  case,  a,  Fig.  2,  having  a  number  of  thin  metal  diaphragms, 
or  wings  b,  which  keep  the  cartridge  in  the  center  of  the  case  c  which  FIG.  2 
contains  water.  A  detonator  is  inserted  in  the  cartridge  and  its  wires 
connected  up  to  the  firing  wires  of  a  battery.  After  the  detonator  is  placed, 
the  outer  case  is  filled  with  water  and  its  mouth  tightly  tied  around  the  wires  d. 
There  is,  also,  a  guide  wire  e  used  to  keep  the  cartridge  lengthwise  in  the 
center  of  the  case.  The  apparatus  is  delicate,  requires  a  large  size  hole,  and 
materially  reduces  the  effect  of  the  explosive. 


GENERAL  CONSIDERATIONS  AFFECTING  BLASTING 

Definitions. — A  free  face,  or  free  end,  is  the  exposed  surface  of  a  mass  of  rock, 
or  of  coal.  Thus,  AB,  BC,  etc.,  are  free  faces  in  the  room  of  a  coal  mine  shown 
in  plan  in  Fig.  1,  and  represent  parts  of  the  coal  detached  from  the  main 
body  of  the  seam  by  blasting  or  undercutting.  That  part  of  the  seam  in  which 
the  shot  hole  6-7  is  placed  has  but  one  free  face  CD,  whereas  those  portions 
of  the  seam  in  which  the  holes  11-14  and  1-2  are  placed  have  two  free  faces 
AB  and  BC,  and  DE  and  EF.  In  the  latter  cases,  additional  free  faces  could 
be  secured  by  shearing  into  the  rib  in  the  direction  of  the  length  of  the  room 
at  A  and  F,  or  at  right  angles  to  the  room  at  C  and  D,  or  by  undercutting  the 
seam.  When  a  block  of  coal  has  the  maximum  number  of  free  faces,  six,  it  is, 
of  course,  entirely  detached  from  the  rest  of  the  seam. 

The  heel  of  a  shot  is  the  distance  1-E  from  the  mouth  of  the  drill  hole  to 
the  corner  of  the  nearest  free  face  ED;  or  is  that  portion  1-2  of  the  hole  that  is 
filled  with  the  tamping;  or  is  that  portion  1-2-5-E  of  the  coal  to  be  broken 
that  is  entirely  outside  the  powder. 

The  toe  of  a  shot  is  the  distance  3-4  from  the  inner  end  of  the  hole  to  the 
adjacent  free  face  measured  at  right  angles  to  the  direction  of  the  hole;  or  is 
that  portion  of  the  hole  2-3  that  is  filled  with  powder;  or  is  that  part  2-3-4-5 
of  the  seam  to  be  broken  lying  between  the  powder  and  a  free  face. 

The  line  of  least  resistance  is  the  distance  from  the  charge  of  powder  in  a  hole  to 
the  nearest  free  face.  In  the  case  of  the  hole  11-14,  the  line  of  least  resistance 


688 


EXPLOSIVES  AND  BLASTING 


is  1S-C.     In  the  hole  6-7,  the  line  of  least  resistance  is  not  the  line  7-8,  but  a 
shorter  line,  a  perpendicular  from  7  to  the  face  CD. 


FIG.  1 


A  dead,  hole  is  one  that  extends  into  the  solid  coal  beyond  that  part  that 
can  be  broken  by  the  maximum  safe  charge  of  explosive.  Thus,  the  hole  11-14 
is  dead  because  the  part  13-14  extends  into  the  solid  beyond  the  line  of  least 
resistance  13-C.  Sometimes  such  a  hole  is  spoken  of  as  being  dead  for  9  or  10 
or  any  number  of  inches,  depending  on  the  length  of  the  portion  13-14-  A 
definition  taken  from  the  mining  laws  of  a  Western  state  is:  "A  dead  hole 
is  a  shot  hole  so  placed  that  its  width  at  the  point  (toe),  measured  at  right 
angles  to  the  drill  hole,  is  so  great  that  the  heel  is  not  strong  enough  to  at 
least  balance  the  resistance  at  the  point  (toe)."  The  hole  1-3  would  be  dead 
if  the  point  3  was  so  far  to  the  right  of  its  indicated  position  that  the  explosion 
of  the  charge  would  fail  to  break  the  portion  of  the  coal  marked  1-3-4-E,  and 
would  result  in  a  blown-out  shot,  or  in  merely  breaking  off  a  part  of  the  heel. 
The  hole  9-10  drilled  directly  into  the  solid  is  a  dead  hole. 

A  gripping  hole  is  one  whose  direction  is  inclined 
away  from  the  adjacent  free  face,  or  may  be  denned 
as  one  whose  width  at  the  toe  is  greater  than  at  the 
heel.  In  the  figure,  both  6-7  and  1-3  are  gripping 
shots.  The  degree  of  grip  is  indicated  by  the  angle 
between  the  hole  and  the  face  it  is  intended  to  break. 
Thus,  in  the  hole  6-7,  the  greater  the  angle  7-6-8,  the 
stronger  or  greater  is  the  grip.  Similarly,  in  the  hole 
1-3,  the  greater  the  angle  between  the  lines  1-3  and 
E-D,  the  stronger  is  the  grip.  By  increasing  the 
angle  mentioned,  gripping  holes  become  dead  holes. 

In  a  balanced  shot,  the  width  of  the  toe  and  heel  are 
equal  and  are  less  than  the  length  of  the  drill  hole. 
The  shot  1-3  would  be  balanced  were  its  direction 
parallel  to  the  free 

face  E-D.   Similar- .a          « a        A 

ly,  the  shot  11-14™ 
would  be  balanced 
did  it  not  extend 
beyond  13.  A  bal- 
anced hole  will  do 
the  work  expected 
of  it  with  the  mini- 
mum expenditure  of 
powder. 

Note    that    the  FlG>  3 

definitions    of    the 


FIG.  2 


terms  used  in  connection  with  drill  holes  are  not  uniform  throughout  the 
country;  the  foregoing  are  believed  to  be  in  accord  with  general  practice. 

Effect  of  Free  Faces  in  Mining. — The  form  of  cavity  produced  when  a  single 
drill  hole  is  fired  in  a  mass  of  rock  having  one  free  face  is  usually  that  of  a  cone; 


FIG.  4 


EXPLOSIVES  AND  BLASTING  689 

thus,  in  Fig.  2,  if  ab  represents  a  vertical  drill  hole,  the  rock  broken  will  theo- 
retically have  the  form  cbd,  the  line  cd  being  the  diameter  of  the  base  of  a  cone. 
If  the  strength  of  the  explosive  is  not  sufficient  to  overcome  the  tenacity  of  the 
rock  to  so  large  an  extent  as  represented,  the  cone  might  have  the  form  ebf, 
or  igh.  It  is  more  than  probable  that  a  shot  hole  perpendicular  to  the  face  will 
break  no  rock  at  all  but  will  result  in  a  blown-out  shot,  as  it  is  in  the  worst 
position  to  do  effective  work.  This  is  because 
any  pressure  exerted  in  the  direction  of  m  or  n 
is  opposed  by  the  resistance  of  an  indefinite 
thickness  of  rock  and  the  line  of  least  resis- 
tance along  which  the  force  of  the  explosive 
naturally  will  act  will  be  the  resultant  of  the 
forces  acting  on  m  and  n,  or  in  the  line  of  the  " 
drill  hole. 

When  a  hole  is  inclined  to  the  face,  as  ab  f 
in  Fig.  3,  the  line  of  least  resistance  eb  is  per- 
pendicular to  the  face,  and  the  cross-section  of 
the  piece  of  rock  broken  out  will  be  approxi- 
mately of  the  form  abc  and  rarely  that  of 
dbc.  Commonly,  one  edge  will  coincide  with 
the  drill  hole  and  the  other  will  be  between 
the  lines  eb  and  cb.  The  angle  eab  is  usually 
about  35°  for  the  best  results,  and  45°  is  its 
limit.  Less  and  less  rock  will  be  broken  as  the  angle  becomes  less  and  when 
the  direction  of  the  drill  hole  ab  is  the  same  as  that  of  the  free  face  aci  that  is, 
when  the  powder  is  placed  on  top  of  the  ground,  no  rock  will  be  broken  out. 
Similarly,  as  the  drill  hole  becomes  more  nearly  perpendicular  the  less  will 
be  the  volume  of  the  rock  broken  and  when  the  hole  is  vertical  as  eb,  it  will, 
in  the  very  great  majority  of  cases,  result  in  a  blown-out  shot. 

The  more  free  faces  there  are,  the  greater 
£_  will  be  the  ease  with  which  an  explosive  will 
accomplish  its  work.  Fig.  4  is  a  cross-section 
showing  a  hole  ab  placed  in  a  rock  having  two 
free  faces  C  and  D.  If  there  were  but  the  one 
free  face  C,  the  force  from  the  charge  at  b  would 
break  out  the  cone  or  crater  ebg',  if  the  face  D 
were  the  only  one  exposed,  the  charge  b  would 
break  out  the  crater  ebj.  With  the  charge  b 
equally  distant  from  the  faces  C  and  D,  and  of 
just  the  right  size,  the  bounding  surface  between 
the  two  craters  will  coincide  in  the  line  be,  but 
as  the  force  of  the  explosion  at  b  is  divided  be- 
tween the  two  craters  and  a  portion  of  it  is 
reflected  by  the  solid  rock,  the  crater  actually 
broken  out  will  be  approximately  hbi;  that  is,  a  crater  that  is  not  equal  to  the 
sum  of  the  two  craters  ebg  and  ebj. 

If  the  charge  b,  Fig.  5,  is  located  so  that  bf  is  greater  than  ba,  the  force 
acting  on  each  face  separately  will  break  the  craters  gbk  and  jbl,  the  wedge- 
shaped  piece  ekbl  not  being  included  in  either.  With  the  charge  b  acting  on 
both  faces  C  and  D  together,  part  of  the  force  is  used  in  breaking  down  the 
mass  ekbl  and  the  crater 
broken  out  is  bounded 
by  the  lines ,hbi,  instead 
of  by  the  lines  gbj. 

Similar  reasoning 
may  be  applied  to  any 
increase  in  the  number 
of  free  faces.  The 
greater  the  number  of 
free  faces  the  larger 
the  amount  of  material 
that  can  be  broken 
down  with  a  single  shot;  or  what  amounts  to  the  same  thing,  a  smaller  charge 
will  do  the  same  amount  of  work,  the  greater  the  number  of  free  faces,  but 
the  increased  amount  of  material  loosened  will  not  be  proportional  to  the 
increase  in  the  number  of  free  faces. 

There  is  a  general  rule  that  the  longest  line  of  resistance  should  not  exceed 
three-halves  of  the  shortest  line  of  least  resistance  if  the  maximum  effect  of 
44 


D 


FIG.  5 


FIG.  6 


690 


EXPLOSIVES  AND  BLASTING 


the  explosive  is  to  be  obtained.  If  possible,  the  shots  should  be  placed  so  that 
the  shortest  line  of  resistance  is  horizontal  and  the  longest  vertical  so  that  the 
weight  of  the  rock  may  assist  the  breaking  down. 

It  is  evident,  therefore,  that  in  blasting  it  is  advantageous  to  have  as  many 
free  faces  exposed  as  possible,  not  only  on  account  of  the  decrease  in  the  amount 
of  powder  required,  but  also  because  it  is  possible  to  obtain  the  material  blasted 
in  larger  lumps  than  when  blasting  is  done  with  a  single  free  face.  This  is 
advantageous  particularly  in  coal  mining  where  the  lump  coal  is  more  valuable 
than  the  fine  coal. 

Fig.  6  represents  two  drill  holes  h,  V  drilled  at  a  distance  W  from  the  free 
faceA-B.  If  these  holes  are  fired  independently,  each  will  break  out  approx- 
imately the  same  amount  of  material,  as  mhn  or  nh'o.  If  they  are  fired  together , 


amount  of 

powder  required  to  break  the  two  masses  mhn  and  nh'o.  The  distance  D 
between  the  holes  must  be  varied  according  to  the  character  of  the  rock.  In 
comparatively  soft  material  it  is  less  than  in  hard  rock,  though  probably  the 
limit  is  twice  the  distance  W. 

Fig.  7  illustrates  another  case.  Here  three  holes  h,  h',  h"  have  been  drilled 
close  together,  and  each  one  loaded  with  a  charge  the  depth  of  which  will  be 
represented  by  HE.  Any  one  of  the  holes, 
if  fired  separately,  will  not  be  able  to  break 
through  the  distance  W,  but,  by  firing  the 
three  together,  the  mass  ehh"gg'GHe'e  may 
be  removed  at  one  shot.  By  this  means, 
greater  masses  of  rock  can  be  removed  with 
smaller  drilled  holes  than  is  possible  with- 
out the  combined  effect  of  the  several 
charges. 

The  form  of  cavity  and  the  amount  of 
material  dislodged  by  a  shot  are  largely 
theoretical  and  no  universal  rules  can  be 
given.  Experience  is  the  only  safe  guide 
in  choosing  the  location  and  size  of  the 
holes  and  the  amount  of  the  charge  of  ex- 
plosive, and  an  experienced  miner  will  study 
the  character  of  the  rock  to  be  blasted  so 
as  to  place  his  holes  at  such  an  angle  that 
he  may  get  the  maximum  effect  from  them 
and  avoid  blown-out  shots,  and  take  advan- 
tage of  slip  and  cleavage  in  the  rock. 

Diameter  of  Shot  Holes. — When  driv- 
ing tunnels  or  sinking  shafts,  holes  having 
a  diameter  between  J  and  1$  in.  at  the  bot- 
tom give  the  most  economical  results  in 


FIG.  7 


hard  rock  if  they  are  charged  with  the  strongest  of  the  high  explosives. 
When  the  rock  is  weaker,  the  explosive  should  be  of  less  strength,  but  the 
diameter  of  the  holes  should  be  increased  to  1$  to  2,\  in.  All  holes  should  be 
of  the  same  diameter,  each  should  have  an  equal  resistance  of  rock  to  work 
against,  and  each  should  be  so  placed  that  it  will  receive  the  greatest  benefit 
from  the  free  faces  formed  by  blasting  the  holes  previously  fired. 

Amount  and  Kind  of  Explosive. — The  maximum  pressure  or  effect  that  an 
explosive  can  develop  is  obtained  when  it  entirely  fills  the  space  in  which  it  is 
exploded;  hence,  the  greatest  efficiency  is  obtained  when  the  charge  fills  the 
hole  up  to  the  tamping.  There  are  no  rules  from  which  the  amount  of  explosive 
necessary  to  be  used  in  charging  a  given  hole  or  series  of  holes  can  be  deter- 
mined. If  the  right  amount  of  explosive  has  been  used  in  a  properly  placed 
hole,  upon  detonation  there  will  be  a  deep  boom  and  the  material  will  not  be 
thrown  with  great  force  from  the  solid.  If  the  charge  is  too  heavy,  there  will 
be  a  sharp  cracking  report  and  the  excess  of  explosive  will  throw  the  broken 
material  away  from  the  solid  and  will  shatter  it  badly.  If  insufficient  explosive 
is  used  or  the  hole  has  been  badly  placed,  the  rock  will  not  be  broken,  but  the 
tamping  will  be  blown  from  the  hole,  resulting  in  a  blown-out  shot.  The  depth 
of  the  hole  is  to  be  considered  when  estimating  the  amount  of  powder  to  be 
used  as  a  shallow  hole  requires  less  powder  than  a  deep  one.  In  some  parts 
of  the  bituminous  coal  field,  where  the  seam  is  of  moderate  hardness  and 
from  4  to  6  ft.  thick,  it  is  a  common  practice  to  make  the  holes  from  2  to  2*  in. 


EXPLOSIVES  AND  BLASTING  691 

in  diameter  and  to  charge  them  with  2  to  6  Ib.  of  black  powder.  Two  Ib.  of 
black  powder  is  not  an  excessive  amount  in  a  well-balanced  hole,  but  any 
weight  over  this  is  dangerous,  particularly  if  the  mine  is  noticeably  dusty  or 
gaseous. 

The  length  of  the  charge  of  explosive  for  single  holes  should  not  exceed 
from  eight  to  twelve  times  the  diameter  of  the  hole;  that  is,  a  1-in.  hole  should 
never  have  a  charge  of  more  than  12  in.  of  explosive  placed  in  it.  Where 
several  holes  are  fired  together  this  rule  is  sometimes  slightly  deviated  from. 
It  is  usually  best  to  employ  a  length  of  charge  between  these  two  limits,  as,  for 
instance,  about  ten  times  the  diameter  of  the  hole.  After  the  proper  relation 
between  the  diameter  of  hole  and  the  length  of  charge  has  been  determined 
by  experiment  for  a  certain  diameter  of  hole  under  given  conditions,  it  is  safe 
to  conclude  that  the  same  ratio  of  length  of  charge  to  diameter  may  be  taken 
for  other  diameters.  Thus,  if  it  has  been  found  that  for  a  hole  2  in.  in  diameter 
the  best  results  are  obtained  from  a  charge  24  in.  long  (2X12),  it  may  be 
assumed  that  in  a  hole  2£  in.  in  diameter  the  charge  should  be  25X12  =  30  in. 
long.  If  the  diameter  of  the  hole  ab,  Fig.  4,  remained  the  same  and  the  length 
of  the  line  of  least  resistance  was  increased,  a  place  would  soon  be  reached 
where  the  charge  of  explosive  would  fail  to  break  out  the  rock.  It  is  not  good 
practice  to. have  a  powder  charge  occupy  more  than  one-half  the  hole;  hence, 
in  order  to  increase  the  effect  of  a  charge  the  diameter  ab  of  the  hole  should  be 
increased;  that  is,  as  the  distance^  increases,  the  diameter  of  the  hole  ab  must 
be  increased;  or  there  must  be  a  chamber  formed  at  the  lower  end  of  the  hole 
in  which  the  powder  charge  is  to  be  contained,  so  as  to  increase  the  size  of  the 
cone  of  throw  toward  any  free  face.  This  chamber  is  sometimes  formed  by 
using  some  form  of  expansion  bit  or  reamer,  but  the  usual  custom  is  to  introduce 
a  small  charge  of  high  explosive  that  will  enlarge  the  end  of  the  hole.  By 
continuing  this  process,  an  opening  of  sufficient  size  to  contain  the  desired 
charge  may  be  formed.  This  operation  is  called  chambering  or  squibbing. 
Where  large  masses  of  soft  material  are  to  be  loosened,  it  is  common  practice 
to  use  dynamite  or  nitroglycerine  for  chambering  the  hole  and  black  powder 
for  the  blasting.  Holes  are  sometimes  drilled  as  much  as  20  ft.  deep  and 
several  kegs  of  powder  introduced  into  the  chamber  formed  by  firing  the  high 
explosive.  This  method  of  blasting  is  used  in  open-cut  ore  mines,  milling, 
and  in  steam-shovel  mines;  also  in  side  cuts  of  earth works; 

When  mining  soft  cleavable  minerals,  powerful  explosives  are  not  generally 
used,  their  effect  being  to  shatter;  on  the  other 'hand,  in  tenacious  minerals, 
powerful  explosives  are  used  for  their  shattering  properties.  Less  powerful 
explosives,  such  as  gunpowder,  are  used  where  a  rending  action  is  desired,  such 
as  in  mining  coal,  but  they  are  not  desirable  in  tough  ore  formations,  because 
they  break  down  the  mineral  in  large  pieces  that,  to  be  handled,  must  be 
block-holed  and  reblasted. 

While  the  power  of  most  explosives  can  be  calculated,  the  theoretical  power 
can  never  be  obtained  in  practice."  The  factors  that  enter  into^  the  problem 
vary  so  widely  and  are  so  numerous  that  seldom  can  exactly  similar  results 
be  obtained  from  blasts  fired  apparently  under  similar  conditions. _  The  weight 
of  a  mass  of  rock  opposes  the  action  of  a  blast,  and  this  weight  is  assisted  by 
the  atmosphere  that  presses  on  it  with  a  weight  of  14.7  Ib.  per  sq.  in.  at  sea 
level.  If  the  hole  is  damp  or  wet  or  the  rock  cold,  the  heat  produced  by  the 
discharge  and  the  power'  of  the  explosive  will  be  decreased.  Slips,  joints,  and 
cleavage  planes  affect  the  blast,  as  do  also  texture  and  structure  of  the  rock 
The  shape  and  location  of  the  drill  hole  and  the  method  with  which  it  is 
charged  and  tamped  are  important  factors. 

Brittle  rocks  are  easily  fractured,  while  strong,  compact  rocks  in  which  the 
cohesive  powers  are  great  are  much  harder  to  break.  Plastic  materials,  like 
fireclay,  which  are  neither  brittle  not  tenacious,  are  very  difficult  to  blast. 

Fissures,  or  joints,  and  bedding  planes,  when  open,  have  something  the 
effect  of  free  faces,  and  as  a  consequence  they  influence  _the  best  position  for 
placing  a  blast.  When  possible,  the  charge  of  explosive  should  never  be 
placed  in  contact  with  a  fissure  or  bedding  plane,  but  should  be  located  in  the 
firm  rock,  in  order  to  avoid  the  escape  of  the  gases  through  the  fissure,  that 
would  thus  reduce  the  effect  of  the  blast.  If  it  is  possible  to  avoid  it,  a  drill 
hole  should  not  cross  crevices  and  slips. 

In  compact  and  brittle  rocks  the  limit  of  elasticity  is  soon  reached  and  they 
rupture  under  the  shock  of  exploding  charges  before  there  has  been  an  appreci- 
able enlargement  of  the  drill  hole.  With  porous  rocks  and  sand,  the  blast 
tends  to  solidify  the  rock  and  to  fill  empty  spaces,  thereby  increasing  the  size 
of  the  drill  hole  and  decreasing  the  force  of  the  explosion. 


692  SUPPORTING  EXCAVATIONS 


SUPPORTING  EXCAVATIONS 


INTRODUCTION 

The  various  methods  of  supporting  the  surface  overlying  a  seam  from  which 
the  coal  has  been  or  is  being  removed  may  be  roughly  divided  into  those  that 
use  natural  and  those  that  use  artificial  materials  for  the  purpose.  The  sole 
example  of  the  use  of  natural  means  is  afforded  by  the  familiar  American 
room-and-pillar  system  of  mining  in  which  natural  pillars  of  coal  are  left,  in 
the  course  of  working,  either  to  support  the  overlying  rock  indefinitely  or. 
throughout  the  life  of  the  mine.  There  are  numerous  examples  of  the  second 
method;  the  use  of  wood  or  steel  posts  or  beams,  called  timbering;  the  use  of 
built-up  packs,  cribs,  etc.,  of  timber,  stone,  or  timber  and  stone;  and  the 
flushing  of  culm  into  the  workings. 

A  distinction  must  be  made  between  the  methods  and  materials  used  for 
supporting  the  surface  lying  several  hundred  or  several  thousand  feet  above  the 
coal  bed,  and  those  used  to  support  the  roof  or  that  portion  of  overlying  rocks 
usually  but  1  to  2  ft.  thick  or  in  rare  cases  as  much  as  40  ft.  The  use  of  wooden 
or  steel  timbering  is  confined  to  supporting  the  comparatively  thin  roof  rock, 
whereas  pillars  of  coal,  built-up  cribs,  and  flushing  are  resorted  to  to  sustain 
the  weight  of  the  many  hundred  feet  of  rock  between  the  coal  bed  and  the 
surface.  

COAL  PILLARS 

GENERAL  CONSIDERATIONS  AFFECTING  SIZE  OF  PILLARS 

Amount  of  Pillar  Coal. — The  amount  of  coal  left  in  the  pillars  for  the 
support  of  the  workings  is  generally  expressed  as  a  percentage,  or  a  certain 
portion,  of  the  total  volume  of  the  bed  within  the  area  included  by  the  pillars. 
The  term  pillar  coal,  therefore,  includes  not  only  the  coal  left  in  the  room  pillars, 
but  also  that  left  in  the  pillars  supporting  the  entries.  The  amount  of  coal 
left  in  the  pillars  in  the  first  working  varies  widely  under  different  conditions, 
but  the  best  practice  now  counts  on  ample  pillars  in  the  first  working  so  as  to 
minimize  the  danger  from  squeezes.  Many  of  the  collieries  in  the  anthracite 
region  of  Pennsylvania  are  now  extracting  but  one-third  of  the  coal  in  the  first 
working,  leaving  two-thirds  of  all  the  coal  as  pillars  to  be  taken  out  later  as 
the  different  sections  of  the  mine  are  worked  up  to  the  limit.  In  many  of  the 
mines  in  the  Connellsville  region  of  Western  Pennsylvania,  the  rooms  are  only 
12  ft.  wide  and  the  pillars  from  60  to  72  ft.  wide,  so  that  only  one-fifth  to  one- 
sixth  of  the  coal  is  taken  out  in  the  first  working,  but  the  removal  of  the  pillars 
begins  as  soon  as  the  rooms  have  been  driven  their  full  length. 

The  proportion  of  coal  left  in  the  pillars  along  the  entries  to  the  amount 
of  coal  taken  out  in  mining  the  entries  is  relatively  larger  than  the  percentage 
of  pillar  coal  between  the  rooms,  as  the  entry  pillar  sxusually  have  to  stand  a 
much  longer  time  than  the  room  pillars. 

The  amount  of  pillar  coal  left  depends  on  the  method  of  working  the  mine, 
on  the  nature  of  the  coal,  the  top  and  the  bottom,  on  the  thickness  of  the  coal, 
and  the  depth  of  cover,  and  on  the  time  of  drawing  the  pillars. 

Practical  Considerations  Determining  Size  of  Pillars. — It  is  impossible 
to  give  exact  rules  or  formulas  for  determining  proper  size  of  pillars  and  rooms 
that  will  be  universal  in  their  application.  Each  mine  is  a  special  problem, 
and  in  laying  out  the  rooms  and  pillars  it  is  well  to  find  out  what  is  the  success- 
ful practice  in  the  same  field  or  in  similar  fields  worked  under  the  same  condi- 
tions. Similar  practice  should  not  be  followed  blindly,  as  a  great  deal  of  the 
lack  of  progress  in  mining  has  been  due  to  this  copying  of  other  methods. 
Still  it  is  always  well  to  find  out  how  others  have  succeeded  and  why  they  have 
failed. 

In  general,  the  thicker  the  bed  and  the  greater  its  depth  below  the  surface, 
the  wider  must  be  the  pillars  and  the  narrower  the  opening.  This  rule  is  not 
invariable,  however,  for  certain  coals  deteriorate  very  rapidly  when  exposed 
to  the  atmosphere  and  the  pillars  must  be  much  larger  than  with  hard,  compact 
coals  under  similar  conditions. 


SUPPORTING  EXCAVATION'S  693 

The  length  of  time  that  a  pillar  must  stand  before  it  is  to  be  drawn  should 
be  considered  in  determining  the  width  of  the  pillar  required.  If  a  pillar  is 
to  be  drawn  in  a  short  time,  it  need  not  be  as  large  as  one  that  is  to  be  more 
permanent,  as  it  is  not  subject  to  the  disintegration  due  to  pressure  and  to 
atmospheric  effects. 

Extremely  large  pillars  are  usually  left  to  protect  surface  buildings,  and 
also  under  swamps  or  large  bodies  of  water,  to  avoid  any  possibility  of  a  break 
in  the  roof  through  which  the  water  can  enter  the  mine. 

Some  coals  are  of  such  a  nature  that  the  sides  and  corners  of  pillars  chip 
or  split  off  when  the  coal  is  opened  up,  due  to  the  disintegrating  effect  of  the 
atmosphere,  to  the  pressure  of  gas  in  the  coal,  or  to  the  pressure  of  the  roof. 
When  this  chipping  or  splitting  off  of  pillar  coal  occurs,  pillars  of  greater  area 
are  required. 

Strong  heavy  strata,  such  as  limestone  or  sandstone  above  the  coal,  that 
do  not  break  and  fall  easily,  act  as  a  lever  to  crush  the  edge  of  the  coal  pillar 
and  require  larger  pillars  to  prevent  creep  and  squeeze  than  where  the  pres- 
sure is  distributed  over  the  pillar  and  not  so  much  along  the  edge;  under  a 
friable  roof,  such  as  black  shale  or  slate,  that  breaks  and  falls  easily,  and  thus 
relieves  the  pressure  on  the  edge  of  the  pillar,  a  smaller  pillar  can  often  be  used 
than  under  a  strong  compact  roof,  which  brings  the  weight  on  the  edge  and 
constantly  chips  off  the  pillar.  With  a  strong  roof  that  does  not  break,  there 
is  danger  from  a  movement  of  the  strata  over  the  pillar  when  robbing  begins. 
A  soft  bottom  requires  a  large  pillar  to  prevent  the  heaving  of  the  bottom. 
Faults,  slips,  and  similar  geological  disturbances  in  the  roof  generally  increase 
the  size  of  the  pillars,  and  also  the  difficulty  and  danger  of  drawing  them. 

If  the  floor  is  soft  and  the  roof  hard,  a  creep  is  likely  to  occur,  and  in  such  a 
case  small  pillars  are  so  squeezed  down  into  the  floor  as  to  be  both  trouble- 
some and  expensive  to  remove.  If  the  floor  is  hard  and  the  roof  brittle,  the 
latter  will  fall  more  or  less  in  spite  of  all  efforts,  and  the  expense  of  cleaning  up 
and  timbering  is  heavy.  If  top  and  bottom  are  both  strong,  the  weaker  sub- 
stance— the  coal  if  left  too  long  or  in  too  small  an  amount — is  crushed,  and  its 
value  decreased  or  lost. 

If  the  seam  of  coal  is  gaseous,  the  length  of  the  pillar  is  decreased  on  account 
of  the  length  of  the  cross-cuts  or  breakthroughs  required  to  ventilate  the  rooms, 
thus  necessitating  a  wider  pillar  than  would  otherwise  be  required. 

While  it  is  desired  to  have  a  certairr  excess  of  strength  in  the  mine  pillars, 
the  expense  of  driving  long  cross-cuts  through  them  for  ventilating  the  open- 
ings, as  well  as  the  necessity  for  realizing  as  large  a  percentage  as  possible  of 
coal  in  the  first  working,  makes  it  desirable  in  many  cases  to  use  the  minimum 
width  of  pillar  required  for  the  safe  support  of  any  given  roof  pressure. 

When  the  room-and-pillar  system  is  used,  the  best  results  as  regards  the 
percentage  of  coal  won  from  a  coal  bed  are  undoubtedly  obtained  where  narrow 
rooms  are  driven  in  the  first  working  with  ample  pillars  left  between,  and  when 
the  pillars  are  withdrawn  as  quickly  as  possible  after  the  rooms  are  worked  up 
their  full  length. 

When  two  or  more  beds  are  worked  at  the  same  time,  the  width  of  pillar 
required  in  the  lowest  bed  will,  in  most  cases,  determine  the  maximum  width 
for  all  the  overlying  beds,  for  the  pillars  should  be  placed  with  their  center  lines 
vertically  one  above  the  other,  and  if  any  difference  is  made  in  the  size  of  pillars 
in  overlying  beds  the  lower  of  the  pillars  should  be  the  larger.  This  is  the  more 
important  the  closer  the  seams  are  together. 

The  inclination  of  the  seam,  although  decreasing  the  normal  pressure  or 
the  pressure  perpendicular  to  the  roof  and  floor,  gives  rise  to  a  tendency  of  the 
roof  to  slide  on  the  pillars  when  the  coal  is  removed.  This  tendency  greatly 
increases  when  the  work  of  drawing  the  pillars  is  begun,  especially  if  the  roof 
is  hard  and  fails  to  break.  Although  the  decreased  pressure  in  an  inclined  seam 
will  call  for  a  narrower  pillar  than  for  a  flat  bed,  the  tendency  of  the  roof  to 
slip  necessitates  an  increased  width  over  what  will  be  required  in  a  flat  bed 
with  the  other  conditions  similar. 

Depth  of  Cover. — The  depth  of  cover,  or  the  thickness  of  the  rocks  lying 
between  the  seam  and  the  surface,  is  the  prime  factor,  other  things  being  the 
same,  in  determining  the  size  of  coal  pillars.  The  table  on  page  694  gives 
the  weight,  in  pounds  per  cubic  foot,  of  the  coal-measure  rocks  of  the  United 
States.  For  practical  purposes,  the  weight  of  the  overlying  cover  may  be  taken 
as  160  Ib.  per  cu.  ft.  Thus,  every  12f  ft.  in  depth  of  cover  causes  a  weight  of 
1  T.  on  each  square  foot  of  pillar.  The  pressure  at  a  depth  of  100  ft.  will  be 
8  T.  per  squ.  ft.;  at  500  ft.,  40  T.;  at  1,000  ft.,  80  T.,  and  similarly  for  other 
thicknesses  of  cover. 


694 


SUPPORTING  EXCAVATION'S 


WEIGHT  OF  ROCKS  Crushing   Strength  of    Anthracite. 

The  following  table  gives  the 
crushing  strength  of  anthracite  as 
determined  by  experiments  made  under 
the  auspices  of  the  Engineers'  Club,  of 
Scran  ton,  Pa.  The  results  are  averages 
of  a  large  number  of  tests  made  on 
samples  from  a  number  of  different  beds 
and  from  different  parts  of  the  anthra- 
cite field.  The  test  pieces  were  right 
prisms  with  a  2  in.  square  base,  and 
of  heights  of  1,  2,  and  4  in.,  respec- 
tively, corresponding  to  a,  b,  and  c  in 
the  headings  in  the  table.  These  tests 
suggest  the  following  conclusions  in 
regard  to  the  samples  tested : 

Although  the  area  of  the  base,  or  the 
area  pressed,  is  the  same  in  each  case, 
the  total  crushing  load  and  the  crushing 
load  per  square  inch  are  not  the  same 

in  the  different  samples,  but  vary,  approximately,  inversely  as  the  square  root 
of  the  height  of  the  sample;  that  is  to  say,  sample  c  having  four  times  the 
height  of  sample  a  has  approximately  but  one-half  the  crushing  strength  of  the 
former.  Other  experients  indicate  that  similar  samples  (samples  whose  heights 
and  bases  are  proportional)  have  the  same  unit  crushing  load,  or  require  the 
same  crushing  load  per  square  inch  of  the  area  of  the  base,  and  the  total  crush- 
ing load  in  this  case  is  proportional  to  the  area  of  the  base.  For  example,  a 
cube  measuring  2  in.  on  a  side  requires  four  times  the  total  crushing  load 
required  by  a  cube  measuring  1  in.  on  a  side,  but  the  unit  crushing  load  or  load 
per  square  inch  of  the  area  of  the  base  is  the  same  in  each.  If  this  can  be  con- 
clusively proved  for  small  test  samples,  it  is  fair  to  reason  by  analogy  that  the 
same  rule  holds  for  mine  pillars,  so  that  if  the  strength  of  the  pillar  or  the  unit  load 
supported  is  constant  for  similar  pillars,  a  pillar  40  ft.  wide  in  a  seam  20  ft.  thick 
has  the  same  strength  as  a  10-ft.  pillar  in  a  5  ft.  seam;  or  a  60-ft.  pillar  in  a 

AVERAGE  COMPRESSIVE  STRENGTH  OF  ANTHRACITE 


Rock 

Weight  per 
Cubic  Foot 
Pounds 

Clay                  

115 

Earth  

100 

Gravel  
Limestone     •           .  . 

117 
165 

Sand  
Sand  full  of  water  .  . 
Sandstone 

117 
120 
150 

Shale  

162 

Slate  

175 

Sample  a 

Sample  b 

Sample  c 

Total  crushing  load,  in  pounds  
Crushing  load  per  square  inch,  in 
pounds 

23,000 
5  750 

16,348.000 
4087  000 

11,416.0 
2  854  0 

Load  producing  first  crack  in  sample 
in  pounds  

3  022 

2025000 

1  8750 

Height  h 

1 

2  000 

4  0 

V* 

1 

1  414 

2  0 

Approximate      relative      crushing 

strength—,—  =  
V/t 

Mi|.  --t 

.707 

.5 

15-ft.  seam  has  the  same  strength  as  a  40-ft.  pillar  in  a  10-ft.  seam;  the  unit 
load  supported,  or  the  load  per  square  foot  of  pillar,  being  the  same  in  each  case. 
Also,  if  this  be  so,  the  crushing  strength  of  any  coal  pillar,  per  square  inch, 
can  be  found  by  multiplying  the  crushing  strength  of  a  unit  cube  1  in.  on  a  side 
by  the  square  root  of  the  ratio  of  the  area  of  the  base  to  the  height  of  the  pillar. 
The  crushing  strength  of  the  unit  cube  as  given  by  these  experiments  is  4,000  Ib. 
The  unit  loads  producing  the  first  crack;  that  is,  when  the  coal  begins  to  scale 
off  on  the  outside  of  the  block,  are  approximately  one-half  of  the  unit  crushing 
loads  in  each  case,  except  in  sample  c,  where  the  height  of  the  sample  is  four 
times  the  width  of  the  base.  This  form,  however,  need  not  be  considered  in 
the  study  of  the  crushing  strength  of  mine  pillars,  which  usually  have  a  broad 
base  as  compared  to  the  height  of  the  pillar,  and  are  represented  more  closely 
by  samples  a  and  b.  Hence,  the  unit  load  producing  the  first  crack  in  mine 
pillars  may  be  assumed  as  one-half  of  that  obtained,  or  2,000  Ib. 


SUPPORTING  EXCAVATIONS  695 

Crushing  Strength  of  Bituminous  Coal. — There  are  no  figures  for  bituminous 
coal  similar  to  those  given  for  anthracite,  and  owing  to  the  great  variation  in 
the  character  of  different  bituminous  coals,  an  average  value  cannot  be  given. 
In  order  to  make  similar  calculations  for  bituminous  coal,  tests  of  the  coal  from 
the  particular  mine  in  question  must  be  made. 

ROOM,  ENTRY,  AND  SLOPE  PILLARS 

Load  on  Pillars. — As  the  removal  of  the  coal  throws  the  total  load  on  the 
pillars,  the  roof  pressure  per  square  foot  on  the  pillars  is  increased  in  the  ratio 
of  the  total  area  of  the  opening  and  pillars  to  the  area  of  the  pillars.  In  the 
accompanying  illustration,  o  represents  the  width  of  an  opening  separated 
from  other  similar  openings  by  pillars,  the  width  of  each  pillar  being  w.  A 
weight  of  cover  equal  to  w-+-o  then  rests  on  each  pillar  w,  and  if  L  represents 
the  roof  pressure  or  load  per  square  foot  on  each  pillar, 


EXAMPLE. — Find  the  roof  pressure  at  a  depth  of  900  ft.  below  the  surface, 

when  the  rooms  are  driven 

on  70-ft.  centers  with  pillars     {feffiffiffl  A  ''. '  / T  "^_  Vj  r : :  i      ~£~~r '      ~ 
50  ft.    wide  between   them 
and  the  width  of  the  rooms 
is  20  ft. 

SOLUTION. — -In  this  case, 
d  =  900,  «>+o  =  70,  and  w 
=  50.  Substituting  these 
values  in  the  formula, 
L  =  160X900Xi8  =  201,6001b.  per  sq.  ft.;  201, 600  *  144-1, 400  Ib.  per  sq.  in.; 
201,600-7-2,000  =  100.8  T.  per  sq.  ft.  This  roof  pressure  must  be  below  the 
safe  crushing  strength  of  the  coal  if  the  pillars  are  to  stand  and  not  be  immedi- 
ately ground  to  powder. 

Strength  of  Pillars. — The  safe  strength  of  pillars  may  be  estimated  as 
one-half  or  one-third  of  the  squeezing  strength — that  is,  the  point  at  which 
the  first  cracks  appear-^-or  one-fourth  to  one-sixth  of  the  crushing  strength, 
according  to  the  conditions  of  mining;  that  is,  using  the  values  given  in  the 
table  on  page  694,  the  safe  load  for  anthracite  should  not  be  estimated  as 
greater  than  2,000-f-3,  say,  700  Ib.  per  sq.  in.  under  adverse  conditions;  or, 
under  more  favorable  conditions,  2, 000 -f- 2  =  1,000  Ib.  per  sq.  in.  Expressed 
in  tons  per  square  foot,  these  values  will  vary  from  50  to  70  T. 

If  the  conclusions  deduced  from  the  experiments  made  on  anthracite  are 
verified  by  other  experiments,  the  allowable  unit  load  on  a  pillar  of  anthracite 
may  be  expressed  by  a  formula  as  follows: 


in  which  S  =  unit  load  that  can  be  supported,  in  tons  per  square  foot; 
C  =  constant  expressing  safe  crushing  strength  of  a  unit  sample  of 

anthracite,  in  tons  per  square  foot; 
w  =  width  of  pillar,  in  feet; 
t  =  thickness  of  seam,  in  feet. 

EXAMPLE.  —  Find  the  safe  load  that  can  be  put  on  anthracite  pillars  having 
a  width  of  20  ft.  in  a  seam  5  ft.  thick. 

Solution.  —  Substituting  the  given  values  in  the  formula,  the  safe  load  on 
these  pillars  is  5  =  50  X  V^  =  100  T.  per  sq.  ft.  Ans. 

Width  of  Room  Pillars.  —  The  strength  of  mine  pillars,  or  the  safe  unit  load 
they  will  support,  must  be  at  least  equal  to  the  roof  pressure  or  load  per  square 
foot  resting  upon  them;  hence,  to  sustain  the  roof,  L  =  S.  Calling  the  percent- 

age of  room-pillar  coal  to  be  left  in  the  mine  J  (expressed  decimally),  J  —  —  ;  —  ; 

w-\-o 

multiplying  the  right-hand  side  of  the  equation  for  S  by  2,000  to  reduce  tons 
to  pounds;  and  equating  L  and  S,  and  solving  for  w, 
f    160  d    \2 


in  which         w  =  width  of  pillar,  in  feet; 

J  —  percentage  of  coal  in  room  pillars; 
d  =  depth  of  cover,  in  feet; 

C  —  constant  for  safe  unit  crushing  strength  of  coal; 
/  =  thickness  of  coal  seam,  in  feet. 


696  SUPPORTING  EXCAVATIONS 

The  percentage  of  pillar  coal  to  be  left  between  the  rooms  is  often  assumed, 
and  it  depends,  of  course,  on  the  relative  size  of  pillar  and  room  openings. 
The  safe  width  of  opening  is  best  determined  by  practical  experience  and 

In  the 'foregoing  equations  there  are  two  variable  quantities,  w  and  o,  which 
may  have  any  values.  Hence,  if  the  width  of  the  room  o  is  assumed,  the  value 
for  w  selected  must  satisfy  the  equations  for  both  J  and  w.  This  can  only  be 
accomplished  by  trial,  as  appears  from  the  following  example. 

EXAMPLE. — Assume  that  a  16-ft.  seam  of  anthracite  lying  600  ft.  below  the 
surface  is  overlaid  with  alternate  layers  of  shale  and  sand  rock.  Find  the 
width  of  pillar  that  should  be  left  between  the  rooms  if  the  rooms  are  made  20  ft. 

SOLUTION. — Assume  a  width  of  pillar  w  =  40  ft.  Substituting  this  and 
o  =  20  ft.  in  the  formula  for  J,  J  =  66|%.  Substituting  this  value  of  J  in  the 
second  formula,  w  =  23+ft.;  very  much  less  than  the  assumed  value  of  40  ft. 

For  a  second  trial,  assume  w  =  35  ft.,  whence  /  =  63  +  %,  and  a;  =  36.4  ft. 
This  second  value  is  close  enough  for  practical  purposes,  but  another  may  be 
made  by  placing  w  =  36  ft.,  whence  J  =  64  +  %  and  w  =  35.7  ft. 

From  this,  the  pillars  should  be  36  ft.  wide,  and  the  rooms  are  driven  on 
20+36  =  56  ft.  centers. 

For  bituminous  coal  of  medium  hardness  and  good  roof  and  floor,  a  rule 
often  used  is  to  make  the  thickness  of  room  pillars,  equal  to  1%  of  the  depth 
of  cover  for  each  foot  of  thickness  of  the  seam,  according  to  the  expression 

t    „ 


in  which  Wp  =  pillar  width; 

t  =  thickness  of  seam; 
D  =  depth  of  cover. 
Then  make  the  width  of  breast  or  opening  equal  to  the  depth  of  cover 

divided  by  the  width  of  pillar  thus  found,  according  to  the  expression  Wo  =  ^-, 

Wp 
where  Wo  =  width  of  room. 

Frail  coal  and  coal  that  disintegrates  readily  when  exposed  to  the  air,  and 
a  soft  bottom,  may  increase  the  width  of  pillar  required  as  much  as  50%  of 
the  amount  just  found;  also,  a  hard  roof  may  increase  the  same  as  much 
as  25%;  while  on  the  other  hand,  a  frail  roof  or  a  hard  coal  or  floor  may  reduce 
the  width  of  pillar  required  25%.  The  hardness  of  the  roof  affects  both  the 
width  of  pillar  and  width  of  opening  alike,  which  is  not  the  case  with  any  of 
the  other  factors. 

In  the  accompanying  table,  the  weight  thrown  upon  pillars  at  different  depths 
by  the  removal  of  different  proportions  of  coal  is  given: 

WEIGHT  ON  PILLARS  AT  VARIOUS  DEPTHS 


Percentage  of  Coal  Left  in  Pillars 

Depth 

Seam 

90 

80 

70 

60 

50 

40 

30 

20 

10 

Feet 

Weight  on  Pillars  in  Pounds  per  Square  Inch 

100 

111 

125 

142 

166 

200 

250 

333 

500 

1,000 

500 

555 

625 

710 

830 

1,000 

1,250 

1,665 

2,500 

5.000 

1,000 

1,111 

1,250 

1,428 

1,666 

2,000 

2,500 

3,333 

5,000 

10,000 

1,500 

1,666 

1,875 

2,138 

2,496 

3,000 

3,750 

4,998 

7,500 

15,000 

2,000 

2,222 

2,500 

2,956 

3,333 

4,000 

5,000 

6,666 

3,000 

3,333 

3,750 

4,384 

4,999 

6,000 

7,500 

4,000 

4,444 

5,000 

5,912 

6,666 

8,000 

5,000 

5,555 

6,250 

7,340 

10,000 

11,110 

12,500 

Slope  Pillars. — A  slope  should  have  a  pillar  along  its  full  length  and  theoreti- 
cally the  pillar  should  gradually  increase  in  width  from  top  to  bottom  as  the 


SUPPORTING  EXCAVATIONS  697 

thickness  of  cover  increases,  but  in  practice  this  is  seldom  done  and  the  slope 
pillar  is  the  same  width  throughout.  The  frequency  of  squeezes  on  slopes 
indicates  that  this  is  faulty  practice.  The  width  of  the  slope  pillar  is  some- 
times prescribed  by  law. 

There  is  not  much  danger  of  the  draw  destroying  a  slope  sunk  in  the  coal, 
except  that  due  to  mining  in  an  underlying  seam,  because  the  line  of  the 
slope  is  in  the  same  plane  as  the  bed  in  which  the  mining  is  done  and  nearly  at 
right  angles  to  the  plane  of  fracture,  whereas  in  a  shaft,  the  lines  of  fracture 
may  reach  or  cross  the  line  of  the  shaft,  and  in  a  pitching  seam  this  danger  is 
even  greater  than  in  a  flat  seam. 

Entry  Pillars. — Much  that  has  been  said  with  reference  to  room  and  slope 

The  chief  factors  determin- 
thickness,  and  character 

opening.  The  size  of  entry  pillars,  as  of  room 
pillars,  is  determined  almost  entirely  by  practical  experience.  The  best 
practice  advises  leaving  large  pillars  about  the  entries  and  all  airways  so  as  to 
avoid  all  possibility  of  a  squeeze. 

SHAFT  PILLARS 

Great  diversity  of  opinion  exists  among  mining  authorities  as  to  the  size 
of  shaft  pillars  and  the  matter  must  be  decided  largely  by  local  considerations 
and  practical  experience  in  the  district  in  which  the  shaft  is  sunk.  The  shaft 
pillar  should  be  large  enough  so  that  the  effect  of  the  draw  cannot  reach  the 
shaft  or  the  buildings  on  the  surface  about  the  shaft  and  thus  interfere  with 
its  alinement.  The  same  general  rules  apply  to  shaft  pillars  as  to  other  pil- 
lars; namely,  in  general,  the  deeper  the  shaft  and  the  thicker  the  seam  the 
larger  must  the  pillar  be,  while  the  harder  the  coal  the  smaller  the  pillar. 

Pillars  in  Flat  Seams. — In  flat  seams,  the  size  of  the  shaft  pillar  required 
depends  chiefly  on  the  depth  of  the  seam  below  the  surface,  that  is,  the  depth 
of  cover,  and  to  a  less  extent  on  the  thickness  of  the  seam.     The  rules  given  for 
determining  the  size  of  the  shaft  pillar  afford  widely  varying   results,  owing 
to  the  varying  conditions  under  which  each  rule  was  formulated,  and  for  this 
reason  that  rule  should  be  employed  that  seems  best  suited  to  the  particular 
conditions  of  the  case.     These  rules  are  given  as  formulas  and  the  results 
obtained  by  applying  them  to  determine  the  shaft  pillars  required  at  depths 
of  300  feet  and  600  feet,  respectively,  are  tabulated  later. 
Let         D  =  diameter  of  round  pillar,  or  side  of  square  pillar,  in  yards; 
d  =  depth  of  cover,  in  yards; 
t  =  thickness  of  seam,  in  yards. 

Merivale's  Rule. — Diameter  of  circular  pillar,  or  side  of  square  pillar,  in 
yards,  is  equal  to  twenty-two  times  the  square  root  of  the  depth  of  the  shaft,  in 
fathoms,  divided  by  50. 


*  \2X50 

Andre's  Rule.  —  Minimum  diameter  of  circular  pillar,  or  side  of  square  pillar, 
35  yd.  to  a  depth  of  150  yd.;  add  5  yd.  for  each  25  yd.  of  additional  depth. 


(2) 


Wardle's  Rule.  —  Minimum  diameter  of  circular   pillar,  or  side  of  square 
pillar,  40  yd.  to  a  depth  of  60  falh.;  add  10  yd.  for  each  20  fath.  of  additional  depth. 

(3, 


Pamely's  Rule.  —  Minimum  diameter  of  circular  pillar,  or  side  of  square  pil- 
lar, 40  yd.  to  a  depth  of  100  yd.,  add  5  yd.  for  each  20  yd.  of  additional  depth. 

(4) 


Mining  Engineering  (London)  Rule.  —  Radius  of  circular  pillar,  or  half  side 
of  square  pillar,  in  yards,  is  equal  to  SO  yd.  plus  one-tenth  of  the  product  obtained 
by  multiplying  the  depth  of  shaft,  in  yards,  by  the  square  root  of  the  thickness  of 
the  seam,  in  yards. 


Z,  =  40+  (5) 

Foster's  Rule.  —  Radius  of  circular  pillar,  or  half  side  of  square  pillar,  in 
feet,  is  equal  to  three  times  the  square  root  of  the  product  of  the  depth  of  cover,  in 
feet,  and  the  thickness  of  the  seam,  in  feet.  _ 

(6) 


698  SUPPORTING  EXCAVATIONS 

Dron's  Rule. — Draw  a  line  enclosing  all  surface  buildings  that  should  be  pro- 
tected by  the  shaft  pillar.  Make  the  pillar  of  such  size  that  solid  coal  will  be  left 
in  all  around  this  line  for  a  distance  equal  to  one-third  of  the  depth  of  the  shaft. 

D  =  s+j  (7) 

in  which  5  =  diameter  of  circle,  or  side  of  square,  in  yards,  at  the  surface. 

Hughes's  Rule. — For  the  diameter  of  a  circular  pillar,  or  the  side  of  a  square 
pillar,  allow  1  yd.  for  each  yard  in  depth. 

D  =  d  (8) 

Central  Coal  Basin  Rule. — In  the  Central  Coal  Basin  of  the  United  States, 
for  shaft  mines  worked  on  the  room-and-pillar  method,  the  rule  is:  Leave 
100  sq.ft.  of  coal  for  each  foot  that  the  shaft  is  deep,  it  being  understood  that  a  main 
entry  of  average  width  is  driven  through  this  pillar.  If  the  bottom  is  soft,  the  result 
given  by  this  rule  is  increased  by  one-half. 


SIZE  OF  SHAFT  PILLAR  OBTAINED  BY  USE  OF  SEVERAL  FORMULAS 


Authority 

Diameter  of  Side  of  Pillar 
Yards 

Shaft  100  Yd. 
Deep 

Shaft  200  Yd. 
Deep 

Merivale                           

22.0 
35.0 
40.0 
40.0 
68.3 
84.8 
100.0 
100.0 
100.0 

31.00 
45.00 
60.00 
65.00 
96.50 
120.00 
166.66 
200.00 
142.00 

Andre  ;  .  . 

Wardle             

Pamely  

Mining  Engineering  (London)  *  

Foster* 

Dronf  

Hughes                                                  

Central  basin  

*The  seam  is  assumed  to  be  2  yd.  (6  ft.)  in  thickness. 

fAn  allowance  of  100  ft.  has  been  made  for  the  diameter  of  the  circle,  or  side 
of  the  square,  enclosing  the  buildings  on  the  surface. 

When  using  formulas  2,  3,  and  4,  negative  results  in  the  fractional  part  must 
be  rejected,  as  the  diameter  of  pillar  cannot  be  less  than  the  minimum  diameter 
or  side  allowed  by  the  rule.  For  example,  it  is  useless  to  apply  Andre's  rule  to 
depths  less  than  150  yd.,  Wardle's  rule  to  depths  less  than  60  fath.  (120  yd.), 
or  Pamely's  rule  to  depths  less  than  100  yd. 

The  foregoing  table  shows  clearly  that  no  hard-and-fast  rule  can  be 
given  for  determining  the  size  of  shaft  pillar  required  in  any  particular  case. 
The  rules  stated,  however,  determine  the  size  of  pillar  required  within  certain 
practical  limits,  and  suited  to  different  conditions  of  roof  strata,  and  are,  there- 
fore, useful  and  desirable.  The  presence  of  faults  or  slips  in  the  roof  makes 
larger  pillars  necessary. 

Pillars  in  Inclined  Seams. — The  inclination  of  the  seam  increases  the 
uncertainty  in  respect  to  the  draw  in  the  strata  overlying  the  seam,  making  it 
more  difficult  to  give  any  rule  of  universal  application.  The  general  practice 
in  regard  to  the  size  of  pillar  required  when  the  seam  is  inclined,  is  to  increase 
the  pillar  on  the  rise  side  of  the  shaft,  while  that  on  the  dip  side  of  the  shaft  is 
often  made  the  same  as  for  a  flat  seam.  To  what  extent  it  is  necessary  to 
increase  the  pillar  on  the  rise  side  is  largely  a  matter  of  experience  and  judgment 
in  particular  localities,  and  this  is  always  the  most  reliable  guide. 

One  method  is  to  calculate  the  extent  of  the  pillar  on  the  dip  side  of  the 
shaft  by  the  rules  given  for  flat  seams,  choosing  for  this  purpose  the  rule  that 
seems  best  suited  to  the  conditions  with  respect  to  the  character  of  the  seam 
and  overlying  strata.  The  diameter  of  the  circular  pillar,  or  the  side  of  a  square 
pillar,  thus  obtained,  will  give  the  width  of  the  pillar  measured  on  the  strike 


SUPPORTING  EXCAVATIONS  699 

of  the  seam,  and  half  of  this  width  will  give  the  extent  of  the  pillar  measured 
below  the  shaft  on  the  dip  of  the  seam.  Then,  calling  the  width  of  the  pil- 
lar D,  the  depth  of  the  shaft  d,  and  the  inclination  of  the  seam  a,  the  extent  of 

the  pillar  measured  on  the  pitch  of  the  seam  may  be  taken  as  —  +  j  d  sin  a. 

This  rule  is  arbitrary,  but  approximates  to  a  certain  extent  the  condition  rela- 
tive to  the  inclination  of  the  seam.  All  the  rules  and  formulas  given  for  deter- 
mining the  sizes  of  pillars,  both  in  flat  and  inclined  seams,  are  only  suggestive 
of  what  is  required,  and  must  always  be  modified  according  to  the  experience 
and  judgment  of  the  person  in  charge  of  the  work. 

PILLARS  FOR  MISCELLANEOUS  PURPOSES 

Pillars  for  Supporting  Buildings,  Etc. — Dron's  rule  for  shaft  pillars  is 
probably  the  most  practicable,  as  it  provides  for  a  given  pillar  of  coal  all  around 
the  buildings,  etc.,  to  be  supported. 

Reserve  Pillars. — Extra  large  pillars  of  coal  are  often  left  at  regular  inter- 
vals in  the  workings;  their  purpose  is  to  divide  the  mine  into  sections  or  districts 
so  as  to  localize  the  effect  of  any  squeeze  that  may  start  in  one  of  these  districts 
by  breaking  the  roof  at  the  reserve  pillar.  These  pillars  are  usually  equal  to 
the  width  of  one  room  and  two  pillars,  and  are  formed  by  not  driving  one  room 
as  called  for  by  the  plan  of  the  mine.  They  are  taken  out  before  the  entry  or 
gangway  is  abandoned. 

Chain  Pillar. — A  chain  pillar  is  usually  left  across  the  ends  of  a  group  of 
rooms  to  protect  the  gangway,  or  entry,  toward  which  the  rooms  are  being 
driven.  The  miners  frequently  drive  their  rooms  too  far  and  hole  through  into 
the  next  gangway  in  spite  of  the  precautions  that  are  taken  to  prevent  this 
occurrence.  To  avoid  the  possibility  of  rooms  being  driven  too  far  and  holing 
through  the  chain  pillar,  a  cut-off  room  is  sometimes  driven  parallel  to  the 
entries  or  gangways.  This  place  is  driven  wide  enough  to  avoid  the  expense 
of  yardage,  and  rooms  driven  from  the  next  gangway  are  allowed  to  hole  into 
it,  thus  avoiding  the  necessity  of  accurately  measuring  the  length  of  the  rooms 
and  of  carefully  watching  the  miners  to  see  that  they  do  not  exceed  the  limit 
allowed.  The  method  also  possesses  the  advantage  of  giving  a  regular  width 
to  the  entry  pillar  and  thereby  avoiding  the  loss  of  a  considerable  amount  of 
pillar  coal  when  these  entries  are  abandoned  and  their  pillars  drawn.  When 
drawing  back  an  ordinary  chain  pillar,  any  irregularity  in  the -width  of  the  pil- 
lar may  cause  a  loss  of  some  of  the  coal,  which  cannot  occur  when  a  cut-off 
room  is  driven  as  described. 

Barrier  Pillars. — The  laws  of  some  states  require  a  pillar  of  coal  to  be  left 
in  each  bed  of  coal  worked  along  the  line  of  adjoining  properties,  of  such  width, 
that,  taken  in  connection  with  the  pillar  to  be  left  by  the  adjacent  property 
owner,  it  will  be  a  sufficient  barrier  for  the  safety  of  the  employes  of_mines  on 
either  property  in  case  one  should  be  abandoned  and  allowed  to  fill  with  water. 
These  pillars  are  known  as  barrier  pillars.  The  width  of  such  pillars  is  deter- 
mined by  the  engineers  of  the  adjoining  property  owners  and  the  mine  inspec- 
tor in  whose  district  the  properties  are  located. 

An  arbitrary  rule  for  the  width  of  barrier  pillars,  adopted  by  a  number  of 
coal  companies  and  by  the  state  mine  inspectors  of  the  anthracite  districts 
of  eastern  Pennsylvania,  is  as  follows: 

Rule. — Multiply  the  thickness  of  the  deposit,  in  feet,  by  1%  of  the  depth  below 
drainage  level,  and  add  to  this  five  times  the  thickness  of  the  bed. 

Thus,  for  a  bed  of  coal  6  ft.  thick  and  400  ft.  below  drainage  level,  the  bar- 
rier pillar  will,  according  to  this  rule,  be  (6 X 400 X. 01) +  (6X5)  =  54  ft.  wide. 

The  Bituminous  Mine  Law  of  Pennsylvania  requires  a  thickness  of  1  ft.  of 
pillar  for  each  1J  ft.  of  water  head  if,  in  the  judgment  of  the  engineer  of  the 
property  and  of  the  district  mine  inspector,  this  thickness  is  necessary  for  the 
safety  of  the  persons  working  in  the  mine.  The  same  law  makes  it  lawful  for 
any  operator  whose  mine  is  endangered  by  an  accumulation  of  water  in  aband- 
oned workings  located  on  an  adjoining  property,  to  drive  a  drift  or  entry  pro- 
tected by  bore  holes,  across  the  barrier  line,  for  the  purpose  of  tapping  and 
draining  such  water,  and  makes  it  unlawful  for  any  person  to  attempt  to,  or  in 
any  way  to  obstruct  the  flow  of  such  water  to  a  point  of  drainage.  The  law 
also  provides  that  no  coal  shall  be  mined  within  50  ft.  of  any  abandoned  work- 
ings containing  a  dangerous  accumulation  of  water,  until  such  danger  has  been 
removed  as  described  above. 


700  SUPPORTING  EXCAVATIONS 

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SUPPORTING  EXCAVATIONS  701 

SQUEEZE  AND  CREEP 

When  the  roof  and  floor  are  strong  and  unyielding  and  the  pillars  are  insuf- 
ficient to  withstand  the  pressure  thrown  on  them,  they  are  filled  with  breaks 
and  cracks,  large  pieces  split  off,  and  the  pillars  are  finally  crushed  into  small 
coal  and  the  roof  comes  down.  This  is  known  as  a  squeeze,  thrust,  or  crush. 

When  the  material  composing  the  floor  or  roof,  or  both,  is  soft  and  weak 
and  the  pillars  left  are  too  small,  the  weight  on  them  causes  the  roof  to  sag  or 
the  floor  to  bulge  upwards,  or  both.  This  result  is  known  as  a  creep.  The 
soft  character  of  the  floor  or  roof  permits  the  pillars  under  the  enormous  roof 
pressure  either  to  sink  into  the  floor  or  to  be  forced  into  the  roof,  pressing  out 
the  softer  material,  which  fills  the  openings.  Fireclay  is  particularly  suscepti- 
ble to  creep,  and  many  of  the  fireclays  that  are  hard  when  dry  become  extremely 
soft  and  plastic  when  moist;  it  is  important  to  keep  such  a  clay  bottom  dry. 

The  terms  squeeze,  thrust,  crush,  and  creep  are  often  incorrectly  used 
synonymously.  A  squeeze  and  a  creep  may  be  going  on  at  the  same  time.  A 
squeeze  or  a  creep  does  not  generally  come  suddenly,  but  the  pillars  and  tim- 
bers usually  give  evidence  of  the  too  great  roof  pressure  by  cracking  and  by 
pieces  flaking  off  at  the  sides.  The  chipping  or  nicking  of  the  pillar  coal,  indi- 
cating that  the  pillars  are  too  small,  should  not  be  mistaken  for  the  gradual 
spalling  or  chipping  due  to  weathering  alone.  When  pillars  or  timbers  thus 
give  evidence  of  increased  pressure,  they  are  sometimes  said  to  be  taking  the 
weight.  The  coming  of  a  squeeze  is  often  first  told  by  the  departure  of  the 
rats  from  the  affected  area,  as  their  sense  of  hearing  is  more  acute  than  man's; 
next  the  coal  begins  to  crack;  and  then  the  timbers  split  and  crush. 

Stopping  a  Squeeze. — When  any  sign  of  a  squeeze  appears,  the  pillars 
should  be  reenforced  as  much  as  possible  by  wooden  chocks,  or  cribs,  as  here 
shown,  and  by  supports  of  any  kind  that  can  be  put  up  just  outside  of  the  part 
affected.  If  the  action  of  the  squeeze 
is  slow,  some  of  the  pillars  may  be 
removed  rapidly,  which  will  allow  the 
top  to  break  and  thus  relieve  the  stand- 
ing pillars  of  part  of  the  weight. 

The  treatment  of  a  squeeze  should 
be  determined  by  the  inspection  of  an 
accurate  and  complete  map  of  the 
workings.  If  the  disturbed  region  can- 
not be  isolated  by  timbering  and  build- 
ing strong  stoppings  in  all  the  roads 
round  about  it,  the  trouble  may  often 
be  stopped  with  little  expense  by  draw- 
ing out  some  of  the  timber  already  in  place,  and  throwing  the  weight  on  some 
small  outlying  patches  of  coal  that  can,  with  advantage,  be  sacrificed  to  save  the 
roads  and  pillars  of  the  district  affected.  In  many  cases,  such  trouble  can  more 
quickly  be  arrested  by  helping  it  than  by  trying  to  prevent  it.  When  once  the 
roof  becomes  unsteady  and  the  timbers  are  breaking  and  the  floor  is  lifting, 
a  force  is  operating  that  cannot  be  stopped  by  artificial  means;  it  can.  however, 
be  directed  by  assisting  it  to  find  relief  where  the  least  damage  will  be  done. 
If  the  roof  does  not  break  readily,  dynamite  should  be  used  at  different  points 
to  start  the  fall.  By  this  means,  the  power  of  the  squeeze  may  be  broken  and 
the  danger  of  its  spreading  to  adjacent  workings  lessened.  The  building  of 
large  cribs  to  avoid  the  disastrous  results  of  squeeze  often  acts  to  increase  the 
evil  rather  than  to  diminish  it,  especially  if  the  cribs  are  placed  at  points  where 
complete  settlement  is  desired.  The  cribs  are  not  easily  removed,  and  serve 
as  fulcrums  by  which  the  weight  is  carried  forwards  to  other  points.  As  per- 
manent supports  for  the  roof,  cribs  are  of  great  advantage,  but  care  should  be 
taken  to  break  the  roof  back  of  them  when  the  weight  comes  on,  in  the  same 
manner  as  over  entry  pillars,  by  the  use  of  shots  placed  in  the  roof  near  them. 
Confining  a  squeeze  to  a  certain  limit  is  a  difficult,  expensive,  and  dangerous 
operation,  requiring  the  utmost  skill  and  care  in  every  individual  engaged  in 
the  work. 

The  creep  will  continue  until  the  excavations  are  filled,  and  the  whole 
becomes  compact  enough  to  resist  the  weight.  This  sometimes  takes  many 
months,  but  it  is  a  sure  result,  whether  the  action  is  fast  or  slow.  A  creep  can- 
not be  resisted  unless  the  space  from  which  the  coal  has  been  removed  is  filled 
with  other  material  like  culm. 

Reopening  a  District  Closed  by  Squeeze. — Time  should  be  given  for  the 
complete  settlement  of  the  roof  before  any  attempt  is  made  to  reopen  a  dis- 
trict closed  by  a  squeeze,  for  if  work  is  begun  before  the  action  of  the  squeeze 


702  .  SUPPORTING  EXCAVATIONS 

has  wholly  ceased,  the  movement  will  begin  again  and  may  extend  to  other 
parts  of  the  mine.  The  work  of  reopening  is  expensive  and  seldom  pays  in  thin 
seams  unless  the  coal  is  very  valuable.  Where  the  entries  are  wholly  closed, 
it  is  often  possible  to  drive  a  new  entry  in  the  old  pillars,  or  even  across  the 
pillars. 

It  is  not  usually  economical  to  attempt  to  reopen  old  entries  closed,  or  par- 
tially closed,  by  squeeze,  as  a  larger  amount  of  material  must  be  handled,  and 
more  timber  will  be  required  than  when  a  new  opening  is  driven. 

In  the  treatment  of  creep,  it  is  usually  better  to  excavate  in  the  roof  and 
leave  the  bottom  undisturbed  as  the  bottom  often  keeps  working  and  fills  up 
about  as  rapidly  as  it  can  be  taken  out. 

Whenever  practicable,  the  work  of  reopening  can  be  done  to  better  advan- 
tage by  driving  a  pair  of  entries  beyond  the  affected  district,  and  coming  back 
on  the  coal.  By  this  means,  the  least  affected  portion  of  the  district  will  be 
reached  first  and  as  much  of  the  coal  recovered  as  is  found  desirable;  the  demand 
for  coal,  however,  will  not  always  permit  the  adoption  of  this  method. 


FLUSHING  OF  CULM 

In  the  anthracite  regions  of  Pennsylvania,  in  Europe,  and  in  South  Africa, 
worked-out  portions  of  the  mine  are  now  commonly  filled  with  refuse  mate- 
rial brought  in  on  streams  of  water.  This  is  done  not  only  to  support  the  roof 
over  the  workings  but  also  to  permit  the  recovery  of  the  coal  or  the  ore  which 
would  otherwise  have  to  be  left  in  the  pillars. 

Abroad,  the  material  used  for  filling  is  very  generally  sand,  but  in  Pennsyl- 
vania, the  culm,  or  fine  refuse  from  the  breakers,  washeries,  etc.,  is  commonly 
employed.  In  addition  to  culm,  ashes  from  the  boiler  house,  crushed  slate, 
and  the  like  are  employed,  either  alone  or,  preferably,  mixed  with  culm. 

The  plants  for  handling  culm  are  more  or  less  elaborate.     The  Dodson 

S'ant  cost  $7,473.42  with  a  capacity  of  flushing  119  T.  a  da.  and  the  Black 
iamond  plant,  with  a  daily  capacity  of  287  T.,  cost  $6,280.12.  They  usually 
consist  of  crushers  (where  needed),  troughs,  conveyers,  settling  or  mixing 
tanks,  and  in  some  instances  storage  tanks.  Where  culm  alone  is  employed, 
it  is  usually  brought  from  the  breaker  or  culm  bank  by  means  of  a  scraper 
conveyer  to  a  mixing  tank,  which  may  be  anything  from  a  simple  oil  barrel 
at  a  small  operation  to  extensive  wooden  and  concrete  tanks  at  the  larger  ones, 
If  a  number  of  openings  are  being  flushed  at  the  same  colliery,  the  mixing  tank 
is  generally  set  on  a  hill  and  is  made  of  large  size,  pipes  radiating  from  it  to  the 
various  bore  holes  through  which  flushing  is  going  on.  Where  coal  is  wet 
screened,  the  screenings  from  the  breaker  are  generally  caught  in  settling  tanks 
so  that  the  excess  water  flows  away,  the  dewatered  culm  alone  being  elevated 
to  the  central  mixing  or  distributing  tank.  At  the  Shenandoah  City  colliery, 
Shenandoah,  Pa.,  all  the  waste  material  from  the  breaker  is  sent  through  the 
mine.  The  slate  and  screenings  are  brought  out  on  separate  conveyers.  The 
screenings  are  dumped  directly  into  the  first  of  two  flights  of  conveyers,  which 
carry  them  to  a  distributing  tower  where  enough  water  is  added  to  flush  them 
into  the  mine.  The  slate  is  carried  first  to  a  No.  3  Williams  crusher  where 
everything  over  2f  in.  is  broken  and  then  conveyed  back  to  be  mixed  with 
the  breaker  screenings.  The  ashes  from  the  boiler  house  are  run  into  the  slate 
conveyer  so  that  the  lumps  of  clinker  may  be  broken  by  the  crusher  and  are 
thus  mixed  intimately  with  the  culm  and  slate.  When  the  breaker  is  not  run- 
ning the  ashes  pass  to  a  concrete  storage  bin  holding  1  wk.'s  supply,  from 
which  they  may  subsequently  be  flushed  when  the  breaker  is  running.  The 
composition  of  the  slush  or  sludge,  the  material  used  for  flushing,  is  50%  screen- 
ings or  culm,  44%  slate,  and  6%  ashes. 

The  amount  of  water  required  for  flushing  depends  on  the  material  being 
flushed,  the  pitch  of  the  seam  and  that  of  the  pipe,  and  the  distance  to  which 
the  sludge  has  to  be  carried.  At  West  Shenandoah,  the  proportion  between 
water  and  screenings  is  made  as  nearly  2  to  1  as  can  be  estimated.  At  this 
mine,  the  seam  pitches  45°  and  less  water  is  required  than  if  the  seam  was 
flatter.  At  the  Kohinoor  colliery,  565  cu.  yd.  of  culm  were  flushed  daily  with 
an  expenditure  of  water  of  from  67  to  334  gal.  per  cu.  yd.  of  culm;  an  average 
of  200  gal.  of  water  per  yd.  of  dry  material.  Experience  has  shown  that  from 
1$  to  If  Ib.  of  water  is  required  to  flush  1  Ib.  of  culm  to  level  and  down-hill 
places;  3  to  6  Ib.  of  water  to  1  Ib.  of  culm  to  flush  up-hill  for  heights  varying 
from  10  to  100  ft.  above  the  level  of  the  shaft  bottom.  Any  elevation  of  the 
pipe  very  materially  increases  the  amount  of  water  necessary.  Mr.  James  B. 


SUPPORTING  EXCAVATIONS  703 

Davis,  when  superintendent  of  the  Dodson  and  Black  Diamond  mines,  ascer- 
tained by  experiment  that  1  cu.  ft.  of  anthracite  ground  to  culm  can  be  flushed 
into  a  space  of  nearly  l£  cu.  ft.,  and  it  is  therefore  impossible  to  compress  the 
culm  more  than  one-third.  In  addition  to  acting  as  a  filling  and  a  support, 
to  prevent  squeezes  and  crushing,  flushing  has  been  advantageously  used  for 
fighting  and  sealing  off  mine  fires.  No  instance  has  been  recorded  where 
spontaneous  combustion  has  taken  place  in  the  flushed  culm. 

On  the  surface,  the  culm  is  generally  conducted  to  the  yari°us  openings 
through  which  it  enters  the  mine  in  wooden  troughs  lined  with  sheet  iron  or 
terra-cotta,  the  latter  being  preferred.  For  handling  culm,  wooden  pipe  is 
preferred  to  iron,  although  the  latter  is,  of  course,  largely  used.  The  life  of 
the  pipe  is  dependent  on  the  kind  of  material  passing  through  it  and  the  grade 
on  which  it  is  laid.  Breaker  screenings  and  culm  will  not  wear  a  pipe  as  quickly 
as  ashes  and  broken  slate.  A  6-in.  iron  pipe  laid  at  West  Shenandoah  colliery, 
which  carried  crushed  slate  for  a  distance  of  1,500  ft.  on  a  considerable  grade 
was  worn  out  after  passing  16,000  cu.  yd.,  whereas  wooden  pipes  carrying 
breaker  screenings  have  lasted  1,  2,  and  3  yr.  Wrought-iron  pipe  is  often 
used  where  ashes  are  being  flushed  separately.  Wooden  pipes  should  be  turned 
after  being  in  one  position  for  a  certain  length  of  time.  On  very  light  grades, 
it  may  be  necessary  to  turn  them  every  6  mo.  On  steep  slopes,  they  had  better 
be  turned  every  few  weeks  to  distribute  the  wear  evenly  over  the  interior  and 
thus  lengthen  the  life  of  the  pipe.  The  life  of  wrought-irqn  pipe  depends  on 
the  nature  of  the  water  used  and  the  material  flushed.  With  fresh  water  and 
small  culm  from  the_  buckwheat  screen,  it  lasts  18  mo.;  when  carrying  culm 
from  the  bank,  ranging  from  dust  to  pea  coal  and  some  chestnut,  9  mo.;  and 
when  mixed  with  ashes,  6  mo.  The  smaller  the  material  the  better. 

The  sludge  is  usually  let  into  the  mine  through  bore  holes  sunk  with  a  rope 
drill  and  from  6  in.  to  8  in.  in  diameter,  although  the  opening  to  a  room  driven 
to  the  crop,  an  old  slope,  or  even  an  abandoned  shaft  have  been  used  for  the 
purpose.  No  rules  can  be  given  as  conditions  vary  at  each  mine. 

The  handling  of  the  culm  underground  will  also  vary  from  place  to  place. 
Basicly,  the  methods  are  the  same  in  that  brattices  or  dams  are  built  at  the 
mouths  of  the  rooms  or  headings,  the  sludge  let  into  the  excavations  through 
pipes  and  the  water  allowed  to  drain  off  through  a  pipe  in  the  dam,  leaving 
the  solid  material  behind.  If  the  sludge  can  be  let  in  at  the  tops  of  pitching 
breasts  it  is  naturally  the  best  way,  as  they  then  fill  by  gravity.  At  several 
mines,  gangways  have  been  driven  along  the  faces  of  a  series  of  pitching  breasts 
and  along  these  gangways  the  sludge  is  conveyed  in  pipes,  which  are  tapped 
at  the  face  of  each  room.  The  mouths  of  the  rooms  on  the  main  gangways 
are  blocked  with  heavy  bulkheads,  so  that  the  material  is  retained  in  the  desired 
place.  These  bulkheads,  or  batteries,  are  built  of  material  of  a  size  and  strength 
to  suit  the  pitch  of  the  seam.  The  steeper  the  pitch,  the  larger  the  props  and 
the  closer  together  are  they  placed.  On  pitches  of  20°  to  30°  and  upwards, 
12-in.  to  14-in.  and  larger  props  are  used,  set  2  ft.  apart  with  braces  between 
them.  Care  must  be  taken  to  place  the  props  with  their  inside  faces  in  line, 
so  that  the  lining  planks  can  be  securely  fastened.  The  lining  or  facing  con- 
sists of  a  double  layer  of  1^-in.  plank  securely  hitched  into  the  coal  and  all 
cracks  stopped  with  hay.  The  tops  and  bottoms  of  the  main  posts  are  hitched 
into  the  roof  and  floor  to  a  depth  proportionate  to  the  weight  they  will  have  to 
sustain. 

The  surplus  water  may  be  drained  off  in  various  ways.  At  some  mines, 
small  iron  pipes  are  inserted  in  the  bulkheads;  in  others,  it  merely  drains  off 
through  the  cracks.  At  Indian  Ridge  colliery  and  some  others,  the  water 
drains  off  in  wooden  pipes  placed  in  the  brattices.  These  pipes  are  made  of 
1-in.  boards  and  are  4  in.  square  inside.  On  their  sides,  saw  cuts  about  1  ft. 
long  are  made,  four  series  of  slots  being  made  in  each  board.  These  slots  allow 
the  water  to  pass  while  holding  the  culm.  Three,  four,  or  six  pipes  may  be 
placed  in  a  battery  as  desired.  Where  the  seam  has  not  much  pitch,  a  couple 
of  square-board  pipes  are  run  up  the  breast.  These  are  provided  at  the  upper 
end  with  an  upright  branch  pipe.  When  the  dewatered  material  reaches  the 
top  of  the  upright,  the  pipe  is  closed  with  a  board.  Where  the  seam  is  flat,  the 
flushing  pipes  are  fastened  along  the  roof  for  the  full  length  of  the  chamber. 
Then  as  the  chamber  fills  and  the  slush  rises  up  to  the  pipe,  a  length  of  pipe  is 
taken  off  and  the  flushing  continued.  In  this  case  the  seam  cannot  be  filled 
completely,  a  little  space  always  being  left  between  the  flush  and  the  roof. 
After  flowing  for  1  or  2  hr.  into  one  room,  the  slush  is  commonly  turned  into 
an  adjacent  room  for  the  same  length  of  time,  during  which  interval  the  first 
place  drains.  The  slush  is  then  turned  back  to  the  first  place  while  the  second 


704 


SUPPORTING  EXCAVATIONS 


one  drains.  A  room  having  a  pitch  of  5°  or  more  can  be  filled  with  slush  if  it 
is  poured  in  at  the  high  end.  If  ashes  are  used  alone,  a  pitch  of  10°  or  more  is 
needed,  as  ashes,  being  porous,  allow  the  water  to  drain  away  quickly  and  will 
not  flow  in  a  stream  as  readily  as  breaker  screenings.  In  caved  areas,  slush 
makes  an  excellent  filling  as  it  completely  fills  the  spaces  between  the  broken 

The  pipes  used  to  convey  the  sludge  underground  are  6  in.  in  size  and  will 
carry  any  material  coming  to  them,  as  the  sludge  has  to  pass  through  a  2  J-in. 
screen  placed  over  the  mouth  of  the  bore  hole.  A  common  trouble  in  flush- 
ing is  to  have  the  pipe  become  blocked.  This  will  happen  if  the  pipe  is  not  full 
of  clear  water  without  solids  before  flushing  is  begun,  and  if  the  pipe  is  not 
cleaned  out  with  clear  water  after  flushing  is  stopped.  Water  must  be  turned 
into  the  pipe  and  be  flowing  before  the  slush  enters  and  must  be  kept  flowing 
after  the  slush  is  stopped.  The  slush  should  be  so  mixed  that  there  is  a  con- 
stant uniform  flow.  Sudden  rushes  of  slush  are  likely  to  block  the  pipe.  To 
quickly  locate  a  block,  holes  are  bored  in  wooden  pipes  and  closed  with  plugs. 
The  pipe  is  likely  to  clean  itself  out  below  any  block,  and  by  knocking  the  plugs 
out  the  blocks  can  be  located  and  the  pipes  need  be  taken  apart  only  at  the 

When  roadways  are  cut  through  slush  the  sides  will  stand  without  tim- 
bering unless  they  become  water  soaked.  When  drawing  pillars  after  flushing, 
regular  systems  are  followed  as  much  as  possible.  One  method  is  to  take  out 
every  third  pillar,  and  it  is  mined  from  the  gangway  advancing,  ventilation 
being  maintained  by  means  of  a  door  on  the  gangway  and  a  brattice  up  to  the 
working  face,  as  no  breakthroughs  can  be  maintained.  The  coal  pillars  of  the 
original  working  are  now  the  rooms.  As  soon  as  one  is  drawn,  a  battery  is  built 
at  its  mouth,  and  the  empty  space  is  flushed.  When  one  pillar  is  drawn  the 
next  one  is  mined,  care  being  taken  that  the  pillars  on  which  work  is  being  done 
are  three  apart  and  that  all  rooms  in  between  are  flushed.  When  the  pillars 
are  irregular,  no  system  can  be  followed.  Pillars  in  underlying  seams  can  be 
taken  out  without  disturbing  those  in  seams  above,  but  it  is  better  to  take  them 
but  simultaneously  and  have  the  rooms  flushed  in  sections  one  over  the  other. 
When  removing  the  pillars  certain  precautions  have  to  be  followed.  In  doing 
this  the  face  of  the  pillar  along  the  gangway  is  attacked,  and  a  road  driven 
up  through  the  pillar,  splitting  it,  as  shown  at 
z  in  the  accompanying  illustration.  This  road 
may  be  the  full  width  of  the  pillar,  but  in 
general  it  is  necessary  to  leave  a  narrow  stump 
of  coal  on  either  side  to  keep  up  the  fine  flushed 
material  in  the  adjoining  breasts.  The  thick- 
ness of  this  supporting  coal  depends  entirely  on 
the  condition  of  the  flushed  material  behind  it. 
If  that  is  fine,  it  will  set  firmly  and  form  a 
compact  mass  that  will  not  run.  In  such  a 
case,  the  pillar  may  be  entirely  taken  out, 
leaving  a  vertical  wall  of  solidly  packed  flushed 
culm.  When  the  flushed  material  is  of  a  size 
larger  than  buckwheat,  it  will  not  set  com- 
pactly, but  will  run  when  it  is  opened  up,  and 
when  such  material  fills  the  adjoining  breasts, 
the  thin  pillar  of  coal  must  be  left  to  keep 
back  the  culm.  Timbers  are  placed  flush  up 
against  the  culm  or  the  coal  stumps,  as  the 
case  may  be,  and  if  there  is  a  tendency  for 
the  culm  to  run,  lagging  is  placed  behind  the 
timbers.  In  some  cases,  as  much  as  700  ft.  of 
timber  have  been  used  per  100  ft.  of  pillar  taken  out.  As  the  pillar  is  removed, 
the  top  settles  until  it  finally  rests  upon  the  flushed  culm,  and  as  the  weight 
from  the  top  and  the  pressure  from  the  sides  comes  upon  these  props,  they  are 
broken,  while  the  coal  that  has  been  left  will  also  be  crushed.  At  the  Black 
Diamond  colliery,  the  props  used  are  16  ft.  long,  and  at  this  colliery  the  top 
settles  about  4  ft.  if  the  flushed  material  is  packed  tightly  before  the  roof  pres- 
sure comes  on  it.  After  this  settling,  new  props  12  ft.  in  length  are  put  in  close 
up  against  the  culm  and  the  broken  stump  of  the  original  pillar,  and  they  serve 
to  keep  the  road  open  up  to  the  working  face. 

The  Mammoth  seam,  ranging  from  40  to  60  ft.  thick,  at  the  Kqhinoor 
colliery  is  being  mined  by  a  flushing  and  slicing  system.  A  room  is  driven  in 
the  bottom  bench  and  as  soon  as  finished  is  flushed  solidly  full.  With  the  top 


SUPPORTING  EXCAVATIONS  705 

of  the  flushing  as  a  floor,  about  10  ft.  more  of  coal  is  mined  out,  and  this  second 
space  again  filled  with  culm.  In  a  similar  manner  the  rest  of  the  seam  is 
sliced  out  and  the  openings  flushed  until  the  roof  is  reached.  In  working  the 
first  or  bottom  bench,  the  track  is  laid  on  the  regular  floor  of  the  seam,  but  in 
working  the  remaining  slices,  a  buggy  or  small  car  pushed  by  hand  is  used  to 
carry  the  coal  to  a  chute  through  which  it  is  dumped  into  the  regular  mine  car 
standing  on  the  gangway.  _ 

The  saving  from  flushing  of  culm  over  depositing  it  on  the  surface  varies 
for  the  ordinary  anthracite  colliery  from  $5  to  $15  per  da.  The  average  cost 
of  putting  in  stoppings  in  a  9  ft.  seam  is  given  by  Mr.  James  B.  Davis  as  $9.50, 
including  the  material.  

BUILT-UP  PACKS  AND  CRIBS 

While  the  term  pack  is  sometimes  applied  to  any  built-up  structure  of  stone 
used  to  support  the  roof  where  the  coal  has  been  removed  from  a  wide  area, 
the  word  should  be  restricted  in  its  meaning  to  the  walls  built  up  of  roof  slate, 
etc.,  used  in  longwall  mining  as  a  support  for  the  roadways.  In  this  system 
of  mining,  the  packs  must  be  carefully  built,  the  larger  and  flatter  stones  used 
for  facing,  and  all  of  them  bedded  in  fine  material  so  that  the  rock  pressure  may 
compact  the  pack  into  a  solid  mass.  The  face  stones  should  be  well  bonded, 
and  a  number  of  them  should  extend  back  into  the  center  of  the  pack  so  as  to 
bind  the  face  walls  and  prevent  their  bulging  out  when  the  weight  comes  on 
them. 

Cribs,  or  chocks,  consist  of  a  square  building  of  round  logs  built  in  log-cabin 
style  and  either  notched  into  each  other  or  pinned  together  at  the  ends.  The 
interior  is  closely  packed  with  loose  slate,  rock,  spalls,  etc.,  and  when  well  built 
cribs  offer  substantial  support  to  the  roof.  They  are  quite  commonly  employed 
to  strengthen  the  corners  of  pillars  that  have  been  left  too  small;  as  permanent 
supports  where  the  pillars  have  been  entirely  removed ;  and  to  cause  a  break  to 
the  surface  and  thus  stop  a  squeeze.  Cribs  are  of  almost  universal  employ- 
ment in  longwall  mines,  and  especially  in  those  where  there  is  a  scarcity  of  mate- 
rial from  which  to  build  the  necessary  packs.  Cribs  are  not  adapted  as  per- 
manent supports  if  the  seam  is  more  than  a  short  distance  beneath  the  surface, 
as  they  crush  and  may  even  be  ground  to  powder  under  the  enormous  pressure 
at  great  depths. 

Strength  of  Packs  and  Cribs. — In  1911,  Prof.  Frank  P.  McKibben  made  at 
the  Fritz  Engineering  Laboratory  of  the  Lehigh  University,  South  Bethlehem, 
Pa.,  a  series  of  important  tests  upon  the  crushing  strength  of  various  kinds  and 
forms  of  artificial  mine  supports.  These  investigations  were  undertaken  on 
behalf  of  Messrs.  William  Griffith  and  Eli  T.  Connor,  appointed  by  the  city  of 
Scranton,  Pa.,  to  investigate  mining  conditions  under  that  municipality  and  to 
suggest  methods  by  which  the  surface  might  be  supported  over  extended  areas 
while,  at  the  same  time,  mining  and  removal  of  coal  was  going  on  beneath. 

The  results  of  these  investigations  are  summarized  in  the  table  on  page  706, 
and  while,  naturally,  made  upon  structures  much  smaller  than  those  used  in 
actual  mining  operations,  give  an  excellent  idea  as  to  the  relative  value  of  the 
various  types  of  support  in  common  use.  It  will  be  noted  that,  in  a  general 
way,  the  tests  were  made  upon  two  types  of  support.  In  the  one,  the  sup- 
ports consisted  of  cribs  or  piers  of  rock,  or  of  rock  and  timber,  or  of  piles 
of  stone  which  were  free  to  expand  laterally.  That  is,  they  represented  on  a 
small  scale  the  larger  structures  frequently  built  in  open  places  in  the  mine 
upon  the  approach  of  a  squeeze.  The  other  type  represented  the  various 
methods  of  filling  in  which  the  material  used  as  a  support  is  contained  within 
the  confines  of  a  room  in  the  mine  and  is  not  free  to  expand  laterally,  being 
held  in  place  by  the  coal  in  the  ribs  and  face. 

Supports  of  the  first  class,  whether  artificial  structures  or  piles  of  loose 
material,  are  not  as  strong  as  those  of  the  second  class  except  for  small  amounts 
of  compression.  Under  heavy  pressure  and  a  consequent  high  percentage  of 
compression,  they  are  not  to  be  recommended  except  for  temporary  use.  It 
will  be  noted  that  circular  piers,  particularly  if  the  interstices  are  filled  with  fine 
shovel  stuff  so  that  the  voids  are  reduced  to  a  minimum,  are  much  stronger 
than  the  usual  square  or  rectangular  pier.  Timber  cogs,  while  stronger  than 
square  gob  piers,  are  of  short  life  owing  to  the  decay  of  the  wood,  which  is  par- 
ticularly rapid  in  warm,  humid  mine  atmospheres.  Concrete  piers,  as  in 
test  14,  give  most  excellent  results  up  to  a  pressure  sufficient  to  produce  about 
3%  of  compression  and  cracking,  beyond  which  very  little  increased  weight 
will  grind  them  to  powder.  Test  6' was  made  upon  slabs  of  sandstone,  such 

45 


706 


SUPPORTING  EXCAVATIONS 


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SUPPORTING  EXCAVATIONS  707 

as  would  result  from  shooting  down  the  roof  over  a  wide  area.  The  material 
was  not  packed,  stowed,  or  built  up  artificially  but  was  used  as  it  fell  and  proved 
as  good  a  support,  practically,  as  the  built-up  circular  gob  pier  used  in  test  2. 

Tests  7,  8,  and  9  represent  unstowed  material  resulting  from  shooting  down 
the  roof  in  a  room;  this  gives  much  greater  support  when  the  voids  are  filled 
with  fine  material;  in  fact,  is  as  strong  as  the  best  sand  flushing  under  the 
maximum  pressure.  It  will  be  noted  that  the  sand  flushing,  so  largely  used 
abroad,  affords  a  better  support  in  the  ratio  of  about  4  to  1  than  the  culm  flush- 
ing commonly  employed  in  the  United  States. 


TIMBERING  WITH  WOOD 

GENERAL  REMARKS 

Nature  of  Rock  Pressure. — The  weight  of  the  rocks  overlying  a  coal  seam 
exerts  both  a  major  and  a  minor  pressure  on  the  timbering.  The  major,  or 
greater,  pressure  is  practically  irresistible  and  is  due  to  the  weight  of  all  the 
overlying  rocks  from  the  coal  seam  to  the  surface,  and  at  a  depth  of  1,000  ft. 
is  equal  to  about  80  T.  per  sq.  ft.  It  cannot  be  supported  by  timbering  and 
cannot  be  entirely  resisted  by  flushing  culm  into  the  workings.  Solid  masonry 
or  concrete  will  alone  withstand  the  major  pressure.  The  minor  pressure  is 
caused  primarily  by  the  weight  of  the  draw  slate,  which  may  vary  from  a  few 
inches  to  several  feet  in  thickness,  producing  a  pressure  of  as  much  as,  say, 
500  Ib.  per  sq.  ft.  In  some  places,  to  the  weight  of  the  draw  slate  must  be 
added  that  of  from  5  to  40  ft.  of  so-called  soapstone,  which  crumbles  on  expo- 
sure to  the  weather  and  gradually  falls  until  some  solid  stratum  is  reached. 
If  as  much  as  40  ft.  thick,  this  will  cause  an  additional  pressure  of  some  3  T. 
per  sq.  ft.  It  follows  that  mine  timber  is  ordinarily  designed  to  withstand  a 
pressure  of  from,  say,  50  Ib.  to  3  T.  per  sq.  ft. 

Choice  of  Timber. — Timber  should  be  long  grained  and  elastic,  strong 
but  not  too  heavy  for  easy  handling  in  thick  seams  and  in  pitching  places. 
Elasticity  combined  with  the  proper  strength  is  of  prime  importance.  The 
timber  must  be  strong  enough  to  resist  the  minor  pressure  for  which  it  is 
designed  and  at  the  same  time  elastic  so  that,  while  resisting  the  minor  pres- 
sure, it  will  bend  without  breaking  and  give  warning  of  the  approach  of  a 
major  pressure  caused,  say,  by  a  squeeze.  Oak,  beech,  and  similar  hardwoods 
while  very  strong  are  heavy,  and,  being  short  grained,  are  not  elastic,  com- 
monly breaking  with  but  slight  bending.  The  softer  coniferous  woods,  such 
as  pine,  fir,  and  spruce,  possess  considerable  strength  and  great  elasticity  and 
make  the  most  desirable  mine  timbers.  Very  elastic  timbers,  such  as  cypress 
and  willow,  are  not  satisfactory  for  props  because  they  bend  like  a  bow  without 
offering  the  resistance  necessary  to  keep  the  draw  slate  in  place  even  for  a  short 
time. 

When  selecting  props,  the  principal  points  to  be  observed  are:  Straight- 
ness,  slowness  of  growth  as  indicated  by  narrow  annular  rings,  freedom  from 
knots,  indents,  resin,  gum,  and  sap. 

ROOM  TIMBERING  IN  FLAT  SEAMS 

Props. — Single  props  are  set  to  support  the  draw  slate  during  the  process 
of  removing  the  coal.  They  are  generally  made  of  natural  logs,  cut  and  sea- 
soned in  the  woods,  with  a  diameter  of  from  6  to  18  in.,  depending  on  the  weight 
of  the  roof  and  the  thickness  of  the  seam,  and  of  a  length  some  2  in.  less  than 
the  height  of  the  coal.  Where  the  seam  varies  in  thickness  in  different  por- 
tions of  the  mine,  props  of  proportionate  lengths  are  kept  on  hand. 

If  it  is  necessary  to  reduce  the  size  of  an  individual  stick,  it  is  usually  better 
to  split  than  to  saw  it  (thus  forming  a  split  prop},  especially  in  the  case  of  wood 
from  coniferous  trees,  as  splitting  does  not  destroy  the  sap  wood,  or  unduly 
injure  the  grain  or  fiber  of  the  stick.  If  a  prop  must  be  shortened,  the  ends 
should  be  sawed  off  square  and  parallel,  and  not  cut  with  an  ax. 

Props  should  be  straight,  have  square  ends,  rest  fully  and  firmly  on  the 
floor,  have  a  cap  piece  between  them  and  the  roof,  and"  be  set  perpendicularly. 

The  stronger  the  roof  is,  the  stronger  must  be  the  props  required,  because 
the  roof,  if  broken,  is  in  much  larger  pieces;  conversely,  where  the  roof  is  broken 
and  tender,  the  props  set  must  be  more  numerous,  and  if  these  must  be  set  so 
thick  as  to  interfere  with  the  carrying  on  of  the  work,  or  the  ventilation,  cross- 
bar sets  with  lattice-work  lagging  must  be  substituted. 


708  SUPPORTING  EXCAVATIONS 

Where  there  is  a  strong  roof  and  bottom,  the  props  should  be  set  so  as  to 
permit  the  roof  to  ease,  or  gradually  settle  down,  or  the  bottom  to  heave,  and 
thus  prevent  the  breaking  of  the  prop  or  prolong  its  usefulness  as  such.  Under 
such  conditions,  they  should  not  be  driven  very  tight  and  caps  of  soft  timber 
should  be  used,  otherwise  the  prop  will  be  bent  and  later  on  broken.  To  accom- 
plish and  extend  the  same  purpose,  tapered  props  have  been  introduced,  which 
have  given  great  satisfaction,  both  from  a  safe  and  economic  standpoint.  The 
face  of  the  tapered  end  is  usually  about  3  in.  in  diameter  and  is  about  one- 
fourth  of  the  area  or  section  of  the  body  of  the  prop. 

In  some  localities,  the  butt  end  of  the  prop  is  placed  toward  the  roof  in 
order  to  afford  more  surface  for  the  cap  to  rest  on.  This  position  is  unstable 
and  the  stick  is  also  harder  to  handle,  but  the  butt  end  up  gives  greater  bear- 
ing surface  at  the  point  where  the  prop  is  wedged  and  driven. 

Whether  posts  should  be  set  with  their  butt  ends  up  or  down  is  largely  a 
matter  of  opinion,  as  practice  differs  in  different  localities.  Some  timbermen 
set  the  thick  end  down,  while  others  set  the  larger  end  against  the  weaker 
stratum,  whether  it  is  top  or  bottom.  The  splitting  or  furring  of  the  post  is 
more  apt  to  take  place  at  the  small  end,  and  many  prefer  that  this  should  occur 
at  the  bottom  rather  than  at  the  top  where  the  cap  or  other  timbers  are  resting 
on  the  post. 

Other  things  being  equal,  the  strength  of  a  prop  varies  directly  as  the 
square  of  the  diameter  and  inversely  as  the  length.  The  ratio  of  the  diameter 
to  the  length  of  the  prop,  in  order  to  have  equal  power  of  resisting  compres- 
sion and  deflection,  is  1  to  12.  However,  if  by  reason  of  physical  defects,  such 
as  knots,  splits,  worm  holes,  or  disease,  the  wood  is  weaker,  the  diameter  of 
the  post  should  be  increased. 

The  crushing  strengths  of  various  American  timbers  are  given  in  the  sec- 
tion entitled  Strength  of  Materials.  For  illustration,  taking  chestnut  with  an 
average  strength  of  5,300  Ib.  per  sq.  in.,  and  allowing  75%  of  the  material  to 
be  sound  and  straight  in  fiber,  a  prop  with  a  cross-section  of  Ifrsq.  in.  will  sup- 
port .75X16X5,300  =  63,600  Ib.  If  the  prop  is  8  ft.  long,  the  weight  required 
to  crush  it  will  be  63,600-5-8  =  8,000  Ib.,  about.  This  represents  the  weight 
of  approximately  50  cu.  ft.  of  draw  slate,  equivalent  to  that  of  a  piece  a  little 
more  than  7  ft.  square  and  1  ft.  thick,  or  of  a  piece  3  ft.  X  4  ft.  and  a  trifle 
more  than  2  ft.  thick. 

If  the  draw  slate  is  not  more  than  3  in.  thick,  the  best  plan  is  to  take  it 
down  and  stow  it  in  the  gob,  making  no  attempt  to  hold  it  by  propping.  When 
the  slate  is  from  3  in.  to  6  in.  thick,  a  row  of  props  is  placed  along  the  gob  side 
at  a  sufficient  distance  from  the  track  to  allow  cars  to  pass.  Where  the  roof 
is  poor,  the  arrangement  shown  in  Fig.  1  is  employed.  This  consists  of  an 
extra  long  cap  set  on  the  post  at  one  end  and  set  in  a  hitch  cut  in  the  coal  at  the 
other.  Over  the  cap  is  driven  lagging  b,  which  extends  from  one  set  to  another. 
The  cross-bar  is  not  usually  jointed  to  the  post,  but  is  merely  laid  on  top  of  it. 
The  sticks  used  for  this  purpose  are  about  6  in.  thick;  sometimes  split  props 
are  used,  as  the  timbering  is  temporary  and  is  needed  only  until  the  room  is 
worked  out. 

Systematic  Timbering. — In  systematic 
timbering,  props  are  placed  at  regular  dis- 
tances apart,  both  in  the  direction  of  the 
length  and  in  that  of  the  width  of  the 
room,  and  are  placed  whether  the  appear- 
ance of  the  top  does  or  does  not  indicate 
the  necessity  for  support  at  the  particular 
point  where  the  prop  is  placed.  The  idea 
involved  is  that  a  much  greater  number  of 
roof  falls  will  be  prevented  if  the  props  are 
placed  systematically  and  symmetrically, 
than  if  their  placing  is  left  to  the  judg- 
ment of  the  miner.  The  H.  C.  Frick 
pIG<  i  Coke  Co.,  working  the  8-ft.  Pittsburg  seam 

in  the  Connellsville  region  of  Pennsylvania, 

in  connection  with  rooms  10  ft.  to  12  ft.  wide  and  separated  by  pillars  from 
40  ft.  to  80  ft.  thick,  have  adopted  a  center-to-center  spacing  of  the  posts 
of  4  ft.  6  in.  Where  rooms  are  of  the  usual  width  of  20  to  25  ft.,  there 
will  be  several  series  of  posts  set  in  parallel  rows  from  4  ft.  6  in.  to  6  ft.  apart 
as  local  experience  dictates.  Alternate  parallel  rows  are  set  in  such  a  way  that 
a  plan  of  the  room  timbering  suggests  the  arrangement  of  the  spots  on  the  five 
of  a  suite  of  playing  cards.  Along  the  roadway,  the  props  are  commonly  pro- 


SUPPORTING  EXCAVATIONS 


709 

The 


vided  with  a  long  cap,  and  sometimes  with  lagging  as  shown  in  Fig.  1. 
printed  rules  of  this  company  in  regard  to  systematic  timbering  are: 

"  In  rooms  exceeding  10  ft.  in  width,  posts  must  be  set  as  near  the  center 
of  the  room  as  practicable,  and  the  distance  between  centers  must  not  exceed 
4  ft.  6  in.  In  rooms  where  coal  is  mined  by  hand,  the  distance  between  the 
last  post  and  the  face  must  not  exceed  6  ft.  In  rooms  undercut  by  machine, 
the  distance  between  the  last  post  and  the  face  shall  be  such  as,  in  the  opinion 
of  the  mine  foreman  and  the  mine  inspector,  affords  the  best  protection  for  the 
workmen. 

"  In  all  rib  or  pillar  drawing,  where  the  coal  can  be  reached  without  additional 
track,  a  line  of  posts  not  exceeding  4  ft.  6  in.  between  centers  must  be  set  in  the 
working  places,  and  when  widening  out,  other  posts  not  exceeding  4  ft.  6  in. 
between  centers  must  be  set  parallel,  and  at  right  angles,  to  the  first  line.  In 
rib  or  pillar  drawing,  where  additional  track  must  be  laid  when  cutting  over 
near  the  end  of  the  rib  or  pillar,  posts  not  exceeding  4  ft.  6  in.  between  centers 
must  be  set  in  line  on  both  sides  of  the  opening;  and  in  the  following  named 
mines,  cross-bars  or  collars  must  be  set  over  them.  The  idea  of  setting  these 
cross-bars  across  the  track,  where  the  roof  is  comparatively  good,  is  that  they 
may  give  warning,  by  their  condition,  of  any  unusual  condition  in  the  roof, 
as  the  presence  of  smooth  slips  or  great  weight;  therefore,  where  the  roof  is 
usually  of  good  character,  they  may  be  of  lighter  weight  than  where  bad  or 
dangerous  conditions  are  known  to  exist. 

"  In  all  mines,  when  the  gob  is  reached,  a  line  of  posts  shall  be  set  around  its 
edge;  the  distance  between  such  posts,  or  between  the  post  and  coal,  must  not 
exceed  4  ft.  6  in.  between  centers." 

Timbering  Bad  Roofs. — Slips  are  vertical  or  inclined  cracks  reaching 
through  the  draw  slate  to  a  sound  stratum  above.  Where  the  roof  is  known 
to  contain  slips,  the  props  should  be  close  together  and  kept  as  close  to  the  face 
as  possible.  When  the  slip  is  vertical,  a  post  is  set  immediately  under  it; 
if  inclined,  the  post  is  set  back  from  the  crack  a  short  distance  so  as  to  be  more 
nearly  under  the 
place  of  greatest 
weight.  The  cap 
is  usually  larger 
and  thicker  than  in 
ordinary  prop  tim- 
bering under  a  uni- 
form roof,  and  is 
usually  placed  at 
right  angles  to  the 
crack.  Where  the 
roof  is  very  bad, 
the  arrangement 
shown  in  Fig.  1 
may  be  used,  the 


FIG.  2 


slate  being  allowed  to  fall  in  the  gob,  or  the  form  of  timbering  illustrated 
in  Fig.  2  may  be  employed.  The  caps  a  are  placed  on  the  props  b, 
but  are  not  notched,  being  secured  by  the  wedges  c.  In  all  cases,  they 
should  have  a  regular  arrangement  through  the  room.  Props  for  tim- 
bering under  a  cracked  roof  should  be  about  8  in.  in  diameter  and  the  caps 
about  6  in.  thick.  The  props  should  be  about  8  ft.  apart,  but  the  cross-bars 
can  project  18  in.  over  their  ends.  After  the  room  is  completed  and  the  track 
removed,  such  timbering  may  be  drawn  and  saved  for  future  use,  the  roof 
then  being  allowed  to  fall.  It  may  be  necessary,  in  some  extreme  cases  where 
the  cross-joints  occur,  to  have  two  sets  of  cross-bars,  one  across  the  room  and 
the  other  parallel  to  the  ribs. 

Where  the  slips  are  not  visible,  but  are  known  to  be  present,  some  form  of 
systematic  timbering  should  be  employed. 

Timbering  is  varied  to  meet  the  conditions  of  the  roof  at  each  mine;  there- 
fore, at  mines  with  good  roofs,  but  little  is  needed,  but  it  is  always  safe  prac- 
tice to  timber  under  sags  in  the  roof,  as  these  suggest  the  bed  of  a  stream  of 
water  in  the  past  and  an  opportunity  for  its  accumulation  in  the  present;*  in 
fact,  in  flat  beds,  water  is  nearly  always  encountered  in  depressions  of  this 
kind.  If  the  roof  and  bottom  are  both  hard,  the  props  are  driven  in  as  solidly 
as  possible,  the  number  of  props  used  and  their  arrangement  depending  on  the 
width  of  the  opening  and  the  nature  of  the  roof,  whether  it  is  firm  or  shaly. 
In  long  wall  work,  where  the  roof  is  allowed  to  settle  gradually,  the  props  may 
be  set  on  mounds  of  dirt.  Where  the  roof  of  the  bottom  is  soft,  extra  large  cap 


710 


SUPPORTING  EXCAVATIONS 


pieces  or  foot  pieces  are  used,  so  as  to  give 
as  great  a  bearing  surface  as  possible  be- 
tween the  top  or  bottom  and  the  props. 

Supporting  the  Face  While  Undercut- 
ting.— As  the  coal  is  being  undercut,  it  is 
usually  necessary  to  support  the  web  of 
coal  over  the  miner's  head  to  prevent  its 
falling  on  him.  The  simplest  method  of 
doing  this  is  by  means  of  a  sprag  a,  Fig.  3, 
which  may  be  placed  either  at  the  opening 
of  the  undercut,  or  may  be  placed  within 
the  undercut. 

The  combination  of  timbers  be  used  for 
supporting  the  face  is  termed  a  cockermeg. 
It  consists  of  two  braces  b  between  which 
a  horizontal  stick  of  timber  c  is  placed  along  the  face.  If  the  angle  that  the 
braces  b  make  with  the  vertical  is  less  than  20°,  they  will  not  slip  and  they  may 
be  driven  tightly  against  the  roof  and  floor  so  as  to  bear  against  the  stick  c. 
If  the  braces  b  are  placed  at  a  greater  angle  than  20°,  the  ends  should  be  put 
in  hitches  as  shown. 

ENTRY  TIMBERING  IN  FLAT  SEAMS 

Two-Stick  Sets. — A  two-stick  set  of  timber,  sometimes  used  for  timbering 
entries,  consists  of  two  round  or  sawed  sticks,  wedged,  but  not  framed,  together 


FIG.  3 


FIG.  1 


FIG.  2 


The  post-and-bar  or  post-and-cap  arrangement  is  shown  in  Fig.  1.  A  hitch  a 
12  or  15  in.  deep  and  only  high  enough  to  receive  the  cap  is  cut  in  the  coal. 
The  post  c  is  then  set  close  to  the  rib  and  the  cap  b  placed  in  position.  After 
tightening  the  post  by  driving  the  wedge  e,  the  wedge  /  is  fitted  in  place.  Where 
the  coal  is  soft,  it  is  advisable  to  make  the  hitch  a  wide  enough  to  receive  a  piece 
of  heavy  planking.  By  driving  wedges  between  the  cap  and  plank,  a  much 
better  bearing  surface  is  secured  and  the  pressure  thrown  upon  a  greater  area 
of  coal. 

Where  the  roof  re- 
quires lagging,  the  ar- 
rangement shown  in 
Fig.  2  is  quite  frequent- 
ly employed,  but  is  to 
be  severely  condemned. 
The  ribs  should  be  ver- 
tical as  the  overhanging 
coal  will  weather  and 
fall  into  the  entry,  and 
the  shoulder  of  coal  b 
is  so  small  that  very 
little  roof  pressure  will 
break  it  oft,  causing  the  set  to  fall.  Further,  it  is  not  usually  good  practice 
to  gouge  out  the  roof  slate  to  receive  the  lagging,  as  it  weakens  the  roof  and  may 
open  a  seam  of  water.  The  leg  /  has  too  much  batter  to  withstand  heavy 
pressure  and  should  be  set  vertically. 

>  Instead  of  having  the  post  the  full  height  of  the  opening,  a  method  some- 
times used  is  to  have  short  posts  set  on  a  ledge  in  the  coal,  Fig.  3,  or  on  top  of 
the  coal  when  the  top  rock  is  taken  down,  as  shown  in  Fig.  4. 


FIG.  3 


FIG.  4 


SUPPORTING  EXCAVATIONS 


711 


FIG.  5 


Three-Stick  Sets. — A  set  composed  of  two  legs  and  a  cap  is  the  standard 

form  of  entry  timbering  in  both  wood  and  steel;  such  a  set,  used  in  a  seam  of 

gentle  pitch,  is  shown  in  Fig.  4,  page  714. 

The  lagging  is  only  necessary  when  the 

roof  is  weak  and  the  coal  at  the  sides  of 

such  a  nature  as  to  readily  weather  and 

fall  into  the  roadway.     Also,  in  flat  seams 

where  the  pressure  is  almost  entirely  in  a 

vertical    direction,    the    legs    are    made 

plumb,  or  with  a  batter  of  about  1  in.  to 

the  foot.      In   Fig.    1,   if  the   hitch   a   is 

omitted  and  a  second  leg  placed  under  the 

cap,  the  ordinary  form  of  entry  timbering 

will  be  illustrated. 

A  variant  of  the  three-stick  set,  used 

extensively  abroad  for  timbering  wide  en- 
tries, turnouts,  etc.,  is  shown  in  Fig.  5. 

The  regular  three-stick  set  is  first  put  in 

place  and  is  then  reinforced  with  the  tim- 
bers, c,   d,  and  e.     The  system  is  costly 

and   interferes  to  some  extent  with   the 

ventilating  currents,  but  is   serviceable  in  timbering   underground  stables, 

engine  rooms,  and  the  like. 

Certain  materials  composing  the  floor,  such  as  fireclay,  while  giving  little 

trouble  as  the  entries  are  being  driven ,  frequently  soon  afterwards  soften  under 

the  action  of  the  damp  mine  air  and  swell.  The  trouble  is  greater  where  it  is 
necessary  to  lift  the  bottom  or  brush  the  top 
to  get  height  for  haulage.  In  ground  of  this 
character  various  modifications  of  the  three- 
stick  set  are  used,  one  of  which  is  shown  in 
Fig.  6.  The  timbers  a  and  b  running  length- 
wise of  the  heading  are  commonly  10  ft.  long 
and  extend  over  several  sets,  holding  them 
together.  These  timbers  are  temporarily  held 
in  place  while  the  struts  c  and  d  and  the  cap 
piece  e  are  driven  into  position.  The  lower 
ends  of  the  struts  are  inclined  away  from  the 
legs  to  further  strengthen  the  latter  against 
pressure  from  the  sides. 

In  timbering  in  such  swelling  ground,  the 
best  results  appear  to  be  obtained  by  using 
fairly  strong  timbers  and  excavating  some  of 
•pir   fi  the  material  behind  them  whenever  the  swell- 

m  ing  begins  to  exert  too  great  a  pressure.     The 

lagging  is  usually  light,  sometimes  1-in.  plank,  is  open  in  construction,  and  by 

its  bending  and  breaking,  gives  warning  that  the  sets  are  in  danger  of  being 

crushed.     In  some  cases  skin-to-skin  timbering  is  used;  that  is,  heavy  logs 

set  in  close  contact,  or  any  of  the  forms  shown  on  pages  710  and  715  may  be 

used  when  placed  close  together  and  closely 


lagged. 
Fou 


four-Stick  Sets. — A  four-stick  set  of  tim- 
bering is  the  same  as  a  three-stick  set,  with  the 
addition  of  a  sill  laid  across  the  floor,  which 
serves  as  a  support  for  the  ends  of  the  legs  and 
is  designed  to  resist  the  upward  pressure  of  the 
floor.  A  method  of  framing  such  sets  is  shown 
in  Fig.  7.  In  some  instances,  the  legs  are  ten- 
oned to  fit  into  a  mortise  in  the  sill,  but  this  is 
unnecessary  if  the  angle  the  leg  makes  with  the 
vertical  does  not  exceed  15°. 

When  the  ground  is  so  heavy  that  this 
method  of  timbering  is  demanded,  modern 
practice  suggests  the  use  of  concrete  or  con- 


FIG.  7 


crete-and-steel  construction,  particularly  on  main  haulage  roads  designed 
to  be  open  during  the  life  of  the  mine,  at  shaft  and  slope  bottoms,  main 
partings,  andother  important  places  in  the  haulage  system.  Sets  composed 
of  structural  steel  shapes  have  been  advantageously  used  in  such  places. 


712 


SUPPORTING  EXCAVATIONS 


ROOM  TIMBERING  IN  PITCHING  SEAMS 

The  general  arrangement  of  the  timbering  at  the  mouths  of  rooms  or  breasts 
worked  on  a  pitch,  and  which  is  designed  primarily  to  keep  the  loose  coal  from 
rushing  into  the  roadway  rather  than  as 
a  support  for  the  roof,  is  shown  under  the 
title  Working  Pitching  Seams. 

In  room  timbering  in  pitching  seams, 
the  posts  are  not  set  quite  at  right  angles 
to  the  roof,  but  are  given  a  slight  pitch, 
known  as  underset,  up  hill  as  shown  in  an 
exaggerated  degree  in  b,  Fig.  1.  Any 
movement  of  the  roof  will  cause  the  top  of 
the  prop  a  to  move  in  the  direction  of  the 
arc  shown  by  the  dotted  lines  and  thus  to 
fall  down.  The  top  of  the  prop  b,  moving 
in  a  similar  arc  will,  however,  be  bound 
more  tightly  against  the  roof. 

The  following  table,  from  "Sawyer's 
Accidents  in  Mines,"  gives  the  maximum 
and  minimum  angles  at  which  props  should 
be  set  for  varying  inclinations.  This  table 
can  be  taken  as  a  general  guide,  but  it 
does  not  take  account  of  the  length  of  prop 

nor  the  varying  amounts  of  movement  of  the  top  rock  under  different  con- 
ditions. 

UNDERSETTING  OF  PROPS 


FIG.  1 


Rate  of  Inclination  of 
Seam 
Degrees 

Angle  of  Underset  of  Props 

Minimum 
Degrees 

Maximum 
Degrees 

6 
12 

18 
24 
30 
36 
42 
48 
54  and  upwards 

0 
0 
1 
1 
2 
2 
2 
3 
3 

1 
2 
3 
4 
5 
6 
7 
8 
9 

To  prevent  the  coal  from  falling  on  the  roadway,  it  is  also  often  necessary 
to  place  a  series  of  props  as  shown  in  Fig.  2.  The  prop  a  is  underset,  its  foot 
being  placed  in  a  hitch  in  the  floor. 
Part  of  the  draw  slate  b  is  taken 
down  to  prevent  its  falling  and  the 
remainder  is  held  up  by  the  prop  a 
and  cap  c.  To  prevent  the  coal 
from  falling  into  the  gangway,  the 
props  are  placed  short  distances 
apart  and  covered  with  stout  lag- 
ging d.  It  is  necessary  to  wedge 
the  foot  of  the  prop  and  drive  the 
cap  c  in  tightly;  then,  any  move- 
ment of  the  roof  will  tighten  the 
joint  between  the  prop  and  the  cap. 

If  the  seam  is  very  steeply  in- 
clined, so  that  there  is  danger  of  the 
cap  between  the  roof  and  the  prop 

slipping  out,  a  hitch  is  cut  in  the  F,r   2 

roof  rock  so  that  the  prop  may 

have  rock  rests  at  each  end.     The  pressure  that  the  prop  then  has  to  sus- 
tain is  from  the  coal,  and  the  prop  is  in  the  position  of  a  beam  uniformly  loaded 


SUPPORTING  EXCAVATIONS 


713 


along  its  length.  This  system,  shown  in  Fig.  3,  is  the  better  method  in  highly 
inclined  beds,  but  the  hitches  cut  in  the  roof  must  be  at  least  12  in.  deep  and 
the  prop  thoroughly  wedged  at  both  ends.  The  object  of  wedging  timbers 
when  placed  in  such  positions  is  to  give  them  stiffness,  for  if  they  bend  they 


FIG.  3 


FIG.  4 


will  eventually  break;  by  wedging  the  ends,  the  bending  is,  in  a  great  measure, 
prevented. 

Fig.  4  shows  the  method  of  timbering  a  wide  coal  bed  at  one  mine  in  Penn- 
sylvania. The  logs  a  were  about  20  ft.  long  and  18  in.  in  diameter  at  the  top. 
They  were  placed  8  ft.  apart  and  lagged  with  8-in.  round  sticks.  Handling 
these  sticks  and  placing  them  were  laborious  operations  and  the  method  is  not 
recommended. 

The  use  of  single  props  for  timbering  deposits  exceeding  12  to  15  ft.  in  thick- 
ness is  limited,  as  large,  heavy  timbers  must  be  handled  in  such  cases,  making 
the  system  an  expensive  one;  furthermore,  the  resistance  of  a'  prop  to  bending 
is  not  great  when  the  length  is  more  than  twelve  to  fifteen  times  its  diameter. 

ENTRY  TIMBERING  IN  PITCHING  SEAMS 

Two-Stick  Sets. — Fig.  1  shows  a  form  of  two-stick  timbering  that  may  be 
used  where  the  seam  has  a  slight  pitch  and  is  so  thin  that  the  floor  must  be 
blasted  to  secure  entry  height.  To  stiffen  the  collar,  it  must  be  thoroughly 
wedged  at  d  and  at  its  joint  with  the  leg  e,  by  wedges  /.  Lagging  is  necessary 
to  prevent  the  coal  falling  into  the  entry.  This  form  of  timbering  is  good,  pro- 
vided the  wedges  /  are  tight  so  that  the  bulk  of  the  pressure  is  transferred  to 
the  leg  e.  The  beveled  joint  will  become  tighter  as  the  side  pressure  from  the 
coal  increases. 


FIG.  1 


FIG.  2 


A  similar  form  of  timbering  is  shown  in  Fig.  2,  which  is  used  in  thicker  seams 
where  the  roof  is  good.  As  the  joint  between  the  post  p  and  collar  b  is  by  no 
means  as  strong  as  that  shown  in  Fig.  1,  this  arrangement  is  more  adapted  to 
holding  back  the  coal  than  to  supporting  the  roof. 


714 


SUPPORTING  EXCAVATIONS 


The  arrangement  in  Fig.  3  is  adapted  to  thin,  highly  inclined  seams.  Even 
if  the  top  rock,  or  hanging  wall  b,  is  good,  in  order  to  prevent  the  leg  c  being 
pushed  into  the  roadbed,  it  is  advisable  to  set  its  foot  in  a  hitch  in  the  coal  and 


FIG.  3 


FIG.  4 


to  make  a  notched  joint  between  it  and  the  collar.  The  collars  must  be  lagged 
to  keep  back  the  overhead  coal,  and,  if  the  top  rock  b  is  poor,  the  leg  c  may  be 
lagged  as  well.  Seasoned  lagging  should  be  used  in  such  places;  split  lagging 
with  the  flat  side  laid  next  the  leg  c  is  preferable  because  the  rounded  side 
is  stronger  in  compression  than  in  tension. 

Three-Stick  Sets. — Fig.  4  shows  the  standard  form  of  three-stick  sets  as 
used  in  seams  of  moderate  pitch  where  the  sides  are  weak  and  require  the  use 
of  lagging.  Where  the  sides  are  very  weak  the  sets  may  be  placed  skin  to  skin, 
but  they  are  commonly  set  3  or  4  ft.  apart. 

Fig.  5  shows  the  method  of  timbering  where  the  dip  is  great,  the  bottom 
hard,  and  the  seam  is  not  thick  enough  for  full  entry  height.  This  method 
avoids  the  cost  of  taking  out  enough  rock  to  get  in  a  set  of  timber  having  legs 
of  equal  length.  The  shorter  leg  /  is  given  a  firm  hold  on  the  rock  bottom. 

Fig.  6  shows  a  form  of  timbering  used  in  pitching  seams  where  the  coal  is 
soft  and  falls  to  a  height  greater  than  that  required  for  the  gangway.  The 
leg  I  on  the  high  side  is  made  long  enough  to  reach  up  to  the  roof  to  support 
the  lagging,  which  keeps  the  soft  coal  from  continually  sliding  down  into  the 
gangway.  The  collar  c  strengthens  the  leg  /.  The  coal  is  allowed  to  fall  off 
on  the  low  side  where  no  lagging  is  necessary. 

Fig.  7  shows  the  method  of  timbering  the  levels  in  thin  pitching  seams, 
when  the  top  is  supposed  to  be  weak.  The  legs  /  and  the  collar  c  are  made  of 
round  timber  about  12  in.  in  diameter,  and  are  so  jointed  together  that  the 


FIG.  5 


FIG.  6 


collar  c  will  stand  great  pressure.  The  lagging  a  consists  of  round  poles  taken 
direct  from  the  woods,  and  usually  from  3  to  6  in.  in  diameter.  The  poles  are 
used  to  keep  the  loose  coal  and  roof  from  falling  between  the  sets  of  timbers, 


SUPPORTING  EXCAVATIONS 


715 


which  are  from  3  to  5  ft.  apart.     Where  the  lateral  pressure  is  slight,  planks  p 
are  used.     The  road  is  made  level  by  filling  in  the  low  side  with  refuse  /,  as 


SHAFT  TIMBERING 
General  Principles.  —  The 

general  arrangement  of  shaft 
timbers  and  some  of  the  de- 
tails thereof  are  illustrated 
under  the  title  Opening  a  Mine. 
The  nature  and  amount  of  the 
timbering  will  vary  with  the 
character  of  the  ground  pene- 
trated. 

In  hard  material,  only  such 
timbers  are  introduced  as  are 
necessary  to  furnish  support 
to  the  guides,  pipes,  wires, 
etc.  that  are  carried  down  the 
shaft.  In  loose  material,  the 
object  of  timbering  is  to  give 
support  also  to  the  sides  of  the 
excavation.  In  watery  strata, 
the  pressure  of  the  water  be- 
hind the  timber  is  another 
point  that  must  be  considered. 
Water  encountered  in  the  sink- 


FIG.  7 


ing  of  a  shaft  finds  its  way  at  once  to  the  excavation  or  follows  down  behind 
the  lining  and  collects  in  the  bottom  of  the  shaft,  unless  kept  out  by  the  shaft 
lining.  If  the  lining  is  built  tightly  against  the  sides  of  the  excavation,  so  as 
to  impede  or  stop  the  flow  altogether,  the  water  rises  behind  the  lining  to  the 
water  level  of  the  strata  and  the  lining  is  subjected  to  a  pressure  dependent 
on  the  head  of  water.  The  strength  of  the  lining  must  be  sufficient  to  with- 
stand this  pressure.  In  such  cases,  the  following  formula  may  be  employed 
to  determine  the  thickness  of  white-pine  lining  that  will  resist  a  given  head  of 
water:  *  =  .016sV5 

in  which  t  =  thickness  of  white-pine  lining,  in  inches; 

5  =  clear  unsupported  span  of  timber,  in  inches; 
d  —  depth,  or  head,  of  water,  in  feet. 

NOTE. — While  in  the  statement  of  this  formula  white-pine  timber  is  used, 
the  same  formula  will  give  results  that  are  practically  correct  for  the  other 
varieties  of  timber  used  in  shaft  linings. 

It  must  be  remembered  that  the  head  of  water  supported  by  the  curbing 
does  not  mean  the  depth  of  the  curbing  below  the  surface,  as  the  water  rarely 
if,  ever,  heads  to  the  surface. 

EXAMPLE. — Find  the  thickness  of  white-pine 
curbing  required  for  a  coffer  dam  when  the  depth 
of  the  water  head  is  100  ft.,  the  clear  span  of  the  end 
plates  of  the  shaft  being  7  ft. 

SOLUTION. — Substituting  the  given  values  in  the 
formula,  t  =  . 016  X  (7X12)  X  V 100  =  13.44;  hence  a 
14-in.  timber  would  be  used. 

Timbering  in  Rock. — Where  a  shaft,  or  a  por- 
tion of  a  shaft,  is  excavated  from  hard -rock  strata, 
the  only  timbering  necessary  is  the  cross-timbers, 
or  buntons,  to  support  the  guides  in  the  hoisting 
compartments  of  the  shaft  and  the  lines  of  pipes, 
or  wires.     The  buntons  b,  Fig.  1,  are  set  in  hitches 
h  cut  in  the  rock  face  and  firmly  wedged  in  line, 
one  above  the  other,  by  wedges  w.     At  times,  the 
hitches  are  cut  square  and  those  on  one  side  made 
deeper  to  permit  the  other  end  of  the  stick  to  be 
placed  in  the  hole  opposite. 
The  buntons  are  spaced  from  6  to  8  ft.  apart,  one  above  another,  on  each 
end  of  the  shaft,  and  between  the  several  compartments  of  the  shaft.     When 
it  is  desired  to  separate  the  compartments  of  the  shaft,  as  in  the  caes  of  an  air- 


FIG.  1 


716 


SUPPORTING  EXCAVATIONS 


way  or  manway,  planks  are  spiked  to  the  buntons  or  built  between  them  to  form 
the  partition. 

Timbering  in  Loose  Dry  Material. — In  good  ground,  shafts  have  been  sunk 
to  a  depth  of  200  to  300  ft.  by  using  3"X  12"  planking  set  on  edge,  but  beyond 

this  depth  it  is  better  to  use 
4-in.  or  5-in.  planks.  When 
an  especially  soft,  wet,  or  crum- 
bling stratum  is  met,  such  as 
wet  sand  or  fireclay,  the  plank- 
ing is  sometimes  laid  flatwise. 
If  the  sides  of  the  shaft  are  not 
self-supporting  and  tend  to 
crumble  into  fragments  of  vary- 
ing size,  if  boulders  that  are 
likely  to  become  detached  are 
found,  or  if  the  strata  are 
jointed  and  faulted,  to  preserve 
the  shaft  and  to  avoid  accident 
from  earth  or  rock  falling  to  the 
bottom  from  the  side  walls,  it 
is  necessary  not  only  to  line  the 
entire  excavation  with  plank, 
but  to  support  this  planking  by 
heavy  timber  sets  placed  inside 
the  planking,  as  shown  in  Fig.  2. 
These  timber  sets  a  are 
placed  at  regular  distances 
apart  and  are  separated  by  the 
posts  b.  The  lagging  c,  com- 
posed of  closely  fitting  planks, 
may  be  driven  in  behind  the 
timber  sets  or  it  may  be  first, 
placed  in  position  and  the 
timber  sets  or  frames  added  afterwards.  Cross-buntons  d  are  also  inserted 
in  each  set  to  separate  the  compartments.  Where  a  greater  strength  of  tim- 
bering is  required  than  is  given  by  this  form,  the  sets  a  may  be  placed  one  on 
top  of  the  other,  i.  e.,  skin  to  skin. 

An  open  crib  of  timbers,  similar  to  that  shown  in  Fig.  3,  may  also  be 
employed  in  loose  ground,  the  openings  between  the  timbers  being  gradually 
filled  up  compactly  by  the  loose  material.  After  the  timbers  have  been  placed 
in  position,  triangular  strips,  or  corner  pieces,  A  are  spiked  to  them  in  each 
corner  of  the  shaft.  This  open  crib  may  be  built  either  from  the  top  down- 
wards or  from  the  bottom  upwards. 

Instead  of  building  the  timbering  from  the  top  downwards,  it  is  frequently 
built  upwards  from  the  bottom  in  sections  of  10  to  15  ft.,  depending  on  the 
character  of  the  ground.  The  bottom  of  the  shaft  is  carefully  leveled  with  a 
carpenter's  level  and  straightedge;  and,  by  measurements  made  from  the  plumb- 
lines  hung  from  the  shaft  corners,  a  set 
of  timbers  is  placed  so  that  the  inside  is 
in  line  with  the  edge  of  the  sills,  or  shaft 
templet.  After  the  whole  set  is  accu- 
rately leveled  and  joined,  wooden  wedges 
are  driven  between  the  timbers  and  earth 
at  each  corner.  The  wedges  should  be 
long  and  tapering,  and  should  be  driven 
into  position  while  the  set  is  held  in 
place  with  a  bar.  Great  care  must  be 
taken  to  get  this  first  set  level  and  in 
line  with  the  shaft  templet,  as  it  is  the 
foundation  for  the  other  sets.  After  this 
foundation  set  has  been  placed  in  position 
and  wedged,  another  set  is  placed  on  it, 
leveled,  and  wedged  in  like  manner.  In  _, 

this  manner,  the  work  is  continued  until  * IG-  • 

the  templet  or  next  section  of  timbering  is  reached.  If  the  sinker  has  measured 
correctly  and  has  made  due  allowance  for  the  number  of  sets  required  to  close 
the  distance  between  the  shaft  bottom  and  templet,  his  sets  will  close  this  space 


SUPPORTING  EXCAVATIONS 


717 


FIG.  4 


exactly.    The  inside  edges  of  the  planking  are  brought  flush  with  the  inside  edges 

of  the  templet,  and  iron  straps,  about  2£  in.  X  i  in.  X  15  ft.,  provided  with  nail 

holes  are  hung  from  the  surface  downwards,  connecting  all  the  planking  and  hang- 
ing it  from  the  templet.     The  straps  or  hangers  are  placed 

on  the  sides  and  ends  of  the  shaft  at  distances  of  2  to  3  ft. 

apart,  and  they  break  joints  vertically  as  the  timbering 

proceeds.     If  a  small  space  is  left  between  the  last  set 

and  the  templet  and  the  planking  does  not  close  exactly, 

a  closing  set  is  necessary.     For  this  purpose,  a  regular  set 

is  cut  down  to  the  required  size  by  the  rip  saw  or  adz. 

However,  the  sinker  should  make  his  measurements  and 

calculations  so  that  no  closing  sets  are  required. 

No  cavities  should  be  allowed  to  remain  behind  the 

timbering  after  it   is   completed,  except  in  ground  that 

swells.     If  cavities  are  found  in  the  strata,  or  if  more  earth 

has  been  taken  out  than  was  necessary,  the  space  must  be 
filled  with  ashes,  straw,  etc. 

Timbering  in  Swelling  Ground. — A  form  of  timbering  often 
employed  in  swelling  ground  is  a  cribwork  of  heavy  timbers,  such 
as  is  shown  in  Fig.  4.  These  timbers  are  notched  together  after 
the  fashion  of  a  log  cabin.  One  side  of  the  timbers  may  be  faced, 
so  as  to  form  the  face  of  the  shaft,  but  the  back  of  the  timbers  is 
preferably  left  round.  When  the  ground  swells,  the  material 
._  more  readily  works  out  between  the  timbers,  and  can  be  removed 
Hs  from  time  to  time,  as  it  may  be  found  necessary.  An  important 
feature  of  the  work  in  dealing  with  swelling  ground  is  to  keep  the 
material  as  dry  as  possible,  because  the  moisture  causes  the  swell- 
ing. In  such  ground,  a  space  at  least  6  in.  wide  is  sometimes  cut 
out  all  around  the  sides  and  ends  of  the  shaft,  and  filled  in  loosely 
with  moss,  straw,  sand,  or  ashes,  allowance  being  made  for  the 
probable  expansion  of  the  ground.  When  the  timbering,  by  bulg- 
ing, shows  signs  of  excessive  pressure  behind,  the  difficulty  may  be 
overcome  by  carefully  removing  two  or  more  planks  from  the  shaft 
at  this  point,  and  excavating  such  material  as  may  be  necessary, 
all  around  behind  the  timbers.  The  manway  thus  formed  should 
be  carefully  drained  by  a  pipe  conducting  the  water  to  the  sump  or 
other  lodgment.  This  manway  should  be  timbered  and  cleaned 
out  from  time  to  time,  as  may  be  necessary;  the  bulged  timbers 
of  the  shaft  should  also  be  replaced  by  good  ones. 

Timbering  in  Very  Wet  Ground  or  Quicksand. — In  wet  ground, 
timbers  should  be  closely  joined.  At  times,  it  is  desired  to  make 
a  water-tight  joint  between  each  set  of  timbers  to  keep  the  water 
from  entering  the  shaft;  for  this  purpose,  timbers  have  been  laid 

in  cement,  but  better  results  are  obtained  by  backing  the  timbers  with  cement. 

A  form  of  timbering  that  always  gives  good  results,  introduced  for  the  first 

time  in  the   sinking  of  the   Ladd 

shaft  at  Ladd,  Illinois,  is  that  shown 

in  Fig.  5,  which  illustrates  a  section 

of  curbing  passing  through  a  stra-  , . 

turn  of  quicksand,  and  through  soft  efgStfi 

material  overlying  the  same.     At  a  £v.:::.- 

point  above  the  soft  material,  the  jSjjvs! 

3"X8"  curbing  plank  a  employed  feVx-t 

for  the  shaft  lining  is  laid  flatwise,  fjj£ji 

increasing  the  thickness  of  the  curb-  5&i$:s 

ing  from  3  to   8    in.     When    the  'S**™ 

quicksand    is    reached,    the    8-in. 

plank  is  alternated  by  6-in.  plank, 

forming     the    corrugated    backing 

shown  at  b;  the  effect  of  this  rough 

backing  is  to  clog  the  drainage  that 

would  otherwise  find  its  way  down 

the  back  of  the  curbing,  and  greatly 

reduces  the  amount  of  water  enter- 
ing the  shaft. 


FIG. 


FIG.  6 


. 

The  chief  difficulty  in  sinking  through  quicksand  is  that  arising  from  the 
flow  of  the  soft  material  into  the  excavation  before  the  timbers  can  be  placed 
in  position.  To  prevent  this  as  far  as  possible,  the  excavation  should  be  tim- 


718 


SUPPORTING  EXCAVATIONS 


bered  well  down  to  the  bottom  of  the  shaft.  Fig.  6  shows  more  or  less  accu- 
rately the  inflow  of  sand  and  the  method  of  setting  the  timbers.  The  lower  tim- 
bers have  been  set,  jacked  up, 
and  spiked.  Blocks  a  are  used 
to  support  the  back  of  the  lin- 
ing. These  blocks  are  knocked 
out  by  the  next  set  of  timbers 
when  it  is  driven  to  its  place. 
It  is  necessary  to  provide  a 
temporary  foundation  for  the 
jacks,  which  in  this  case  is  af- 
forded by  the  sills  shown.  The 
form  of  lining  employed  is  the 
alternate  narrow  and  wide 
plank  laid  flatwise.  To  reduce 
the  flow  of  sand  temporarily, 
spiling  has  been  driven  between 
the  timbers:  but  the  spiles  must 
be  removed  before  they  throw 
too  mucn  weight  on  the  lining. 

pIG  7  To   support   the  timber  while 

the  jacks  under  the  set  are  being 

lowered  far  enough  for  a  new  timber  to  be  placed  over  them,  cleats  are  spiked 
on  the  timbers  as  fast  as  each  timber  set  is  laid  in  place.  If  the  timbers  can- 
not be  forced  into  place  by  hand  or  driven  with  a  sledge,  a  jack,  similar  to  those 
shown  in  Fig.  6,  is  used,  being  fastened  to  a  piece  of  6"X6"  or  8"X8"  timber, 
about  1  ft.  shorter  than  the  inside  dimensions  of  the  shaft. 

Square  Frame  at  Foot  of  Shaft. — When  tbe  bottom  of  the  shaft  is  reached 
and  the  sump  has  been  made  by  carrying  the  excavation  several  feet  below  the 
floor  of  the  seam,  a  heavy  substantial  frame  must  be  built  for  the  support  of 
the  shaft  timbers.  The  cage  landing  is  first  made  by  placing  two  heavy  square 
timbers  a,  Fig.  7,  under  each  hoistway.  These  timbers  should  be  10  in.  X  12  in. 
or  12  in.  X  16  in.,  according  to  the  size  and  weight  of  the  cage,  and  should 
occupy  a  position  about  under  the  rails  on  the  cage.  They  are  well  bedded  in 
the  strata  on  each  side  of  the  shaft,  and  set  low  enough  to  make  the  floor  of  the 
cage,  when  the  latter  is  resting  on  the  timbers,  level  with  the  floor  of  the  land- 
ing. When  this  has  been  done  in  each  hoistway,  heavy  longitudinal  sills  & 
are  laid  over  them,  one  at  each  side  of  the  shaft;  cross-timbers  c  are  boxed  into 
the  sills  to  keep  them  the  right  distance  apart  and  to  form  a  solid  frame  for 
the  cage  landing.  Substantial  posts  d  are  then  set  at  the  corner  of  each  com- 
partment. Heavy  caps,  or  collars,  e  are  framed  to  rest  on  these  posts,  and 
cross-timbers  /  are 
boxed  into  these  caps 
above.  The  whole 
frame  is  brought  to 
such  a  height  as  will 
correspond  to  the 
height  of  the  heading, 
and  the  shaft  timbers, 
or  lining,  g  are  made 
to  rest  on  the  top  of 
this  frame. 

Underneath  the 
cage  timbers  a  heavy 
planks  are  inserted  so 
as  to  cover  the  sump 
to  prevent  material 
from  falling  in  and 
avoid  the  necessity  of 
frequent  cleaning. 
Without  a  cover, 
there  is  also  the  dan- 
ger of  animals  falling 
r_i  _  Ai  _  I?. 


FIG.  8 


into  the  sump  and  being  drowned  before  they  can  be  got  out.  This  cover 
should  be  so  arranged  that  it  may  be  easily  and  quickly  removed  at  any  time. 
Square-Set  Timbering. — Square-set  timbering  is  adapted  to  large  shafts  or 
heavy  pressures.  It  is  extravagant  in  the  use  of  timber  on  account  of  both  the 
size  and  the  quantity  of  timber  required.  The  form  of  joint  is  simple,  as  the 


SUPPORTING  EXCAVATIONS 


719 


timbers  are  for  the  most  part  boxed  slightly  into  one  another.  Fig.  8  shows  the 
general  construction  of  the  timbering  in  a  three-compartment  shaft  by  square 
sets;  in  it,  some 
of  the  timbers 
are  omitted  for 
the  purpose  of 
showing  the 
form  of  joint 
employed.  At 
A  are  shown  the 
wall  plates  ;atB, 
the  end  plates; 
at  C,  cross-bun- 
tons;  and  at  D, 
posts  or  punch 
blocks  or  stud- 
dies.  The  joints 

may  be  varied  FIG.  9 

as  shown  in  Fig. 

9.  With  the  joint  shown  in  (6),  the  cross-bunton  is  put  in  place  from  below. 
The  advantage  of  this  is  that,  if  the  timbering  must  be  kept  close  to  the  bot- 
tom while  sinking,  the  bunton  going  in  from  below  can  be  left  out  at  first,  so 

as  to  allow  more  room  for  the  workmen.     Fig.  10 

shows   another  method   of  joining   end   and   wall 

plates,  the  post  F  being 

boxed    into    the    plates 

both  above  and  below. 

In    this  figure,  a  2-in. 

strip    S    is    shown    on 

which  the  lagging  is  to 

rest.     Numerous  other 

forms  of  joints  are  used 

in  square-set  timbering, 

but  these  will  serve  to 

illustrate  the  principle, 
pIG   jo  namely,  that  as  little  of 

the   timber   should    be 


I 
FIG.  11 


cut  out  as  possible,  so  as  not  to  weaken  the  timber.  When  framing  these 
timbers,  regard  must  always  be  had  to  the  manner  in  which  they  are  put  to- 
gether in  the  shaft.  When  the  timbering  is  done  from  the  top  downwards  the 
sets  are  suspended  by  means  of  hanger  bolts  made  of  round-iron  rods,  bent  to 
a  hook  shape  on  one  end  and  having  a  thread  and  nut  on  the  other  end,  Fig.  11. 

MISCELLANEOUS  FORMS  OF  TIMBERING 

Fig.  1  shows  a  method  of  placing  drift  sets  in  the  case  of  very  heavy  or 
swelling  ground.  Here  a  are  the  posts;  c,  the  sills;  b,  the  caps;  d,  the  collar 
braces  that  bear  against  both  the  caps  and  the  posts;  e,  foot  or  heel  braces 


1         l 

J 

FIG.  1 


FIG.  2 


that  bear  against  both  the  sills  and  the  posts;  /,  diagonal  braces  that  are  halved 
together  and  placed  as  shown. 

Fig.  2  is  a  set  employed  in  the  case  of  an  extra  wide  gangway,  or  parting, 
there  being  a  post  set  under  the  middle  of  the  cap.  This  form  of  set  may  be 
provided  with  a  sill  when  the  floor  is  soft. 


720 


SUPPORTING  EXCAVATIONS 


Fig.  3  shows  a  form  of  drift  set  surrounded  by  bridging  and  used  where 
such  bad  ground  is  encountered  as  to  necessitate  forepoling.  At  a  are  shown 
the  posts;  at  b,  the  caps;  at  c,  the  sill  of  the  regular  set;  at  d,  upright  bridge 
pieces;  at  e,  a  horizontal  bridge  piece  separated  from  the  set  proper  by  blocks  / 
so  as  to  provide  spaces  h  around  the  regular  set  through  which  the  spiles  or 
forepoles  can  be  driven. 


FIG.  3 


FIG.  4 


FIG.  5 


Fig.  4  shows  a  form  of  drift  set  sometimes  employed  in  very  heavy  or  swell- 
ing ground.  This  method  of  framing  the  timbers  shortens  each  piece  and 
reduces  the  transverse  strain  on  all  the  timbers. 

Fig.  5  shows  an  ordinary  drift  set  provided  with  a  sollar  for  ventilation 
purposes.  An  additional  brace  b  is  placed  parallel  to  the  cap  c,  and  this  is 
covered  with  plank  lagging  a,  so  as  to  provide  a  passage  above  the  regular 
drift,  which  may  be  used  as  a  return  air-course. 


FRAMING  TIMBERS 

Limiting  Angle  of  Resistance. — In  Fig.  4,  page  714,  the  legs  of  the  timber 
are  inclined  so  that  the  pressure  coming  on  the  collar  is  transmitted  equally 
to  both  legs.  If  the  legs  are  placed  at  different  angles,  the  pressure  will  bear 
unequally  on  them,  the  greater  pressure  coming  on  the  leg  making  the  smaller 
angle  with  the  vertical.  The  tendency  for  the  foot  of  a  post  to  slip  increases 
with  the  inclination ;  and  if  the  angle  between  the  post  and  the  vertical  is  more 
than  20°,  the  post  is_apt  to  slip,  but  the  legs  are  not  apt  to  spread  on  a  level 
rock  surface  when  this  angle  is  less  than  20°.  It  is,  of  course,  possible  to  block 
the  foot  of  the  leg  against  the  side  of  the  gangway,  but  even  then  the  hori- 
zontal pressure  against  the  foot  of  the  post  increases  rapidly  and  it  is  advis- 
able to  keep  the  inclination  of  the  legs  less  than  20°  from  the  vertical. 

When  the  pressure  comes  from  four  sides,  four-stick  timbering  must  be 
used.  In  some  instances,  the  legs  are  tenoned  for  a  mortise  in  the  sill,  but  this 
is  unnecessary  if  the  angle  the  leg  makes  with  the  vertical  does  not  exceed  15°, 
which,  according  to  Morin's  experiments,  is  the  limiting  angle  of  contact  of 
oak  on  oak  when  the  fibers  of  the  moving  surface  are  perpendicular  to  the  sur- 
face of  contact  and  those  of  the  surface  at  rest  are  parallel  to  the  direction  of 
the  motion.  In  Fig.  7,  page  711,  the  moving  surface  is  the  lower  end  of  the 
inclined  leg  and  the  surface  at  rest  is  the  portion  of  the  sill  on  which  this  end 
of  the  leg  rests.  The  friction  of  two  surfaces  that  have  been,  for  a  consider- 
able time,  in  contact  and  at  rest,  is  different  not  only  in  amount,  but  also  in 
nature  from  the  friction  of  surfaces  in  continuous  motion.  A  jar  or  shock 
producing  an  almost  imperceptible  movement  of  the  surfaces  of  contact  causes 
the  friction  of  contact  at  rest  to  pass  to  that  which  accompanies  motion. 

Placing  Timber  Sets. — It  is  important  in  the  framing  of  a  set  of  timbers 
to  out  the  joints  between  the  two  pieces  of  timber  so  accurately  that  the  bearing 
surfaces  are  in  close  contact.  The  lower  end  of  each  leg  must  also  be  cut  so 
as  to  be  in  contact,  over  its  whole  surface,  with  the  floor  in  order  to  get  the  full 
benefit  of  the  cross-section  of  the  timber.  When  wedging  the  cap  piece,  care 
should  be  taken  to  drive  the  wedges  as  uniformly  as  possible  over  the  full  length 
of  the  cap  piece;  for  if  some  wedges  are  driven  more  tightly  than  others,  the 


SUPPORTING  EXCAVATIONS 


721 


weight  will  be  concentrated  at  these  points,  at  which  place  the  cap  is  apt  to 
break.  In  placing  wedges,  care  should  be  taken  to  secure  the  roof  without 
throwing  an  unnecessary  strain  on  any  part  of  the  timber  set. 

Timber  Joints. — Fig.  1  shows  a  joint  sometimes  used  to  resist  pressure  from 
above  rather  than  from  the  side.     This  joint  is  objectionable  from  the  fact 


mf 


...«.      I 


FIG.  1 


FIG.  2 


FIG.  3 


that  continued  pressure  on  the  collar  a  will  cause  it  to  sag  and  thus  raise  the 
scarf  b  of  the  joint  from  the  post  c,  throwing  all  the  weight  on  the  part  d.  This 
has  a  tendency  to  split  the  post  c  and  the  cap  a,  as  shown  by  the  dotted  lines; 
if  this  occurs,  the  entire  weight  is  thrown  on  the  collar  above  the  dotted  line  e, 
and  on  the  part  of  the  post  to  the  left  of  d,  the  part  d  and  that  below  e  being 
useless  in  sustaining  weight.  The  same  bending  trouble  will  take  place,  but  to 
a  less  extent,  if  the  timbers  are  joined  as  in  Fig.  2,  unless  the  wedge  /  stiffens 
the  collar  sufficiently  to  prevent  its  bending;  it  is  doubtful,  however,  if  sufficient 
stiffening  will  occur  when  continued  heavy  pressure  comes  on  the  collar.  In 
case  the  collar  a  bends  so  as  to  open  the  joint  b,  the  upper  part  above  e  is  use- 
less for  sustaining  pressure.  The  side  wedge  g  is  intended  to  keep  the  joint 
tight. 

The  joint  in  Fig.  2  is  better  able  to  withstand  pressure  from  above  than 
that  in  Fig.  1,  for  the  pressure  is  along  the  fibers  of  the  post  c  and  not  across 
them. 

The  joints  in  Figs.  3  and  4  have  proved  very  satisfactory  in  practice,  as 
the  timbers  are  not  so  apt  to  split  as  when  the  joints  shown  in  Figs.  1  and  2  are 
used. 

If  the  cap  begins  to  sag,  there  is  much  less  chance  for  the  joint  shown  in 
Figs.  3  and  4  to  open  than  there  is  with  the  joint  shown  in  Figs.  1  and  2,  as 
there  are  no  sharp  angles  in  the  joint  between  the  timbers  a  and  c.  The  pres- 
sure also  comes  on  the  faces  b  and  d  of  the  joint  much  more  uniformly,  and  the 
absence  of  the  heel  or  sharp  corner  in  the  joint  also  greatly  reduces  the  tendency 
of  the  cap  to  split  along  the  dotte'd  line.  In  case  the  pressure  is  greater  from 
the  side  than  the  top,  the  leg  is  given  an  inclination  less  than  20°  from  the 
vertical  and  a  double-notched  joint  is  made,  as  in  Fig.  5.  The  foot  of  the  leg 
is  placed  in  a  hitch  in  the  floor  to  prevent  its  being  pushed  inwards. 


FIG.  4 


FIG.  5 


FIG.  6 


If  the  leg  a,  Fig.  6,  is  let  into  the  sill  b  as  shown,  the  pressure  p  along  the  leg 
may  be  resolved  into  the  two  components  cd  and  ce.  The  more  nearly  verti- 
cal the  leg  a  is,  the  greater  will  be  the  component  cd,  which  is  resisted  by  the 
cross-grain  of  the  wood,  and  the  stronger  will  be  the  joint.  The  tendency  of 

46 


722  SUPPORTING  EXCAVATIONS 

the  leg  a  to  slip  is  also  less  the  more  nearly  vertical  a  is.  If  the  leg  a  is  bent 
inwards,  the  heel  /  acts  as  a  fulcrum  of  a  lever  and  the  corner  e  tends  to  split 
off  the  block  above  the  line  eg. 

If  the  leg  a.  Fig.  7,  is  jointed  to  the  sill  b  as  shown,  there  is  less  danger  of 
its  slipping  or  of  its  splitting  the  timber  than  when  the  joint  shown  in  Fig.  8 
is  used.  The  pressure  p  acting  along  the  leg  a, 
Fig.  7,  can  be  resolved  into  the  two  components, 
one  cd  acting  vertically  and  across  the  grain  of  the 
wood,  and  the  other  ce  acting  parallel  to  the  grain 
of  the  wood.  In  this  case,  if  the  leg  a  bends  to- 
ward the  right,  the  tendency  is  for  the  heel  /  to 
split  the  sill  along  the  line  /g,  but  the  length  of 
wood  fiber  fg  in  this  case  is  longer  than  the  length 
of  wood  fiber  eg  in  the  joint  shown  in  Fig.  6,  and 
there  is,  therefore,  not  the  same  danger  of  the 
block  above  fg  splitting  off.  Again,  in  case  of  a 
sudden  shock,  the  wood  tends  to  slide  along  the 
face  fh,  that  is,  perpendicularly  to  the  direction  in 
which  the  pressure  is  transmitted  along  the  leg. 
Fir  7  The  timber  a  could  not,  therefore,  slide  on  the 

timber  b  as  readily  with  the  joint  in  Fig.  7  as  it 

could  with  the  joint  in  Fig.  6,  where  the  angle  of  inclination  between  the 
faces  of  the  timber  is  greater.  In  other  words,  with  the  joint  in  Fig.  7,  there 
will  be  much  more  friction  between  the  faces  of  the  timber  to  oppose  move- 
ment than  with  the  joint  shown  in  Fig.  6;  and  to  start  a  movement  of  the  leg, 
the  jar  must  be  much  more  severe. 

The  method  of  framing  heavy  shaft  timbering  is  described  under  the  head 
of  Square-Set  Timbering. 

CARE  AND  PRESERVATION  OF  TIMBER 

CUTTING  AND  STORING  TIMBER 

Time  to  Cut  Timber. — The  presence  of  much  sap  in  the  tree  when  it  is 
cut  causes  the  timber  to  decay  more  rapidly  than  it  would  otherwise,  owing  to 
the  fermentation  of  the  sap  permitting  the  growth  of  fungi  that  feed  on  the 
life  of  the  timber.  In  growing  timber,  the  sap  ceases  to  run  about  the  middle 
of  December  and  starts  again  about  the  middle  of  February.  Timber  cut, 
therefore,  in  the  months  of  December,  January,  and  February  will  contain 
the  least  sap  and  prove  more  lasting  than  the  same  timber  cut  at  other  times 
of  the  year.  The  work  of  cutting  timber  in  winter  gives  employment  also  to 
farm  hands  during  their  idle  season;  moreover,  the  task  of  transporting  tim- 
ber on  sleds  to  the  mines  or  the  railroads  is"  a  much  easier  one  in  winter  than 
during  the  seasons  when  wagons  must  be  used. 

Peeling. — Peeling  timber  is  a  simple  and  inexpensive  method  of  increasing 
its  durability,  and  under  some  conditions  is  fairly  effective.  Bark  retards 
the  loss  of  moisture  from  timber,  and  unbarked  wood  therefore  offers  more 
favorable  conditions  for  fungus  growth  than  wood  from  which  the  bark  has  been 
removed.  Moreover,  the  space  between  the  bark  and  the  wood  is  an  excellent 
breeding  place  for  many  forms  of  wood-destroying  insects.  In  dry  workings, 
the  life  of  timber  may  be  increased  from  10  to  15%  by  peeling,  although  in  wet 
situations  peeling  seems  to  have  little  effect. 

Besides  increased  durability,  there  are  other  advantages  to  be  derived  from 
the  use  of  peeled  timber.  The  bark  of  unpeeled  timber  often  flakes  off  soon 
after  placement,  causing  an  accumulation  of  inflammable  rubbish  in  the 
workings,  which  must  be  removed  at  some  expense.  To  peel  timber  in  the 
woods  or  at  the  shipping  point  effects  a  saving  in  freight  and  in  cost  of  handling. 
With  loblolly  and  shortleaf  pine  the  weight  of  bark  usually  amounts  to  from  8  to 
10%  of  the  original  green  weight. 

Seasoning  and  Storing  Timber. — The  durability  of  timber  may  in  some 
cases  be  increased  by  seasoning.  In  dry,  well-ventilated  workings  the  life 
of  seasoned  timber  is  sometimes  25%  greater  than  that  of  green  timber.  In 
wet  .locations,  however,  the  effects  of  seasoning  are  counteracted  by  the 
reabsorption  of  moisture. 

Whenever  practicable,  timber  should  be  seasoned  in  the  woods  or  at  the 
shipping  point,  in  order  to  realize,  through  loss  of  weight,  a  substantial  saving 
in  the  cost  of  freight  and  handling. 


SUPPORTING  EXCAVATIONS  723 

The  timbers  should  not  be  permitted  to  lie  on  the  ground  after  seasoning 
operations  are  commenced,  but  should  be  placed  on  blocks  so  that  they  will 
be  exposed  to  a  circulation  of  air.  The  blocks  should  not  be  so  far  apart  that 
the  timbers  will  sag;  and  the  timbers,  if  exposed  to  the  sun,  should  be  turned 
regularly,  otherwise  they  may  check  or  warp.  Sawed  timbers  should  be 
stacked  up,  with  air  spaces  between  the  sticks;  they  should  also  be  kept  under 
sheds  when  seasoning  and  before  they  are  taken  below  ground.  If  this  is 
not  possible,  they  should  be  stacked  so  that  they  will  shed  water. 

The  several  lengths  of  timber  should  be  stored  together  so  that  they  can 
be  readily  obtained  as  required.  To  prevent  warping  and  checking,  the  tim- 
ber should  not  be  seasoned  too  quickly,  as  is  frequently  the  case  when  artificial 
heat  is  employed,  or  when  the  timber  is  exposed  to  a  strong  sun,  especially 
when  the  circulation  of  air  is  not  sufficient. 

PRESERVATION  OF  MINE  TIMBER 

Destructive  Agencies. — The  relative  importance  of  the  various  destructive 
agencies  affecting  timber  varies  greatly  with  the  conditions  in  the  mines. 
Under  average  conditions,  the  different  destructive  agencies  cause  the  follow- 
ing percentages  of  loss:  Wear,  5%;  breakage  and  fire,  20%;  waste  from  all 
causes,  25%;  decay  and  insect  attack,  50%.  Dry  rot  and  fungus  growth  are 
diseases  common  to  most  timbers.  Some  timbers  are  more  apt  to  be  infested 
with  insects  and  suffer  from  this  cause  more  than  others,  owing,  probably,  to 
the  nature  of  the  wood  or  bark  as  furnishing  food  or  nesting  places  for  insects. 
Climatic  conditions  have  much  to  do  with  this  trouble;  in  some  climates,  the 
insects  multiply  rapidly  and  completely  destroy  the  timber  they  infest.  At 
times,  the  bark  of  the  timber  is  completely  filled  with  the  eggs  and  the  larvee 
of  insects,  and  must  be  removed  in  order  to  protect  the  timber  from  their 
inroads. 

When  wood  is  not  properly  seasoned,  the  sap  is  liable  to  ferment,  especially 
in  a  dry,  warm  place,  and  dry  rot  occurs,  beginning  in  the  center  of  the  stick 
and  working  outwards.  In  general  appearance  such  a  stick  looks  sound, 
but  by  thrusting  a  knife  blade  into  it  the  damage  is  discovered.  Fresh-air 
circulation,  when  the  stick  is  away  from  decaying  timber,  is  one  preventive 
of  dry  rot,  as  in  such  situations  the  stick  seasons. 

When  timber  is  placed  in  warm,  moist  air,  damp  rot  takes  place;  this  is  the 
usual  rot  affecting  mine  timbers.  It  commences  on  the  outside  and  gradually 
finds  an  entrance  into  the  interior  of  the  stick  through  some  check.  The 
destruction  of  a  timber  by  damp  rot  is  not  so  rapid  as  by  dry  rot  and  is  notice- 
able from  the  fungus  growth  on  the  outside  of  the  stick.  In  mines,  dry  rot 
occurs  in  the  intake  airways  and  in  poorly  ventilated  workings,  while  damp 
rot  occurs  in  the  return  airways  and  damp  rooms.  When  fungus  of  the  damp- 
rot  species  appears,  it  may  be  possible  to  save  the  timber  and  prevent  the  fun- 
gus reaching  the  heart  wood  by  washing  the  stick  down  with  lime  or  alum  water 
from  time  to  time. 

General  Principles  of  Timber  Preservation. — .The  partial  removal  of 
sap  will  retard  decay,  for  which  reason  timbers  are  sometimes  submerged  for 
several  months,  then  removed  and  air-dried.  A  temperature  of  between  60° 
and  100°  F.  combined  with  moisture  is  favorable  to  decay;  but  mine  timbers 
must  often  be  placed  where  such  conditions  prevail.  It  may  be  possible,  by 
special  wood  preservatives,  to  increase  the  life  of  timbers;  but  even  then  the 
sap  must  be  either  dried  or  removed,  as  wood  covered  with  paint  before  being 
thoroughly  seasoned  will  propagate  dry  rot  in  a  warm,  dry  place,  or  damp  rot 
in  a  moist,  warm  place.  With  good  sound  timber,  creosoted  joints  will  pro- 
long its  life,  especially  if  the  ends  have  been  submerged  in  creosote  a  month  or 
more.  Different  species  of  trees  differ  in  their  resistance  to  decay.  Cedar, 
tamarack,  and  locust  are  more  durable  than  pine,  oak,  or  cypress,  although 
in  certain  situations  they  may  all  have  the  same  life.  Contact  with  earth  is 
particularly  destructive  to  timber;  and  nearness  to  decaying  timber  is  a  source 
of  disease.  The  principal  means  adopted  to  arrest  the  processes  of  decay 
and  preserve  timber  are  creosoting,  salting,  and  charring  the  timber.  The 
first  two  methods  consist  in  impregnating  the  timber  with  cresote  or  a  solu- 
tion of  salt  so  as  to  fill  the  pores.  The  acid  acts  to  coagulate  the  albuminous 
matter  of  the  sap.  By  this  means,  the  pores  of  the  wood  are  filled  with  a 
deposit  of  salt  or  with  the  coagulated  albumen,  which  prevents  the  absorption 
of  moisture  and  arrests  the  process  of  decay  in  the  timber.  The  acid  also 
destroys  the  organic  life  of  the  wood.  In  the  third  method,  the  charring  of 
the  ends  and  surface  of  the  timber  closes  the  pores  of  the  wood  and  prevents 
the  absorption  of  moisture;  the  charred  surface  of  the  wood  will  not  then  decay. 


724  SUPPORTING  EXCAVATIONS 

Attempts  have  been  made  to  coat  mine  timber  with  some  substance,  as  tar, 
to  prevent  or  retard  its  decay;  in  other  cases,  the  timber  has  been  treated  with 
chemicals  with  the  same  end  in  view.  The  objection  to  the  use  of  creosote  or 
tar  for  preserving  mine  timbering  is  that  they  make  the  timber  more  inflam- 
mable than  it  would  otherwise  be.  Timbers  are  sometimes  treated  with  solu- 
tions of  the  chlorides  or  the  sulphates  of  the  various  metals.  When  a  regular 
plant  is  installed  for  this  W9rk,  timbers  are  first  placed  in  specially  prepared 
chambers  from  which  the  air  is  afterwards  exhausted,  and  then  the  solution 
for  preserving  the  timber  is  forced  in  under  pressure,  the  exhausting  of  the  air 
having  reduced  the  pressure  on  the  timber  and  opened  the  cells.  After  the 
preserving  material  enters  the  chamber,  it  is  forced  into  the  pores  of  the  wood 
in  such  a  manner  as  to  thoroughly  saturate  it. 

Before  timber  is  treated  with  preservatives,  it  should  be  peeled,  and,  as  a 
rule,  thoroughly  seasoned.  All  timbers  should  be  cut  and  framed  to  their 
final  dimensions  and  form  before  treatment,  because  the  sawing  and  cutting 
of  treated  timber  frequently  exposes  untreated  surfaces  to  attack  by  wood- 

We  are  indebted  to  the  reports  of  the  U.  S.  Forest  Service  for  the  following 
information. 

Brush  Treatments. — A  fairly  effective  and  cheap  treatment  is  to  paint 
timber  with  two  or  three  coats  of  hot  creosote  or  some  similar  preservative. 
It  is  important  that  the  wood  be  seasoned  before  treatment,  for  otherwise 
checking  may  later  expose  untreated  portions  of  the  timber  to  fungus  attack. 
Care  should,  moreover,  be  taken  to  get  the  preservative  well  into  all  checks, 
knot  holes,  and  surface  inequalities;  otherwise  decay  is  likely  to  develop  at  these 
points. 

The  amount  of  preservative  required  for  treatments  of  this  character  is 
relatively  small  and  no  special  equipment  is  needed.  Brush  treatments  are 
therefore  advisable  when  the  amount  of  timber  to  be  treated  is  too  small  to 
warrant  the  erection  of  even  a  small  plant,  or  when  it  is  necessary  to  restrict 
the  initial  cost  of  treatment  to  the  lowest  possible  figure.  The  main  disad- 
vantage of  brush  treatments  is  that  the  slight  penetration  secured  is  not  enough 
to  insure  the  protection  of  the  interior  of  the  timber  for  any  considerable  period. 
The  thin  coating  of  treated  wood  may  be  broken  or  split,  or  fungus  spores  may 
enter  through  nail  holes,  checks,  or  splits,  causing  decay  in  the  interior  of  the 
timber,  while  the  outside  appears  sound. 

Open-Tank  Treatments. — A  more  effective  method  of  treatment  is  the 
open  tank.  In  this  the  timber  is  first  immersed  in  a  tank  of  suitable  capacity 
containing  the  preservative,  and  the  charge  is  then  heated  to  a  sufficiently  high 
temperature  to  drive  off  a  portion  of  the  air  and  moisture  contained  in  the  wood. 
As  excessive  heating  is  likely  to  result  in  checks  that  will  weaken  the  timber, 
and  as  large  quantities  of  preservative  may  be  lost  by  volatilization,  the  maxi- 
mum temperature  of  the  hot  bath  should  not,  in  the  case  of  creosote  oils, 
exceed  220°  F.  and,  if  an  aqueous  salt  solution  is  used,  the  temperature  should 
be  kept  slightly  below  the  boiling  point  of  the  solution.  Following  the  hot 
bath,  the  timber  is  immersed  in  preservatives  at  a  lower  temperature,  or  it  may 
be  left  in  the  hot  liquid,  which  is  allowed  to  cool. 

The  treatment  of  timber  by  the  open-tank  process  insures  a  greater  pene- 
tration of  the  wood  by  the  preservative  than  does  the  brush  method,  and  for 
this  reason  has  proved  more  effective.  In  general,  it  is  well  adapted  for  the 
treatment  of  species  that  are  easily  impregnated. 

Pressure  Treatments. — With  many  species,  a  satisfactory  treatment  can 
be  secured  only  by  the  use  of  pressure.  The  essential  difference  between  the 

E-tank  process  and  the  pressure  processes  is  that  in  the  former  atmos- 
ic  pressure  is  relied  on  to  secure  the  penetration  of  the  wood,  while  in  the 
r  the  preservative  is  forced  into  the  timber  by  artificial  means.     Owing 
chiefly  to  the  difficulty  of  impregnating  many  species  of  wood  by  the  open-tank 
process,  the  pressure  treatments  are  the  most  widely  used. 

Pressure  processes  may  be  employed  for  either  full-cell  or  empty -cell  treat- 
ment. The  object  of  the  former  is  to  leave  the  treated  portion  of  the  wood 
completely  filled  with  the  preservative,  while  the  latter  aims  to  inject  the  pre- 
servative as  deep  into  the  timber  but  leave  n9  free  oil  in  the  wood  cells.  The 
oldest  process  of  full-cell  pressure  treatment  with  creosote  is  known  as  Bethelliz- 
ing.  A  similar  treatment  with  zinc-chloride  solution  is  called  Burnetlizing. 

Comparison  of  Open-Tank  and  Pressure  Treatments. — Experiments  made 
by  the  two  principal  processes  upon  different  kinds  of  timber  indicate: 

1.  Thoroughly  seasoned  loblolly  and  Pennsylvania  pitch  pine  round  mine 
timbers  may  be  satisfactorily  impregnated  by  the  open-tank  process. 


SUPPORTING  EXCAVATIONS  725 

2%  Green  timber  of  these  species  is  much  more  difficult  to  treat  than  sea- 
soned timber. 

•  3.  Satisfactory  results  may  be  secured  in  the  treatment  of  seasoned  west- 
ern yellow  pine  by  the  open-tank  process,  the  sapwood  of  this  species  being 
impregnated  without  difficulty. 

4.  In  general,  pressure  treatments  are  more  satisfactory  than  o^en-tank 
treatments.     By  the  former,  the  time  of  treatment  is  reduced  considerably 
and  the  preservative  is  more  generally  diffused  through  the  timber. 

5.  Heart  Douglas  fir  is  impregnated  with  difficulty. 

Cost  of  Open-Tank  Plant. — The  open  tank  is  the  simplest  type  of  apparatus 
used  for  the  impregnation  of  timber.  The  necessary  equipment  consists  mainly 
of  an  uncovered  tank  provided  with  a  device  for  submerging  the  timber.  The 
tank  may  be  so  arranged  that  a  fire  can  be  built  under  it,  but  if  a  supply  of 
steam  is  available  it  should  be  equipped  with  coils  for  heating  purposes.  If 
large  timbers  are  to  be  treated,  a  derrick  or  gin  pole  is  necessary  for  their  con- 
venient handling.  A  plant  of  this  character,  with  an  annual  capacity  of  100,000 
cu.  ft.  may  be  erected  at  a  cost  of  from  $1,500  to  $2,500.  The  low  cost  of  an 
open-tank  plant  places  it  well  within  the  reach  of  most  mine  operators,  and  this, 
perhaps,  is  its  main  advantage. 

Cost  of  Pressure  Plant. — The  cost  of  pressure  plants  depends  chiefly  on 
their  capacity.  The  total  cost  of  a  plant  having  a  capacity  of  approximately 
1,000  cu.  ft.  per  run,  or  750,000  cu.  ft.  per  yr.*  will  amount  to  from  $12,000 
to  $20,000.  The  following  is  a  list  of  the  main  items  of  equipment:  One 
horizontal  treating  cylinder,  65  ft.  long,  with  inside  diameter  of  6  ft.  2  in, 
capable  of  withstanding  an  internal  pressure  of  175  Ib.  per  sq.  in.;  two  vertical 
measuring  tanks,  each  of  15,000  gal.  capacity;  one  storage  tank  of  50,000  gal. 
capacity;  one  hoist  engine;  one  pressure  pump,  capacity  150  G.  P.  M.  at  175  Ib. 
pressure  per  sq.  in.;  one  air  compressor,  capacity  460  cu.  ft.  of  free  air  per  min. 
at  20  Ib.  pressure  per  sq.  in.;  sixteen  cylinder  cars;  one  zinc-chloride  mixing  tank 
of  2,000  gal.  capacity.  Special  attention  should  be  given  to  the  design  and 
construction  of  a  storage  yard  of  adequate  capacity  for  both  treated  and 
untreated  material,  as  handling  the  timber  before  and  after  treatment  is  an 
important  factor  in  the  cost  of  operation.  It  is  also  important  to  locate  the 
plant  at  a  convenient  point  in  the  mining  district,  so  that  treated  timber  may 
be  readily  distributed  to  points  where  it  is  to  be  used. 

A  pressure  plant  was  designed  by  the  Forest  Service  and  erected  by  the 
Anaconda  Copper  Mining  Co.  at  Rocker,  Mont.  Its  capacity  is  about  570  cu. 
ft.  of  timber  per  run.  The  equipment  is  as  follows:  One  treating  cylinder  43  ft. 
long  and  6  ft.  in  diameter,  working  pressure  100  Ib.  per  sq.  in.;  one  receiving 
tank,  47  ft.  long  and  5  ft.  in  diameter;  two  measuring  tanks,  12  ft.  in  diameter 
and  17  ft.  high;  one  general  service  pump,  360  G.  P.  M.  at  125  Ib.  per  sq.  in.; 
one  pressure  pump,  60  G.  P.  M.  at  125  Ib.  per  sq.  in.;  one  vacuum  pump  7  in. 
X  10  in.  X6  in.,  and  jet  condenser;  eighteen  cylinder  cars;  one  hoist  engine. 
The  total  cost  of  the  plant,  erected,  was  approximately  $15,000. 

A  plant  designed  by  the  Forest  Service  for  the  Tennessee  Coal,  Iron  & 
Railroad  Co.,  and  erected  at  McAdory,  Ala.,  has  a  capacity  of  about  830  cu.  ft. 
of  timber  per  run.  The  main  equipment  is  as  follows:  One  treating  cylinder, 
6  ft.  in  diameter  and  65  ft.  long,  working  pressure  100  Ib.  per  sq.  in.;  two  meas- 
uring tanks,  12  ft.  in  diameter  and  18  ft.  high;  two  storage  tanks,  11  ft.  in 
diameter  and  36  ft.  long;  one  settling  tank,  16  ft.  X  6  ft.  X  4  ft.;  one  pres- 
sure pump,  capacity  150  G.  P.  M.  at  100  Ib.  per  sq.  in.;  one  air  compressor, 
capacity  108  cu.  ft.  free  air  at  50  Ib.  per  sq.  in.;  one  air  reservoir  3  ft.  in  diam- 
eter and  15  ft.  long;  one  surface  condenser,  230  sq.  ft.  of  condensing  surface; 
twenty  cylinder  cars;  one  derrick  and  hoist  engine.  The  total  cost  of  this 
plant,  erected,  including  the  necessary  yard  construction,  amounted  to  approxi- 
mately $12,000. 

Cost  of  Treatment. — The  unit  of  cost  handling  timber  at  open-tank  plants 
is  higher  than  at  pressure  plants,  usually  amounting  to  from  3  to  4  c.  per  cu.  ft. 
at  the  former  and  from  2  to  3c.  per  cu.  ft.  at  the  latter.  These  figures  include 
interest,  depreciation,  and  operating  charges,  but  not  the  cost  of  the  preserva- 
tive, which  is  by  far  the  most  important  item.  The  accompanying  table  shows 
the  approximate  costs  of  the  untreated  and  treated  loblolly  pine  gangway  and 
entry  sets  used  in  the  Forest  Service  experiments  in  the  mines  of  the  Phila- 
delphia &  Reading  Coal  &  Iron  Co.  One  set  consists  of  one  7-ft.  collar,  one 
9-ft.  leg,  and  one  10-ft.  leg;  average  diameter  of  timber  13  in.;  approximately 
26  cu.  ft.  in  one  set. 

*Annual  capacity  is  based  on  two  runs  per  day  for  250  da. 


SUPPORTING  EXCAVATIONS 


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SUPPORTING  EXCAVATIONS  727 

Below  is  given,  in  detail,  the  cost  of  untreated  and  creosoted  16  ft.  by  8  in. 
Douglas  fir  shaft  sets  placed  in  the  mines  of  the  Anaconda  Copper  Mining  Co. 
These  sets  contain  1,127  ft.  b.  m.  of  Douglas  fir  squared  timbers  from  the 
Pacific  coast,  and  393  ft.  b.  m.  of  lagging.  The  average  absorption  secured 
in  the  treatment  of  these  timbers  amounted  to  4.5  Ib.  of  creosote  per  cu.  ft. 

Cost  of  Untreated  Sets 

1,127  ft.  b.  m.  squared  timbers,  at  $20.50  per  1,000  ft.  b.  m. .  .  $25.36 

Framing  timbers 13.50 

Cost  of  lagging,  at  $15  per  1,000  ft.  b.  m 5.90 

Switching  and  unloading  charges .85 

Cost  of  placing  set 18.00 

Total  cost  of  untreated  set  in  place $63.61 

Cost  of  Treatment 
Cost  of  treating,  including  interest,  depreciation,  fuel,  and 

labor  charges $  3.34 

Cost  of  creosote,  at   15. 6c.  per  gal.;  absorption  4.5  Ib.  per 

cu.  ft 8.03 

Loading  and  unloading  charges 1.23 

Total  cost  of  treatment $12.60 

Total  cost  of  treated  set  in  place $76.21 

These  examples  show  that  the  cost  of  treating  timbers,  while  a  considerable 
item,  does  not,  when  taken  in  conjunction  with  the  cost  of  the  timber  and  its 
preparation" and  placement,  form  an  unduly  high  proportion  of  the  whole  cost. 
The  actual  costs  for  other  mines  and  other  localities  will,  of  course,  differ  more 
or  less  from  the  figures  just  given,  but  they  serve  to  illustrate  the  relation 
between  the  cost  of  treated  and  untreated  timbers  under  different  conditions. 

Durability  of  Treated  Timbers. — Tests  to  secure  data  on  the  comparative 
durability  of  treated  and  untreated  timber,  begun  by  the  Forest  Service  in  1906, 
in  cooperation  with  the  Philadelphia  &  Reading  Coal  &  Iron  Co.,  have  been 
in  progress  for  a  sufficient  period  to  produce  results  of  practical  importance. 
The  experimental  timbers  were  standard  round  gangway  or  entry  sets,  treated 
and  untreated,  each  set  consisting  of  a  9-ft.  leg,  a  10-ft.  leg,  and  a  7-ft.  cap  or 
collar,  the  average  diameter  of  the  timber  being  13  in.  The  species  used  were 
longleaf,  loblolly,  and  shortleaf  pine,  Pennsylvania  pitch  pine,  and  red  and 
black  oaks. 

The  treated  sets  included  loblolly  and  shortleaf  pine  treated  by  the  brush 
method  with  creosote  and  carbolineum,  by  the  open-tank  method  with  various 
preservatives,  and  by  the  pressure  method  with  creosote  and  zinc  chloride. 
The  accompanying  table  gives  descriptions  of  the  treated  timbers. 

Most  of  the  timber  was  placed  during  1906,  1907,  and  1908;  and  inspections 
were  made  in  December,  1907;  March,  1909;  and  July,  1910. 

Owing  to  the  conditions  in  the  various  collieries,  it  was  not  always  possible 
to  make  a  complete  inspection  of  all  of  the  experimental  timbers,  nor  was  it 
possible  in  all  cases  to  procure  complete  data  on  the  cause  of  failure  of  indi- 
vidual pieces;  but  the  condition  of  the  timber  as  found  in  the  various  inspections 
offers  sufficiently  accurate  data  to  warrant  the  following  conclusions: 

1.  All  of  the  untreated  material  failed  within  from  1  to  3  yr.t  while  brush- 
treated  timber  remained  serviceable  for  from  3  to  4  yr. 

2.  The  life  of  untreated  peeled  loblolly  and  shortleaf  pine  was  from  10 
to  15%  greater  than  that  of  similar  unpeeled  material. 

3.  In  dry,  well- ventilated  workings  the  average  life  of  untreated  seasoned 
loblolly  pine  was  approximately  25%  greater  than  that  of  similar  green  material. 
In  wet  locations,  seasoned  timber  did  not  appear  to  outlast  unseasoned  material. 

4.  Loblolly  and  shortleaf  pine,  brush-treated  with  coal-tar  creosote  and 
Avenarius  carbolineum,  proved  to  be  from  50  to  100%  more  durable  than 
similar  untreated  material.    Moreover,  brush-treated  loblolly  and  shortleaf  pine 
proved  more  serviceable  than  untreated  longleaf  pine,  pitch  pine,  and  red  and 
black   oak.     Brush   treatment  with   Avenarius   carbolineum   was   somewhat 
more  effective  than  similar  treatment  with  coal-car  creosote. 

5.  The  condition  of  timber  treated  by  the  open-tank  process  with  sodium 
and  magnesium  chloride,  although  not  comparing  favorably  with  that  of  tim- 
ber similarly  treated  with  other  preservatives,  was  better  than  that  of  the 
brush-treated  timbers. 


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6.  Open- tank  treat- 
ments of  green  timber  with 
zinc  chloride  proved  fairly 
effective,  but  the  tests  indi- 
cate that  better  results  will 
be  secured  with  seasoned 
material.     About    13%    of 
the    green    timber    treated 
with  zinc  chloride  by  the 
open-tank   process   showed 
marked  signs  of  decay  after 
4  yr.,  while  no  decay   was 
found  after  the  same  period 
of  service  in  seasoned  ma- 
terial similarly  treated. 

7.  With  the  exceptions 
noted,  none  of  the  impreg- 
nated timbers  showed  signs 
of  decay  after  from  3  to  4 
yr.  service,  although  some 
of   them   had   failed    from 
crush  and  squeeze. 

8.  In  some  instances, 
impregnated   timber,   re- 
framed    after    treatment, 
showed  signs  of  decay.    This 
was   probably   due   to   the 
cutting  away  of  treated 
material  and  the  consequent 
exposure  of  untreated  por- 
tions of  the  timber. 

Economy  in  Use  of 
Treated  Timbers.  —  The 
original  cost  of  a  green  un- 
peeled  and  untreated  lob- 
lolly pine  gangway  set,  in- 
cluding removal  of  old  tim- 
bers and  placement  of  new 
ones  amounts  to  about 
$8.50.  The  average  life  of 
such  a  set  is  about  1  yr. 
and  4  mo.  At.  the  end  of 
this  period  the  simple  in- 
terest charges  on  the  ex- 
penditure amount  to  $.57, 
making  the  total  cost  up 
to  that  time  $9.07,  and  to 
this  must  be  added  a  re- 
placement charge  of  $8.50. 
The  total  charges  for  the 
two  installations  and  the 
maintenance  and  simple  in- 
terest on  the  first  installa- 
tion up  to  this  time  amount- 
ed to  $17.57.  After  a 
period  of  2  yr.  and  8  mo. 
the  interest  charges  on  the 
cost  of  the  first  installa- 
tion amount  to  $1.14,  and 
on  the  first  replacement  to 
$.57,  making  the  total  cost 
up  to  this  time  $18.71.  A 
second  replacement  is  then 
necessary,  but  if  a  number 
of  sets  are  considered  it  is 
unlikely  that  all  of  them  will 
fail  at  the  same  time.  In 
2  yr.  the  average  total 


SUPPORTING  EXCAVATIONS  729 

charges  against  the  untreated  set  amount  to  about  $18.10.  With  a  set 
brush-treated  with  creosote,  on  the  other  hand,  the  charges  amount  to 
$11.60,  a  saving  of  $6.50  due  to  the  treatment.  In  4  yr.  this  saving 
amounts  to  $13.80,  which  represents  the  difference  between  $33,  the  total 
cost  of  the  untreated  sets,  and  $19.20,  the  total  cost  of  the  brush-treated  sets 
for  that  period.  The  tests  further  indicate  that  brush  treatment  with  carbo- 
lineum  proved  more  economical  than  brush  treatment  with  creosote.  The 
fact  that  the  initial  cost  of  the  timber  at  different  periods  is  considered  to  be 
the  same  makes  the  conclusions  very  conservative,  as  the  price  of  mine  timbers 
will  unquestionably  continue  to  rise.  On  the  other  hand,  a  certain  salvage 
might  have  been  allowed  for  removed  props,  which  may  be  utilized  for  fuel  or 
sawed  into  lagging.  As,  under  the  conditions  of  the  experiment,  failure  from 
mechanical  causes,  such  as  crush  and  squeeze,  was  more  common  in  treated 
than  in  untreated  props,  the  former  would  have  a  greater  salvage  value,  and 
the  relative  saving  resulting  from  their  use  would  be  greater  than  that  noted. 

Because  the  impregnated  timbers  have  not  been  in  service  long  enough  to 
enable  their  average  life  to  be  determined,  most  of  them  being  still  sound 
when  last  inspected,  it  is  impossible  to  show  the  ultimate  saving  in  money, 
resulting  from  their  use.  Even  for  the  period  since  their  installation,  however, 
they  have  proved  more  economical  than  untreated  or  brush-treated  material. 

Not  only  will  proper  preservative  treatment  result  in  a  direct  saving  in 
money,  but  it  will  make  less  timber  necessary  for  any  given  working.  Further- 
more, the  use  of  treated  timber  makes  it  possible  to  utilize  many  of  the  inferior 
and  more  rapid  growing  species,  which,  though  possessing  most  of  the  require- 
ments of  high-grade  structural  timber,  lack  durability.  Treated  timber  of 
these  species  has  in  many  cases  proved  more  serviceable  than  high-grade 
untreated  material.  Thus,  in  the  Eastern  and  Southern  States,  treated  loblolly 
and  shortleaf  pines  may  take  the  place  of  untreated  longleaf  pine,  while  treated 
red  and  black  oaks  may  be  substituted  for  untreated  white  oak.  Douglas  fir, 
which  is  now  extensively  used  in  the  West,  may  in  turn  be  replaced  by  treated 
hemlock,  larch,  or  western  yellow  pine.  Inferior  grades  of  timber  can  usually 
be  bought  for  less  than  higher  grades,  and  an  additional  saving  thus  realized. 

Timber  that  is  to  be  treated  should,  whenever  possible,  be  round  instead 
of  square,  as  the  sapwood  of  most  species  is  more  easily  impregnated  than  the 
heartwood.  Moreover,  the  use  of  round  timbers  will  do  away  with  the  cost 
of  sawing  and  the  consequent  waste. 

A  further  economy  of  waste  may  be  effected  by  careful  inspection,  and  a 
rigid  condemnation  of  all  unsound  material.  This  is  especially  important 
where  the  timber  is  to  be  treated,  for  it  is  poor  economy  to  apply  an  expensive 
preservative  treatment  to  defective  material. 

The  utilization  of  waste  mine  timbers  has  sometimes  proved  profitable. 
Sound  sections  of  broken  or  partly  decayed  props  have  been  sawed  or  split 
into  laggings,  planking,  etc.,  and  in  some  cases  it  has  been  found  profitable 
to  use  this  material  for  fuel  or  to  sell  it  for  pulp  wood.  In  many  cases  such 
methods  afford  a  considerable  saving  and  also  provide  a  means  of  disposal 
for  waste. 

Summary. — Results  of  recent  investigations  may  be  summarized  as  follows : 

1.  Decay  is,  in  general,  the  agency  most  destructive  to  timber  used 
in  mines. 

2.  Although  decay  may  often  be  retarded  by  peeling  and  seasoning,  treat- 
ment with  a  suitable  preservative  is  more  effective. 

3.  The  average  life  of  green,  unpeeled,  and  untreated  loblolly-pine  gangway 
sets,  under  the  conditions  of  the  experiments  discussed,  was  less  than  1J  yr. 
Brush  treatments  with  creosote  and  carbolineum  increased  this  to  3  and  4  yr., 
while  impregnation  treatments  with  zinc  chloride  and  creosote  left  from  70 
to  90%  of  the  timbers  sound  at  the  end  of  4  yr. 

4.  The  use  of  treated  timber  results  in  a  saving  in  the  cost  of  maintenance 
of  workings  and  a  reduction  in  the  amount  of  timber  required  and  makes 
possible  the  utilization  of  inferior  species  of  wood. 

5.  Brush  treatments  are  economical  when  the  amount  of  timber  to  be 
treated  will  not  warrant  the  erection  of  a  small  open-tank  or  pressure  plant, 
or  when  only  a  short  increase  in  service  is  required. 

6.  The  open-tank  process  is  adapted  to  the  treatment  of  small  quantities 
of  easily  impregnated  timber.     When  a  large  amount  of  material  is  to  be 
treated,  a  pressure  process  should  be  used. 

7.  Mine  timbers  impregnated  with  zinc  chloride,  and  creosote  oils  have 
shown  the  best  results.     Up  to  the  present,  no  difference  in  their  durability 
has  been  noted. 


730 


SUPPORTING  EXCAVATIONS 


8.  An  efficient  system  of  inspection  and  careful  supervision  in  the  use  of 
timber  will  reduce  waste  and  result  in  considerable  economy.  Necessary 
waste  can  in  many  cases  be  utilized. 


FIG.  1 


H 


STEEL  AND  MASONRY  SUPPORTS 

IRON  AND  STEEL  PROPS 

Cylindrical  Cast-iron  Props. — Fig.  1  is  a  hollow  iron  prop  made  in  two 
sections  with  a  sleeve  a.  This  prop  has  been  used  in  longwall  workings  where 
it  is  necessary  to  draw  the  prop  to  let  the 
roof  sag.  By  knocking  up  the  sleeve,  the 
prop  falls  and  can  be  pulled  out  of  danger. 
In  case  one  or  the  other  section  of  the  prop 

is  buried  by  rock,  it  can  usually 

be  recovered  by  the  chain  at- 
tached, which  is  sufficiently 

strong    for    recovering    the    end 

from  under  the  first  fall.     There 

is  considerable  danger  of  the  cast- 
iron  sleeve  a  splitting  when  pres- 
sure conies  on  the  prop. 

Steel    H-Beam  Props.— Steel 

H-beam  props,  arranged  as  shown 

in  Fig.  2,  have  been  used  to  a 

limited  extent  in  American  mines. 

The  section  shown  at  a  is  cut  and 

forged  to  form  level  bearings ;  the 

cost  of  such   props  is  relatively 

high.     At  d  is  shown  a  design  in 

which   clips   are  formed   by   the 

use  of  &-in.  screen  plates  such 

as  are  used   at  the  breakers;  in 

this  case  the  H  section  is  simply 

cut  to  length  without  other  work; 

this  is  also  the  case  with  the  sec.- 

tions  shown  at  b  and  c,  where  2-in 
plank  or  plain  steel  plates,  |  or  $  in.  thick, 
are  used  for  bearings.     These  props  may 
be  secured  in  place  by  wooden  wedges. 

Cast-iron  Posts  With  I-Beam  Caps. — Cast-iron  posts  with  I-beam  caps  have 
been  employed  in  a  Staffordshire  colliery  in  England.  The  posts  were  made 
hollow  and  flanged  at  the  ends  as  in  Fig.  3  (o).  A  cast-iron  chair  a  fits  into  the 
post  and  receives  the  cap  b.  The  chair  was  made  for  a  50-lb.  rail,  which  was 
reversed  so  that  the  head  of  the  rail  would  slip  into  the  horns  of  the  chair  as 
shown  and  the  bottom  of  the  rail  be  upwards.  The  lagging  c  was  of  wood 
and  above  this  were  placed  planks  d  forming 
a  double  lagging  filled  in  above  with  waste  to 
make  a  tight  joint  with  the  roof  rock.  The 
planks  d  placed  on  the  lagging  c  saved  timber. 

STEEL  ENTRY  TIMBERS 
Standard  Forms. — A  set  of  timbers,  whether 
steel  or  wood,  consists  of  two  parts;  the  collar, 
or  cross-beam,  and  the  legs,  or  posts.     Under 
certain  conditions,  the  legs  may  be  dispensed  CW 

with    and    the    collars,    which    ordinarily   are  F  r   ^ 

rolled  I  beams,  may  be  set  in  hitches  cut  fn 

the  coal.  Or  the  collars  may  be  set  upon  wooden  or  hollow  cast-iron  legs,  or 
upon  brick,  masonry,  or  concrete  walls.  All  of  these  methods  have  been  suc- 
cessfully tried  in  many  places  at  home  and  abroad.  However,  the  I-beam 
collar  or  cap  is  generally,  especially  in  entry  timbering,  set  upon  legs  or  posts 
of  steel.  The  legs  are  of  two  general  types — channel  iron  or  H  beam.  The 
former  is  illustrated  in  Fig.  1,  which  is  called  by  the  makers,  the  Carnegie 
Steel  Co.,  Style  E.  This  form  corresponds  to  installations  in  which  steel  I- 
beam  collars  have  been  used  with  wooden  posts,  the  top  of  the  post  being 
cut  to  form  a  seat  for  the  collar.  The  two  channels  forming  the  legs  are 


(6) 


(d) 


FIG.  2 


SUPPORTING  EXCA  VA  TIONS 


731 


connected  by  bolts  and  separators,  carry  angle  brackets  at  their  tops  on  which 

the  collar  rests,  and  foot  on  a  steel  plate  towhich  bars  are  riveted  to  hold 

them  firmly  in  place.     Angles  t    •  .  .     .  .      —  ^ 

riveted  to  their  webs  transmit 

the  load  from  the  collar  to  the 

legs,  and  bent  angle  lugs  pre- 

vent undue   side    motion.     In 

this  form  of  construction,  there 

are    but     five     pieces     to     be 

erected:  the  single  collar  beam, 

two  legs,  and  two  base  plates. 

If  the  footing  is  good,  even  the 

base  plates,  shown  in  Fig.    2, 

can  be  eliminated  or  plain  plates 

can  be  used  instead  of  the 

riveted  bases.  » 

The  second  type  of  leg,  illus- 

trated in  Fig.  3,  consists  of  an 

H  beam  and   in  the  combina- 

tion shown   is  known   by  the 

makers  as  Style  F.     The  lug 

angles  at  the  top  prevent  side 

motion  and  the  bearing  plates  are  perfectly  plain,  as  shown  in  Fig.  4,  although 

base  plates,  Fig.  5,  to  which  the  legs  may  be  bolted  or  riveted  can  be  sup- 
plied upon  request.  This  is  the  simplest  form  of  entry 
timber  and  perhaps  the  one  in  most  general  use.  It 
should  be  noted,  that  where  a  broader  bearing  surface  is 
necessary,  H  beams  may  be  used  for  collars  in  place  of  the 
standard  I  beams. 

Mr.  R.  B.  Woodworth,  in  the  Transactions  of  the  Ken- 
tucky Mining  Institute,  Dec.,  1911,  states  as  follows:  "With 
plain  material  at  1.25c.  a  Ib.  f.  o.  b.  cars  Pittsburg,  and  the 
usual  cost  for  workmanship,  the  comparative  costs  of  these 
styles  are  shown  in  the  two  tables  that  follow,  from  which 


pIG 


FIG  2 


can   be  seen  at  a  glance  how  great  a  part  attention  to  details  may  play  in 

the  economic  use  of  materials  by  the  avoidance  of  unnecessary   work   in 

fabrication.     The  sets  in  each 

table   are   all  of  equivalent 

theoretical    strength.       In   the 

first  table,  are  given  steel  gang- 

way supports  for  a  very  heavy 

double-track    gangway,    collar 

17  ft.   long  between  legs,   legs 

10  ft.  6  in.  high  in  the  clear, 

equivalent  in  strength  to  24-in. 

round,  longleaf,  yellow-pine 

timbers. 

In  the  second  table  are 
given  the  steel  gangway  sup- 
ports for  a  single-track  gang- 
way, collar  10  ft.  long  between 
legs,  legs  8  ft.  high  in  the  clear, 
equivalent  in  strength  to  15-in. 
round,  longleaf,  yellow-pine 
timbers. 

"Figures  in  these  two  tables 


do  not  include  painting,  cost  of 


FIG.  3 

which  varies  with  the  kind  of  paint  used,  but  may 
be  estimated  at  $2  per  T.  additional.  Styles  A, 
B,  D,  and  E,  are  various  combinations  of  I-beam 
collars  and  channel  iron  legs,  while  styles  F,  G,  C, 
and  I  have  H-beam  legs." 

The  details  of  another  form  of  steel  entry  tim- 
bers are  shown  in  Fig.  6,  where  the  legs  are  pin- 
connected  to  the  cap  and  not  joined  by  angle  bars.  The  cap  piece  a  is  an 
I  beam,  while  each  leg  b  consists  of  two  channel  beams  that  rest  in  a 
cast  base  c  at  the  bottom.  The  top  of  each  leg  is  fastened  to  the  cap  by 
means  of  the  pin  d,  held  in  place  by  the  split  cotters  e.  Iron  wedges/  are  also 


FIG.  4 


FIG.  5 


732 


SUPPORTING  EXCAVATIONS 


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SUPPORTING  EXCAVATIONS 


733 


used  to  stiffen  the  connection  between  the  cap  and  the  leg.  Several  pinholes 
are  made  in  both  the  legs  and  the  collars,  so  that  the  same  set  may  thus  be 
used  in  several  positions.  In  order  that  the  legs  may  be  given  a  desired  batter 
the  legs  of  the  posts  fit  into  a  cast  shoe  c 
that  has  a  cylindrical  bottom,  and  this 
bottom  rests  in  a  cast  base  g.  This  forms 
a  very  easily  adjustable  set,  for  by  means 
of  the  base  illustrated  the  legs  can  be  given 
any  desired  batter,  and  the  set  is  then 
stiffened  by  means  of  the  wedges  /. 

Lagging  used  with  steel  timbering  may 
be  of  wood  or,  better,  of  boiler  plate,  or 
corrugated  sheets  of  buckle  plates  where 
extreme  strength  is  needed.  The  thin  con- 
crete slab,  however,  may  well  be  used  where 
acid  water  is  present,  either  plain  or  rein- 
forced with  expanded  metal,  wire-mesh 
reinforcement,  or  plain  rods  or  wire. 

For  pump  houses,  as  shown  in  Fig.  7, 
and  for  underground  stables  steel  framing, 
particularly  in  connection  with  concrete 
lining,  is  daily  growing  in  favor.  In  the 
pump  house  shown,  the  simple  steel  fram- 
ing took  the  place  of  heavy  framed  timbers 
that  it  is  necessary  constantly  to  renew. 

Relative  Cost  of  Steel  and  Wood  Tim- 
bering.—  Owing  to  the  movement  of 


FlG.  6 


^6 '\\23.8 /&• 


the  strata  overlying  the  pump  room  of  the  Dodson  colliery,  of  the  Plymouth, 
(Pa.)  Coal  Co.,  it  was  decided  to  retimber  it  with  steel.  The  original  wooden 
timbering  consisted  of  18-in.  to  22-in.  round  sticks  of  white  pine,  yellow  pine, 
and  oak  placed  2  ft.  center  to  center.  A  great  deal  of  trouble  was  experienced 
from  these  timbers  becoming  forced  in  close  upon  the  pipe  lines  with  the 
possibility  of  breaking  them.  As  new  timbers  were  placed,  they  were  put 
in  between  the  sets  already  in,  so  that  eventually  the  pump  room  had  timbers 
practically  skin  to  skin.  It  is  estimated  that  the  entire  pump  room  was 
retimbered  in  wood  once  a  year. 

The  pump  house  is  100  ft.  long,  8  ft.  high  in  the  clear,  and  18  to  22  ft.  wide. 
Beginning  with  April  18,  1910,  the  seventy  wooden  sets  of  mine  timbers  were 
replaced  by  forty-eight  steel  sets  made  up  of  18-in.,  55-lb.,  and  20-in.  65-lb. 
I-beam  collars  and  6-in.  H-beam  legs,  weighing  23.6  Ib.  per  ft.  The  last  set 
was  installed  about  De- 
cember 15,  1910. 

From  the  following 
statement  it  will  be 
noted  that  the  total  cost 
for  timbering  once  with 
wood  was  $2,415,  and 
the  total  cost  for  tim- 
bering in  steel  $2,889.09 , 
or  a  difference  in  first 
cost  of  not  quite  20%. 
The  steel  cost  at  the 
mines  slightly  over  two 
and  a  half  times  the 
cost  of  wooden  sets, 
and  it  also  cost  33^% 
more  for  placing. 
Fewer  sets  were  re- 
quired, however,  and 
the  ultimate  rate  was 
thereby  lessened. 

The  comparative  FIG.  7 

cost  of  the  two  instal- 
lations   is    shown    in    the    statement     below,   prepared   by    Mr.   Haddock: 


0-6 

^  Pump  Mouse  30-0"Lony 
^  Square  TJmter-5efs 
,f -},  j-0"c.foc. 


734  SUPPORTING  EXCAVATIONS 

Wood 

Number  of  sets 70 

Average  diameter  -of  timber,  inches 20 

Quality  of  timber,  yellow  pine  and  oak. 

Average  weight  per  set,  pounds 4,150 

Cost  per  set  f.  o.  b.  cars  mines $12.00 

Cost  per  set  for  placing $22.50 

Cost  per  set  in  place $34.50 

Total  cost  for  timbering $2,415.00 

Life  of  timber  set,  year 1 

Steel 

Number  of  sets. 48 

Size  of  collars,  18-in.  beam ,  pounds 55 

Size  of  collars,  20-in.  beam,  pounds 65 

Size  of  legs,  6-in.  H  beam,  pounds 23.6 

Quality  of  steel,  structural  grade. 

Average  weight  per  set,  pounds 1,483 

Cost  per  set  f.  o.  b.  mines $31.47 

Cost  per  set  for  placing $30.00 

Cost  per  set  in  place $61.47 

Total  cost  for  timbering $2,889.09 

The  higher  cost  of  placing  the  steel  is  due  to  three  causes: 

1.  The  charge  of  taking  out  the  old  timber,  which,  however,  was  insig- 
nificant, as  the  steel  was  placed  a  set  at  a  time  by  forepoling  ahead,  the  con- 
dition of  the  roof  being  very  bad  and  there  being  loose  material  for  an  unknown 
distance  above. 

2.  Great  care  was  taken  with  the  steel  to  line  it  up  properly  and  provide 
a  good  base,  which  was  made  of  a  solid  concrete  wall  built  the  full  length  of 
the  pump  room  on  each  side.     This  solid  concrete  base  is  unnecessary  with  the 
wood  and  might  have  been  omitted  with  steel,  but  its  use  means  a  real  better- 
ment in  the  construction. 

3.  The  steel  was  placed  without  interfering  with  the  operation  of  the 
pumps,  which  necessitated  very  careful  handling  and  added  something  to  what 
the  expense  would  have  been  had  the  room  been  free  from  obstructions. 

It  is  apparent  that  while  the  first  cost  of  the  steel  construction  is  greater 
than  that  of  wood,  it  will  have  much  more  than  paid  for  itself  if  its  life  extends 
over  15  mo.  only,  and  that  every  additional  length  of  time  it  stands  will  mean 
that  much  less  in  cost  of  maintenance.  The  first  steel  after  being  in  place 
16  mo.  showed  no  sign  of  deflection  in  the  collars,  and  what  is  better,  no 
evidence  of  fracture  in  the  concrete  where  any  overloading  of  the  steel  would 
immediately  show. 

In  1908,  at  their  Maxwell  colliery,  the  Lehigh  and  Wilkes-Barre  Coal  Co. 
timbered  a  double-track  gangway  with  20-in.,  65-lb.,  I-beam  collars  17  ft.  long 
between  legs,  and  8-in.  H-beam  legs  10  ft.  6  in.  high  in  the  clear,  weighing,  with 
base  plates,  1,720  Ib.  per  set.  These  took  the  place  of  wood  sets  made  of  24-in., 
round,  yellow-pine  timbers,  the  cost  of  which  erected  was  $15  per  set,  weight 
5,040  Ib.,  and  the  life  of  which  was  2|  yr.  In  view  of  their  probable  durability 
the  steel  sets  were  erected  on  concrete  bases  which  added  to  the  cost,  which 
reached  a  total  of  $40  per  set.  Capitalized  at  6%  interest,  the  value  of  the 
steel  sets  at  the  end  of  15  yr.  will  be  $95.86  each,  while  the  capitalized  value 
-of  the  six  wooden  sets  needed  in  that  time  will  be  $153.56.  At  the  end  of  the 
15  yr.  the  steel  will  have  a  scrap  value  per  set  of  $12.03,  while  the  wood  will 
be  worth  nothing,  a  saving  by  the  use  of  steel  of  $69.73  per  set  or  $4.65  per  yr. 
The  use  of  steel  in  English  mines  has  effected  a  saving  of  2c.  per  T.  of 
coal  mined. 

At  the  No.  8  mine  of  the  West  Kentucky  Coal  Co.,  Sturgis,  Ky.,  steel  mine 
timbers  are  used  in  the  new  slope,  both  main  heading  and  air-courses.  Sets 
in  use  are  Style  F  composed  of  10-in.,  25-lb.,  I-beam  collar  and  4-in.,  H-beam 
legs.  Sets  a/e  spaced  3  ft.  on  centers  and  lagged  with  oak  plank  3  in.  thick 
on  top  and  2  in.  thick  on  sides.  Between  the  sets  concrete  is  placed  up  to 
4  ft.  high.  This  makes  a  solid  reinforced-concrete  slope  from  the  entrance 
to  the  point  where  ribs  are  hard  and  top  good.  According  to  figures  furnished 
by  Mr.  W.  H.  Cunningham,  general  manager  of  the  company,  the  comparative 
costs  of  wood  and  steel  for  this  mine  were: 

Wood. — Yellow-pine  creosoted;  size  12  in.X12  in.,  264  B.  M.  ft.; 
cost  at  Sturgis  $10.56  per  set;  cost  in  place  $15.70;  weight  1,575  Ib. 
Wood. — Native  white  oak;  size  12  in.X12  in.,  264  B.  M.  ft.;  cost 
at  Sturgis  $7.92;  cost  in  place  $13.06  per  set;  weight  1,340  Ib. 


SUPPORTING  EXCAVATIONS 


735 


Steel. — Cost  of  steel  at  Sturgis  $9.75  per  set;  cost  of  placing  $1; 
cost  of  concrete  per  panel  $5.16;  total  cost  in  place  per  set,  steel 
alone  $10.75,  steel  concreted  $15.91;  weight  of  steel  sets  425  Ib. 
The  saving  in  the  use  of  steel  without  concrete  over  native  white  oak  was 
$2.31  per  set;  over  yellow  pine,  $4.95.     The  excess  cost  of  steel  with  concrete 
over  white  oak  was  $2.85  per  set;  over  yellow  pine,  21c.     This  favorable  com- 
parison is  due  to  the  high  unit  cost  of  the  wood  and  to  the  elimination  of  waste. 
The  safe  uniformly  distributed  load  on  the  wood  collar  is  19,200  Ib.,  on  the 
steel  collar  26,000  Ib.     The  safe  compressive  strength  of  the  steel  leg  is  43,200 
Ib.,  while  that  of  the  wooden  leg  is  105,100  Ib.;  in  the  one  case  more  than  ample, 
in  the  other  case  out  of  all  proportion. 

Advantages  of  Steel  Timbering. — Among  the  benefits  coming  through 
the  use  of  steel  timbering  are: 

1.  Reduced  Excavation. — In  the  Lehigh  and  Wilkes-Barre  installation  the 
same  clear  space  inside  was  had  with  steel  in  an  excavation  4  in.  less  in  height 
and  32  in.  less  in  width  than  that  needed  with  wooden  timbering;  in  the  Dodson 
colliery,  the  space  saved  was  2  in.  in  height  and  28  in.  in  width;  and  in  the 
West  Kentucky  installation,  2  in.  in  height  and  16  in.  in  width. 

2.  Better  Ventilation. — The  headings  being  larger,  the  ventilation  is  better, 
and  further,  the  absence  of  all  stages  of  decay  common  to  wooden  timbers, 
removes  a  serious  source  of  vitiation  of  mine  air. 

3.  Less  Dust-Catchment  Area. — Steel  mine  timbers  afford  a  much  less  area 
for  the  lodgement  of  explosive  coal  dust  than  do  wooden  ones  of  the  same 

strength   and   are  much  more 

easily  cleaned. 

4.  Fireproof    Character. 
One  of  the  greatest  advantages 
of   steel  timber  consists  in  its 
absolute  incombustibility,  ren- 
dering it  especially  suitable  for 
the  construction  of  underground 
shanties,    stables,    pump     and 
engine  rooms,  etc. 

Preservation  of  Steel  Mine 
Timbers.  —  The  corrosion  of 
structural-steel  timbers  within 
the  mine  is  not  so  serious  as 
above  ground,  as  the  conditions 
of  temperature,  humidity,  etc. 
are  practically  uniform.  Mine 
timbering  steel  should  not  be 
placed  unpainted  unless  it  is  to 
be  covered  with  concrete.  If 
well  painted  before  installation, 
steel  timbering,  so  far  as  rust  is 
concerned,  should  outlast  the 
life  of  the  mine.  After  17  yr.  of  use,  the  steel  timbers  installed  in  the 
Sterns  shaft,  of  the  Susquehanna  Coal  Co.  and  in  the  pump  room  of  the 
Hazleton  shaft  colliery,  No.  40  slope,  of  the  Lehigh  Valley  Coal  Co.,  are  still 
in  use  and  in  first-class  condition.  The  steel  timbering  at  the  No.  1  shaft  of 
the  Spring  Valley  (111.)  Coal  Co.,  is  in  good  condition  after  18  yr.  use.  Struc- 
tural steel  does  not  have  the  opportunity  to  corrode  as  does  the  steel  in  track 
rails'  underground  and  consequently  lasts  indefinitely.  Rails  are  laid  where 
they  come  in  direct  contact  with  any  acid  mine  water  and,  their  tops  being 
polished  by  passing  car  wheels,  are  in  the  most  unfavorable  position  to  resist 
corrosion. 

The  possible  effect  of  acid  mine  water  upon  steel  mine  timbers  has  been 
exaggerated.  Tests  under  working  conditions  show  that  the  careful  selection 
and  application  of  good  paint  will  prevent  the  destructive  action  of  mine 
water.  The  paint  should  be  applied  in  two  coats,  the  first  of  which  should  be 
red  lead  or  natural  iron  oxide  and  the  second  a  good  graphite.  The  coating 
should  be  applied  to  a  clean  surface  and  should  be  well  rubbed  in.  The  paints 
should  be  of  the  very  best  grade  mixed  in  pure  linseed  oil,  the  weight  of  the 
paint,  in  pounds,  per  gallon  of  oil  being  about  three  times  its  specific  gravity. 

MASONRY  AND  IRON  SHAFT  LININGS 

Masonry  Shaft  Lining. — Masonry  shaft  lining,  which  may  consist  of  brick, 
rock,  or  concrete,  is  used  where  timber  is  scarce  or  where  the  character  of  the 


FIG. 


736 


SUPPORTING  EXCAVATIONS 


strata  is  such  as  to  render  timber  lining  impracticable.  A  section  only  of  a 
shaft  is  sometimes  thus  lined,  while  the  ordinary  timber  lining  is  used  in  the 
greater  part  of  the  shaft.  These  linings  are  usually  laid  on  a  wedging  curb 
and  are  carried  upwards  in  sections,  as  shown  in  Fig.  1.  Each  section  is  laid 
on  a  ring  a  of  cast  iron  or  timber  resting  on  a  temporary  shelf  or  seat  b  cut  in 
the  rock.  As  the  lower  sections  are  built  up,  the  shelf  b  supporting  the  masonry 
above  is  cut  away  in  places  and  the  masonry  below  carried  up  to  furnish  the 
necessary  support  for  the  upper  section.  In  this  manner,  all  the  shelf  is 
finally  cut  away  and  replaced  by  the  masonry  of  the  lower  section. 

Tubbing. — Tubbing  is  an  English  term  applied  to  the  metal,  or  sometimes 
to  the  timber,  lining  of  a  circular  shaft,  and  is  particularly  used  when  such 
linings  are  employed  to  keep  water  from  flowing  into  a  shaft.  The  three  kinds 
of  metal  tubbing  are:  (1)  that  which  is  made  in  sections  with  outside  flanges 
and  is  simply  wedged  firmly  into  place  by  wedges  placed  between  the  tubbing 
and  the  wall  of  the  shaft;  (2)  that  which  is 
made  in  sections  and  bolted  together  on  the 
inside  both  at  the  vertical  and  horizontal 
joints;  (3)  that  which  is  made  up  of  com- 
plete rings  of  cylinders  bolted  together  by 
means  of  horizontal  flanges. 

The  metal  tubbing  a,  Fig.  2,  consists 
of  cast-iron  segments  varying  in  height 
from  18 to  36  in. .according  to  the  pressure 
to  be  resisted.  The  segments  are  flanged 
at  top,  bottom,  and  ends  and  $-in.  pieces 
of  pine  are  put  between  them  as  they  are 
put  in  place,  thus  making  tight  joints  both 
horizontally  and  vertically.  To  prevent 
breaking  the  metal  lining  by  the  pressure 
of  air  or  gas  behind  it,  the  metal  is  per- 
forated; these  holes  are  loosely  plugged,  so 
that  any  particular  pressure  corning  on 
them  will  force  out  the  plugs.  At  b  is  shown 
a  method  of  walling  a  circular  shaft  with 
brick,  the  brick  being  laid  on  a  cast-iron 
wedge  curb  s. 

Wood  tubbing  may  be  of  two  kinds: 
(1)  planks  2  or  3  in.  thick  placed  vertical- 
ly and  having  edges  like  barrel  staves ;  (2) 
thick  blocks  similarly  beveled  and  placed 
vertically.  At  c  is  shown  an  example  of 
plank  tubbing.  The  planks  have  timber 
curves  m  placed  inside  them  and  spiked 
to  them.  The  curves  are  kept  apart  by 
punch  blocks  n  and  are  tied  together  and 
fastened  to  the  shaft  sills  I  by  the  stringers 
r.  The  sections  of  the  shaft  b  and  c  are 
shown  supported  on  a  rock  bench  while  the 
metal  tubbing  is  being  put  in  place  below. 
When  a  shaft  has  been  lined  up  to  the 
rock  bench,  this  is  cut  away  and  the  metal 
tubbing  joined  to  the  other  portion  of  the 
shaft  lining  by  small  metal  sections,  called 
closers. 


Ml  •  " 


I  •  I  •  »  •  I 


«°«  •  I  •  I -I 


JUJ= 


II °  I  •  I  •  I -I 


FIG.  2 


The  following  formula  is  given  by  Mr.  W.  Galloway  for  calculating  the 
proper  thickness  for.  cast-iron  tubbing,  or  for  cement  or  brick  lining: 

ivhd 

2(r+wh) 
in  which   t  =  thickness  of  lining,  in  inches; 

d  =  internal  diameter  of  shaft,  in  inches; 
h  =  head  of  water,  in  inches; 

w  =  weight  of  cubic  inch  of  water  =  -=^  =  .0361  lb.; 

l,7^o 
r  =  33}%  (one-third)  of  crushing  load  per  square  inch  of  material 

used. 

The  crushing  strength  of  the  material  used  should  be  determined  in  each 
case  by  experiment,  but  the  following  may  be  used  as  a  fair  average  value: 


SUPPORTING  EXCAVATIONS 


737 


Pounds  Per 
Square  Inch 

Crushing  strength  of  cast  iron 80,000 

Crushing  strength  of  brick  laid  in  lime  mortar 1 ,000 

Crushing  strength  of  brick  laid  in  cement  and  lime 1,500 

Crushing  strength  of  brick  laid  in  best  cement  mortar 2,000 

Crushing  strength  of  concrete  made  from  Portland  cement  and 

1  mo.  old 1,000 

Crushing  strength  of  concrete  made  from  Rosendale  cement 

and  1  mo.  old 500 

Crushing  strength  of  concrete  made  from  Portland  cement  and 

1  yr.  old 2,000 

Crushing  strength  of  concrete  made  from  Rosendale  cement 

and  1  yr.  old 1,000 

EXAMPLE. — What  should  be  the  thickness  of  tubbing  for  a  shaft  13  ft.  in 
diameter  at  a  depth  of  800  ft.:  (a)  for  cast  iron?  (b)  for  brick,  assuming  a 
mean  crushing  strength  of  1,500  Ib.  per  sq.  in.?      (c)  for  concrete  made  from 
Portland  cement  and  1  mo.  old? 
SOLUTION. — 


(a)     /< 


.0361X800X12X13X12 


27,031 


26,666  +  347 


=  1  in 


2X 


fM 

L 


+(.0361X800X12) 


.0361X800X12X13X12 


27,031 


2X 


, 
-- 


STEEL  AND  CONCRETE  SHAFT  LININGS 

Steel  Sets. — The  use  of  steel  alone  and  not  in  connection  with  concrete 
lining  is  unusual  in  shaft  timbering.  An  illustration,  however,  is  afforded  by 
the  shaft  at  the  Mt.  Lookout  colliery,  of  the  Temple  Iron  Co.,  and  illustrated 


gjrjf  'Plate 

at>'f  every  e'-o"  4 


FIG.  1 


in  Fig.  1.  The  steel  sets  were  used  to  reinforce  the  worn-out  original  wooden 
sets,  which  were  left  in  place.  The  steel  sets  consisted  of  12-in.  channels  set 
back  to  back,  separated  by  anchor  plates  to  catch  in  the  wood  of  the  original 
lining,  and  double  6-in.  channels  to  take  the  place  of  the  10"X12"  buntons 
47 


738 


SUPPORTING  EXCAVATIONS 


FIG.  2 


originally  separating  the  compartments.  It 
would  seem  that  instead  of  channels,  H  sec- 
tions should  have  been  used  as  better 
adapted  to  resist  compression  than  the 
channels,  as  well  as  being  lighter  and, 
hence,  cheaper. 

Steel  Buntons. — Steel,  in  place  of  wood, 
is  very  commonly  employed  for  buntons 
even  in  shafts  that  are  not  lined  with  con- 
crete. Some  of  the  various  forms  are  shown 
in  Fig.  2,  and  of  these  the  H  section  ap- 
pears the  best  and  is  the  most  generally 
used.  Steel  buntons  are  fireproof,  but  cost 
much  more  than  wood;  four  times  as  much 
if  a  section  as  light  as  35  Ib.  per  ft.  is  used. 
On  the  other  hand,  with  proper  care,  they 
will  last  indefinitely. 

Concrete  and  Steel  Shaft  Linings. 
Practically  all  concrete-lined  shafts  are 
elliptic  in  section,  the  arch  form  being 
adopted  as  better  able  to  withstand  pressure 
than  the  rectangular.  A  full  description 
of  the  concrete-lined  shaft  at  the  Filbert 
mine,  of  the  H.  C.  Fnck  Coke  Co.,  Fayette 
County,  Pa.,  is  given  on  page  230. 

The  rectangular,  concrete-lined  shaft  of 
the  Bunsen  Coal  Co.,  near  Clinton,  Ind.,  is  shown  in  Fig.  3.  The  buntons  are 
6"X8"  concrete  beams  reinforced  with  a  6-in.  8-lb.  channel.  Where  the  shafts 
pass  through  soft 
ground,  the  ends  are  also 
reinforced  with  the  same 
size  channels.  'The  lin- 
ing is  G  in.  thick  through 
firm  material  and  12  in. 
through  soft.  The 
guides  are  6"  X  8"  yellow 
pine  bolted  to  the  rein- 
forced-concretebuntons. 
The  partitions  in  the  air- 
shaft  at  this  mine  are  8 
in.  thick  and  of  rein- 
forced concrete  built 
with  American  Steel  and 
Wire  Co.'s  No.  4  tri- 
angular-mesh reinforce- 
ment on  6"X8"  bun- 
tons  reinforced  with 
channels  as  noted. 

In  the  elliptical 
shaft  of  the  Tennessee 
Coal,  Iron,  and  Rail- 
road Co.,  at  Pratt  mine 
No.  13,  near  Ensley, 
Ala.,  amassive,  unrein- 
forced  concrete  lining  is 
used  with  a  minimum 
thickness  of  15  in. 
through  firm  and  18  in. 
through  soft  material. 
The  buntons  are  6-in. 
steel  H  sections,  weigh- 
ing 23.8  Ib.  per  ft., 
spaced  6  ft.  apart.  The 
guides  are  of  the  same 
material  as  the  buntons 
and  carry,  bolted  to 
them,  cast-steel  safety 
racks.  FIG.  3 


HOISTING  739 


HOISTING 

Hoisting,  or  winding,  engines  may  be  driven  by  hand,  horse,  or  mechanical 
power.  The  mechanical  power  may  be  derived  from  engines,  or  motors,  driven 
by  steam,  electricity,  gasoline,  compressed  air,  water,  etc. 

There  are  two  general  classes  of  hoists:  single  and  double.  In  the  former, 
there  is  but  one  cageway  in  the  shaft  and  up  this  the  cage  and  loaded  car  are 
hoisted  by  an  engine.  After  the  load  is  dumped  at  the  surface,  the  cage  and 
empty  car  descend  through  the  same  compartment,  impelled  by  gravity,  their 
speed  being  controlled  by  the  brakes  on  the  engine  drum.  In  double  hoists, 
there  are  two  cages  which  travel  in  separate  compartments,  one  ascending  with 
the  loaded  car  as  the  other  descends  with  the  empty  car.  Double  hoists  are 
the  prevailing  type,  the  use  of  single  hoists  being  confined  to  prospecting  shafts 
and  to  unimportant  operations  in  the  metal-mining  districts. 

There  is  no  essential  difference  between  stationary  engines  used  for  hoisting 
and  for  haulage.  The  chief  distinction  lies  in  the  direction  of  application  of 
the  power  generated  by  the  engine.  In  hoisting  engines,  the  power  is  applied 
vertically  to  raise  a  weight  through  a  shaft;  in  haulage  engines,  the  power 
is  applied  in  a  horizontal  or  approximately  horizontal  direction  to  move  a 
weight  along  a  track.  Frequently,  the  same  mechanism  after  having  served 
its  purpose  as  a  hoisting  engine  is  used  for  haulage,  and  vice  versa. 

The  subject  of  hoisting  ropes  is  discussed  under  the  head  of  Wire  Ropes. 


HAND-  AND  HORSE-POWER  HOISTS 

Hand-  and  horse-power  hoists  are  of  relatively  small  capacity  and  are  almost 
entirely  used  for  prospecting,  shaft  sinking,  or  the  like. 

The  -windlass,  operated  by  one  or  two  men,  is  frequently  used  for  sinking 
small  shafts  to  depths  of  about  75  ft.,  where  the  loaded  bucket  weighs  but 
a  few  hundred  pounds.  In  form,  it  is  similar  to  the  hoisting  device  used  in 
connection  with  water  wells  and  consists  of  a  wooden  barrel,  about  8  in.  in 
diameter  and  4  or  5  ft.  long,  provided  with  a  1  to  li-in.  iron  axle.  This  axle 
is  supported  at  either  end  in  A-shaped  wooden  standards  nailed  or  mortised 
to  a  heavy  timber  base  placed  over  the  shaft.  The  necessary  crank  and 
handle  is  attached  to  each  end  for  applying  the  power. 

For  hoisting  heavier  weights,  single-  or  double-geared  iron  crab  winches 
are  used.  In  these,  the  power  is  transmitted  to  the  drum  or  barrel  by  rack  and 
pinion,  so  that  one  man  can  raise  1  T.  or  more,  but  at  the  expense  of  speed. 
These  hoists  are  single  and  unbalanced,  the  bucket  being  hoisted  by  one  or 
two  men  and  descends  by  gravity;  its  speed  is  controlled  by  loosening  or 
tightening  the  rope  upon  the  drum. 

For  greater  depths  and  heavier  loads,  horse  whims,  or  gins,  are  used.  These 
consist  essentially  of  a  drum  mounted  on  a  shaft  to  which  are  attached  one 
or  more  cross-sweeps  to  each  of  which  a  horse  or  mule  is  hitched.  Usually 
the  whim  is  placed  a  little  distance  from  the  shaft  and  is  so  arranged  that  the 
movement  of  the  car  is  regulated  by  two  hand  levers,  which  are  connected  to 
the  driving  gear  in  such  a  way  that  the  movement  of  the  drum  may  be  stopped 
or  reversed  independently  of  the  movement  of  the  horse.  One  lever  is  moved 
to  hoist  and  the  other  to  lower  the  load,  and  through  their  use  overwinding 
is  prevented  in  case  the  animal  does  not  stop  on  the  instant. 

In  the  better  classes  of  whims,  the  drum  is  placed  horizontally  underground 
or  below  a  platform  to  be  out  of  the  way  of  the  horses,  motion  being  imparted 
to  it  from  a  vertical  shaft  through  beveled  gearing.  The  vertical  shaft  is 
provided  with,  two,  four,  or  six  sweeps  to  each  of  which  one  or  two  horses 
may  be  hitched,  so  that  as  many  as  twelve  animals  may  be  used.  With  four 
horses,  90  T.  have  been  hoisted  GOO  ft.  in  10  hr.;  and  with  eight  mules  GO  T. 
have  been  hoisted  900  ft.  in  the  same  time.  Some  whims  are  provided  with 
gears  for  hoisting  heavy  loads  at  slow  speed  and  lighter  loads  at  high  speed. 
Such  machines,  at  slow  speed  will  hoist  2,400  Ib.  22  ft.  per  min.;  and  at  fast 
speed,  950  Ib.  55  ft.  per  min. 


740  HOISTING 

STEAM-POWER  HOISTING  ENGINES 

Hoisting  engines  are  almost  invariably  of  the  duplex,  or  two-cylinder,  type 
with  cranks  set  at  right  angles  to  one  another  and  therefore  have  no  dead 
center;  for  which  reason  they  can  be  quickly  started  from  any  position  and 
run  more  smoothly  than  single-cylinder  engines. 

Hoisting  engines  may  be  simple  or  compound,  and  tandem  or  cross-compound. 
The  first  is  by  far  the  most  extensively  used  in  the  shallow  shafts  prevailing 
in  the  coal  regions,  where  the  shortness  of  the  hoisting  period  and  the  frequent 
reversals  of  the  engines  are  not  conducive  to  the  economical  use  of  high- 
pressure  steam  expansively.  In  the  metal-mining  regions,  where  vertical  lifts 
of  1,000  ft.  are  usual,  of  2,500  ft.  fairly  common,  and  where  several  of  from  4,000 
to  over  5,000  ft.  exist,  refinements  in  compounding,  etc.  are  successfully  used. 
Further,  in  metal-mining  regions,  the  price  of  coal  is  such  (from  $4  to  $10  and 
more  per  ton)  that  it  is  imperative  to  secure  all  the  energy  possible  from  each 
pound  of  fuel;  while  at  coal  mines  and  particularly  at  those  where  slack  is  used 
under  the  boilers  the  cost  of  power  has  not,  until  comparatively  recent  years, 
been  thought  worthy  of  consideration. 

A  hoisting  engine  may  be  of  the  slide-valve,  piston-valve,  or  Corliss-valve 
type  and  may  be  condensing  or  non-condensing.  For  a  large  hoisting  engine, 
a  piston-valve  gives  a  much  better  distribution  of  steam  in  the  steam  chest 
than  a  slide-valve,  but  not  so  good  as  a  Corliss  valve.  A  hoisting  engine,  to 
run  condensing,  should  have  an  independent  air  pump  and  condenser;  for  if 
the  air  pump  is  operated  by  the  engine  it  will  stop  when  the  engine  stops  and 
the  vacuum  will  be  lost,  rendering  the  low-pressure  piston,  in  some  cases, 
inadequate  to  pick  up  the  load  at  the  beginning  of  the  next  hoist. 

In  a  hoisting  engine,  the  drum  on  which  the  hoisting  rope  coils  takes  the 
place  of  a  flywheel,  to  a  certain  extent.  The  operation  of  hoisting  is  inter- 
mittent in  character,  and  in  some  cases  the  engine  is  so  connected  that  it  will 
run  only  when  operating  the  drum;  in  other  cases  it  will  run  continuously, 
either  empty  or  under  some  other  load  than  the  hoisting  load,  the  work  of 
hoisting  being  put  on  it,  when  needed,  by  means  of  a  friction  clutch  connecting 
the  engine  with  the  drums.  Where  an  engine  runs  continuously,  its  surplus 
power  may  be  utilized  for  driving  air  compressors,  fans,  electric  generators, 
and  other  machinery;  and,  by  thus  concentrating  the  power,  a  higher  grade 
engine  can  be  made  available  for  hoisting  purposes. 

Second-Motion,  or  Geared,  Hoisting  Engines. — In  a  second-motion  engine, 
power  is  transmitted  from  the  engine  shaft  to  the  drum  shaft  through  gearing. 
This  engine  is  particularly  adapted  for  portable  hoists,  such  as  are  used  in 
shaft  sinking  and  similar  temporary  work,  and  for  shallow  mines,  or  mines 
where  a  small  t9nnage  is  raised.  It  is  cheaper  in  first  cost  and  in  installation 
than  a  first-motion  hoisting  engine,  as  a  smaller  engine  does  the  same  work,  but 
it  cannot  hoist  as  rapidly;  there  is  also  less  liability  of  overwinding.  Geared 
engines  are  used  ordinarily  where  a  hoisting  speed  of  750  ft.  per  min.  or  less  is 
satisfactory,  while  first-motion  engines  are  used  for  greater  speeds.  To  hoist 
the  same  load,  a  first-motion  engine  must  be  three  to  four  times  as  large  as  a 
second-motion  engine,  while  the  hoisting  speed  and  cost  will  also  be  three  to 
four  times  as  much. 

The  relative  number  of  teeth  in  the  gears  may  be  varied  so  that  the  piston 
speed  may  be  made  faster  or  slower  or  equal  to  that  of  the  rope.  The  com- 
monly used  ratios  vary  from  1  to  3  to  1  to  5;  that  is,  if  the  small  gear-wheel 
on  the  engine  shaft  has,  say,  20  teeth,  the  large  gear-wheel  on  the  drum  shaft 
will  have  GO  to  100  teeth,  depending  on  the  ratio,  and  it  will  require  from  three 
to  five  revolutions  of  the  engine  to  equal  one  of  the  drum. 

If  the  ratio  is  exact,  the  teeth  on  the  small  gear  come  in  contact  with  the 
same  teeth  on  the  large  gear  during  every  revolution  and  cause  excessive  wear. 
To  equalize  the  wear,  the  number  of  teeth  in  the  large  wheel  is  commonly  one 
less  or  more  than  that  demanded  by  the  exact  ratio.  Thus,  if  the  engine  is 
geared  1  to  5,  while  20  teeth  on  the  small  wheel  require  100  on  the  large  wheel, 
either  99  or  101  would  be  used. 

Hoists  are  occasionally  built  with  metal  teeth  in  the  pinion  and  wooden 
teeth  in  the  larger  wheels.  The  larger  wheels  in  such  cases  are  cast  with 
mortises,  into  which  are  driven  maple  cogs  that  are  made  secure  by  wedges. 
These  wooden  cogs,  or  teeth,  wear  well  and  are  easily  replaced  when  broken 
without  seriously  interrupting  hoisting  operations;  they  are  almost  noiseless. 
It  a  metal  tooth  breaks,  the  gear  must  be  replaced,  and  hoisting  must  cease 
until  this  can  be  done.  In  cut  gears,  the  teeth  are  finished  by  machine;  this 


HOISTING  741 

adds  slightly  to  the  cost  of  these  gears,  but  they  are  more  serviceable  than 
rough,  cast  gears  and  make  less  noise. 

Geared  engines  may  have  single  or  double  drums,  the  former  being  in  general 
use  at  coal  mines  where  the  shafts  are  relatively  shallow  and  the  material  is 
hoisted  frorn  one  level.  Single-drum  engines  are  commonly  used  in  balance, 
the  drum  being  keyed  directly  to  the  shaft,  one  rope  unwinding  from  the  top 
of  the  drum  as  the  other  rope  winds  up  beneath  it.  Double-drum  engines 
may  be  used  in  balance,  by  leading  the  ropes  as  just  indicated  but  on  the 
separate  drums;  or  they  may  be  used  independently,  each  drum  hoisting  as 
desired  and  both  ropes  leading  on  the  drums  alike,  that  is,  both  on  top  or  both 
underneath. 

The  wearing  surfaces  in  hoisting  engines,  especially  the  main  bearings, 
should  be  made  large  and  the  engines  proportioned  to  stand  severe  work.  In 
the  case  of  two  wide-faced  drums  on  the  shaft,  it  is  sometimes  necessary  to  have 
a  center  bearing,  which  should  be  adjustable  in  every  direction  and  kept  as 
nearly  in  line  with  the  other  bearings  as  possible.  Owing  to  the  difficulty  of 
keeping  three  bearings  in  line,  and  the  danger  of  the  shaft  breaking  in  case  the 
bearings  are  not  in  line,  it  is  well,  where  practicable,  to  omit  the  center  bearing 
and  make  the  shaft  as-short  as  possible  and  ample  in  diameter. 

First-Motion,  or  Direct-Acting,  Hoisting  Engines. — In  first-motion  hoists, 
a  pair  of  engines  (right-  and  left-handed)  are  used  with  their  cranks  on  the  ends 
of  the  same  shaft  as  the  drum,  the  cranks  being  set  at  angles  of  90°  with  each 
other  to  prevent  the  engines  stopping  on  a  dead  center.  A  direct-acting 
hoisting  engine  is  used  wherever  the  depth  of  the  shaft  or  a  large  output  demands 
a  high  speed  of  hoisting.  In  coal-mining  practice, their  use  was  formerly  limited 
to  the  deepest  shafts,  but  the  large  outputs  required  from  modern  mines  have 
caused  them  to  be  introduced  at  comparatively  shallow  shafts. 


HOISTING  ENGINES  USING  OTHER  POWER  THAN 
STEAM 

Compressed-Air  Hoisting  Engines. — Where  available,  compressed  air  may 
be  used  in  place  of  steam  for  power  as  there  is  no  essential  difference  in  the 
engines.  Compressed  air  may  be  used  exclusively  or  interchangeably  with 
steam,  and  should  be  reheated  before  entering  the  engine  cylinders.  In  the 
case  of  a  compound  engine,  the  reheater  may  be  placed  in  the  pipes  leading  to 
the  high-pressure  cylinder;  or,  still  better,  it  may  be  placed  before  each  cylinder; 
otherwise,  the  expansion  will  cause  the  moisture  to  freeze  in  the  low-pressure 
cylinder  and  stop  the  engine. 

Where  a  hoisting  engine  is  located  on  the  surface  and  a  boiler  plant  is 
necessary,  steam  is  generally  preferable  to  compressed  air,  as  the  loss  in  efficiency 
due  to  compressing  the  air  is  avoided.  If,  however,  water-power  is  available, 
it  is  frequently  cheaper  to  use  compressed  air  instead  of  steam,  particularly 
if  compressed  air  is  also  used  at  the  mine  for  coal  cutters  or  rock  drills;  or  if 
for  any  reason  it  is  necessary  to  place  the  hoisting  engine  at  a  distance  from 
the  boiler  plant,  as  there  is  much  less  loss  of  efficiency  in  carrying  compressed 
air  than  in  carrying  steam.  For  underground  hoists,  compressed  air  has  many 
advantages,  particularly  in  gaseous  coal  mines. 

Further  data  on  compressed  air  will  be  found  under  that  heading  and  under 
the  heading  Haulage. 

Gasoline  Hoisting  Engines. — Gasoline  hoists  are  adapted  for  sinking 
prospecting  shafts  in  mpuntainous  districts  where  fuel  is  scarce  and  where  an 
easily  portable  engine  is  desirable.  They  are  not  generally  used  for  permanent 
hoists  in  mines  of  any  great  capacity.  Their  operation  is  essentially  on  the  lines 
of  gasoline  haulage  motors,  which  are  described  under  the  heading  Haulage. 
The  gasoline  is  injected  into  the  engine  cylinder  in  the  form  of  a  spray  and  is 
there  mixed  with  air  and  ignited  by  means  of  an  electric  spark,  producing  an 
explosion  that  moves  the  piston.  When  starting  the  engine,  the  clutch  is 
released  and  the  engine  is  rotated  by  pulling  over  the  flywheel  until  it  has 
received  the  first  impulse,  which  usually  requires  from  one  to  two  complete 
turns.  After  receiving  the  first  exptosion,  the_  engine  continues  to  operate, 
drawing  in  a  supply  of  gasoline  and  air  and  igniting  it  with  an  electric  spark. 
When  operating  the  hoisting  drum,  the  engineer  first  speeds  up  the  engine 
and  then  throws  the  clutch  that  controls  the  hoisting  drum.  Drums  must 
be  well  equipped  with  a  powerful  brake  in  the  use  of  either  gasoline  or  electric 
hoists,  to  avoid  accident  due  to  the  possible  failure  of  the  power. 


742 


HOISTING 


Hydraulic  Hoisting  Engines. — Hoisting  engines  using  the  direct  energy  of 
falling  water  as  a  source  of  power,  while  not  infrequently  employed  in  metal- 
mining  districts,  are  not  known  in  the  coal  fields. 

Electric  Hoisting  Engines. — Electric  hoists  differ  but  slightly  in  mechanical 
construction  from  those  operated  by  steam.  Owing  to  the  high  speed  of  the 
ordinary  motor,  electric  hoists  are  commonly  double  geared.  The  reduction 
between  the  armature  shaft  and  the  intermediate  shaft  is  ordinarily  about 
1  to  4;  between  the  intermediate  shaft  and  the  drum  gear  it  varies  according 
to  the  size  of  the  drum  and  the  hoisting  speed  desired . 

Motors  for  heavy  hoisting  may  be  either  of  the  alternating-current  induc- 
tion type  or  of  the  direct-current  type.  Alternating-current  induction  motors 
are  discussed  under  the  subject  of  Electricity  with  further  notes  under  Haulage. 
When  large  direct-current  motors  are  used  at  a  distance  from  the  power  station, 
the  power  is  transmitted  by  alternating  current  to  the  point  of  its  application 
and  is  there  transformed  to  direct  current,  usually  by  means  of  motor-generators. 

The  getting  up  of  full  speed  (acceleration)  and  maximum  load  (coal  and 
weight  of  entire  rope)  produce  what  is  known  as  a  peak,  or  high  point,  in  the 
curve  diagramming  the  power  required  from  a  hoisting  engine;  and  the  peak 
load  is  often  double  the  average  load  upon  the  engines.  In  electric  hoisting 
as  the  heating  of  the  machines  varies  approximately  as  the  square  of  the  load 


DC 

Hoist  Motor 


FIG.  1 

it  is  important  in  order  to  reduce  the  size  (and  consequently  the  cost  of  the 
equipment)  to  make  the  load  during  the  hoisting  period  as  uniform  as  possible. 
The  partial  equalization  of  the  load  is  accomplished  through  the  use  of  some 
system  of  balanced  hoisting,  such  as  the  Koepe  describeci  later.  These  systems, 
however,  do  not  perfectly  balance  the  load  during  all  portions  of  the  run,  and 
various  methods  have  been  employed  to  produce  what  may  be  called  an 
electric  balance  so  that  the  input  of  electric  energy  may  at  all  times  be  equal 
to  the  output  of  mechanical  energy. 

In  the  Ilgner  system,  shown  in  diagram  in  Fig.  1,  a  motor-generator  set  is 
used  for  supplying  power  to  the  hoist  motor,  which  is  of  the  shunt-wound 
direct-current  type.  The  operation  of  the  hoist  is  controlled  by  varying  the 
voltage  of  the  generator,  to  which  it  is  directly  connected  electrically.  By 
reversing  the  excitation  of  the  generator,  the  direction  of  rotation  of  the  motor 
is  also  reversed.  A  flywheel  is  connected  with  the  motor-generator  set  and 
arrangements  are  made  to  automatically  vary  the  speed  of  the  set  so  that 
during  peak-load  periods  the  speed  of  the  set  is  decreased,  and  part  of  the 
energy  in  the  flywheel  is  used  to  assist  the  motor  in  driving  the  generator. 


HOISTING 


743 


When  the  load  drops  below  a  certain  value,  the  speed  of  the  set  is  gradually 
increased  and  energy  is  again  stored  in  the  flywheel.  By  properly  proportion- 
ing the  flywheel,  assuming  that  the  cycle  of  operation  remains  constant,  it  is 
possible  to  keep  the  input  to  the  hoisting  plant  within  a  few  per  cent,  of  the 
average  load. 

An  objection  to  the  Ilgner  system  of  hoisting  is  the  expensive  nature  of 
the  hoisting  plant,  the  addition  of  a  motor-generator  and  flywheel  increasing 
the  cost  considerably.  To  overcome  this  feature  and  still  provide  for  the 
equalization  of  the  input,  a  system  has  been  introduced  by  the  British  Westing- 
house  Company  which  may  be  used  under  certain  circumstances.  This  scheme 
is  shown  diagrammatically  in  Fig.  2.  The  hoist  motor  in  this  system  may  be 
either  direct  current  or  alternating  current,  depending  on  the  source  of  supply. 
The  diagram  of  connections  shows  the  arrangement  of  the  plant  with  an  alter- 
nating-current source  of  supply.  In  parallel  with  the  generators  an  equalizing 
outfit  is  arranged,  which  consists  of  the  direct-current  machine  coupled  to  the 
flywheel,  which  is  connected  to  the  alternating-current  system  through  a 
rotary  converter. 

This  equalizing  equipment  can  be  located  anywhere  that  may  be  convenient, 
it  not  being  necessary  to  have  it  near  the  hoist.  The  operation  is  as  follows: 
When  the  hoist  load  exceeds  the  value  for  which  the  regulator  is  set,  the  field 


A 


J  J 


A 


Automatic^ 
Regulator 


nierators 
n 


Rheostat 


FlG.  2 


of  the  equalizing  machine  is  automatically  strengthened,  so  that  the  speed  tends 
to  drop  and  the  machine  is  driven  as  a  generator  by  the  flywheel  and  delivers 
energy  through  the  rotary  converters  to  the  alternating-current  system.  The 
rate  at  which  the  energy  is  delivered  is  dependent  on  the  operation  of  the 
regulator.  When  the  demand  drops  below  the  value  for  which  the  regulator 
is  set,  the  field  of  the  equalizing  machine  is  automatically  weakened;  this 
machine  then  runs  as  a  motor  and  absorbs  energy  from  the  alternating-current 
system  through  the  rotary  converter  and  speeding  up  the  flywheel.  In  this 
way  the  demand  on  the  alternating-current  system  is  kept  practically  constant. 
When  this  system  is  used  with  a  direct-current  source  of  supply,  the  rotary 
converter  is  omitted  and  the  equalizing  machine  is  connected  directly  to  the 
line.  This  arrangement,  however,  does  not  provide  for  controlling  the  hoist 
motor,  as  does  the  Ilgner  system,  but  it  has  the  advantage  that  the  equalizing 
machine  has  only  to  deal  with  the  loads  in  excess  of  the  mean  value  for  which 
the  regulator  is  set,  and  the  cost  is  considerably  reduced  compared  with  the 
former  system.  It  also  has  the  advantage  that  a  failure  of  any  part  of  the 
equalizing  equipment  does  not  interfere  with  the  operation  of  the  hoist  motor. 
The  application  of  this  system  is  practically  confined  to  cases  where  the  rheo- 
static  control  of  the  hoist  motors  offers  no  difficulties  and  where  equalization 
of  input  is  all  that  is  required.  In  the  case  of  very  large  plants,  however,  the 


744  HOISTING 

control  question  is  of  such  importance  that  the  Ilgner  system  is  used  almost 
exclusively. 

One  important  feature  in  connection  with  electric  hoisting  is  the  ease  with 
which  safety  devices  can  be  arranged  to  prevent  overwinding  or  overloading. 
In  connection  with  systems  using  either  a  motor-generator  flywheel  or  the 
Ilgner  system  of  control,  automatic  devices  have  been  arranged  so  that  the 
rate  of  acceleration  is  limited  and  the  hoist  is  automatically  retarded  inde- 
pendent of  the  operator,  and  as  these  devices  are  used  every  time  the  hoist 
is  operated  they  are  necessarily  kept  in  order.  With  such  arrangements,  over- 
winding or  starting  up  the  hoist  in  the  wrong  direction  is  absolutely  impossible, 
and  in  view  of  these  features  the  German  mining  authorities  have  allowed  the 
rate  at  which  men  may  be  hoisted  to  be  increased  from  1,200  ft.  per  min.,  which 
is  the  maximum  with  steam-operated  hoists  with  the  best  safety  gears,  to 
2,000  ft.  per  min.  with  electric  hoists,  and  the  question  has  been  under  con- 
sideration for  some  time  of  increasing  this  limit  to  3,000  ft.  per  min. 


BALANCED  HOISTING 

In  hoisting  through  a  double-compartment  shaft  and  from  a  single  level, 
the  weights  of  the  ascending  and  descending  cages  and  cars  balance  each  other, 
leaving  unbalanced  the  weight  of  the  load  and  that  of  the  rope.  The  weight 
of  the  load  is  uniform  during  the  entire  hoisting  period,  but  that  of  the  rope 
is  not.  The  entire  weight  of  the  rope  must  be  raised  at  the  beginning  of  the 
hoist;  at  the  middle  of  the  hoist  there  is  no  rope  weight  to  be  considered,  as 
the  two  ropes  (those  attached  to  the  ascending  and  descending  cages,  respec- 
tively) are  of  the  same  length  and,  consequently,  balance  each  other;  and 
at  the  end  of  the  hoist,  the  weight  of  the  rope  is  acting  in  favor  of  the  load. 
In  fact,  in  extremely  deep  shafts,  the  weight  of  the  rope  attached  to  the  de- 
scending empty  cage,  may  even  exceed  the  weight  of  the  load  on  the  other  cage 
to  such  an  extent  as  to  tend  to  cause  the  engines  to  run  away,  necessitating 
the  shutting  off  of  the  steam  and  the  application  of  the  brakes  in  order  to 
prevent  the  loaded  cage  being  carried  into  the  head-sheaves. 

In  order  to  provide  for  the  time  necessary  to  load  and  unload  the  cages 
at  each  end  of  the  run,  it  is  important  to  reach  the  full  hoisting  speed  as  soon 
as  possible.  Further,  as  the  maximum  load  must  be  raised  at  the  outset,  the 
demand  for  power  is  much  greater  at  the  beginning  of  the  hoist  than  at  any 
other  time.  Therefore,  in  order  to  provide  >  the  power  for  getting  up  speed 
under  the  maximum  load  (the  two  producing  what  is  called  a  peak  load), 
hoisting  engines  must  be  made  much  larger  than  if  the  speed- of  hoisting  and 
the  load  were  uniform  throughout  the  run.  In  hoisting  from  shallow  shafts, 
it  is  not  customary  to  attempt  to  balance  the  load  (that  is,  to  make  it  uniform 
throughout  the  hoisting  period),  the  peak  load  being  taken  care  of  by  pro- 
portioning the  size  of  the  steam  cylinders  and  drums,  and  without  any  very 
serious  increase  in  first  cost  or  in  operating  expense. 

Where  the  shaft  is  deep,  the  loads  large,  and  the  hoisting  speed  is  necessarily 
great  in  order  to  produce  a  large  tonnage,  some  system  of  counterbalancing  is 
employed  to  render  more  uniform  the  demand  for  power  upon  the  hoisting 
engine. 

As  an  illustration  of  unbalanced  hoisting,  assume  that  a  load  of  4,000  Ib.  of 
coal  is  to  be  hoisted  in  a  double-compartment  shaft  1,000  ft.  deep  by  means 
of  a  l|-in.  crucible-steel  rope  weighing  3  Ib.  per  ft.  (3,000  Ib.  in  all)  which 
winds  upon  a  drum  7  ft.  in  diameter.  It  may  be  assumed,  further,  that  the 
car  and  empty  cage  weigh  3,000  Ib.  each,  and  that  friction  is  equal  to  10%  of 
the  load  exclusive  of  that  of  the  rope.  The  friction  adds  to  the  load  to  be 
hoisted  and  decreases  that  to  be  lowered. 

When  the  loaded  cage  is  at  the  bottom  of  the  shaft,  the  total  weight  to  be 
hoisted  is  that  of  the  coal,  the  empty  car  and  the  cage,  a  total  of  10,000  Ib. 
To  this  must  be  added  10%  for  friction,  or  1,000  Ib.,  and  3,000  Ib.  for  the 
weight  of  the  rope,  or  a  grand  total  of  14,000  Ib.  As  the  drum  has  a  radius 
of  3.5  ft.,  the  total  turning  moment  to  be  overcome  by  the  engine  is  14,000 
X3.5  =  49,000  ft.-lb.  But  the  engine  is  assisted  by  the  weight  of  the  empty 
car  and  cage,  or  6,000  Ib.  From  this  must  be  deducted  10%,  or  600  Ib.  for 
friction,  leaving  a  net  load  of  5,400  Ib.  assisting  the  engine,  which  is  equivalent 
to  a  C9unterbalancing  moment  of  5,400X3.5  =  18,900  ft.-lb.  Hence,  at  the 
beginning  of  the  hoist  the  net  load  moment  to  be  overcome  by  the  engine  is 
49,000-18,900  =  30,100  ft.-lb. 


HOISTING  745 

At  the  end  of  the  hoist  the  weight  on  the  loaded-cage  side  is  lessened  by 
the  weight  of  the  rope,  and  is  11,000  Ib.  This  is  equal  to  a  total  load  moment 
of  11.000X3.5  =  38,500  ft.-lb.  On  the  empty  side,  the  weight  assisting  the 
engine  is  increased  by  the  weight  of  the  rope,  3,000  Ib.,  and  is  8,400  Ib.  This 
is  equal  to  a  counterbalancing  load  moment  of  8.400X3.5  =  29,400  ft.-lb. 
Hence  at  the  end  of  the  hoist  the  net  load  moment  to  be  overcome  by  the  engine 
is  38,500-29,400  =  9,100  ft.-lb. 

Since  the  load  moment  upon  the  engine  varies  from  30,100  ft.-lb.  at  the 
beginning  of  the  run  to  9,100  ft.-lb.  at  the  end,  in  the  assumed  case  the  engines 
must  exert  more  than  three  times  as  much  power  at  one  time  as  at  another. 
Further,  as  the  average  load  moment  upon  the  engines  is  but  19,600  ft.-lb.,  and 
the  maximum  load  moment  is  30,100  ft.-lb.,  but  about  65%  of  their  average 
power  is  utilized. 

Tail-Rope  Balancing.  —  Counterbalancing  the  weight  of  the  hoisting  ropes 
may  be  accomplished  by  attaching  to  the  bottom  of  one  cage  a  rope  of  the 
same  size  and  weight  as  the  hoisting  rope,  passing  it  under  a  pulley  or  sheave 
wheel  at  the  bottom  of  the  shaft,  and  attaching  the  second  end  to  the  bottom 
of  the  other  cage.  As  the  length  of  the  balance  rope  is  twice  that  of  either 
hoisting  rope,  the  latter  are  exactly  balanced.  When  this  appliance  is  used, 
the  weight  to  be  hoisted  is  uniform  throughout  the  run  and  is  equal  to  that  of 
the  load  and  friction,  because  the  cars  and  cages  balance  each  other.  Using 
the  foregoing  illustration,  the  net  load  moment  at  starting  is  30,100  ft.-lb. 
From  this  must  be  deducted  the  load  moment  of  the  rope,  which  is  3,000X3.5 
=  10,500  ft.-lb.  Hence  the  net  load  moment,  which  is  constant  throughout 
the  run,  is  30,100-10,500=19,600  ft.-lb.  Hence,  when  the  weight  of  the 
hoisting  ropes  is  counterbalanced,  but  about  65%  of  the  power  is  required 
to  hoist  as  when  the  ropes  are  not  balanced. 

The  use  of  the  tail-rope  gives  its  best  results  where  hoisting  is  done  from 
one  level  only,  and  in  deep  hoisting  it  is  impracticable  because  of  the  extra 
weight  which  must  be  carried  by  the  head-sheave  axle  and  because  of  possible 
excessive  swaying  of  the  rope. 

Conical  Drums.  —  Conical  drums  are  designed  to  make  the  work  of  the 
engine  throughout  the  hoist  as  nearly  uniform  as  possible.  To  accomplish 
this,  when  the  cage  is  at  the  bottom  of  the  shaft  and  the  weight  of  the  rope 
is  added  to  that  of  the  cage  and  its  load,  the  rope  winds  on  that  part  of  the 
drum  having  the  smallest  diameter.  As  hoisting  continues,  the  rope  winds 
on  a  gradually  increasing  diameter  of  drum,  and  when  the  cage  is  at  the  top 
of  the  hoist  and  the  load  is  only  that  due  to  the  cage  and  the  loaded  car,  the 
rope  is  winding  on  that  part  of  the  drum  having  the  greatest  diameter;  in  this 
way,  the  moment  of  the  load  at  every  point  of  the  hoist  remains  approximately 
the  same. 

The  ratio  of  the  larger  radius  R  of  a  conical  drum  to  the  smaller  radius  r  is 
found  as  follows: 

Let  Wm  =  weight  of  material  hoisted  ; 

We  =  weight  of  cage  and  car; 
wr  =  weight  of  rope; 
R  =  large  radius  of  drum; 
r  =  small  radius  of  drum. 

The  moment  of  cage,  car,  load,  and  rope  at  the  bottom  of  the  shaft  is 
(wc+w»t+wr)r.  The  moment  of  cage  and  car  at  the  top  of  the  shaft  is  wcR. 
The  net  moment  at  beginning  of  hoist  is  (wc-\-Wm  +  Wr)r  —  WcR. 

When  the  loaded  cage  has  arrived  at  the  top  and  the  other  cage  has  reached 
the  bottom,  the  moment  of  cage,  car,  and  load  at  the  top  is  (wc-\-wm)R  and  the 
moment  of  cage,  car,  and  rope  at  the  bottom  is  (wc-\-  wr)r.  The  net  moment 
at  end  of  hoist  is  (wc+wm)R—  (wc+Wr\r. 

Finally,  placing  the  moment  at  beginning  of  hoist  equal  to  that  at  end  of 
hoist,  and  finding  the  value  of  the  ratio  of  the  two  diameters  which  is  equal 
to  that  of  the  two  radii, 


~  2-U'c 

EXAMPLE.  —  Using  the  foregoing  illustration,  d  =  7  ft.;  w?»  =  4,000  Ib.;  wc 
=  3,000+3,000  =  6,000  Ib.;  wr  =  3,000  Ib.;  it  is  required  to  find  the  larger 
diameter  of  a  conical  drum  for  balanced  hoisting. 

SOLUTION.  —  Substituting  in  the  foregoing  formula, 


9  ft. 


746 


HOISTING 


From  the  equations  representing  the  net  load  moment  at  the  beginning  of 
hoisting,  the  net  load  moment  upon  the  engines  is  (6,000+4,000+3,000)  X  3.5 
-6,000X4.8125  =  16,625  ft.-lb.,  which  load  moment  is  constant  throughout 
the  hoist  as  when  counterbalancing  with  the  tail-rope  is  used,  but  with  no 
extra  strain  upon  the  head-sheave  axle. 

The  use  of  the  conical  drum  permits  of  the  practical  equalization  of  the 
load  on  the  engine  during  the  entire  hoisting  period,  and  requires  less  power 
in  starting  under  load. 

The  disadvantages  of  the  conical  drum  are  as  follows:  To  maintain  a 
certain  average  speed  of  hoisting,  the  speed  toward  the  end  of  the  hoist  is  of 
necessity  higher  than  the  average  and  comes  at  a  time  when  a  slowing  up 
should  be  taking  place,  so  that  more  care  must  be  exercised  when  making  the 
landing.  To  prevent  the  rope  from  being  drawn  out  of  the  grooves,  the  latter 
must  be  made  deep  and  with  a  large  pitch,  thereby  increasing  the  width  of  the 
face  or  length  of  the  drum.  In  making  a  landing,  when  the  rope  is  on  the 
conical  face,  the  rope  must  be  kept  taut,  as  any  slackness  will  permit  the  rope 
to  leave  the  groove,  with  the  result  that  all  the  rope  will  pile  up  in  the  bottom 
grooves  of  the  drum  allowing  the  cage  to  drop  into  the  mine,  unless  it  is  resting 
on  the  chairs.  If  there  are  several  levels  to  be  hoisted  from,  the  equalizing 
of  the  load  on  the  engines  can  only  be  realized  for  one  level;  for  all  other  levels 
this  advantage  will  be  lost.  For  large  depths,  conical  drums  become  very  long 
and  require  correspondingly  long  leads  from  head-frame  to  drum.  To  hold 

the  same  amount  of 
rope,  conical  drums  are 
heavier  than  cylindrical 
ones,  and  as  a  result, 
the  power  required  in 
starting  the  load  is 
somewhat  i  n  c  r  e  a  se  d 
owing  to  the  greater 
inertia  of  the  rotating 
parts. 

Some  of  these  disad- 
vantages  have  been 
overcome  by  making  a 
combination  of  cone 
and  cylindrical  drums. 
The  drums  are  so  des- 
ignated that  the  land- 
ing takes  place  only 
when  the  rope  is  on  the 
cylindrical  portion  of 
the  drum.  For  deep 
hoisting,  the  greater 
diameter  of  the  drum 
and  its  length  must  be  inconveniently  large  if  the  load  is  equalized.  The 
length  and  diameter"  can  be  reduced  by  making  one-half  of  the  drum  cylin- 
drical and  by  having  the  rope  from  each  end  wind  on  the  same  cylindrical 
portion  of  the  drum.  In  all  cases  however,  these  modifications  are  made  at 
the  expense  of  the  equalization  of  the  load  on  the  engines,  and  it  is  not  pos- 
sible to  obtain  the  latter  without  including  some  serious  disadvantage. 

There  are  certain  objections  to  both  cylindrical  and  conical  drums:  their 
great  size  and  weight,  for  large  hoists,  make  them  very  expensive;  their  width 
necessitates  placing  the  engines  far  apart,  which  adds  to  the  cost  of  the  engines, 
foundations,  and  buildings;  the  great  weight  of  the  drums  is  also  objectionable, 
because  it  forms  a  large  part  of  the  mass  to  be  put  in  motion  and  brought  to 
rest  at  each  hoist. 

Flat  Ropes  and  Reels. — To  overcome  the  objections  to  conical  and  cylin- 
drical drums, _  flat  ropes  wound  on  reels,  Fig.  1,  may  be  used.  In  this  case 
the  hub  a  is  increased  in  diameter,  above  what 'is  necessary  for  strength,  to 
such  a  size  as  is  suitable  to  wind  the  rope  on.  It  is  then  cored  out  from  the 
inside,  so  as  not  to  contain  too  great  a  mass  of  metal. 

The  arms  b  of  the  reel  extend  radially  from  the  hub  to  confine  the  rope 
laterally  when  it  is  all  wound  on  the  drum.  These  arms  are  connected  at  their 
outer  ends  by  a  continuous  flange  c,  which  is  flared  out,  as  shown  at  d,  so  as 
to  take  in  the  rope  easily,  if  it  is  deflected  at  all  sidewise. 

f    In  the  larger-sized  reels,  the  arms  are  bolted  to  the  hub,  and  often  the  outer 
rim  connecting  the  arms  is  omitted.     Hardwood  lining  was  formerly  used  on 


FIG.  1 


HOISTING  747 

the  arms  under  the  impression  that  the  wear  on  the  rope  would  be  less  than  with 
bare  iron  arms,  but  sand  and  grit  become  embedded  in  the  wood  and  grind 
the  rope.  Polished  iron  arms  with  rounded  corners  and  lubricated  with  oil  or 
tar  are  best.  The  end  of  the  rope  is  fastened  in  a  pocket  e  provided  for  it  in 
the  hub. 

The  rope  winds  on  itself  so  that  the  diameter  of  the  reel  increases  as  the 
hoist  is  made  and  as  the  load  due  to  the  weight  of  the  rope  decreases.  This 
serves  to  equalize  the  load  due  to  the  rope  in  the  same  manner  as  the  conical 
drum.  Two  reels  are  generally  put  on  the  same  shaft,  and  while  one  is  hoist- 
ing from  one  compartment  of  the  shaft  the  other  is  lowering  into  another 
compartment.  The  periphery  of  the  hub  where  the  rope  winds  should  not  be 
round  but  of  gradually  increasing  radius,  for  if  a  flat  rope  is  wrapped  about  a 
round  hub  the  rope  will  have  to  abruptly  mount  itself  at  the  end  of  the  first 
revolution  and  so  on  for  every  revolution.  The  radius  of  the  hub  should 
increase  at  such  a  rate  as  to  raise  the  rope  an  amount  equal  to  its  thickness 
in  the  first  wrap,  so  that  it  will  wind  on  itself  without  jar  at  the  point  of 
attachment,  as  well  as  on  succeeding  wraps. 

In  America,  it  is  customary  to  wind  on  reels  of  small  diameter,  that  is, 
starting  at  3  or  5  ft.  and  increasing  to  8  or  12  ft.;  but  several  large  plants  have 
been  built  with  reels  starting  at  8  ft.  and  increasing  to  19  ft.  In  England,  reels 
have  been  made  starting  at  16  ft.  and  increasing  to  20  or  22  ft.  Such  large 
reels  are  easier  on  the  rope  but  require  large  engines,  as  hoisting  in  balance  is 
used  to  only  a  slight  extent.  The  large  reel  is  easy  on  the  rope,  both  from  the 
fact  that  it  bends  the  rope  but  little  and  also  gives  less  pressure  on  the  bottom 
wraps,  as  each  wrap  adds  to  the  pressure.  These  reels  are  driven  by  means  of 
plain  jaw  or  friction  clutches. 

The  wear  of  a  flat  rope  is  excessive  and  the  rope  itself  costs  more  than  a 
round  rope  of  the  same  strength,  does  not  last  as  long,  and  requires  more  care 
and  attention. 

When  calculating  the  dimensions  of  a  reel  for  flat  rope,  the  determination 
of  the  size  of  the  rope  and  of  the  large  and  small  diameters  of  the  reel  must 
proceed  together.  The  smaller  diameter  d  is  that  of  the  hub  of  the  reel,  and 
the  larger  diameter  D  is  that  of  the  last  coil  of  rope  after  the  reel  is  full.  The 
large  diameter  D  determines  the  length  of  the  arms,  b,  Fig.  1. 

EXAMPLE. — Using  a  factor  of  safety  of  9,  what  size  of  flat  rope  will  be 
required  to  hoist  5,000  Ib.  of  material  in  a  skip  weighing  3,000  Ib.  through  a 
two-compartment  shaft  2,000  ft.  deep;  and  what  will  be  the  dimensions  of 
the  reel? 

SOLUTION. — The  load  to  be  hoisted,  allowing  10%  for  friction,  is  8,800  Ib. 
Assuming  a  6"X*"  rope  with  a  breaking  strength  of  150,000  Ib.,  this  will 
weigh  5.1  Ib.  per  ft.,  or  10.200  Ib.  for  2,000  ft.  The  total  load  will  be  8,800 
+  10,200=19,000  Ib.  The  factor  of  safety  will  be  150,000-7-19,000  =  7.8, 
which  is  too  low  under  the  assumed  conditions. 

The  breaking  strength  of  an  8"X  3"  rope  is  200,000  Ib.  This  weighs  6.9  Ib. 
per  ft.,  or  13,800  Ib.  for  the  entire  rope.  With  this  larger  rope,  the  total  load 
will  be  8,800+13,800  =  22,600  Ib.,  and  the  factor  of  safety  will  be  200,000 
-T- 22,600  =  8.8,  which  is  close  enough  for  all  practical  purposes.  Using  the 
formula  given  under  the  heading  Conical  Drums, 

n     .V2X  (3.000 +  13.800) +5.000 

D  =  dX 2X3.000+5,000 =  3'5d 

that  is,  the  diameter  when  the  last  coil  is  wound  on  the  reel  must  be  3.5  times 
that  of  the  hub. 

The  area  of  the  hub  about  which  the  rope  is  to  coil  is  }W2,  and  the  area 
included  in  the  outer  coil  of  rope  is  iir£>2;  hence,  the  area  of  the  annular  space 
occupied  by  the  rope  is 

l*£>2-i7rd2=i7r(Z)2-d2) 

Such  values  for  D  and  d  must  be  chosen  that  the  equation  of  moments,  D  =  3.5d, 
is  satisfied,  while  the  area  of  the  annular  space,  iir(D2— d2),  must  correspond 
to  the  space  occupied  by  the  given  rope  when  coiled.  In  the  assumed  case 

2  ooo X 12 

2,000  ft.  of  rope  \  in.  thick  requires  — — ^^^  12'000  sq-  in>  m  which  to  be 
coiled.  To  satisfy  the  equation  of  moments,  D  must  equal  3.5d;  hence,  to 
satisfy  both  these  conditions  iir[(3.5rf)2-d2]  =  12,000;  whence  d  =  37  in.,  or 
3  ft.  1  in.;  and  Z?  =  37X3.5  =  129.5  in.,  or  10  ft.  9i  in. 

The  dimensions  of  the  reel  will  then  be:  diameter  of  hub  3  ft.  1  in.;  width 
between  flanges,  8|  in.,  allowing  i  in.  on  each  side  of  the  rope  for  clearance; 
diameter  of  the  flanges  where  they  flare,  10  ft.  9  j  in. 


748 


HOISTING 


Koepe  System. — In  its  lightest  form,  a  drum  requires  a  large  amount  of 
power  to  set  it  in  motion,  which  power  is  absorbed  by  the  brake  and  lost  when 
it  is  brought  to  rest  again.  Furthermore,  with  deep  shafts  requiring  long 
drums,  the  fleet,  or  angle  that  the  rope  makes  with  the  head-sheave  due  to  its 
traveling  from  one  end  of  the  drum  to  the  other,  is  not  only  a  disadvantage 
and  possible  cause  of  accident,  but  it  is  a  source  of  wear.  To  overcome  these 
objections  and  also  the  great  cost  of  large  cylindrical  or  conical  drums,  the 
Koepe  system  of  hoisting,  shown  in  Fig.  2,  was  devised  by  Mr.  Frederick 
Koepe.  A  single-grooved  driving  sheave  a  is  used  in  place  of  a  drum.  The 
winding  rope  b  passes  from  one  cage  A  up  over  a  head-sheave,  thence  around  the 
sheave  a  and  back  over  another  head-sheave,  and  down  to  a  second  cage  B; 
it  encircles  a  little  over  half  the  periphery  of  the  driving  sheave  and  is  driven 
by  the  friction  between  the  sheave  and  rope.  A  balance  rope  c  beneath  the 
cages  and  passing  around  the  sheave  d  gives  an  endless-rope  arrangement 
with  the  cages  fixed  at  the  proper  points.  The  driving  sheave  is  stronger  than 
an  ordinary  carrying  sheave,  as  it  has  to  do  the  driving,  and  is  usually  lined 

with  hardwood,  which 
is  grooved  to  receive  the 
winding  rope,  the  depth 
of  the  groove  being  gen- 
erally equal  to  twice 
the  diameter  of  the 
rope.  Instead  of  being 
placed  parallel,  the 
head-sheaves  are  placed 
at  an  angle  with  each 
other,  each  pointing  to 
the  groove  in  the  driv- 
ing sheave,  thus  reduc- 
ing the  side  friction  of 
the  rope  on  the  sheaves. 
The  system  has 
been  in  successful  oper- 
ation since  1877,  and 
experiments  made  on  it 
have  determined  that, 
with  a  rope  passing  only 
one-half  turn  around 
the  drum  sheave,  the 
coefficient  of  adhesion 
with  clean  ropes  is  about 
.3.  If  the  ropes  are 
oiled,  the  adhesion  be- 
comes less,  and  some- 
times slippage  occurs, 
producing  not  only  wear 
of  the  driving-sheave 
lining  but  giving  an  in- 
correct reading  of  the 
hoist  indicator  and  thus 
possibly  producing 
overwinding,  unless  the 


FIG.  2 


position  of  the  cage  is  indicated  by  marks  on  the  rope,  or  unless  the  engineer 
can  see  the  cage. 

At  the  end  of  the  hoist,  if  the  upper  cage  is  allowed  to  rest  on  the  keep,  its 
weight  and  the  weight  of  the  tail-rope  are  taken  from  the  hoisting  rope,  and 
there  is  then  not  enough  pull  on  the  hoisting  rope  to  produce  sufficient  friction 
with  the  drum  sheave  to  start  the  next  hoist.  To  prevent  this  trouble,  the 
keeps  are  dispensed  with,  or  the  rope  is  made  continuous  and  independent  of 
the  cage.  To  do  this,  crossheads  are  placed  above  and  below  each  cage  and 
connected  by  ropes  or  chains  outside  of  the  cages.  The  bridle  chains  are  then 
hung  from  the  top  crosshead,  and  when  the  cage  rests  on  the  keeps,  the  weight 
of  the  winding  and  tail-ropes  remains  on  the  driving  sheaves. 

With  this  system,  only  one  driving  sheave  is  necessary  for  the  operation  of 
two  compartments,  and  it  is  light,  inexpensive  to  build,  and  very  narrow, 
admitting  of  a  short  sheave  shaft  and  small  foundations.  This  system  permits 
a  perfect  balance  of  rope  and  cage,  so  that  the  work  to  be  done  by  the  engine  is 
uniform,  except  for  the  acceleration,  and  consists  only  in  lifting  the  material 


HOISTING 


749 


and  overcoming  the  friction.  There  is  no  fleeting  of  the  rope  between  the 
driving  sheaves  and  the  head-sheaves. 

The  system  has  the  following  disadvantages,  which  prevent  its  being  used 
to  any  considerable  extent:  Liability  to  slippage  of  the  rope  on  the  drum;  if 
the  rope  breaks,  both  cages  may  fall  to  the  bottom;  hoisting  from  different  levels 
cannot  be  well  done,  for,  since  the  cages  are  at  fixed  distances  from  each  other, 
the  length  of  the  rope  is  such  that  when  one  cage  A  is  at  the  top,  the  other 
cage  B  is  at  the  bottom.  If  hoisting  is  to  be  done  from  the  bottom,  this 
is  satisfactory,  but  if  hoisting  is  to  be  done  from  some  upper  level,  cage  B, 
which  is  at  the  bottom,  must  be  hoisted  to  that  level  to  be  loaded  before  it 
can  go  to  the  top.  Then,  when  cage  B  goes  to  the  top  with  its  load,  cage  A 
must  go  to  the  bottom,  wait  there  while  cage  B  is  being  unloaded,  and  then 
be  hoisted  to  the  upper  level  to  receive  its  load.  For  each  trip,  therefore,  the 
time  required  for  a  cage  to  go  from  the  bottom  to  the  upper  level  and  be 
loaded  is  lost;  and  two  movements  of  the  engines  are  necessary  for  a  hoist 
instead  of  one. 

Whiting  System. — In  the  Whiting  system,  two  rope  wheels  placed  tandem 
are  used  in  place  of  cylindrical  or  conical  drums.  As  shown  in  Fig.  3,  for  a 
two-compartment  shaft  the  rope  passes  from  one  cage  a  up  over  a  head-sheave  c, 


QIJ 


FIG.  3 


down  under  a  guide  sheave  d,  and  is  then  wound 
three  times  about  the  rope  wheels  e  and  /,  to  secure 
a  good  hold,  then  around  a  fleet  sheave  g,  and  back 
under  another  guide  sheave  h,  up  over  another 
head-sheave  *",  and  down  to  the  other  cage  b. 
When  the  system  is  to  be  used  for  a  single-com- 
partment shaft,  one  end  of  the  rope  carries^  the 
cage  and  the  other  end  carries  a  balance  weight, 
which  is  run  up  and  down  in  a  corner  of  the  shaft. 
A  balance  rope  below  the  cages,  as  shown,  is  gener- 
ally used,  though  it  is  not  as  ^essential  to  the  work- 
ing of  the  system,  as  it  is  in  the  Koepe  system. 
When  sinking  a  shaft,  a  balance  rope  cannot  be 
used  as  it  interferes  with  the  work  at  the  bottom  of  the  shaft. 

The  drums  or  wheels  e  and  /  are  light,  inexpensive,  and  narrow,  thus  per- 
mitting short  sheave  shafts  and  small  foundations.  They  are  lined  with 
hardwood  blocks,  each  lining  having  three  rope  grooves  turned  in  it.  The 
main  wheel  e  is  driven  by  a  hoisting  engine,  which  may  be  either  first-  or  second- 
motion.  The  following  wheel  /  is  coupled  to  the  main  wheel  by  a  pair  of  parallel 
rods,  one  on  each  side,  like  the  drivers  of  a  locomotive.  As  the  rope  wraps 
about  the  wheels  e  and  /  three  times,  there  are  six  semi-circumferences  of 
driving  contact  with  the  rope,  as  compared  with  the  one  semi-circumference 
in  the  Koepe  system,  and  there  is  no  slipping  of  the  rope  on  the  wheels.  The 
following  wheel  /  is  best  tilted  or  inclined  from  the  vertical  an  amount  equal, 
in  the  diameter  of  the  wheels,  to  the  pitch  of  the  rope  on  the  wheel,  so  that 
the  rope  may  not  run  out  of  its  groove  and  may  run  straight  from  one  wheel 
to  the  other  without  any  chafing  between  the  ropes  and  the  sides  of  the  grooves. 

The  capacity  of  the  wheels  e  and  /  is  unlimited,  while  grooved  cylindrical 
drums,  conical  drums,  and  reels  will  hold  only  the  fixed  length  of  rope  for 
which  they  are  designed. 

As  shown  by  the  dotted  lines,  the  fleet  sheave  g  is  arranged  to  travel  back- 
wards and  forwards,  in  order  to  change  the  working  length  of  the  rope  from 
time  to  time  to  provide  for  an  increased  depth  of  shaft,  and  for  changes  in  the 
length  of  rope  due  to  stretching  and  when  the  ends  are  cut  off  to  resocket  the 


750  HOISTING 

rope.     The  fleet  sheave  g  is  moved  a  distance  equal  to  one-half  the  change  in 
the  length  of  rope. 

Hoisting  from  intermediate  levels  can  be  readily  done  with  the  Whiting 
system;  for  instance,  if  the  cage  a  is  at  the  top  and  cage  b  at  the  bottom,  and 
hoisting  is  to  be  done  from  some  upper  level,  it  is  only  necessary  to  run  the 
fleet  sheave  g  out,  and  thus  shorten  the  working  length  of  the  rope  until  cage  b 
comes  up  to  the  upper  level.  It  can  then  be  loaded  and  go  to  the  top.  While 
cage  b  goes  to  the  top,  cage  a  descends  to  the  same  level,  where  it  can  be  loaded 
while  cage  b  is  being  unloaded,  and  can  then  go  directly  to  the  top  without  any 
lost  time,  as  is  the  case  in  the  Koepe  system. 

The  system  permits  a  perfect  balance  of  rope  and  cage,  so  that  the  work  to 
be  done  by  the  engines  is  uniform,  except  for  the  acceleration,  and  consists 
only  in  lifting  the  material  and  overcoming  the  friction. 

There  is  no  fleeting  of  the  rope,  so  the  rope  wheels  can  be  placed  as  close 
to  the  shaft  as  may  be  desired. 

This  system  was  tried  as  early  as  1862  in  Eastern  Pennsylvania,  but  it  was 
not  used  extensively  because  hoisting  from  great  depths  was  not  necessary, 
since,  for  depths  of  less  than  1,000  ft.,  cylindrical  and  conical  drums  are  quite 
satisfactory.  Two  of  the  Whiting  hoists  in  the  Lake  Superior  copper  region 
are  among  the  largest  hoisting  plants  in  the  world.  Each  of  these  consists  of 
a  pair  of  triple-expansion,  vertical,  inverted-beam  engines,  driving  direct  a 
pair  of  19-ft.  drums.  The  high-pressure  cylinders  are  20  in.  in  diameter,  the 
intermediate  cylinders  32  in.,  and  the  low-pressure  cylinders  50  in.,  and  all  six 
of  them  have  a  72-in.  stroke.  The  rope  used  is  a  2i-in.  plow-steel  rope  and 
hoists  10  T.  of  material  at  a  trip,  in  one  case  from  a  depth  of  4,980  ft. 

Modified  Whiting  System. — A  modification  of  the  Whiting  system  is 
sometimes  used  in  which  a  large  drum  keyed  to  the  crank-shaft  replaces  the 
small  tandem  drums,  and  even  the  slight  probability  of  the  rope  slipping  in 
the  Whiting  system  is  thus  obviated.  One  rope  is 
fastened  to  one  end  of  the  drum,  and  the  other  rope 
to  the  other  end  in  such  a  way  that  while  one  is  wind- 
ing on  the  other  will  be  winding  off  the  drum.  One 
rope  passes  directly  to  the  head-sheave  while  the  other 
passes  first  around  a  fleet  sheave,  similar  to  that  used 
for  the  Whiting  system,  but  preferably  placed  hori- 
zontal, and  thence  to  the  head-sheave.  This  system 
possesses  the  same  advantages  as  the  Whiting  system 
except  that  the  depth  of  hoist  is  limited  by  the  size 
of  the  drum,  and  that  there  is  a  fleet  of  the  rope.  Up 
to  the  limiting  depth,  as  determined  by  the  size  of  the 
drum,  this  system  can  be  used  with  equal  economy  for 
any  depth.  This  hoist,  as  well  as  the  Whiting,  is 
therefore  especially  suitable  for  a  place  where  one 
F  ,  mining  company  operates  several  mines,  for  it  enables 

the  company  to  select  one  size  for  all  their  permanent 
work,  with  all  the  advantages  that  come  from  duplicate  machinery. 

Despritz  System. — The  general  arrangement  of  the  Despritz  system  is 
shown  in  Fig.  4.  A  drum  with  a  radius  T  is  keyed  to  the  same  shaft  as  the 
rope  drum  with  a  radius  jR,  and  carries  a  small  rope  to  which  is  attached  a 
chain  whose  length  2V  is  one-half  of  the  distance  between  landings  H . 

The  small  rope  is  so  wound  on  to  its  drum  that  at  the  commencement  of 
the  hoist  the  chain  is  suspended  at  full  length  in  a  small  compartment  specially 
provided.  Immediately  the  hoisting  commences,  the  small  rope  starts  to 
unreel,  piling  up  the  chain  at  the  bottom  of  its  compartment  until  the_  cages 
reach  their  point  of  passing  midway  of  the  shaft,  at  which  instant  the  hoisting- 
rope  loads  balance,  the  piling  up  of  the  entire  chain  length  is  complete,  and  its 
load  moment  on  the  main  shaft  is  zero.  At  this  instant,  also,  the  small  rope, 
carrying  the  chain,  has  all  unreeled  from  its  drum  and  its  point  of _  fastening 
is  about  to  pass  around  underneath  and  take  the  rope  into  the  position  shown 
by  the  dotted  line. 

Hence,  as  soon  as  the  cages  have  passed  each  other  the  chain  rope  begins 
to  reel  up  again,  extending  the  chain  upwards  until,  at  the  termination  of  the 
hoist,  it  again  hangs  at  full  length,  giving  a  load  moment  of  opposite  sign 
to  that  which  it  had  at  starting  of  the  hoist.  That  is,  during  the  first  half 
of  the  hoisting  period  the  load  moment  of  the  chain  on  the  drum  shaft  is  plus, 
while  during  the  second  half  of  the  period  it  is  minus. 
If  W= weight  of  hoisting  rope  per  foot; 

w  =  weight  of  chain  per  foot; 


HOISTING 


751 


l?  =  radius  of  rope  drum,  in  feet; 
T  =  radius  of  chain  drum,  in  feet; 


Monopol  System.  —  The  system  outlined  in  Fig.  5  is  known  as  the  Monopol. 
An  auxiliary  drum  of  diameter  equal  to  the  winding  drums,  is  keyed  to  the 
main  shaft  and  is  of  sufficient  width  to  carry 
two  relatively  small  ropes,  one  of  which  is  un- 
derwound  and  the  other  overwound.         » 

These  ropes  support  a  length  of  heavier 
balancing  rope  in  the  position  shown;  this 
balancing  rope  is  usually  a  length  of  old  hoist- 
ing rope  of  the  size  used  in  the  hoisting  oper- 
ations and  which  has  been  discarded  on  account 
of  wear.  A  glance  at  the  diagram  makes  it 
evident  that  if  this  balancing  rope  is  adjusted 
at  the  outset,  so  that  each  of  its  ends  is  in 
position  opposite  one  of  the  cages,  as  shown, 
they  will  so  remain  whatever  the  position  the 
cages  take  during  a  hoisting  period,  and  the 
load  moment  on  the  drum  shaft,  so  far  as  the 
hoisting  ropes  are  concerned,  will  be  equalized 
throughout.  As  in  the  former  case,  the  weight 
of  the  small  rope  can  be  neglected. 

In  practice  either  of  the  foregoing  systems 
requires  that  a  small  compartment  be  provided 
for  the  accommodation  of  the  balancing  device. 
This  is  usually  partitioned  off  from  one  end  of 


i 


FIG.  5 


the  pump  compartment  of  the  main  shaft  at  a  nominal  expense.  As  for  the 
rest  of  the  arrangements,  almost  any  mechanic  at  the  mines  will  find  little 
trouble  in  providing  whatever  may  be  required  for  the  installation. 


CALCULATIONS  FOR  FIRST-MOTION  HOISTING 
ENGINES 

General  Considerations. — Owing  to  the  fact  that  many  of  the  resistances 
that  have  to  be  overcome  can  only  be  estimated  approximately,  the  determi- 
nation of  the  horsepower  required  to  hoist,  as  well  as  the  dimensions  of  the 
engines  required  for  that  purpose,  cannot  be  made  exactly.  The  usual  pro- 
cedure is  to  calculate  an  average  or  minimum  horsepower  by  means  of  some 
simple  formula  and  then  to  add  to  this  an  amount  that  experience  has  indicated 
to  be  necessary  to  provide  for  uncertainties  both  in  resistances  to  be  overcome 
and  in  the  future  demands  for  power.  The  horsepower  having  been  obtained, 
the  actual  design  of  the  engines  should  be  left  to  a  skilled  mechanical  engineer; 
in  fact,  the  entire  matter,  even  including  the  calculation  of  the  horsepower,  is 
more  properly  the  work  of  the  engine  builder  than  the  mine  superintendent. 

The  methods  involved  in  the  solution  of  hoisting-engine  problems  are  best 
explained  by  the  working  out  of  the  following  example. 

EXAMPLE. — What  should  be  the  horsepower  and  dimensions  of  a  first- 
motion  engine  to  hoist  1,500  T.  of  coal  per  da.  of  8  hr.  from  a  shaft  1,000  ft. 
between  landings  under  the  following  conditions:  One-half  hour  is  allowed 
for  delays  of  various  kinds,  7  sec.  for  caging  each  trip,  and  5  sec.  each  for 
acceleration  and  retardation;  the  car  holds  5,000  lb.  of  coal  and  weighs  2,500  lb.; 
the  cages  weigh  4,000  lb.  each;  the  drum  is  cylindrical,  8  ft.  in  diameter  and 
8  ft.  wide;  the  head-sheaves  are  8  ft.  in  diameter;  the  mean  effective  pressure  of 
the  steam  in  the  cylinder  is  100  lb.  per  sq.  in.,  the  plant. has  an  efficiency 
of  .85% ;  and  the  resistance  of  friction  is  taken  to  be  the  same  as  that  required 
to  move  a  weight  equal  to  5%  of  the  total  load? 

SOLUTION. — 1.  Hoisting  Period. — The  operation  of  hoisting  through  a 
shaft  may  be  divided  into  three  periods.  First,  a  period  of  acceleration,  during 
which  the  load,  rope  drum,  sheaves,  moving  parts  of  the  engine,  etc.,  are 
brought  from  rest  to  full  speed.  Second,  a  full-  or  constant-speed  period 
during  which  the  load  is  hoisted  at  the  uniform  velocity  attained  at  the  end 
of  the  period  of  acceleration.  Third,  a  period  of  retardation,  during  which 
the  load  and  moving  parts  are  brought  from  full  speed  to  rest. 


752  HOISTING 

In  practice,  the  time  required  for  acceleration  is  variously  estimated  as 
being  equal  to  one-seventh  of  the  net  time  of  hoisting,  as  from  3  to  7  sec. 
depending  on  the  depth  of  the  shaft  and  speed  of  hoisting,  as  the  time  required 
for  the  drum  to  make,  say,  three  revolutions,  as  the  time  required  to  hoist 
the  cage  50  or  150  ft.  starting  from  rest,  etc.  The  period  of  retardation  is 
usually  taken  to  be  equal  in  time  to  that  of  acceleration,  although  it  may  be  a 
little  shorter.  The  full-speed  period  is  the  longest  of  the  three,  and  consumes 
about  three-fourths  of  the  net  time  of  hoisting. 

Because,  in  addition  to  raising  the  load,  it  as  well  as  the  drum,  sheaves,  and 
moving  parts  of  the  machinery  must  be  accelerated  or  brought  up  to  full  speed 
from  rest,  the  power  required  to  hoist  is  very  much  greater  during  the  period 
of  acceleration  than  at  any  later  time;  and  hoisting  engines  should  be  designed 
with  this  fact  in  view. 

2.  Net  Time  of  Hoisting.  —  The  gross  time  actually  devoted  to  hoisting 
is  8-£  =  7.5hr.     The  weight  of  coal  hoisted  per  hour  =  1,  500  -J-  7.5  =  200  T. 
As  5,000  Ib.  =  2.5  T.,  the  number  of  hoists  per  hour  is  200^-2.5  =  80.     As  there 
are  3,600  sec.  in  1  hr.,  the  gross  time  of  hoisting  per  trip  is  3,600-7-80  =  45  sec. 
As  7  sec.  is  allowed  for  caging,  the  net  time  of  hoisting  is  45  —  7  =  38  sec. 

3.  Speed  of  Hoisting.  —  Assuming  that  the  acceleration,  that  is,  the  increase 
in  velocity  of  the  cage,  is  uniform,  the  speed  attained  at  the  end  of  the  period 
of  acceleration  may  be  found  from  the  formula, 

H        1,000      .  .  , 


in  which  »  =  full  speed  of  hoisting,  in  feet  per  second; 

tf  =  distance  between  landings,  in  feet  =  1,000; 
/«  =  net  time  of  hoisting,  in  seconds  =  38; 

/  =  time  of  acceleration,  in  seconds  =  5. 
As  the  cage  starts  from  rest  and  attains  a  velocity  of  30.3  ft.  per  sec.  at  the 

end  of  5  sec.,  the  space  traversed  during  acceleration  is  -X/  =  75.75  ft.,  because 

the  average  velocity  is  one-half  the  final.   > 

The  acceleration,  a  is  found  from  the  formula  a  =  v-r-t  =  30.3-7-5  =  6.06  ft. 
per  sec.  per  sec.  The  space  passed  over  during  acceleration  is  not  the  same 
for  each  of  the  5  sec.  In  the  first  second,  the  cage  is  raised  a  distance  of 
but  $a,  or  3.03  ft.;  during  the  second  second,  it  is  raised  ia  +  o  =  9.09  ft.;  and 
during  each  succeeding  second  it  is  raised  a  distance  a  =  6.06  ft.  more.  The 
distances  passed  over  in  the  single  seconds  making  up  the  period  of  acceleration, 
are,  respectively,  3.03,  9.09,  15.15,  21.21,  and  27.27  ft.,  the  sum  of  which  is 
75.75  ft.  as  determined  before. 

The  velocity  attained  at  the  end  of  any  particular  second  is  found  from  the 
formula  v  =  aL  Thus,  at  the  end  of  the  fourth  second,  the  velocity  of  the  cage 
is  6.06X4  =  24.24  ft.  per  sec.;  that  is,  if  the  accelerating  force  ceased  to  act 
at  the  end  of  the  fourth  second,  the  cage  would  enter  the  fifth  second  with 
sufficient  velocity  to  carry  it  24.24  ft.  But  during  the  fifth  second,  the  acceler- 
ative  force  still  acts,  and  adds  $a  or  3.03  ft.  to  the  distance  traveled.  Similarly, 
at  the  end  of  the  fifth  second,  the  cage,  after  traveling  27.27  ft.  begins  the  sixth 
second  with  a  velocity  sufficient  to  carry  it  27.27  -f£a  =  30.3  ft.  during  that 
second  without  further  acceleration. 

4.  Revolutions  of  Drum  per  Minute.  —  If  D  is  the  diameter  of  the  rope 
drum,  in  feet,  the  number  of  revolutions  per  minute  made  by  it  during  the  full- 
speed  period  may  be  found  from  the  formula, 


30.3X60      1,818     . 
rev.  per         .i.-.—.vm  say,  72.5 


The  total  number  of  revolutions  made  by  the  drum  during  acceleration  or 
retardation  is  75.75-5-25.13  =  3,  very  nearly.  The  number  of  revolutions, 
or  fractions  of  a  revolution,  made  by  the  drum  during  the  individual  seconds 
of  the  acceleration  period  is  found  by  dividing  the  distance  passed  over  in  any 
second  by  the  circumference  of  the  drum.  In  the  problem,  the  approximate 
number  of  revolutions  in  each  of  the  5  sec.  will  be,  respectively,  |,  $,  f,  I,  1&. 

5.  Friction  in  Hoisting.  —  In  well-designed  and  well-built  first-motion 
hoisting  engines,  the  resistance  due  to  friction  should  not  exceed  that  due  to 
raising  a  weight  equal  to  5%  of  the  total  load  including  the  weight  of  the 
ropes,  but  in  second-motion  or  geared  hoists  this  resistance  may  amount  to 
7.5  to  10%. 

The  method  of  allowing  for  the  effects  of  friction  varies.  By  some,  the 
friction  is  added  to  the  load  and  treated  as  part  of  it;  by  others,  the  area  of  the 
steam  cylinders  is  calculated  on  the  basis  of  there  being  no  friction  and  from 


HOISTING  753 

10  to  15%  added  to  this  area  as  an  allowance  for  friction,     Probably  the  first 
method  is  the  more  generally  used. 

In  the  problem,  the  total  load  to  be  moved  is  equal  to  the  weight  of  the 
(coal+2  cages+2  cars+2  ropes)  =  (5,000+8,000+5,000+4,000)  =22.000  Ib. 
At  5%,  the  resistance  of  friction  is  equivalent  to  raising  a  weight  of  1,100  Ib. 

6.  Size  of  Hoisting  Rope.  —  The  load  on  the  rope  is  a  maximum  during  the 
first  period  of  hoisting  because,  in  addition  to  raising  the  load  and  overcoming 
friction,  there  is  a  further  resistance  due  to  acceleration. 

Assuming  that  the  rope  weighs  2  Ib.  per  ft.,  when  the  cage  is  at  rest  just 
clear  of  the  bottom,  the  load  on  the  rope  is  equal  to  the  weight  of  the  (coal 
+  cage  +  car  +  rope)  =  (5,000+4,000+2,500+2,000  =  13,500  Ib.)  As  soon  as 
motion  begins,  the  frictional  resistance  must  be  added,  and  the  total  load  upon 
the  rope  is  13.500X.  05+  13,500  =  14,175  Ib. 

If  the  acceleration  of  gravity  g  is  taken  as  32.2  ft.  per  sec.  per  sec.,  the 
stress  P  on  the  hoisting  rope  during  acceleration  due  fo  raising  the  weight  W 
(load  and  friction)  is 

p=TF+  —  Xa  =  14,175+^|-X6.06==  14,175+2,667  =  16,842  Ib. 

The  factor  of  safety  commonly  used  in  American  practice  in  calculating 
the  strength  of  hoisting  ropes  is  5;  hence,  to  sustain  a  load  of  16,842  Ib.,  the 
ultimate  strength  of  the  rope  must  be  84,210  Ib.  The  manufacturers'  tables 
show  that  the  ultimate  strength  (breaking  strength)  of  a  li-in.  extra  cast-steel 
rope  weighing  2  Ib.  per  ft.  is  86,000  Ib.;  hence,  it  would  be  selected. 

In  choosing  a  rope  of  this  size,  no  allowance  is  made  for  the  strain  due  to 
bending  around  the  drum  and  sheaves,  .which,  if  the  same  as  the  load  on  the 
rope,  is  13,500  Ib.  The  total  strain  on  the  rope  during  acceleration  is,  then, 
16,842  +  13,500  =  30,342  Ib.,  and  the  true  factor  of  safety  is  86,000  -=-30,342 
=  2.83.  Although  this  seems  a  small  margin  of  strength  for  live  loads,  Amer- 
ican practice  seems  to  warrant  it. 

7.  Size  of  Drum.  —  The  manufacturers'  tables  indicate  a  minimum  diameter 
of  5  ft.  for  the  drum  and  sheaves  to  be  used  with  a  l|-in.  rope.     While  a  drum 
of  this  size  might  be  used  on  contractors'  hoists,  a  mine  hoisting  engine  would 
have  drums  8  ft.  or  more  in  diameter.     The  greater  the  diameter  of  the  drum, 
the  less  will  be  its  width  for  the  same  depth  of  hoist,  the  shorter  will  be  the 
drum  shaft,  and  the  less  the  strain  upon  it.     Also,  the  greater  the  diameter  of 
the  drum,  the  fewer  will  be  the  revolutions  necessary  to  move  the  cage  a  given 
distance  and  the  less  will  be  the  piston  speed  of  the  engine.     Further,  large 
drums  reduce  the  bending  strain  on  the  rope  and  thus  conduce  to  a  longer 
life.     On  the  other  hand,  during  acceleration,  the  power  required  to  overcome 
the  inertia  of  the  drum  increases  very  rapidly  with  the  increase  in  its  diameter. 

8.  Ordinary  Method  of  Calculating  Power  Required  to  Hoist.  —  The  usual 
method  of  calculating  the  horsepower  required  to  hoist  is  to  multiply  the 
unbalanced  load,  in  pounds,  by  the  speed  of  hoisting,  in  feet  per  second,  and 
divide  the  product  by  550.     The  unbalanced  load  is,  in  any  case,  taken  as  the 
weight  of  coal  and  one  rope,  or,  in  the  problem,  as  7,000  Ib.     To  the  unbalanced 
load  is  added  the  friction,  which  is  variously  estimated  as  5  or  10%  of  the  total 
weight  being  moved.     Assuming  the  former  figure,  the  resistance  due  to  fric- 
tion is  22.000X.  05=  1,100  Ib.,  making  the  total  load  8,100  Ib.     The  speed  of 
hoisting  should  be  taken  at  30.3  ft.  per  sec.  (1,818  ft.  per  min.),  which  allows 
for  the  time  lost  in  acceleration  and  retardation.     With  these  data,  the  horse- 
power is  (8,  100X30.3)  -T-  550  =  446.2. 

Sometimes  in  calculating  the  speed  of  hoisting,  the  depth  of  the  shaft  is 
divided  by  the  total  time  of  hoisting,  which  gives  a  speed  of  1,000  -=-38  =  26.3  ft. 
per  sec.  With  this  incorrect  speed,  the  horsepower  obtained  is  too  low  and 
is  (8,100X26.3)^550  =  387.3. 

The  horsepower,  as  thus  obtained,  is  often  divided  by  a  factor  representing 
the  assumed  efficiency  of  the  plant,  and  sometimes  is  further  increased  by  an 
arbitrary  amount  as  an  allowance  for  so-called  contingencies.  As  will  be 
shown  in  paragraph  12,  the  horsepower  determined  by  this  method,  no  allow- 
ance having  been  made  for  acceleration,  is  about  one-half  that  really  required 
to  hoist. 

9.  Piston  Speed  and  Length  of  Stroke.  —  The  piston  speed  of  hoisting  engines 
varies  from  300  to  500  ft.  per  min.,  a  commonly  accepted  value  being  500  ft. 
Because  the  engine  makes  two  strokes  for  each  revolution  of  the  drum,  if  the 
piston  speed  is  called  S,  the  length  of  stroke  I  may  be  found  from 


48 


754  HOISTING 

In  the  foregoing,  S  is  taken  as  500  ft.  per  min.,  and  the  revolutions  per 
minute  as  determined  in  paragraph  4. 

10.  Dimensions  of  Engine  to  Produce  a  Given  Horsepower. — After  the 
power  necessary  to  hoist  and  the  piston  speed  have  been  determined,  the  total 
area  of  cylinder  necessary  to  yield  the  calculated  horsepower  at  the  mean  effec- 


Because  there  are  two  cylinders,  each  should  have  an  area  of  294. 492  -f-  2 
=  147.246  sq.  in.  The  diameter  d  of  each  cylinder  will  be  d=>  \/— z^-— 

if     »/oO4 

=  13.7,  say,  14  in.  As  the  length  of  stroke  is  42  in.,  the  use  of  a  14"X  42"  engine 
is  indicated. 

By  this  method  of  calculation,  no  allowance  is  made  for  the  power  necessary 
to  accelerate  the  load  and  machinery,  which  frequently  amounts  to  as  much  as 
that  required  to  raise  the  load.  It  is  usually  assumed  that  if  one  cylinder 
will  develop  sufficient  power  to  start  the  load,  the  power  from  two  cylinders 
will  be  great  enough  to  accelerate  it.  This  will  commonly  prove  to  be  the  case, 
even  if  no  allowance  is  made  for  the  efficiency  of  the  plant;  although,  to  provide 
for  contingencies,  it  is  advisable  to  make  such  an  allowance.  Thus,  if  a  single 
cylinder  must  be  of  a  size  sufficient  to  raise  the  entire  load,  it  must  have  an  area 
of  294.492  or  of  294.492-i- .85  =  346.46  sq.  in.,  depending  on  whether  the  plant 
is  assumed  to  have  an  efficiency  of  100%  or  of  85%.  In  the  first  case,  d  =  19.4, 
say,  20  in.,  and  in  the  second  case  d  =  21  in.  From  this,  the  dimensions  of  the 
engine  will  be  20  in.X42  in.  or  21  in.X42  in.,  depending  on  the  efficiency 
assumed  for  the  plant.  These  dimensions  are  very  nearly  those  obtained  by 
the  use  of  more  accurate  methods. 

11.  Resistance  and  Force  in  Hoisting. — The  resistance  that  must  be  overcome 
in  hoisting  arises  in  part  from  raising  the  load  and  overcoming  friction,  and  in 
part  from  accelerating  the  load  and  machinery,  particularly  the  drum  and  sheaves . 

The  friction  is  constant  throughout  the  run  and  may  be  considered  as  a 
portion  of  the  load,  or  it  may  be  included  in  an  allowance  made  to  cover  the 
various  uncertainties  entering  into  all  calculations  of  this  nature.  If  con- 
sidered as  a  portion  of  the  load,  it  may  be  estimated  as  22.000X. 05=  1,100  Ib. 

The  unbalanced  load  is  the  weight  of  the  coal  and  the  hoisting  rope.  The 
weight  of  the  coal  is  constant  throughout  the  run,  but  that  of  the  rope  decreases 
as  the  loaded  cage  ascends.  When  the  cages  pass  in  the  shaft,  the  ropes 
attached  to  them  are  of  equal  length  and  their  weights  balance.  Beyond  the 
passing  point,  the  length  and  weight  of  the  rope  attached  to  the  empty  cage 
becomes  greater  than  that  attached  to  the  loaded  cage  and  acts  in  favor  of  the 
engine.  Hence,  because  the  weights  of  the  rope  wound  off  and  wound  on  the 
drum  are  equal,  the  unbalanced  load  at  any  instant  is  less  than  the  original 
load  by  twice  the  weight  of  the  rope  wound  on  the  drum.  For  convenience  in 
calculation,  the  friction  may  be  considered  as  part  of  the  unbalanced  load. 
At  the  beginning  of  hoisting,  the  unbalanced  load  including  friction,  is  5,000 
+2,000+1,100  =  8,100  Ib.  At  the  end  of  the  acceleration  period  when  75.75  ft. 
of  rope,  weighing  2  Ib.  per  ft.,  has  been  wound  upon  and  unwound  from  the 
drum,  the  original  load  is  reduced  by  2X2X75.75  =  303  Ib.,  and  is  7,797  Ib. 
At  the  end  of  the  full-speed  period,  924.25  ft.  of  rope  will  have  been  wound 
on  the  drum,  and  the  load  will  be  reduced  by  2X2X924.25  =  3,697  Ib.,  and 
will  be  4,403  Ib.  At  the  end  of  the  period  of  retardation  when  the  cage 
comes  to  rest  at  the  landing,  all  the  rope  will  have  been  wound  on  the  drum, 
and  the  original  load  will  be  reduced  by  2X2X1,000  =  4,000  Ib.,  and  will  be 
4,100  Ib.  These  loads,  all  having  a  positive  sign,  are  entered  in  the  first 
column  of  the  following  table. 

The  force,  in  pounds,  required  to  accelerate  the  load  is  —  X  a,  in  which  W 

is  the  total  weight,  or  22,000  Ib.,  placed  in  motion;  a  is  the  linear  acceleration 

22  000 
or  6.06  ft.  per  sec.  per  sec.;  and  g  is  32.2.     The  acceleration   is  then  -   ' 

O.4.4 

X  6.06  =  4,140  Ib.     The  retardation  is  equal  to  the  acceleration,  but  has  a  nega- 
tive sign ;  this  force  is  entered  in  the  second  column  of  the  table  with  its  proper 
sign.     The  acceleration  ceases  as  soon  as  the  cage  is  moving  at  full  speed. 
The  drum  may  be  taken  to  weigh  25,760  Ib.,  and  the  force  required  to 

accelerate  it  is  2~^X 6.06  =  4,848  Ib. 


HOISTING 


755 


The  sheaves  may  be  taken  to  weigh  805  Ib.  each,  and  the  force  required  to 

OQC 

accelerate  them  is  2X^^X6.06  =  303  Ib. 
o2*« 

The  total  force  required  to  accelerate  the  drum  and  sheaves  is,  thence, 
4,848  +  303  =  5,151  Ib.,  and  is  the  same  in  amount  but  negative  in  sign  during 
retardation.  The  algebraic  sum  of  all  the  forces  necessary  to  hoist  and  acceler- 
ate are  given  in  the  fourth  column  of  the  table.  A  negative  force  indicates 
that  the  resistance  opposing  it  is  acting  to  turn  the  drum  and  raise  the  load; 
hence,  the  brakes  must  be  applied  to  prevent  the  engine  running  away. 

FORCES  AND  MOMENTS  IN  HOISTING 


Period 

Raising 
Load 
and 
Friction 

.  Accelerating 

Total 
Force  or 
Resistance 

Total 

Moment 

Load 

Drum 
and 
Sheaves 

Beginning  acceleration  .  . 
End  acceleration 

+  8,100 
7,797 
7,797 
4,403 
4,403 
4,100 

+4,140 
4,140 

-4,140 
4,140 

+5,151 
5,151 

-5,151 
5,151 

+  17,391 
17,088 
7,797 
4,403 
-   4,888 
5,191 

+69,564 
68,352 
31,188 
17,612 
-19,552 
20,764 

Beginning  full  speed  
End  full  speed 

Beginning  retardation.  .  . 
End  retardation.  . 

12.  Load  Moments  in  Hoisting. — The  calculation  of  the  area  of  the  steam 
cylinder  of  a  hoisting  engine  is  based  on  the  principle  that  the  force  resisting 
motion  (or  the  resistance)  multiplied  by  its  lever  arm,  or'the  distance  through 
which  it  acts,  must  equal  the  force  producing  motion  multiplied  by  its  lever 
arm;  the  forces  being  expressed  in  pounds  and  the  lever  arms  (or  distances) 
in  feet. 

The  forces  resisting  motion  at  any  instant  are  entered  in  the  fourth  column 
of  the  table.  Each  has  the  same  lever  arm,  which  is  the  radius  R  of  the  drum, 
or  4  ft.  When  the  forces  are  multiplied  by  this  lever  arm,  they  give  the  total 
moments,  or  load  moments,  in  foot-pounds,  which  are  given  in  the  fifth  column. 

If  the  weights  of  the  drum  and  sheaves  are  not  known,  the  moments  of  the 
force  required  to  accelerate  them  may  be  calculated  by  formulas  suggested  by 
Mr.  Wilfred  Sykes  in  the  Transactions  of  the  American  Institute  of  Electrical 
Engineers.  The  formula  for  the  drum  is  Id  =  100 R*X  width,  and  for  sheaves  Is 
=  25R2.  The  inertia  Id  or  Is,  when  multiplied  by  the  angular  acceleration  A  a 
of  the  drum  and  sheaves,  gives  the  turning  moment,  which  is  the  same  as  the 
load  moment.  Thus,  in  the  present  problem,  as  R  =  4  ft.  and  the  width  of  the 
drum  is  8  ft.,  the  inertia  Id  =  100X42X8  =  12,800  Ib.  As  there  are  two  sheaves, 
their  inertia  will  be  7j  =  2X25X42  =  800  Ib.  The  inertia  of  the  drum  and 
sheaves  taken  together  is,  therefore,  13,600  Ib.  The  angular  acceleration  is 
equal  to  the  linear  acceleration  a-i-radius  of  drum  =  6.06^-4  =  1.515  radii  per 
sec.  per  sec.  From  this,  the  turning  moment  or  load  moment  of  the  drum  is 
13,600X1.515  =  20,604  ft.-lb. 

Suppose  that  it  is  desired  to  calculate  the  total  moment  at  the  end  of 
acceleration.  The  moment  of  the  load  is  7.797X4  =  31,188  ft.-lb.,  and  that 
of  the  force  required  to  accelerate  the  load  is  4,140X4  =  16,560.  The  sum  of 
these  three  moments  is  20,604+31,188  +  16,560  =  68,532  ft.-lb.,  which  corre- 
sponds to  the  value  in  the  last  column  of  the  table  and  which  was  determined 
from  the  weights  of  the  drum  and  sheaves. 

If,  as  shown  in  the  accompanying  figure,  a  base  line  OO  is  divided  to 
correspond  with  the  length,  in  seconds  of  time,  of  the  various  hoisting  periods 
there  may  be  laid  off  above  it  the  positive  moments  and  below  it  the  negative 
ones.  If  the  points  so  determined  are  joined  by  lines,  there  will  result  the 
curve  abed efg h,  which  may  be  called  the  curve  of  moments.  This  curve  shows 
graphically  the  variation  in  the  load  upon  and  the  duty  demanded  of  the 
engine  from  second  to  second  during  the  hoisting  period.  At  the  start,  the 
moments  are  a  maximum,  showing  that  the  greatest  power  is  required  during 
the  first  few  seconds.  At  the  end  of  acceleration,  there  is  a  very  great  drop 


756 


HOISTING 


in  the  load;  in  the  present  example  it  amounts  to  55%.  During  the  full- 
speed  period,  the  load  drops  regularly  until  at  its  end,  and  coincident  with  the 
beginning  of  retardation,  there  is  another  great  falling  off  in  the  load,  which, 
with  its  moment,  becomes  negative  and  tends  to  turn  the  engine.  A  large 
amount  of  brake  power  is  required  during  retardation;  this  power  is  supplied 
by  reversing  the  engine  and  turning  steam  gently  into  the  cylinders  against 
the  load  and  by  the  use  of  the  brakes.  As  a  result,  for  quick  and  heavy  hoist- 
ing, an  engine  must  be  run  at  much  above  its  economical  load.  In  fact,  during 
acceleration,  the  engine  may -be  called  upon  to  deliver  more  than  twice  the 
power  required  during  full  speed.  In  the  present  example,  at  the  end  of 
acceleration  when  the  cage  is  moving  with  a  speed  of  30.3  ft.  per  sec.,  the 
horsepower  exerted  by  the  engine  is  (17,088X30.3)  +  550  =  941.4.  At  the 
beginning  of  full  speed,  the  horsepower  is  (7,797X30.3) -7-550  =  429.5,  or 
about  46%  of  what  it  was  during  acceleration.  At  the  end  of  full  speed,  the 
horsepower  drops  to  (4,403  X  30.3) -J- 550  =  242.5,  and  at  the  beginning  of 
retardation  there  is  a  further  drop  to  (-4, 888X30.3) -7-550= -269.3  H.  P. 
It  may  be  urged  that  the  weight  to  be  accelerated  is  not  that  of  the  entire 
load,  or  22,000  lb.,  but  rather  that  attached  to  the  loaded  rope,  or  13,500  lb., 
because  gravity  accelerates  the  weight  of  the  empty  cage,  car,  and  rope.  If 
this  line  of  reasoning  is  carried  farther,  it  follows  that  the  weight  to  be  acceler- 
ated is  that  of  the  unbalanced  load,  or  7,000  lb.  On  the  other  hand,  no  account 
has  been  taken  in  the  calculation  for  the  power  necessary  to  overcome  the 
inertia  of  the  crank,  piston  rod,  etc.,  which  in  the  aggregate  is  considerable,  so 
that  it  is  undoubtedly  true  that  the  dimensions  of  an  engine  calculated  on  the 
basis  of  accelerating  a  load  of  22,000  lb.  will  be  none  too  great  for  the  work 
demanded  of  it.  In  fact,  it  would  seem  advisable  in  any  case  to  add  something 
to  the  area  of  the  cylinders  to  provide  for  uncertainties  in  the  resistances  to 
be  overcome  and  for  future  demands  for  power. 


The  variation  in  the  load  and  moments  is  of  the  greatest  importance  in 
electric  hoisting,  because  the  motor  is  called  on  at  the  outset  to  furnish  very 
much  more  power  than  at  the  end  of  the  full-speed  period.  /This  reduces  the 
load  factor,  which  is  the  ratio  between  the  total  energy  used  in  hoisting  a  trip 
under  the  given  conditions  and  the  energy  required  if  the  load  and  speed  were 
uniform  and  the  motor  working  at  its  full  rated  capacity;  and  a  low  load  factor 
indicates  low  efficiency  in  the  hoisting  plant. 

This  great  range  in  the  demands  for  power,  in  the  present  example  amount- 
ing to  nearly  1,250  H.  P.  in  38  sec.,  also  indicates  the  importance  of  counter- 
balancing the  weight  of  the  rope  not  only  to  reduce  the  unbalanced  load  to 
be  raised,  but  also,  and  more  particularly,  to  cut  down  the  excessive  power 
required  to  accelerate  the  load  and  machinery. 

13.  Determination  of  Engine  Dimensions  From  Load  Moments. — If  the 
base  line  in  the  figure  on  this  page  is  divided  into  revolutions  instead  of  into 
seconds,  and  perpendiculars  are  drawn  through  the  points  of  division,  the 
average  load  moment  for  any  revolutfon  can  be  determined.  This  moment 
divided  by  the  crank  radius  of  the  engine  gives  the  average  pressure  on  the 
crankpin  for  that  revolution;  from  this,  the  required  average  piston  pressure 
is  obtained.  If  the  initial  steam  pressure  is  known,  the  point  at  which  the  steam 
may  be  cutoff  at  any  revolution  can  be  obtained,  and  the  steam  consumption 
per  hoist  can  be  accurately  ascertained.  Calculations  of  this  nature,  however, 
are  properly  the  work  of  the  mechanical  engineer  and  not  of  the  mine  foreman 
or  superintendent. 

If  the  maximum  load  moments  are  known  and  the  length  of  stroke  has  been 
determined  by  assuming  a  piston  speed,  as  in  paragraph  9,  the  proper  area 
of  cylinder  may  be  found  from  the  formula, 

ML+MA 
PNCRc 


HOISTING 


757 


in  which     A  =  area  of  a  single  cylinder,  in  square  inches; 

ML  =  moment  of  unbalanced  load,  coal,  one  rope,  friction; 

MA  =  moment  of  force  required  to  accelerate  total  load,  drum,  two 

sheaves,  machinery; 
P  =  mean  effective  pressure  of  steam  in  cylinders,  in  pounds  per 

square  inch; 

N  =  number  of  cylinders; 
C  =  constant  to  reduce  angular  space  passed  through  by  crank  to 

that  passed  through  by  piston  in  the  same  time  =  .64; 
Rc  —  radius  of  crank  circle,  one-half  length  of  stroke. 

In  the  present  problem,  ML  =  8,  100X4  =  32,400  ft.-lb.;  MA  -  (4,140+5,151) 
X4  =  37,164;  P  =  100  lb.;  N  =  2;  C  =  .64;  and  Rc  =  42  in.-j-2  =  21  in.  =  1.75  ft. 
Substituting  in  the  formula, 

32,400  +37,164 


From  this  value  of  A,  d  is  found  to  be  19.99,  say,  20  in.  The  length  of 
stroke  having  been  previously  determined,  the  use  of  a  20"X42"  engine  is 
indicated.  In  some  cases  an  allowance  is  made  for  the  efficiency  of  the  plant. 
In  the  present  case,  the  efficiency  has  been  assumed  to  be  85%;  hence,  the 
proper  area  for  the  cylinders  will  be  310.55-7-  .85  =  365.35  sq.  in.,  and  d  =  21.6, 
say,  22  in.  With  this  allowance,  the  dimensions  of  the  engine  will  be  22  in. 
X42  in. 

It  is  not  unusual  in  calculations  of  this  nature  to  assume  a  ratio  r  between 
the  length  of  stroke  (length  of  cylinder)  /  and  the  diameter  of  cylinder  d  such 
that  l  =  rd.  In  this  case,  the  diameter  of  cylinder  may  be  found  directly  from 
a  modification  of  the  preceding  formula.  A  common  value  for  r  is  2,  that 
is,  the  length  of  stroke  is  made  twice  the  diameter  of  the  cylinder.  The 
formula  for  d  (d3)  follows,  its  application  being  shown  by  using  the  preceding 
data  with  a  value  of  r  =  2: 

96(ML+MA)     96X  (32,400+37.164) 

*rPNC          3.14X2X100X2X.64  =  8'307'77  CU'  im 

From  this,  d  =  20.25  in.,  and  l  =  rd  =  2X20.25  =  40.5  in.  A  21"X42"  engine 
would  probably  be  selected,  the  extra  power  of  the  larger  size  being  desirable. 


CALCULATIONS  FOR  SECOND-MOTION  HOISTING 
ENGINES 

When  less  than  200  to  250  H.  P.  is  required  to  hoist,  second-motion  engines 
are  commonly  preferred  to  first-motion  engines  because  of  their  smaller  size, 
lower  first  cost,  and  generally  greater  ease  in  handling.  Their  small  horse- 
power limits  their  use  to  shallow  shafts,  those,  say,  not  over  250  to  350  ft.  deep, 
where  the  net  daily  tonnage  does  not  exceed  750  to  1,000,  and  where  the  speed 
of  hoisting  is  not  more  than  500  to  750  ft.  per  min.  The  standard  or  stock 
sizes  of  second-motion  engines  are  given  in  the  following  table,  in  which  the 
hoisting  speed  is  the  rate  of  travel  of  the  cage  and  the  horsepower  is  based  on 
a  steam  pressure  of  between  80  and  90  lb. 

STANDARD  SIZES  OF  SECOND-MOTION  HOISTING  ENGINES 


Cylinders 

Hoisting 

Cylinders 

Hoisting 

Horse- 
power 

Speed 
Feet 

Minute 

Horse- 
-  power 

Speed 
Feet 

Minute 

Diam- 
eter 
Inches 

Stroke 
Inches 

Diam- 
eter 
Inches 

Stroke 
Inches 

6£ 

8 

12 

250 

10 

12 

50 

400 

7 

10 

20 

275 

12J 

15 

75 

450 

81 

10 

30 

350 

14 

18 

100 

450 

9 

10 

35 

350 

16 

18 

150 

450 

81 

12 

40 

375 

18 

24 

200 

550 

758  HAULAGE 

Dimensions  of  Second-Motion  Engines. — While  the  load  moments  may  be 
determined  in  the  same  way  as  for  first-motion  hoisting  engines,  after  which 
the  size  of  the  cylinders  may  be  calculated,  it  is  not  customary  to  do  so.  The 
usual  practice  is  to  determine  the  horsepower  by  the  method  explained  in 
paragraph  8,  an  allowance  being  made  for  the  time  spent  in  acceleration  and 
retardation,  and  to  select  from  the  manufacturers'  stock  sizes  an  engine  of 
slightly  more  than  the  calculated  horsepower.  Thus,  if  an  engine  of  185  H.  P. 
is  required,  an  engine  with  18"X24"  cylinders  and  rated  at  200  H.  P.  will  be 
selected,  the  extra  horsepower  being  desirable.  As  these  engines  cost  from 
$40  to  $60  per  H.  P.  (list  prices,  subject  to  discount)  depending  on  the  acces- 
sories furnished,  the  cost  of  a  few  extra  horsepower  is  not  to  be  compared  with 
the  increased  efficiency  gained  through  the  use  of  the  larger  size. 

The  necessary  diameter  of  cylinder  to  yield  a  given  horsepower  may  be 
calculated  from  the  formula, 

792.000  XH.  P. 
vPrGXR.  P.  M. 
in  which  G  =  ratio  of  gearing,  which  is  very  commonly  3; 

R.  P.  M.  =  revolutions  of  drum  per  minute; 

and  the  other  letters  have  the  meanings  previously  given.  The  revolutions 
of  the  crank-arm  per  minute  are  equal  to  the  revolutions  of  the  drum  multiplied 
by  the  gear  ratio.  That  is,  if  the  drum  makes  50  rev.  per  min.  and  (7  =  3,  the 
revolutions  per  minute  of  the  crank  will  be  GXR.  P.  M.  =  3X50  =  150. 

In  the  ratio  l  =  rd,  r  varies  between  1.11  and  1.41,  and  should  be  taken  to 
be  essentially  the  same  as  the  ratio  in  the  table  for  engines  of  the  required 
horsepower. 

EXAMPLE. — What  should  be  the  dimensions  of  a  second-motion  engine  to 
develop  200  H.  P.,  when  the  mean  effective  pressure  of  the  steam  is  80  Ib. 
per  sq.  in.,  the  hoisting  speed  is  550  ft.  per  min.,  the  drum  is  6  ft.  in  diam.,  and 
the  gear  ratio  is  3? 

SOLUTION. — Here  the  revolutions  per  minute  of  the  drum  =  550 -i-  (6X3.1416) 
=  29.2,  about,  and  r  may  be  assumed  as  in  the  engine  table  to  be  as  18  :  24  or 
as  1  :  1.33.  Substituting  in  the  formula, 

792.000X200 
3.14X80X1.33X3X29.2       '     ' 

From  this,  d  =  17.56,  say,  18  in.,  and  l  =  rd  =  1.33X18  =  24  in.  Hence  the 
dimensions  of  the  cylinders  are  18  in.X24  in. 

In  calculations  relating  to  this  type  of  engine,  it  is  rarely  necessary  to 
determine  the  accelerating  force.  Sufficiently  accurate  results  may  be  obtained 
by  determining  the  horsepower  required  to  hoist  the  unbalanced  load  (with 
friction  at  10%)  at  the  sustained  speed,  and  then  to  make  one  cylinder  large 
enough  to  do  all  the  work.  Where  uncertainty  exists  as  to  the  efficiency  of 
the  plant  or  as  to  future  possible  increased  demands  for  power,  the  determined 
horsepower  should  be  increased  from  10  to  25%  or  more. 


HAULAGE 


RESISTANCES  TO  HAULAGE 

Total  Resistance  to  Haulage. — The  total  resistance  R,  in  pounds,  which 
must  be  overcome  in  bringing  a  car  or  a  trip  of  cars  from  rest  to  full  speed,  may 
be  represented  by  the  expression, 

R=F+C+G+I 

in  which  F  =  resistance  due  to  friction,  in  pounds; 

C  =  resistance  due  to  curvature,  in  pounds; 
G  =  resistance  due  to  grade,  in  pounds; 
1 1  =  resistance  due  to  inertia,  in  pounds. 
When  the  trip  is  moving  at  a  uniform  speed,  the  resistance  is 

R=F+C+G 

When  the  track  is  level,  G  =  0,  and  when  it  is  straight  C  =  0. 
Resistance  Due  to  Friction. — The  frictional  resistance  to  haulage  is  due 
both  to  the  friction  of  the  wheels  upon  their  axles,  or  car  resistance,  and  to  the 
friction  of  the  wheels  upon  the  rails,  or  track  resistance.  It  is  customary  to 
consider  these  as  one  under  the  head  of  train  resistance.  On  surface  railroads, 
it  is  found  that  the  train  resistance  increases  with  the  speed  and  is  materially 


HA  ULAGE  759 

less  for  heavy  than  for  light  cars.  The  Baldwin  Locomotive  Works,  quoting 
the  experiments  of  Prof.  E.  C.  Schmidt,  gives  the  following  formula  for  the 
resistance  of  freight  cars,  in  pounds  per  ton, 


in  which  W=  weight  of  car,  in  tons; 

V  =  velocity  of  train,  in  miles  per  hour. 

The   same   authority   gives   the   resistance   for   light   standard-gauge   and 
narrow-gauge  locomotives  and  tenders  as 


and  for  heavy  standard-gauge  locomotives  as, 
F  =  4.3  +  .003V2 

Both  in  mine-  and  surface-railroad  practice,  it  is  found  that  the  train 
resistance  depends  on  the  diameter  of  the  wheels,  the  kind  of  lubricant  used 
and  the  amount  of  lubrication,  the  kind  of  axles  and  journal  boxes,  the  condi- 
tion of  the  track,  the  presence  or  absence  of  curves,  etc.  A  large  journal  bear- 
ing reduces  journal  friction,  and  car  wheels  of  large  diameter  roll  more  easily 
than  small  ones  over  inequalities  in  the  rails.  Flat  and  grooved  wheels  add 
materially  to  the  resistance.  With  ordinary  self-oiling  wheels  turning  on 
fixed  axles,  as  used  in  bituminous  coal  mines,  many  experiments  have  shown 
that  the  frictional  resistance  averages  30  Ib.  per  T.,  or  1.5%,  when  the  cars 
are  properly  oiled  and  kept  in  good  repair.  When  the  wheels  are  fixed  and  the 
axles  revolve  in  self-oiling  journal  boxes,  the  resistance  should  be  under  20  Ib. 
per  T.,  or  1%.  •  In  surface-railroad  practice,  at  low  speeds,  the  resistance  will 
be  from  4  Ib.  to  10  Ib.  per  T.,  a  working  average  being  6.5  Ib.  In  mines  where 
roller-bearing  wheels  are  used,  the  resistance  should  not  exceed  15  Ib.  per  T., 
or  .75%.  Where  the  track  is  poor  and  wheels  have  much  play  on  fixed  axles, 
the  resistance  may  easily  amount  to  50,  60,  or,  in  extreme  cases,  to  100  Ib.  per  T. 

The  track  resistance  is  ordinarily  but  a  small  fraction  of  the  total  resistance 
and  may  be  found  from  the  formula, 

£TSE 

in  which    W  =  weight  of  car,  in  pounds; 

r  =  radius  of  car  wheel,  in  inches; 
C  =  coefficient  that,  for  iron  wheels  rolling  on  steel  rails,  is  .02. 

Thus  the  track  resistance  per  ton  of  2,000  Ib.,  when  20-in.  wheels  are  used, 
is  (2,000  X  .02)  -h  10  =  4  Ib. 

If  a  coefficient  of  friction  /is  assumed,  the  total  frictional  resistance  may  be 
found  from 

F=fWcosX 
in  which  W=  weight  of  car; 

X  =  angle  of  inclination  of  track. 

If  the  track  is  level,  X  =  0,  cos  X  =  l,  and  F=fW.  Where  the  pitch  is 
under  10%,  say  5°  30',  no  error  of  importance  is  made  if  this  latter  and  more 
simple  formula  is  used. 

EXAMPLE.  —  What  is  the  frictional  resistance  to  moving  a  loaded  mine  car 
weighing  8,000  Ib.  on  a  level  and  on  a  slope  of  20°  when/=  1.5%? 

SOLUTION.—  On  a  level  track  X  =  0  and  F=fW=.  015X8,000  =  120  Ib. 
On  the  slope,  F  =  .  015  X  8,000  X.  937  =  112.5  Ib.,  about. 

EXAMPLE.  —  Assuming  the  conditions  of  the  preceding  problem,  what 
horsepower  must  be  exerted  to  move  the  car  at  a  rate  of  2  mi.  per  hr.  on  a 
level  track? 

SOLUTION.—  A  speed  of  2  mi.  per  hr.  =  (2  X  5.280)  -r-  3,600  =  2.9  ft.  per  sec. 
The  work  per  second  required  to  overcome  a  resistance  of  120  Ib.  is  120X2.9 
=  348  ft.-lb.  As  1  H.  P.  is  equal  to  550  ft.-lb.  of  work  per  sec.,  the  required 
horsepower  will  be  348  -=-550  =  .63. 

Resistance  Due  to  Curvature.  —  On  surface  railroads,  it  is  customary  to 
compensate  for  the  resistance  due  to  curvature  by  reducing  the  grade  by  .03  to 
.05  ft.  per  100  ft.  for  each  degree  of  curve.  Thus,  on  an  8°  curve,  where  the 
grade  would  otherwise  be,  say,  2%,  it  would  be  reduced  to  (2.00  —  .05X8) 
=  1.60%. 

This  correction  is  not  made  on  mine  roads,  whereat  is  not  generally  possible 
or  even  necessary  to  do  so.  Centrifugal  force  pressing  the  wheels  against  the 
outer  rail  is  the  chief  cause  of  curve  resistance  on  surface  railroads  where  the 
speed  is  high,  the  cars  heavy,  the  curves  of  long  radius,  and  where,  in  particular, 
the  trucks  being  pivoted  on  king  bolts,  the  axles  are  free  to  assume  a  position 
in  the  direction  of  the  radius  of  the  curve.  On  mine  roads,  however,  where 


760  HAULAGE 

the  speed  is  low,  the  cars  light,  the  curves  of  small  radius,  and  the  axles  are 
fixed  so  that  they  cannot  adjust  their  direction  to  that  of  the  radius  of  the 
curve,  the  chief  cause  of  curve  resistance  is  the  binding  of  the  wheels  against 
the  rails. 

The  centrifugal  force  pressing  the  wheels  against  the  outer  rail  of  a  curve 
may  be  found  from  the  formula, 

c=~2 

gr 
in  which  W=  weight  of  car  or  trip,  in  pounds; 

v  =  velocity  of  car  or  trip,  in  feet  per  second; 
r  —  radius  of  curve,  in  feet. 

EXAMPLE.  —  A  train  weighing  400  T.  is  moving  on  an  8°  curve  at  a  speed 
of  50  mi.  per  hr.  What  is  the  pressure  against  the  outer  rail? 

SOLUTION.—  400  T.  =  800,000  Ib.  A  speed  of  50  mi.  per  hr.  =  (SOX  5,280) 
-7-3,600  =  73  ft.  per  sec.  The  radius  of  an  8°  curve  is  about  717  ft.,  and  g  may 
be  taken  at  32.2  ft.  per  sec.  per  sec.  Substituting, 

C=832'.2°x7ir=20()'000  lb-  approximatelv 

This  is  the  total  pressure  of  the  train.  If  there  are  8  cars  each  with  two 
four-wheel  trucks,  the  pressure  per  truck  is  200,000-7-16=12,500  lb.,  and  for 
each  wheel  bearing  against  the  outer  rail  is  6,250  lb. 

The  following  formula,  based  on  'experiments  with  mine  cars  moving  at 
usual  speeds,  gives  the  approximate  average  resistance  due  to  curvature  : 


in  which  b  =  wheel   base,  in  feet,  and  C,  W,  and  r  have  the  meaning  given  in 
the  preceding  formula. 

EXAMPLE.  —  What  will  be  the  resistance  to  the  passage  of  a  motor  weighing 
20  T.  (40,000  lb.),  and  having  a  wheel  base  of  10  ft.,  around  a  curve  with  a 
radius  of  200  ft.? 


SOLUTION.—  By  substituting  in  the  formula,  C  =  =  4(X>  lb. 


The  preceding  formula  brings  out  the  important  point  that,  for  equal 
resistance,  the  sharper  the  curve  the  less  must  be  the  wheel  base  of  the  car. 
Although  not  considered  in  the  formula,  it  should  be  stated  that  for  equal 
resistance,  the  sharper  the  curve  the  less  should  be  the  gauge  of  the  track. 

Resistance  Due  to  Grade.  —  The  grade  or  slope  of  a  track  may  be  expressed 
in  various  ways. 

1.  As  an  angle  made  by  the  track  with  the  horizontal. 

2.  As  the  ratio  between  the  rise,  taken  as  1,  or  unity,  and  the  horizontal 
distance  required  to  gain  the  rise;  as  1  in  1,  1  in  5,  etc. 

3.  As  the  rise  in  any  horizontal  distance,  as  a  grade  of  2  in.  per  ft.,  or  of 
6  in.  per  yd. 

4.  As  a  per  cent.;  this  is  a  modification  of  3,  the  horizontal  distance  being 
taken  as  100  ft.     Thus  a  2%  grade  is  one  in  which  the  rise  is  2  ft.  per  100  ft., 
or  105.6  ft.  per  mi. 

5.  As  the  rise  in  feet  per  mile  of  length  of  track;  this  is,  also,  a  modification 
of  3,  the  horizontal  distance  being  taken  as  1  mi. 

Of  these  ways  of  expressing  grades,  the  second  and  third  are  awkward  and 
practically  obsolete.  The  first  and  fourth  are  in  common  use  by  mining  engi- 
neers, and  the  fourth  and  fifth  by  civil  engineers. 

If  X  =  angle  of  slope,  V  =  vertical  rise,  H  =  horizontal  distance,  and  5 
=  slope  distance,  then, 

V  V  H 

tan  X  =  jj  sin  X  =  -=•  cos  X  =  -= 

V  =  H  tan  X  =  S  sin  X     S  =  V  cos  X  =  H  sec  X      H  =  V  cot  X  =  S  cos  X 

The  per  cent,  of  grade  is  the  tangent  of  the  angle  of  inclination.  A  10% 
grade  =  angle  whose  tangent  is  .10000  =  5°  43',  about.  A  pitch  of  7°  58',  the 
tangent  of  which  is  .13995,  equals  a  grade  of  .13995X100  =  13.995,  say,  14%. 

A  10%  grade  equals  a  rise  of  5,280  X  .10  =  528  ft.  per  mi.  A  grade  of  460  ft. 
per  mi.  equals  one  of  (460-7-5,280)  X  100  =  8.71%. 

The  resistance,  due  solely  to  the  grade,  which  must  be  overcome  in  hauling 
up  an  incline  at  a  uniform  speed  is 

G=Wsin  X 

On  a  level  track,  where  sin  X  =  sin  0°  =  0,  G  =  0  and  there  is  no  resistance 
due  to  the  weight  while  the  trip  is  moving  at  a  uniform  speed.  In  shaft  hoist- 


HAULAGE 


761 


ing,  where  sin  JV  =  sin  90°  =  1,  G=W  and  the  resistance  is  equal  to  the  total 
load. 

If  the  grade  is  expressed  in  feet  per  mile,  instead  of  degrees,  the  formula 
becomes, 

G=  PFXgrade  in  ft.  per  mi. X. 3788 

If  the  grade  is  expressed  as  a  per  cent,  instead  of  in  degrees,  the  formula 
becomes,  G=  WXper  cent,  of  grade.  This  last  relation  is  true  only  for  com- 
paratively flat  grades,  say,  those  not  exceeding  10%,  where  the  tangent  and 
sine  of  the  angle  of  inclination  are  practically  equal. 

GRADE  EQUIVALENTS 


Per  Cent. 

4 

Degrees 
Minutes 

Per  Cent. 

P; 

fs 
*+$ 

p. 

r/1             W 

1!    « 

$    * 

P    S 

Per  Cent. 

1 

£ 

is 

fefe 
c. 

Degrees 

Minutes 

.01 

.53 

0         .34 

2.80 

147.84 

1     36.23 

6.40 

337.92 

3     39.72 

.02 

1.07 

0         .69 

2.90 

153.12 

1     39.67 

6.50 

343.20 

3     43.14 

.03 

1.58 

0       1.03 

3.00 

158.40 

1     43.10 

6.60 

348.48 

3     46.56 

.04 

2.11 

0       1.37 

3.10 

163.68 

1     46.54 

6.70 

353.76 

3     49.99 

.05 

2.64 

0       1.72 

3.20 

168.96 

1     49.97 

6.80 

359.04 

3     53.41 

.06 

3.17 

0       2.06 

3.30 

174.24 

1     53.41 

6.90 

364.32 

3     56.83 

.07 

3.70 

0       2.41 

3.40 

179.52 

1     56.84 

7.00 

369.60 

4         .25 

.08 

4.22 

0       2.75 

3.50 

184.80 

2         .27 

7.10 

374.88 

4       3.67 

.09 

4.75 

0       3.09 

3.60 

190.08 

2       3.71 

7.20 

380.16 

4       7.09 

.10 

5.28 

0       3.44 

3.70 

195.36 

2       7.14 

7.30 

385.44 

4     10.51 

.20 

10.56 

0       6.88 

3.80 

200.64 

2     10.57 

7.40 

390.72 

4     13.93 

.30 

15.84 

0     10.32 

3.90 

205.92 

2     14.01 

7.50 

396.00 

4     17.35 

.40 

21.12 

0     13.75 

4.00 

211.20 

2     17.44 

7.60 

401.28 

4     20.77 

.50 

26.40 

0     17.19 

4.10 

216.48 

2     20.87 

7.70 

406.56 

4     24.19 

.60 

31.68 

0     20.63 

4.20 

221.76 

2     24.30 

7.80 

411.84 

4     27.60 

.70 

36.96 

0     24.07 

4.30 

227.04 

2     27.73 

7.90 

417.12 

4     31.02 

.80 

42.24 

0     27.50 

4.40 

232.32 

2     31.16 

8.00 

422.40 

4     34.44 

.90 

47.52 

0     30.94 

4.50 

237.60 

2     34.60 

8.10 

427.68 

4     37.85 

1.00 

52.80 

0     34.38 

4.60 

242.88 

2     38.03 

8.20 

432.96 

4     41.27 

1.10 

58.08 

0     37.81 

4.70 

248.16 

2     41.45 

8.30 

438.24 

4     44.68 

1.20 

63.36 

0     41.25 

4.80 

253.44 

2     44.89 

8.40 

443.52 

4     48.09 

1.30 

68.64 

0     44.69 

4.90 

258.72 

2     48.32 

8.50 

448.80 

4     51.51 

1.40 

73.92 

0     48.13 

5.00 

264.00 

2     51.75 

8.60 

454.08 

4     54.92 

1.50 

79.20 

0     51.56 

5.10 

269.28 

2     55.18 

8.70 

459.36 

4     58.33 

1.60 

84.48 

0     55.00 

5.20 

274.56 

2     58.60 

8.80 

464.64 

5       1.75 

1.70 

89.76 

0     58.43 

5.30 

279.84 

3       2.03 

8.90 

469.92 

5       5.16 

1.80 

95.04 

1.88 

5.40 

285.12 

3       5.46 

9.00 

475.20 

5       8.57 

1.90 

100.32 

5.31 

5.50 

290.40 

3       8.89 

9.10 

480.48 

5     11.98 

2.00 

105.60 

8.75 

5.60 

295.68 

3     12.32 

9.20 

485.76 

5     15.39 

2.10 

110.88 

12.18 

5.70 

300.96 

3     15.74 

9.30 

491.04 

5     18.80 

2.20 

116.16 

15.62 

5.80 

306.24 

3     19.17 

9.40 

496.32 

5     22.20 

2.30 

121.44 

19.06 

5.90 

311.52 

3     23.59 

9.50 

501.60 

5     25.61 

2.40 

126.72 

22.49 

6.00 

316.80 

3     26.02 

9.60 

506.88 

5     29.02 

2.50 

132.00 

25.93 

6.10 

322.08 

3     29.45 

9.70 

512.16 

5     32.42 

2.60 

137.28 

1     29.36 

6.20 

327.36 

3     32.87 

9.80 

517.44 

5     35.83 

2.70 

142.56 

1     32.80 

6.30 

332.64 

3     36.29 

9.90 

522.72 

5     39.23 

10.00 

528.00 

5     42.64 

EXAMPLE. — (a)  What  is  the  resistance  opposing  motion  when  a  trip  of  cars 
weighing  10,000  Ib.  is  moved  upwards  on  a  plane  pitching  8°.  (b)  If  the 
speed  of  the  trip  is  10  mi.  per  hr.,  what  is  the  horsepower  required  to  produce 
this  motion  when  the  coefficient  of  friction  /  is  .025? 

SOLUTION. — (a)  As  the  trip  is  moving  on  a  straight  track  at  a  uniform 
speed,  A  and  C  are  both  equal  to  zero,  and  R  =  F-\-G.  Substituting  for  F, 
and  G  their  values, 

R=fW  cosX+Wsin  X  =  (.025X10,OOOX.99027)  +  (10,OOOX.  13917) 
=  247.57+1,391.70  =  1,639.27  Ib. 


762  HAULAGE 

(b)  A  speed  of  10  mi.  per  hr.  =  (10X5,280)%-  3,600  =  14.7  ft.  per  sec. 
Whence  the  foot-pounds  of  work  in  1  sec.  =  1,639.27X14.7  =  24,097.27.  But 
1  H.  P.  =  550  ft.-lb.  of  work  in  1  sec.,  hence  to  move  the  trip  up  the  grade  at 
a  uniform  speed  of  10  mi.  per  hr.  will  require  the  expenditure  of  24,097.27 
-4-550  =  43.8  H.  P. 

Resistance  Due  to  Inertia.  —  The  resistance  due  to  the  inertia  of  the  trip  is 
frequently  called  the  starting  resistance  because  it  exists  only  during  the 
period  of  acceleration  and  ceases  as  soon  as  the  car  is  moving  at  a  uniform 
speed.  The  force  necessary  to  overcome  this  resistance  is  not  uncommonly 
called  the  acceleration,  although  the  word  acceleration  properly  means  the 
gain  in  the  velocity  of  the  body  in  feet  per  second  per  second  under  the  influence 
of  a  constant  force.  During  the  time  of  its  existence  and  application,  the 
accelerating  force,  in  haulage  problems,  may  be  considered  as  constant  and  is 
the  same  in  value  whether  the  load  is  moved  horizontally,  on  an  inclined  track, 
or  vertically. 

The  force  7,  in  pounds,  that  constantly  applied  to  a  body  will  give  it  a 
specified  velocity  uniformly  accelerated  from  rest  at  the  end  of  a  specified 
number  of  seconds,  may  be  found  from  the  formula, 
,      ,.       W       Wv     Wv* 
I  =  M  a  =  —  a  =  —  -  =  -  --- 
•  g          gt       g2s 
W 
in  which  M=  —  =  mass  of  body,  and  the  other  symbols  have  the  meaning 

given  them  under  Calculations  f9r  First-Motion  Hoisting  Engines. 

EXAMPLE.  —  (a)  Neglecting  friction,  what  force  is  required  to  bring  a  loaded 
mine  car  weighing  5,000  Ib.  from  rest  to  a  uniform  speed  of  8  mi.  per  hr.  at 
the  end  of  10  sec.?  (b)  What  will  be  the  maximum  work  per  second  and  maxi- 
mum horsepower  during  acceleration? 

SOLUTION.—  (a)  Here  TF=5,000  Ib.;  *  =  10  sec.;  »  =  (5,280  X  8)  -J-  3,  600 
=  12  f  t.  per  sec.  ;  a  =  12  -j-  10  =  1  .2  f  t.  per  sec.  per  sec.  Substituting, 

,,^  =  |2fxi.2-lS6«,,  about 

(b)  Because  the  speed  during  acceleration  increases  from  0  to  12  ft.  per 
sec.,  the  maximum  work  is  done  during  the  last  second,  and  is  186X12  =  2,232 
ft.-lb.  From  this,  the  maximum  horsepower  is  2,232-5-550  =  4.06. 

It  is  to  be  noted  that  the  average  work  performed  and  the  average  horse- 
power required  to  perform  this  work  during  acceleration  are  one-half  of  the 
maximum  called  for  during  the  last  second. 

EXAMPLE.  —  (a)  What  is  the  total  resistance  to  be  overcome  in  bringing  a 
trip  of  10  loaded  mine  cars  weighing  5,000  Ib.  each,  from  rest  to  a  speed  of 
8  mi.  per  hr.  at  the  end  of  10  sec.;  the  slope  is  8°,  and  the  track  is  laid  in  a 
10°  curve?  (b)  What  is  the  maximum  work  and-  what  is  the  maximum  horse- 
power required  to  do  the  work  during  acceleration? 

SOLUTION.  —  (a)  The  resistance  to  be  overcome  is  equal  to  the  sum  of  the 
individual  resistances  and  is, 

W?|2  W 

R  =  F+C+G+I=fW  cos  X+  ^-+W  sin  X+-~a 

In  the  problem,  it  may  be  assumed  that/=.02;  1^=5,000X10  =  50,000  Ib.; 
X  =  8°;  g  =  32.2  ft.  per  sec.  per  sec.;  v=  (5,280  X  8)  H-  3,600  =  12  ft.  per  sec.; 
r  =  radius  of  an  8°  curve  =  717  ft.,  about;  c  =  12-f-  10  =  1.2  ft.  per  sec.  per  sec. 
Substituting  in  the  foregoing  formula; 


R  =  (.02  X  50,000  X  .99027)  +  (^~  X  ~)  +  (50,000  X  .13917)  +  (x  1  .2) 

=  990+312  +  6,958  +  1,863  =  10,123  Ib. 

(6)  The  maximum  work  is  at  the  end  of  the  last  second  of  acceleration 
when  the  trip  has  acquired  its  full  speed  and  is  10,123X12=121,476  ft.-lb. 
As  this  work  is  performed  in  1  sec.,  the  horsepower  is  121,476-5-550  =  221,  about. 


TRACKWORK* 

Choice  of  Grade. — The  grade  of  entries  is  rarely  a  matter  of  choice,  but  is 
determined  by  natural  causes,  particularly  by  the  dip  of  the  seam,  the  location 
of  the  main  haulage  road  with  respect  to  the  property  lines,  by  the  direction 
and  strength  of  the  cleavage  planes  of  the  coal,  etc. 

*  See  further  under  Railroad  Surveying. 


HAULAGE  763 

Where  possible  the  entries  should  be  given  a  rising  grade  of  from  6  in. 
to  1  ft.  per  100  ft.  to  insure  good  drainage,  as  the  flow  in  the  ditches  will  be 
more  or  less  impeded  by  material  falling  from  overloaded  cars,  with  road  dirt, 
etc.  At  shaft  and  slope  bottoms,  unless  the  cars  are  fed  along  by  a  chain  haul 
or  some  similar  device,  it  is  customary  to  give  both  the  loaded  and  empty 
tracks  a  favoring  grade  of  about  1.25%,  even  if  the  roof  and  floor  have  to  be 
shot  to  do  this. 

Where  capital  is  available,  main  haulage  roads,  which  must  last  the  life  of 
the  property  and  along  all  or  most  of  the  length  of  which  all  the  coal  must 
be  moved,  are  graded  with  Almost  the  same  care  as  first-class  surface  railroads. 
More  economical  haulage  is  obtained  where  the  grade  is  all  in  one  direction, 
and  not  alternately  up  and  down  hill,  because  of  the  excessive  power  temporarily 
required  to  overcome  the  inertia  and  to  bring  the  trip  up  to  speed  in  pulling 
out  of  swamps.  A  motor  will  deliver  to  the  drift  mouth  no  more  coal  than  it 
can  pull  over  the  sharpest  grade,  and  for  this  reason  it  is  not  unusual  to  see  the 
output  of  a  motor  reduced  to  50%  of  what  it  would  be  were  a  little  money  spent 
in  making  the  grades  uniform. 

Curvature. — Curves  on  mine  tracks  are  generally  designated  by  the  length 
of  their  radius  rather  than  by  their  degree  of  curvature,  as  is  customary  on 
surface-railroad  work.  In  fact,  a  curve  of  50  ft.  radius  is  the  sharpest  that 

Kf\ 

can  be  defined  in  terms  of  its  deflection  angle,  because  for  it  sin  §D=    -  =  1, 

K 

and  D=180°. 

It  is  well  to  make  all  curves  of  as  long  radius  as  possible.  Room  turnouts 
are  commonly  given  a  radius  of  25  to  35  ft. ;  turnouts  from  main-haulage  roads 
to  cross-  or  butt-entries,  a  radius  of  60  to  100  ft.;  and  where  a  curve  is  necessary 
on  a  main-haulage  road,  its  radius  should  be  as  great  as  possible,  say,  150  to 
200  ft.,  or  more,  in  order  to  permit  of  high-speed  traffic. 

Rails  on  curves  should  not  be  sprung  into  place  and  then  spiked,  but  should 
be  bent  to  the  required  radius  with  a  rail  bender,  or  jim-crow,  as  explained 
under  Railroad  Surveying.  The.  marked  difference  in  length  between  the 
outer  and  inner  rails  on  sharp  mine  curves  may  be  found  from  the  following 
rule: 

Rule. — Multiply  the  gauge  of  the  track  by  the  length  of  the  curve  and  divide 
the  product  by  the  radius,  all  dimensions  being  given  in  feet. 

EXAMPLE. — What  is  the  difference  in  length  between  the  outer  and  inner 
rails  on  a  curve  of  50  ft.  radius  and  100  ft.  long,  when  the  gauge  is  3  ft.  6  in.? 

SOLUTION. — As  3  ft.  6  in.  =  3.5  ft.,  the  difference  in  length  between  the 
outer  and  inner  rails  will  be  (3.5  X  100)  -J- 50  =  7  ft.  0  in. 

With  fixed  axles  and  on  a  sharp  curve,  the  running  gear  of  a  car  or  loco- 
motive binds  as  the  front  wheel  presses  against  the  outside  rail  and  the  rear 
wheel  against  the  inside  rail.  To  overcome  this,  the  difference  in  gauge  between 
the  car  and  the  track  is  increased  on  curves.  The  amount  of  this  increase 
depends  on  the  gauge  of  the  track,  the  wheel  base  of  the  car,  and  the  radius 
of  the  curve,  the  maximum  being  limited,  of  course,  by  the  tread  of  the 
wheels.  Experiments  have  shown  that,  with  a  narrow-gauge  track  having 
sharp  curves  over  which  locomotives  and  cars  with  short  wheel  bases  pass,  a 
good  rule  is  to  widen  the  gauge  of  the  track  ff  in.  for  each  2|°  of  curvature,  that 
is,  on  a  40°  curve  the  track  gauge  should  be  increased  1  in.  On  the  very  sharp 
curves  frequently  necessary  in  mines,  the  gauge  should  be  widened  as  much 
as  the  wheel  tread  will  allow,  and  in  some  cases  it  is  well  to  lay  guard-rails 
on  the  curves  inside  the  rails,  so  that  if  one  wheel  mounts  the  track  the  other 
will  not  follow,  but  will  pull  it  back  on  to  the  track. 

In  motor  haulage,  in  passing  around  curves  the  centrifugal  force  crowds 
the  outer  wheel  against  the  rails  and  tends  to  overturn  the  cars.  To  counter- 
act this  tendency,  the  outer  rail  is  elevated  by  an  amount  proportionate  to  the 
speed  of  the  trip  and  the  sharpness  of  the  curve. 

In  rope  haulage,  as  the  pull  of  the  rope  on  curves  tends  to  overturn  the 
cars  inwards,  the  inner  instead  of  the  outer  rail  is  elevated. 

On  a  slope  haulage,  however,  operated  by  a  single  rope,  when  the  weight 
of  the  cars  traveling  on  the  slope  is  sufficient  to  draw  the  rope  off  the  hoisting 
drum,  the  rails  on  curves  should  be  elevated  on  the  outside,  as  the  centrifugal 
force  only  acts  on  the  cars  being  lowered;  the  elevation  in  such  a  case  should, 
however,  be  moderate,  so  as  not  to  interfere  with  the  trip  when  being  drawn 
out  by  the  rope,  when,  of  course,  the  tendency  is  to  tip  the  cars  inwards.  The 
table  on  page  764  gives  the  elevation  of  rail  for  different  degrees  of  curvature 
and  for  a  42-in.  track,  assuming  a  speed  of  10  to  15  mi.  per  hr. 


764 


HAULAGE 
RAIL  ELEVATION 


Degree 
of  Curve 

Radius 
of  Curve 
Feet 

Elevation 
of  Outer 
Rail 
Inch 

Degree 
of  Curve 

Radius 
of  Curve 
Feet 

Elevation 
of  Outer 
Rail 
Inches 

1 

5,729.6 

, 

10.0 

573.7 

H 

2 

2,864.9 

j 

12.0 

478.3 

1  A 

3 

1,910.1 

JL 

15.0 

383.1 

if 

4 

1,432.7 

A 

18.0 

319.6 

1H 

5 

1,146.3 

A 

20.0 

287.9 

2-fg 

6 

955.4 

if 

60.0 

100.0 

4 

7 

819.0 

I? 

112.9 

60.0 

M 

8 

716.8 

j 

180.0 

50.0 

4f 

9 

637.3 

i 

It  is  not  generally  advisable  to  elevate  the  rail,  more  than  4$  in.,  as  it  is 
not  good  practice  to  attempt  to  run  trips  around  sharp  curves  at  a  high  speed. 

The  rule  for  standard-gauge  roads  (4  ft.  8$  in.  or  56$  in.)  on  surface  and 
for  speeds  of  25  to  35  mi.  per  hr.  is  to  elevate  the  outer  rail  £  in.  for  each 
degree  of  curvature.  An  approximate  rule  often  given  for  narrower  gauges 

TABLE  OF  RAILS 

(Carnegie  Steel 


«o 

s 

& 

For  One  Joint 

For  1,000  T.  of  Rail 

_- 

;> 

pq 

fel 

8 

i 

o 

V 

1 

5 

Is 

|| 

•si 

4, 

Number 

g 

2 

sj 

°f 

I 

"o   " 

o«1 

1?! 

'SJu  -o 

5 

•a 

.5? 

OM 

s  *"* 
CO 

S5!  ° 

*  ^ 

"3  !  <2 

?« 

!i 

1 

1 

1 

•3 

"o 

J 

'S'o 

p 

1° 

S 

51 

I? 

« 

* 

^ 

CO 

110 

6 

t 

34 

X4 

5i 

X- 

v 

99.50 

5.60 

105.10 

1,892 

11,350 

61,760 

100 

5- 

34 

X4 

5. 

X 

4 

87.00 

5.36 

92.36 

2,075 

12,450 

67.710 

95 

5- 

iff 

34 

X4 

5^ 

X 

Sg. 

80.80 

2 

5.36 

86.16 

2,184 

13,100 

71,270 

90 
85 

5 
6] 

j 

34 
34 

X4 
X4 

5^ 
5. 

x- 

4 
\ 

74.00 
68.13 

<5 

« 

5.20 
5.20 

79.20 
73.33 

2,305 
2,441 

13,830 
14,640 

75.230 
79,660 

80 

5 

34 

X4 

si 

x 

I 

63.13 

0 

5.05 

68.18 

2,593 

15,560 

84,640 

75 

4-1 

i 

34 

X4 

5J 

X- 

4 

58.50 

4.96 

63.46 

2,766 

16,590 

90,270 

70 

4 

34 

X3 

Si 

X 

4 

54.64 

4.76 

59.40 

2,963 

17,780 

96,720 

65 

v 

24 

X3 

si 

X 

t. 

35.55 

3.18 

38.73 

3,192 

12,770 

104,200 

60 

41 

. 

24 

X33 

5^ 

X 

4 

32.40 

3.12 

35.52 

3,458 

13,830 

112,900 

55 

v 

24 

X 

v 

28.90 

3.12 

32.02 

3,772 

15,090 

123,100 

50 

3' 

24 

X3- 

5i 

X 

4 

25.50 

3.00 

28.50 

4,149 

16,600 

135,400 

45 
40 

3i 

3- 

1 

20 
20 

X3* 
X3 

si 

5 

x^ 

•• 

18.75 
16.10 

2.90 
2.90 

21.65 
19.00 

5,148 
5,790 

20,590 
23,160 

150,500 
169,300 

35 

3i 

5 

X2 

4^ 

12.10 

^2 

1.74 

13.84 

6,618 

26,470 

193,500 

30 

3 

16 

X2 

4 

X- 

10.45 

"3 

1.74 

12.19 

7,722 

30,890 

225,700 

25 
20 

2- 

2 

16: 
16 

X2 
X2 

4 
3^ 

X 

5.70 
4.86 

PQ 

.97 
.91 

6.67 
5.77 

9,264 
11,580 

37,060  270,800 
46.330  338,500 

16 

2 

16 

3 

4.36 

.865 

5.225 

14,480 

57,920  423,200 

14 

2] 

V 

16 

Xl^ 

3 

3.44 

.865 

4.305 

16,540 

66,180 

483,600 

12 

2 

16 

3 

X 

3.44 

.865 

4.305 

19,300 

77,200 

564,100 

10 
8 

I 

16: 

Xli 
Xli 

II 

x, 
x, 

t 

2.60 
2.00 

.45 
.45 

3.05 
2.45 

23,170 
28,960 

92,680 
115,800 

677,300 
846,400 

HAULAGE 


765 


is  to  make  the  elevation  proportional  to  the  gauge  based  on  the  amount  given 
for  standard  gauge.  Thus,  for  a  36-in.  gauge,  the  elevation  would  be  about 
two-thirds  of  the  elevation  for  a  56£-in.  gauge  of  the  same  speed  and  curve. 

The  elevations  of  the  outer  rail  given  in  the  table  correspond  to  the  middle 
ordinates  of  the  respective  curves  for  a  chord  of  20  ft.  Hence,  a  common  rule 
to  determine  the  amount  of  the  elevation  of  the  outer  rail,  for  a  speed  of  15  mi. 
per  hr.  for  a  3-ft.  gauge,  is  to  measure  the  middle  ordinate  of  a  string  20  ft.  long, 
stretched  as  a  chord  on  the  gauge  line  of  the  outer  rail.  For  higher  or  lower 
speeds,  make  the  length  of  the  string  proportional  to  the  speed;  thus,  for  a 
speed  of  12  mi.  per  hr.,  use  a  16-ft.  string,  for  9  mi.  per  hr.,  a  12-ft.  string,  etc. 
Also  the  elevation  should  be  proportional  to  the  gauge;  thus,  for  a  30-in.  gauge, 
use  five-sixths  of  the  above  elevation,  etc. 

The  general  rule  is  to  begin  to  elevate  the  rail  a  short  distance  before  the 
curve  begins,  this  distance  depending  on  the  amount  of  elevation  required.  It 
is,  however,  not  always  practicable  to  do  this  in  mine  work. 

Gauge  of  Track. — The  gauge  of  track  selected  must  conform  to  local  con- 
ditions. The  thickness  of  the  seam  and  the  character  of  roof  and  floor  deter- 
mine in  a  general  way  the  size  of  the  haulage  roads,  and  consequently  of  the 
mine  cars  that  pass  through  them.  The  question  of  economical  haulage 
considers  a  minimum  number  of  cars  having  a  maximum  capacity.  As  the 
car  length  is  limited  by  the  necessarily  short  wheel  base  to  about  10  ft.,  and 
its  height  by  the  thickness  of  the  seam  and  limit  of  easy  hand  loading,  the 
remaining  dimension,  or  the  width  of  the  car,  is  usually  the  variable  factor. 
To  obtain  the  maximum  capacity  required,  the  width  of  the  car  must  be 
increased,  thereby  requiring  a  broader  gauge  for  stability.  A  broader  gauge 

AND  ACCESSORIES 

Company) 


For  1,000  T.  of  Rail 

For  1  Mi.  Single  Track 

Weight  in  Gross  Tons 

Number 

Weight,  in  Gross  Tons 

| 

c 

1 

Total 
Accessories 

Pair  of 
Splice  Bars 

I1 

1 

Splice  Bars 

J| 

u 

C/3 

Total 
Accessories 

'3 

Total 
Complete 

84.04 

4.80 

16.22 

105.06 

326 

1  ,956 

10,640 

14.48 

.83 

2.80 

18.11 

172.29 

190.40 

80.56 

5.03 

17.78 

103.37 

326 

1,956 

10,640 

12.66 

.79 

2.80 

16.25 

157.14 

173.39 

78.77 

5.29 

18.72 

102.78 

326 

1  ,956 

10,640 

11.76 

.79 

2.80 

15.35 

149.29 

164.64 

76.15 

5.39 

19.75 

101.29 

326 

1,956 

10.64U 

10.77 

.76 

2.80 

14.33 

141.43 

155.76 

74.26 

5.71 

20.94 

100.91 

326 

1,956 

10,640 

9.92 

.76 

2.80 

13.48 

133.57 

147.05 

72.15 

5.96 

22.23 

100.34 

326 

1  ,956 

10,640 

9.07 

.75 

2.80 

12.62 

125.71 

138.33 

72.28 

6.25 

23.70 

102.23 

326 

1,956 

10,640 

8.52 

.74 

2.80 

12.06 

117.86 

129.92 

72.36 

6.48 

25.40 

104.24 

326 

1  ,956 

10,640 

7.96 

.71 

2.80 

11.47 

110.00 

121.47 

50.63 

4.65 

27.36 

82.64 

326 

1,304 

10,640 

5.17 

.48 

2.80 

8.45 

102.12 

110.57 

49.95 

4.84 

29.63 

84.42 

326 

1,304 

10,640 

4.71 

.46 

2.80 

7.97 

94.29 

102.26 

48.60 

5.28 

32.33 

86.21 

326 

1  ,304 

10,640 

4.20 

.46 

2.80 

7.46 

86.43 

93.89 

47.22 

5.59 

35.56 

88.37 

326 

1,304 

10,640 

3.71 

.44 

2.80 

6:95 

78.57 

85.52 

42.99 

6.69 

39.51 

89.19 

364 

1,456 

10,640 

3.04 

.47 

2.79 

6.31 

70.71 

77.02 

41.68 

7,52 

30.83 

80.03 

364 

1,456 

10,640 

2.62 

.47 

1.94 

5.03 

62.86 

67.89 

35.84 

5.43 

32.29 

73.56 

364 

1,456 

10,640 

1.97 

.30 

1.78 

4.05 

55.00 

59.05 

36.06 

6.33 

33.60 

75.99 

364 

,456 

10,640 

1.70 

.30 

1.59 

3.59 

47.14 

50.73 

23.67 

4  10 

40.32 

68.09 

364 

,456 

10,640 

.93 

.16 

1.59 

2.68 

39.29 

41.97 

25.13 

4.96 

48.74 

78.83 

364 

,456 

10,640 

.79 

.16 

1.53 

2.48 

31.43 

33.91 

28.24 

576 

32.30 

66.30 

364 

,456 

10,640 

.71 

.15 

.81 

1.67 

25.14 

26.81 

25.45 

6.58 

34.82 

66.85 

364 

,456 

10,640 

.56 

.15 

.77 

1.48 

22.00 

23.48 

29.69 

767 

40.61 

77.97 

364 

,456 

10,640 

.56 

.15 

.77 

1.48 

18.86 

20.34 

26.73 
26.25 

4.65 
5.82 

27.50 
34.37 

58.88 
66.44 

364 
364 

,456 
1,456 

10,640 
10,640 

.42 
.33 

.07 
.07 

.43 
.43 

.92 

.83 

15.71 
12.57 

16.63 
13.40 

766 


HAULAGE 


reduces  wear  and  tear  on  tracks  and  rolling  stock,  and  requires  outside  wheels, 
which  are  cheap,  easy  to  lubricate,  and  easy  to  replace.  Cars  with  a  relatively 
narrow  gauge  run  more  easily  around  sharp  curves,  and  they  are  generally 
made  with  inside  wheels.  With  wheels  inside  the  frame,  the  capacity  of 
narrow-gauge  cars  may  be  made  to  almost  equal  that  of  cars  of  broader  gauge, 
but  they  lack  the  stability  of  the  latter.  With  narrow  gauges,  shorter  ties 
can  be  used,  reducing  the  amount  of  cutting  in  the  bottom  of  a  thin  inclined 
seam,  and  leaving  more  room  available  for  ditching  and  for  gob  room,  but 
with  a  very  narrow  gauge  too  little  room  is  given  for  the  mules  to  tread,  and 
they  frequently  slip  on  the  rails  or  inclines  and  at  curves. 

The  most  common  track  gauges  in  coal  mines  are  30,  36,  42,  and  48  in.,  but 
these  are  not  absolute,  as  smaller  and  larger  gauges  are  often  employed.  Gauges 
less  than  26  in.  make  the  cars  top  heavy  and  gauges  more  than  48  in.  require 
large  curves  and  extra  wide  haulage  ways,  room  necks,  etc. 

In  proportioning  the  gauge  of  a  track  to  a  given  width  of  entry,  provision 
should  be  made,  if  possible,  to  allow  for  a  passageway  between  the  car  and 
the  ribs,  or  at  least  between  the  car  and  one  rib,  so  that  a  man  and  a  mule 
can  pass  between  the  car  and  the  rib. 

Rails. — The  size,  that  is,  the  weight  per  yard,  of  rails  to  be  used  depends 
on  the  nature  of  the  traffic.  Nothing  is  gained  by  having  rails  of  too  light  a 
section.  If  the  mine  water  is  acid,  light  rails  are  soon  eaten  through,  and  in 
any  case  they  are  apt  to  spring  and  cause  wrecks,  the  cost  of  cleaning  up  which 
will  soon  pay  for  the  difference  in  cost  of  the  heavier  rails. 

Main  haulage  roads,  particularly  where  heavy  motor  or  high-speed  rope 
haulage  is  used,  are  very  commonly  laid  with  rails  weighing  50  to  60  Ib.  per  yd. 

TABLE  OF  RAILS 

(Carnegie  Steel 


ij 

For  One  Joint 

For  1,000 
Tonnes  of  Rail 

Is 

t)  g 

C  -JH 

« 

8  g 

|i 

I  to 

•3j 

£43 

Number 

ll 

*O    M 

il 

li 

•Sj 

CO  ^ 

V 

|1  S 

2   rn    rd 

Is  g 

v  u    § 

*!l 

:|i 

!« 

1 

13 

'53  0 

i 

ll 

«  p, 

.,s  £j 

oO  £j 

I1 

a 

"o 

Cfl 

54.56 

155.60 

864 

19.0X121 

140X14.3 

45.13 

2.54 

47.67 

1,854 

11,124 

49.60 

146.00 

864 

19.0X114 

140X14.3 

39.46 

2.43 

41.89 

2,040 

12,240 

47.12 

141.30 

864 

19.0X114 

140X14.3 

36.65 

jn 

2.43 

39.08 

2,146 

12,876 

44.64 

136.50 

864 

19.0X108 

140X14.3 

33.57 

"3 

2.35 

35.92 

2,270 

13,620 

42.16 

131.80 

864 

19.0X108 

140X14.3 

30.90 

pq 

2.35 

33.25 

2,400 

14.400 

39.68 

127.00 

864 

19.0X105 

140X14.3 

28.63 

CO 

2.29 

30.92 

2,550 

15,300 

37.20 

122.20 

864 

19.0X102 

140X14.3 

26.54 

2.25 

28.79 

2,718 

16,308 

34.72 

117.50 

864 

19.0X95.2 

140X14.3 

24.78 

2.16 

26.94 

2,916 

17,496 

32.24 

112.70 

610 

19.0X95.2 

140X14.3 

16.10 

.44 

17.54 

3,140 

12,560 

29.76 

107.90 

610 

19.0X88.9 

140X14.3 

14.70 

.42 

16.12 

3,410 

13,640 

27.28 

103.20 

610 

19.0X88.9 

140X14.3 

13.10 

.42 

14.52 

3,710 

14,840 

24.80 

98.42 

610 

19.0X82.5 

140X14.3 

11.60 

.36 

12.96 

4,080 

16,320 

22.32 

93.66 

508 

19.0X76.2 

140X14.3 

8.50 

.32 

9.82 

8,960 

35,840 

19.84 

88.89 

508 

19.0X76.2 

127X12.7 

7.30 

.32 

8.62 

10,080 

40,320 

17.36 

84.13 

410 

15.9X63.5 

114.3X12.7 

5.50 

£ 

.79 

6.29 

11,520 

46,080 

14.88 

79.37 

410 

15.9X63.5 

101.6X12.7 

4.74 

"8 

.79 

5.53 

13.440 

53,760 

12.40 

69.85 

410 

12.7X57.1 

101.6X12.7 

2.58 

PQ 

.45 

3.03 

16,140 

64,560 

9.92 

66.67 

410 

12.7X50.8 

88.9X12.7 

2.20 

•<* 

.41 

2.61 

20,160 

80,640 

7.94 

60.32 

410 

12.7X44.4 

88.9  X   9.5 

1.98 

.39 

2.37 

25,200 

100,800 

6.94 

52.38 

410 

12.7X44.4 

76.2X   9.5 

1.56 

.39 

1.95 

28,820 

115,280 

5.95 

50.80 

410 

12.7X44.4 

76.2X   9.5 

1.56 

.39 

1.95 

33,620 

134,480 

4.96 

44.45 

410 

9.5X38.1 

63.5X   7.9 

1.18 

.20 

1.38 

40,320 

161,280 

3.97 

39.68 

410 

9.5X38.1 

63.5  X   7.9 

.91 

.20 

1.11 

50,380 

201,520 

HAULAGE 


767 


In  motor  haulage,  it  is  recommended  that  the  rails  used  weigh  not  less  than 
10  Ib.  per  yd.  for  each  ton  in  weight  coming  on  a  single  driver.  Thus,  a  20-T., 
four-wheeled  motor  will  have  5  T.  on  each  wheel  and  will  require  a  50- Ib. 
rail,  which  is  light  enough. 

Side,  cross,  butt,  or  room  entries,  are  commonly  laid  with  30-  or  35-lb.  rail, 
as  the  motors  used  for  gathering  are  light  and  their  speed  low. 

In  rooms,  16-,  20-,  and  25-lb.  rails  are  used,  depending  on  the  weight  of  the 
loaded  mine  car  and  whether  the  gathering  motor  does  or  does  not  enter  the 
rooms.  Wooden  rails,  from  16  to  20  ft.  in  length  and  3  in.X4  in.  or  4  in.XS  in., 
in  section,  and  nailed  to  the  ties  with  wire  nails  were  formerly  much  used  but 
are  now  rarely  seen.  Room  tracks,  and  in  small  mines  the  cross-entries,  were 
not  infrequently  laid  with  light  wooden  rails  upon  which  were  nailed  strips  of 
strap  iron  about  f  in.XlJ  in.  in  section. 

Rule  I. — To  find  the  weight  of  rail,  in  long  tons  (2,240  Ib,),  required  to  lay 
1  mi.  of  single  track,  multiply  the  weight  of  the  rail,  in  pounds  per  yard,  by  ty,  or 
by  1.5714- 

Rule  II. — To  find  the  weight  of  rail,  in  long  tons  (2 #40  Ib.),  required  to  lay 
1 ,000  ft.  of  single  track,  multiply  the  weight  of  the  rail,  in  pounds  per  yard,  by 
.29761. 

Thus,  the  weight  of  70-lb.  steel  for  1  mi.  and  for  1,000  ft.  of  single  track  will 
be,  respectively,  70X-V-=HO  long  tons  and  70 X. 29761  =  20.833  long  tons. 
For  lengths  of  track  other  than  1,000  ft.,  multiply  the  quantity  required  for 
1,000  ft.  by  the  ratio  the  given  length  bears  to  1,000.  Thus,  for  the  materials 
required  for  600,  1,580,  and  4,000  ft.  of  track,  multiply  the  quantities  of  fish- 

AND  ACCESSORIES 

Company) 


For  1.000  Tonnes  of  Rail 

For  1  Kilometer,  Single  Track 

Num- 
ber 

Weight  in  Tonnes 

Number 

Weight  in  Tonnes 

§ 

-a 

j 

52 

*o  rt 

•fi 

i 

t) 

g 

| 

1 

PQ 

§  -2 

1 

*c3  o 

W3 

rt  g 

1 

'  PQ 

rt  g 

1 

13  o 

,3 

*c3  ~ 

I 

CO 

I* 

CO 

m 

*1 

pq 

°a 

CO 

| 
& 

r 

I 

O   w 

d 

*l 

61,100 

83.7 

4.7 

16.3 

104.7 

204 

1,224 

6,668 

9.21 

.52 

1.78 

11.51 

109.12 

120.63 

67,200 

80.5 

5.0 

17.9 

103.4 

204 

1,224 

6,668 

8.05 

.50 

1.78 

10.33 

99.20  109.53 

70,800 

78.7 

5.2 

18.8 

102.8 

204 

1,224 

6,668 

7.48 

.50 

1.78 

9.76 

94.24  104.00 

74,700 

76.2 

5.3 

19.9 

101.4 

204 

1,224 

6,668 

6.85 

.48 

1.78 

9.11 

89.28 

98.39 

79,100 

74.3 

5.6 

21.1 

101.0 

204 

1,224 

6,668 

6.30 

.48 

1.78 

8.56 

84.32 

92.88 

84,000 

73.0 

5.9 

22.4 

101.3 

204 

1,224 

6,668 

5.84 

.47 

1.78 

8.09 

79.36 

87.45 

89,600 

72.1 

6.1 

23.9 

102.1 

204 

1,224 

6,668 

5.41 

.46 

1.78 

7.65 

74.40 

82.05 

96,000 

72.3 

6.3 

25.6 

104.2 

204 

1,224 

6,668 

5.06 

.44 

1.78 

7.28 

69.44 

76.72 

103,400 

50.6 

4.5 

27.6 

82.7 

204 

816 

6,668 

3.28 

.29 

1.78 

5.35 

64.48 

69.83 

112,000 

50.1 

4.9 

29.9 

84.9 

204 

816 

6,668 

3.00 

.29 

1.78 

5.07 

59.52 

64.59 

122,200 

48.6 

5.3 

32.6 

86.5 

204 

816 

6,668 

2.67 

.29 

1.78 

4.74 

54.56 

59.30 

134.400 

47.3 

5.5 

35.9 

88.7 

204 

816 

6,668 

2.37 

.28 

.78 

4.43 

49.60 

54.03 

149,360 

76.2 

11.9 

40.0 

128.1 

400 

1,600 

6,668 

3.40 

.53 

.78 

5.91 

44.64 

50.36 

168,000 

73.6 

13.3 

32.6 

119.5 

400 

1,600 

6,668 

2.92 

.53 

.29 

4.74 

39.68 

44.42 

192,000 

63.4 

9.1 

34.2 

106.7 

400 

1,600 

6,668 

2.20 

.32 

.19 

3.71 

34.72 

38.43 

224,000 

63.7 

10.7 

36.3 

110.7 

400 

1,600 

6,668 

1.90 

.32 

.08 

3.30 

29.76 

33.06 

268.800 

41.7 

7.3 

43.6 

92.6 

400 

1,600 

6,668 

1.03 

.18 

1.08 

2.29 

24.80 

27.09 

336,000 

44.4 

8.3 

49.2 

101.9 

400 

1,600 

6,668 

.88 

.17 

.98 

2.03 

19.84 

21.87 

419,800 

49.9|   9.9  32.1 

91.9 

400 

1,600 

6,668 

.79 

.16 

.52 

1.47 

15.88 

17.35 

480,360 

45.0  11.3 

35.2 

91.5 

400 

1.600 

6,668 

.62 

.16 

.49 

1.27 

13.88 

15.15 

560,200 
672,000 

52.5  13.1 
47.6    8.1 

41.0 
27.1 

106.6 
82.8 

400  11,600 
400  1,600 

6,668 
6,668 

.62 
.47 

.16 
.08 

.49 
.27 

1.27 
.82 

11.90 
9.92 

13.17 
10.74 

839,600 

45.9 

10.1 

33.9 

89.9 

400 

1,600  6,668 

.36  .08 

.27 

.71 

7.94 

8.65 

768 


HAULAGE 


WEIGHT  OF  RAILS,  IN  TONS  OF  2,240  LB.,  REQUIRED  TO  LAY  1,000  FT. 
SINGLE  TRACK 


Weight  of 
Rail 

Tons  For 
1,000  Ft. 

Weight  of 
Rail 

Tons  For 
1,000  Ft. 

Weight  of 
Rail 

Tons  For 
1,000  Ft. 

per  Yard 

of  Track 

per  Yard 

of  Track 

per  Yard 

of  Track 

8 

2.381 

40 

11.905 

75 

23.321 

12 

3.571 

45 

13.393 

80 

23.809 

16 

4.762 

50 

14.881 

85 

25.298 

20 

5.952 

55 

16.369 

90 

26.786 

25 

7.441 

60 

17.858 

95 

28.274 

30 

8.929 

65 

19.346 

100 

29.761 

35 

10.417 

70 

20.833 

110 

32.737 

plates,  bolts,  and  spikes  as  well  as  rails,  required  for  1,000  ft.  by  .600,  1.58, 
and  by  4,  respectively. 

It  will  be  noted  that  each  increase  of  5  Ib.  per  yd.  in  the  weight  of  the  rail, 
increases  by  1.488  (1.5,  nearly)  T.,  the  quantity  required  to  lay  1,000  ft. 
of  track. 

The  two  following  tables  give  the  gross  tons,  of  2,240  Ib.,  required  for  1  mi., 
and  the  metric  tonnes,  or  2,204  Ib.  (about)  required  for  1  km.  of  single  track, 
as  well  as  the  necessary  fish-plates  (splice-bars),  bolts,  nuts,  and  ties.  It  should 
be  especially  noted  that  above  50  Ib.  per  yd.  rails  are  33  ft.  long,  the  length 
adopted  by  the  American  Railway  Association  in  1908,  the  American  Railway 
Engineering  and  Maintenance  of  Way  Association  in  1907,  the  American 
Society  of  Testing  Materials  in  1907,  and  the  American  Society  of  Civil  Engi- 
neer's in  1908.  The  first  table  is  based  on  90%  of  rails  to  be  33  ft.  long,  and 
10%  not  less  than  24  ft.  long,  varying  by  even  feet.  Ties  are  to  be  placed  to 
centers  or  2,640  ties  per  mile.  Rails  below  50  Ib.  per  yd.  are  furnished  30  ft. 
long,  and  10%  not  less  than  20  ft.  long.  No  excess  has  been  allowed.  The 
second  table  is  based  on  90%  of  rails  to  be  10  m.  long,  with  10%  varying  down 
to  8  m.  in  length.  Ties  are  to  be  spaced  600  mm.  to  centers  or  1,641  ties  per 
km.  Rails  below  24.80  km.  per  m.  are  furnished  5  m.  long.  No  excess  has 
been  allowed.  For  1,000  ft.  of  single  track,  there  will  be  required  sixty-eight 
30-ft  rails,  68  pairs  of  splice  bars,  272  bolts  when  four  are  used  per  joint,  or 
408  bolts  when  six  are  used  per  joint. 

Ties. — Main-entry  ties  should  have  at  least  a  5-  to  8-in.  face,  and  be  4  to 
6  in.  deep;  their  length  will  depend  on  the  gauge  of  the  track,  but  they  slwuld 
project  from  8  to  12  in.  on  each  side  of  the  rail  to  give  the  roadbed  stability 
and  the  ties  a  resting  surface  for  the  transmission  of  weight  to  the  roadbed. 
The  wood  of  main-track  ties  should  be  chestnut,  oak,  or  hard  pine.  Locust 
ties  are  very  serviceable,  but  it  is  not  probable  that  they  can  be  had  in  sufficient 
numbers  to  meet  the  demand.  In  case  these  woods  are  not  to  be  had,  other 
woods  will  naturally  take  their  place,  but  if  such  is  the  case  their  faces  should 
be  enlarged.  Sawed  ties  are  not  as  durable  as  hewed  ties  with  the  bark  removed. 

On  cross-entries  where  20-  to  30-lb.  rails  are  used,  the  ties  may  have  a  4-  to 
6-in,  face  and  be  4  to  5  in.  thick.  In  rooms,  the  ties  need  only  be  faced  3  or  4  in., 
or  sufficient  to  form  a  flat  surface  for  the  rail  to  rest  on. 

Steel  ties  for  mine  use  are  a  comparatively  recent  introduction.  In  some 
cases,  channel  or  even  I  beams  are  used  to  which  the  rails  are  bolted,  but  the 
common  form  of  steel  tie  consists  of  some  special  rolled  shape,  frequently 
corrugated,  provided  with  a  lug  under  which  the  outside  edge  of  the  base  of 
the  rail  fits.  The  rail  is  held  in  position  by  a  clip  that  presses  against  the 
inside  base.  In  order  to  prevent  slipping,  the  ties  have  small  projections, 
on  the  bottom,  that  cut  into  the  floor.  Owing  to  their  thinness,  steel  ties 
materially  reduce  the  amount  of  brushing  necessary  in  low  seams. 


HAULAGE 
SIZES  AND  QUANTITIES  OF  SPIKES* 


769 


Quantity 

Size 
Measured 
Under 
Head 
Inches 

Average 
Number 

oFloO  Lb. 

Weight  of 
Rail  per 
Yard 
Pounds 

Per  1,000  Ft. 

Per  Mile 

I 

Pounds 

Kegs 

Pounds 

Kegs 

2*Xf 

1,342 

300 

1 

1,575 

71 

8  to    16 

3   Xf 

1,240 

324 

1 

1.710 

8| 

16  to    20 

31X| 

1.190 

340 

1 

1,780 

9 

16  to    20 

4    XI 

1,000 

360 

Ij 

2.090 

10* 

16  to    25 

3JX& 

900 

445 

2J 

2,350 

11 

16  to    25 

4    X& 

720 

550 

2- 

2,910 

14f 

20  to    30 

4*XA 

680 

590 

3 

3,110 

15l 

20  to    30 

4    XI 

600 

670 

3> 

1 

3,520 

17f 

25  to    35 

4iXj 

530 

750 

3 

3,960 

20 

30  to    35 

5   X* 

450 

880 

4i 

4,660 

23  1 

35  to    40 

5   X& 

400 

980 

5 

5,170 

26 

40  to    55 

5JX£ 

375 

1,112 

Si 

5,870 

29| 

45  to  100 

NOTE. — In  ordering  spikes,  a  reasonable  allowance  should  be  made  for  waste 
For  ordinary  mine  tracks  with  two  spikes  to  the  tie,  divide  by  2  the  quantities 
given  in  the  table.  For  other  spacing  than  2  ft.,  proceed  as  follows:  For 
30  in.,  multiply  the  quantity  of  spikes  by  .80;  for  28  in.,  by  .858;  for  26  in.  by 
.893;  for  22  in.,  by  1.092;  for  20  in.,  by  1.20;  and  for  18  in.,  by  1.334. 

NUMBER  OF  TRACK  BOLTS  IN  A  KEG  OF  200  LB. 


Bolts 

Size  of  Nuts 

Bolts 

Bolts 

Size  of  Nuts 

Bolts 

Inches 

Inches 

in  Keg 

Inches 

Inches 

in  Keg 

X4i 

H 

square 

195 

X2* 

1    square 

654 

X4 

1 

square 

200 

X3* 

1  1  hexagonal 

170 

X3J 

11 

square 

208 

X3| 

If  hexagonal 

237 

11 

square 

216 

1*  hexagonal 

228 

X4 

1 

-  square 

305 

X4 

If  hexagonal 

220 

X3i 

1 

square 

329 

1X3* 

1    hexagonal 

415 

*X3* 

1    square 

576 

SPACES  BETWEEN  ENDS  OF  RAILS 


Temperature 
When  Laying 
Track 

Space  to  be 
Left  Between 
Ends  of  Rails 
Inch 

Temperature 
When  Laying 
Track 

Space  to  be 
Left  Between 
Ends  of  Rails 
Inch 

90°  above  zero 
70°  above  zero 
50°  above  zero 

! 

30°  above  zero 
10°  above  zero 
10°  below  zero 

1 

*  In  this  table  the  ties  are  placed  2  ft.  center  to  center  and  four  spikes  are 
placed  in  each  tie. 
49 


770  HAULAGE 

FEET,  BOARD   MEASURE,  IN   MINE  TIES   OF  VARIOUS   LENGTHS 


Length  of  Tie 

Size  of  Tie 

Inches 

4  Ft. 

5  Ft. 

5  Ft. 

6  Ft. 

6  Ft. 

7  Ft. 

7  Ft. 

8  Ft. 

6  In. 

OIn. 

6  In. 

OIn. 

6  In. 

OIn. 

6  In. 

OIn. 

3X  5 

5.6250 

6.2500 

6.8750 

7.5000 

8.1250 

8.7500 

9.3750 

10.0000 

4X  5 

7.5000 

8.3333 

9.1667 

10.0000 

10.8333 

11.6667 

12.5000 

13.8333 

5X  5 

9.3748 

10.4167 

11.4583 

12.5000 

13.5416 

14.5833 

15.6250 

16.6667 

4X  6 

9.0000  i  10.0000 

11.0000 

12.0000 

13.0000 

14.0000 

15.0000 

16.0000 

5X  6 

11.2500 

12.5000 

13.7500 

15.0000 

16.2500 

17.5000 

18.7500 

20.0000 

6X  6 

13.5000 

15.0000 

16.5000 

18.0000 

19.5000 

21.0000 

22.5000 

24.0000 

5X  7 

13.1250 

14.5833 

16.0418 

17.5000 

18.9583 

20.4167 

21.8750 

23.3333 

6X  7 

15.7500 

17.5000 

19.2500 

21.0000 

22.7500 

24.5000 

26.2500 

28.0000 

7X  7 

18.3748 

20.4167 

22.4582 

24.5000 

26.5416 

28.5833 

30.6250 

32.6667 

6X  8 

18.0000 

20.0000 

22.0000 

24.0000 

26.0000'28.0000 

30.0000 

32.0000 

7X  8 

21.0000 

23.3333 

25.6667 

28.0000 

30.3333!32.6667 

35.0000 

37.3333 

8X  8 

24.0000 

26.6667 

29.3333 

32.0000 

34.6667  37.3333 

40.0000 

42.6667 

7X  9 

23.6250 

26.2500 

28.8750 

31.5000 

34.1250  36.7500 

39.3750 

42.0000 

8X  9 

27.0000 

30.0000 

33.0000 

36.0000 

39.0000  42.0000 

45.0000 

48.0000 

9X  9 
8X10 

30.3750  33.7500  37.1250 
30.0000  33.3333  36.6667 

40.5000 
40.0000 

43.8750  47.2500 
43.3333!46.6667 

50.6250 
50.0000 

54.0000 
53.3333 

9X10 

33.7500 

37.5000 

41.2500 

45.0000 

48.750052.5000 

56.2500 

60.0000 

10X10 

37.5000 

41.6667 

45.8333 

50.0000 

54.1667 

58.3333 

62.5000 

66.6667 

NUMBER  OF  TIES  PER  1,000  FT.,  AND  PER  MILE  OF  TRACK 


Distance,  Center  to  Center,  in  Inches 


18 

20 

22 

24 

26 

28 

30 

1,000ft  

667 

600 

545 

500 

462 

429 

400 

1  mi  

3,520 

3  168 

2880 

2,640 

2,437 

2,267 

2,112 

EXAMPLE. — How  many  feet,  board  measure,  in  the  ties  required  to  lay 
1,500  ft.  of  track,  the  ties  being  6  ft.  6  in.  long,  5  in.X6  in.,  and  spaced  22  in. 

between  centers? 

SOLUTION. —  1,500 
ft.  =  1.5  thousands  of  feet. 
From  the  two  tie  tables,  1 .5 
X546X  16.25  =  13,308.75, 
-sayr  13,500  £t.  JB.  M. 

Entry  Switches.  — In 
large  mines,  the  switches 
connecting  the  main-road 
tracks  with  those  of  the 
cross-entries  are  of  the 
standard  surface  railroad 
type,  as  described  under 
the  heading  Railroad  Sur- 
veying. In  smaller  mines, 
the  layout  shown  in  Fig. 
1  is  commonly  employed. 
It  will  be  noted  that  what 
is  known  as  a  cast  frog 

pIG.  i  ^  is  used  and  that  the  latch 

rails  are  pivoted  or  bolted 


HAULAGE 


771 


FIG.  2 


and  so  are  not  sprung  into  place  as  on  surface  roads.     Owing  to  the  limited 

room  for  side  tracks  on  mine  roads,  the  lead  of  the  switches  is  commonly  much 

less  than  on  surface  roads  and  generally  consists  of  but  a  single  length  of  rail. 

Where  either  motor 

or  rope    haulage  is 

used,    the    lead    is 

greater  than  where 

the  hauling  is  done 

with  mules.    In  this 

latter    case,    the 

switch  rails  may  be    _  JJ |f[f|       flffl]       (l||j< 

any  length  up  to 
about  15  ft.,  de- 
pending on  the  lead. 
On  side  entries,  the 
length  of  the  switch 
points  is  frequently 
but  2  or  3  ft.,  when 
they  are  known  as 
latches.  These 
latches  may  con- 
sist of  a  piece  of 
bar  iron  tapered  to 
a  point  so  as  to  fit 
more  snugly  against  the  rail,  and  may  be  held  in  place  by  a  bolt  through  a 
hole  in  the  end. 

The  stub  switch  shown  in  Fig.  2  is  in  common  use  where  mule  haulage 
is  still  employed,  as  it  is  much  cheaper  than  the  standard  split  switch,  and 
answers  every  purpose  where  speeds  are  low.  The  rails  a  and  b  are  free  to 
swing  from  a  point  a  little  to  the  left  of  the  last  bridle,  and  their  points  slide 
on  flat  iron  plates  spiked  to  the  switch  tie,  which  is  broader  and  thicker  than 
the  other  ties.  The  frog  may  be  of  the  plate  or  cast  type,  or  may  be  made  by 
bending  the  rails  composing  the  switch  as  shown  in  the  figure. 

Frogs. — On  first-class  main  roads,  either  standard  types  of  surface  railroad 

frogs  or  plate 
frogs,  as  shown 
in  Fig.  3,  are 
employed.  The 
latter  consist  of 
rails  of  the  same 
section  as  those 
used  on  the  mine 
FlG.  3  track,  shaped 

as  shown  in  the 

cut,  and  riveted  to  a  heavy  iron  plate,  usually  i  in.  thick.  The  frog  rails 
are  fish-plated  and  bolted  to  the  track  rails,  and  the  plate  is  spiked  to  the  ties 
either  at  its  sides  or  through  holes  in  the  plate.  While  these  plate  frogs  may 
be  made  by  any  competent  blacksmith,  it  is  much  cheaper  to  buy  them. 

One  form  of  cast  frog  is  shown  in  Fig.  4  and  another  placed  in  a  turnout 
in  Fig.  1.  These  frogs  are  cast  in  one  piece  and  are  inexpensive,  but  can  only 
be  used  for  temporary  work,  as  they  soon  work  loose  from  the  tie  and  require 
constant  attention.  It  is  very  difficult  to  get  a  straight  workmanlike  connec- 
tion between  them  and  the  track  rails,  as  they  are  not  fish-plated  thereto. 
When  the  spikes  once  work  loose,  the  ties  must  be  shifted  to  bring  new  wood 
under  the  lugs,  as  the  spikes  will  not  hold  in  the  same  holes.  However,  cast 
frogs  are  largely 
used  on  room  entries 
where  mule  haulage 
is  employed.  The 
frog  shown  in  Fig. 
5  is  made  by  weld- 
_  ing  or  bolting  to- 

FlG-  4  gether  two  rail  ends  FIG.  5 

beveled  so  that  they  fit  properly.  An  oak  block  a  placed  in  the  frog  angle 
between  the  rails  helps  to  stiffen  it. 

Room  and  Branch  Switches. — In  mines  of  large  capacity  where  motor 
haulage  is  employed  on  the  cross-entries  and  gathering  is  done  with  motors, 
the  room  switches  are  laid  as  carefully  as  those  on  the  main  haulage  road, 


772 


HAULAGE 


with  plate  frogs,  points,  etc.  The  following  figures  show  various  forms  of  simple 
switches  often  used  where  the  cars  are  pushed  by  hand  or  hauled  by  mules,  but 
which  cannot  be  used  where  motor  haulage  is  employed. 

Fig.  6  shows  a  room  switch  with  a  cast-iron  frog  /  and  fixed  points  a  and  b. 
The  advantages  of  this  switch  are  fixed 
points  and  the  time  saved  when  bringing 
cars  from  the  rooms.  Unless  the  point  a  is 
in  line  with  the  main  track,  the  point  b  is 
liable  to  derail  the  car  or  cause  it  to  run  into 
the  switch.  This,  however,  can  usually  be 
avoided  by  making  the  rail  c  somewhat 
lower  than  the  rail  a,  thus  causing  the  car 
while  passing  to  cling  to  the  rail  c,  and 
readily  pass  between  the  point  b  and  the 
rail  c,  and  at  the  same  time  causing  the 
wheel  on  the  opposite  side  to  take  the  rail  a. 
Another  great  trouble  experienced  with  this 
kind  of  switch  is  that  where  the  wheels 


FIG.   6 


are  allowed  to  remain  on  the  cars  after  grooves  have  been  worn  in  their  treads, 
the  wheel  will  invariably  follow  the  rail  d.  The  point  b  should  be  higher 
than  the  rail  c,  so  that  the  tread  of  the  wheel  will  not  strike  the  rail  c  while 
the  car  is  leaving  the  switch.  The  rail  c  being  lower  than  the  rail  a,  it  is 
obvious  that  when  a  car  is  to  be  taken  into  the  switch,  the  driver  •will  have  to 
push  the  car  toward  the  rail  d,  so  that  the  wheel  will  take  the  rail  b  and  the 
flange  of  the  wheel  on  the  opposite  side  will  pass  between  the  point  a  and  the 
rail  d.  This  form  of  switch  is  not  applicable  in  the  case  of  mechanical  haul- 
age, because  it  does  not  give  an  unbroken  main  line,  which  is  essential  to  the 
Steady  movement  of  the  trip. 

-fill      (U      ill 


FIG.  7 


FIG.  8 


The  switch  shown  in  Fig.  7  has  loose  latches  b.  Instead  of  a  frog,  a  frog 
latch  c  is  used,  which  requires  the  lead  rail  a  to  be  raised  a  certain  height  above 
the  rail  of  the  main  track,  so  that  the  latch  c  can  be  thrown  across  this  rail. 
The  latch  c  is  held  in  position  at  one  end  by  a  strong  bolt,  and  at  the  other 
end  by  a  piece  of  iron  spiked  to  a  plank  underlying  the  frog,  as  shown.  By  the 
use  of  this  switch,  the  main  track  is  broken  only  at  the  point  of  switch. 

Fig.  8  shows  a  form  of  switch  giving  an  unbroken  main  track.  The  lead 
rail  of  this  switch  has  a  fixed  point;  a  frog  latch  c  is  used  similar  to  that  shown 
in  Fig.  7,  and  a  switch  latch  a  is 
used  on  the  follower  rail.  This 
latch  has  a  slight  projection  on  its 
under  side  to  prevent  its  slipping  off 
the  rail  of  the  main  track  when  in 
use.  This  form  of  latch  is  unde- 
sirable, since,  if,  by  the  negligence 
of  the  driver  the  latch  is  not  re- 
moved after  being  used,  it  will 
derail  cars  on  the  main  road,  since 

it  is  not  easily  pushed  aside  by  a  _       Q 

car  passing  out.  r  IG.  9 

Fig.  9  shows  a  rough  arrangement  where  a  turnout  or  any  other  condition 
requires  the  temporary  use  of  a  switch.  The  ordinary  form  for  narrow  gauges 
consists  of  a  movable  rail  a,  about  6  ft.  long,  pivoted  on  a  center  ft.  Where 
the  curve  is  not  great,  this  arrangement  acts  admirably  where  cars  are  pushed 
by  hand,  but  for  mule  or  locomotive  haulage  it  is  not  recommended.  The 
dotted  line  shows  the  position  of  the  rail  a  when  the  straight  road  is  in  use. 


HAULAGE 


773 


Fig.  10  shows  a  switch  for  permanent  tracks  in  coal  mines.  No  frog  or 
latch  is  required.  By  turning  the  lever  h,  the  throw  rod  o  moves  the  cranks  ikm, 
so  that  the  rails  r  will  face  the  rail  df,  the  rail  n  will  face  the  rail  b,  and  the 
rail  g  will  face  the  rail/.  The  lead  and  other  rails  can  be  reduced  to  any  required 
length  to  suit  circumstances.  When  the  lead  rail/d  is  from  12  to  16  ft.  long, 
and  the  other  lengths  are  in  proportion,  the  switch  gives  excellent  results.  It 
should  not  be  made  of  less  than  20-lb.  rail,  and  heavier  will  be  better.  The 
objection  to  this  switch  is  that  the  point  of  curve  comes  where  the  stub  ends 
of  the  rails  face  each  other  and  the  angle  formed  causes  the  car  to  lurch. 

Diamond  Switch.  —  What  is  called  a  diamond  switch  in  trackwork 
is  a  double  crossover,  such  as  is  shown  in  Fig.  11  (a),  (6),  and  (c).  The  laying 
out  of  a  diamond  switch  is  similar,  as  far  as  the  calculation  is  concerned,  to 
the  laying  out  of  a  turnout  switch.  A  simple  method,  and  one  that  is  often 
used  in  mine  work,  especially  where  track  room  is  limited,  is  as  a  follows: 

Through  a  central  point  a.  Fig.  11  (a),  midway  between  the  two  tracks, 
draw  two  straight  lines  at  right  angles  to  each  other,  each  making  an  angle 
of  45°  with  the  track  rails.  Extend  these  lines  until  each  intersects  lines  drawn 
through  the  points  of  switch  c\,  cz,  cs,  and  a  to  which  the  latches  come,  if  used, 
and  at  right  angles  to  the  track  rails  at  these  points.  These  intersecting  points 
are  the  centers  of  the  turnout  curves,  and  are  marked  d\,  dz,  dz,  and  d^,  respec- 
tively. Where  the  diagonal  lines  cross  the  inner  rails  of  the  two  tracks,  bi,  bz,  bz, 
and  &<  are  the  main-rail  frog  points. 

It  is  evident  that,  in  this  construction,  according  to  the  distance  between 
the  track  centers,  the  diamond-frog  points,  at  each  side  of  the  diamond,  will 
lie  between  the  two  tracks,  as  shown  in  (c),  or  they  will  be  coincident  with  the 
two  inner  rails  of  these  tracks,  as  shown  in  (b),  or  they  will  lie  within  the  track 
rails,  as  shown  in  (a). 
The  position  of  these 
frog  points  depends  on 
the  length  of  the  cross-  m 
ing  or  the  distance  be- 
tween the  opposite 
switch  points  measured 
on  the  main  rail,  as  com- 
pared with  the  distance 
between  the  track  cen- 
ters. 

Notes  on  Tracklay- 
ing.  —  As  explained  un- 
der the  heading  Survey- 
ing,  it  is  advisable  to 


pIG 


have  the  points  (sights,  sight  plugs,  strings,  etc.)  on  which  the  entries  are 
driven  set  such  a  distance  from  the  rib  that  they  come  over  one  of  the 
rails  and  may  thus  be  used  to  aline  the  track.  The  distance  the  points 
are  set  from  the  rib  depends  on  the  width  of  the  car  but  is  commonly  from 
2  ft.  to  3  ft.  By  keeping  one  rail  in  line  with  the  plugs,  the  ample  and  uniform 
clearance  demanded  by  the  laws  of  most  states  may  be  maintained  between  the 
side  of  the  car  and  the  other  rib. 

It  is  not  customary  to  lay  the  permanent  track  as  fast  as  the  entries  are 
driven.  Light  rails  spiked  to  widely  spaced  and  unballasted  ties  laid  on  the 
floor  are  used  at  first,  and  after  the  entry  has  advanced  three  or  four  rail 
lengths  (90  to  120  ft.)  the  permanent  track  is  laid. 

Before  the  ties  are  put  down,  the  roadbed  should  be  surfaced  and  brought 
to  grade.  While  this  is  not  always  done,  it  is  the  better  practice  except  where 
surfacing  material  must  be  brought  from  a  distance,  because  by  so  doing  the 
roadbed  will  be  firm  from  the  outset  and  will  not  require  attention  because 
of  subsequent  settling. 

After  the  ties  are  placed  at  about  the  proper  spacing,  the  rails  are  placed 
upon  them  and  fish-plated  together.  The  ends  of  the  ties  should  be  lined 
up  so  that  on  some  one  side  their  ends  project  a  uniform  distance,  say  8  or  10  in. 
from  the  rail.  A  preliminary  lining  up  is  given  by  the  sight  strings  and  before 
the  rails  are  laid  in  position,  but  the  final  lining  of  the  ends  of  the  ties  is  done 
by  measuring  with  a  foot  rule  as  the  rail  is  about  to  be  spiked  to  the  tie.  After 
the  rail  lengths  on  one  side  of  the  entry  are  spiked,  the  rails  for  the  other  side 
are  laid  in  place  and  fish-plated  together,  and  before  being  spiked  are  brought 
to  gauge. 

In  first-class  entry  work  the  track  is  ballasted  with  crushed  stone  as  in 
surface  railroad  practice  and  surfaced  with  finer  material  of  the  same  kind. 


774 


HAULAGE 


Neither  draw  slate  nor  bottom  rock  make  satisfactory  ballast,  particularly  if 
the  mine  is  wet,  as  they  soon  disintegratein  to  an  impervious  clay  that  holds 
water  and  becomes  soft  and  mushy,  a  condition  that  results  in  the  track  soon 
being  out  of  line  and  grade.  Under  no  circumstances  should  coal  or  bone 
be  used  for  ballast,  as  they  soon  are  ground  into  powder  and  furnish  an  excellent 
material  for  the  propagation  of  a  dust  explosion. 

In  side-entry  work,  where  the  track  is  not  ballasted  and  the  ties  are  laid 
upon  a  fireclay  floor  that  is  wet,  they  soon  sink  into  it,  and  if  animals  travel 
over  such  a  roadbed,  it  soon  becomes  muddy  and  affords  an  insecure  footing. 

Where  depressions  in 
the  floor  allow  water  to 
accumulate,  this  state 
of  affairs  is  particularly 
apt  to  occur,  so  that 
especial  attention 
should  be  paid  to  the 
ditching  in  order  to  drain 
off  the  water.  If  the 
water  comes  from  the 
roof  and  drips  on  the 
track,  the  soft  clay  must 
be  dug  out  and  ashes 
substituted.  The  ashes 
may  absorb  the  moisture 
and  dry  the  fireclay  to 
such  an  extent  as  to 
make  the  roadbed  ser- 
viceable, but  in  case 
they  do  not,  additional 
ties  should  be  put  in  so 
that  they  are  close  to- 
gether. If  it  is  neces- 
sary to  place  the  ties 
close  together  when  the 
road  is  first  laid,  only 
a  part  of  the  ties  are 
spiked  to  the  rails  un- 
til the  track  and  bed 
have  been  put  in  shape; 
then  the  rails  are  spiked 
fast  to  the  other  ties. 
This  forms  a  corduroy 
roadbed  and  will  afford 
a  fair  roadbed  and 
track,  although  it  may 
need  overhauling  from 
time  to  time  as  the  clay 
swells  up  and  mixes 
with  the  cinders. 

In  some  mines  that 
have  soft  clay  bottoms, 
it  is  the  custom  to  lay 
mudsills  of  3"X12" 
plank  parallel  with  the 
track  and  on  these  to 
place  the  cross-ties.  The 
planks  are  sometimes 
placed  skin  to  skin ;  the 
same  care,  however,  is 
necessary  in  this  as  in 
the  former  case  to  pro- 


FIG.  11  - 


vide  for  drainage  and  to  prevent  the  clay  oozing  up  between  the  planks. 
The  ordinary  spacing  of  ties  on  main  entries  is  from  18  in.  to  2  ft.,  measured 
between  the  centers  of  the  adjacent  ties.  In  speaking  of  the  spacing  of  ties, 
the  distance  between  the  edges  of  the  ties  is  sometimes  used  instead  of  the 
distance  between  centers.  Thus,  if  the  ties  have  an  8-in.  face  and  are  spaced 
2  ft.  from  edge  to  edge,  there  will  be  2|  ft.  between  the  centers,  which  is  too 
great  a  distance  for  a  roadbed  on  which  there  is  a  heavy  traffic. 


HAULAGE  775 

On  cross-entries  where  mule  haulage  is  employed,  a  distance  of  2 §  to  3  ft. 
between  centers  is  allowable  where  30-lb.  rails  are  used.  Ties  for  room  track 
have  a  3-  to  4-in.  face  and  sufficient  thickness  to  take  the  spike,  and  are  placed 
from  3  to  4  ft.  apart,  where  the  cars  are  pushed  by  hand,  but  where  motors 
enter  the  rooms  the  ties  must  be  spaced  as  in  entry  work,  but  ballasting  and 
grading  is  rarely  necessary. 

On  room  entries,  it  is  advisable  to  lay  the  room  switches  at  the  same  time 
the  permanent  track  is  put  down.  This  prevents  any  subsequent  interference 
with  traffic  and,  further,  the  work  can  be  done  much  better  when  the  track- 
layers are  not  stopped  by  passing  trips.  If  the  rooms  are  driven  on  points  set 
a  uniform  distance  apart  along  the  entry,  the  room  sight  plugs  may  be  used 
by  the  tracklayer  as  a  guide  in  placing  the  frogs.  In  many  mines  where  the 
rooms  are  evenly  spaced  and  a  standard  frog,  etc.  are  used,  the  entire  switch 
is  purchased,  all  the  lead,  follower,  switch,  and  point  rails  being  cut  to  an 
exact  length  and  properly  drilled  for  plating  and  bonding.  This  is  a  great 
help  toward  securing  a  first-class  track,  as  the  frog  at  No.  1  room  haying 
been  placed  exactly,  those  on  the  rooms  inside  must  of  necessity  come  right. 

Unless  the  pillars  are  to  be  drawn  as  soon  as  the  rooms  reach  their  limit,  it 
is  customary  to  take  up  the  room  tracks  and  in  some  cases  the  frogs  on  the 
entry,  relaying  them  when  pillar  drawing  is  about  to  begin.  Whether  this  is 
a  wise  policy  depends  on  circumstances.  In  wet  mines  where  the  rails  may  be 
eaten  by  acid  water,  or  where  the  roof  is  bad  and  the  track  is  apt  to  be  buried 
under  falls,  or  when  5  or  10  yr.,  or  more  may  elapse  before  pillar  drawing 
begins,  it  is  advisable  to  remove  the  rails  from  worked-up  rooms  and  to  use 
them  elsewhere.  But  where  the  mine  is  comparatively  dry,  the  roof  good,  and 
pillar  drawing  will  begin  in  a  year  or  two,  the  rails  had  better  be  left  in  place, 
as  the  cost  of  taking  up  and  relaying  them  will  more  than  offset  the  interest 
on  the  idle  capital. 

Rails  should  be  stacked  and  not  thrown  in  irregular  piles.  Three  heavy 
timbers  should  be  laid  upon  level  ground  in  such  a  way  that  they  support  the 
ends  and  centers  of  the  rails,  which  are  placed  side  by  side  upon  them.  When 
one  row  of  rails  is  filled,  additional  and  lighter  timbers  are  laid  upon  it,  and 
another  row  filled,  and  so  on,  untiUhe  stock  on  hand  is  neatly  piled,  each  length 
by  itself.  Ties-should  be  stacked  in  a  similar  way  to  props,  as  explained  under 
the  heading  Timbering.  Both  ties  and  rails  are  better  kept  outside  the  mine,  a 
day's  or  a  week's  supply  being  brought  in  at  intervals  as  needed. 


ANIMAL  HAULAGE 

Selection  of  Stock. — While  horses  and  ponies  are  generally  used  abroad 
for  mine  haulage,  mules  are  preferred  in  the  United  States,  as  being  hardier, 
less  nervous,  and  more  easily  broken  to  their  work.  Large  heavy  mules  with 
long  backs  and  relatively  short  legs  can  exert  their  strength  to  greater  advantage 
than  short-bodied  long-legged  ones,  although  this  is  not  always  admitted. 
Mere  weight  is  not  an  indication  of  strength,  as  it  may  be  due  to  fat,  but  a  good 
working  weight,  say  up  to  1,400  Ib.  without  clumsiness  or  thick  hocks,  is  to  be 
desired  in  a  mule.  Perhaps  the  best  mules  come  from  Missouri  and  Kentucky 
and,  for  mine  use,  have  an  average  weight  of  about  1,200  Ib.  and  a  height  of 
about  16  hands. 

Mules  from  4  to  6  yr.  of  age  that  have  been  worked  are  easier  to  break  to 
mine  work  than  those  without  training  of  any  kind.  Mules  are  naturally 
influenced  by  changes  of  water,  diet,  altitude,  etc.,  and  before  being  tried  in 
a  mine  should  be  given  ample  time  to  become  accustomed  to  their  new  condi- 
tions. If  this  was  always  done,  probably  a  much  smaller  number  would  be 
rejected  as  being  unsuited  to  mine  work,  for  a  mule  cannot  be  expected  to  work 
when  it  is  not  well. 

While  some  mules  give  absolutely  no  trouble  when  first  taken  into  the  mine 
and  will  pull  loads  from  the  outset,  the  average  mule  has  to  be  broken,  and  for 
this  purpose  should  be  handled  by  two  men,  the  driver  and  an  expert  in  manag- 
ing stock.  At  ffrst,  the  load  should  be  light,  the  trips  short,  and  the  mule 
not  worked  for  more  than  2  or  3  hr.  The  load,  length  of  trip,  and  number  of 
hours  worked  may  be  increased  daily.  When  properly  harnessed  and  cared 
for  and,  above  all,  kindly  treated,  the  average  mule  soon  learns  his  duties, 
will  back  up  to  the  trip  without  command,  and  will  follow  his  driver's  call 
or  whistle. 

Feeding  Mules. — Mr.  H.  W.  Hughes,  gives  the  average  daily  ration  at  an 
English  colliery  for  80  horses  averaging  15  hands  high,  the  figures  covering 


776  HAULAGE 

a  period  of  8  yr.,  as  follows:  Grain,  7.25  lb.:  bran,  9.25  lb.;  hay,  18.75  lb.; 
total,  35.25  lb.  The  grain  was  composed  of  beans,  3  lb.;  maize  (corn),  2.75  lb.; 
and  oats,  1.50  lb.  The  last  item  was  hay,  14  lb.;  clover,  1  lb.;  and  straw, 
3.25  lb. 

The  American  mule  appears  to  be  fed  about  two-thirds  as  much  as  the 
English  horse.  Mr.  Chas.  E.  Bowron,  gives  the  food  allowance  for  mules  at 
several  mines  in  Alabama  and  Tennessee,  the  first  figures  being  pounds  of  hay 
and  the  second,  pounds  of  grain:  9.54  and  17.44,  7.92  and  19.20,  7.94  and 
15.04,  and  12.62  and  15.50.  The  total  daily  food  allowance  in  these  cases  was 
26,98,  27.12,  22.98,  and  28.12  lb.,  respectively.  It  will  be  noticed  that  the 
weight  of  the  hay  was  about  one-half  that  of  the  grain,  reversing  the  usual 

§ractice.  Mr.  Bowron  further  gives  the  allowance  for  army  mules  during  the 
panish- American  war  as  hay  14  lb.  and  grain  9  lb.,  and  for  the  horses  hay 
14  lb.  and  grain  12  lb. 

In  the  anthracite  regions  of  Pennsylvania,  the  average  ration  for  mules 
from  1,000  to  1,200  lb.  in  weight  is  12  lb.  of  grain  and  15  lb.  of  hay.  The 
composition  of  the  grain  varies  from  two-thirds  cracked  corn  and  one-third 
oats,  to  equal  proportions  of  each.  Corn  is  richer  in  fat-producing  elements 
than  oats  and  is  fed  to  give  strength,  but  too  much  grain  will  cause  acute 
indigestion,  paralysis  of  the  walls  of  the  stomach,  and  usually  results  in  death. 
A  feed  of  bran  once  a  week  is  recommended  as  a  laxative:  also  a  handful  of  pure 
coarse  ground  salt  twice  a  week. 

Mules  should  be  fed  three  times  a  day,  although  some  large  companies  feed 
but  twice  daily.  On  idle  days,  the  food  allowance  may  be  reduced  25  to  30%. 
Hay  is  digested  chiefly  in  the  intestines  and  grain  in  the  stomach,  hence,  if 
possible,  a  mule  should  be  first  watered,  then  given  hay,  and  lastly  grain.  If 
the  water  is  given  last,  it  washes  the  food  into  the  intestines  before  it  is  acted 
on  by  the  gastric  juices  in  the  stomach.  If  the  hay  is  given  after  the  grain, 
it  carries  the  grain  with  it  into  the  intestines.  This  order  of  feeding  is  not 
always  practicable  in  a  mine  and  it  is  of  advantage  to  place  watering  troughs 
about  the  mine  so  that  the  mules  can  be  watered  during  the  day  while  at 
work.  As  the  feed  is  in  the  boxes  when  a  mule  is  put  in  the  stable  at  night, 
there  should  also  be  water  in  his  water  trough  so  that  he  can  drink  at  intervals 
while  feeding.  Fresh  food  should  never  be  placed  on  top  of  any  left  over  from 
the  previous  feeding.  A  mule  should  have  plenty  of  water  the  first  thing  in 
the  morning,  and  care  should  be  taken  to  have  the  water  pure  and  the  troughs 
clean. 

Care  of  Mules. — Mine  mules  should  have  clean  comfortable  quarters,  with 
pure  water  and  food.  Their  feet  and  legs  should  be  washed  every  night  and 
their  hocks  dried ;  and  they  should  be  combed  regularly.  Extreme  care  should 
be  taken  that  they  are  shod  properly,  and  a  competent  shoer  is  imperative  at 
mines  where  many  mules  are  used.  If  the  mine  is  too  small  to  warrant  the 
constant  employment  of  a  veterinarian,  arrangements  should  be  made  for  one 
to  visit  the  stables  monthly  to  look  over  the  stock,  paying  particular  attention 
to  their  feet. 

The  stable  boss  or  mine  foreman  should  inspect  the  harnessing  of  the 
mules  before  they  begin  work.  All  parts  of  the  harness  must  fit  properly, 
particularly  the  collar,  which  transmits  the  weight  to  the  mule's  shoulders;  the 
names,  to  which  the  traces  are  attached,  should  bear  evenly  upon  the  collar. 
The  traces  should  be  of  equal  length  and  free  from  knots:  many  insert  a  coiled 
spring  between  the  trace  and  the  car  to  take  up  the  jar  of  starting. 

Mules  should  not  be  worked  more  than  one  shift  per  day,  and  if  overtime 
is  necessary,  should  be  given  a  chance  to  rest  the  next  day.  If  stabled  under- 
ground, they  should,  unless  the  expense  is  prohibitory,  be  brought  to  the 
surface  from  the  close  of  work  Saturday  until  Monday  morning.  This  pro- 
cedure is  not  only  humane,  but  the  fresh  air  with  the  chance  to  run  and  roll  in 
the  pasture  and  to  nibble  at  the  fresh  grass,  keeps  the  animals  in  health,  adds 
to  their  efficiency,  and  prolongs  their  life. 

Estimates  of  the  length  of  the  working  life  of  mine  horses  and  mules  vary 
so  widely  that  it  seems  impossible  to  give  an  average.  Mr.  Hughes,  quoted 
before,  gives  the  average  useful  life  of  horses  working  in  English  mines  as 
more  nearly  9  than  8  yr.  This  figure  is  based  on  13  yr.  experience  at  some  large 
collieries  and  should  be  considered  authoritative.  Mules  seem  to  have  a 
much  shorter  working  life  than  horses.  Mr.  Bowron  assumes  the  average  work- 
ing life  of  a  mule  in  the  mines  of  the  Birmingham,  Alabama,  district,  to  be  6  yr. 
The  records  of  the  Fairmont  Coal  Co.  for  1905,  show  that  in  that  year,  26%  of 
their  stock  either  died,  was  killed,  or  had  to  be  disposed  of  on  account  of  being 
crippled  or  worn  out.  This  shows  a  working  life  of  between  3  5  and  4  yr.  In 


HAULAGE 


777 


estimating  the  cost  of  mule  haulage  it  is  probably  well  to  count  on  the  life  of  a 
mule  as  5  yr.,  and  that  10%  of  the  stock  is  in  the  stable  either  sick  or  tempo- 
rarily disabled. 

Work  of  Mules. — The  amount  of  work  that  a  mule  can  do  is  dependent 
on  the  strength  and  condition  of  the  mule,  the  condition  of  the  track  and 
rolling  stock,  the  relative  sizes  of  paying  and  dead  load  hauled,  length  of  trip, 
presence  or  absence  of  grades  that  may  be  for  or  against  the  loads,  etc.  Mr. 
Bowron  gives  the  following  figures  for  mines  in  Alabama  and  Tennessee; 

WORK  DONE  BY  MULES 


Group 

Average 
Haul 
Mile 

Average 
Output 
Tons 

Average  Ton-  Miles 
per  Mule 

Net 
Cost  per 
Ton- 
Mile 

Conditions 

Gross 

Net 

1 
2 
3 

4 

.32 
.37 
.78 
.64 

513 
861 
502 

887 

12.4 
24.8 
41.4 
38.3 

6.9 
13.8 
23.0 
21.4 

35.7 
17.9 
10.7 
11.5 

Unfavorable 
Average 
Best 
Average 

The  average  haul  is  the  distance  traveled  in  bringing  out  the  loaded  car; 
the  total  haul  is  twice  this.  In  the  columns  headed  Average  Ton-Miles  Per 
Mule,  the  figures  under  the  heading  Net  are  for  the  paying  load  of  coal  hauled. 
The  figures  in  the  column  headed  Gross  are  based  on  the  assumption  that  the 
car  weighs  40%  as  much  as  the  coal  carried,  but  is  carried  twice  as  far.  The 
mines  in  Group  1  are  four  in  number  with  unfavorable  conditions  caused  by 
short  hauls,  and  steep  adverse  grades.  In  all  but  one  of  these  mines,  the  mules 
were  employed  solely  for  gathering.  In  the  seven  mines  in  Group  2  and  the 
two  mines  in  Group  4,  the  mules  were  employed  only  for  gathering,  and  average 
conditions  preyailed,  the  mines  being  fully  developed,  the  hauls  of  fair  length, 
and  the  track  in  reasonable  shape,  etc.  In  the  three  mines  of  Group  3,  mules 
were  used  both  for  main-line  haulage  and  gathering.  A  comparison  of  Group  2 
with  Groups  3  and  4  shows  that  better  results  are  obtained  when  the  hauls  are 
of  fair  length,  as  less  time  proportionately  is  taken  up  in  changing  trips. 

It  is  estimated  that  a  horse  or  mule  will  exert  a  tractive  effort  equal  to 
one-fifth  of  its  weight  at  a  speed  of  2  to  4  mi.  an  hr.  for  1,000  to  1,200  hr.  per  yr.. 
say  for  4  to  5  hr.  per  da.  in  a  mining  year  of  200  to  220  da.  In  starting  a  load 
from  rest,  a  much  greater  effort  is  exerted  for  a  limited  time. 

When  gathering  single  cars,  where  the  most  distant  room  is  not  much  over 
J  to  |  mi.  from  the  parting,  a  mule  should  make  two  to  three  round  trips  per 
hour,  and  bring  in  fifteen  to  twenty-five  loads  per  day.  In  seams  of  moderate 
thickness  where  the  cars  hold,  say,  1.5  T.,  this  means  the  delivery  of  a  paying 
load  of  from  22.5  to  37.5  T.  per  da.  In  thick  seams,  where  the  load  is  2.5 
to  3  T.,  the  production  per  mule  will  vary  between  60  and  75  T. 

In  hauling  from  an  inside  parting  to  the  drift  mouth,  where  the  distance 
is  from  £  to  J  mi.,  and  the  grades  are  such  that  a  mule  can  haul  two  loaded 
cars,  one  animal  will  deliver  from  thirty  to  forty  loaded  cars  per  day,  equivalent 
to  a  paying  load  of  from,  say,  45  to  100  T.,  depending  on  the  size  of  the  car. 

These  results  cannot  be  obtained  unless  the  management  is  competent, 
and  sees  to  it  that  the  rails,  roadbed,  and  cars  are  in  first-class  condition,  that 
the  miners  are  properly  distributed  so  that  there  are  no  unnecessary  delays  at 
the  face  in  waiting  for  loads,  and  that  the  mules  are  well  fed,  well  shod,  and 
properly  cared  for. 

When  the  seam  is  pitching  and  the  entries  are  crooked  with  irregular  grades 
and  the  track  is  soft,  as  in  the  anthracite  fields  of  Pennsylvania,  no  average 
figures  can  be  given  because  the  conditions  vary  so  from  mine  to  mine,  but,  in 
general,  the  efficiency  of  a  mule  is  about  one-half  that  of  the  same  animal  in 
flatter  and  more  regular  seams. 

Cost  of  Mule  Haulage. — In  order  to  compare  the  cost  of  haulage  at  one 
mine  with  that  at  another,  haulage  costs  should  be  given  in  cents  per  ton-mile; 
that  is,  the  cost  of  hauling  1  T.  of  coal  1  mi.  Further,  the  underground  con- 
ditions should  be  known,  for  it  is  possible  that  there  is  greater  efficiency  where 
the  cost  is,  say,  15  c.  per  T.-mi.,  than  where  it  is  but  10  c. 


778  HAULAGE 

The  cost  of  mule  haulage  is  made  up  of  three  items;  depreciation,  feed 
and  care,  drivers'  wages. 

If  ten  working  mules  per  day  are  required  for  a  given  tonnage,  eleven  must 
be  provided,  as  one  is  practically  certain  to  be  laid  up  for  the  time  being,  either 
sick  or  crippled.  If  the  life  of  an  American  mine  mule  is  but  5  yr.,  and  his 
cost  is  $250,  $55  must  be  allowed  annually  per  working  mule  for  renewals,  on 
the  basis  that  10%  of  the  stock  is  idle. 

If  the  mule  is  fed  12  Ib.  of  corn  and  oats  in  equal  proportions  and  15  Ib.  of 
hay  per  day,  his  total  food  consumption  will  be  5,475  Ib.  of  hay  and  2,190  Ib. 
each  of  oats  and  corn  per  year.  At  $25  per  T.  for  hay,  45  c.  per  bu.  of  32  Ib, 
for  oats,  and  80  c.  per  bu.  of  56  Ib.  for  shelled  corn,  the  individual  cost  of  these 
items  will  be  $68.44,  $30.80,  and  $31.29,  or  a  total  of  $130.53  per  yr.  Allowing 
for  the  feed  of  the  idle  mule,  the  annual  cost  per  working  mule  will  be  $144.06. 
The  wages  of  the  stable  boss,  harness,  shoeing,  services  of  veterinarian,  etc., 
will  be  fully  $60  per  yr.  per  mule  at  large  mines  and  from  $100  to  $125  per  yr. 
at  small  ones.  Allowing  for  the  idle  stock,  probably  $90  per  yr.  is  a  reasonable 
charge.  One  working  mule  will  therefore  cost  $55  for  renewals,  $144.06  foi 
feed,  and  $90  for  stable  charges,  etc.,  or  a  total  of  $289.06  per  year  of  365  da.,  or 
79.2  c.  per  da.  However,  the  mines  do  not  run  365  da.  per  yr.,  the  working 
days  averaging  about  220.  On  this  basis  the  fixed  charges  per  working  mule 
per  working  day  will  be  $289.06-7- 220  =  $1.314.  To  this  must  be  added  the 
driver's  wages,  which  at  present  vary  from  $1.75  to  $2.50,  averaging,  say, 
$2.125,  making  the  total  cost  per  working  mule  per  working  day,  $3.439.  The 
cost  per  ton  of  coal  shipped  is  found  by  dividing  the  cost  of  all  the  mules  by 
the  total  tonnage.  Thus,  if  ten  mules  at  a  total  cost  of  10X $3.439  =  $34. 39 
handle  an  output  of  900  T.,  the  cost  per  ton  is  $34.39 -f- 900  =  3.821  c.  If 
the  average  distance  hauled  is  f  mi.,  the  cost  per  ton-mile  per  ton  of  output 
is  3.821  X§  =  10.189  c.  Since  each  mule  delivers  an  average  of  90  T  hauled 
f  mi.,  the  ton-mileage  per  mule  is  90X1  =  33.75.  Assuming  the  cars  to 
hold  2.5  T.,  the  output  requires  the  delivery  of  900-7-2.5  =  400  cars  per  da. 
If  the  cars  weigh  1  T.  each,  the  total  weight  handled  by  the  ten  mules  per 
day  will  be,  coal  900  T.;  outbound  loaded  cars  400  T.;  inbound  empty  cars 
400  T.;  or  a  total  of  1,700  T.  hauled  f  mi.  at  a  cost  of  $34.39.  This  is  equiva- 
lent to  637.5  T.  hauled  1  mi.  for  ten  mules,  or  63.75  T.-mi.  per  mule,  at  a 
cost  of  $34.39-7-1,700  =  2.02  c.  per  T.  gross  (cars  and  coal)  of  material  hauled, 
and  $34.39-7-637.5  =  5.4  c.  per  T.-mi. 

The  haulage  costs  given  by  Mr.  Bowron  in  the  preceding  table  are  based 
on  drivers'  wages  of  $1.762;  depreciation  $25  per  mule  per  year;  feed  and 
stable  attendance  34.9  c.  per  da.  for  365  da.;  interest  3.3  c.  per  da.  for  365  da.; 
making  the  total  cost  per  working  mule  per  working  day,  of  which  there  were  276 
in  the  year,  $2.46. 

In  the  reports  of  some  coal  mining  companies,  a  charge  of  50  c.  per  da.  per 
mule  is  made  for  all  items  other  than  drivers'  wages.  This  is,  obviously, 
altogether  too  little. 

Safe  Grade  for  Mule  Haulage. — While  the  grade  against  empties  on  the 
main  haulways  can  be  1.5%  the  grade  on  cross-entries  should  not  exceed  .5 
to  1%,  where  mules  must  gather  cars  in  a  hurry.  If  the  mules  are  winded  in 
taking  in  empties,  the  loaded  cars  must  necessarily  come  out  slower,  so  that  the 
advantage  gained  by  quick  delivery  of  empty  cars  is  offset  by  the  loss  of  time 
in  returning  the  loaded  cars.  Often  mine  mules  are  injured  by  winding  them 
and  then  not  giving  them  time  to  recover  their  breath  for  the  return  trip.  The 
driver  has  not  so  much  control  over  his  car  and  animal  that  he  can  stop  instantly, 
and  if  the  mule  lags  or  stumbles,  the  car  will  probably  run  against  the  mule  and 
injure  its  legs.  A  safe  down  grade  for  mule  haulage  should  not  exceed  3%  and 
great  care  will  be  needed  in  that  case.  On  such  steep  grades,  while  the  mule 
can  pull  up  the  ordinary  mine  car,  the  brakeman  or  driver  should  run  the  car 
down  independent  of  the  mule.  A  loaded  mine  car  will  slide  on  rails  even 
with  four  wheels  spragged  when  the  grade  is  6  to  8% ,  depending  on  the  condition 
of  the  rails.  

SELF-ACTING  INCLINES* 

In  a  self-acting  incline,  otherwise  known  as  a  gravity  incline,  gravity  plane, 
or  simply,  as  an  incline,  the  weight  of  a  loaded  car  descending  an  inclined  plane 
is  utilized  to  raise  an  empty  car.  In  hilly  regions,  where  the  coal  seams  outcrop 
at  a  considerable  elevation  above  the  valley,  inclines  are  in  common  use  to  lower 

*  See  also  Slope  Bottoms. 


HAULAGE  779 

|;  the  loaded  cars  from  the  mine  to  the  tipple.     They  are  also,  but  far  less  fre- 
;  quently,  used  underground  to  lower  loaded  cars  from  one  level  to  another. 

Tracks,  Switches,  Etc. — The  tracks  upon  inclines  may  be  arranged  in  one 

>  of  three  ways.     The  best  arrangement  consists  in  two  separate  tracks  thrpugh- 

>  out  the  entire  length  of  the  incline.     Where  the  amount  of  coal  handled  is  not 
I  large  or  where  the  capital  is  not  available,  it  is  quite  common  to  use  three  rails 
\  both  above  and  below  a  parting  or  turnout  midway  of  the  incline  where  there 

are  four  rails.  That  is,  both  above  and  below  the  parting  where  there  are 
two  independent  tracks,  the  middle  rail  of  the  three  is  common  to  both  the 
ascending  and  descending  tracks.  In  the  third  arrangement,  while  there  are 
three  rails  above  the  parting,  there  are  but  two  below_it. 

Self-acting  switches  set  by  the  mine  cars  are  provided  at  both  the  top  and 
bottom  of  the  incline  where  the  rails  join  to  form  a  single  track,  and  similar 
switches  are  used  at  both  ends  of  the  turnout  on  three-rail  inclines.  Safety 
switches  for  derailing  runaway  cars  are  frequently  used.  These  are  usually 
of  the  spring-latch  type,  which  are  closed  by  the  ascending  empty  car  and 
open  automatically  after  it  has  passed.  They  are  thrown  to  permit  the  passage 
of  the  loaded  car  by  means  of  a  lever  at  the  head  of  the  incline,  the  connection 
between  the  switch  and  lever  being  made  by  wire  or  rods  in  the  same  manner 
as  that  employed  on  surface  railroads  to  throw  distant  switches.  Safety 
blocks  are  used  at  the  top  of  the  incline  near  the  knuckle  to  prevent  the  cars 
running  away  down  the  incline  before  they  are  attached  to  the  rope.  The 
blocks  may  be  heavy  timbers  placed  by  hand,  or  a  more  elaborate  arrange- 
ment of  iron  set  by  levers  or  automatically  by  the  cars. 

The  weight  of  the  rail  used  should  be  proportioned  to  that  of  the  loaded 
car.  As  the  incline  must  last  the  life  of  the  mine  and  all  the  coal  shipped 
must  pass  over  it,  rails  weighing  less  than  50  Ib.  per  yd.  are  not  to  be  recom- 
mended where  the  loaded  car  weighs  as  much  as  5,000  to  6,000  Ib.  Lighter 
rails  may  be  used  for  lighter  loads,  but  are  hardly  to  be  advised  as  the  smaller 
sections  require  a  closer  spacing  of  the  ties,  more  attention  on  the  part  of  the 
repairmen,  and  are  more  apt  to  be  bent  in  case  a  runaway  trip  jumps  the  track. 
First-class  ties  should  be  used  and  the  roadbed  should  have  a  uniform  slope 
and  should  be  well  ballasted.  In  fact,  incline  tracks  should  be  laid  with  as 
good  material  and  with  as  much  care  as  those  on  a  main  entry  where  motor 
haulage  is  employed.  In  order  to  prevent  the  track  creeping  or  sliding  down 
hill  on  steep  pitches,  every  second  or  third  tie  is  made  long^enough  to  extend 
across  both  tracks  and  its  ends  are  anchored  in  hitches  cut  in  the  sides  of  the 
excavation,  are  braced  by  posts  firmly  planted  in  the  ground,  or  are  held  by 
wire  ropes  or  iron  rods  fastened  to  solid  objects  such  as  iron  bolts  sunk  in  a 
ledge  of  rock,  large  trees,  etc.  Square  notches  should  be  cut  in  the  base  of  the 
rail  at  intervals  of  10  or  15  ft.  depending  on  the  slope  of  the  incline.  These 
notches  should  come  upon  the  long  or  anchor  ties,  to  which  the  rails  are  in 
turn  anchored  by  track  spikes  through  the  notches. 

Rollers. — Rollers  for  supporting  the  rope  should  be  set  closer  together 
than  upon  flat  or  upon  steep  inclines.  Their  distance  apart  varies  from  12  to 
18  ft.,  an  average  spacing  being  15  ft.  It  is  better  to  vary  the  spacing  of  the 
rollers  by  a  foot  or  more  each  way  from  the  average,  as  this  will,  in  a  very  great 
measure,  prevent  the  flapping  of  the  rope  which  is  so  wearing  upon  it  and 
the  rollers  and  which  is  almost  sure  to  occur  when  the  rollers  are  exactly  the 
same  distance  apart.  The  jolting  of  the  cars  shakes  much  coal  from  them,  and 
this  soon  fills  the  spaces  between  the  ties  and  clogs  the  rollers  and  prevents 
their  turning.  When  the  rollers  are  not  free  to  revolve,  the  frictional  resis- 
tance to  the  passage  of  the  rope  and  the  wear  upon  it  and  the  rollers  is  very 
great;  consequently,  the  track  around  the  rollers  should  be  cleaned  frequently, 
sometimes  as  often  as  once  or  twice  a  day.  With  tracks  in  fair  shape  and 
rollers  12  to  15  ft.  apart,  actual  tests  have  shown  that  the  resistance  due  to 
the  friction  of  the  rope  in  running  empty  cars  down  grades  of  from  3.8  to 
6.2%,  varied  from  6  to  15%  of  the  weight  of  the  rope. 

Ropes,  Drums,  Barneys,  Etc. — The  strain  on  the  hoisting  rope  is  equal  to 
the  force  required  to  accelerate  and  hoist  the  load  and  to  overcome  friction, 
and  may  be  calculated  by  the  formula  R  =  F+G+I,  as  explained  under  the 
heading  Resistance  to  Haulage,  noting  that  the  weight  of  the  rope  must  be 
added  to  that  of  the  car.  As  the  wear  on  the  rope  from  passing  over  idle 
rollers,  trailing  on  the  ground,  and  the  jerks  due  to  dropping  the  trip  over  the 
head  of  the  incline  is  so  great,  a  much  higher  factor  of  safety  should  be  used 
than  in  the  case  of  shaft  hoisting  ropes;  10  is  none  too  large.  Ropes  for  inclines 
are  commonly  made  with  six  strands  of  seven  wires  each  laid  around  a  hemp 
center  (see  section  on  Wire  Rope)  and  those  of  the  lang-lay  and  locked-coil 


780  HAULAGE 

types  are  often  favored  because  of  their  larger  wearing  surface  and  consequent 
longer  life.  The  rope  is  usually  attached  to  the  car  by  a  chain  15  to  20  ft. 
in  length,  socketed  or  clamped  to  the  rope  and  provided  with  a  clevis  or  hook. 
Where  the  pitch  is  very  steep  and  slope  carriages  or  gunboats  are  used,  bridle 
chains  similar  to  those  used  on  shaft  cages  are  attached  to  the  corners  of  the 
carriage  or  gunboat  and  to  the  rope  at  some  point  above  the  socket. 

Where  cars  are  attached  to  the  rope  by  couplings  they  are  subject  to  strains 
that  rack  them  while  being  pushed  over  the  knuckle;  there  is  possibility  of  acci- 
dent from  their  running  over  the  head  of  the  incline  before  the  rope  is  attached ; 
time  is  lost  in  hooking  the  cars  to  and  unhooking  them  from  the  rope;  and 
the  rope  is  liable  to  be  kinked  and  unduly  strained  in  the  hooking-on  process. 
To  avoid  these  causes  of  wear  and  danger,  it  is  a  common  practice,  where  con- 
ditions are  otherwise  favorable,  to  attach  to  the  end  of  the  rope  what  is  called 
a  barney.  The  barney  consists  of  a  small  car  or  truck  running  on  light  rails 
placed  between  those  of  the  regular  tracks  of  the  incline.  At  the  bottom  of 
the  plane,  the  barney  passes  into  the  barney  pit  so  that  the  mine  car  may  pass 
over  it  to  the  tipple.  When  cars  are  being  hoisted,  the  barney  comes  out  of 
the  pit  and  pushes  the  cars  ahead  of  it  up  the  incline.  Similarly,  at  the  top  of 
the  incline,  the  cars  are  dropped  against  the  barney  and  are  held  back  by  it 
as  they  are  lowered.  A  barney  may  be  built  of  heavy  timber  or  iron  and  must 
have  sufficient  weight  to  prevent  its  being  lifted  from  the  track  at  the  bottom 
of  the  incline  by  the  weight  of  the  cars  pushing  against  it.  The  face  of  the 
barney  should  be  covered  for  its  full  width  and  height  by  a  sheet  of  heavy  plate 
iron  to  afford  a  wide  bearing  for  the  bumpers  of  the  car.  Cars  intended  for 
use  on  inclines  operated  with  barneys  should  have  bumpers  of  larger  face  than 
usual  so  that  they  may  not  ride  or  interlock  while  being  raised  or  lowered. 
To  avoid  the  cost  of  a  special  track  for  the  barney,  one  form  of  this  device 
is  provided  with  wheels  which  have  double  grooves  on  their  face  and  a  lateral 
play  on  their  axles.  For  most  of  the  trip  the  outer  grooves  of  the  wheels  run 
on  the  same  track  as  the  cars,  but  at  the  bottom  of  the  incline  the  inner  grooves 
engage  a  supplementary  barney  track,  the  wheels  are  forced  inwards  on  their 
axles  to  accommodate  themselves  to  the  narrower  gauge,  and  the  barney  passes 
into  the  usual  pit. 

At  the  head  of  the  incline,  the  ropes  pass  around  a  drum  set,  usually,  at 
such  an  elevation  that  the  cars  may  pass  under  it,  one  rope  winding  on  the  drum 
as  the  other  winds  off.  The  diameter  of  the  drum  is  determined  by  the  same 
rules  that  apply  in  the  case -of  hoisting  engines,  and  its  width  should  be  such 
that  when  the  cars  are  in  the  middle  of  the  incline  (but  not  on  a  turnout  in 
the  case  of  three-rail  inclines)  the  ropes  will  be  in  the  centers  of  their  respective 
tracks.  If  the  head  of  the  incline  is  built  upon  a  trestle,  in  order  to  secure 
strength  and  steadiness  and  to  avoid  massive  and  expensive  construction,  it 
is  usual  to  place  the  drum  below  instead  of  above  the  car  tracks.  Where  the 
pitch  is  steep  and  a  single  drum  is  used  upon  which  one  rope  winds  on  at  the 
top  and  the  other  winds  off  at  the  bottom,  the  upper  rope  will  be  so  high  if 
the  lead  is  short  (that  is,  if  the  drum  is  near  the  knuckle)  that  the  cars  will  be 
lifted  from  the  track  as  they  drop  over  the  knuckle.  This  difficulty  can  be 
overcome  by  the  use  of  two  drums  geared  together  so  as  to  turn  in  opposite 
directions.  This  allows  the  ropes  to  run  off  the  same  side  of  their  respective 
drums  and  at  the  same  height  above  the  track.  The  drums  can  then  be  placed 
such  a  distance  back  from  the  knuckle  and  such  a  distance  above  the  track  that 
the  ropes  are  tangent  to  the  rollers  on  the  incline.  This  arrangement  calls  for 
the  use  of  two  brakes,  one  for  each  drum,  which,  however,  may  be  placed 
close  together  on  the  same  stand.  Instead  of  drums,  a  pair  of  wheels  each  with 
a  series  of  parallel  grooves  on  its  face,  may  be  employed.  The  rope  is  in  one 
piece  and  after  making  several  turns  around  the  pair  of  wheels  has  its  end 
hitched  to  the  loaded  and  empty  trips  respectively  or  to  barneys.  These  wheels 
are  set  below  the  floor  of  the  drum  house  at  the  head  of  the  incline  so  that  they 
revolve  horizontally,  and  their  axles  are  vertical  and  in  the  center  line  between 
the  two  incline  tracks.  They  are  made  of  such  a  diameter  that  the  ropes  are 
in  the  center  of  the  tracks;  that  is,  the  diameter  is  equal  to  the  distance 
between  the  center  lines  of  the  tracks.  The  greater  the  tension  necessary  to 
prevent  the  rope  from  slipping,  the  greater  is  the  number  of  grooves;  four  or 
six  are  commonly  used.  Sometimes,  to  give  a  greater  bearing  surface  between 
the  rope  and  the  wheels,  the  rope  is  lapped  in  the  form  of  a  figure  8;  but  this 
is  to  be  avoided  because  of  the  undue  bending  strain  thus  thrown  upon  the  rope. 

The  brakes  controlling  the  speed  of  the  drums  must  be  very  powerful, 
strongly  constructed,  and  continually  watched  that  they  may  be  in  good  and 
effective  condition.  This  is  particularly  necessary  with  steep  pitches  and 


HAULAGE  781 

heavy  loads,  owing  to  the  increase  in  the  momentum  as  the  pitch  and  the  loads 
increase  and  to  the  fact  that  the  load  is  constantly  increasing  as  the  rope  on 
the  load  side  winds  from  the  drum  while  that  on  the  empty  side  winds  on  it. 

Grades  and  Their  Effects. — On  short  inclines  where  the  difference  between 
the  weight  of  the  loaded  and  empty  cars  is  considerable  (say,  those  where  the 
length  does  not  greatly  exceed  500  ft.  and  the  load  is  equal  to  or  greater  than 
the  weight  of  the  car),  a  pitch  of  3°,  equal  to  a  grade  of  5.24%,  may  be  sufficient 
to  impart  motion  to  the  cars  if  they  and  the  track  are  in  first-class  condition. 
Where  the  incline  is  long  or  where  the  weight  of  the  empty  car  bears  a  greater 
ratio  to  that  of  the  loaded  car  than  that  noted,  pitches  up  to  10°,  or  17.64%, 
may  be  necessary  to  start  the  trip.  The  greatest  pitches  on  which  cars  can 
generally  be  run  without  spilling  their  contents  over  the  end  gate  are  about  15° 
(26.8%),  for  cars  with  topping  to  20°  (36.4%),  for  cars  loaded  level  full.  In 
some  cases  where  the  seam  is  thick  enough  to  permit  their  use,  cars  with  high 
backs  are  employed  where  the  incline  is  steep.  Where  the  pitch  exceeds,  say, 
20°  and  where  the  breakage  of  the  coal  is  not  objectionable  (as  where  the  mine 
run  coal  is  coked)  the  contents  of  several  mine  cars  are  dumped  at  the  head  of 
the  incline  into  a  large  sheet-iron  car,  or  tank,  called  a  gunboat  or,  sometimes, 
a  skip.  These  are  not  detached  from  the  rope  and  are,  of  course,  run  in  pairs  in 
balance,  and  dump  or  discharge  automatically  at  the  foot  of  the  incline  into 
bins  or  upon  screens.  When  breakage  must  be  avoided  and  the  pitch  is  too 
steep  to  permit  the  cars  being  lowered  in  the  usual  way,  they  may  be  placed 
upon  a  platform  on  wheels  attached  to  the  ropes.  These  platform  cars  are 
variously  known  as  slope  carriages,  dummys,  etc.  When  these  are  used,  the 
tracks  at  both  the  head  and  foot  of  the  incline  are  generally  at  right  angles  to 
those  on  the  plane  so  that  the  car  rests  sidewise  on  the  rails  of  the  carriage. 
The  loading  and  unloading  of  the  carriage  is  performed  in  much  the  same  way 
as  on  a  shaft  cage;  that  is,  the  loaded  car  pushes  off  the  empty  car  at  the  top 
of  the  incline,  and  the  empty  car  pushes  off  the  loaded  one  at  the  bottom.  If 
the  car  is  placed  on  the  carriage  endwise  on  instead  of  sidewise,  particular 
attention  must  be  taken  to  lock  it  securely  in  place. 

If  the  cars  are  attached  to  the  rope  in  trips,  the  drawbars  must  be  con- 
tinuous and  they  and  the  couplings  must  be  of  heavier  metal  than  in  hauling 
on  a  level.  Further,  the  steeper  the  pitch  and  the  longer  the  trip,  the  heavier 
must  be  the  couplings.  When  barneys  are  used,  special  couplings  are  not 
necessary. 

Conditions  Unfavorable  to  Use  of  Inclines. — Inclines  requiring  for  their 
operation  a  large  number  of  cars,  say,  six  or  more,  are  expensive  to  operate 
and  maintain.  Barneys  cannot  be  used  as  the  bumpers  are  practically  certain 
to  interlock  if  the  cars  are  pushed  up  a  track  that  may  not  be  in  the  best  con- 
dition. Further,  as  the  barney  must  generally  be  placed  the  length  of  a  trip 
below  the  knuckle  and  the  trip  dropped  down  upon  it,  the  strain  upon  the  rope 
and  drum  from  the  impact  of  the  cars  is  so  great  as  to  be  extremely  dangerous. 
Running  a  large  trip  attached  to  a  rope  also  has  objectionable  features.  The 
cars  must  be  very  heavy  in  all  their  parts  to  withstand  the  strain  upon  the 
couplings  as  the  trip  is  pushed  over  the  knuckle  on  the  loaded  side  and  as  the 
slack  between  the  empty  cars  is  taken  up  at  the  foot  of  the  incline.  For  this 
reason,  the  strain  upon  the  rope  and  drum  is  great.  The  labor  required  at 
both  the  top  and  bottom  to  handle  such  a  large  number  of  cars  is  excessive, 
and  its  cost  would  pay  a  good  interest  on  a  rope  haulage  plant,  retarding  car 
haul,  or  electric  motor  for  transporting  the  coal  from  the  mine  to  the  tipple. 

Inclines  give  excellent  results  at  mines  of  limited  output  where  the  plane 
is  short  and  one-car  trips  can  be  run  with  barneys,  but  even  under  the  most 
favorable  conditions  it  is  a  question  for  consideration  if  they  may  not  well 
be  replaced  by  a  retarding  conveyer  or  car  haul. 

Calculations  for  Self -Acting  Inclines. — Because  the  same  number  of  cars 
is  attached  to  each  of  the  ropes,  their  weights  balance  and  an  incline  will  be 
self-acting  if  the  weight  of  the  coal  to  be  lowered  is  greater  than  the  weight  of 
the  rope  to  be  raised  together  with  the  weight  representing  friction  and  other 
resistances.  The  following  formulas  may  be  used  in  solving  problems  connected 
with  motion  on  self-acting  inclined  planes: 

a  =  -jyg  (sin  X-fcos  X)  =  "?  v  =  at,  /  =  ? 

These  formulas,  with  the  exception  of  the  first,  are  the  familiar  ones  appli- 
cable to  all  cases  of  uniformly  accelerated  motion;  s,  however,  is  the  length 
of  the  incline.  Because  motion  on  an  inclined  plane  is  due  solely  to  gravity 
that  component  of  it  g  sin  X  that  acts  parallel  to  the  plane  is  the  measure  of 


782  HAULAGE 

the  acceleration.  But  this  constant  acceleration  is  diminished  by  the  constant 
resistance  of  friction  fg  cos  X;  whence,  the  net  acceleration  is  the  difference 
of  the  two. 

It  is  apparent  that  when  sin  X  =/cos  X,  the  plane  is  in  equilibrium  with  the 

p 
forces  on  the  two  sides  balancing,  because  then  o  =  — XgXO  =  0,  and  when  there  is 

no  acceleration  there  can  be  no  motion.  From  the  relation  sin  X  =/cos  X,  there 
results =?  =/,  whence  tan  X  =/.  This  is  the  general  formula  for  equilibrium 

COS  A 

on  an  inclined  plane,  for  when  tan  X  is  greater  than/,  the  plane  is  self-acting; 
when  tan  X  =/,  the  plane  is  in  equilibrium ;  and  when  tan  X  is  less  than  /,  the 
plane  is  not  self-acting  and  it  will  require  more  force  than  the  weight  of  the 
coal  to  overcome  the  friction.  This  formula  is  very  valuable  in  making  pre- 
liminary calculations. 

EXAMPLE. — (a)  If  friction  /is  4%  (.04),  can  a  plane  pitching  2°  be  made 
self-acting?  (6)  Friction  remaining  the  same,  can  a  plane  pitching  8°  be 
made  self-acting?  (c)  With  friction  as  before,  what  is  the  least  pitch  at  which 
the  plane  will  be  self-acting? 

SOLUTION. — (a)  Here,  tan  X  =  tan  2°  =  .03492,  is  less  than /=. 04000  and 
the  plane  is  not  self-acting. 

(b)  Here,  tan  X  =  tan  8°  =  .14054,  is  greater  than  /=  .04000,  and  the  plane 
may  be  self-acting. 

(c)  Here  it  is  required  to  find  the  angle  of  elevation  of  the  plane  when  its 
tangent  is  known.     Since  tan  A"=/=.04000,  X  =  2°  17'  27".     At  any  greater 
pitch,  motion  will  result  and  the  plane  will  be  self-acting. 

It  does  not  follow,  however,  that^because  motion  is  possible  that  a  plane 
can  be  operated  in  practice.  Thus,  in  (c),  while  motion  will  result  when  the 
pitch  is  increased  to,  say,  2°  30',  the  number  of  cars  that  would  have  to  be 
handled  in  a  trip  would  be  so  very  great  as  to  be  impracticable  from  an  operat- 
ing standpoint.  ( 

After  it  has  been  determined,  by  the  use  of  the  preceding  formula,  that 
the  pitch  is  sufficient  to  permit  of  the  plane  being  made  self-acting,  the  number 
of  cars  required  in  a  trip  to  start  motion  on  the  plane  is  commonly  found  from 
the  formula, 

R  (sin  A-+/COSA-) 
C  sin  X-  (C+2E)f  cos  X 
in  which,  N  =  number  of  cars  in  trip; 

C  =  weight  of  coal  in  loaded  cars,  in  pounds; 
E  =  weight  of  empty  cars,  in  pounds; 
R  =  weight  of  rope  attached  to  empty  trip,  in  ppunds. 

In  the  formula,  all  the  terms  are  known  except  /,  which,  while  commonly 
taken  as  .025  may  be  very  much  more,  especially  on  flat  inclines  where  the 
rope  sags  on  the  ground  between  the  rollers  or  where  the  track  is  in  bad  condi- 
tion and  the  rollers  so  clogged  with  dirt  that  they  do  not  turn. 

EXAMPLE. — How  many  cars  will  it  require  to  start  the  trip  on  an  inclined 
plane  2,000  ft.  long  and  pitching  8°,  when  the  car  that  weighs  2,500  Ib.  carries 
a  load  of  like  amount,  the  rope  weighs  2  Ib.  per  ft.,  and  the  friction  is  4  per 
cent.  (.04)? 

SOLUTION. — Substituting  in  the  last  formula,  there  results, 

,,     4,OOOX(.13917+.04X.99Q27) 

=  2,500  X  .19317 -(2,500+  2X2,500)  X. 04  X. 99027  C&rS 

From  this,  it  will  require  fifteen  cars  to  start  the  trip. 

In  the  formula,  a  =  =^g  (sin  X—  /cos  X),  a  =  acceleration  in  feet  per  second 

per  second,  produced  by  an  unbalanced  force  C,  which  is  weight  of  coal  in 
descending  cars,  in  setting  in  motion  weight  W,  which  is  weight  of  coal  + 
weight  of  qars+ weight  of  rope  R+ weight  of  drum  D.  The  formula  may, 
thence,  be  transformed  to  read 


In  a  general  sense  it  may  be  said  that  the  weight  of  the  coal  C  is  the  motive 
power  that  sets  in  motion  all  the  other  weights  including  its  own. 

EXAMPLE. — In  the  preceding  example,  assuming  that  the  rope  drum  is 
8  ft.  m  diameter  and  10  ft.  wide  and  weighs  32,000  Ib.,  and  that  there  are 
fifteen  cars  in  a  trip,  (a)  what  will  be  the  time  of  descent  down  the  plane? 
(o)  What  is  the  final  speed,  in  feet  per  second  and  in  miles  per  hour?  (c)  Fur- 


HAULAGE  783 

ther,  assuming  that  the  speed  is  not  allowed  to  exceed  25  mi.  per  hr.,  what 
will  be  the  capacity  of  the  incline  in  an  8-hr,  da.,  making  the  usual  allowance 
for  delays,  etc.? 

SOLUTION.  —  As  there  are  fifteen  loads  of  coal,  C  =  15X2,500  =  37,500  lb., 
2E  =  2X15X2,500  =  75,000    lb.,    #  =  4,000   lb.f    £>  =  32,000    lb.,    and    (C+2E 


+R+D)  =  148,500  lb. 
-.  04  X.  99027)  =  .81  ft.  per  sec.  per  sec. 
From  this  the  time  of  descent  is  /  = 

The  final  velocity  reached  at  the  foot  of  the  incline  will  be  #  =  .81X703 
=  56.94  ft.  per  sec.,  or  (3,600X56.94)  ^5,280  =  38.8  mi.  per  hr. 

As  the  speed  is  limited  to  25  mi.  per  hr.,  or  36  ft.  per  sec.,  the  brakes  must 

be  applied  at  the  end  of  /=  —  =  44.4  sec.,  when  the  trip  has  traveled  down 

.ol 

the  incline  a  distance  of  s  =  -  -  —  —  =  799.2  ft.     As  retardation  and  accelera- 

tion are  equal,  the  time  required  to  start  and  stop  the  trip  will  be  88.8  sec.,  and 
the  distance  traveled  during  these  periods  will  be  1,588.4  ft.  The  remaining 
2,000  —  1,588.4  =  412.6  ft.  of  the  trip  will  be  made  in  412.6-^-36  =  11.4  sec. 
The  entire  time  of  descent  will  be  88.8+11.4  =  100.2  sec.,  or  1  min.  40  sec., 
practically. 

If  50  sec.  is  allowed  for  handling  the  ropes  between  trips,  a  trip  will  require 
2%  min.,  and  24  trips  will  be  made  in  1  hr.  As  (15X2,500)  -f-  2,000=  18.75  T. 
of  coal  is  lowered  each  trip,  the  capacity  of  the  incline  will  be  450  T.  per  hr.  If 
1  hr.  a  day  is  lost  in  various  delays,  the  incline  will  handle  an  average  net  daily 
output  of  450X7  =  3,150  T. 

In  the  example,  the  radius  of  gyration  has  been  taken  as  equal  to  that  of 
the  drum.  The  true  radius  of  gyration  is  probably  about  AR,  but  the  error 
arising  through  the  use  of  the  larger  and  more  easily  obtained  value  is  on  the 
safe  side. 

Profile  of  Inclines.  —  If  an  incline  is  a  plane  of  uniform  pitch,  as  commonly 
is  the  case,  the  weight  of  the  descending  trip  constantly  increases  and  that  of 
the  descending  trip  decreases,  as  one  rope  winds  off  and  the  other  winds  on  the 
drum.  Hence,  the  force  F  and,  consequently,  the  acceleration  a  constantly 
increase  and,  therefore,  the  force  that  must  be  applied  through  the  brake  to 
keep  the  speed  of  the  trip  within  the  established  limits  greatly  increases  from 
the  start  to  the  end  of  the  run. 

The  most  easily  operated  incline,  that  is,  one  on  which  the  force  applied 
through  the  brake  is  constant,  has  a  vertical  tangent  for  such  a  distance  below 
the  knuckle  that  the  trip  in  descending  it  acquires  the  proper  velocity;  it  also 
has,  from  the  end  of  this  tangent  to  a  point  near  the  foot  of  the  incline,  the 
shape  of  a  curve  such  that  the  velocity  of  the  descending  trip  is  constant  and, 
hence,  the  brake  resistance  is  uniform,  and  ends  with  a  curve  of  such  shape  that 
the  velocity  of  the  trip  at  the  end  of  the  run  is  just  sufficient  to  carry  it  to 
the  tipple. 

From  the  fact  that  after  a  trip  has  been  started  and  has  descended  the 
incline  some  distance  much  less  weight  is  needed  to  keep  it  in  motion,  if  the  upper 
end  of  the  incline  is  given  a  greater  pitch  a  much  smaller  trip  may  be  set  in 
motion.  In  fact,  relatively  flat  inclines  can  often  be  made  to  work  only  by 
increasing  the  grade  for  from  25  to  75  ft.  at  the  upper  end  to  double  or  more 
than  double  what  it  is  on  the  body  of  the  plane.  This  increased  grade  is  known 
as  the  steep  pilch.  All  inclines,  regardless  of  their  pitch,  terminate  in  a  curve 
that  is  tangent  to  the  plane  at  one  end  and  to  the  tipple  floor  at  .the  other. 
The  object  of  this  curve  is  to  reduce  the  speed  of  the  trip  to  an  amount  just 
sufficient  to  carry  it  to  the  dump. 


JIG  PLANES 

A  jig  plane  is  a  modification  of  the  self-acting  incline  in  which  the  weight 
of  a  descending  loaded  car  raises  a  counterweight  running  on  wheels  on  a  track, 
and  the  descending  counterweight  raises  the  empty  car.  The  counterweight, 
or  balance  truck,  runs  on  a  track  between  and  slightly  below  the  rails  of  the 
car  track,  and  its  weight  is  made  equal  to  one-half  the  sum  of  the  weights  of 
the  loaded  and  empty  cars  or  trips;  that  is,  if  ithe  loaded  car  weighs  5,000  lb. 


784  HAULAGE 

and  the  empty  car  2,500  lb.,  the  counterweight  will  weigh  (5,000  +  2,500)  4-  2 
=  3,750  lb. 

In  pitching  seams,  where  the  coal  will  not  run  by  gravity  in  a  chute  or 
where  it  will  be  broken  if  allowed  to  run,  the  jig  is  often  employed  with  advan- 
tage to  lower  loaded  cars  from  the  face  to  the  gangway.  For  this  purpose,  a 
sheave  is  arranged  at  the  head  of  the  track,  near  the  face,  between  two  posts 
wedged  firmly  between  the  roof  and  floor.  The  rope  is  passed  over  this  sheave, 
one  end  is  fastened  to  the  balance  truck,  and  the  other  end  is  coupled  to  the 
car  by  any  standard  hitching.  A  brake  wheel,  securely  fastened  to  one  side  of 
the  sheave,  and  a  strong  lever  furnish  the  means  of  controlling  the  motion  of 
the  car.  Jig  planes  are  generally  used  to  drop  single  cars  short  distances. 
Where  the  grade  is  so  flat  that  two  or  more  cars  must  be  employed  to  impart 
motion,  a  more  cheaply  installed  and  operated  arrangement  is  generally  possi- 
ble. The  rooms  may  be  driven  across  the  pitch  on  such  a  grade  that  a  mule  can 
pull  the  empty  car  to  the  face,  or  the  car  may  be  drawn  up  by  a  block  and 
tackle  operated  by  a  mule  or  by  a  windlass,  or  by  a  rope  passing  over  a  sheave 
at  the  head  of  the  room  track,  one  end  of  the  rope  being  fastened  to  the  car 
and  the  other  wound  on  a  drum  on  the  haulage  motor,  the  drum  being  turned 
by  current  from  the  entry  wires  while  the  motor  is  blocked  on  the  rails. 

Calculations  for  Jig  Planes.  —  While  the  formulas  given  under  the  head 
of  Self-Acting  Inclines  apply  equally  to  jig  planes,  it  is  better  to  determine  the 
pitch  of  the  track  necessary  to  make  the  plane  self-acting  under  the  known 
conditions.  If  the  necessary  pitch  is  greater  than  that  of  the  seam,  a  jig 
plane  cannot  be  installed.  The  formula  for  the  angle  of  pitch  may  be  deduced 
from  that  given  for  N,  as  follows: 


-—  - 

in  which,  F  =  friction  in  pounds  =  (C+B+R)  Xf; 
C  =  weight  of  loaded  car,  in  pounds; 
B  =  weight  of  balance  car,  in  pounds; 
R  =  weight  of  rope,  in  pounds. 

EXAMPLE.  —  It  is  desired  to  install  a  jig  plane  to  lower  a  single  loaded  car 
weighing  5,000  lb.  a  distance  of  200  ft.  from  the  face  to  the  entry.  If  the  empty 
car  weighs  2,000  lb.,  the  rope  2  lb.  per  ft.t  and  friction  is  taken  as  .025,  what 
is  the  proper  grade  to  make  the  plane  self-acting? 

SOLUTION.—  Here,  F=  (5,000+3,500+2  X  200)  X.  025  =  222.5  lb.;  C=5,000 
lb.;  B  =  (5,000+2,000)^2  =  3,500  lb.;  12  =  2X200  =  400  lb.  Substituting  in 
the  formula, 


whence,  X  =  14°  40'.  On  any  greater  pitch  than  this,  the  plane  will  be  self- 
acting,  and  on  any  lesser  one  it  cannot  be  operated  with  one  car,  although  it 
may  be  by  two  or  more. 

EXAMPLE.  —  With  the  conditions  of  the  preceding  problem,  but  with  two- 
car  trips,  on  what  pitch  will  the  plane  be  self-acting? 

SOLUTION.—  Here  C  =  10,000  lb.;  B=  (10,  000  +4,  000)  -=-2  =  7,  000  lb.; 
F=  (10,000+7,000+400)  X.  025  =  435  lb.;  and  #  =  400  lb.,  as  before.  Sub- 
stituting, 


whence  X 


SLOPES  AND  ENGINE  PLANES 


Slopes.  —  A  slope  is  an  inclined  plane  up  which  loaded  cars  are  hauled  on 
one  track  by  an  engine  of  any  convenient  type  at  the  same  time  as  a  corre- 
sponding number  of  empty  cars  descend  by  gravity  on  a  second  and  parallel 
track.  A  slope,  in  many  of  its  features,  is  a  combination  of  the  self-acting 
incline  and  the  standard  double-compartment  shaft.  In  all  that  relates  to 
track,  rollers,  the  use  of  barneys  or  gunboats,  slope  carriages,  etc.,  a  slope  is 
identical  with  an  incline;  in  all  that  relates  to  the  motive  power  and  the  calcu- 
lation of  engine  dimensions,  a  slope  differs  from  a  shaft  only  in  that  counter- 
balancing is  not  attempted  and  that  the  weights  moved  must  be  multiplied  by 
sin  X  and  the  friction  of  the  moving  weights  by  cos  X  as  in  haulage  on  inclines 
and  for  the  same  reason.  It  should  be  remembered,  -however,  that  the  inertia 
of  the  drum  and  sheaves  is  not  influenced  by  the  inclination  of  the  slope. 

Slopes  are  the  usual  means  of  opening  and  operating  pitching  seams,  and 
are  sometimes  used  underground  in  raising  coal  from  a  lower  to  a  higher  level. 


HAULAGE  785 

While  they  are  sometimes  laid  with  three  rails  and  a  passing  track,  as  some 
inclines,  all  first-class  main  slopes  are  double-tracked  throughout.  The 
profile  of  a  slope  is  that  of  the  dip  of  the  seam  slightly  dished  or  concave  at  the 
bottom  to  reduce  the  speed  of  the  descending  trip.  At  the  surface,  the  slope 
tracks  are  commonly  extended  upwards  on  a  trestle  having  the  same  pitch  as 
the  seam  so  that  the  knuckle  is  at  the  tipple  platform,  in  order  that  the  cars, 
when  released  from  the  rope,  may  run  by  gravity  to  the  dump. 

The  controlling  factor  in  determining  whether  a  certain  grade  is  or  is  not 
adapted  to  slope  haulage,  is  that  it  must  be  sufficiently  sharp  to  allow  the 
empty  trip  to  run  down  by  gravity  dragging  the  rope  after  it.  The  proper 
angle  of  slope  is  found  from  the  formula  tan  X=f,  for  Self-Acting  Inclines. 
The  coefficient  of  friction  /  should  be  made  sufficiently  great  to  allow  for  any 
increase  in  resistance  due  to  the  clogging  of  the  rollers  by  material  dropped 
from  the  cars.  The  pitch  must  also  be  steep  enough  to  insure  that  the  descend- 
ing trip  has  at  least  the  velocity  imparted  by  the  engine  to  the  ascending 
trip;  otherwise,  the  empty  rope  will  buckle  and  double  on  itself. 

Both  first-  and  second-motion  engines  are  used  for  hoisting  on  slopes;  the 
choice  between  the  two  types  is  governed  by  the  principles  given  under  the 
head  of  Hoisting.  Slopes  up  to  500  or  600  ft.  in  length  and  of  moderate  pitch 
are  now  generally  operated  with  rope  or  chain  hauls,  the  advantages  obtained 
through  the  regular  delivery  of  single  cars  to  the  dump  through  the  use  of  these 
appliances  more  than  offsetting  their  greater  first  cost. 

Engine  Planes. — An  engine  plane  is  a  single-track  slope,  without  central 
turnout,  up  which  an  engine  pulls  a  loaded  car  as  one  operation  and  down 
which,  as  a  second  operation,  the  empty  car  descends  by  gravity,  dragging  the 
rope  after  it.  There  is  frequent  confusion  in  the  use  of  the  terms  slope  and 
engine  plane  and  what  is  always  and  rightly  known  as  engine  plane  when  on 
the  surface  is  miscalled  a  slope  or  a  single-track  slope  when  used  underground. 

The  engines  used  on  planes  are  commonly  of  the  friction-clutch  type.  The 
drum  is  thrown  in  when  it  is  desired  to  hoist  and  thrown  out  and  allowed  to 
turn  on  its  shaft  as  the  empty  trip  descends,  its  speed  being  controlled  by 
powerful  brakes.  When  hoisting  on  a  plane,  the  load  is  that  of  the  loaded 
trip  and  the  weight  of  the  rope,  the  latter  diminishing  uniformly  as  the  rope 
winds  on  the  drum.  When  lowering,  the  load  at  the  outset  is  that  of  the 
empty  trip  but  it  is  uniformly  increased  by  the  weight  of  the  rope  as  the  latter 
unwinds  from  the  drum. 

The  question  of  hoisting  the  load  is  merely  one  of  installing  a  sufficiently 
powerful  engine,  which  must  develop  more  power  in  engine  plane  than  in  slope 
haulage  because  in  the  former  there  is  no  balancing  of  the  moving  weights. 
In  slope  haulage,  the  inertia  of  the  drum  is  overcome  by  the  engine;  but  in 
engine-plane  haulage,  this  is  true  only  in  the  case  of  the  ascending  loaded  trip. 
Hence,  in  engine-plane  haulage  the  grade  must  be  sharper  than  in  slope  haulage 
because  the  empty  trip  must  overcome  the  inertia  of  the  drum.  In  both 
forms  of  haulage,  the  length  of  the  empty  rope  becomes  constantly  greater, 
and  the  unchanging  weight  of  the  empty  trip  may  not  always  be  sufficient  to 
overcome  the  increasing  rope  resistance.  For  this  reason  and  to  attain  an 
average  speed  of,  say,  10  mi.  per  hr.,  the  grade  of  an  engine  plane  should  not 
be  less  than  3%. 

Flat  slopes  and  planes  are  fully  as  unsatisfactory  in  operation  as  fiat  self- 
acting  inclines.  On  the  surface,  their  use  may  often  be  avoided  by  the  employ- 
ment of  a  motor  running  on  a  track  laid  on  a  flatter,  but  longer  grade  than  the 
plane.  If  motors  cannot  be  employed  and  a  plane  must  be  used,  it  is  better  to 
install  a  tail-rope  or  endless-rope  system  for  its  operation.  Underground,  where 
their  use  is  local  and  the  amount  of  material  handled  over  them  is  not  great, 
the  use  of  flat  slopes  and  planes  is  not  so  objectionable,  although  if  short,  and 
cheap  power  is  to  be  had,  a  mechanical  haul  of  some  kind  is  to  be  preferred. 


ENDLESS-ROPE  HAULAGE 

In  endless-rope  haulage  systems,  a  wire  rope  passes  from  the  haulage-engine 
drum  to  and  through  the  main  entry  to  a  sheave  at  the  end  of  the  workings, 
thence  around  the  sheave  and  back  along  the  main  entry  or  a  parallel  entry 
to  the  engine  drum.  The  ends  of  the  rope  are  spliced  together,  forming  an  end- 
less rope  to  which  the  cars  are  attached  singly  by  grips  or  in  trips  pulled  by  a 
grip  car. 

As  usually  installed,  the  system  requires  two  tracks,  which  may  be  laid  in 
the  same  entry  if  the  roof  is  sound  enough  to  permit  the  necessary  width. 
50 


786  HAULAGE 

If  the  roof  is  bad,  it  is  usually  cheaper  to  lay  single  tracks  in  parallel  entries  of 
standard  width,  using  one  road  for  inbound  and  the  other  for  outbound  traffic. 

There  are  two  general  types  of  endless-rope  haulage  based  on  the  speed  of 
the  rope.  In  the  low-speed  system,  which  is  the  original  type,  the  rope  moves 
continuously  in  the  same  direction  at  a  rate  of  2  to  4  mi.  an  hr.;  there  are 
two  separate  tracks;  the  cars  are  attached  to  the  rope  singly  at  intervals  of 
100  to  200  ft.;  and,  as  far  as  possible,  there  are  as  many  inbound  empty  cars  as 
there  are  outbound  loaded  ones.  In  the  high-speed  system,  the  rope  travels 
at  a  rate  of  15  to  25  mi.  per  hr.;  the  cars  are  attached  to  the  rope  in  trips  of 
as  many  as  fifty  or  more  by  means  of  a  grip  car;  there  is  usually  but  one  track, 
which  is  used  for  both  inbound  and  outbound  traffic;  and  the  direction  of 
motion  of  the  rope  is  reversed  to  correspond  to  the  direction  in  which  the 
trip  is  being  moved. 

The  low-speed  system  has  been  highly  developed  in  England,  where  the 
cars,  as  well  as  the  mine  output,  are  relatively  small,  where  the  grades  are 
undulating  and  the  curves  numerous,  where  many  branches  (cross-entries) 
must  be  worked  from  the  main  rope,  and  where  there  is  not  storage  room  at 
the  foot  of  the  shaft  for  long  trips  of  cars.  While  this  requires  much  less 
power  than  the  high-speed  system  and  insures  a  uniform  and  regular  delivery 
of  loaded  cars  to  the  shaft  bottom,  it  is  costly  in  labor,  as  at  least  one  attendant 
is  required  at  each  branch.  Although  at  such  low  speeds  there  is  but  little 
danger  of  a  car  jumping  the  track,  when  such  an  accident  does  happen  the 
damage  may  be  serious  to  both  cars  and  rope,  as  there  is  no  attendant  to  signal 
promptly  for  the  immediate  stoppage  of  the  rope. 

The  strain  upon  the  rope  in  starting  a  car  from  rest  varies  as  the  square 
of  the  rope's  velocity,  hence  the  higher  the  speed  the  greater  must  be  the 
diameter  of  the  rope.  Further,  if  the  velocity  is  as  great  as  4  mi.  per  hr.,  the 
ropes  become  flattened,  kinked,  and  unduly  strained,  much  sooner  than  at 
velocities  of  2  to  3  mi.  per  hr.  For  these  reasons,  the  last-named  speeds  are 
preferred  for  slow-moving  ropes.  When  attaching  it  to  the  rope,  the  attend- 
ant usually  pushes  the  car  by  hand  until  it  has  acquired  the  velocity  of  the 
rope  before  gripping  it  to  the  rope.  Grips  for  low-speed  haulage  are  very 
largely  of  the  automatic  detaching  type. 

The  high-speed  system  is  in  more  general  use  in  the  United  States  where 
the  cars  and  the  required  output  are  large;  where  the  track  is  straight  and  the 
grades  against  the  loads;  where  there  are  no  branches;  and  where  there  is  ample 
storage  room  for  long  trips  of  cars.  The  system  is  economical  in  labor,  as 
no  handling_of  the  trip  is  necessary  except  at  the  points  of  origin  and  delivery, 
but  it  requires  powerful  engines  to  give  the  acceleration  to  the  trip  when 
started  on  the  heavy  grades  that  usually  prevail  where  this  system  is  used. 
The  rope  must  be  hearvier  than  in  the  low-speed  system,  the  rails  should  weigh 
60  Ib.  or  more  per  yard,  the  track  must  be  kept  clean  and  in  perfect  alinement, 
and  the  cars  must  be  of  the  best  type.  The  amount  of  coal  that  may  be 
delivered  by  this  system  is  practically  only  limited  by  the  power  of  the  engines, 
particularly  if  inbound  and  outbound  trips  are  run  at  the  same  time.  At  the 
tipple,  the  long  trips  are  fed  into  the  dump  by  car  hauls,  imposing  little  if  any 
extra  labor  over  that  required  when  the  low-speed  system  is  used. 

Endless-rope  haulage  is  particularly  adapted  to  mines  where  the  entries 
are  level  or  have  a  slight  uniform  grade.  In  the  low-speed  system,  the  cars 
should  be  fastened  to  the  rope  at  regular  intervals  to  make  the  load  on  the 
engine  constant  and  to  insure  a  uniform  delivery  of  cars  to  the  tipple.  How- 
ever, owing  to  the  delays  incident  to  all  mining  operations,  it  is  impossible 
to  keep  the  cars  regularly  spaced  and  they  become  bunched.  Thus,  the  cars 
may  accumulate  on  a  grade  or  on  several  grades  in  opposite  directions  and  so 
throw  a  variable  load  upon  the  engine,  which  makes  its  regulation  very  difficult 
where  the  grades  are  not  uniform  in  amount  or  direction.  Where  variable 
grades  occur,  the  rope  will  lift  from  the  track  in  low  places  and  may  lash  to 
such  an  extent  as  to  throw  the  cars  from  the  track;  while  on  an  up-grade,  the 
rope  will  bear  heavily  on  the  rollers,  producing  excessive  wear  and  greatly 
increasing  the  friction. 

General  Arrangement  of  Endless-Rope  Haulage  Systems. — Fig.  1  shows 
the  general  arrangement  of  an  endless-rope  haulage  system,  which  will  answer 
for  either  low  or  high  speed.  The  rope  passes  back  of  the  engine  drums  a  and  b 
to  the  balance  car  c,  where  it  is  given  a  half  turn  around  the  sheave  d.  From  d 
the  rope  passes  back  past  the  engine  drums  and  through  the  mine,  where  it  is 
supported  on  rollers,  to  the  tail-sheave  e  which  is  carried  on  the  balance  car  /. 
After  making  a  half  turn  around  this  sheave  e,  the  rope  returns  along  the 
parallel  track  to  the  drum,  thus  completing  the  circuit.  The  balance  cars  are 


HAULAGE 


787 


intended  to  keep  the  rope  tight. 
The  passage  of  the  rope  under 
the  pulleys  g,  over  the  pulleys 
h,  and  to  one  side  of  the  pulleys 
*,  is  for  the  purpose  of  deflect- 
ing it  to  the  center  of  the  mine 
tracks.  In  the  plan  shown,  the 
rope  k  in  going  into  the  mine 
pulls  the  empty  cars  /  to  the 
curve  m  where  they  are  un- 
hooked and  distributed  to  the 
working  places.  At  the  same 
point,  but  on  the  track  «,  the 
loaded  cars  are  attached  to  the 
outgoing  rope  p  and  hauled  to 
the  curve  q  where  they  are  un- 
hooked and  sent  to  the  tipple. 

Endless-Rope  Haulage  En- 
gines and  Drums. — The  engines 
for  an  endless-rope  haulage 
plant  are  almost  invariably  of 
the  second-motion  type  and 
may  be  fitted  with  plain  slide 
or  Corliss  valves;  the  latter  is 
preferred  if  the  grades  are  vari- 
able as  they  are  more  economical 
in  the  use  of  steam  and  are  auto- 
matic. In  the  low-speed  sys- 
tem, the  engines,  if  run  contin- 
uously in  one  direction,  should 
use  steam  expansively,  and, 
where  the  loads  are  variable, 
should  be  provided  with  a  fly- 
wheel and  governor. 

There  are  generally  two 
narrow  drums,  arranged  tan- 
dem on  separate  shafts.  One 
of  the  drums  is  driven  by  gear- 
ing and  the  other,  frequently 
called  the  follower,  is  turned  by 
the  rope  passing  around  it. 
The  drums  vary  in  diameter 
according  to  the  size  of  rope, 
size  of  engine,  length  of  haul, 
and  should  be  of  ample  size  to 
reduce  the  bending  strain  on 
the  rope.  The  driven  drum, 
or  follower,  is  sometimes  inde- 
pendent of  the  engine  and  made 
smaller  than  the  driving  drum; 
it  is  also  sometimes  permitted 
to  run  loose  on  its  shaft  so  that 
the  rope  will  lead  .properly  from 
one  groove  to  another.  Drums 
with  a  concave  rim  are  some- 
times used,  but  with  such  there 
is  considerable  surging  and  jerk- 
ing of  the  rope,  and  grooved 
drums  are  preferable.  The  best 
results  appear  to  be  obtained 
when  the  drums  are  placed  12 
to  15  ft.  apart,  in  order  that 
there  maybe  a  slight  sag  to  the 
rope  and  a  better  bite  on  the 
drum.  The  number  of  grooves 
on  the  driving  pulley  may  be 
two,  four,  or  more,  depending 
on  the  strain  coming  upon  the 


788  HAULAGE 

rope;  the  follower  pulley  adds  but  little  to  the  tension.  To  increase  the 
tension,  the  rope  is  sometimes  bent  around  the  drums  in  the  form  of  a 
horizontal  figure  8,  but  the  extra  bending  strain  thus  thrown  on  the  rope 
materially  shortens  its  life.  Because  the  tension  on  the  different  turns 
of  the  rope  gradually  and  uniformly  decreases  from  the  first  to  the  last,  the 
wear  on  the  lining  of  the  grooves  is  not  equal.  This  results  in  time  in  the 
drum  having  as  many  diameters  as  it  has  grooves.  The  velocity  of  a  point 
on  the  circumference  of  the  drum  will  be  greater  on  the  unworn  grooves  than 
on  the  worn  ones,  and,  as  the  rope  and  drum  cannot  travel  at  different  speeds, 
an  increasingly  violent  rubbing  action  is  set  up  between  the  rope  and  drum, 
materially  reducing  the  life  of  the  former.  To  prevent  this  rubbing  action,  the 
follower  drum  is  sometimes  made  up  of  as  many  single  drums  as  there  are 
grooves,  each  drum  being  free  to  revolve  at  a  speed  determined  by  that  of  the 
groove  opposite  it  on  the  solid  driving  drum.  There  are  various  forms  of 
differential  drums  on  the  market,  designed  to  overcome  the  trouble  under 
discussion.  In  some  of  them,  the  lining  of  the  grooves  is  free  to  move  upon 
the  circumference  of  the  drum  and  so  to  adjust  itself  to  the  variation  in  the 
speed  of  the  rope  from  groove  to  groove. 

Rope-Tightening  Arrangements. — Owing  to  the  stretching  of  the  rope 
under  loads,  balance-  or  tension-  cars  or  sheaves  are  placed  at  both  ends  of  the 
rope  line  to  keep  it  tight.  The  general  arrangement  is  a&  shown  in  Fig.  1. 
The  weight  of  the  balance  car  is  determined  by  experiment.  Unless  the  track 
upon  which  the  balance  car  runs  has  considerable  length,  a  piece  must  be  cut 
from  the  rope  and  a  new  splice  made  when  the  car  reaches  the  end  of  the 
track.  In  order  to  avoid  the  expense  of  blasting  out  an  inclined  track  as 
shown  in  Fig.  1,  the  balance  car  may  be  run  on  the  grade  of  the  entry  and  a 
more  than  usually  heavy  counterweight  employed;  in  which  case  the  only 
excavation  necessary  is  that  of  the  counterweight  pit.  The  counterweight 
is  then  supported  from  a  pulley  wheel  riding  on  a  chain.  One  end  of  the  chain 
is  fastened  to  the  balance  car  and  the  other  end,  after  passing  down  into  the 
pit  to  form  a  loop  upon  which  the  pulley  wheel  rides,  is  carried  up  to  and 
around  a  small  drum,  which  may  be  turned  by  worm-gearing  operated  by  a 
hand  wheel.  When  the  stretch  of  the  rope  has  allowed  the  counterweight 
to  rest  on  the  pit  bottom,  it  is  raised  therefrom  by  winding  some  of  the  chain 
upon  the  drum. 

Grips  and  Grip  Cars.— Messrs.  W.  G.  Salt  and  A.  L.  Lovatt,  in  the  Trans- 
actions of  the  Institution  of  Mining  Engineers  (England),  give  the  following 
as  the  seven  essential  qualities  of  a  good  grip,  or  clip,  as  it  is  called  in  England: 

1.  A  clip  must  be  sufficiently  strong,  with  a  margin  of  safety,  to  do  the 
work  required  and  to  withstand  rough  usage.     If,  however,  the  design  of  the 
clip  is  too  strong,  the  desired  results  will  not  be  obtained;  for  if  the  tub  or  tubs 
(car  or  cars)  are  derailed,  serious  damage  might  be  caused  to  the  rope  or  hauling 
machinery  if  the  clip  does  not  act  as  a  safety  valve. 

2.  Its  design  and  construction  should  be  such  that  it  can  obtain  and  retain 
a  firm  grip  on  the  rope  when  it  is  attached. 

3.  The  jaws  of  the  clip  should  have  a  bearing  of  at  least  70%  on  the 
circumference  of  the  rope  and  should  embrace  all  the  strands  of  the  rope  within 
a  minimum  length  of  the  clip  jaw. 

4.  There  should  be  a  good  margin  for  wear  and  the  clip  should  be  capable 
of  easy  adjustment  by  the  person  using  it. 

5.  The  design  and  construction  should  be  as  simple  as  possible;  the  fewer 
parts  there  are  the  better,  and  these  should  be  such  as  to  allow  of  the  clip  being 
easily  attached  and  detached  from  the  rope  with  certainty,  the  detachment 
being  clean  and  certain. 

6.  The  gripping  surfaces  should  be  so  arranged  as  not  to  kink  the  rope 
under  working  conditions.     If  the  kink  effect  is  reduced  to  a  minimum  the 
wear  on  the  rope  will  be  reduced,  and  consequently  the  life  of  the  rope  will  be 
increased. 

7.  A  clip  should  be  capable  of  being  automatically  detached  from  the  rope, 
and  ideally  should  be  of  such  design  as  to  work  satisfactorily  under  any  one  or 
all  of  the  conditions  prevailing  at  a  mine. 

The  following  controlling  factors  must  be  taken  into  account  in  the  adoption 
of  a  clip:  Inclination,  undulating  or  varying  gradients,  level  roads,  direction 
of  roads  (straight  or  otherwise) ;  and  under-  or  over-rope  haulage. 

The  article  by  Messrs  Salt  and  Lovatt  is  reprinted  in  The  Colliery  Engineer 
for  Feb.,  1914,  and  illustrates,  compares,  and  criticizes  the  majority  of  the 
grips  used  in  England,  where  the  slow-moving  endless  rope  system  with  single 
cars  has  been  very  successfully  developed. 


HAULAGE 


789 


On  undulating  grades  single  grips  have  not  proved  universally  successful, 
and  it  is  usually  necessary  to  have  grips  at  each  end  of  the  car  to  prevent  its 
running  forwards  or  backwards  and  bending  the  rope  at  every  change  of  grade. 

Where  the  cars  are  run  in  trips  instead  of  singly,  grip  cars  are  used.  These 
are  four-wheeled  trucks  carrying  the  grip  below  the  platform.  The  grip  is 
frequently  of  the  jaw  type  with  one  fixed  jaw;  the  movable  jaw  being  brought 
down  upon  the  rope  by  a  lever  or  by  turning  a  hand  wheel.  In  handling 
heavy  loads,  the  grip  must  be  thrown  in  slowly  so  that  the  speed  of  the  trip 
is  gradually  accelerated  from  rest  to  that  of  the  moving  rope.  This  is,  perhaps, 
best  accomplished  by  substituting  for  the  jaw  grip,  the  form  used  on  street 
railways,  some  suspension  bridges,  etc.  This  grip  consists  essentially  of  three 
grooved  wheels  set  in  the  same  plane  with  their  axles  at  the  vertices  of  an 
equilateral  triangle.  The  rope  runs  tangent  to  the  upper  edge  of  two  wheels 
and  tangent  to  the  lower  side  of  the  other.  As  the  axles  of  the  wheels  are 
brought  together  by  suitable  mechanism  a  greater  and  greater  pressure  is 
exerted  upon  the  rope.  At  first  the  wheels  revolve  freely,  but  as  the  pressure 
is  increased  they  grip  the  rope  more  and  more  firmly  at  the  same  time  imparting 
an  increasing  velocity  to  the  trip,  until,  when  the  grip  wheels  no  longer  revolve, 
the  trip  is  traveling  at  the  same  speed  as  the  rope.  Where  grip  cars  are 
employed,  there  is  a  device  by  which  the  frame  carrying  the  grip  wheels  can 
be  raised  a  sufficient  height  to  clear  the  rollers.  In  fact,  any  grip  to  be  service- 
able must  pass  over  the  track  rollers,  deflection  sheaves  on  curves,  and  the  like. 
A  grip-man  rides  on  the  grip  car  not  only  to  handle  the  grip,  but  also  to  release 
it  and  apply  the  brakes  when  needed. 

Rollers  and  Sheaves. — When 
placing  rollers  on  endless-rope  haul- 
age roads,  the  same  precautions  are 
to  be  followed  as  when  setting  them 
on  inclined  planes.  The  rollers  are 
very  commonly  hollow,  cast-iron 
cylinders  12  to  18  in.  long,  and  6  in. 
in  diameter,  with  raised  rims  to  pre- 
vent the  rope  running  off  them. 


FIG.  2 


Other  rollers,  10  to  12  in.  long,  have  a  decidedly  concave  face  to  carry  the 
rope  to  a  central  groove.  At  the  bottom  of  a  dip,  it  is  usually  necessary 
to  have  a  roller  in  the  roof  to  prevent  the  rope  scraping  against  the  roof;  such 
a  roller  may  be  of  the  types  just  described.  Too  much  care  cannot  be  taken 
to  see  that  the  rollers  are  strongly  and  properly  set  and  are  in  good  condition 
and  free  to  revolve  at  all  times. 

Sheaves  are  a  type  of  roller  with  their  axles  vertical  and  are  used  to  guide  the 
rope  around  curves.  When  possible  they  are  placed  outside  the  rails  on  the  inside 
of  the  curve ;  this  arrangement  permits  the  use  of  sheaves  as  large  as  6  ft.  in  diame- 
ter, thus  greatly  prolonging  the  life  of  the  rope  above  what  it  would  be  if  the 
sheaves  were  in  the  center  of  the  track  where  their  diameter  would  be  less  than 
one-half  the  track  gauge.  The  sheave  shown  in  Fig.  2,  which  may  be  set  with 
its  axle  inclined,  is  a  very  common  form  for  use  on  the  outside  of  curves.  The 
planking  a  is  intended  to  guide  the  rope  to  the  sheave  and  may  be  covered 
with  sheet  iron  held  in  place  by  bolts  or  nails  with  countersunk  heads. 

Where  rollers  or  sheaves  are  placed  outside  the  track  on  curves,  some  arrange- 
ment is  necessary  to  prevent  the  rope  catching  under  the  head  of  the  rail  as  it 
is  deflected  from  the  center  line.  A  familiar  arrangement  consists  of  wedge- 
shaped  pieces  of  wood  spiked  to  the  ties,  the  highest  point  of  the  wedge  rising 
a  little  aoove  the  top  of  the  rail.  A  wedge  is  placed  on  each  tie  and  is  set  as 
close  to  the  rail  as  possible,  leaving  clearance<  for  the  flange  of  the  car  wheel. 
The  face  of  the  wedge,  along  which  the  rope  slips  into  position,  may  be  covered 
with  sheet  iron  held  in  place  by  spikes  or  bolts  with  countersunk  heads.  Numer- 
ous devices  similar  to  the  one  illustrated 
in  Fig.  3  are  used  for  the  same  purpose. 
The  finger  a,  the  lower  end  of  which  is 
much  the  heavier,  is  pivoted  at  b  so  that 
it  normally  hangs  vertical.  When  the 
rope  presses  against  it,  it  assumes  the 
position  shown  in  (b) ,  and  after  guiding 
the  rope  over  the  rails,  falls  back  to  its 
original  position  (a).  Arrangements 
must  be  made  at  all  switches  to  prevent  the  rope  being  caught  in  the  frogs. 
Side-Entry  Haulage. — The  endless-rope  system  is  not  readily  adapted  to 
haulage  on  side  or  cross-entries.  As  ordinarily  arranged,  each  entry  has  its 


(a) 


FIG.  3 


790 


HAULAGE 


own  rope,  which  passes  over  a  sheave  at  the  face  and  makes  a  couple  of  turns 
over  a  grip  or  driving  wheel  at  the  mouth.  On  the  main  entry  is  placed  a 
vertically  turning  wheel  around  which  the  main  rope  makes  two  turns  to  give 
it  sufficient  power  to  turn  the  driving  pulley  on  the  side-entry  haulage;  this 
it  does  by  means  of  a  friction  clutch,  which  may  be  thrown  in  and  out  of  gear. 
There  is  usually  a  reducing  gear  so  that  the  speed  of  the  side-entry  rope  is  less 
than  that  of  the  main  line.  Loaded  cars  on  the  main  line  must  be  detached 
from  the  rope  on  arriving  at  a  cross-entry,  because  of  the  wheel  around  which 
the  main  rope  passes,  and  must  be  coupled  on  again  after  passing  the  entry. 
Similarly,  cars  to  be  delivered  to  a  side  entry  or  which  are  received  therefrom 
must  be  uncoupled  and  coupled  at  the  junction  with  the  main  line.  On  a  level 
track  or  on  down  grades,  the  cars  on  the  main  line  will  run  past  the  branches 
under  their  acquired  momentum,  but  on  sharp  up  grades  this  may  not  be  possi- 
ble. In  any  case,  much  labor  is  required  at  junctions  and  the  grip  must  be 
of  a  type  that  is  quickly  adjusted. 

Overhead  Endless-Rope  Haulage. — The  overhead  endless-rope  haulage 
system  is  a  modification  of  the  original  low-speed  type  in  which  the  rope  is 
carried  over  the  cars  instead  of  under  them.  As  the  cars  are  spaced  from  100 
to  200  ft.  apart,  it  is  unusual  for  the  rope  to  sag  low  enough  to  drag  either  on 
the  track  or  on  the  rollers;  hence,  the  wear  on  the  rope  is  much  less  than  when 
it  runs  under  the  cars. 

Most  of  the  grips  or  clips  used  with  an  under-running  rope  may  be  used 
with  the  overhead  rope.  A  common  form  of  grab,  or  dutch,  is  shown  in  Fig.  4, 
where  the  rope  rests  in  the  groove  a.  The  friction  due  to  the  motion  of  the 

rope  in  the  grab  causes  it  to  turn 
slightly  sidewise  and  grip  the  rope. 
The  heavier  the  car  or  the  steeper  the 
grade,  the  more  firmly  will  the  grab 
take  hold  of  the  rope.  As  the  grab 
is  free  to  turn  in  the  sockets  b,  it  pulls 
the  car  on  an  up  grade  and  holds  it 
back  on  a  down  grade.  When  the 
cars  reach  their  destination,  they  are 
automatically  released  by  an  increase 
in  the  down  grade  and  by  the  gradual 
rise  of  the  rope  to  an  overhead  sheave, 
which  lifts  the  rope  from  the  grab  and 
allows  the  cars  to  run  to  the  dump 
by  gravity. 

The  overhead  endless-rope  sys- 
tem does  not  work  very  well  on 
curves,  which  should  be  made  as  short 

FIG.  4  as  possible  so  that  one  large  wheel  is 

sufficient  to  carry  the  rope  around 

them.  Branches  may  be  worked  by  the  overhead  rope  system  by  setting  the 
driving  pulley  conveying  power  to  the  side-entry  pulley  so  that  it  will  revolve 
horizontally  above  the  cars  instead  of  vertically  below  them.  As  the  rope 
rises  to  pass  around  the  pulley,  the  cars  are,  of  course,  automatically  detached, 
and,  after  passing  over  the  cross-entry  switches  by  gravity,  are  automatically 
attached  to  the  rope.  The  branch-entry  driving  pulley  is  operated  by  a  friction 
clutch  as  in  the  case  of  an  under-running  rope. 

High  Speed,  or  Reversing,  Endless-Rope  Haulage. — In  high-speed  endless- 
rope  haulage,  the  rope  is  only  in  motion  when  the  cars  are  being  moved.  At 
the  inside  parting,  the  grip  car  pulling  the  trip  is  attached  to  the  rope,  which 
is  put  m  motion  upon  receipt  of  the  proper  signal  at  the  engine  room  outside 
the  mine.  At  the  tipple,  a  flying  switch  is  usually  made  so  that  the  cars  can 
run  m  by  gravity,  and  the  rope  is  stopped.  After  attaching  the  empty  trip 
to  the  grip  cart>the  rope  is  started  in  the  opposite  direction  and  the  empty  trip 
hauled  to  the  inside  parting  usually  upon  the  same  track  used  by  the  loaded 
trip,  but  sometimes  upon  a  separate  track  laid  in  a  parallel  entry.  Where 
but  one  track  is  used  for  traffic  in  both  directions,  the  rope  may  be  returned 
upon  rollers  laid  at  one  side  of  the  main  entry,  or  the  return  air-course  or 
manway  may  be  used  for  the  purpose. 

There  is  no  balancing  of  loads  in  this  system  and  large  and  powerful  engines 
are  required  because  there  may  be  fifty  or  more  cars  in  a  trip  running  at  a 
speed  of  15  to  25  mi.  an  hr.  against  grades  of  3%  and  more.  Balancing  is 
possible  when  two  tracks  are  used  and  an  empty  trip  leaves  the  tipple  for  the 
mine  at  the  same  time  a  loaded  trip  leaves  the  inside  parting  for  the  tipple. 


HAULAGE  791 

The  high-speed  and  endless-rope  and  the  tail-rope  systems  are  used  in  the 
United  States  on  straight  hauls  too  steep  for  motors  and  where  a  large  output 
is  demanded. 

Endless-Rope  Haulage  on  Inclines.— Either  the  underneath  or  overhead 
endless- rope  system  is  well  adapted  to  lowering  coal  over  an  incline  where  the 
grades  are  not  too  steep.  The  rope  is  given  a  sufficient  number  of  turns  around 
the  head-sheave  to  secure  it  against  slipping.  The  head-sheave  is  a  flat, 
grooved  wheel,  similar  to  the  driving  drum  ordinarily  used,  and  its  speed  is 
controlled  by  a  brake.  The  diameter  of  the  head-sheave  and  of  the  tail- 
sheave  at  the  foot  of  the  incline  is  equal  to  the  distance  between  the  center 
lines  of  the  tracks,  which  is  from  8  to  10  ft.  Unlike  ordinary  incline  haulage, 
the  rope  is  in  balance,  and  as  there  are  the  same  number  of  cars  on  each  side 
of  the  rope,  they  also  will  be  in  balance  and  the  weight-producing  motion,  that 
of  the  coal,  is  constant  throughout  the  run;  hence,  less  powerful  brakes  are 
required  than  on  ordinary  inclines.  Where  the  cars  are  not  equally  spaced,  it 
may  possibly  be  necessary  to  install  a  small  engine  at  the  head  of  the  incline 
to  keep  the  rope  in  motion  at  a  speed  of,  say,  3  to  4  mi.  per  hr. 

Calculations  for  Low-Speed,  Endless-Rope,  Haulage  Engines. — In  deter- 
mining the  horsepower  required  of  low-speed,  endless-rope,  haulage  engines 
it  is  usual  to  assume  that  the  conditions  demanded  of  the  plant  are  perfectly 
fulfilled  and  then  to  add  a  liberal  amount  for  the  power  required  to  overcome 
the  irregularities  and  uncertainties  always  met  in  practice.  Thus,  it  is  assumed 
that  there  are  as  many  inbound  empty  cars  as  there  are  outbound  loaded  ones 
and  that  they  are  equally  spaced:  that  the  track  is  level  or  has  a  uniform  grade 
either  for  or  against  the  loaded  side;  that  the  rope  is  continuously  in  motion 
and  the  cars  will  have  the  velocity  of  the  rope  when  they  are  gripped  thereto. 
In  practice,  it  may  happen  that  at  some  given  instant  there  are  no  inbound 
empty  cars,  that  the  outbound  loaded  cars  are  badly  bunched  on  a  steep 
adverse  grade,  where,  the  rope  having  for  some  reason  been  stopped,  they 
must  be  accelerated  from  rest  to  full  speed.  For  these  reasons,  the  engines 
for  low-speed,  endless-rope  haulage  should  have  from  two  to  three  times  the 
horsepower  calculated  on  the  assumption  that  the  conditions  are  perfectly 
fulfilled. 

The  load  to  be  moved  is  that  of  the  coal,  for  the  cars  and  rope  are  in  balance. 
To  the  weight  of  the  coal  must  be  added  the  friction  based  on  the  resistance  to 
motion  of  the  entire  rope  and  all  the  cars.  The  force  required  to  accelerate 
the  system  may  be  neglected. 

EXAMPLE. — In  a  low-speed,  endless-rope,  haulage  system  5,000  ft.  long, 
the  rope,  which  weighs  2  lb.  per  ft.,  has  a  speed  of  3.5  mi.  per  hr.  The  grade 
is  undulating,  but  averages  2%  (1°  9')  against  the  loads.  The  mine  car, 
which  weighs  2,500  lb.,  holds  4,000  lb.  of  coal.  If  friction  is  estimated  at  3%, 
what  will  be  the  theoretical  horsepower  of  the  engines  to  deliver  180  T.  of 
coal  per  hr.  to  the  tipple? 

SOLUTION. — The  speed  of  the  rope  is  (5,280X3.5)^-60  =  308  ft.  per  min. 
There  must  be  delivered  to  the  tipple  1 80 -T- 60  =  3  T.  or  3-7-2  =  1.5  cars  of  coal 
per  minute.  As  the  rope  travels  308  ft.  per  min.,  the  cars  will  be  spaced  308 
-r- 1.5  =  205.3  ft.  apart.  There  will  be  5,000 -=-205.3  =  24.5,  say,  25  cars  on  each 
side  of  the  rope. 

The  total  weight  in  motion  is,  rope  2X5,000X2  =  20,000  lb.;  coal,  25  car- 
loads weighing  25X4,000  =  100,000  lb.;  cars,  2X25  =  50,  weighing  50X2,500 
=  125,000  lb.;  grand  total,  245,000  lb.  At  3%,  the  friction  will  be,  7,350  lb. 

The  formula  for  the  horsepower  is, 

_  (W  sin  X+F  cos  X)S  =  (W  tan  X+F)S 

33.000  33,000 

since,  on  such  a  flat  grade  and  for  practical  purposes  sin  X  =  tan  X  and  cos  X 
=  1.  5  is  the  distance  traveled  by  the  rope,  in  feet  per  minute. 

As  W = 3  T.  =  6,000  lb.  per  min.,  tan  X  =  grade  in  per  cent.  =  .02,  F  =  7,350  lb. 
and  5  =  308  ft.  per  min.,  the  theoretical  horsepower  required  to  keep  the  rope 
and  cars  in  motion  is 

_(W  sin  X+y)5_(6.000X. 02+7.350) X308  , 

'  33,000  33,000 

If  the  rope  should  come  to  rest  at  a  time  when  there  were  no  inbound 
empty  cars  and  the  loads  were  bunched  on  an  adverse  grade,  it  is  probable 
that  150  H.  P.,  possibly  more,  might  be  required  to  get  the  system  again 
in  motion. 

Calculations  for  High-Speed,  Endless-Rope,  Haulage  Engines. — Because, 
in  high-speed,  endless-rope  haulage,  the  entire  system  "must  be  brought  from 


792  HAULAGE 

rest  to  full  speed,  the  engines  must  be  made  sufficiently  large  to  provide  the 
power  required  for  acceleration. 

EXAMPLE. — A  high-speed,  endless-rope,  haulage  system  is  1J  mi.  long. 
The  rope,  which  weighs  2  Ib.  per  ft.,  has  a  sustained  speed  of  15  mi.  per  hr. 
at  the  end  of  60  sec.,  starting  from  rest.  The  grip  car  weighs  5,000  Ib.,  the 
empty  car  weighs  2,500  Ib.  and  carries  5,000  Ib.  of  coal.  The  grade  averages 
2%  against  the  loads  and  friction  is  2.5%.  If  but  one  track  is  used  for  haul- 
age, how  many  cars  must  be  run  in  a  trip  to  give  an  output  of  200  T.  per  hr., 
and  what  must  be  the  net  horsepower  of  the  engines? 

SOLUTION.— The  full  speed  of  the  trip  is  (5,280X1.5) -=-3,600  =  22  ft.  per 
sec.  The  acceleration  is  fl  =  t>-f-/  =  22-f-60  =  .367  ft.  per  sec.  per  sec.,  and  the 
retardation  will  be  the  same.  During  the  joint  periods  of  acceleration  and 
retardation,  the  trip  will  travel  2 X (22X60) -7-2  =  1,320  ft.  in  2  min.  =  120  sec. 
The  remaining  (5,280X1.5)  -1,320  =  6,600  ft.  will  be  covered  in  6,600 -=-22 
=  300  sec.,  and  the  total  time  required  to  haul  out  the  loaded  trip  will  be  120 
+300  =  420  sec.,  or  7  min.  If  3  min.  is  allowed  for  coupling  and  uncoupling 
and  all  delays,  a  trip  will  require  10  min.  and  six  trips  will  be  made  per  hour. 

But  for  each  loaded  trip  going  out  there  must  be  an  empty  trip  going  in. 
Hence,  on  a  single-track  system  but  three  loaded  trips  per  hour  will  be  delivered 
to  the  tipple.  As  each  car  carries  5,000 -J-  2  =  2.5  T. ,  200  -^  2.5  =  80  loaded  cars 
must  be  delivered  each  hour.  The  number  of  cars  per  trip  will  be  80  -5-  3  =  27. 

The  cars  and  the  grip  car  will  weigh  27  X  (5,000+2,500)  +5,000  =  207,500  Ib. 
The  rope  will  weigh  2X(5,280X1.5)X2  =  31,680  Ib.  Hence,  the  total  load 
will  be  239,180  Ib.  As,  on  such  a  flat  grade  cos  X=l,  the  friction  will  be 
239, 180 X. 025  =  5,979. 5  Ib.,  at  a  speed  of  22  ft.  per  sec.,  the  horsepower  neces- 
sary to  overcome  friction  will  be  (5,979.5X22) -7-550  =  239  H.  P. 

To  haul  the  trip  up  grade  will  require,  since  for  practical  purposes  sin  X 
-  tan  X  =  per  cent,  of  grade,  (Wtan  XX  22)  -i-  550=  (207,500  X.  02X22)  -*-  550 
- 166  H.  P. 

To  accelerate  the  entire  system  from  rest  to  a  speed  of  22  ft.  per  sec.  in 
60  sec.,  will  require  the  outlay,  in  force,  of 

f-2-f|f-0X.36T-2,726,b. 

The  horsepower  required  to  accelerate  will  be  (2,726X22)  -f- 550  =  104  H.  P. 

Thence,  the  total  net  horsepower  required  to  overcome  friction,  to  raise 
the  trip  up  the  grade,  and  to  accelerate  the  haulage  system  from  rest  to  full 
speed,  will  be  239  +  166+104  =  509  H.  P.  To  allow  for  the  friction  of  the 
engines,  their  efficiency,  future  demands  for  power,  at  least  600  H.  P.  should 
be  provided,  and  700  would  be  better. 

NOTE. — If,  in  the  example,  the  system  was  double  tracked,  six  loaded 
trips  of  14  cars  each  could  be  brought  out  per  hour  and  as  many  equal  size 
trips  of  empties  hauled  in;  the  capacity  of  the  plant  would  then  be  increased 
from  81  to  84  cars.  The  horsepowers  required  to  overcome  the  various  resis- 
tances would  be,  for  friction  171  H.  P.,  for  grade  56  H.  P.,  and  for  acceleration 
76  H.  P.,  a  total  of  303  H.  P.  Thus,  double  tracking  the  system  and  reducing 
the  loads,  effects  a  saving  in  power  of  a  trifle  more  than  40%.  Similar  economy 
may  be  had  by  reducing  the  speed  from  15  to  7.5  mi.  per  hr.,  but  running 
twenty-seven  car  trips  as  before.  On  the  other  hand,  for  the  same  expenditure 
of  power,  the  capacity  of  a  double-track  system  should  be  about  60%  more 
than  a  single  track. 

TAIL-ROPE  HAULAGE 

General  Arrangement. — The  tail-rope  system  of  haulage  resembles  the 
high-speed  endless-rope  system  in  that  a  single  track  is  used  upon  which  trips 
of  cars  are  run  at  high  speed  (6  to  25  mi.  per  hr.)  in  opposite  directions.  It 
differs  from  the  latter  in  that  the  rope  is  not  continuous  and  that  plain  cylin- 
drical drums  and  not  driving  and  tightening  pulleys  are  used  on  the  haulage 
engine.  There  are  two  ropes  used  in  this  system;  a  main  or  haulage  rope  and 
a  smaller  tail-rope  each  winding  and  unwinding  from  its  own  drum,  which 
revolves  freely  on  its  shaft  and  may  be  thrown  in  gear  by  friction  clutches. 
When  a  loaded  trip  is  to  be  hauled  from  the  inside  parting,  the  main  rope  is 
coupled  to  the  first  car  and  the  tail-rope  to  the  last.  Upon  signal,  the  main- 
rope  drum  is  thrown  in,  the  tail-rope  drum  is  free  on  its  shaft,  and  the  engine 
started.  The  main  rope,  which  is  wound  entirely  on  the  drum  at  the  com- 
pletion of  the  run,  pulls  the  trip  from  the  mine  and  the  trip  drags  the  tail- 
rope  after  it  unwinding  it  from  its  drum.  The  reverse  process,  the  tail-rope 


HAULAGE 


793 


pulling  the  trip  which,  in  turn,  pulls  the  main  rope,  returns  the  empties  to  the 
mine. 

The  general  plan  of  a  tail-rope  plant  with  the  engines  placed  underground 
near  the  foot  of  the  shaft  5  is  shown  in  the  accompanying  figure.  Here  T  is 
the  drum  for  the  tail-rope,  M  that  for  the  main  rope,  and  w  are  the  sheaves, 
one  of  which  is  at  the  end  of  the  main  entry  and  one  at  the  end  of  each  side 
entry  or  district. 
Each  side  entry  has 
a  rope  reaching  from 
its  mouth  to  a  tail- 
sheave  w  at  or  near 
its  inbye  end  and 
back  again  to  the 
main  entry ;  the  rope 
is  provided  at  each 
end  with  couplings 
similar  to  those  on 
the  main-entry 
ropes.  When  an 
empty  trip  is  to  be 
pulled  into  a  side 
entry,  the  main  tail- 
rope  n  is  uncoupled 
from  the  trip  and 
the  branch  rope  / 
coupled  in  its  place. 
The  main  tail-rope 
is  uncoupled  at  h 
and  the  branch  rope 
g  coupled  to  it.  The 
branch  rope  can 
now  pull  the  empties 
and  the  .main  rope 
to  the  end  of  the  side 
entry,  and  the  re- 
verse operation  will 
haul  the  loads  to 
the  mouth  of  the 
side  entry.  If  full 
trips  are  pulled  from 
the  side-entry  part- 
ing to  the  shaft  bot- 
tom, it  is  customary 
to  disconnect  the 
main-line  ropes  in- 
bye n  and  run  the 
trips  through  to  des- 
tination without 
stopping,  effecting 
a  considerable  sav- 
ing in  power  in  hav- 
ing to  accelerate  the 
system  but  once. 

Engines,  Drums, 
Etc.  — Tail-rope 
haulage  engines  are 
almost  always  sec- 
ond-motion or 
geared,  as  the  loads 
and  grades  in  mine 
haulage  are  com- 
monly too  variable  to  permit  of  the  successful  use  of  first-motion  engines. 
Reversing  gear  is  not  needed,  as  the  engines  run  continuously  in  the  same  direc- 
tion, the  direction  of  motion  of  the  trip  being  controlled  by  throwing  the 
proper  drum  in  gear. 

The  drums  are  necessarily  of  much  smaller  diameter  than  those  of  hoisting 
engines,  in  order  to  keep  the  speed  of  the  rope  within  the  prescribed  limits. 
The  flanges  of  the  drums  are  also  deeper  than  usual,  as  several  coils  of  rope  must 


794  HAULAGE 

be  wrapped  upon  one  another,  particularly  if  the  haul  is  long.  The  brake 
power  should  be  ample,  and  the  engineman  must  use  care  not  to  permit  the  idle 
drum  to  turn  too  rapidly  and  thus  pay  off  one  rope  more  rapidly  than  the 
engine  is  winding  the  other  rope  on  its  drum.  Indicators  must  be  provided  to 
show  the  location  of  the  trip  along  the  entry  so  that  it  may  be  stopped  at  the 
mouth  of  any  of  the  side  entries  as  well  as  at  the  end  of  the  main  road.  They 
are 'also  necessary  where  the  direction  of  the  grade  varies,  because,  when  the 
grade  changes  to  one  in  favor  of  the  trip,  steam  must  be  shut  off  and  the  brakes 
applied  to  prevent  the  trip  over-riding  the  rope. 

Sheaves,  Rollers,  Etc. — The  sheaves  used  for  changing  the  direction  of  the 
rope  and  the  method  of  placing  them  under  given  conditions  are  the  same  in 
endless-  and  tail-rope  haulage.  In  some  instances,  large  wood-lagged  drums 
are  used  in  place  of  the  ordinary  iron  deflection  sheaves.  These  drums  may  be 
as  much  as  6  ft.  in  diameter  and  2  ft.  wide,  set  with  their  axles  vertical.  When 
the  grooves  become  too  deep,  the  drum  is  reversed  end  for  end,  thus  subjecting 
all  parts  of  the  lagging  to  wear  and  requiring  less  frequent  renewals.  There 
is,  however,  a  marked  difference  in  the  tail-sheaves  employed  in  the  two 
systems.  In  endless-rope  haulage,  they  are  mounted  upon  a  counterbalance, 
or  tightening  car,  which  is  employed  to  keep  the  rope  at  the  proper  tension; 
in  tail-rope  haulage,  the  tail-sheaves,  which  are  made  of  as  large  diameter  as 
possible  and  may  revolve  either  horizontally  or  vertically,  are  very  firmly 
anchored,  as  the  proper  degree  of  tension  is  maintained  by  manipulating  the 
drums  on  the  engine. 

The  track  rollers  are  the  same  in  the  two  systems.  The  tail-rope  is  usually 
carried  along  one  side  of  the  haulage  entry  near  the  roof  and  upon  short  rollers, 
the  journals  of  which  are  supported  by  parallel  uprights,  2  in.XS  in.  or  a  little 
larger,  which  are  firmly  wedged  between  roof  and  floor. 

Usually,  15  to  20  ft.  of  chain  is  used  between  the  end  of  the  rope  and  the 
trip,  to  prevent  injury  to  the  rope  through  kinking  when  the  trip  is  stopped. 
Knock-off  links,  detaching  hooks,  etc.,  many  of  which  are  automatic,  are  in 
use  for  rapidly  uncoupling  the  rope  from  the  trip.  The  selection  of  any  auto- 
matic device  must  be  made  with  care,  as  accidents  may  arise  through  the 
mechanism  either  acting  at  the  wrong  time  or  place  or  failing  to  act  when  and 
where  it  should. 

Signaling  apparatus  must  be  installed  so  that  the  engineer  may  be  promptly 
notified  to  stop  or  start  the  trip  at  any  point  in  its  course.  At  permanent 
stations,  such  as  the  mai.n  parting  and  the  mouth  and  inbye  end  of  side  entries, 
signals  of  the  push-button  type  or  telephones  are  commonly  used.  To  signal 
from  any  point  along  the  main  roads,  two  bare  copper  wires  are  suspended 
about  6  to  9  in.  apart  along  the  side  of  the  entry.  By  bringing  the  wires  together 
or  by  bridging  the  space  between  them  with  a  piece  of  copper  or  iron,  a  signal 
may  be  sent  to  the  engine  room. 

Comparison  of  Endless-  and  Tail-Rope  Haulage. — Where  the  road  is 
straight,  the  grades  uniform,  and  no  branches  are  worked,  there  is  little  choice 
between  the  high-speed  endless-rope  and  the  tail-rope  haulage  systems,  except 
that  the  latter  requires  50%  more  rope,  but,  on  the  other  hand,  it  can  use  a 
simpler  engine,  as  its  direction  of  motion  is  not  reversed.  On  curves,  the 
endless  rope  must  be  carried  around  small  sheaves  placed  in  the  center  of  the 
track;  this  arrangement  is  not  nearly  as  satisfactory  as  in  the  tail-rope  system 
where  large  sheaves  are  placed  outside  the  rails.  On  down-grades,  since  the 
trip  is  attached  to  the  rope  at  but  one  point  (the  grip  car),  there  is  always 
the  possibility  of  its  over-riding  and  injuring  the  rope.  The  tail-rope  system 
is  greatly  the  superior  of  the  endless-rope  in  working  branches,  not  only  from 
the  standpointtof  labor,  but  of  ease  and  efficiency.  The  horsepower  demanded 
of  the  engines  is  the  same  in  either  system. 

The  chief  advantages  of  the  ordinary,  low-speed,  endless-rope,  haulage 
system,  are  the  regular  delivery  of  single  cars  to  the  tipple  permitting  a  better 
regulation  of  labor  than  where  the  cars  come  in  large  trips;  economy  in  instal- 
lation, as  the  low  speed  does  not  demand  the  use  of  such  large  engines  or  such 
heavy  rails,  ties,  etc.;  less  liability  of  accident  through  the  cars  jumping  the 
track;  less  cost  for  upkeep,  as  the  wear  on  the  roadbed  and  rolling  stock  is 
much  less_at  low  than  at  high  speeds;  less  power,  and  consequently  less  fuel,  is 
required ;  it  is  more  easily  extended ;  and  requires  one-third  less  rope. 

The  disadvantages  of  the  low-speed  endless-rope  system  are  the  cost  of 
laying  and  keeping  up  two  sets  of  tracks,  which,  where  the  roof  is  poor  may  be 
a  serious  matter  even  if  parallel  entries  instead  of  one  double-width  entry  are 
used ;  where  branches  must  be  worked,  the  cost  for  labor  is  high  and  the  service 
is  not  satisfactory;  and  it  is  not  so  efficient  on  crooked  roads  with  undulating 


HAULAGE  795 

grades  as  the  tail-rope  system  for  the  reasons  just  given.  Also,  when  the 
workings  become  extensive  and  the  haulageways  long,  the  number  of  cars 
required  to  keep  up  the  output  is  excessive,  and  the  large  number  of  cars  con- 
siderably increases  the  strain  on  the  rope  and  the  power  demanded  of  the 
engine. 

The  tail-rope  system  is  at  a  disadvantage  in  those  states  where  the  speed 
of  the  trip  is  limited  by  law  to  6  to  8  mi.  per  hr.  Where  the  track  and  cars 
are  in  poor  condition  and  the  entries  are  crooked  a  speed  of  even  8  mi.  per  hr. 
may  be  excessive,  but  on  modern  roads,  as  maintained  in  first-class  mines,  and 
with  proper  rolling  stock,  speeds  of  20  mi.  per  hr.  and  more  are  perfectly 
allowable;  and  high  speed  is  an  essential  to  the  successful  operation  of  tail- 
rope  haulage. 

Calculations  for  Tail-Rope  Haulage. — The  calculations  for  the  horsepower 
required  in  tail-rope  haulage  are  made  in  the  same  way  as  those  in  high-speed 
endless-rope  haulage,  provision  being  made  for  the  power  required  to  acceler- 
ate the  drum.  In  the  event  of  the  grades  being  variable,  the  power  should 
be  sufficient  to  start  and  accelerate  the  trip  on  the  most  adverse  grade. 


STEAM-LOCOMOTIVE  HAULAGE 

The  large  volumes  of  dense  smoke  given  off  by  the  fuel,  combined  at  times 
with  sulphur  fumes  and  always  with  the  exhaust  steam,  have  prevented 
the  extensive  use  of  steam  locomotives  in  the  bituminous  mines  of  the  United 
States.  For  these  reasons  and  because  of  the  danger  from  fire,  either  through 
igniting  the  timbers  or  methane,  the  use  of  these  locomotives  has  been  pro- 
hibited by  _  law  in  many  states.  In  the  anthracite  regions  of  Pennsylvania, 
where,  until  recent  years,  the  coal  worked  was  much  thicker  than  in  the  bitu- 
minous fields  and  where,  also,  the  coal  is  smokeless,  steam  locomotives  have 
not  proved  so  objectionable,  and  they  are  still  quite  extensively  used  for 
underground  haulage  on  return  air-courses  and  on  the  surface  for  hauling 
between  the  mine  and  the  breaker,  etc. 

The  steam  locomotive  possesses  the  advantages  of  low  first  cost,  of  not 
requiring  a  power  plant,  as  do  compressed-air  or  electric  locomotives,  and  of 
being  readily  understood  and  operated  by  the  average  mine  mechanic.  The 
last  feature  is  of  importance  in  securing  an  engine  runner  in  outlying  districts 
where  skilled  labor  is  scarce.  The  advantage  of  carrying  their  own  power, 
that  is,  of  being  self-contained,  is  shared  alike  with  compressed-air,  gasoline, 
and  storage-battery  electric  locomotives.  For  the  reasons  given  in  the  first 
paragraph,  they  can  only  be  used  on  return  air-courses  and  not  then  if  the 
amount  of  gas  present  is  at  all  considerable  or  if  the  mine  is  liable  to  sudden 
outbursts  of  methane;  hence,  they  are  not  adapted  to  gathering  either  from 
rooms  or  from  side  entries.  This  necessitates  the  use  of  some  power  other 
than  steam  for  that  purpose ;  and  the  use  of  two  kinds  of  power  is  not  generally 
economical  and  is  to  be  avoided  whenever  possible. 

Steam  Mine  Locomotives. — Steam  mine  locomotives  are  generally  similar  to 
the  small  locomotives  used  for  switching  on  surface  railroads.  They  have  four  or 
six  drivers,  no  pony  truck  or  tender,  and  carry  their  water  in  a  saddle  tank  over 
the  boiler  and  their  coal  in  a  box  in  the  cab.  When  four  drivers  are  used,  all 
have  flanges;  when  six  drivers  are  used,  the  middle  pair  are  not  flanged  in  order 
that  the  locomotive  may  more  readily  pass  around  curves.  The  height  of  the 
locomotive  should  be  from  14  in.  to  16  in.  less  than  the  thickness  of  the  seam, 
in  order  to  give  about  4  in.  overhead  clearance. 

The  wheel  base  of  these  locomotives,  which  must  be  as  small  as  possible 
to  permit  of  easy  passage  around  the  sharp  curves  common  in  mines,  varies 
from  3  ft.  0  in.  on  the  small  four-wheel  engine  weighing  8,000  lb.,  to  8  ft.  6  in. 
on  the  largest  six-wheel  engine  weighing  64,000  lb.  These  locomotives  are 
provided  with  reversing  gear,  couplers  at  both  ends,  and  the  sand  box  is  arranged 
to  deliver  sand  to  the  rail  when  the  engine  is  running  in  either  direction. 

The  table  on  page  796  gives  the  manufacturers'  dimensions,  weights,  power, 
etc.,  of  standard  four-wheel  steam  mine  locomotives. 

Power  of  Steam  Locomotives. — The  tractive  force,  or  tractive  effort,  of  a 
locomotive  is  the  total  force  developed  by  it  that  is  available  for  moving  a 
load ;  this  depends  on  the  size  of  the  cylinders,  the  diameter  of  the  driving  wheels, 
and  the  steam  pressure.  The  tractive  power  of  a  locomotive  is  the  measure  of 
its  ability  to  pull  a  load  and  depends  on  the  adhesion  between  the  driving 
wheels  and  the  rails,  which,  in  turn,  depends  on  the  weight  of  the  locomotive 
and  the  coefficient  of  friction.  Under  ordinary  conditions,  and  also  on  a  wet. 


796 


HAULAGE 


sanded  rail,  the  adhesion  or  adhesive 
power  as  it  is  generally  called,  is  about 
one-fifth  the  weight  of  the  locomotive; 
with  favorable  conditions  and  a  dry 
rail  without  sand,  it  is  about  one-fourth; 
and  on  a  well-sanded  dry  rail,  about 
one-third  the  weight. 

If  the  tractive  force  of  a  locomotive 
exceeds  the  adhesive  power,  the  wheels 
will  slip  and  part  of  the  tractive  power 
will  be  wasted.  The  power  driving  the 
locomotive  and  the  weight  on  the  driv- 
ing wheels  must,  therefore,  be  properly 
proportioned  to  obtain  satis  factory 
results,  for  if  the  cylinders  of  a  steam 
or  an  air  locomotive  are  too  large  the 
driving  wheels  will  slip,  showing  that 
there  is  too  much  power  for  the  weight. 
A  locomotive  in  this  condition  is  said 
to  be  over 'Cylinder -ed.  On  the  other 
hand,  if  there  is  not  enough  power  for 
the  weight,  so  that  the  wheels  will  not 
move,  the  locomotive  is  said  to  be 
under  cylinder  ed.  The  sustained  trac- 
tive power,  that  is,  the  power  exerted 
by  a  locomotive  when  traveling  at  its 
normal  speed  and  which  is  a  measure 
of  the  load  it  will  pull  continuously  is 
commonly  taken  as  25%  of  the  weight 
of  the  locomotive;  and  this,  whether 
the  motive  power  is  steam,  compressed- 
air,  gasoline,  or  electricity. 

The  drawbar  pull  of  a  locomotive  is 
that  portion  of  its  tractive  power  that 
is  available  for  pulling  a  load;  that  is, 
it  is  the  total  tractive  power  less  the 
power  required  to  move  the  machine 
itself.  The  drawbar  pull  may  be  meas- 
ured by  a  dynamometer  placed  between 
the  locomotive  and  the  first  car  of  the 
trip.  The  terms  tractive  power  and 
drawbar  pull  are  often  used  to  express 
the  same  idea.  While  such  use  is  never 
strictly  correct,  on  a  level  track  the 
weight  of  the  locomotive  is  such  a  very 
small  proportion  of  the  weight  it  can 
pull,  that  the  statement  is  practically 
true.  Thus,  the  hauling  capacity  of  a 
42,000-lb;  locomotive  is  given  by  the 
manufacturers  as  1,255  T.  on  a  level 
track.  As  the  weight  of  the  locomo- 
tive is  but  21  T.,  or  less  than  2%  of  the 
weight  it  can  pull,  the  reduction  to  be 
made  from  the  tractive  power  to  get 
the  drawbar  pull  is  of  no  practical  im- 
portance. On  an  up  grade,  however, 
while  the  tractive  power  remains  the 
same,  the  drawbar  pull  decreases  rapidly 
on  account  of  the  increased  amount  of 
power  required  to  run  the  locomotive 
itself. 

On  long  hauls,  the  average  draw- 
bar pull  required  should  be  well  within 
the  rated  pull,  while,  on  short  hauls 
and  for  intermittent  service,  a  locomo- 
tive may  be  operated  at  its  rated  ca- 
pacity. The  sharpest  grade  against  the 
loaded  trip  should  be  used  in  calculat- 


HAULAGE  797 

ing  the  size  of  a  locomotive,  and  on  a  short  grade,  a  locomotive  may  be  worked 
very  close  to  the  maximum  adhesive  power,  or  slipping  point,  as  it  is  called. 
The  following  empiric  formula  is  C9mmonly  used  by  manufacturers  to 
determine  the  tractive  power  of  steam  mine  locomotives: 


d 
in  which  T  =  tractive  power,  in  pounds; 

D  =  diameter  of  cylinder,  in  inches; 

L  =  length  of  piston  stroke,  in  inches; 

P  =  boiler  pressure,  in  pounds  per  square  inch; 

d  =  diameter  of  driving  wheels,  in  inches. 

From  this  formula,  it  is  apparent  if  the  steam  pressure  is  increased  or 
decreased,  the  tractive  power  will  be  similarly  affected.  Likewise,  if  the  boiler 
pressure  remains  the  same,  an  increase  in  the  diameter  of  the  driving  wheels 
is  accompanied  by  a  decrease  in  the  tractive  power,  and  vice  versa.  Thus, 
on  surface  railroads,  freight  locomotives  which  must  have  great  tractive  power 
have  relatively  small  drivers,  whereas  locomotives  used  in  express  service 
where  speed  and  not  ability  to  haul  heavy  loads  is  of  the  greatest  importance, 
have  large  drivers.  Taking  the  mean  effective  pressure  of  the  steam  in  the 
cylinders  as  85%  of  the  boiler  pressure  (.85£)  allows  for  the  friction  of  the 
locomotive  itself;  hence,  on  level  roads  the  drawbar  pull  may  be  taken  to  be 
the  same  as  the  tractive  power  calculated  by  the  formula.  The  internal 
frictional  resistance  of  locomotives  is  usually  taken  as  6.5  to  7.5  Ib.  per  T. 
of  the  weight  on  the  drivers,  while  the  tractive  power  is  taken  as  300  to  450  Ib. 
per  T. 

EXAMPLE.  —  What  are  the  tractive  power  and  drawbar  pull  of  a  steam  mine 
locomotive,  weighing  14,000  Ib.,  with  6"X10"  cylinders  and  drivers  23  in.  in 
diameter,  when  the  boiler  pressure  is  140  Ib.  per  sq.  in.,  both  on  a  level  track 
and  on  a  2.5%  grade? 

SOLUTION.  —  By  substituting  in  the  foregoing  formula,  the  tractive  power  on 
a  level  track  is  found  to  be 

e^X  IPX.  85X140 
j=  —    —  —  —     —  =  1,  sou  ID. 

The  drawbar  pull  may  be  taken  as  the  same. 

On  the  grade,  while  the  tractive  power  is  the  same,  the  drawbar  pull  is  less 
than  this  by  the  amount  of  power  required  to  move  the  locomotive  itself  up 
grade,  or  by  14,000  X.  025  =  350  Ib.  The  drawbar  pull  on  a  2.5%  grade  is, 
thence,  1,860-350  =  1,510  Ib. 

EXAMPLE.  —  How  many  loaded  cars  weighing  7,500  Ib.  each  can  be  pulled 
up  a  2%  grade  by  a  locomotive  weighing  25,000  Ib.,  if  it  has  9"X  14"  cylinders, 
28-in.  drivers,  and  a  steam  pressure  of  140  Ib.;  the  friction  of  the  mine  cars 
being  taken  as  30  Ib.  per  T.? 

SOLUTION.  —  The  tractive  power,  which  may  be  calculated  from  the  formula 
or  taken  from  the  table,  is  4,800  Ib.  The  resistance  to  motion,  in  pounds 
per  ton,  is  for  friction  30  Ib.  and  for  the  grade  2,000  X.  02  =  40  Ib.;  or  a  total 
of  70  Ib.  Whence  the  total  tractive  power  of  the  locomotive  on  a  2%  grade, 
when  expressed  in  terms  of  car  resistance,  is  4,820-f-70  =  69  T.,  very  nearly. 
Since  the  locomotive  weighs  25,000  lb.  =  12.5  T.,  the  drawbar  pull,  in  the 
same  terms,  is  69.0-  12.5  =  56.5  T.  Because  each  car  weighs  7,500  Ib.  =  3.75  T., 
the  locomotive  can  pull  up  the  grade  56.5-7-3.75  =  15  cars. 

The  method  just  given  assumes  that  the  friction  of  the  locomotive  is  the 
same  as  that  of  the  cars,  which  is  not  correct.  The  friction  of  the  locomotive 
is  only  about  one-quarter  that  of  a  car  and,  as  stated,  is  allowed  for  in  the 
formula  by  means  of  which  the  tractive  power  of  the  locomotive  is  calculated. 
The  following  method  may,  then,  be  preferred:  The  power  required  to  move 
the  locomotive  up  the  grade  is  25,  000  X.  02  =  500  Ib.  Whence,  the  drawbar 
pull  is  4,820-500  =  4,320  Ib.  The  grade  resistance  per  car  is  7.500X.02 
=  150  Ib.  and  the  frictional  resistance  is  3.75X30=  112.5  Ib.;  whence  the  total 
resistance  per  car  is  262.5  Ib.,  and  the  locomotive  can  haul  4,320  -T-  262.5 
=  16+  cars. 

In  the  foregoing  calculations,  no  allowance  is  made  for  the  power  required 
to  accelerate  the  locomotive  and  train,  n9r  is  such  an  allowance  generally 
necessary  because  of  the  slow  speed  of  mine  traffic  and  because  the  excess 
of  power  that  may  be  temporarily  developed  on  a  well-sanded  rail  is  generally 
ample  to  produce  the  acceleration.  However,  it  may  be  readily  calculated 
when  necessary. 


798  HAULAGE 

EXAMPLE. — If,  in  the  last  example,  it  requires  1  min.  to  bring  the  trip  from 
rest  to  the  legal  speed  of  6  mi.  per  hr.,  how  many  cars  can  the  locomotive  pull 
up  grade? 

SOLUTION.— A  speed  of  6  mi.  per  hr.  =  (5,280X6)4-3,600  =  8.8  ft.  per  sec., 
and  the  acceleration  is  a  =  Z>-H<  =  8.8-7-60  =  .147  ft.  per  sec.  per  sec.  The 

TTT  O  PC   OOO 

power  required  to  accelerate  the  locomotive  is  — a  =  -;^—-X.147  =  114  Ib. 

From  this,  the  net  drawbar  pull  is  4,320— 114  =  4,206  Ib.     The  power  required 

7  500 
to  accelerate  a  mine  car  is  ^r-r-X.147  =  35  Ib.,  and  the  total  resistance  of 

O4.<& 

each  car  is  262.5+35  =  297.5  Ib.  Hence,  the  locomotive  can,  on  this  grade, 
start  a  trip  of  4,206 -f- 297.5  =  14+  cars  and  bring  them  to  a  speed  of  6  mi.  per 
hr.  at  the  end  of  1  min.  The  gain  in  adhesion  by  sanding  the  rails  will  unques- 
tionably permit  of  the  locomotive  accelerating  the  15  cars  which  the  preceding 
example  shows  it  can  pull  up  the  grade. 

Speed  of  Steam-Locomotive  Haulage. — A  locomotive  cannot  pull  a  maxi- 
mum load  at  a  maximum  speed.  As  the  load  increases  the  speed  decreases  and 
vice  versa,  but  no  general  rule  or  formula  can  be  given  which  exactly  fixes  the 
relation  between  the  load  and  the  speed.  Experience  has  shown  that  the  rela- 
tion between  the  load  and  speed  of  mine  locomotives  is  approximately  as  follows: 

Under  usual  track  conditions,  the  speed  in  miles  per  hour  attainable  when 
hauling  a  train  as  heavy  as  the  locomotive  can  start,  will  be  equal,  to  about 
one-fifth  the  diameter  of  the  driving  wheels,  in  inches. 

If  the  load  is  reduced  to  two-thirds  to  three-fourths  of  the  maximum,  the 
speed  will  be  about  one-half  the  diameter  of  the  driving  wheels,  in  inches. 

If  the  load  is  very  light,  say  about  one-eighth  of  the  maximum,  the  speed 
will  be  equal  to  or  greater  than  the  diameter  of  the  drivers,  in  inches. 

Thus,  a  locomotive  with  30-in.  wheels  which  can  start  a  load  of,  say,  800  T. 
on  a  level  track,  will  pull  this  at  a  speed  of  30-j-5  =  6  mi.  per  hr.;  if  the  load  is 
reduced  to,  say,  550  to  600  T.,  the  speed  will  be  increased  to  about  50 -r- 2 
=  25  mi.  per  hr.;  and  if  the  load  is  still  further  reduced  to  about  100  T.,  the 
speed  will  rise  to  30  mi.  per  hr.,  or  more. 

Horsepower  of  .Locomotives. — The  horsepower  that  may  be  developed  by 
a  steam  locomotive  is  usually  calculated  from  the  formula, 
„  p  _D*XLX.85PXS 

dX375 

that  is,  the  horsepower  of  a  locomotive  is  equal  to  the  tractive  power  multi- 
plied by  the  speed  5,  in  miles  per  hour,  divided  by  375. 


COMPRESSED-AIR  HAULAGE 

As  compressed-air  locomotives  are  self-contained  they,  like  steam  and 
storage-battery  locomotives,  can  travel  wherever  tracks  are  laid.  They  have 
the  great  advantage  over  steam  locomotives  that  they  cannot  set  fire  to  methane, 
timber,  or  coal  dust,  and  therefore  may  safely  be  used  in  gaseous,  heavily 
timbered,  or  dusty  mines.  There  are  no  boilers  or  fireboxes,  and  hence  fewer 
repairs  are  needed ;  there  is  no  danger  from  boiler  explosions,  and  they  are  more 
easily  and  cheaply  kept  in  repair  than  steam  locomotives.  As  they  do  not  give 
off  any  smoke  or  injurious  gas,  they  may  be  used  in  any  part  of  any  mine,  and 
for  gathering,  and  their  exhaust  tends  to  improve  the  ventilation.  On  the 
other  hand,  their  use  requires  the  installation  of  a  more  or  less  expensive 
power  plant,  storage  tanks  or  lines,  pipe  lines,  etc.,  although  only  a  part  of  the 
entire  outlay  is  chargeable  to  haulage  where  compressed-air  coal-cutting 
machines  are  used.  They  are  not  so  high  as  steam  locomotives  of  the  same 
tractive  power  and  may  therefore  be  used  in  thinner  seams,  but  their  greater 
length  prohibits  their  employment  on  sharp  curves  if  the  entries  are  narrow. 
They  are,  also,  no  exception  to  the  rule  that  locomotives  of  all  types  work 
uneconomically  on  grades  because  of  the  large  amount  of  power  required  to 
propel  the  motor  itself.  A  compressed-air  haulage  plant  will  generally  cost 
more  than  an  electric  plant  of  the  same  working  capacity,  but  there  is  no  danger 
of  electric  shock  where  it  is  used,  nor  of  igniting  methane  or  coal  dust  by  the 
arc  produced  when  electric  power  lines  come  in  contact  with  one  another  or 
with  metal. 

A  compressed-air  haulage  plant  consists  of  an  air  compressor  driven  by  a 
steam  engine  or  by  an  electric  or  hydraulic  motor,  which  compresses  the  air 
to  a  pressure  of  1,000  Ib.  per  sq.  in.  or  more;  a  storage  system  for  the  air  until 


HAULAGE  799 

it  is  needed  by  the  locomotive,  which  may  consist  of  receivers  or  tanks,  but  is 
usually  the  pipe  line  connecting  the  compressor  with  the  charging  stations 
where  the  engine  receives  its  supply  of  air;  and  one  or  more  locomotives,  which 
may  be  either  simple  or  compound. 

Simple,  or  Single-Stage,  Compressed-Air  Locomotives. — A  compressed-air 
locomotive  has  the  driving  and  running  gear  of  a  steam  locomotive,  but  the 
boiler  of  the  latter  is  replaced  by  a  long,  riveted,  steel-plate,  storage  tank 
containing  the  supply  of  air  under  a  pressure  of  from  800  to  1,000  Ib.  per  sq.  in. 
These  tanks  vary  from  26  to  42  in.  in  diameter,  from  7  to  22  ft.  in  length,  and 
from  50  to  350  cu.  ft.  in  capacity,  their  size  depending  on  the  air  consumption 
of  the  locomotive,  which  is  determined  largely  "by  the  length  of  time  it  must 
run  without  recharging.  When  necessary  to  reduce  the  height  of  the  loco- 
motive, the  single  tank  may  be  replaced  by  two  or  more  smaller  ones,  the 
combined  capacity  of  which  is  equal  to  the  one  large  one.  In  cases  where 
the  length  of  the  haul  requires  unusual  storage  capacity  and  the  size  of  the 
locomotive  is  limited  by  the  height  or  width  of  the  entry  or  like  practical 
considerations,  it  is  customary  to  use  pressures  up  to  2,000  to  2,500  Ib.  per 
sq.  in.  The  single  riveted-steel  tank  is  then  replaced  by  a  series  of  very  heavy 
seamless  steel  tubes  about  9  in.  in  diameter;  but  these  excessive  pressures  are 
very  rarely  used  about  mines. 

The  air  passes  from  the  high-pressure,  main  storage  tank  to  the  auxiliary 
tank  or  reservoir,  which  is  about  9  in.  in  diameter  and  two-thirds  as  long  as 
the  main  tank.  In  this  it  is  held  at  the  working  pressure  of,  usually,  140  Ib. 
per  sq.  in.,  and  passes  from  it  directly  to  the  cylinders.  Between  the  tanks  is 
an  automatic  reducing  valve  and  sometimes  a  stop-valve.  The  object  of  the 
former  is  to  maintain  automatically  a  uniform  pressure  in  the  auxiliary  reservoir 
and  consequently  in  the  cylinders.  The  stop-valve,  when  used,  is  placed 
between  the  storage  tank  and  the  reducing  valve  and  is  controlled  by  the  same 
lever  as  the  throttle  valve.  When  the  latter  is  open  the  stop-valve  is  open, 
thus  admitting  air  to  the  auxiliary  reservoir  only  as  air  is  drawn  from  that  into 
the  cylinders,  and  preventing  leakage  between  the  two. 

The  air  passes  from  the  auxiliary  tank  to  the  cylinders  through  a  balanced 
throttle  valve,  which  permits  of  the  maintenance  of  a  constant  working  pres- 
sure, prevents  waste  of  air,  and  makes  the  locomotive  more  easily  managed. 
A  stop- valve  is  placed  between  the  auxiliary  tank  and  the  throttle  valve  to 
prevent  leakage  of  air  past  the  latter  into  the  cylinders. 

These  locomotives  are  provided  with  a  safety  valve,  reversing  gear,  oil 
cups,  whistle,  head-  and  tail-lights,  sand  box,  and  the  other  accessories  of 
steam  locomotives.  They  may  have  either  four  or  six  drivers,  the  latter, 
because  of  their  relatively  long  wheel  base,  being  the  better  adapted  to  long 
straight  hauls.  The  table  on  page  800  gives  the  dimensions  of  the  standard, 
or  stock,  sizes  of  these  locomotives  as  made  by  the  H.  K.  Porter  Company, 
Pittsbucg,  Pa.,  although  they  have  been  largely  displaced  by  the  two-stage 
motors  described  later. 

Reheating  Compressed  Air. — The  efficiency  of  compressed  air  can  be 
greatly  increased  by  reheating  before  admitting  it  into  the  cylinders,  but  in 
haulage  machinery  the  added  complication  of  the  mechanism  needed  for  the 
purpose  is  seldom  justified  by  the  saving  in  fuel  or  the  increased  efficiency, 
except  where  the  haul  is  very  long  or  where  the  price  of  fuel  is  high.  The 
first  condition  rarely  and  the  second  never  exists  in  coal-mining  practice.  The 
air  may  be  heated  before  entering  the  cylinders  by  partially  filling  the  auxiliary 
air-storage  tank  with  water,  which  is  kept  hot  by  the  injection  of  steam  while 
the  main  tanks  are  being  filled  at  the  charging  station.  Indirectly,  this 
method  of  heating  increases  the  efficiency  in  another  way;  the  moisture  taken 
up  by  the  air  from  the  hot  water  improves  the  lubrication  in  the  valves  and 
cylinders.  The  cylinders  of  compressed-air  locomotives  are  not  lagged  as  are 
those  of  steam-locomotives  and,  further,  they  are  sometimes  cast  with  the 
outside  corrugated  so  as  to  increase  the  surface  exposed  to  the  relatively  warm 
mine  air. 

The  air  may  be  effectively  heated  in  a  device  known  as  an  interheater,  which 
is  explained  under  Compound  Locomotives. 

Compound,  or  Two-Stage,  Compressed-Air  Locomotives. — There  is  no 
essential  difference  in  mechanical  construction  and  accessories  between  the 
simple,  or  single-stage,  and  the  compound,  or  two-stage,  compressed-air 
locomotive.  -  In  the  latter,  the  air  in  the  auxiliary  reservoir  is  under  250  Ib.  per 
sq.  in.  pressure  (as  opposed  to  140  Ib.  in  the  simple  locomotive)  and  passes 
to  a  single  high-pressure  cylinder  through  the  usual  stop  and  throttle  valves. 
In  the  high-pressure  cylinder,  the  air  is  expanded  down  from  250  to  50  Ib. 


800 


HAULAGE 


.     2 


s 


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o     10 

3.fO        CO 
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5  §§« 


1.B 


HAULAGE  801 

pressure  and  is  reduced  in  temperature  to  about  140°  P.  below  that  of  the 
atmosphere  or,  say,  from  60°  above  to  80°  below  zero.  In  order  to  restore  as 
much  as  possible  of  this  lost  heat  to  the  air,  the  high-pressure  exhaust  passes 
into  an  interheater,  which  consists  of  a  cylindrical  tank  surrounding  a  number 
of  brass  or  aluminum  tubes  of  small  diameter.  The  exhaust  from  the  low- 
pressure  cylinder,  by  means  of  a  device  like  the  exhaust  nozzle  of  a  steam 
locomotive,  draws  the  warm  mine  air  through  the  thin  tubes  of  the  interheater, 
and  the  high-pressure  exhaust  which  is  circulating  around  and  between  these 
tubes  is  raised  in  temperature  to  within  about  15°  of  that  of  the  mine  air 
or,  say,  to  45°  F.  After  being  heated,  the  air  is  led  to  the  low-pressure  cylinder 
or  cylinders,  where  its  pressure  is  reduced  from  50  Ib.  t9  that  of  the  atmosphere, 
and  is  then  exhausted  and  used  to  draw  air  through  the  interheater,  as  explained. 
In  expanding  from  250+14.7  =  264.7  Ib.  pressure  at  460 +60  =  520°  tempera- 
ture to  50  + 14.7  =  64.7  Ib.  pressure  at  460  —  80  =  380°  temperature,  both  pressure 
and  temperature  being  absolute,  one  volume  of  exhaust  air  from  the  high- 
pressure  cylinder  will  be  increased  to  -^~-  X^  =  2.99  volumes.  In  the 
interheater,  the  temperature  is  increased  from  380°  to  460+45  =  505°  absolute, 
and  its  volume  from  2.99  to  2.99X~  =  3.97+,  or  to,  say,  4  volumes.  For 

OoU 

this  reason,  the  area  of  the  low-pressure  cylinder  or  cylinders  is  made  four 
times  as  great  as  that  of  the  high-pressure  cylinder  so  that  the  work  don«  in 
them  may  be  the  same. 

The  cylinders  _  are  arranged  in  one  of  two  ways.  In  the  smaller  locomo- 
tives, there  are  single  high-pressure  and  low-pressure  cylinders,  one  on  each 
side,  the  latter  having  twice  the  diameter  or  four  times  the  area  of  the  former. 
Consequently,  the  over-all  width  of  the  locomotive  is  greater  on  the  low-pressure 
than  on  the  high-pressure  side.  In  the  larger  locomotives,  there  are  two 
low-pressure  cylinders  arranged  in  tandem  whose  joint  area  is  four  times  that 
of  the  single  high-pressure  cylinder  but  whose  diameters  are  to  that  of  the 
high-pressure  cylinder  as  1  :  A/2,  that  is,  as  1  :  1.414.  The  object  of  two, 
instead  of  one,  low-pressure  cylinders  is  to  reduce  the  over-all  width  on  the 
low-pressure  side. 

These  locomotiyes  are  furnished  with  either  four  or  six  drivers,  but  the 
latter,  owing  to  their  long  wheel  base  and  consequent  stiffness  on  sharp  curves, 
are  not  recommended  unless  the  haulage  road  is  straight  or  the  lightness  of  the 
rail  requires  that  the  weight  of  the  engine  should  be  distributed  over  a  greater 
length  of  track.  Where  loaded  cars  must  be  pulled  out  of  dip  places  to  the 
entry  or  where  empty  cars  must  be  pulled  to  the  face  of  a  pitching  room,  the 
locomotive  is  provided  with  a  reel  or  drum  holding  from  300  to  1,000  ft.  of  wire 
rope,  the  drum  being  turned  by  a  small  engine  operated  by  compressed  air 
while  the  motor  is  blocked  on  the  rails.  For  use  in  very  narrow  places,  the 
cylinders  are  placed  between  the  drivers,  that  is,  the  locomotive  is  inside 
connected.  For  exceptionally  long  hauls  an  extra  supply  of  air  may  be  carried 
in  a  tender  but  as  the  weight  of  the  latter  reduces  the  paying  load  the  loco- 
motive can  haul,  it  is  better  practice  to  increase  the  pressure  in  the  main 
storage  tank  2,000  or  2,500  Ib.,  as  heretofore  explained. 

The  gain  in  efficiency  through  using  two-stage  instead  of  single-stage 
expansion  is  very  considerable,  amounting  to  40  and  even  60%  in  cases. 

Dimensions  of  Two-Stage  Compressed-Air  Locomotives. — The  following 
table  gives  the  dimensions  of  standard  two-stage  compressed-air  locomotives 
manufactured  by  the  H.  K.  Porter  Company,  Pittsburg,  Pa.  In  all  cases,  the 
charging  pressure  is  between  700  and  1,200  Ib.  and  the  working  pressure  is 
250  Ib.  in  the  high-pressure  and  50  Ib.  in  the  low-pressure  cylinder.  The 
tank  pressure  and  capacity  are  adjusted  by  the  manufacturer  to  suit  local 
conditions  and  requirements.  The  weight  of  the  locomotive  for  the  same 
size  of  cylinders  depends  on  the  gauge  of  the  track,  capacity  of  the  storage 
tanks,  etc.  In  special  cases,  the  width  outside  the  gauge  line  may  be  made 
less  than  that  given  in  the  table.  The  height  of  the  entry  must  be  at  least  2 
in.  more  than  that  of  the  locomotive  above  the  rail  to  provide  the  necessary 
headroom. 

The  first  four  locomotives,  which  have  one  high-  and  one  low-pressure 
cylinder,  make  a  class  by  themselves.  By  reason  of  their  moderate  storage 
capacity  and  lightness  they  are  adapted  to  gathering  and  the  short  wheel 
base  recommends  them  for  use  on  crooked  entries.  They  can  be  made  for  any 
width  of  track  and  their  height,  which  is  not  given  in  the  table,  is  less  for  wide 
then  for  narrow  gauges. 

51 


802 


HAULAGE 


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HAULAGE 


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Main  r 
Weigh 
Tracti 
Lighte 
Radius 
Radius 


The  second  four  locomotives,  all 
but  the  first  of  which  have  two  low- 
pressure  cylinders,  have  four  drivers 
and  are  standard  for  main  line  service. 

The  last  four  locomotives  are  also 
standard  for  main  line  use,  and  are 
the  same  as  the  preceding  four  except 
that  they  have  six  drivers  and  conse- 
quently are  stiffer  on  curves. 

Tractive  Power  of  Compressed- 
Air  Locomotives.  —  The  tractive  power 
and  drawbar  pull  of  compressed-air 
locomotives  are  calculated  by  the  same 
methods  as  those  of  steam  locomo- 
tives. Since  the  efficiency  of  the  air 
is  increased  by  absorbing  heat  from 
the  cylinders,  pipes,  etc.,  at  seven- 
eighths  cut-off,  which  is  practically 
full  stroke,  the  cylinder  pressure  may 
be  taken  as  98%  of  the  auxiliary-tank 
pressure  and  not  as  85%  of_the  boiler 
pressure  as  in  steam  locomotives.  For 
earlier  cut-offs,  the  efficiency  is  less 
than  this;  but  in  any  case,  for  equal 
cut-off,  the  efficiency  of  air  is  greater 
than  steam.  The  formula  for  the 
tractive  power  of  a  compressed-air 
locomotive,  as  modified  from  that  of 
a  steam  locomotive  is,  thence, 


^ 


d 


in  which  the  symbols  have  the  mean- 
ings given  for  steam  locomotives,  ex- 
cept p,  which  is  the  working  pressure 
in  the  auxiliary  tank. 

The  tractive-  power  given  in  the 
preceding  tables  is  calculated  by  this 
formula,  but  in  practice,  as  in  the  case 
of  all  self-contained  haulage  locomo- 
tives, but  50  to  90%  pf  the  theoretical 
power  can  be  continuously  exerted 
owing  to  poor  track,  imperfect  lubri- 
cation, etc. 

Locomotive  Storage  Tanks.  —  The 
amount  of  air  that  a  locomotive  must 
carry  at  high  pressure  in  its  main 
storage  tanks  depends  _in  part  on  the 
length  of  the  run  and  in  part  on  the 
tractive  effort  that  it  must  exert. 
The  length  of  the  run  is  readily  de- 
termined and  is  twice  the  distance 
from  the  charging  station  to  the  place 
where  the  loaded  trip  is  made  up. 
The  tractive  effort  that  the  locomo- 
tive exerts  depends  on  the  weight  of 
the  empty  and  loaded  cars  that  must 
be  hauled  on  the  inbound  and  out- 
bound runs,  respectively,  and  the 
grades  that  must  be  overcome.  In 
order,  then,  to  determine  the  net 
tractive  effort  at  any  part  of  the  run, 
it  is  necessary  to  have  a  profile  of  the 
road  showing  the  grades  with  their 
amount  and  length.  The  tractive 
effort  required  to  overcome  any  grade 
determines  the  average  cylinder  pres- 
sure; this  determines  the  point  of  cut- 


804  HA  ULAGE 

off;  and  this,  in  turn,  determines  the  volume  of  air  consumed  per  stroke  of 
the  piston.  The  number  of  strokes  of  the  piston  made  while  moving  any 
distance  multiplied  by  the  volume  of  air  consumed  per  stroke,  gives  the 
total  volume  of  air  used  during  that  part  of  the  run.  The  sums  of  the  volumes 
of  air  required  to  overcome  the  various  grades  gives  the  total  amount  of  air 
required  for  the  round  trip;  and  to  this  20%  is  added  as  an  allowance  for  emer- 
gencies. Storage  capacity  is  provided  for  this  volume  of  air  when  compressed 
from  four  to  six  times  the  working  or  cylinder  pressure.  Favorable  grades  are 
of  much  more  importance  in  compressed-air  than  in  steam  haulage,  because 
in  the  former  the  locomotive  must  carry  all  its  power  (compressed-air)  with 
it,  while  in  the  latter  the  power  (steam)  is  generated  in  the  locomotive  itself 
while  in  motion. 

Air  is  sometimes  admitted  to  the  cylinders  throughout  nearly  full  stroke 
and  consequently,  as  the  exhaust  is  at  high  pressure,  the  efficiency  is  lower 
than  it  should  be.  This  practice  is  doubtless  due  to  the  tendency  to  use  as  small 
a  motor  as  possible  for  the  service  required,  on  account  of  the  limited  headroom 
and  narrow  crooked  gangways  so  common  in  mines.  Better  economic  results 
are  obtainable,  however,  by  using  the  air  expansively  and  increasing  the  size 
of  the  locomotive  and  the  weight  on  the  drivers;  this  is  almost  always  done  with 
large  locomotives.  "Ample  reserve  power  is  available  when  necessary,  because 
full  tank  pressure  can  be  admitted  to  the  cylinders  in  starting  a  heavy  load,  or 
in  pulling  on  steep  grades  and  sharp  curves. 

In  using  the  air  expansively,  as  can  be  done  with  properly  proportioned 
cylinders,  there  should  be  no  trouble  from  freezing  of  the  moisture.  Although 
the  cold  developed  will  produce  a  low  cylinder  temperature,  as  the  initial  work- 
ing pressure  is  so  much  higher  than  that  employed  for  pumps  and  other  com- 
pressed-air machinery,  the  expanded  air  becomes  relatively  dry,  and  the  force 
of  the  exhaust  will  be  sufficient  to  keep  the  ports  clear  of  accumulated  ice. 
To  this  end,  the  exhaust  ports  should  be  large,  straight,  and  short. 

Stationary  Storage.  —  The  stationary  storage  system  from  which  the  main 
storage  tanks  of  a  compressed-air  locomotive  are  charged  may  consist  of  a  pipe 
line  or  of  one  or  more  storage  tanks.  For  short  hauls,  the  storage  tank  is 
probably  more  convenient,  but  under  all  ordinary  conditions  the  pipe  line 
from  the  air  compressor  to  the  locomotive  charging  station  is  made  of  a 
diameter  and  strength  sufficient  to  serve  as  a  storage  reservoir.  The  volume 
of  stationary  storage  is  found  from  the  formula, 


"  (P-P)' 

in  which     V  =  volume  of  stationary  storage,  in  cubic  feet; 
v  —  volume  of  locomotive  storage,  in  cubic  feet; 
P  =  pressure  in  stationary  storage,  in  pounds  per  square  inch; 
p  =  pressure  in  locomotive  storage,  in  pounds  per  square  inch; 
p'  =  pressure  in  locomoitve  storage  at  time  of  charging,  in  pounds  per 
square  inch. 

EXAMPLE.  —  The  storage  tanks  of  a  compressed-air  locomotive  have  a 
capacity  v  of  160  cu.  ft.  at  a  pressure  p  of  800  Ib.  per  sq.  in.  If,  at  the  time 
of  charging  the  pressure  p'  in  the  locomotive  storage  tanks  is  250  Ib.  and  the 
pressure  P  in  the  pipe  line  (stationary  storage)  is  1,000  Ib.,  what  must  be  the 
volume  V  of  the  stationary  storage? 

SOLUTION.  —  By  substituting  the  given  values  in  the  formula, 


It  should  be  noted  that  the  pressure  P  in  the  pipe  line  is,  in  this  case, 
200  Ib.  per  sq.  in.  more  than  that  in  'the  locomotive  storage  tanks,  in  order 
that  the  latter  may  be  charged  as  speedily  as  possible.  The  time  of  charging 
is  about  1.5  min.,  during  but  40  to  50  sec.  of  which  the  valve  connecting  the 
pipe  line  to  the  locomotive  is  open.  The  pressure  p'  in  the  locomotive  tanks 
has  here  been  taken'  at  250  Ib.,  the  same  as  the  working  or  cylinder  pressure 
maintained  in  the  auxiliary  tank  and  to  which  it  has  been  reduced  from  the 
charging  pressure  of  800  Ib.  in  the  main  tank  because  of  the  air  consumed  by 
the  locomotive  in  doing  its  work.  On  short  hauls,  by  reason  of  the  small 
consumption  of  air,  _the  pressure  of  that  remaining  in  the  locomotive  storage 
tanks  _at  charging  time  may  be  considerably  more  than  the  working  pressure 
as  maintained  in  the  auxiliary  reservoir,  but  can  hardly  be  less  without  reduc- 
ing the  tractive  power  of  the  locomotive. 


HA  ULAGE 


805 


In  the  preceding  example,  if  the  pipe  line  from  the  compressor  to  the 
charging  station  is,  say,  4,000  ft.  long,  each  linear  foot  must  have  a  capacity  of 

=  .  1 1  cu.  ft.  in  order  to  store  the  440  cu .  f t.  of  air.  From  the  accompany- 
ing table  of  pipe  suitable  for  compressed-air  haulage  plants,  a  45-in.  pipe,  having 
a  capacity  of  .1105  cu.  ft.  per  ft.  of  length,  will  be  required.  In  order  that 
the  time  of  charging  may  be  as  short  as  possible,  the  volume  of  the  pipe  line 
storage  is  usually  made  two  to  three  times  that  of  the  locomotive  tanks,  although 
this  ratio  will  depend  on  the  line  pressure  and,  in  some  measure,  on  the  number 
of  locomotives  and  charging  stations,  the  frequency  of  charging,  etc.  In  the 
example,  the  ratio  of  locomotive  to  pipe  line  storage  capacity  is  160  :  440 
or  1  :  2.75.  If  there  is  but  one  charging  station,  the  storage  capacity  is  ample, 
and  the  compressor  is  of  sufficient  size  and  power,  the  drop  in  pressure  due  to 
charging  one  locomotive  is  practically  certain  to  be  recovered  before  another 
can  be  coupled  to  the  charging  station.  If  there  are  several  charging  stations, 
which  may  be  in  use  at  or  about  the  same  time,  it  is  advisable  to  increase  the 
storage  capacity  of  the  line  unless  a  wait  of  a  few  minutes  is  not  of  importance. 


STANDARD    STEAM   AND    EXTRA-STRONG   PIPE   USED   FOR   COM- 
PRESSED-AIR HAULAGE  PLANTS 


Linear 

Steam 

Extra  Strong 

Trade 
Diameter 
Inches 

Cubic 
Feet  in 
1  Lin. 
Ft. 

Feet 
Neces- 
sary to 
Make 
1  Cu. 

Trade 
Diameter 
Inches 

Thick- 
ness 

Weight 
per  Foot 

Thick- 
ness 

Weight 
per  Foot 

Ft. 

Inch 

Pounds 

Inch 

Pounds 

2 

.0218 

45.41 

.15 

3.61 

.22 

5.02 

2 

2* 

.0341 

29.32 

.20 

5.74 

.28 

7.67 

2} 

3 

.0491 

20.36 

.21 

7.54 

.30 

10.20 

3 

3* 

.0668 

15.00 

.22 

9.00 

.32 

12.50 

3i 

4 

.0873 

11.52 

.23 

10.70 

.34 

15.00 

4 

4J 

.1105 

9.05 

.24 

12.30 

.35 

17.60 

4* 

5 

.1364 

7.33. 

.25 

14.50 

.37 

20.50 

5 

&* 

.1650 

6.06 

.26 

16.40 

.40 

24.50 

5J 

G 

.1963 

5.10 

.28 

18.80 

.43 

28.60 

6 

If  the  length  and  diameter  and,  hence,  the  volume  V  of  the  storage  line 
are  determined  by  piping  already  in  place,  the  pressure  P  required  in  the  pipe 
line  to  instantly  charge  the  locomotive  may  be  found  by  transposing  the 
preceding  formula,  and  is, 

V( 

EXAMPLE. — If  the  volume  v  of  the  locomotive  storage  tanks  is  160  cu.  ft.; 
the  full  pressure  p  in  the  locomotive  storage  tanks  is  800  Ib.  per  sq,  in.;  the 
pressure  remaining  in  these  tanks  at  the  time  of  charging  is  250  Ib.;  and  the 
storage  line  is  4,000  ft.  of  4|-in.  pipe,  to  what  pressure  must  the  air  in  the  storage 
line  be  compressied  to  charge  the  locomotive? 

SOLUTION. — A  4^-in.  pipe  has  a  volume  of  .1105  cu.  ft.  per  ft.  of  length. 
If  this  volume  is  taken  as  .11  cu.  ft.,  that  of  the  storage  line  4,000  ft.  long  will 
be  4,OOOX.11  =  440  cu.  ft.  =  F.     Substituting, 
p  =  160X(80Q-250)+440X800 
440 

Pipe  Lines  and  Charging  Stations. — Pipe  lines  should  be  as  straight  as 
possible  and  should  not  be  placed  in  a  trench  and  covered,  as  leakage  is  then 
difficult  to  detect  and  general  inspection  is  impossible.  Expansion  joints 
are  not  necessary  underground  where  the  temperature  is  practically  uniform 
but  one  may  be  needed  on  the  surface  between  the  compressor  and  the  mouth 
of  the  mine.  The  lengths  of  pipe  should  be  connected  by  heavy,  threaded, 


806  HA  ULAGE 

screw  couplings  that  are  cqunterbored  with  an  annular  groove  into  which  a 
strip  of  soft  metal  can  be  driven  to  stop  any  leakage.  Flanged  or  union  coup- 
lings should  be  placed  at  all  charging  stations  and  at  intervals  of  300  ft.  or 
so  along  the  line.  The  ends  of  the  pipe  are  riveted  into  recesses  in  the  flanges 
and  are  hammer-faced  flush  with  the  center  bore.  The  flanges  are  also  counter- 
bored  to  hold  a  soft-metal  or  vulcanized-rubber  gasket.  The  introduction  of 
these  flange  couplings  permits  of  the  easy  repair,  extension,  or  alteration  of  the 
line.  The  pipe  should  be  given  one  or  more  heavy  coats  of  some  non-corrosive 
paint. 

A  valve  should  be  placed  between  the  C9mpressor  and  the  pipe  line,  at 
each  charging  station  and  at  convenient  points  along  the  line,  so  that  the 
compressor  or  parts  of  the  line  may  be  inspected  and  repaired  without  loosing 
any  of  the  air  in  the  pipes.  Where  the  line  runs  down  a  shaft,  a  heavy  cast  tee 
with  several  feet  of  pipe  below  it  is  placed  at  the  bottom  of  the  shaft  to  collect 
water.  A  waste  valve  is  inserted  at  the  bottom  of  the  pipe  to  permit  the 
water  to  be  blown  off. 

The  charging  stations  are  simple  in  construction  and  repair.  Attached 
to  the  pipe  line  by  a  flange  is  a  special  tee  to  which  is  fitted  a  H-in.  gate  valve 
having  a  short  nipple  into  which  is  screwed  a  Moran  flexible  joint  to  which  is 
attached  a  short  length  of  pipe.  The  Moran  joint  is  of  the  ball-and-socket 
type  so  that  the  pipe  may  be  turned  in  any  direction  necessary  to  couple  up 
with  the  locomotive  tanks.  When  not  in  use,  the  supply  pipe  is  turned  parallel 
to  the  track.  The  locomotive  is  also  provided  with  a  pipe  having  ball-and- 
socket  joints  and  a  gate  valve  opening  into  the  locomotive  tanks  but  which 
closes  as  soon  as  the  gate  valve  on  the  pipe  line  is  closed  to  cut  off  the  pressure. 
A  special  coupling  is  used  to  connect  the  supply  line  and  locomotive  pipes. 
This  coupling  cannot  be  broken  as  long  as  any  pressure  remains  in  the  pipes 
between  the  gate  and  check-valves,  so  a  small  globe  valve  is  placed  in  the 
line  immediately  above  the  gate  valve  in  order  to  bleed  off  the  remaining  air. 
All  valves  must  be  kept  tight,  packing  must  be  replaced  when  worn  out  or  lost, 
and  all  joints  and  connecting  pipes  must  be  supported  to  prevent  undue  stress 
coming  upon  them. 

Air  Compressors  for  Haulage  Plants.  —  The  capacity  of  an  air  compressor 
for  a  given  plant  depends  on  the  number  of  locomotives,  the  capacity  of  their 
tanks,  and  the  length  of  time  between  chargings.  The  number  of  cubic  feet  F 
of  free  air  (air  at  atmospheric  pressure,  14.7  Ib.)  required  to  charge  a  loco- 
motive may  be  found  from  the  formula 


14.7          .«:. 

in  which  the  letters  have  the  meaning  of  those  in  the  preceding  formula. 
Having  found  F,  the  capacity  of  the  compressor  C  in  cubic  feet  of  free  air  per 
minute  may  be  found  from 


in  which  n  equals  the  number  of  charges  in  the  time  /. 

EXAMPLE.  —  A  haulage  system  requires  that  the  single  locomotive  in  use 
shall  be  charged  three  times  an  hour.  The  storage-tank  pressure  is  800  Ib. 
and  the  pressure  remaining  in  the  tank  at  the  time  of  charging  is  250  Ib.  If 
the  locomotive  tanks  have  a  capacity  of  160  cu.  ft.,  what  must  be  the  size 
of  the  compressor  in  cubic  feet  per  minute? 

SOLUTION.  —  Here  z>  =  160,  £  =  800,  £'  =  250,  «  =  3,  and  *  =  60  min.  By 
substitution, 

.  ft.,  about 


The  required  capacity  of  the  compressor  is, 
3X00 


Compressors  for  charging  are  of  the  three-stage  type  for  pressures  up 
to  1,000  Ib.  per  in.,  and  for  higher  pressures  are  usually  four  stage.  They 
are  provided  with  intercoolers  as  explained  under  Compressed  Air. 

The  horsepower  required  to  compress  the  air  may  be  found  from  the  follow- 
ing table.  Thus,  in  the  example,  to  compress  300  cu.  ft.  of  air  per  min.  to 
800  Ib.  in  a  three-stage  compressor  will  require  3X32.5  =  97.5  H.  P. 


HAULAGE 


807 


HORSEPOWER  NECESSARY  TO  COMPRESS  100  CU.  FT.  OF  FREE  AIR 

TO  VARIOUS  PRESSURES  AND  WITH  TWO-,  THREE-,  AND 

FOUR-STAGE  COMPRESSORS 


Gauge 
Pressure 
Pounds 

Horsepower  Necessary 

Gauge 
Pressure 
Pounds 

Horsepower  Necessary 

Two- 
Stage 

Three-        Four- 
Stage         Stage 

Two- 
Stage 

36.3 
37.8 
39.7 
41.3 
43.0 
44.5 
45.4 

Three- 
Stage 

Four- 
Stage 

100 
200 
300 
400 
500 
600 
700 
800 

15.7 
21.2 
24.5 
27.7 
29.4 
31.6 
33.4 
34.9 

15.2 
20.3 
23.1 
25.9 
27.7 
29.5 
31.2 
32.5 

14.2 

18.8 
21.8 
24.0 
25.9 
27.4 
28.9 
30.1 

900 
1,000 
1,200 
1,400 
1,600 
1,800 
2,000 
2,500 

33.7 
34.9 
36.5 
37.9 
39.4 
40.5 
41.6 
43.0 

31.0 
31.8 
33.4 
34.5 
35.6 
36.7 
37.8 
39.0 

GASOLINE-MOTOR  HAULAGE 

Construction  of  Gasoline  Locomotives.— Gasoline  locomotives,  except  for 
the  absence  of  a  trolley  pole,  greatly  resemble  electric  locomotives  in  appear- 
ance as  all  their  moving  parts,  gasoline  tanks,  engines',  etc.,  are  enclosed  in 
the  same  form  of  iron  or  steel  casing  in  order  to  protect  them  from  injury 
from  falling  roof,  collision,  etc.  These  locomotives  are,  at  present,  made  in 
various  sizes  up  to  20  T.  in  weight,  those  under  5  T.  being  generally  used  for 
gathering. 

The  engines  are  of  the  four-cycle  type,  and  usually  have  four  cylinders, 
although  the  larger  ones  may  have  six.  The  cylinders  may  be  vertical  or 
horizontal,  the  latter  construction  being  necessary  in  mines  where  the  head- 
room is  limited.  The  engine  shaft  is  placed  lengthwise  of  the  frame  and  is 
connected  by  gearing  to  a  cross-  or  jack-shaft  near  the  front  end  of  the  loco- 
motive. From  the  cross-shaft,  power  is  transmitted  to  the  axle  of  the  nearest 
pair  of  driving  wheels  either  by  spur  gearing  or  by  a  chain  passing  around 
sprocket  wheels.  The  two  pairs  of  drivers  are  connected  either  by  rods,  as  in 
steam  or  compressed-air  locomotives,  or  by  a  chain  drive  passing  over  sprocket 
wheels  on  each  axle.  By  either  arrangement,  each  axle  is  a  driving  axle  and 
the  full  power  of  the  engines  is  utilized.  There  is  no  general  or  fixed  ratio 
between  the  weight,  in  tons,  of  a  gasoline  locomotive  and  the  horsepower 
developed  by  its  engines.  The  various  manufacturers,  in  their  catalogs,  indi- 
cate a  ratio  of  from  6  to  8  to  even  10  engine  horsepower  to  each  ton  weight  of 
the  locomotive,  but  the  engines  are  rated  much  below  their  capacity.  Thus, 
an  engine  rated  in  the  catalog  as,  say,  40  H.  P.  will  commonly  develop  50  to 
55  or  more  H.  P.  upon  brake  tests,  and  will  exceed  this  if  its  speed  is  allowed 
to  exceed  the  600  to  800  rev.  per  min.,  to  which  these  engines  are  commonly 
limited. 

The  smaller  locomotives  are  made  with  low  and  high  gears  and  the  larger 
ones,  sometimes  but  not  always,  are  made  with  low,  intermediate,  and  high 
gears,  which  allows  of  two  and  three  speeds,  respectively,  both  forwards  and 
reverse;  and  other  speeds  may  be  had  by  varying  that  of  the  engine.  The 
low  gear,  giving  a  speed  of  from  3  to  5  mi.  per  hr.,  is  used  while  bringing  the 
trip  from  rest  to  full  speed  (accelerating)  or  while  doing  very  heavy  pulling, 
while  the  high  (or  intermediate)  gear  is  used  under  all  ordinary  conditions. 
The  speed  changes  are  made  by  means  of  jaw  clutches  and  the  forward  and 
reverse  motions  by  means  of  friction  clutches,  both  mechanisms  being  operated 
by  levers  from  the  engine  cab.  The  transmission  gearing  is  contained  in  an 
oil-tight  casing  or  box  through  which  a  continuous  flow  of  oil  is  circulated 
from  the  engine  shaft,  and  which  is  in  operation  only  while  the  locomotive 
is  in  motion. 

After  circulating  through  the  water-jackets  surrounding  the  cylinders,  the 
cooling  water  passes  to  radiators  or  cooling  tanks,  being  forced  through  the 


808  HA  ULAGE 

system  by  a  small  pump  operated  by  gearing  from  the  main  engine-shaft. 
The  radiators  are  cooled  by  air  from  a  small  muitiblade  fan  placed  on  the 
forward  end  of  the  engine  shaft.  The  gasoline  fuel  is  carried  in  two  seamless 
drawn-steel  or  copper  tanks,  which  are  provided  with  safety  valves  (thus  giving 
each  tank  two  valves)  to  prevent  leakage.  It  is  almost  always  .arranged  that 
the  tanks  cannot  be  removed  or  charged  except  at  a  regular  charging  station, 
which,  in  the  case  of  drift  mines,  is  always  outside  but  near  the  opening.  The 
charging  is  done  in  a  few  minutes  by  removing  the  empty  tanks  and  replacing 
them  with  full  ones,  which  hold  about  5  gal.  each. 

The  exhaust  gases  from  the  cylinders  pass  to  some  device  intended  to  cool 
them  and  to  prevent  back  firing  and  the  escape  of  sparks  and  flame  to  the 
atmosphere.  In  most  cases,  this  consists  of  a  muffler  provided  with  steel 
tubes,  baffle  plates,  wire  gauze,  etc.,  the  gases  being  sometimes  led  over  water 
as  an  additional  precaution  against  fire.  The  muffler  also  serves  to  make 
the  motor  as  nearly  noiseless  as  possible.  In  one  type  of  locomotive,  the 
exhaust  is  passed  through  a  series  of  parallel  perforated  pipes  contained  in 
what  is  called  a  deodorizing  tank,  which  is  filled  with  a  liquid  preparation 
that  extinguishes  the  flame  and  neutralizes  the  smell  before  the  gases  finally 
escape. 

The  more  recent  types  of  these  locomotives  are  provided  with  a  self-starter, 
which  consists  of  an  electric  motor  receiving  current  from  a  storage  battery,  and 
which,  by  means  of  reducing  gear,  can  be  made  to  drive  the  crank-shaft  of  the 
main  engine.  The  storage  battery  is  automatically  charged  by  a  generator 
driven  by  the  main  engine,  and  requires  no  attention.  The  chief  advantage 
of  the  self-starter  is  that  it  allows  the  engines  of  the  heavy  locomotives,  which 
are  difficult  to  start  by  hand  particularly  when  cold,  to  be  shut  down  when 
the  motor  is  not  in  motion,  and  to  be  readily  started  when  the  trip  must  be 
moved.  Not  only  does  this  effect  a  material  reduction  in  fuel  consumed,  but 
is  of  prime  importance  in  that  it  prevents  the  pollution  of  the  mine  air  by  the 
exhaust  gases  if  the  engine  is  kept  in  motion  while  the  locomotive  is  still,  the 
common  procedure  when  the  self-starter  is  not  used.  The  self-starting  device 
is  also  made  a  source  of  current  for  operating  electric  headlights. 

These  engines  are  provided  with  headlights,  and  tail-lights,  a  bell,  one 
or  more  sand  boxes,  and  a  whistle  operated  by  compressed  air.  All  have 
efficient  hand-brakes  and  some  of  the  larger  ones  have  a  complete  air-brake 
system,  the  air  being  supplied  by  a  small  compressor  operated  from  the  engine 
shaft,  or  otherwise.  In  this  connection,  the  subject  of  Internal-Combustion 
Engines,  on  page  532,  etc.,  may  be  consulted. 

Hauling  Capacity  and  Fuel  Requirements. — The  maximum  tractive  power 
of  a  gasoline  locomotive  is  exerted  under  low  gear  and  may  be  taken  as  one- 
fifth  of  its  weight  under  ordinary  conditions  and  as  one-quarter  under  favor- 
able ones.  The  tractive  power  under  high  gear  is,  in  the  case  of  locomotives 
with  two  gears,  about  one-half  that  under  low  gear  and  should  be  made  the 
basis  of  estimating  the  size  or  weight  of  a  locomotive  to  meet  the  prevailing 
conditions.  That  is,  power  is  sacrificed  to  gain  speed.  The  drawbar  pull, 
resistance  of  the  cars,  etc.,  are  figured  in  exactly  the  same  way  as  for  steam 
locomotives. 

Some  choice  in  the  matter  of  speed  is  offered.  Thus  the  two-speed  loco- 
motives supplied  by  a  leading  manufacturer  may  be  had  with  speeds  of  3  and  6 
or  4  and  8  mi.  per  hr.,  respectively.  The  16-T.  locomotive  of  the  same  maker 
is  offered  with  four  combinations  of  speeds  on  the  low,  intermediate,  and 
high  gears,  respectively,  of  3,  9,  and  15,  or  4,  12,  and  20,  or  5,  15,  and  25,  or  6. 
18,  and  30  mi.  per  hr.  The  relative  speed  ratios  for  low,  intermediate,  and 
high  gear  are  1  :  3  :  5,  or  between  the  low  and  intermediate  1  :  3  and  between 
the  intermediate  and  high  1  :  If.  While  it  is  true  that  the  increase  in  speed 
is  accompanied  by  a  loss  in  drawbar  pull,  yet  these  locomotives  under  ordinary 
conditions  should  pull  at  full  speed  under  high  gear  the  load  they  can  start 
and  accelerate  under  low  gear.  In  mine  practice,  the  speed  is  very  commonly 
limited  by  law  to  6  or  8  mi.  per  hr.,  but  there  seems  no  good  reason  why,  in 
main-line  haulage  where  the  track  and  equipment  are  in  first-class  modern 
condition,  that  speeds  of  20  and  30  mi.  per  hr.  would  not  be  perfectly  safe. 

The  gasoline  consumption  of  these  locomotives  depends  on  their  size,  the 
loads  hauled,  the  grades,  the  length  of  shift,  and  whether  they  are  operated 
continu9usly  or  intermittently.  When  operated  continuously  at  full  power, 
the  engines  will  probably  use  a  pint,  or  a  little  less,  gasoline  per  horsepower 
per  hour.  Thus,  a  10-T.  locomotive  with  engines,  say,  of  62.5  H.  P.,  will 
burn  62.5X8  =  500  pt.  =  62.5  gal.  of  gasoline  per  8-hr,  shift.  But  these  loco- 
motives are  usually  over-engined,  so  that  on  the  heaviest  grades  they  rarely 


HA  ULAGE  809 

exert  more  than  three-fourths  power.  Further,  no  gasoline  is  used  when 
descending  a  grade  nor,  if  provided  with  a  self-starting  device,  when  standing 
waiting  a  trip,  and  but  little  is  required  for  switching,  etc.  Experience  has 
shown  that  it  is  very  unusual  for  the  engines  to  develop  for  an  entire  shift 
more  than  one-half  their  rated  horsepower.  In  the  example  just  cited,  this 
would  reduce  the  gasoline  consumption  from  62.5  to  31.25,  say,  30  gal.  per  shift, 
which  is  at  the  rate  of  3  gal.  per  T.  of  weight  of  the  locomotive.  This  is  a 
maximum.  One  manufacturer  estimates  the  daily  fuel  requirements  at  8 
to  10  gal.  for  a  locomotive  with  25-H.  P.  engines  (one  weighing  3.5  T.),  and  as 
10  to  20  gal.  for  one  with  engines  of  50  H.  P.  (weighing  8  T.).  Mr.  Carl  Scholz, 
speaking  of  the  gasoline  locomotives  in  his  own  mines,  where  average  conditions 
prevail,  says:  "The  average  consumption  of  gasoline  and  oil  for  an  8-hr, 
shift  on  a  6-T.  motor  is  about  $2,  gasoline  costing  17  c.  per  gal."  This  would 
indicate  a  fuel  consumption  of  12  gal.  per  shift,  perhaps  a  little  more,  as  the 
amount  paid  for  oil  is  not  stated.  At  Gatliff,  Tenn.,  a  5-T.  motor  uses  11  gal. 
of  gasoline  in  9  hr.  Available  figures  indicate  that  under  average  working 
conditions  the  consumption  of  gasoline  per  shift  is  at  the  rate  of  2  gal.  per  T. 
of  weight  of  the  locomotive,  although  in  some  cases  it  may  be  as  high  as  2.5  gal., 
and  in  rare  instances  3  gal.  It  should  be  noted  that  the  larger  locomotives, 
particularly  when  fitted  with  self-starting  devices,  require  relatively  less  fuel 
than  the  smaller  ones,  or  those  that  must  be  started  by  hand.  In  comparison 
with  steam  locomotives,  a  manufacturer  states  that  the  cost  of  fuel  is  about  the 
same  for  each  type  of  motor  for  the  same  capacity. 

Cost  of  Gasoline-Locomotive  Haulage. — At  the  No.  2  entry  of  the  Roane 
Iron  Co.,  Rockwood,  Tenn.,  the  round-trip  haul  is  3  mi.  with  a  uniform  grade 
of  1.5%  in  favor  of  the  loads.  The  average  weight  of  the  empty  cars  is  1,400  lb., 
of  the  loaded  cars  3,640  lb.,  and  the  live  load  or  weight  of  coal  per  car  is  2,240  lb. 
Ten  20-car  trips  of  empties  are  hauled  in  and  the  same  number  of  loads  hauled 
out  from  the  mine  in  one  shift.  The  inbound  empties  have  a  total  daily  weight 
of  140  T.,  the  outbound  loads  one  of  364  T.;  the  total  daily  weight  moved  is 
504  T.,  and  that  of  the  coal  delivered  to  the  tipple  is  224  T.  The  following 
are  the  details  of  the  haulage  costs  by  mule  and  by  gasoline  motor: 

COST  OF  HAULAGE  AT  ROCKWOOD,  TENN. 
By  mules: 

4  drivers,  at  $1.65 $6.60 

9  mules,  at  $.50 4.50      $11.10 

By  motor: 

1  motorman,  per  day $2.05 

1  coupler,  per  day 1.65 

13  gal.  gasoline,  at  11£  c 1.50 

2  lb.  carbide,  at  4  c 08 

J  gal.  gasoline  engine  oil,  at  23  c .12 

1  gal.  transmission  case  oil .24      $  5.64 

Saving  by  motor $  5.46 

Or,  49.1%. 

The  cost  per  ton  of  coal  delivered  to  the  tipple  is  4.955  c.  by  mules  and 
2.518  c.  by  locomotive.  140  T.  of  empties  are  hauled  into  the  mine  a  distance 
1.5  mi.  and  364  T.  of  loads  are  hauled  out  the  same  distance.  This  is  equal 
to  504  T.  hauled  1.5  mi.  or  756  T.  hauled  1  mi.,  at  a  cost  of  $11.10  or  1.468  c. 
per  T.-mi.  by  mules  and  $5.64  or  .746  c.  per  T.-mi.  by  motor.  If  the  cost 
of  hauling  the  live  load  of  224  T.  of  coal  1.5  mi.  (equivalent  to  336  T.  moved 
1  mi.)  is  considered,  the  cost  per  ton-mile  by  mules  is  3.303  c.  and  by  motor 
1.678  c.  In  neither  cost  statement  is  any  allowance  made  for  depreciation, 
repairs,  renewals,  interest  on  the  investment,  etc.  As  the  majority  of  these 
charges,  particularly  the  first  and  third,  are  much  greater  in  the  case  of  mule 
than  motor  haulage,  the  difference  in  favor  of  the  locomotive  will  be  greater 
than  that  shown  by  the  foregoing  figures. 

A  5-T.  gasoline-haulage  motor  at  the  mines  of  the  Southern  Coal  and  Coke 
Co.,  Gatliff,  Tenn.,  handles  500  net  T.  of  coal  daily  in  9  hr.,  working  22  da. 
per  mo.  The  average  daily  haul  is  354  cars  weighing  1,200  lb.  when  empty 
and  a  little  more  than  4,000  lb.  when  loaded.  The  haul  is  from  an  inside 
parting  2,500  ft.,  say  £  mi.  from  the  tipple,  on  an  undulating  road,  which 
varies  in  grade  from  1.5%  against  the  loads  to  3.5%  in  their  favor.  The 
details  of  mule  and  motor  haulage  are  as  follows; 


. 

11  gal.  g 
Carbide, 


810  HA  ULAGE 

COST  OF  HAULAGE  AT  GATLIFF,  TENN. 
1  gal.  lubricating  oil  ............  ..............      $     .15$ 

i  gal.  gasoline  engine  oil  ......................  .16  J 

gasoline,  at  14  c  .......................  1.54 

use  lights  but  little  ..................  .15 

M9torman  ..................................  2.50          * 

Trip  rider    ..................................  1.83 

Cleaning  and  repairs  .........................  .40 

6%  int.  on  difference  of  cost  of  mules  and  motor.  .52 

Extra  upkeep  on  track  over  mules  .............  .50 

Motor  replaces  7  mules,  at  42  c.  per  day  for  feed  $  2.94 

Three  drivers  ...............................  7.23 

Reduction  to  stable  boss  ......................  .35 

Daily  saving  by  use  of  motor  ..................  2.76 

$10.52      $10.52 

The  cost  per  ton  of  coal  delivered  to  the  tipple,  on  the  basis  of  500  T.  per 
da.,  is  2.104  c.  by  mules  and  1.552  c.  by  gasoline  motor.  The  empty  cars  have 
a  total  weight  of  212  T.  and  the  loaded  cars  708  T.,  making  a  total  weight  of 
920  T.  hauled  |  mi.,  which  is  equivalent  to  460  T.  moved  1  mi.  The  cost  is, 
hence,  2.287  c.  per  T.-mi.  for  mule  haulage  and  1.687  c.  for  locomotive  haul- 
age. On  the  basis  of  the  live,  or  paying,  load  only,  the  cost  for  transporting 
500  T.  $  mi.  (250  T.  for  1  mi.)  is  4.208  c.  per  T.-mi.  by  mules  and  3.104  c.  per 
T.-mi.  by  locomotive. 

A  gasoline  locomotive  at  the  mine  of  the  Mid  valley  Coal  Co.,  Wilburton, 
Pa.,  which  displaces  a  steam  locomotive  and  five  mules,  when  making  but 
24  mi.  per  da.,  or  about  one-half  its  capacity,  effects  a  saving  over  mule 
haulage  of  32.2%.  The  locomotive  is  rated  at  9  T.  and.  uses  15  gal.  of  naptha 
per  day  at  a  cost  of  10  c.  per  gal.,  or  $1.50  for  fuel.  It  is  estimated  that  the 
consumption  of  gasoline  would  be  12  gal.  per  da.,  which,  at  15  c.  per  gal.,  would 
cost  $1.80.  For  a  period  of  6  mo.,  during  which  2  hr.  of  each  9  hr.-da.  were 
devoted  to  switching  and  were  not  properly  chargeable  to  haulage,  the  average 
daily  mileage  for  the  loaded  and  empty  cars  was  12  for  each.  The  empty 
cars  weighed  2.5  T.  and  the  total  weight  of  them  handled  in  1  da.  was  250  T. 
The  loaded  cars  weighed  5.5  T.,  and  the  total  weight  of  them  handled  in  1  da. 
was  550  T.  The  net  weight  of  coal  delivered  to  the  mine  mouth  was,  hence, 
300  T.  per  da.  The  daily  cost  for  motor  haulage  only  was  as  follows: 

COST  OF  HAULAGE  AT  WILBURTON,  PA. 
Wages  of  motorman  and  helper  .........................     $3.35 

15  gal.  of  naptha  at  10  c  ...............................        1.50 

Lubricating  oil  .......................................          .12 

Maintenance,  $65.14  for  6  mo.,  20  da.  per  mo  ..............  54 

Total  ...........................................      $5.51 

The  cost  is,  then,  1,837  c.  per  T.  of  coal  delivered  to  the  mine  mouth,  or 
but  1.429  c.  per  T.  if  the  cost  of  the  time  spent  in  switching  is  deducted.  From 
the  figures  furnished,  there  appear  to  have  been  an  average  of  12.5  trips  per 
day,  and  the  length  of  haul  was  not  far  from  1  mi.  With  this  understanding, 
the  cost  per  ton-mile  was  .687  c.  for  the  combined  weight  of  the  loads  and 
empties  (800  T.)  and  1.429  c.  per  T.-mi.  for  the  300  T.  of  coal  delivered. 

At  the  plant  of  the  Shade  Coal  Mining  Co.,  Windber,  Pa.,  the  haulage  cost 
per  ton  of  coal  delivered  to  the  tipple  was  6.4  c.  by  mules  and  3.15  c.  by  gaso- 
line locomotive.  On  the  ton-mile  basis,  the  cost  of  mule  haulage  was  12.8  c. 
and  of  gasoline  haulage  3.79  c.  for  the  coal  delivered  to  the  tipple. 

Comparison  of  Gasoline  and  Other  Types  of  Haulage  Motors.  —  Like  other 
self-contained  locomotives  (steam,  compressed-air,  and  storage-battery  elec- 
tric), the  gasoline  motor  has  the  advantage  over  the  ordinary  electric  mine 
locomotive  operated  through  a  trolley  from  overhead  wires,  that  it  can  go 
anywhere  in  the  mine  that  the  tracks  are  laid.  As  compared  with  the  com- 
pressed-air and  overhead  and  storage-battery  electric  locomotives,  it  does  not 
require  a  more  or  less  expensive  plant  for  the  generation  of  power.  As  com- 
pared with  the  steam  locomotive,  it  is  as  cheaply  operated,  does  not  so  greatly 
befoul  and  befog  the  air  with  unpleasant  or  dangerous  gases,  and  when  the 
exhaust,  carbureter,  etc.,  are  properly  protected,  is  not  so  likely  to  ignite  either 
coal  dust  or  methane.  It  -is  questionable  if  the  danger  of  igniting  either  of 


HA  ULAGE 


811 


these  explosive  agents  is  as  great  with  a  well-designed  and  well-managed 
gasoline  motor  as  with  the  ordinary  overhead-trolley  electric  locomotive. 

The  chief  objections  made  to  this  type  of  locomotive  relate  to  the  cost  of 
power  and  the  difficulty  of  obtaining  competent  operators  and  to  the  danger  to 
the  health  of  the  underground  workers  from  the  exhaust  gases.  When  the 
power-plant  charges  are  considered  in  the  cost  of  electric  or  compressed-air 
locomotives,  the  cost  of  power  for  a  gasoline  locomotive  will  be  found  to  be 
very  much  less  than  for  the  other  two  types.  On  the  other  hand,  if  the  mine  is 
already  piped  or  wired  for  compressed-air  or  for  electric  coal-cutting  machinery, 
some  study  will  be  required  to  determine  if  the  haulage  can  be  done  more 
cheaply  by  gasoline  motors  than  by  those  operated  by  the  power  already  in 
use.  Competent  operators  are  readily  obtained  from  outside  workers  familiar 
with  motor  trucks,  the  use  of  which  as  a  substitute  for  horse-drawn  wagons  is 
rapidly  increasing.  Attracted  by  the  better  wages  prevailing  in  the  mine,  a 
little  training  in  the  use  of  the  gasoline  locomotive  and  a  familiarity  with  under- 
ground work,  makes  them  first-class  motormen;  The  complaint  that  gasoline 
locomotives  will  not  take  an  overload  as  will  electric  locomotives  does  not  seem 
well-founded.  It  is  a  question  of  proportioning  the  engine  power  to  the 
weight  of  the  locomotive,  and  a  gasoline  motor  that  has  engine  power  enough 
to  slip  its  drivers,  will  pull  as  great  a  tonnage  as  any  other  locomotive  of  the 
same  weight. 

It  is  unquestionably  true,  however,  that  a  gasoline  locomotive  does  dis- 
charge into  the  mine  air  a  certain  amount  of  obnoxious  and  harmful  gases, 
carbon  dioxide  and  carbon  monoxide,  respectively.  At  the 'same  time,  a 
definite  amount  of  oxygen  is  withdrawn  from  the  air  and  used  in  the  combustion 
of  the  gasoline.  The  amount  of  these  gases  will  depend  on  how  well  the 
engine  is  working,  and  this,  in  turn,  will,  in  a  very  great  measure,  depend  on 
the  skill  of  the  operator.  The  following  analyses  of  mine  air  taken  from  work- 
ings where  a  gasoline  locomotive  was  used  are  furnished  by  Mr.  A.  J.  King, 
in  an  article  read  before  the  West  Virginia  Coal  Mining  Institute  and  reprinted 
in  the  Colliery  Engineer  for  October,  1913;  the  samples  having  been  taken 
by  Mr.  P.  A.  Grady,  formerly  mine  inspector  for  the  12th  District,  West 
Virginia. 

ANALYSES  OF  MINE  AIR  AS  AFFECTED  BY  EXHAUST  OF 
GASOLINE  LOCOMOTIVES 


Number  of 
Sample 

C02 

02 

CO 

CHt 

N2 

1 

.07 

20.87 

.03 

.10 

78.93 

2 

.11 

20.92 

.07 

.13 

78.77 

3 

.13 

20.80 

.06 

.32 

78.69 

4 

.09 

20.78 

.03 

.33 

78.77 

5 

.15 

20.91 

.05 

.11 

78.78 

6 

.15 

20.86 

.07 

.10 

78.82 

Sample  No.  1  was  taken  80  ft.  ahead  of  the  air  at  the  face  of  a  room  in  which 
the  locomotive  had  been  5  min.  with  the  engines  running.  The  grade  was  3% 
in  favor  of  the  loaded  car  and  6,000  cu.  ft.  of  air  per  min.  was  passing  on  the 
entry. 

Sample  No.  2  was  taken  in  the  same  place  as  sample  1,  the  locomotive 
having  been  run  up  to  the  face  and  had  pulled  out  a  loaded  car. 

Sample  No.  3  was  taken  at  the  face  210  ft.  ahead  of  the  ventilating  current, 
after  the  locomotive  with  its  engines  running  had  stood  in  the  place  for  5  min. 
and  then  come  out;  the  fumes  were  noticeable. 

Sample  No.  4  was  taken  in  the  same  place,  the  locomotive  having  run  to  the 
face  and  coupled  to  a  loaded  car  which  it  pulled  down  a  3%  grade  in  1  min. 

Samples  Nos.  5  and  6  were  taken  on  the  entry,  which  had  a  cross-section 
of  15  ft.  by  5  ft.,  an  area  of  75  sq.  ft.,  and  through  which  6,000  cu.  ft.  of  air 
per  minute  was  passing.  The  samples  were  gathered  after  the  ^locomotive  had 
been  made  to  perform  hard  work  by  running  up  the  entry,  which  had  a  grade 
of  5%. 

Mr.  O.  P.  Hood,  in  the  October,  1914,  Bulletin  of  the  American  Institute  of 
Mining  Engineers,  gives  the  following  table,  which  shows  the  amount  of  CO 
and  COz,  in  cubic  feet  per  minute,  given  off  by  gasoline  locomotives  with 
cylinders  of  various  sizes,  when  running  under  both  good  and  bad  conditions. 


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HA  ULAGE  813 

Referring  to  the  West  Virginia  experiments  in  the  first  of  the  preceding 
tables  and  disregarding  the  CO,  the  greatest  amount  of  gases  foreign  to  normal 
air  is  met  in  the  third  sample,  which  shows  the  presence  of  .45%  of  COz  and  CHi 
combined,  neither  of  which  gases  is  poisonous  even  in  very  much  larger  amounts 
than  there  shown.  The  dangerous  gas  is  CO,  the  maximum  amount  of  which 
that  maybe  breathed  fora  short  time  and  intermittently  without  injurious 
effects  is  commonly  stated  to  be  .19%.  When  breathed  continuously,  air  should 
not  contain  more  than  .05%  of  this  gas,  and  preferably  but  .025%  unless  those 
exposed  to  its  effects  are  in  good  health  and  are  not  working  violently.  All 
the  samples  show  less  than  the  maximum,  and  the  average  of  all  is  the  safe 
minimum  of  .05%.  All  the  samples  appear  to  have  been  taken  in  the  inner 
workings  at  places  (the  face  of  a  room  or  entry)  where  the  locomotive  would 
not  usually  go  more  than,  say,  once  an  hour,  and  probably  not  more  than  five 
or  six  times  a  shift.  In  the  intervals  between  trips,  the  CO  would  soon  diffuse 
even  if  there  was  no  circulation  of  air,  so  that  the  mine  cited  was  by  no  means 
in  a  bad  condition  although  every  effort  should  be  made  to  keep  the  content 
of  CO  to  .05%.  In  the  mine  in  question,  this  could  readily  have  been  done  by 
increasing  the  volume  of  the  air-current  from  6,000  to  9,000  cu.  ft.  per  min., 
which  would  have  raised  the  velocity  of  the  air  from  80  to  120  ft.  per  min.;  and 
neither  the  volume  nor  the  velocity  are  high.  Mr.  King  recommends  that 
where  gasoline  locomotives  are  used,  in  addition  to  the  air  that  would  ordinarily 
be  circulated  through  the  entry,  there  should  be  a  further  amount  of  1,000  cu. 
ft.  per  min.  for  each  ton  in  weight  of  the  locomotive. 

Mr.  King's  requirements  are  considerably  in  excess  of  those  of  one  of  the 
leading  manufacturers,  who  advocates  that  where  the  locomotive  is  in  con- 
tinuous operation  there  should  be  in  circulation  800  to  1,000  cu.  ft.  of  air  per 
min.  per  ton  of  weight  of  the  locomotive,  depending  on  whether  the  hauling  is 
done  upon  the  intake  or  return.  An  occasional  trip  to  a  side  entry  or  even  to 
a  working  place  beyond  the  air  will  not  require  a  material  increase  in  the 
quantity  of  air  in  circulation,  as  the  normal  volume  of  air  in  motion  assisted 
by  diffusion  will  carry  off  the  CO  before  a  return  trip  is  made  to  the  same  part 
of  the  workings.  On  the  other  hand,  it  is  admitted  that  if  the  consumption 
of  gasoline  is  the  maximum,  the  air  requirements  will  be  doubled;  but  it  is 
stated  that  it  appears  impossible  to  consume  this  maximum  under  ordinary 
normal  conditions. 

Mr.  Hood's  figures  are  of  value  in  giving  the  quantities  of  harmful  (COz) 
and  poisonous  (CO)  gases  exhausted  per  minute  by  gasoline-locomotive  engines 
of  various  standard  sizes  when  operating  continuously  with  good  and  with  bad 
carburation.  But  haulage  motors  are  not  working  continuously  under  full 
load;  in  fact,  they  are  idle  so  much  of  the  time  that  the  fuel  consumption  is 
commonly  about  one-third  the  maximum,  in  rare  cases  rising  to  one-half. 
Whether  the  air  circulated  shall  be  based  on  average  or  on  extreme  conditions 
is  a  question  for  the  mine  manager.  If  extreme  conditions  are  to  be  provided 
for,  the  use  of  gasoline  locomotives  will  be  prohibited  in  many  mines,  where 
the  assumption  of  average  conditions  would  permit  it.  The  advocates  of 
gasoline  haulage  claim  if  extreme  conditions  (for  no  engines  will  be  permitted 
to  work  badly  for  a  longer  time  than  that  required  to  shut  off  the  fuel  supply) 
must  be  assumed  in  dealing  with  this  type  of  locomotive,  then  electric  haulage 
should  be  prohibited  because  of  the  possibility  of  a  fall  of  roof  bringing  down 
the  trolley  wires  with  the  consequent  chance  of  a  dust  explosion  through  the 
electric  arc  almost  certain  to  be  produced;  and  compressed-air  and  wire-rope 
haulage  should  not  be  allowed  as  the  compressor  might  explode  or  the  trip 
jump  the  track. 

The  variation  in  the  quantity  of  air  required  by  a  motor  in  constant  use 
and,  thus,  consuming  the  maximum  quantity  of  fuel,  both  when  the  carburation 
is  good  and  when  it  is  bad  and  when  the  proportion  of  CO  in  the  air  is  to  be 
kept  at  .10%  and  at  .05%  may  be  illustrated  in  the  case  of  two  locomotives 
as  follows:  A  5-T.  motor  with  5"X  6"  cylinders  suitable  for  side-entry  haulage 
will  require  3,300  cu.  ft.  per  min  of  air  when  working  properly  if  the  CO  in 
the  air  is  to  be  kept  at  .10%  and  6,600  cu.  ft.  if  the  CO  is  to  be  kept  at  .05%. 
The  same  motor,  when  working  badly,  will  require  nearly  four  times  as  much 
air  or  12,560  and  25,120  cu.  ft.,  respectively,  depending  on  the  allowable  per- 
centage of  CO.  Similarly,  a  9-T.  motor  with  6.5"  X  8"  cylinders  and  adapted 
to  main-line  haulage  will  require  6,040  or  12,080,  and  23,000  or  46,000  cu.  ft. 
per  min.  of  air,  depending  on  whether  the  carburation  is  good  or  bad  and 
whether  the  CO  is  to  be  kept  at  .10  or  .05%.  The  range  in  air  requirements 
between  the  best  and  worst  conditions  of  operation  is  from  3,300  to  25,120  cu.  tt. 
per  min,  in  the  case  of  the  smaller  locomotive,  and  in  the  case  of  the  larger  one, 


814  HA  ULAGE 

from  6,040  to  46,000  cu.  ft.  per  min.  Such  an  increase  in  the  quantity  of 
air,  the  ratio  being  1  to  8,  cannot  be  made  from  time  to  time  as  it  may  be 
temporarily  needed,  and  must  be  permanently  provided  for  in  the  ventilating 
scheme  of  the  mine. 

Gasoline  locomotives  have  been  in  use  too  short  a  time  to  have  permitted 
a  solution  of  all  the  problems  connected  with  their  employment,  and  the 
following  suggestions  in  their  selection  and  management  may  be  of  value: 

1.  Buy  a  high-grade  motor  from  a  responsible  manufacturer  and  be  guided 
by  his  advice  in  its  selection. 

2.  Do  not  use  a  larger  motor  than  necessary  to  do  the  work;  this  will  save 
in  first  cost,  in  fuel  consumption,  and  particularly  in  the  amount  of  CO  dis- 
charged. 

3.  Use  only  high-grade  gasoline  and  employ  only  experienced  motormen, 
who  might  be  given  a  bonus  for  low  fuel  consumption ;  this  will  lessen  both  the 
fuel  bill  and  the  quantity  of  CO  admitted  to  the  air. 

4.  If  possible,  arrange  the  main-line  haulage  so  that  the  grades  favor  the 
outbound  loads.     If  this  is  done,  and  the  return  air-current  is  made  the  haulage 
road,  the  engines  may  be  shut  down  and  the  loads  dropped  out  by  gravity, 
saving  in  fuel  and  in  CO  discharged.     The  empties  will  be  taken  in  under 
power  against  the  air,  and  the  resultant  velocity  of  the  air-current  will  be 
that  of  the  inbound  locomotive  added  to  that '  of  the  outbound  air.     If  the 
velocities  of  the  locomotive  and  the  air-current  are  the  same,  this  will  double  the 
quantity  of  air  passing  the  locomotive  and  may  provide  enough  excess  air  to 
take  care  of  possible  temporary  bad  carburation  which  is  more  apt  to  happen 
under  full  than  under  part  load. 

5.  Do  not  have  the  speed  of  the  locomotive  and  the  air-current  the  same 
when  they  are  moving  in  the  same  direction;  to  do  so  will  cause  a  concentration 
of  gas  around  the  locomotive,  which  will  prove  harmful  to  the  motorman. 

6.  Where  possible,  avoid  pulling  from  dip  workings  unless  the  air  supply 
is  ample,  because  the  maximum  amount  of  gasoline  is  consumed  and  CO  pro- 
duced when  starting  up  grade  under  full  load. 

7.  Do  not  use  the  locomotive  ahead  of  the  air  either  in  rooms  or  entries 
more  than  necessary.     It  is  in  tight  places  that  the  effects  of  small  amounts 
of  CO  are  the  most  marked.     If  compelled  to  enter  such  places,  remain  there 
as  short  a  time  as  possible,  and  do  not  allow  the  miners  to  return  to  the  face 
until  some  time  has  elapsed  in  order  that  the  air-currents  set  up  by  the  moving 
trip  and  diffusion  may  have  an  opportunity  to  dilute  the  CO  to  the  safe  limit. 

8.  In  event  of  carbureter  troubles,  shut  off  the  gasoline  instantly;  an  excep- 
tion might  be  made  when  hauling  against  the  full  strength  of  the  air-current. 

9.  Except  in  a  strong  air-current,  do  not  allow  the  locomotive  to  stand 
with  the  engines  running;  this  precaution  is  particularly  to  be  observed  in  places 
ahead  of  the  air.     To  this  end,  have  the  locomotive  provided  with  a  self- 
starting  device. 

10.  If  the  men  complain  of  sickness,  remove  the  locomotive  from  that 
part  of  the  mine  until  the  reason  for  the  trouble  is  found.     Frequently  a 
slight  adjustment  of  the  ventilating  current  made  by  opening  or  closing  a 
regulator  will  remedy  the  trouble. 

11.  Overhaul  and  clean  the  locomotive  thoroughly  at  the  end  of  each 
shift.     Under  no  circumstances  is  it  safe  to  use  a  locomotive  underground 
when  the  carbureter  and  ignition  are  out  of  order. 

12.  As  the  effects  of  CO  upon  the  system  are  dangerous,  the  percentage 
of  it  in  the  air  must  be  kept  as  low  as  possible.     Unfortunately,  there  are  no 
simple  tests  for  this  gas  that  may  be  applied  by  the  miner  or  the  foreman,  and 
the  first  indication  of  its  presence  is  it«  ill  effects.     It  might  be  well,  then,  at 
the  time  of  installing  gasoline-motor  haulage  to  employ  a  competent  chemist 
for  a  sufficient  length  of  time  to  follow  the  locomotive  to  all  parts  of  the  mine 
to  secure  samples  for  analysis  of  the  air  in  the  places  the  motor  has  been. 
The  expenditure  of  a  few  hundred  dollars  in  taking  and  analyzing  such  samples 
will  either  satisfy  the  management  that  the  use  of  gasoline  motors  is  perfectly 
safe,  or  will  suggest  changes  in  the  ventilating  system  or  in  the  haulage  schedules, 
or  in  the  use  of  certain  roads  for  haulage,  etc.,  that,  if  carried  out,  will  make 
the  use  of  such  motors  unobjectionable. 

Purification  of  the  Exhaust. — No  satisfactory  way  of  getting  rid  of  the  CO 
in  the  exhaust  of  gasoline  locomotives  has  as  yet  been  devised.  It  is  probable 
that  absorption  by  cuprous  chloride  (CuzCk),  the  reagent  used  for  the  purpose 
in  gas-analysis  apparatus, -is  not  practicable  because  of  the  expense. 

Solutions  of  lime  or  caustic  soda  or  even  plain  water  will  absorb  COz  to  a 
certain  extent,  and  at  the  same  time  will  remove  the  odor. 


HA  ULAGE  815 

ELECTRIC-LOCOMOTIVE  HAULAGE 

GENERAL  CONSIDERATIONS  AFFECTING  ELECTRIC  HAULAGE 

Advantages  and  Disadvantages  of  Electric  Locomotives. — All  well-designed 
and  well-built  haulage  motors  are  practically  equal  in  first  cost,  in  the  labor 
cost  of  running,  and  in  the  cost  of  repairs,  therefore,  as  an  effective  machine 
for  gathering  and  hauling  coal,  an  electric  locomotive  possesses  no  marked 
advantages  over  one  propelled  by  steam,  gasoline,  compressed  air,  or  storage 
battery.  The  advantages  and  disadvantages  commonly  attributed  to  one 
type  of  locomotive  as  compared  with  another,  are  in  reality  due  more  to  the 
power  employed  than  to  qualities  inherent  in  the  locomotive  itself. 

There  is,  however,  one  disadvantage  possessed  by  the  electric  locomotive 
that  does  not  exist  in  the  case  of  self-contained  locomotives  propelled  by 
steam,  gasoline,  or  compressed  air;  it  can  be  used  only  in  those  parts  of  the 
mine  where  trolley  wires  have  been  hung  for  conveying  the  power  and  where, 
at  the  same  time,  iron  rails  have  been  laid  for  the  return  circuit.  This  objection 
has  been  largely  overcome  through  the  use  of  a  combination  trolley  and  storage- 
battery  locomotive,  which  can  go  anywhere  in  the  mine;  through  the  use  of  a 
cable-reel  locomotive,  which  can  go  the  length  of  the  cable  beyond  the  end 
of  the  trolley  line;  and  through  the  use  of  the  crab  locomotive,  which,  while 
standing  on  the  main  road  and  drawing  current  from  the  trolley  line  can  pull  a 
car  from  a  distance  equal  to  the  length  of  the  rope  carried  on  its  rope  drum. 

So  far  as  safety  is  concerned,  the  only  locomotive  that  cannot  possibly 
ignite  either  methane  or  coal  dust  is  one  operated  by  compressed-air;  and  it 
cannot  cause  death  from  shock.  These  are  objections  made  rather  unjustly 
to  the  electric  locomotive  and  should  be  charged  against  the  means  of  conveying 
power  to  it,  the  naked  overhead  trolley  wire,  and  not  to  the  locomotive  itself 
which,  in  its  modern  form,  is  an  eminently  safe  machine.  It  may  be  argued 
that  the  ventilating  current  should  be  sufficient  to  prevent  the  existence  of 
dangerous  quantities  of  methane  either  in  entries  or  rooms,  that  accumulations 
of  coal  dust  should  be  avoided,  and  that  the  mine  should  be  watered  or  treated 
with  shale  dust,  and  that  men  should  be  careful  and  not  come  in  contact  with 
naked  live  wires,  but  while  the_  first  two  conditions  are  successfully  met  in  the 
majority  of  mines  and  there  is  usually  little  danger  of  an  electric  spark  or 
arc  igniting  either  methane  or  dust,  there  is  always  the  possibility  of  this 
happening  even  in  the  best-managed  mines.  The  dangers  of  shock  or  death 
through  contact  with  live  overhead  wires  can  hardly  be  removed  because  of 
the  seeming  impossibility  of  teaching  the  average  mine  worker  to  be  even 
reasonably  careful.  The  possibility  of  setting  fire  to  partitions,  timbers,  etc. 
is  so  slight  if  even  moderate  care  in  properly  insulating  the  wires  is  taken  as  to 
be  negligible.  A  danger  chargeable  to  the  locomotive  itself  may  arise  when  an 
unusually  heavy  trip  is  started  or  when  the  customary  load  is  pulled  up  a 
heavy  grade.  In  both  cases,  it  is  usual  to  sand  the  rails  and  if  too  much  sand 
is  used,  the  contact  between  the  locomotive  wheels  and  the  rails  for  the  return 
circuit  is  broken,  and  the  current  will  take  a  longer  but  easier  path.  This 
may  result  in  serious  shock  to  the  motorman,  or  if  the  current  passes  from  the 
locomotive  through  the  drawbars  of  the  cars  and  thence  to  the  rail  at  some 
unsanded  place,  those  riding  in  the  cars  may  be  injured,  powder  in  metallic 
cans  may  be  exploded,  etc.  The  last  is  such  a  real  danger,  numerous  acci- 
dents having  happened  therefrom,  that  in  many  states  it  is  prohibited  by  law 
to  transport  powder  in  cars  hauled  by  an  electric  locomotive.  _This  last_  danger 
may  be  overcome  in  a  very  great  measure  by  using  a  locomotive  of  a  size  pro- 
portioned to  the  work,  and  then  not  overloading  it. 

Where  many  power-consuming  machines  are  used  in  and  around  a  mine, 
rather  than  have  each  run  by  its  own  independent  power  generating  engine r 
it  is  cheaper  and  better  to  have  a  common  power  for  all  and  to  produce  this 
at  some  central  plant  and  transmit  it  to  the  various  points  of  application,  and 
it  is  the  general  adaptability  of  electricity  to  all  power  purposes  that  has  led 
to  its  extensive  use  in  the  operation  of  haulage  locomotives.  Electric  energy 
may  be  generated  at  any  reasonable  distance  from  the  mine  where  power 
may  be  had  and  may  be  easily  and  cheaply  transmitted  to  any  place  needed 
where  it  is  available  not  only  for  the  operation  of  haulage  motors  but  also  for 
that  of  coal-cutting  machinery,  pumps,  ventilating  fans,  shot-firing  systems, 
lighting  etc.  Hence,  in  mines  where  many  power-requiring  machines  are 
used,  and  particularly  where  these  are  scattered  throughout  the  workings, 
electricity  is  a  favorite  source  of  energy  and,  being  used  for  all  other  purposes, 
is  used  for  haulage.  On  the  other  hand,  in  mines  where,  aside  from  haulage, 


816 


H  A  ULAGE 


power  is  required  only  to  run  the  ventilating  fan,  it  will  unquestionably  prove 
cheaper  in  first  cost  and  probably  in  operation  to  install  a  steam  or  gasoline 
locomotive.  Compressed  air  may  also  be  transmitted  from  a  central  plant 
and  is  available  for  the  same  purposes  as  electricity,  except  shot  firing  and 
lighting  and  is  further  absolutely  safe  under  all  underground  conditions,  but  a 
compressed-air  plant,  including  the  piping,  is  more  costly  to  install,  extend, 
and  operate  than  an  electric  plant. 

Current  and  Voltage. — Direct  current  is  generally  used  for  electric  haulage; 
the  pressure  most  commonly  used  is  about  250  volts,  although  500  volts  has  been 
tried  and  is  still  used  in  some  places.  The  objection  to  the  higher  pressure 
is  the  greater  danger  of  injurious  or  fatal  shocks,  as  well  as  the  greater  difficulty 
of  insulating  the  wires  from  ground.  The  higher  pressure  can-  be  profitably 
used  only  where  all  the  passages  through  which  the  wires  are  strung  are  high 
or  roomy  enough  to  permit  placing  the  wires  where  there  will  be  little  danger 
of  contact  with  them,  and  dry  enough  to  preserve  the  insulation. 

Electric  Generators. — If  the  power  house  is  near  the  mouth  of  the  mine, 
direct-current  dynamos  are  generally  used  to  generate  the  electric  energy  for 
haulage  purposes,  and  at  the  pressure  used  in  the  mine,  250  or  500  volts  as  the 
case  may  be.  It  is  frequently  advantageous  to  locate  the  power  house  at  some 
distance  from  the  mine,  so  as  to  take  advantage  of  a  water  fall  to  generate 
the  power,  or  for  other  economic  reasons;  in  such  cases,  in  order  to  reduce  the 
cost  of  line  copper,  it  is  customary  to  transmit  a  high-voltage  alternating 
current  to  the  mouth  of  the  mine,  or  sometimes  to  the  interior  near  where  it 
is  to  be  used,  there  transform  it  in  step-down  transformers,  and  convert  it  by 
means  of  rotary  converters  to  direct  current  at  ordinary  mine  voltage,  after 
which  it  is  treated  in  the  mine  installation  precisely  as  would  be  the  case  with 
a  direct  current  generated  at  the  mouth  of  the  mine. 

Classes  of  Electric  Locomotives. — According  to  the  kind  of  current  used, 
electric  locomotives  may  be  divided  into  direct-current,  alternate-current,  and 
storage-battery  locomotives.  The  direct-current  locomotives  are  those  in 
general  use  in  the  United  States  and  may  be  single  or  tandem.  The  standard 
form  of  direct-current  locomotive  is  used  for  main-line  haulage;  the  modifica- 
tions of  it  used  for  gathering  are  known  as  combination,  cable-reel,  and  rope- 
reel,  or  crab,  locomotives.  A  special  type,  known  as  a  rack  or  third-rail 
locomotive,  is  used  on  heavy  grades. 

WIRING  FOR  ELECTRIC  HAULAGE 

Arrangement  of  Power  Lines. — In  a  shaft  mine  or  a  steep  slope,  insulated 
feeder  wires  are  run  from  the  dynamo  on  the  surface  down  the  shaft  or  the 
slope,  or  occasionally  down  a  bore  hole,  into  the  mine,  where  they  are  connected 
to  the  trolley  wire  and  rails  in  the  gangways;  or,  feeder  wires  may  be  con- 
tinued along  the  haulage  roads  for  a  distance  depending  on  the  length  of  the 
haulage  road  and  the  amount  of  electric  current  that  must  be  carried.  Where 

the  mine  opening  is  a  shallow  slope 
or  a  drift,  the  power  is  sometimes 
carried  into  the  mine  by  bare-wire 
conductors  fastened  at  intervals 
to  the  caps,  or  legs,  of  the  tim- 
bers. If  the  mine  opening  is  wet, 
the  power  is  transmitted  through 
lead-covered  cables.  In  shafts, 
the  cables  may  be  held  in  position 
by  wooden  brackets  placed  on  the 
sides  of  the  shaft,  or  suspended 
from  the  top  by  block  and  tackle, 
by  means  of  which  the  cables  may 
be  moved  up  or  down.  In  a  wei 
shaft,  the  lead  cable  is  carried  far 
enough  into  the  mine  from  the 

bottom  of  the  shaft  to  be  free  from  the  shaft  water,  and  is  then  connected  with 
the  bare  wire  used  in  haulage.  A  main  switch  should  be  provided  at  the 
foot  of  the  shaft  or  the  slope,  so  that  the  power  can  be  turned  off  or  on  instantly. 
Shape  of  Trolley  Wire. — Trolley  wire  is  made  with  round,  figure-8,  or 
grooved-cross-section,  as  shown  in  Fig.  1  (a),  (&),  and  (c),  respectively.  The 
round  wire,  shown  at  (a),  has  been  generally  used  for  the  purposes  of  mine 
haulage  and  for  transmitting  electric  power  into  the  mine.  The  preference  for 
mine  work  now  inclines  to  the  grooved  form  shown  at  (c).  This  wire  is  sup- 


Ear 


(a) 


FIG.  1 


HA  ULACE 


817 


ported  by  the  clamp  ears  a,  which  fit  into  grooves  in  the  sides  of  the  wire  just 
above  the  center.  The  figure-8  wire,  shown  at  (&),  is  liable  to  twist  between 
supports  and  throw;  off  the  trolley;  the  round  or  the  grooved  wire,  which  is 
practically  circular  in  section,  may  be  twisted  without  interfering  in  any  way 
with  the  trolley.  When  rounding  curves,  the  figure-8  wire  is  also  more  liable 
to  pull  or  twist  out  of  shape  or  out  of  the  clamps  entirely  than  either  of  the 
other  shapes. 

Location  of  Wires. — The  trolley  wire  is  located  above  the  track,  preferably 
along  one  side  and  from  6  to  15  in.  outside  the  rail,  so  as  to  be  out  of  the  way 
of  men  and  animals  passing  along  the  road.  Where  the  roof  is  good,  the  trolley 
wire  may  be  supported  directly  from  it.  The  trolley  construction  should  be  of 
the  most  substantial  nature,  and  the  work  of  installation  should  be  in  charge 
of  an  experienced  man,  as  the  care  and  thoroughness  with  which  this  is  done 
determine  largely  the  successful  operation  of  the  plant.  The  mining  laws  of 
many  states  provide  that  when  the  haulage  road  is  used  as  a  traveling  way, 
the  trolley  wire  shall  be  set  in  an  inverted  wooden  trough  or  boxing  with  sides 
from  3  to  5  in.  deep.  Various  provisions  are  made  for  the  safety  of  men 
compelled  to  pass  and  repass  under  the  trolley  wires  at  some  particular  point 
as  at  the  foot  of  a  shaft,  at  a  parting,  etc.  At  such  places  it  is  not  unusual  to 
compel  the  wires  to  be  placed  at  their  lowest  point  at  least  6  ft.  6  in.  above  the 
top  of  the  rail. 

Trolley  Frogs. — Fig.  2  (a)  shows  the  under  side  of  an  overhead  switch,  or 
trolley  frog,  used  to  guide  the  trolley  wheel  from  one  wire  to  another.  This 
is  a  simple  V  frog;  it  is  shown  in  its  natural  position  in  (b).  The  trolley  wires 
are  held  by  clamps  b,  and  the  span,  or  supporting,  wires  are  attached  to  the 
ears  a.  The  frog  must  be  placed  with  reference  to  the  track  so  that  the  motion 


c  and 
o  the 


of  the  locomotive,  as  it  takes  the  switch,  will  have  given  the  trolley  an  incli- 
nation in  the  right  direction  before  the  trolley  wheel  strikes  the  frog.  The 
frog  must  also  be  hung  level,  or  it  will  cause  the  wheel  to  leave  the  wire. 

A  simple  method  of  finding  the  proper  location  for  the  trolley  frog  is  shown 
in  Fig.  3.     Measure  the  distance  from  the  point  of  switch  a  to  the  fr 
half  way  between  these  points  make  a  chalk  mark  on  the  rail  at  b. 
same  on  the  straight  rail,  and  mark  the  half- 
way point  d.     Stretch  a  line  from  a  to  d  and 
one  from  e  to  b.     Directly  above  their  point  of 
intersection  /  is  the  place  for  the  frog. 

Resistance  of  Steel  Rails.  —  As  the  rails  form 
the  return  circuit  for  the  electric  current,  they 
must  be  considered  in  connection  with  the 
voltage  drop.  The  rail  itself,  on  account  of  its 
large  cross-section,  has  a  large  current-carrying 
capacity  and  the  bonding  should  be  done  so 
that  no  appreciable  drop  will  take  place  in  the 

joints.  The  weight  of  rail,  in  pounds  per  yard,  is  fixed  by  traffic  considera- 
tions and  is  usually  determined  by  allowing  10  Ib.  per  yd.  for  each  ton  of 
locomotive  weight  per  driving  wheel.  Thus,  a  10-T.,  four-wheel  locomotive 
will  have  10-7-4  =  2.5  T.  on  each  driver  and  the  required  weight  of  rail  will  be 
2.5X10  =  25  Ib.  per  yd.  This  formula  gives  the  minimum  weight  of  rail,  but 
much  better  results  will  be  obtained  by  using  the  heavier  rail  recommended  in 
the  accompanying  table. 

52 


FIG.  3 


818  HAULAGE 

SIZES  OF  LOCOMOTIVES,  RAILS,  AND  BONDS 


Weight  of 
Locomotive 
Tons 

Minimum  Weight  of  Rail 
per  Yard  and  Size  of  Bond 

Weight  of  Rail  per  Yard 
Recommended  and  Size 
of  Bond 

Rail 
Pounds 

Bond 
Number 

Rail 
Pounds 

Bond 
Number 

3 

4 
5 
6 
7 
,     8 
10 
15 
20 
25 

16 
16 
16 
16 
20 
20 
25 
40 
50 
60 

4 
4 
4 
4 
0 
0 
0 
00 
0000 
0000 

20 
25 
25 
30 
40 
40 
45 
50 
60 
80 

0 
0 
0 
0 
00 
00 
00 
0000 
0000 
0000 

RESISTANCE  OF  STEEL  RAILS 


The  resistance  of  steel  rails  to  the  passage  of  an  electric  current  varies 
considerably  with  the  composition  of  the  metal.  For  the  purpose  of  calculation 
it  is,  however,  common  to  take  the  specific  resistance  of  steel  rails  as  twelve 
times  that  of  copper.  While  this  value  may  seem  somewhat  high,  it  is  conser- 
vative and  will  allow  for  the  slight  additional  resistance  at  the  joints.  By  using 
the  values  from  the  following  table,  the  rails  can  therefore  be  considered  as 
continuous.  The  resistance  values  given  are  for  two  rails  in  parallel;  that  is, 
per  mile  of  track.  These  values  are  based  on  the  following  formula : 

.,  2.63 

ohms  per  mile  =  — :— j— — j rr— -r 

weight  of  rail  per  yard 

Bonding. — The  larger  part 
of  the  track  resistance  occurs 
at  the  joints  between  the  rails, 
and  as  the  fish-plates  do  not 
form  sufficient  electric  contact, 
the  ends  of  the  rails  at  the  joints 
are  always  connected  by  a  cop- 
per conductor  known  as  a  bond. 
The  first  of  the  two  tables  just 
given  shows  that  the  area  of 
metal  in  the  bond  is  essentially 
the  same  as  that  in  the  trolley 
wire. 

There  are  many  types  of  rail 
bonds,  but  these  may  be  divided 
into  two  general  classes;  pro- 
tected bonds,  or  those  placed  be- 
tween the  fish-plate  and  the  rail, 
and  unprotected  bonds,  which 
either  span  the  fish-plate  or  are 
placed  under  the  rail.  All 
should  be  attached  to  the  rail  in  such  a  way  that  the  contacts  between  the 
copper  and  steel  are  clean  and  bright  when  made. 

Fig.  4  (a)  shows  a  protected  bond  of  the  double-loop  type,  shaped  so  as  to 
give  flexibility  and  at  the  same  time  allow  openings  for  the  track  bolts.  This 
bond  is  made  of  thin  copper  strips  on  which  copper  terminals  ab  are  cast.  After 
the  terminals  have  been  passed  through  the  holes  in  the  rail,  they  are  com- 
pressed by  a  special  screw  compressor,  which  forces  the  metal  out  sidewise 
firmly  against  the  sides  of  the  holes.  View  (7>)  shows  this  bond  in  position, 
part  of  the  fish-plate  being  cut  away  to  expose  the  bond  to  view.  The  holes 
through  the  rail  for  track  bolts  show  through  the  loops  of  the  bond. 

Fig.  5  shows  one  form  of  unprotected  bond.  The  copper  terminals  are 
pressed  into  the  holes  in  the  rails  by  a  powerful  screw  press,  which  expands 


Weight  of  Rail 
per  Yard 

Resistance  per  Mile 
of  Track 

Pounds 

Ohms 

16 

.1642 

20 

.1313 

25 

.1051 

30 

.0876 

40 

.0657 

45 

.0583 

50 

.0525 

60 

.0438 

80 

.0328 

HA  ULAGE 


819 

All  bonds 


the  metal  in  the  hole  so  as  to  give  complete  contact  with  the  rails, 
should  be  inspected  frequently,  as  they  may  work  loose. 

A  poor  return  circuit,  which  is  due  to  poor  bonding,  is  responsible  for  much 
of  the  motor  trouble.  If  the  voltage  drops  because  of  poor  bonding  or  from 
any  other  cause  the  amperes  will  be  increased  with  the  result  that  the  armatures 
will  heat  and  possibly  burn  out.  Poor  bonding  is  commonly  indicated  by 
the  marked  drop  in  the  illuminating  power  of  the  headlight  (which  then  burns 
with  a  dull  red  glow)  when  a 
trip  is  started. 

Cross-Bonding. — In  addition 
to  the  regular  bonding  at  the 
joints,  the  one  line  of  rails 
should  be  electrically  joined,  or 
cross-bonded,  to  the  other  at 
intervals  of  not  more  than  500 
ft.  and  by  conductors  of  the  size 
used  for  bonding.  The  object 
of  cross-bonding  is  to  still  pro- 
vide a  complete  return  circuit 
in  event  of  some  of  the  rail 
bonds  jarring  loose.  Instead  of 
the  standard  form  of  cross- 
bonding  both  the  D.,  L.,  &  W. 
R.  R.  and  the  L.  C.  &  N.  Co. 
have  successfully  used  old  wire 
hoisting  rope  as  a  portion  of 
the  return  -circuit.  The  largest 
size  of  rope  is  used  on  the  main 
haulage  roads  and  H-in.  rope 

on  the  branches.     The  rope  is  FIG.  4 

suspended  near  the  bottom  of 

the  props  which  carry  the  feed  wire  and  is  bonded  to  the  rails  every  250  to 
300  ft.  Where  the  rope  has  to  be  spliced,  the  abutting  ends,  after  being  thor- 
oughly cleaned  and  brightened,  are  inserted  in  the  opposite  ends  of  short 
pieces  of  lead  pipe  that  are  filled  with  solder.  The  attachments  for  bonding 
the  rope  to  the  rail  are  made  by  soldering  a  clamp  to  the  rope,  using  the 
regular  bonding  hole  on  the  rail.  Tests  have  shown  that  the  current-carrying 
capacity  of  a  Is-in.  hoisting  rope  made  of  steel  low  in  carbon  and  manganese 
is  the  same  as  that  of  a  rail  weighing  30  Ib.  per  yd. 

Feeders. — Current  is  generally  fed  to  the  locomotive  through  an  overhead 
trolley  system  with  the  track  rails  forming  the  return  circuit  as  explained. 
In  addition  to  the  trolley  wire,  it  is  also  almost  always  necessary  to  install 
feeders  to  reduce  the  drop  in  voltage.  A  feeder  is  a  heavy  insulated  or  bare 

copper  cable  suspended  along  one 
side  of  the  heading  and  is  tapped 
into  the  trolley  wire  at  intervals 
along  the  route. 

In  the  early  days  of  electric  mine 
haulage,  the  size  of  trolley  wire  was 
much  smaller  than  now  used,  the 
size  varying  from  No.  0  to  No.  0000. 
The  former  is  only  used  in  small 
one-  or  two-locomotive  installa- 
tions, and  experience  has  shown 
that  a  heavy  trolley  wire  is  of  con- 
siderable advantage.  For  this  rea- 
pIG  ^  son  the  use  of  No.  0000  trolley  wire 

is  now  very  common. 

The  size  of  the  feeders  depends  on  the  length  of  the  haul,  the  distribution 
of  the  load,  the  current  to  be  transmitted,  and  the  permissible  voltage  drop. 
Excessive  drop  is  a  very  common  cause  for  complaint  in  a  mine  using  electric 
haulage  and  it  always  pays  to  put  sufficient  copper  in  the  feeders  to  prevent 
the  voltage  at  the  locomotives  from  falling  to  too  low  a  value.  Low  line 
voltage  makes  it  difficult  to  maintain  the  schedule  and  gives  rise  to  trouble 
with  the  motors,  to  say  nothing  of  the  cost  of  the  power  loss.  As  an  approxi- 
mate rule,  the  voltage  drop  from  the  point  of  supply  to  any  locomotive  should 
be  kept  within  20%. 

An  approximate  estimate  of  what  the  drop. in  the  rails  will  be  can  easily 


820  HA  ULAGE 

be  formed  at  the  outset  by  means  of  the  table  on  page  818.     The  balance  of 
the  drop  will  then  give  that  allowed  for  the  trolley  and  feeders  combined,  and 
their  cross-section  can  be  determined  from  the  following  formula: 
.          .       .       ,          .„       10.8XLX7 
Area,  in  circular  mills  =  -  —  — 

in  which  L  =  distance  between  point  of  supply  and  load,  in  feet; 
7=  maximum  current,  in  amperes; 
Z?  =  drop  in  trolley  and  feeders,  in  volts. 

From  the  value  so  found  is  subtracted  the  cross-section  of  the  trolley,  in 
circular  mils,  the  result  being  the  required  size  of  the  feeders.  The  calculation 
is  easy,  the  only  difficulty  being  the  variation  in  the  load  both  in  magnitude 
and  position. 

In  order  to  illustrate  the  method  of  calculation  assume  the  following 
examples: 

EXAMPLE  1.  —  Find  the  size  of  feeder,  if  the  voltage  is  500;  rails,  40  lb.; 
trolley,  No.  0000;  length  of  road,  1  mi.;  load,  400  K.  W.,  bunched  at  end  of 
line;  permissible  drop,  20%  =  100  volts. 

SOLUTION.  —  Resistance  of  1  mi.  of  two  40-lb.  rails  =  .0657;  current  =  400,000 
^500  =  800  amp.;  drop  in  rails  =  800  X.  0657  =  52.6  volts.  This  leaves  a  drop 
of  100  —  52.6  =  47.4  to  take  place  in  the  trolley  wire  and  feeder.  Assuming  the 
same  conductivity  of  the  material  in  these,  their  combined  cross-section  should 


The  trolley  wire  is  No.  0000  and  has  a  cross-section  of  211,600  cir.  mils. 
Deducting  this  from  the  total  cross-section  of  965,000,  leaves  965,000  —  211,600 
=  753,400  or  about  750,000  cir.  mils. 

EXAMPLE  2.  —  Suppose  that  the  total  load  of  400  K.  W.  is  equally  distributed, 
what  size  of  feeder  is  required? 

SOLUTION.  —  This  is  equivalent  to  an  average  load  of  200  K.  W.  transmitted 
over  the  whole  circuit.     The  drop  in  the  rails  is  now  only  half  the  former 
value  or  26.3  volts,  leaving  100  —  26.3  or  73.7  volts  to  be  consumed  in  the 
trolley  and  feeders.     Their  combined  cross-section  will  therefore  be: 
10.8X5,280X400     r 

-  ^-=  --  =  310,000  cir.  mils 
7o.7 

Deducting  from  this  211,600  cir.  mils  for  the  trolley  leaves  only  about 
100,000  cir.  mils,  which  corresponds  to  No.  0  feeder. 

In  making  these  calculations,  attention  must  be  paid  to  the  carrying 
capacity  of  the  wires  and  cables.  This  must  be  kept  in  mind,  because  if  the 
lines  are  simply  figured  out  on  the  basis  of  giving  the  allowable  drop,  the  current 
may  be  sufficient  to  overheat  the  wires.  In  most  cases,  however,  the  size  of 
wire  necessary  to  keep  the  drop  within  the  specified  limits  will  be  considerably 
larger  than  necessary  to  handle  the  current  without  overheating.  It  is  always 
well,  however,  to  compare  the  sizes  obtained  and  the  current  carrying  capacity, 
which  will  be  found  in  the  wire  table. 

By  referring  to  Example  1,  it  is  seen  that  there  is  no  danger  of  overheating, 
but  in  Example  2  it  will  be  necessary  to  increase  the  size  considerably  in  the 
section  nearest  the  station  where  the  current  value  is  too  high. 

The  pressure  at  which  the  current  is  supplied  to  the  motors  is  limited  by 
considerations  of  safety.  It  would  otherwise,  of  course,  be  desirable  to  use  a 
higher  pressure,  because  this  would  mean  a  lower  current,  less  drop  and  smaller 
feeders  for  the  same  power.  For  this  reason  500  volts  is  used  in  a  few  mine 
haulage  systems,  although  250  volts  evidently  is  somewhat  safer  in  operating. 

In  mines  of  ordinary  capacity,  it  will  be  uneconomical  to  use  the  direct- 
current  system  only,  when  the  current  has  to  be  transmitted  for  distances 
over  1  mi.,  and  many  mines  have  during  the  last  few  years  been  changing 
over  their  systems  to  a  combination  alternating  current  and  direct  current. 
That  is,  alternating  current  is  generated  and  transmitted  at  a  higher  voltage 
to  substations  distributed  along  the  tracks.  In  these  substations,  the  alter- 
nating current  is  changed  to  direct  current  by  means  of  synchronous  converters. 
In  this  manner  the  250-  volt,  direct-current  supply  can  be  brought  near  the 
centers  of  distribution  and  the  losses  in  the  lines,  feeders,  and  rails  are  consider- 
ably reduced,  also  smaller  size  conductors  can  be  used. 

The  following  table  shows  the  distance  to  which  100-K.  W.,  three-phase 
current  can  be  transmitted  over  different  sizes  of  wires  at  different  potentials, 
assuming  an  energy  loss  of  10%.  A  power  factor  of  85%  is  shown  by  the 
table. 


HA  ULAGE 


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EXAMPLE. — What  size  of 
wires  should  be  used  to  de- 
liver 500  K.  W.  at  6,000 
volts,  at  the  end  of  a  three- 
phase  line  12  mi.  long,  allow- 
ing energy  loss  of  10%  and 
a  power  factor  of  85%? 

SOLUTION. — If  the  ex- 
ample called  for  the  trans- 
mission of  100  K.  W.  (on 
which  the  table  is  based), 
look  in  the  '6,000- volt 
column  for  the  nearest 
figure  to  the  given  distance, 
and  take  the  size  wire  cor- 
responding. But  the  ex- 
ample calls  for  the  trans- 
mission of  five  times  this 
amount  of  power,  and  the 
size  of  wire  varies  directly 
as  the  distance,  which  in 
this  case  is  12  mi.  There- 
fore, look  for  the  product 
5X12  =  60  in  the  6,000-volt 
column  of  the  table.  The 
nearest  value  is  60.44  and 
the  size  wire  corresponding 
is  No.  00,  which  is,  there- 
fore, the  size  capable  of 
transmitting  100  K.  W.  over 
a  line  60.44  mi.  long,  or  500 
K.W.  over  a  line  12  mi.  long. 

If  it  is  desired  to  ascer- 
tain the  size  wires  that  will 
give  an  energy  loss  of  5%, 
or  one-half  the  loss  for 
which  the  table  is  com- 
puted, it  is  only  necessary 
to  multiply  the  value  ob- 
tained by  2,  for  the  dia- 
meter varies  directly  as  the 
per  cent,  energy  loss. 


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822  HA  ULAGE 

DIRECT-CURRENT  LOCOMOTIVES 

Number  and  Arrangement  of  Motors. — Direct-courrent  electric  locomotives 
with  two  pairs  of  driving  wheels  may  have  one  or  two  motors,  while  those 
with  three  pairs  of  drivers  commonly  have  three  motors. 

In  the  single-motor  locomotive,  the  armature,  which  is  set  lengthwise  of 
the  frame,  is  geared  at  each  end  to  a  driving  axle  with  the  result  that  both 
pairs  of  wheels  revolve  at  the  same  time  and_  with  the  same  speed.  This 
arrangement  insures  a  high  degree  of  adhesion  with  consequent  strong  tractive 
effort,  together  with  perfect  distribution  of  the  weight  on  the  drivers  and 
good  contact  between  the  wheels  and  the  rail. 

There  are  two  standard  methods  of  mounting  the  motors  in  two-motor 
locomotives.  In  the  tandem  mounting,  one  motor  is  placed  between  the  axles 
and  the  other  between  the  forward  axle  and  the  front-end  frame.  In  the 
central,  or  inside,  mounting,  both  motors  are  placed  between  the  axles.  The 
tandem  mounting  permits  of  a  short  wheel  base  and  is  adapted  for  .light-  and 
medium-weight  locomotives,  which  are  commonly  required  to  operate  upon 
sections  of  the  track  having  short-radius  curves.  The  central,  or  inside, 
mounting  requires  a  longer  wheel  base  and  is  adapted  for  heavy  locomotives 
used  in  main-line  haulage,  where  the  roads  are  commonly  straight  or  with 
curves  of  long  radius.  With  either  arrangement,  the  locomotive  frame  is 
proportioned  to  give  an  equal  distribution  of  the  weight  between  both  pairs 
of  driving  wheels.  The  motors  may  also  be  end  mounted  by  placing  each 
motor  in  the  space  between  the  axle  and  the  forward  and  rear  frames,  respec- 
tively. This  permits  of  a  minimum  wheel  base,  but  is  only  used  to  meet 
very  unusual  conditions.  An  advantage  claimed  for  the  two-motor  locomotive 
is  that,  in  case  of  accident  to  one  of  the  motors,  the  defective  one  may  be 
disconnected  and  the  machine  run  with  one  motor  to  the  repair  shop  or  it  may  be 
kept  in  operation  although  able  to  do  less  work.  The  advocates  of  the  two- 
motor  machine  also  claim  for  it  higher  efficiency  and  better  speed  control 
than  is  possible  with  the  single-motor  locomotive. 

Six-wheel,  three-motor  locomotives  of  15  to  25  T.  weight  may,  to  a  certain 
extent,  be  used  instead  of  the  tandem  locomotives  described  on  page  826,  for 
long  and  heavy  runs  over  a  main  haulage  road.  Their  application  is,  however, 
more  or  less  restricted,  as  on  account  of  their  greater  length  they  may  not 
take  the  sttarp  curves  usually  found  in  mine  work.  Where  this  is  not  objec- 
tionable, locomotives  of  this  kind  have  advantages,  one  being  the  possibility 
of  using  lighter  rails  than  for  a  two-motor  locomotive  of  the  same  weight,  due 
to  the  equalization  of  the  weight  on  all  three  pairs  of  driving  wheels.  To  insure 
this,  irrespective  of  any  irregularities  of  the  track,  three-motor  locomotives 
are  supported  from  the  journal-boxes,  thus  insuring  at  all  times  an  even  division 
of  the  load  among  the  three  motors.  The  equalizing  system  also  furnishes 
a  flexible  suspension  of  the  weight  and  produces  an  easy  running  locomotive, 
greatly  minimizing  the  wear  and  tear  on  the  track  and  roadbed.  The  center 
pair  of  wheels  is  generally  furnished  without  flanges  so  as  to  prevent  any 
binding  on  the  curves. 

Construction  of  Motors. — In  the  design  and  construction  of  mine  loco- 
motive motors,  the  following  requirements  are  essential:  Maximum  capacity 
within  the  gauge  limitations;  large  overload  capacity;  accessibility  for  inspec- 
tion and  repair;  large  bearing  surface  to  minimize  wear;  protection  against  dust 
and  moisture;  accurate  machining  to  insure  interchangeability  of  parts; 
rugged  construction  to  withstand  rough  usage. 

The  motors  are  always  of  the  series  type  and  should  preferably  be  equipped 
with  commutating  poles.  In  this  kind  of  motor,  the  same  current  passes 
through  the  main-series  and  commutating-pole  field  coils.  The  torque  exerted 
and  the  speed  at  which  it  will  run,  depend  on  the  flux  entering  the  armature,  the 
number  of  conductors  on  the  armature,  and  the  amount  of  current  flowing  in 
the  winding.  The  flux,  in  turn,  depends  on  the  strength  of  the  field  magnets, 
which  in  their  turn  depend  on  the  number  of  turns  in  the  field  coil  and  the 
amount  of  current  flowing  therein.  The  advantage  of  the  commutating  poles, 
which  are  connected  in  series  with  the  armature,  lies  in  the  fact  that  the  electrical 
and  mechanical  neutrals  are  made  to  coincide  for  all  loads  and  for  either 
direction  of  rotation,  thus  assuring  good  commutation  under  all  conditions 
of  operation. 

The  motor  frames  are  split  diagonally  so  that  the  upper  part  can  be  lifted 
off,  exposing  the  interior  for  inspection.  The  bearing  heads  are  securely 
clamped  between  the  upper  and  lower  frames,  making  it  possible  to  readily 
take  out  the  armature  for  repairs.  The  laminations,  armature  windings,  and 


HA  ULAGE  823 

commutator  are  all  mounted  on  a  common  spider  so  that  the  shaft  may  be 
removed  without  disturbing  them,  and  interchange  can  therefore  readily  be 
made. 

The  armature  bearings  are  commonly  of  the  Babbitt-lined,  bronze-sleeve 
construction,  designed  for  oil  and  waste  lubrication.  The  Babbitt  is  of  such  a 
thickness  that  should  it  be  melted  from  lack  of  lubrication,  the  shaft  will  be 
supported  by  the  sleeves  before  the  armature  strikes  the  pole  pieces. 

The  use  of  ball  bearings  in  mine-locomotive  motors  is  a  new  feature.  Where 
they  have  been  tried,  they  have  given  excellent  results,  and  at  present  they  bid 
fair  to  displace  the  plain  bearings  for  this  class  of  service.  The  principal  advan- 
tage gained  by  the  use  of  ball  bearings  is  the  small  amount  of  lubricant  required. 
This  lubricant  being  vaseline  or  some  similar  grease  in  small  amounts,  there  is 
very  little  possibility  of  its  getting  into  the  motor  windings.  There  is  a  great 
advantage  in_this,  as  a  large  percentage  of  the  motor  troubles  can  be  traced 
directly  to  oil  having  worked  its  way  into  the  windings.  When  properly 
lubricated,  ball  bearings  have  another  advantage,  in  that  there  is  but  a  small 
amount  of  wear.  This  decreases  the  liability  of  the  armature  coming  down 
on  the  pole  faces  with  damaging  results. 

The  field  coils  are  held  securely  in  place  by  spring-steel  flanges,  which  are 
pressed  against  the  coils  by  the  pole  pieces  when  the  latter  are  bolted  in  place. 

Controllers. — The  controllers  are  of  the  rheostat  magnetic  blow-out  kind. 
A  commutating  switch  is  incorporated  in  the  reverse  cylinder,  the  handle  of 
which  has  four  on-positions,  two  for  each  direction  of  motion,  one  with  motors 
in  series  and  the  other  with  motors  in  multiple.  The  main  and  reverse  cylinders 
are  interlocked  in  the  usual  manner  and  the  main  cylinder  provides  for  speed 
regulation  with  motors  in  series  or  multiple.  This  system  of  control  by  per- 
mitting motors  to  be  started  in  multiple,  allows  them  to  exert  their  maximum 
tractive  effort  independently,  so  that  the  slippage  of  one  motor  does  not  affect 
the  other — a  valuable  feature  for  starting  heavy  trains. 

When  the  operating  handle  is  in  the  off-position,  all  parts  of  the  motor 
and  rheostat  equipment  are  dead  and  it  is  also  impossible  to  retard  the  train 
by  bucking  the  motors — a  practice  of  motormen  that  is  liable  to  cause  trouble. 

While  single-end  control  may  be  considered  standard,  locomotives  are  often 
built  with  a  controller  at  each  end,  a  construction  often  of  advantage. 

Frames. — The  general  construction  of  electric  mine  locomotives  involves 
two  distinct  forms,  one  in  which  the  side  frames  are  placed  outside  the  wheels, 
and  the  other  in  which  they  are  placed  inside  the  wheels. 

For  a  given  track  gauge,  the  outside  frame  allows  the  maximum  space 
between  the  wheels  for  the  motors  and  other  parts  of  the  equipment,  renders 
the  journal-boxes  more  accessible,  and  gives  somewhat  more  space  at  the 
operating  end  for  the  mototman.  The  inside  frame  restricts,  to  a  certain 
extent,  the  space  between  the  wheels  available  for  motors  and  other  equipment, 
but  allows  for  the  minimum  overall  width,  a  construction  that  is  necessary 
in  those  mines  where  the  props  are  set  close  to  the  track  or  the  space  outside 
the  rails  is  otherwise  limited.  The  wheels  being  outside  the  frame,  this  loco- 
motive in  case  of  derailment  is  somewhat  more  readily  replaced. 

The  locomotives  may  be  supplied  with  side  frames  of  cast  iron  or  rolled 
steel  plate,  the  latter  construction  being  now  the  most  generally  used.  Ihe 
end  frames  as  a  rule  consist  of  steel  channels  fitted  with  heavy  wooden  bumpers, 
except  on  large  locomotives  where  cast-iron  bumpers  may  be  advantageous 
in  order  to  get  more  dead  weight.  The  bumpers  and  coupling  devices  must 
be  designed  to  suit  the  mine  cars. 

Wheels  and  Journals.— The  weight  of  the  locomotive  is  ordinarily  supported 
from  the  journal-boxes  on  heavy  helical  springs.  The  journals  are  somewhat 
similar  to  those  on  railway  cars  that  have  removable  brasses  and  are  lubricated 
from  oil  cellars  filled  with  waste. 

The  construction  of  the  journal-boxes  is  such  that  the  brasses  can  be  removed 
without  disturbing  the  axles  or  frame  stay-plates.  On  outside-frame  loco- 
motives, this  is  accomplished  by  jacking  up  the  frame  to  relieve  the  pressure 
on  the  journal-box  spring  and  removing  two  vertical  retaining  plates.  Ihe 
inside-frame  journal-boxes  are  fitted  with  a  removable  oil  cellar,  which  can  be 
lowered  for  repacking. 

Plate  wheels  are  generally  used  for  outside-frame  locomotives,  while  for  the 
inside-frame  construction  spoked  wheels  are  used,  in  order  to  give  access  to 
the  journal-boxes. 

Chilled  cast-iron  and  steel  tires  or  rolled-steel  wheels  are  in  general  use, 
the  first  named  being,  however,  the  more  common.  These  are  approximately 
60%  cheaper  than  steel-tired  wheels  and  45%  cheaper  than  those  of  rolled 


824  HAULAGE 

steel.  The  higher  cost  of  the  steel  wheels  is,  however,  largely  offset  by  the 
fact  that  the  treads  can  be  refaced  several  times,  if  facilities  are  provided 
therefor  in  the  repair  shop. 

A  somewhat  increased  adhesion  is  generally  realized  by  the  adoption  of 
steel  wheels  for  mine  service.  While  opinions  differ  greatly  as  to  how  much 
this  really,  amounts  to,  it  is  generally  conceded  to  be  about  5%.  A  considerable 
portion  of  this  increased  effort  is  often  found  to  be  due  to  the  geater  weight 
of  such  wheels,  and  a  comparison  is  difficult  to  make,  as  both  the  wheel  tread 
and  rail  are  always  subject  to  wide  variations  caused  by  moisture,  nature  of 
the  surface,  amount  and  quality  of  sand  used,  etc. 

Brakes. — Several  kinds  of  brake  mechanisms  are  in  use.  In  an  exception- 
ally strong  and  efficient  one,  the  brake  shoes  are  automatically  locked  in  any 
position  in  which  they  are  left  by  the  operator  without  the  use  of  pawls  or 
ratchets.  The  brake  shoes,  made  of  cast  steel,  are  removable  in  order  to 
insure  a  long  life  and  in  addition  exert  a  dressing  action  on  the  wheel  tread. 

In  certain  instances  where  there  is  a  heavy  down  grade,  in  order  to  be 
sure  of  controlling  the  loaded  trains,  a  special  rail-grip  brake  is  provided  in 
addition  to  the  usual  wheel  brakes.  Jaws  are  arranged  to  press  the  shoes 
against  a  third  rail,  which  is  laid  in  the  center  of  the  track.  This  brake  is 
powerful  enough  to  stop  a  train  within  a  distance  of  100  ft.  on  an  8%  grade, 
the  train  weighing  100  T.,  exclusive  of  locomotive,  and  running  at  a  speed 
of  8  mi.  per  hr. 

Sand  riggings  are  always  provided,  and  the  sand  boxes  so  arranged  that 
the  rails  may  be  sanded  ahead,  when  running  in  either  direction. 

Trolleys. — In  the  standard  mine  trolley,  the  wheel  is  mounted  in  a  swiveled 
harp,  which  permits  it  to  aline  itself  with  the  trolley  wire,  irrespective  of  the 
direction  of  the  pole.  The  pole  is  of  wood  and  the  lower  end  is  inserted  in  a 
swiveled  base,  which  fits  into  sockets  on  either  side  of  the  locomotive.  The 
force  of  the  compressed  spiral  spring  is  so  applied  to  the  pole  that  the  pressure 
of  the  trolley  wheel  against  the  wire  is  approximately  uniform  throughout 
the  limits  of  vertical  variation  and  the  swivel  harp  permits  a  wide  lateral 
variation  of  the  wire.  The  pole  being  of  wood  is  thoroughly  nonconducting, 
and  is  so  located  that  the  motorman  can  easily  handle  and  reverse  it  without 
leaving  his  position.  The  trolley  cable  terminates  in  a  contact  plug,  which 
fits  in  a  receptacle  placed  on  each  side  of  the  locomotive  so  that  the  change 
from  one  side  to  the  other  is  readily  effected. 

Some  locomotives  are  made  with  two  trolley  poles,  one  at  each  side. 
This  construction  is  convenient  in  those  mines,  where  for  any  reason  it  is 
necessary  to  hang  the  trolley  wire  on  the  side  opposite  to  the  one  where  it 
is  usually  placed. 

Headlights. — The  headlights  provided  at  each  end  of  the  locomotive,  are 
usually  each  fitted  with  a  32-c.p.  incandescent  lamp,  which  gives  sufficient 
illumination.  A  luminous-arc  mine  headlight  is,  however,  manufactured,  the 
mechanism  of  which  is  simple  and  requires  little  attention.  The  upper  electrode 
is  made  of  copper  and  lasts  from  2,000  to  3,000  hr.,  while  the  lower  one, 
which  is  made  of  a  composition  of  magnetite,  lasts  from  50  to  75  hr. 

Capacity  of  Locomotives. — Local  conditions  must  be  given  a  very  careful 
study  in  laying  out  a  system  of  electric  mine  haulage.  Not  only  should  the 
present  output  be  considered  but  also  the  possibilities  of  increased  output 
and  longer  hauls.  The  number  of  cars  to  be  handled  per  trip  and  per  hour, 
the  time  of  lay-over,  etc.,  must  be  correctly  determined  so  as  to  result  in  the 
most  efficient  operation.  It  is  also  important  that  the  main-haul  locomotives 
have  sufficient  capacity  to  place  on  the  parting  enough  empty  cars  per  trip 
to  serve  the  gathering  locomotives  simultaneously  in  order  to  prevent  any 
reduction  in  the  output  from  delays. 

The  amount  of  load  that  a  locomotive  is  capable  of  hauling  depends  on 
the  weight  of  the  locomotive,  the  adhesion  between  the  driving  wheels  and  the 
track,  the  frictional  resistance  of  the  trailing  load,  and  the  curvature  and 
gradients  of  the  track. 

The  adhesion  varies  greatly,  depending  on  the  condition  of  the  surfaces 
in  contact,  but  experience  has  shown  that  with  clean  dry  rails  on  a  level  track 
the  coefficient  of  adhesion  can  safely  be  assumed  to  be  20%  for  cast-iron  wheels 
and  about  25%  for  steel-tired  wheels.  A  10-T.  locomotive  with  steel-tired 
wheels,  for  example,  will  develop  on  a  straight  level  track  a  maximum  tractive 
effort  of  10  X  2,000 X. 25  =  5,000  lb.,  before  slipping  the  wheels. 

With  wet  and  slippery  rails,  when  starting  heavy  trains  or  on  steep  grades, 
sand  is  used  to  increase  the  adhesion,  which  by  this  means  may  be  increased 
to  about  25  to  30%  for  cast-iron  wheels  and  30  to  33J%  for  steel-tired  wheels. 


HA  ULAGE  825 

Due  to  excessive  wear  of  wheels  and  other  undesirable  effects  when  it  is  used 
too  freely,  sand  should  be  limited  in  application  to  starting  heavy  trips  and 
climbing  the  steepest  grades.  It  is  therefore  not  advisable  to  load  a  locomotive 
to  its  maximum  tractive  effort  continuously,  but  about  10  or  15%  reserve 
capacity  should  preferably  be  left. 

Only  moderate  acceleration  and  retardation  are  as  a  rule  required  in  mine- 
haulage  service,  .2  mi.  per  hr.  per  sec.  being  a  sufficient  value.  This  corre- 
sponds to  a  force  of  about  20  Ib.  per  gross  ton  of  the  combined  load  and  loco- 
motive. This  factor,  however,  is  usually  neglected  unless  the  train  is  to  be 
started  on  a  grade,  as  the  slack  can  be  taken  up  at  the  several  couplings  and 
thus  only  one  car  at  a  time  is  actually  started.  Quite  steep  grades  exist  also 
in  the  majority  of  cases,  and  the  increased  capacity  of  the  locomotive  to  take 
care  of  these  is  usually  greater  than  the  percentage  increase  in  weight  of  the 
locomotive  demanded  due  to  acceleration. 

Where  the  service  demands  a  high  rate  of  acceleration,  the  weight  of  the 
locomotive  must  be  increased  accordingly.  The  unit  of  acceleration  is  gener- 
ally taken  as  1  mi.  per  hr.  per  sec.,  and  the  force  required  to  accomplish  this 
is  about  95.  Ib.  per  T.  above  the  frictional  resistance. 

Frictional  load  resistance  is  caused  by  the  friction  of  the  wheel  treads  and 
flanges  against  the  rails  and  by  the  friction  of  the  car  journals.  It  may  be 
as  low  as  10  Ib.  a  T.  or  as  high  as  60  Ib.,  depending  on  the  nature  and  condition 
of  the  bearings,  the  size  of  rails,  etc.  For  narrow-gauge  roads  with  light 
rails  and  ordinary  mine  cars,  from  20  to  30  Ib.  per  T.  is  a  fair  figure. 

For  the  locomotives,  a  resistance  of  from  12  to  15  Ib.  per  T.  is  quite  common, 
but  this  is  generally  such  a  small  percentage  of  the  total  tractive  effort  that  it 
can  be  neglected. 

The  resistance  due  to  curves  can  generally  be  neglected  unless  the  curves 
are  very  long  or  have  a  very  short  radius.  Ordinarily,  only  a  portion  of  the 
trip  will  be  on  a  curve  at  one  time,  so  that  the  drawbar  pull  to  be  added  should 
be  based  only  on  the  actual  number  of  cars  that  are  moving  around  the  curve. 
Many  grades  in  mining  work  are  so  short  that  only  a  part  of  the  trip  can 
occupy  the  up  grade  at  one  time,  the  balance  of  the  trip  being  on  a  lesser  grade, 
on  a  level,  or  on  a  down  grade.  By  accelerating  to  a  high  speed  as  the  hill,  is 
approached,  quite  steep  grades  of  short  length  may  be  mounted  without  diffi- 
culty, and  in  such  cases  the  locomotive  can  be  worked  close  to  the  slipping  point. 

The  resistance  due  to  grades  is  always  20  Ib.  per  T.  for  each  per  cent,  grade 
and  not  only  does  a  grade  greatly  increase  the  total  train  resistance,  but  it  also 
reduces  the  available  drawbar  pull  of  the  locomotive,  for  of  the  total  tractive 
effort  developed  at  the  drivers,  20  Ib.  per  T.  for  each  1%  grade  is  consumed 
solely  in  driving  the  locomotive  itself  up  the  grade. 

The  size  of  a  locomotive  for  a  given  load  is  therefore  principally  determined 
by  the  limiting  grade.  For  example,  assume  a  trailing  load  of  80  T.,  a  frictional 
car  and  track  resistance  of  20  Ib.  per  T.,  and  a  track  that  is  practically  level 
throughout  with  the  exception  of  a  stretch  of  2%  grade.  The  total  train 
resistance  on  the  level  portion  of  the  track  is  SOX  20  =  1,600  Ib.,  but  on  the  grade 
it  is  80  (20+2X20)  =4,800  Ib.,  and  in  addition  the  force  required  for  propelling 
the  locomotive  up  the  grade.  A  4-  or  5-T.  locomotive  can  easily  handle  this 
on  the  level,  while  a  13-  or  14-T.  locomotive  will  be  required  to  get  it  over 
the  grade. 

Selection  of  Motors. — Motors  for  mine  locomotives  are  generally  rated 
on  the  1-hr,  basis;  that  is,  the  load  that  they  will  carry  continuously  for  1  hr. 
without  exceeding  a  certain  specified  temperature,  usually  75°  C.  Standard 
equipments  are  furthermore  so  selected  that  the  motors  will  develop  the  rated 
drawbar  pull  and  speed  of  the  locomotive  on  the  above  basis.  Short  overloads 
of  15  or  20%  can  generally  be  taken  care  of,  while  at  overloads  of  about  25% 
the  wheels  will  begin  to  slip. 

The  1-hr,  rating  of  a  motor  depends  largely  on  the  terminal  capacity,  while 
the  real  capacity  is  its  ability  to  perform  its  cycle  of  operations  during  the 
entire  day.  The  selection  of  the  proper  motor  equipment  on  this  basis,  after 
its  weight  has  been  decided  on,  involves  a  complete  knowledge  of  the  profile 
of  the  road,  the  number  of  cars  to  be  handled  per  trip  and  per  hour,  the  weight 
of  the  empty  and  loaded  cars  and  the  frictional  resistance.  The  motor  capacity 
depends  on  the  temperature  that  the  windings  will  attain,  and  this  in  turn  on 
the  average  heating  value  of  the  current.  As  this  is  proportional  to  the  square 
of  the  current  value,  the  average  heating  for  an  all-day  service  must  be  deter- 
mined from  the  square  root  of  the  mean  square  of  the  current. 

A  motor  is  selected  from  the  various  sizes  that  will  fit  the  locomotive  in 
question,  and  from  the  foregoing  data  and  the  characteristics  of  this  motor 


826  HA  ULAGE 

equipment,  the  current  and  speed  are  obtained  for  each  part  of  the  cycle. 
The  current  values  are  then  squared  and  multiplied  with  the  time  during  which 
they  last.  To  allow  for  the  extra  heating  produced  by  the  acceleration  and  the 
switching  and  making  up  of  trips  at  the  ends  of  the  run,  about  10%  should  be 
added  to  the  sum  of  the  time-current-squared  values  for  fairly  long  runs  and 
about  15%  for  short  runs.  The  sum  of  all  these  values  is  then  divided  by 
the  total  time,  including  lay-overs,  and  the  result  is  the  average  squared  current 
value.  By  taking  the  square  root  of  this  value,  the  root-mean-squared  value 
of  the  current  for  the  complete  cycle  is  obtained.  If  the  continuous  capacity 
of  the  motor  selected  is  below  this  value,  a  larger  motor  must  be  selected.  As 
the  motor  curves  usually  give  values  for  one  motor,  the  locomotive  and  trailing 
weights,  etc.,  should  naturally  be  divided  by  two  to  give  the  weight  each  motor 
will  be  required  to  handle. 

The  tendency  to  use  larger  motors  than  formerly  is  quite  common  and 
is  justified  largely  by  the  lower  maintenance  cost,  but  this  can  be  carried  too 
far,  especially  in  small  mines  where  the  cycle  of  duty  is  such  that  the  motors 
could  not  be  overheated.  In  large  mines,  and  especially  for  the  long  main- 
haulage  duties,  a  careful  comparison  of  the  required  duty  and  the  motor  char- 
acteristics should  be  made  to  insure  a  safe  motor  temperature.  An  approximate 
rule,  easy  to  remember,  is  that  a  total  motor  capacity  of  about  10  H.  P.  is 
required  for  every  ton  the  locomotive  weighs. 

Tandem  Locomotives. — In  the  past,  a  mining  locomotive  was  generally 
considered  satisfactory  so  long  as  its  motors  could  develop  the  torque  required 
for  the  necessary  traction.  Owing  to  the  relatively  short  and  infrequent  runs, 
heating  was  not  the  limiting  feature,  but  as  mine  headings  have  increased  in 
length  to  6  and  7  mi.  in  some  cases,  the  motors  that  were  formerly  good  for 
runs  of  1  and  2  mi.  are  no  longer  adequate  for  the  longer  service  unless  the 
loads  are  correspondingly  reduced.  A  reduction  in  loads  is  impossible,  because 
for  the  same  output,  the  longer  the  runs  the  larger  must  be  the  trains,  and 
larger  trains  means  larger  motor  capacity.  The  space  mine  locomotives  can 
occupy  is  limited  by  the  gauge  of  the  track,  and  the  only  way  to  increase 
the  hauling  capacity  is  either  to  run  two  locomotives  in  tandem  or  to  use 
three-motor  locomotives. 

The  weight  of  a  large  two-motor  locomotive  may  furthermore  be  pro- 
hibitive due  to  the  track  construction.  On  well-laid  tracks  having  50-  or 
60-lb.  rails,  25-  or  30-T.  four-wheel,  two-motor  locomotives  will  operate  success- 
fully, but  where  lighter  rails  exist,  it  is  inadvisable  to  concentrate  the  weight 
on  four  drivers.  Instead,  therefore,  of  using  a  single  20-T.  locomotive,  two 
10-T.  locomotives  coupled  in  tandem  may  be  used,  because  while  developing 
the  same  tractive  effort,  with  this  combination  the  weight  will  be  distributed 
on  eight  driving  wheels. 

Cases  are  on  record  where  large  sums  of  money  have  been  saved  by  the  use 
of  tandem  locomotives,  where  the  increased  lengths  of  hauls  or  tonnage  neces- 
sitated larger  locomotive  capacities.  In  one  particular  instance,  it  would  have 
been  necessary  to  widen  the  funnel  for  many  miles,  while  in  another,  seveial 
miles  of  track  would  have  had  to  be  relaid  with  heavier  rails.  It  is  extremely 
simple  to-couple  the  locomotives  in  tandem. 

The  first,  or  primary,  locomotive  is  provided  with  a  four-motor  controller 
and  the  second,  or  secondary,  locomotive,  with  a  two-motor  controller.  The 
two  are  electrically  interconnected  so  that  there  is  a  complete  control  of  all  the 
motors  from  the  operating  end  of  one.  Similarly  the  brakes  and  sand  valves 
of  both  locomotives  can  be  operated  from  the  same  place. 

The  Iocom9tives  can  also  be  operated  singly  as  independent  units  by 
separation,  which  requires  but  a  few  minutes,  and  only  involves  the  pulling 
out  of  the  cable  plugs,  disconnecting  the  brake  chain,  and  turning  the  primary 
brake  stand  parallel  to  the  end  frame. 

Cable-Reel  Locomotives.— ^Gathering  locomotives  of  the  cable-reel  type 
are  provided  with  a  conductor  in  the  form  of  a  flexible  insulated  cable  that  can 
be  connected  to  the  trolley  wire  on  the  entry  and  through  which  current  can 
be  conveyed  to  the  locomotive  when  it  is  necessary  for  it  to  go  beyond  the  end 
of  the  trolley  line.  The  arrangement  is  designed  to  do  away  with  the  cost  of 
stringing  wires  in  the  rooms  as  well  as  to  overcome  the  danger  of  shock  to  the 
miners. 

The  cable  may  be  either  single  or  double.  The  single  cable  is  used  where 
the  rooms  are  laid  with  steel  rails,  which  are  bonded  to  form  the  return  circuit. 
The  double  cable  is  used  where  the  rails  are  of  wood  and  the  return  circuit  must 
be  made  through  the  cable  itself. 

The  cable  reel  may  be  driven  mechanically  from  the  axle,  or  by  an  inde- 


HA  ULAGE  827 

pendent  motor.  The  mechanically  driven  cable  reel  is  driven  by  a  chain  from 
the  locomotive  axle.  As  the  locomotive  moves  ahead  the  cable  is  paid  out 
automatically,  being  kept  taut  and  the  reel  prevented  from  spinning  by  a 
friction  device.  As  the  locomotive  returns  from  the  face,  the  reel  is  wound 
through  a  clutch.  In  all  cases,  it  is  arranged  that  the  tension  on  the  cable 
cannot  exceed  a  safe  amount. 

The  motor-driven  reel  is  generally  preferred  particularly  for  gathering 
on  steep  grades,  because  the  motive  power  is  independent  of  the  axles,  the 
cable  'is  always  taut  and  there  is  no  danger  of  its  being  run  over  should  the 
locomotive  slide  down  grade  with  its  wheels  locked.  The  form  and  arrange- 
ment of  the  cable  reel  and  its  motor  vary  somewhat.  In  one  standard  type 
of  gathering  locomotive,  the  reel  is  drum  shaped,  is  set  above  and  on  the  end 
frames  in  such  a  way  that  it  does  not  project  above  the  main  casing  of  the 
locomotive,  and  contains  within  it  the  necessary  motor.  In  another  standard 
type,  the  reel  is  flat  and  turns  horizontally  on  ball  bearings  on  top  of  the  loco- 
motive. The  reel  is  driven  through  a  double  reduction  gearing  by  a  small, 
vertical,  series-wound  motor,  the  armature  of  which  is,  as  a  rule,  provided 
with  ball  bearings.  The  motor  is  connected  directly  across  the  line,  with  a 
fuse  and  a  switch  inserted  in  the  circuit,  the  former  to  protect  against  short- 
circuits  and  the  latter  in  case  for  some  reason  it  should  be  desired  to  open  the 
circuit.  A  permanent  resistance  is  also  inserted  in  this  circuit  in  order  to  limit 
the  heavy  rush  of  current  that  would  take  place  when  the  locomotive  is  stand- 
ing still.  The  motor,  however,  has  sufficient  capacity  to  permit  its  being  stalled 
for  any  length  of  time  without  overheating. 

The  cable  is  generally  about  500  ft.  long,  flexible,  and  heavily  insulated 
to  withstand  the  wear  to  which  it  necessarily  is  subjected.  The  inner  end  is 
connected  to  a  collector  ring  on  the  underside  of  the  reel  and  the  outer  end  is 
fitted  with  a  copper  hook  for  attaching  to  the  trolley  wire.  A  carbon  brush 
mounted  on  an  insulated  stud  attached  to  the  motor  frame  collects  current 
from  the  ring  from  which  it  is  conducted  to  the  controller  circuit. 

The  arrangement  and  design  of  the  reel  motor  is  such  that  at  all  times  it 
will  produce  a  tension  on  the  cable.  Thus,  as  the  locomotive  moves  forwards, 
the  counter  torque  will  produce  a  tension  in  the  cable  and  cause  it  to  pay  out 
evenly  and  drop  along  the  roadbed  without  kinks.  Owing  to  the  braking  effect 
of  this  counter  torque,  the  reel. will  also  come  to  a  standstill  when  the  loco- 
motive stops;  and  as  it  starts  on  the  return  trip  and  the  cable  is  slackened,  the 
motor  action  will  immediately  come  into  play  and  the  reel  will  commence  to 
wind  up  the  cable  as  the  locomotive  moves  along,  the  peripheral  rim  speed  of 
the  reel  being  higher  than  the  linear  speed  of  the  locomotive.  The  operation 
of  the  reel  is  thus  entirely  automatic  and  requires  no  controller,  ratchet,  or 
clutch  to  be  handled  by  the  motorman,  but  leaves  the  motorman  free  to  give 
his  entire  attention  to  operating  the  controller  and  brakes  and  the  proper 
running  of  the  locomotive. 

Gathering  locomotives  are  equipped  with  a  regular  mine  trolley  so  that 
they  can  be  used  in  the  same  manner  as  regular  hauling  locomotives.  When 
the  cable  reel  is  not  being  used  and  the  locomotive  is  collecting  current  through 
the  trolley  pole  in  the  regular  way,  the  current  flow  through  the  reel  motor 
is  cut  off  by  throwing  the  reel  and  trolley  switch  to  the  trolley  side. 

Crab  Locomotives. — Crab,  or  traction-reel,  locomotives  carry  a  reel  or  drum 
mounted  in  a  similar  position  to  that  of  a  cable-reel  locomotive,  but  upon 
which  is  wound  350,  500,  or  more  feet  of  wire  rope.  In  operation,  the  loco- 
motive remains  on  the  entry  with  the  brakes  set,  and  the  rope  is  dragged  to 
the  face  and  coupled  to  the  loaded  car  by  the  motor  helper;  when  the  reel 
motor  is  started,  the  car  is  pulled  to  the  entry.  If  the  rope  is  long  enough  to 
reach  from  the  entry  to  the  face  of  the  room,  where  it  is  passed  around  a  sheave, 
and  back  again  to  the  entry,  this  locomotive  may  be  used  to  pull  empty  cars 
up  a  grade  to  the  face.  Crab  locomotives  are  in  general  use  in  mines  where 
the  room  track  is  too  weak  to  sustain  the  weight  of  the  motor,  or  where  the 
working  places  are  on  such  a  pitch  that  the  locomotive  cannot  propel  itself 
in  them. 

Combination  Cable-Reel  and  Crab  Locomotives. — Gathering  locomotives 
are  sometimes  built  with  both  a  cable  and  a  rope  reel.  By  the  use  of  the 
cable,  the  locomotive  itself  can  enter  any  place  where  the  track  is  suitable 
and  the  grades  are  not  too  steep,  and  on  heavy  pitches  the  locomotive  can 
stand  on  the  entry  and  pull  cars  to  it  by  means  of  the  wire  rope. 

Rack-Rail  Locomotives. — Traction  locomotives  may  be  used  on  short 
grades  of  5%,  but  above  that  they  are  not  to  be  considered.  To  handle  trips 
on  heavy  grades  without  resorting  to  rope  haulage,  rack-  or  third-rail  loco- 


828  HA  ULAGE 

motives  are  often  employed.  In  these,  the  teeth  of  steel  gear  wheels  carried 
on  the  axle  of  the  locomotive  and  turned  by  an  electric  motor,  engage  slots 
cut  in  an  iron  bar  (the  rack  rail)  laid  between  the  track  rails,  thus  mechanically 
pulling  the  locomotive  forward  up  the  grade.  As  the  hauling  capacity  of  the 
locomotive  does  not  depend  on  its  adhesion  but  on  the  horsepower  developed 
by  its  motors,  it  tnay  be  made  much  lighter  than  the  trolley  locomotive  with  a 
corresponding  gain  in  the  weight  it  is  able  to  haul. 

The  rack  rail  may  be  either  live  or  dead.  In  the  first  case,  the  current  for 
operating  the  locomotive  is  carried  by  the  rack  rail;  in  the  second,  the  current 
is  received  from  an  overhead  trolley  wire  and  returns  through  the  rails  of  the 
regular  track. 

A  combination  rack  and  traction  locomotive  is  also  made,  which  is  arranged 
to  run  as  a  rack  locomotive  on  grades  and  as  a  traction  locomotive  on  a  level, 
where  no  rack  rail  need  be  laid. 

Rack-rail  locomotives  are  planned  on  the  unit  system;  that  is  to  say,  any 
number  of  units  of  50,  100  H.  P.,  etc.,  may  be  run  as  a  single  locomotive  where 
the  grades  and  the  loads  warrant  it. 

Operation  of  Electric  Locomotives. — Before  an  electric  mining  locomotive 
is  put  into  service,  it  should  be  inspected  to  see  that  all  parts  are  in  proper 
condition.  It  should  be  well  oiled  and  the  sand  boxes  should  contain  plenty  of 
dry  sand.  The  sand  levers  and  brakes  should  be  tried  to  see  that  they  are 
operating  satisfactorily,  and  the  controller  should  be  on  the  off-position  before 
the  trolley  pole  is  put  on. 

When  starting  the  locomotive,  the  current  should  be  thrown  on  gradually 
and  due  consideration  paid  to  the  load  that  the  locomotive  is  to  haul.  The 
slack  in  the  couplings  will  often  relieve  the  starting  condition  so  that  it  will  'not 
be  necessary  to  start  all  the  cars  in  the  train  simultaneously.  The  controller 
should  be  advanced  from  one  notch  to  another,  quickly,  being  allowed  to 
remain  on  one  point  until  the  locomotive  has  gathered"  speed  to  correspond , 
when  it  is  moved  quickly  to  the  next  notch,  etc.  If,  however,  the  controller 
is  advanced  too  rapidly  and  the  wheels  begin  to  slip  the  controller  must  not  be 
thrown  backwards  one  or  two  steps  but  must  be  thrown  off  quickly,  completely, 
and  advanced  again  in  the  usual  manner.  If  the  control  is  moved  backwards 
slowly,  arcing  at  the  contact  fingers  may  cause  burning  and  blistering. 

The  controller  is  only  intended  for  starting  duty  and  the  locomotive  should 
not  be  run  continuously  with  the  controller  on  intermediate  position,  as  this  is 
liable  to  cause  a  burn-out  of  the  resistance  or  other  damage  to  the  controller. 

If  the  locomotive  runs  too  fast  with  the  controller  in  the  on-position  and 
the  motors  in  parallel,  the  motors  should  be  placed  in  series  or  the  current 
thrown  on  for  a  short  time  and  then  off,  letting  the  locomotive  coast. 

When  it  is  necessary  to  brake,  the  controller  should  be  thrown  to  the 
off-position  before  the  brakes  are  applied.  The  controller  should  not  be  used 
for  braking,  by  reversing  the  motors,  except  in  case  of  emergency.  This 
practice  is  sometimes  resorted  to,  but  is  very  severe  on  the  motors,  controllers, 
and  in  fact  on  the  entire  equipment.  Reversing  the  motors  when  running  at 
full  speed  is  apt  to  break  the  gears  and  spring  the  armature  shaft. 

Troubles  of  Electric  Locomotives. — 1.  Failure  to  Start. — The  most  com- 
mon cause  of  a  motor  failing  to  start  is  broken  connection  in  the  electric  circuit 
in  the  motors,  the  trolley,  the  track  return,  the  circuit-breaker,  controller,  or 
resistance  grids.  If  the  open  circuit  is  in  the  motors,  the  defective  part 
can  be  located  by  raising  the  brushes  of  each  motor  commutator  successively, 
with  the  controller  in  the  multiple  position  and  the  current  applied.  If,  how- 
ever, neither  of  the  motors  will  operate  when  so  connected,  the  opening  is  in 
some  other  part  of  the  electric  circuit  than  the  motors.  An  examination  to 
determine  this  is  best  made  by  the  use  of  a  bank  of  lamps,  one  end  of  which 
is  connected  to  the  trolley  wire  and  the  other  end  applied  to  different  parts  of 
the  circuit  beginning  with  the  trolley  harps  and  taking  the  circuit  step  by  step 
until  the  open  circuit  is  passed. 

When  the  open  circuit  is  found  to  be  in  the  field  coils  in  one  of  the  motors, 
it  is  necessary  to  cut  this  motor  out  of  circuit  and  drive  the  locomotive  with 
the  other  motor.  Only  half  the  customary  load  should  then  be  hauled, 
although  the  locomotive  will,  to  a  great  extent,  protect  itself,  as  the  wheels 
connected  to  the  driving  motor  will  have  a  tendency  to  slip,  which  of  course  will 
determine  the  amount  of  load  that  the  locomotive  is 'capable  of  hauling.  The 
defective  motor  is  best  cut  out  by  removing  its  brushes. 

Failure  to  start  may  also  be  due  to  faulty  connections  causing  the  motors 
to  buck  each  other.  This  will  cause  a  heavy  current  and  the  fuse  or  circuit- 
breaker  will  blow,  It  is  readily  corrected  by  reversing  the  brush  leads  on  one 


HA  ULAGE  829 

motor.  Grounding  the  current  may  also  prevent  a  locomotive  from  starting, 
while  on  the  other  hand  mechanical  troubles  are  often  the  cause;  for  example, 
the  brakes  may  not  be  released,  the  gears  may  be  broken,  the  bearings  stuck 
or  seized,  etc. 

If  the  locomotive  jumps  or  does  not  start  up  smoothly,  the  trouble  is 
generally  short  circuits  in  the  starting  resistance,  wrong  or  open  connections, 
controller  troubles,  etc. 

2.  Excessive  Heating. — Heating  may  be  due  to  the  motors  being  over- 
loaded when  hauling  heavy  trips,  and  can  then  only  be  remedied  by  reducing 
the  load  or  by  providing  larger  locomotives. 

Low  voltage  is  a  very  common  cause  of  a  motor  not  developing  its  rated 
capacity  causing  overheating  due  to  slower  speed,  breakdowns,  etc.  This  may 
be  the  result  of  insufficient  copper  in  the  overhead  wires,  poor  bonding  of  the 
rails,  poor  connections  in  the  circuit  or  insufficient  prime  mover  or  generator 
capacity. 

A  short  circuit  in  any  armature  turn  will  cause  a  circulation  of  heavy 
current  therein,  followed  by  excessive  heating.  This  current  is  due  to  the 
transformer  action  of  the  field  coils  acting  as  primary  and  the  short-circuited 
armature  turns  as  secondary.  The  trouble  can  generally  be  detected  by  the 
smell  of  burning  insulation  or  by  the  hand,  as  the  short-circuited  coils  will  be 
much  warmer  than  the  other  part  of  the  armature.  As  a  temporary  remedy, 
the  short-circuited  coils  can  be  open  circuited  at  the  commutator  and  dis- 
connected from  it,  the  commutator  being  bridged  at  this  point  to  close 
the  gap. 

Short-circuited  field  turns  will  cause  the  motor  to  speed  up,  particularly 
at  light  loads.  This  tendency  to  speed  up  will  cause  the  motor  to  take  an 
excessive  current,  causing  overheating  of  the  defective  motor  armature.  The 
defective  coil  can  be  located  by  feeling  with  the  hand,  as  it  will  be  much  cooler 
than  the  others.  This  is  due  to  the  reduced  number  of  turns,  which  decreases 
the  resistance  of  the  coil  and  consequently  the  amount  of  loss  therein.  When 
a  field  coil  is  found  to  be  short  circuited  so  as  to  affect  the  operation  of  the 
motor,  the  coil  should  be  removed  and  replaced  by  a  new  one. 

Burn-out  from  excessive  heating  is  also  caused  by  the  armature  coming 
down  on  the  pole  faces.  The  remedy  for  this  is,  of  course,  only  to  give  more 
attention  to  the  motor  bearings,  keeping  them  properly  lubricated  and  by 
frequently  checking  the  air  gap  to  see  if  the  armature  is  getting  dangerously 
close  to  the  pole  faces. 

3.  Sparking. — Excessive  sparking  at  the  brushes  is  frequently  caused  by 
an  open  circuit  in  the  armature  winding.     Such  sparking  may  often  become 
so  violent  as  to  cause  the  motors  to  flash  over  at  the  commutator.     An  exami- 
nation will  show  that  the  commutator  segments,  between  which  the  open  circuit 
occurs,  are  blackened  and  slightly  burned.     If  the  open  circuit  is  not  taken 
care  of  at  once,  it  is  liable  to  cause  a  flat  spot  on  the  commutator,  requiring 
turning.     Temporary  relief  can  be  had  by  bridging  the  open  circuit  at  the 
commutator. 

Short-circuited  field  turns,  if  affecting  a  large  number  of  turns,  are  also 
liable  to  cause  excessive  sparking  at  the  brushes. 

Commutator  troubles  are  a  very  common  cause  of  sparking  and  com- 
mutators should  be  kept  free  from  oil  and  dirt.  If  they  become  very  rough 
from  overheating  and  excessive  sparking,  it  may  be  necessary  to  smooth 
them  with  sandpaper,  and  if  this  does  not  help,  returning  is  the  remedy. 

Trouble  with  the  commutators  is  often  due  to  careless  handling  of  the 
locomotive,  such  as  operating  it  with  a  defective  controller  or  a  defective 
resistance.  When  a  resistance  is  found  to  have  a  broken  grid,  a  new  one 
should  be  put  in  at  once.  The  method  sometimes  resorted  to  of  short  circuiting 
a  broken  grid  should  not  be  allowed,  except  for  temporary  work,  for  when 
doing  so,  a  large  percentage  of  the  resistance  may  be  cut  out  of  one  or  more  of 
the  steps,  causing  the  motors  to  take  excessive  current  when  those  points  on 
the  controller  are  reached.  This  will  cause  the  locomotive  to  start  with  a 
jerk  and  very  likely  burn  the  commutator  and  brushes,  besides  being  hard  on 
the  gears  and  other  mechanical  parts  of  the  locomotive. 

4.  Grounds. — When  a  ground  occurs  in  a  motor,  whether  it  is  confined  to 
the  armature,  field  coils,  or  commutator,  it  will  cause  the  circuit-breaker  or 
fuse  to  blow,  and  it  will  not  be  possible  to  keep  the  circuit-breaker  closed 
without  holding  it  in,  which  should  never  be  done. 

Motors  will  also  sometimes  show  a  ground  when  tested  with  a  voltmeter 
or  a  bank  of  test  lamps,  but  otherwise  will  operate  satisfactorily.  It  is  then 
evident  that  there  is  a  leakage  path  formed  somewhere,  and  if  the  motors 


830  HAULAGE 

are  not  inspected    and  thoroughly  cleaned  to  remove  this  partial  ground  it  is 
only  a  short  time  before  a  permanent  ground  can  be  expected. 

When  a  ground  occurs,  the  motor  containing  it  should  be  cut  out  of  service 
and  the  locomotive  operated  by  the  other  motor  until  such  time  as  the  ground 
can  be  located  and  remedied. 

ALTERNATING-CURRENT  LOCOMOTIVES 

Alternating-current  locomotives  may  be  either  single  or  three  phase. 
Single-phase  locomotives  require  but  one  overhead  trolley  wire,  as  in  direct- 
current  haulage,  whereas  three-phase  locomotives  require  two  trolley  wires, 
the  track  rails  forming  the  third  leg  of  the  circuit.  Three-phase  locomotives 
are  not  generally  recommended  for  underground  use  because  of  the  difficulty 
of  maintaining  and  insulating  two  trolley  wires,  the  increased  complication  of 
the  switches  where  two  wires  are  used,  etc. 

The  single-phase  locomotive,  taking  all  its  current  from  one  phase  of  the 
supply  system,  produces  an  unbalanced  load  on  the  line,  but  this  should  not 
seriously  affect  a  power  station  of  good  capacity.  In  extensive  haulage 
installations,  by  taking  the  power  for  the  various  sections  of  the  main  line  and 
for  the  various  branches  from  different  phases  of  the  supply  line,  it  is  possible 
to  practically  balance  the  load. 

The  three-phase  locomotive  sometimes  used  at  American  mines  for  outside 
haulage,  is  similar  in  general  construction  and  appearance  to  the  direct-current 
machine.  It  has,  however,  either  two  trolley  poles  or  a  pantagraph  trolley 
making  sliding  contact  with  the  wires.  These  locomotives  may  be  had  up  to  8 
to  10  T.  in  weight  and  for  the  standard  frequencies  and  voltages.  They  are 
provided  with  two-torque  induction  motors,  with  suitable  starting  resistances 
in  the  rotor  circuit,  so  that  reduced  speeds  may  be  had  for  starting  (accelera- 
tion), switching,  etc.  As  the  induction  motor  is  a  constant-speed  machine,  the 
locomotive  tends  to  maintain  the  speed  for  which  it  is  geared  regardless  of  the 
load  or  grades.  The  high-speed  of  the  induction  motors  necessitates  a  double- 
gear  reduction  and  consequently  a  different  method  of  mounting  than  is  used 
in  the  direct-current  machine. 

The  advantage  of  the  three-phase  locomotive  is  in  the  saving  in  the  cost  of 
converters  and  the  power  lost  in  converting  from  alternating  to  direct 
current.  The  high  voltages  so  often  used  with  them  are  extremely  dangerous. 

STORAGE-BATTERY  LOCOMOTIVES 

For  gathering  coal,  storage-battery  locomotives  are  recommended  where 
the  grades  are  not  severe ;  where  the  speed  does  not  exceed  3  5  to  4  mi.  per  hr. ; 
where  the  hauls  are  short,  say  not  over  £  mi.,  and  where  the  service  is  inter- 
mittent; that  is,  where  the  locomotive  is  idle  a  good  portion  of  the  time,  as 
when  waiting  on  empties  or  loads.  These  locomotives  are  not  at  present 
advised  for  main-line  haulage  where  the  travel  is  long  because  the  practically 
continuous  service  requires  a  locomotive  of  a  price  and  over-all  dimensions 
that  is  commonly  prohibitory.  In  size,  these  locomotives  range  from  2£ 
to  10  T.,  a  common  size  for  gathering  being  4  T.;  however,  a  20-T.  locomotive 
of  this  type  has  been  built.  In  the  majority  of  cases,  the  battery  is  carried  on 
the  same  truck  as  the  motor  and  is  an  integral  part  of  the  locomotive,  but  in 
some  of  the  larger  machines  designed  for  long  hauls,  heavy  work,  and  the 
like  _  conditions  requiring  more  nearly  continuous  service,  the  batteries  are 
carried  on  a  trailing  truck,  tender,  or  battery  car;  the  weight  of  which  reduces 
the  hauling  capacity  of  the  locomotive.  Recharging  is  done  at  night  with 
usually  a  little  "livening  up"  during  the  noon  hour  or  other  idle  times.  Where 
separate  battery  cars  are  used,  a  fresh  one  may  be  coupled  to  the  locomotive 
at  the  time  the  exhausted  one  is  taken  away  to  be  recharged.  One  type 
of  these  locomotives  is  built  to  use  current  from  the  ordinary  overhead  trolley 
wire  where  such  exists,  thus  saving  the  batteries  for  use  in  parts  of  the  mine 
where  current  is  not  to  be  had.  This  locomotive  is  also  arranged  with  suitable 
switches  so  that  the  batteries  may  be  charged  from  the  trolley  circuit  at  the 
same  time  the  motor  is  being  run  in  the  ordinary  way. 

The  weight  of  a  locomotive  required  to  give  the  necessary  adhesion  to 
haul  the  load  is  calculated  in  the  same  way  as  for  any  other  kind  of  locomotive. 
The  calculation  of  the  battery  capacity  or  power  is  not  easily  made  and  requires 
a  careful  study  of  the  grades,  loads,  and  distances,  from  which  may  be  cal- 
culated the  foot-pounds  of  work  the  locomotive  must  perform.  In  this  calcu- 
lation, perhaps  the  most  important  point  is  estimating  the  ratio  of  the  actual 
discharge  rate  of  the  battery  cells  to  the  normal  rate  of  discharge.  This 


VENTILATION  OF  MINES  831 

depends  on  the  length  of  time  the  locomotive  is  developing  the  maximum 
drawbar  pull  or  some  other  high  value  of  the  drawbar  pull  that  is  sustained 
for  any  considerable  length  of  time.  The  value  finally  selected  depends  largely, 
if  not  entirely,  on  the  judgment  and  experience  of  the  individual.  It  is  gener- 
ally considered  safe  to  make  this  ratio  1  :  3,  although  on  flat  grades  where 
the  maximum  pull  is  exerted  only  at  starting  and  for  a  second  or  two,  the 
ratio  may  be  as  high  as  1  :  5.  The  foot-pound  of  work  may  be  reduced  to 
kilowatt-hours  on  the  basis  of  1  ft.-lb.  =  .000000377  K.  W.-hr.  In  ordinary 
estimates,  it  may  be  assumed  that  the  kilowatt-hours  per  ton-mile  of  load  are 
.125  for  a  level  track,  which  includes  the  losses  in  the  battery  and  locomotive. 


VENTILATION  OF  MINES 


CHEMICAL  AND  PHYSICAL  PROPERTIES  OF  GASES 

CHEMISTRY  OF  GASES 

Matter  and  Its  Divisions. — Matter  is  the  substance  of  which  all  things  are 
composed  and  may  be  denned  as  anything  that  possesses  weight  or  occupies 
space.  There  are  three  divisions  of  matter: 

A  mass  is  a  body  of  matter  of  a  size  to  be  appreciable  to  the  senses. 

A  molecule  is  the  smallest  particle  of  matter  into  which  a  mass  may  be 
divided  by  physical  means;  it  is  the  smallest  particle  of  matter  that  is  capable 
of  a  separate  existence.  The  exact  size  of  a  molecule  cannot  be  determined 
but  it  is  so  small  that  the  most  powerful  microscope  would  tail  to  recognize 
it.  Lord  Kelvin  calculates  that  if  a  single  drop  of  water  was  magnified  until 
it  appeared  as  large  as  the  earth  (approximately  8,000  mi.  in  diameter),  the 
molecules  in  the  drop  would  appear  to  have  a  size  between  that  of  a  baseball 
and  a  small  shot. 

An  atom  is  the  smallest  particle  of  an  element  that  can  enter  into  a  chem- 
ical reaction  and  cannot  further  be  divided.  As  a  rule,  atoms  are  incapable  of 
existing  in  a  free  state,  and  are  generally  found  in  combination  with  other  atoms, 
either  of  the  same  or  of  different  kinds. 

Atoms  unite  to  form  molecules,  and  molecules  unite  to  form  masses. 

Classes  of  Matter. — An  element  is  a  mass  of  matter  composed  of  the  same 
kind  of  molecules  which,  in  turn,  are  composed  of  the  same  kind  of  atoms. 
Thus,  two  atoms  of  hydrogen  unite  to  form  a  molecule  of  hydrogen  and  an 
inconceivable  number  of  molecules  of  hydrogen  unite  to  form  a  mass,  say, 
an  ounce  or  a  pound  of  hydrogen.  In  the  case  of  an  element,  the  mass,  mole- 
cule, and  atom  are  of  the  same  kind. 

A  compound,  or  chemical  compound,  is  a  mass  of  matter  composed  of  the 
same  kind  of  molecules,  but  the  molecules  are  composed  of  two  or  more  atoms 
of  different  kinds.  Thus  a  mass  of  methane  is  composed  of  molecules  of 
methane,  which  are  each  composed  of  one  atom  of  carbon  and  four  atoms 
of  hydrogen. 

A  mixture  is  a  mass  of  matter  composed  of  two  or  more  different  kinds  of 
molecules,  the  one  molecule  being  composed  of  different  atoms  than  the  other 
or  others.  Thus,  afterdamp  is  a  mixture  of  molecules  of  oxygen,  nitrogen, 
carbon  dioxide,  carbon  monoxide,  and  usually  one  or  more  other  gases,  the 
molecules  of  each  of  which  are  composed  of  characteristic  atoms. 

There  are  at  present  (1915)  83  definitely  known  elements  having  properties 
more  or  less  clearly  understood,  together  with  a  number  more  the  identifica- 
tion or  characteristics  of  which  are  in  doubt. 

Forms  of  Matter. — The  atoms  composing  a  molecule  are  held  together 
by  chemical  affinity,  and  molecules  composing  a  mass  are  held  together  by 
cohesion.  In  addition,  molecules  of  all  matter  are  acted  upon  by  an  opposing 
force,  repulsion,  which  tends  to  drive  them  apart.  Repulsion  is  not  inherent 
in  the  mass,  but  is  an  induced  or  applied  force  that  is  largely  the  result  of  heat 
or  the  temperature  of  the  body. 

All  matter  exists  in  one  of  three  forms,  solid,  liquid,  or  gaseous,  according 
to  the  predominance  of  the  attractive  or  the  repulsive  forces  existing  between 
the  molecules.  For  example,  water  exists  as  ice,  or  in  a  solid  form,  when  the 
attractive  force  exceeds  the  repulsive  force  between  its  molecules.  As  the 
temperature  is  raised  or  heat  is  applied,  the  ice  assumes  the  liquid  form  due 
to  the  more  rapid  vibration  of  the  molecules  of  which  it  is  composed.  In 


832  VENTILATION  OF  MINES 

other  words,  the  repulsive  force  existing  between  the  molecules  is  increased, 
and  the  result  is  a  liquid.  If  the  temperature  is  raised  still  further  by  apply- 
ing more  heat,  the  vibration  of  the  molecules  becomes  yet  more  rapid,  the 
repulsive  force  is  increased  between  the  molecules,  and  a  gas  or  vapor  called 
steam  is  formed. 

Changes  in  Matter. — Matter  cannot  be  destroyed  but  its  form  may  be 
changed  or,  if  a  chemical  compound,  it  may  be  broken  up  into  its  component 
elements.  Changes  affecting  the  form  or  state  of  matter  brought  about  by 
physical  causes,  as  heat,  pressure,  electricity,  etc.,  and  affecting  only  the 
molecules  of  a  body  are  physical  changes;  changes  affecting  the  atoms  in  a 
molecule,  by  which  they  are  rearranged  or  combined  in  new  ways  are  chemical 
changes.  Physical  changes  always  accompany  chemical  changes,  a  change 
in  the  arrangement  or  relations  between  the  molecules  of  matter  usually  pre- 
ceding a  change  in  the  arrangement  of  the  atoms  in  the  molecule.  Thus,  the 
change  from  ice  to  water  to  steam  is  a  physical  change  due  to  heat;  if  the  heat 
is  still  further  increased,  the  molecules  of  water  will  be  decomposed  into  hydro- 
gen and  oxygen  gas,  which  is  a  chemical  change. 

Symbols  and  Formulas. — It  is  usual  to  express  the  names  of  the  elements 
by  letters  called  symbols.  The  letters  selected  are  the  first  one  of  the  name 
or  the  first  and  some  letter  following  it.  While  in  the  majority  of  cases,  the 
letters  are  taken  from  the  common  name  of  the  element,  in  others  the  symbol 
is  derived  from  its  Latin  or  other  name.  Thus,  the  symbol  for  iron  is  Fe, 
derived  from  the  Latin  ferrum,  and  for  tungsten  is  W,  from  -wolfram,  an  earlier 
name.  The  symbols  for  antimony,  gold,  silver,  tin,  copper,  sodium,  potas- 
sium, and  mercury,  are  similarly  derived  from  the  Latin.  Two  atoms  of  an 
element,  as  hydrogen,  may  be  written  either  2H  or  Hz. 

A  formula  is  the  expression  of  the  composition  of  a  molecule  by  means  of 
the  symbols  of  the  elements  entering  into  it,  the  number  of  atoms  of  each  kind 
in  the  molecule  being  denoted  by  subscripts.  Thus,  the  formula  for  methane 
is  CH4,  which  indicates  that  a  molecule  of  this  gas  is  composed  of  one  atom 
of  carbon  (symbol  C)  and  four  atoms  of  hydrogen  (symbol  H).  When  there 
are  no  subscripts,  it  is  understood  that  but  one  atom  is  present  in  the  mole- 
cule, as  in  CO,  which  is  composed  of  one  atom  each  of  carbon  and  oxygen. 
Two  molecules  of  methane  would  be  written  2CHt,  three  molecules  3CHt,  etc. 

The  symbol  for  the  element  hydrogen  is  H,  and  the  formula  for  the  molecule 
of  hydrogen  is  Hz,  since  each  molecule  of  this  gas  contains  two  atoms  as  explained 
in  the  next  paragraph. 

Atomicity  of  Elements. — By  atomicity  is  meant  the  number  of  atoms  in 
a  molecule.  The  rare  atnwspheric  gases,  argon,  helium,  krypton,  neon,  and 
xenon  are  monatomic;  that  is,  their  molecules  contain  but  one  atom.  Hence, 
for  these  gases,  the  symbols  A,  He,  Kr,  Ne,  and  Xe,  respectively,  represent 
either  one  atom  or  one  molecule. 

The  common  atmospheric  gases,  hydrogen,  nitrogen,  and  oxygen  are 
diatomic,  or  their  molecule  is  composed  of  two  atoms.  In  these  cases,  the 
symbols  for  the  atoms  are,  respectively,  H,  N,  and  O,  and  the  formulas  for  the 
molecules  are  Hz,  Nz,  and  Oz.  While  sulphur  is  letr atomic  at  temperatures 
of  more  than  800°  C.  and  hexatomic  at  about  500°  C.  and  its  molecule  is  thence 
St  or  Se,  it  is  commonly  written  S,  as  if  monatomic,  in  questions  of  mine  gases. 
The  same  is  true  of  carbon,  which  is  either  diatomic  or  tetratomic. 

Chemical  Reactions. — A  chemical  reaction  is  any  change  in  the  arrangement 
of  the  atoms  in  a  single  molecule  of  a  substance  or  in  the  atoms  of  several 
molecules  of  different  substances  brought  about  by  external  agencies.  The 
agencies  affecting  the  arrangement  of  the  atoms  in  a  molecule  or  molecules  are 
heat,  electricity,  and  chemical  affinity.  In  any  reaction,  no  matter  is  destroyed. 
There  are  always  the  same  number  and  kind  of  atoms  after  the  reaction  as 
before  it  took  place,  but  their  combination,  one  with  the  other,  to  form  mole- 
cules is  different. 

Chemical  Equations. — A  chemical  equation  is  the  expression  of  the  equality 
between  atoms  before  and  after  a  chemical  reaction  takes  place.  The  first, 
or  left-hand,  member  of  the  equation  gives  the  formula  and  the  number  of 
molecules  or  atoms  of  the  substance  acted  upon  or  the  two  or  more  substances 
that  react  upon  one  another,  while  the  second,  or  right-hand,  member  gives 
the  formula  and  the  number  of  molecules  of  the  substance  or  substances  formed 
by  the  reaction. 

There  are  atomic  and  molecular  equations.  The  former,  which  are  the 
simpler,  show  the  relation  between  the  atoms  concerned  in  a  reaction.  The 
atomic  equation  for  the  burning  of  carbon  in  air  is  written  C-\-2O  =  COz. 
The  molecular  equation  for  the  same  reaction  is  C-\-Oz  =  COz.  From  the  first 


VENTILATION  OF  MINES 


833 


equation,  when  the  weight  of  carbon  burned  is  known,  there  may  be  calculated 
the  weight  of  oxygen  required  for  the  combustion  and  that  of  the  carbon 
dioxide  formed.  If  the  weights  per  cubic  foot  of  O  and  COi  are  known,  the 
volumes  of  these  gases  concerned  in  the  reaction  may  then  be  calculated. 
The  molecular  equation,  however,  shows  that  the  volume  of  oxygen  consumed 
is  the  same  as  that  of  the  carbon  dioxide  produced;  hence,  but  one  volume 
calculation  need  be  made. 

Atomic  Weight. — The  absolute  weight  of  an  atom  is  not  known,  but  the 
relative  weights  of  the  atoms  are  known  in  most  cases  with  a  high  degree  of 
accuracy.  As  hydrogen  gas  is  the  lightest  known  substance,  it  is  made  the 
basis  of  comparison,  and  the  relative  weights  of  the  atoms  of  the  other  elements 
are  referred  to  it.  Thence,  the  atomic  weight  of  an  element  is  the  ratio  between 
the  weight  of  its  alom  and  that  of  an  atom  of  hydrogen.  The  atomic  weight 
of  oxygen  =  15.88  when  hydrogen  =  1.  Oxygen  is  a  very  common  constituent  of 
chemical  compounds  and  hydrogen  rather  unusual;  hence,  for  ease  in  calcu- 

THE  ELEMENTS  WITH  THEIR  SYMBOLS  AND  ATOMIC  WEIGHTS 

(0  =  16) 


Element 

Symbol 

Atomic 
Weight 

Element 

Symbol 

Atomic 
Weight 

Aluminum  
Antimony  

Al 
Sb 
A 

27.10 
120.20 
39.88 

Molybdenum  .  . 
Neodymium  .  .  . 
Neon  

Mo 
Nd 
Ne 

96.00 
144.30 
20.20 

Arsenic  

As 
Ba 

74.96 
137.37 

Nickel  
Niton  

Ni 
Nt 

58.68 
222.40 

Bismuth  

Bi 
B 

208.00 
11  00 

Nitrogen  

N 
Os 

14.01 
190.90 

Bromine  

Br 

Cd 

79.92 
112.40 

Oxygen  
Palladium  

0 
Pd 

16.00 
106.70 

Caesium  
Calcium  
Carbon 

Cs 
Ca 

Q 

132.81 
40.07 
12  00 

Phosphorus.  .  .  . 
Platinum  

P 

Ft 
K 

31.04 
195.20 
39.10 

Cerium  

Ce 
Cl 

140.25 
35  46 

Praseodymium  . 

Pr 
Ra 

140.60 
226.40 

Chromium 

Cr 

52.00 

Rhodium  

Rh 

102.90 

Cobalt  
Columbium  
Copper  
Dysprosium  
Erbium  
Europium  
Fluorine  
Gadolinium  
Gallium  
Germanium  
Glucinum  
Gold  
Helium  
Holmium  

Co 
Cb 
Cu 

% 

Eu 

Gd 
Ga 
Ge 
Gl 
Au 
He 
Ho 

58.97 
93.50 
63.57 
162.50 
167.70 
152.00 
19.00 
157.30 
69.90 
72.50 
9.10 
197.20 
3.99 
163.50 

Rubidium  
Ruthenium  .... 
Samarium  
Scandium  
Selenium  
Silicon  
Silver  
Sodium  
Strontium  
Sulphur  
Tantalum  
Tellurium  
Terbium  
Thallium  

Rb 
Ru 

Sa 
Sc 
Se 
Si 
Ag 
Na 
Sr 
S 
Ta 
Te 
Tb 
Tl 

85.45 
101.70 
150.40 
44.10 
79.20 
28.30 
107.88 
23.00 
87.63 
32.07 
181.50 
127.50 
159.20 
204.00 

Hydrogen  
Indium 

H 
In 

1.008 
114.80 

Thorium  
Thulium  

Th 
Tm 

232.40 
168.50 

Iodine  
Indium  
Iron  

Krypton  
Lanthanum  

I 
Ir 
Fe 
Kr 
La 
Pb 

126.92 
193.10 
55.84 
82.92 
139.00 
207  10 

Tin  
Titanium  
Tungsten  
Uranium  
Vanadium  

Sn 
Ti 
W 
U 
V 
Xe 

119.00 
48.10 
184.00 
238.50 
51.00 
130.20 

Lithium  
Lutecium  
Magnesium  
Manganese  
Mercury  

Li 
Lu 
Mg 
Mn 
Hg 

6.94 
174.00 
24.32 
54.93 
200.60 

Ytterbium  
Yttrium  
Zinc  
Zirconium  

Yb 
Yt 
Zn 
Zr 

172.00 
89.00 
65.37 
90.60 

53 


834 


VENTILATION  OF  MINES 


lating,  chemists  have  found  it  advisable  to  consider  the  atomic  weight  of 
oxygen  as  16,  in  which  case  that  of  hydrogen  is  1.008,  the  ratio  of  15.88  :  1  being 
the  same  as  16  :  1.008.  When  the  atomic  weights  are  based  on  oxygen  =16. 
those  of  all  the  elements  must  be  multiplied  by  1.008  if  they  have  been  deter- 
mined on  the  basis  hydrogen  =1.  The  foregoing  table  of  atomic  weights  is 
based  upon  oxygen  =16,  and  is  taken  from  the  report  of  the  International 
Committee  of  Atomic  Weights  for  1914.  All  the  elements  in  the  list  are 
known,  and  there  have  been  omitted  therefrom  sundry  of  the  radioactive 
elements  as  actinium,  polonium,  radiothorium,  etc.,  which  are,  as  yet  imper- 
fectly identified. 

Molecular  Weight. — The  molecular  weight  of  any  substance,  elementary 
or  compound,  is  equal  to  the  sum  of  the  atomic  weights  of  the  atoms  in  its 
molecule.  It  is  customary,  in  all  but  precise  calculations,  to  use  the  approxi- 
mate rather  than  the  exact  atomic  weights.  The  following  are  the  approximate 
atomic  weights  generally  used  for  the  elements  occurring  in  mine  gases,  the 
exact  weight  when  oxygen  =  16  being  given  in  parenthesis:  Carbon  12  (12); 
hydrogen  1  (1.008);  nitrogen  14  (14.01);  oxygen  16  (16);  sulphur  32  (32.07). 
For  illustration,  the  molecular  weight  of  sulphuric  acid,  HzSOt,  is  found  as 
follows: 

Approximate  Exact 

#2  =  2X    1=   2  Ht  =  2X    1.008=    2.016 

5=1X32  =  32  5=1X32.07    =32.070 

04  =  4X16  =  64  04  =  4X16         =64.000 

Molecular  weight  =  98  Molecular  weight  =  98.086 

The  following  table  gives  the  names,  formulas,  and  molecular  weights  of 
the  elementary  (oxygen,  nitrogen,  and  hydrogen)  and  the  compound  gases 
that  may  be  met  in  mines.  For  all  ordinary  purposes,  the  approximate  mole- 
cular weights  may  be  used. 

FORMULAS  AND  MOLECULAR  WEIGHTS  OF  COMMON  GASES 


Name  of  Gas 

Formula 
of 
Molecule 

Molecular  Weight 
When 

0  =  16 

#  =  1 

Approximate 

Acetylene  

CzHz 
COz 
CO 
C*H6 
CzH* 
Hi 
HZS 
CHt 
NO 
Nt 
N02 

02 

502 
H-D 

26.016 
44.000 
28.000 
30.048 
28.032 
2.016 
34.086 
16.032 
30.010 
28.020 
46.010 
32.000 
64.070 
18.016 

25.82 
43.67 
27.79 
29.82 
27.82 
2.00 
33.82 
15.91 
29.78 
27.80 
45.66 
31.76 
63.58 
17.88 

26 
44 
28 
30 
28 
2 
34 
16 
30 
28 
46 
32 
64 
18 

Carbon  dioxide  
Carbon  monoxide  
Ethane  

Ethylene 

Hydrogen  

Hydrogen  sulphide  .... 
Methane  

Nitric  oxide  
Nitrogen 

Nitrogen  dioxide  

Oxygen  
Sulphur  dioxide 

Water,  vapor  

Percentage  Composition. — The  actual  weights  of  the  various  elements  in 
a  given  weight  of  a  chemical  compound  are  proportional  to  the  weights  of  the 
atoms  of  each  element  in  a  molecule  of  the  compound. 

EXAMPLE. — What  is  the  percentage  composition  of  methane,  CHi,  and  how 
many  pounds  of  carbon,  C,  and  hydrogen,  H,  are  there  in  5  Ib.  of  this  gas? 

SOLUTION. — From  the  foregoing  table,  the  weight  of  a  molecule  of  CHt 
is  16,  of  which  12  parts  by  weight  (1X12)  is  C,  and  4  parts  by  weight  (4X1) 
is  H,  From  this,  the  percentage  of  C  in  a  molecule  of  CHt  is  (12 -M  6)  X 100 
=  75;  and  of  H ,  is  (4 -=- 16)  X 100  =  25. 

In  5  Ib.  of  CHt  there  are  5X. 75  =  3.75  Ib.  of  C,  and  5X. 25  =  1.25  Ib.  of  H. 

Weights  of  Substances  Concerned  in  Reactions. — The  actual  weights  of 


VENTILATION  OF  MINES  835 

the  substances  entering  into  any  chemical  reaction  are  proportional  to  the  total 
molecular  weights  of  the  substances  concerned  in  the  reaction. 

EXAMPLE  1.  —  (a)  How  many  pounds  of  oxygen  are  required  to  burn  5  Ib. 
of  methane;  (&)  how  many  pounds  of  carbon  dioxide  and  water  vapor  will  be 
produced? 

SOLUTION.  —  (a)  The  molecular  equation  for  the  reaction  may  be  written 

Cfh  +  2Oz  =  COz  +  2HsO 
Molecular  weights,  16  +  64  =  44+36 

Dividing  by  16,  1+4  =  2.75+2.25 

The  molecular  weights  may  be  taken  from  the  preceding  table  or  may 
be  calculated  from  the  approximate  atomic  weights.  Since  the  reaction  is 
based  upon  a  known  weight  of  CHi,  the  molecular  weights  are  divided  through 
by  the  molecular  weight  of  CHi  to  reduce  the  relative  weight  of  that  gas  to 
unity  or  1.  The  reaction  may  be  read:  Four  pounds  of  O  are  required  to 
burn  1  Ib.  of  C#4,  the  reaction  producing  2.75  Ib.  of  COz  and  2.25  Ib.  of  HiO. 
Since  it  requires  4  Ib.  of  O  to  burn  1  Ib.  of  CHi,  to  burn  5  Ib.  of  CBt  will  require 
5X4  =  201b.  of  0. 

(b)  Since  1  Ib.  of  CH*  in  burning  produces  2.75  Ib.  of  COz  and  2.25  Ib.  of 
HiO,  5  Ib.  of  this  gas  will  produce  5X2.75  =  13.75  Ib.  of  COz  and  5X2.25 
=  11.25  Ib.  of  HzO. 

Note  that  the  sums  of  the  atomic  weights  on  both  sides  of  the  equation  are 
the  same  and  equal  to  80.  Also  that  the  actual  weight  of  the  substances  burned 
is  the  same  as  that  of  the  substances  produced;  thus  5  Ib.  of  CHt+20  Ib.  of  O 
=  25  Ib.,  and  13.75  Ib.  of  COa+11.25  Ib.  of  H*0  =  25  Ib. 

EXAMPLE  2.  —  How  mdny  pounds  of  carbon  monoxide  must  be  burned  in 
oxygen  to  produce  10  Ib.  of  carbon  dioxide,  and  how  many  pounds  of  oxygen 
will  be  required? 

SOLUTION.  —  The  molecular  equation  for  the  reaction  is 

2CO+02  =  2C02 
Molecular  weights,  56+32  =  88 
Dividing  by  88,  .636  +.364  =  1 

The  molecular  weights  taken  from  the  table  or  calculated  are  divided 
by  88,  the  weight  of  two  molecules  of  COz,  since  it  is  the  absolute  weight  of 
that  gas  that  is  required.  It  is  apparent  that  to  produce  10  Ib.  of  COz,  10 
X.  636  =  6.36  Ib.  of  CO  must  be  burned  in  10X.  364  =  3.64  Ib.  of  O. 

Volumes  of  Gases  Concerned  in  Reactions.  —  As  equal  volumes  of  all  gases 
contain  the  same  number  of  molecules,  all  gaseous  molecules  are  of  the  same 
sbe,  whence  the  volumes  of  the  gases  concerned  in  any  reaction  are  directly 
proportional  to  the  number  of  molecules  of  the  respective  gases  involved. 

EXAMPLE  1.  —  How  many  cubic  feet  of  oxygen  will  100  cu.  ft.  of  carbon 
monoxide  consume  in  burning  to  carbon  dioxide,  and  how  many  cubic  feet  of 
the  latter  gas  will  be  produced? 

SOLUTION.  —  The  molecular  equation  is  written 
II        I        II 


The  Roman  numerals  written  above  the  formulas  for  the  gases,  represent 
the  number  of  molecules  of  each  concerned  in  the  reaction.  Hence,  two 
volumes  of  CO  combine  with  one  volume  of  O  to  produce  two  volumes  of  COz. 
In  this  reaction  there  has  been  a  condensation  since  three  volumes  are  reduced 
to  two.  On  the  other  hand,  there  are  six  atoms  on  each  side  of  the  equation, 
and  the  molecular  weights  are  88  on  each  side.  Since  CO  combines  with 
one-half  its  volume  of  O,  it  follows  that  100  cu.  ft.  of  CO  will  combine  with 
50  cu.  ft.  of  O  to  form  100  cu.  ft.  of  COz. 

EXAMPLE  2.  —  How  many  cubic  feet  of  oxygen  are  required  for  the  complete 
combustion  of  100  cu.  ft.  of  methane,  and  how  many  cubic  feet  of  carbon 
dioxide  and  vapor  of  water  will  be  produced? 

SOLUTION.  —  The  molecular  equation  is  written 
I         II        I          II 


The  volume  of  the  O  will  be  twice  that  of  the  CHt.  and  the  volumes  of 
the  COz  and  HzO  will  be  equal,  respectively,  to  those  of  the  CHt  and  O.  Hence, 
to  burn  100  cu.  ft.  of  CHt  will  require  200  cu.  ft.  of  O,  and  there  will  be  pro- 
duced 100  cu.  ft.  of  CO2  and  200  cu.  ft.  of  HzO. 

Volumes  of  Gases  When  Burned  in  Air.—  When  gases  are  burned  m  air, 
in  order  to  compute  the  volume  of  the  products  of  combustion  exactly,  account 
must  be  taken  of  the  nitrogen  in  the  atmosphere.  The  exact  ratio  by  volume 
of  the  oxygen  to  the  nitrogen  in  the  air  is  1  :  3.782;  that  is,  for  every  molecule 
of  oxygen  there  are  3.782  molecules  of  nitrogen,  From  this,  the  formula  for 


836  VENTILATION  OF  MINES 

air  may  be  taken  to  be  (O2+3.7822V2),  and  may  be  substituted  for  the  molecule 
of  oxygen  Oz  in  all  reactions  where  it  occurs.  Where  exactness  is  not  required, 
it  is  usual  to  assume  the  0  :  N  ratio  in  the  air  as  1  :  4,  and  to  write  the  formula 
(O2_|_42V2).  It  should  be  noted  that  the  foregoing  are,  strictly  speaking,  not 
formulas,  but  indicate,  rather,  the  composition  of  a  definite  mixture  of  oxygen 
and  nitrogen,  which  is  known  as  air. 

EXAMPLE  1. — What  is  the  percentage,  by  volume,  of  methane  in  firedamp 
at  its  most  explosive  point? 

SOLUTION. — By  introducing  the  formulas  for  the  ratio  of  oxygen  and 
nitrogen  in  the  air,  the  equation  for  the  combustion  of  methane  is, 

CHt+2(Oz+3.782Nz)  =  C02+2fl2O+7.5642V2 
Relative  volumes,   1        2  X  (1+3.782)        1          2         7.564 
Relative  volumes,   1  9.564  1          2         7.564 

From  this,  one  volume  of  CHi  combines  with  9.564  volumes  of  air  and 
forms  10.564  volumes  of  firedamp.  The  proportion  of  methane  in  the  mixture 
is  (1  -T-  10.564)  X 100  =  9.46%. 

EXAMPLE  2. — Using  the  approximate  O  :  N  ratio  for  air,  what  is  the  per- 
centage composition  of  the  afterdamp  of  an  explosion  of  CO? 

SOLUTION. — The  molecular  equation  may  be  written 

2CO+ (02+42V2)  =  2C02+4AT2 
Relative  volumes,    2  5  24 

In  the  six  parts  of  afterdamp  there  will  be  g  =  1  =  33.33%  of  COz  and  f  =  | 
=  66.67%  of  N. 

Weight  and  Volume  of  Gases  in  Reactions. — When  the  volume,  in  cubic 
feet,  of  1  Ib.  of  gas  is  known,  the  volumes  and  weights  of  the  gases  concerned 
in  a  reaction  may  be  obtained  through  the  use  of  the  ordinary  formulas.  The 
volume  of  1  Ib.,  in  cubic  feet,  of  the  principal  gases  is  given  in  a  following  table. 

EXAMPLE. — Using  the  exact  molecular  weights  _ when  O  =  16,  what  are  the 
weights  and  volumes,  in  cubic  feet,  of  the  gases  involved  in  the  burning  of 
1  Ib.  of  carbon  in  oxygen? 

SOLUTION, — The  molecular  equation  is 

Relative  volumes,  I          I 

C+  Oz  =  COz 

Molecular  weights,  12+32  =  44 
Dividing  by  12,    1  +2.67  =  3.67 

Inspection  shows  that  2.67  Ib.  of  0  are  required  to  burn  1  Ib.  of  C,  and 
that  3.67  Ib.  of  COz  are  produced;  further,  the  volume  of  the  O  required  is 
the  same  as  that  of  the  COz  produced.  From  the  table  on  page  837,  the  volume 
of  1  Ib.  of  0  is  found  to  be  11.208  cu.  ft.;  hence,  2.67  Ib.  will  have  a  volume 
of  2.67  X  11.208  =  29.93  cu.  ft.  Further,  as  the  volume  of  1  Ib.  of  COz  is  8.103 
cu.  ft.,  3.267  Ib.  will  occupy  3.67X8.103  =  29.94  cu.  ft. 

It  will  be  noted  that  the  volumes  of  oxygen  and  carbon  dioxide  as  calculated 
are  practically  equal.  This  is  as  it  should  be  as  the  relathe  volumes  are  the 
same,  as  is  shown  by  the  equation  representing  the  reaction.  In  fact,  in 
reactions  between  gases  or  into  which  gases  enter,  it  is  only  necessary  to  calcu- 
late the  volume  of  one  of  the  gases;  that  of  the  others  may  be  told  from  the 
relative  volumes  given  by  the  equation.  The  volumes  of  the  gases  will  always 
be  equal  or  some  simple  multiple  as  1,  2,  3,  etc.,  of  one  another. 

PHYSICS  OF  GASES 

Avogadro's  Law. — Equal  volumes  of  all  perfect  gases,  whether  simple  or  com- 
pound, contain  the  same  number  of  molecules  when  each  are  under  the  same  con- 
ditions of  temperature  and  pressure.  From  this  law  it  follows: 

The  molecules  of  all  perfect  gases  are  of  the  same  size. 

A  given  volume  of  any  perfect  gas  is  as  much  heavier  than  the  same  volume 
of  hydrogen  as  its  molecular  weight  is  greater  than  the  molecular  weight  of  hydrogen, 
or,  more  simply,  the  weight  of  1  cu.  ft.  of  any  gas  is  proportional  to  its  molecular 
weight. 

Avogadro's  law  and  its  two  corollaries  do  no  apply  to  either  solids  or  liquids, 
and  do  not  hold  strictly  true  for  all  gases  at  all  temperatures,  but  they  are  of 
much  practical  value  in  chemistry  and  physics.  It  has  been  found  that  the 
density  and  specific  gravity  of  gases  calculated  on  the  assumption  of  the  correct- 
ness of  this  law,  do  not  in  all  cases,  agree  with  the  observed  density  and  specific 
gravity. 

Density  of  Gases. — The  density  of  a  gas  is  the  ratio  between  the  weight 
of  a  unit  volume  of  the  gas  and  that  of  the  same  volume  of  hydrogen,  measured 
at  a  temperature  of  32°  F.  and  under  a  barometric  pressure  of  29.92  in.  of 
mercury.  Density  is  sometimes  defined  as  the  specific  gravity  of  a  gas  referred 


VENTILATION  OF  MINES 


837 


to  hydrogen  instead  of  to  air  as  the  standard.  The  following  statements,  based 
on  the  assumed  correctness  of  Avogadro's  law  and  the  fact  that  the  molecule 
of  hydrogen  is  diatomic  (composed  of  two  atoms)  are  correct  when  the  atomic 
weights  are  based  on  H  =  1 . 

1.  The  density  of  any  simple  diatomic  gas  is  equal  to  its  atomic  weight. 

2.  The  density  of  any  compound  gas  is  equal  to  one-half  its  molecular 
weight. 

The  values  in  the  table  are  calculated  from  the  atomic  weights  and  in 
numerous  instances  do  not  agree  with  the  observed  values,  which  they  probably 
would  do  if  Avogadro's  law  was  strictly  correct. 

DENSITY  OF  GASES  AT  32°  F.  AND  29.92  IN.  OF  MERCURY 


Gas 

Formula 

Density 

Exact 

Approximate 

Acetylene  
Air  

C2ff2 

C02 
CO 
C2HS 
CzHi 
Hz 
HtS 
CHt 
NO 
Nt 
NOz 
Ot 
S02 
H,O 

12.910 
14.359 
21.835 
13.895 
14.910 
13.910 
1.000 
16.915 
7.955 
14.890 
13.910 
22.830 
15.880 
31.795 
8.940 

12 
14 
22 
14 
15    ' 
14 
1 
17 
8 
15 
14 
23 
16 
32 
9 

Carbon  dioxide  

Carbon  monoxide  
Ethane 

Ethylene  
Hydrogen  

Hydrogen  sulphide  

Nitric  oxide  
Nitrogen  

Nitrogen  dioxide  
Oxygen  

Sulphur  dioxide  

Water  vapor              

Air  being  a  mixture  and  not  a  true  gas  has,  strictly  speaking,  no  'density, 
but  the  values  given  are  convenient  in  certain  calculations. 

Water  vapor  cannot  exist  at  32°  or  at  any  temperature  below  the  boiling 
point  unless  the  pressure  is  less  than  29.92  in.  The  figures  given  are  theoretical 
but,  as  in  the. case  of  air,  are  useful  at  times. 

Specific  Gravity  of  Gases. — The  specific  gravity  of  a  gas  is  the  ratio  of  its 
weight  to  that  of  an  equal  volume  of  air,  measured  at  a  temperature  of  32°  F. 
and  a  pressure  of  29.92  in.  of  mercury. 


SPECIFIC  GRAVITY,  WEIGHT,  AND  VOLUME  OF  GASES  AT  32< 
AND  29.92  IN.  OF  MERCURY 


F. 


Gas 

Symbol 

Observed 
Specific 
Gravity 

Weight  of 
1  Cu.  Ft. 
Pound 

Volume  of 
1  Lb. 
Cubic  Feet 

CiHz 

.9056 

.07309 

13.682 

Air  

1.0000 

.08071 

12.390 

Carbon  dioxide  
Carbon  monoxide  
Ethane  
Hydrogen  
Hydrogen  sulphide  

COt 

CO 
H6 

1.5291 
.9670 
1.0494 
.0696 
1.1912 

.12341 
.07805 
.08470 
.00621 
.09614 

8.103 
12.813 
11.806 
177.904 
10.401 

Methane             

cm 

.5545 

.04475 

22.346 

N 

.9674 

.07808 

12.807 

Olefiant  gas  (ethylene)  

CiHt 

.9852 
1.1054 

.07952 
.08922 

12.575 
11.208 

Sulphur  dioxide  

2.2131 

.17862 

5.598 

838 


VENTILATION  OF  MINES 


As  in  the  case  of  the  densities,  the  observed  specific  gravities  determined 
by  experiment,  do  not  generally  agree  with  the  theoretical  specific  gravities 
determined  from  the  weight  of  1  cu.  ft.  of  air  and  of  hydrogen  and  the  molecular 
weight  of  the  gases.  This  want  of  agreement  between  the  observed  and 
calculated  specific  gravities  will  affect  the  weights  per  cubic  foot  and  volumes 
per  pound  calculated  from  them.  The  preceding  table  is  based  on  observed 
specific  gravities  and  the  weight  of  1  cu.  ft.  of  air  of  .08071  Ib.  at  32°  F.  and 
29.921  in.  of  mercury  pressure. 

Atmospheric  Pressure. — The  pressure  of  the  air  upon  an  object  on  the 
surface  of  the  earth  is  equal  to  the  weight  of  the  column  of  air  extending  from 
the  object  to  the  upper  limits  of  the  atmosphere,  a  distance  variously  estimated 
as  from  45  to  200  mi.  The  pressure  of  the  atmosphere  decreases  with  the 
elevation  of  the  place  above  sea  level  and  increases  with  the  distance  below  it. 
At  sea  level,  when  the  temperature  is  32°  P.,  the  atmospheric  pressure  is 
14.697  Ib.  per  sq.  in.  This  pressure  of  14.697  Ib.,  which  is  commonly  taken 
as  14.7  Ib.,  is  often  called  an  atmosphere. 

Measurement  of  Atmospheric  Pressure. — The  pressure  of  the  atmosphere 
may  be  measured  by  the  height  of  a  column  of  air  of  uniform  density,  or  that 
of  a  column  of  water  (water  gauge)  or  of  mercury  (barometer),  necessary  to 
produce  such  pressure.  The  following  table  gives  the  heights  of  the  columns 
of  these  various  substances  necessary  to  produce  a  pressure  of  14.697  Ib.  per 
sq.  in.  (one  atmosphere)  at  a  temperature  of  32°  F. 


EQUIVALENT  HEIGHTS  OF  COLUMNS  OF  AIR,  WATER, 
AND  MERCURY 


Pressure  per 
Square  Inch 
Pounds 

Height  of  Column  to  Produce  Pressure 

Air 
Feet 

Water 
Feet 

Mercury 
Inches 

14,697 
.491 
.433 
.036 

26,220 

876 
772 
64 

33.942 
1.134 
1 

A  or  1  in. 

29.921 

1 
.882 
.074 

The  pressure  per  square  foot  due  to  1  in.  of  the  water  and  mercury  columns 
is  5.2  and  70.7  Ib.,  respectively. 

The  height  of  the  air  column  corresponding  to  1  in.  of  the  water  gauge  is, 
more  exactly,  64.43  ft.,  at  32°  F.  and  barometer  29.921  in.  Note  that  in  the 
following  table  the  temperature  is  60°  and  barometer  30  in. 


CORRESPONDING  MERCURY  AND  AIR  COLUMNS,  AND  PRESSURE 
PER  SQUARE  FOOT  FOR  EACH  INCH  OF  WATER  COLUMN 


Air 

Pressure 

Air 

Pressure 

Water 
Gauge 

Mercury 
Column 

Column 
Feet 

Pounds 
per 

Water 
Gauge 

Mercury 
Column 

Column 
Feet 

Pounds 
per 

Inches 

Inch 

(T.  60°, 
B.  30") 

Square 
Foot 

Inches 

Inch 

(T.  60°, 
B.  30") 

Square 
Foot 

1 

.0735 

68 

5.2 

6 

.4412 

407 

31.2 

,2 

.1471 

136 

10.4 

7 

.5147 

475 

36.4 

3 

.2206 

204 

15.6 

8 

.5882 

543 

41.6 

4 

.2941 

272 

20.8 

9 

.6618 

611 

46.8 

5 

.3676 

340 

26.0 

10 

.7353 

679 

52.0 

VENTILATION  OF  MINES 


839 


WATER  COLUMN,  AND  PRESSURE  PER  SQUARE  FOOT  FOR  EACH 
INCH  OF  MERCURY  COLUMN 


Pressure 

Pressure 

Barometer 
Inches 

Water 
Column 
Feet 

Pounds 
per 
Square 
Inch 

Barometer 
Inches 

Water 
Column 
Feet 

Pounds 
per 
Square 
Inch 

1 

1.13 

.49 

16 

18.13 

7.84 

2 

2.27 

.98 

17 

19.27 

8.33 

3 

3.40 

1.47 

18 

20.40 

8.82 

4 

4.54 

1.96 

19 

21.53 

9.31 

5 

5.67 

2.45 

20 

22.67 

9.80 

6 

6.80 

2.94 

21 

23.80 

10.29 

7 

7.93 

3.43 

22 

24.93 

10.78 

8 

9.06 

3.92 

23 

26.07 

11.27 

9 

10.20 

4.41 

24 

27.20 

11.76 

10 

11.33 

4.90 

25 

28.33 

12.25 

11 

12.46 

5.39 

26 

29.47 

12.74 

12 

13.60 

5.88 

27 

30.60 

13.23 

13 

14.73 

6.37 

28 

31.73 

13.72 

14 

15.87 

6.86 

29 

32.87 

14.21 

15 

17.00 

7.35 

30 

34.00 

14.70 

Barometers. — The  aneroid  barometer  and  its  use  in  determining  elevations 
is  described  on  page  140.  The  mercurial  barometer  is  often  called  the  cistern 
barometer;  or.  when  the  lower  end  of  the  tube  is  bent  upwards  instead  of  the 
mouth  of  the  tube  being  submerged  in  a  basin,  it  is  known  as  the  siphon  bar' 
ometer.  The  instrument  is  constructed  by  filling  a  glass  tube  3  ft.  long,  and 
having  a  bore  of  \  in.  diameter,  with  mercury,  which  is  boiled  to  drive  off  the 
air.  The  thumb  is  now  placed  tightly  over  the  open  end,  the  tube  inverted,  and 
its  mouth  submerged  in  a  basin  of  mercury.  When  the  thumb  is  withdrawn, 
the  mercury  sinks  in  the  tube,  flowing  out  into  the  basin,  until  the  top  of  the 
mercury  column  is  about  30  in.  above  the  surface  of  the  mercury  in  the  basin, 
and  after  a  few  oscillations  above  and  below  this  point,  comes  to  rest.  The 
vacuum  thus  left  in  the  tube  above  the  mercury  column  is  as  perfect  a  vacuum 
as  it  is  possible  to  form,  and  is  called  a  Torricelli  vacuum,  after  its  discoverer. 
There  being  evidently  no  pressure  in  the  tube  above  the  mercury  column, 
and  as  the  weight  of  this  column  standing  above  the  surface  of  the  mercury 
in  the  basin  is  supported  by  the  pressure  of  the  atmosphere,  it  is  the  exact 
measure  of  the  pressure  of  the  atmosphere  on  the  surface  of  the  mercury  in 
the  basin.  If  the  experiment  is  performed  at  sea  level,  the  height  of  the 
mercury  will  be  found  to  average  about  30  in.;  at  higher  elevations  it  is  less, 
while  below  this  level,  it  is  greater.  Roughly  speaking,  an  allowance  of  1  in.  of 
barometric  height  is  made  for  each  900  ft.  of  ascent  or  descent  from  sea  level 
(see  Barometric  Elevations).  A  thermometer  is  attached  to  each  mercurial 
barometer  to  note  the  temperature  of  the  reading,  as  it  is  customary  in  all 
accurate  work  with  this  instrument  to  reduce  each  reading  to  an  equivalent 
reading  at  32°  F.,  which  is  the  standard  temperature  for  barometric  readings. 

Mercury  expands  about  .0001  of  its  volume  for  each  degree  Fahrenheit. 
To  reduce,  therefore,  a  reading  at  any  temperature  to  the  corresponding 
reading  at  the  standard  temperature  of  32°  F.,  subtract  TU^  of  the  observed 
height  for  each  degree  above  32°;  or,  if  the  temperature  is  below  32°,  add  T^J™ 
for  each  degree. 

Thus.  30.667  in.  at  62°  F.  is  equivalent  to  a  reading  of  30.555  in.  at  32°  F., 


since  30.667  - 


X  (30.667)  =  30.667  -  .092  =  30.555  in. 


A  scale  is  provided  at  the  top  of  the  mercury  column  with  its  inches  so 
marked  upon  it  as  to  make  due  allowance  for  what  is  called  the  error  of  capacity. 
In  other  words,  the  inches  of  the  scale  are  longer  than  real  inches,  since  the 
level  of  the  mercury  in  the  basin  rises  as  it  sinks  in  the  tube,  and  vice  versa.  The 
top  of  the  mercury  column  is  always  oval,  convex  upwards,  owing  to  capillary 
attraction,  and  the  scale  is  read  where  it  is  tangent  to  this  convex  surface. 


840  VENTILATION  OF  MINES 

Relation  Between  Volume  and  Temperature  of  Gases. — The  pressure 
remaining  the  same,  the  volume  of  a  given  weight  of  any  gas  is  proportional  to 
its  absolute  temperature.  (Gay-Lussac's,  or  Charles'  law.) 

The  meaning  of  absolute  temperature  is  explained  on  page  353.  For  general 
purposes,  the  absolute  zero  is  taken  as  —460°  and  not  at  its  exact  value  of 
-459.64°  F. 

If  V  =  volume  of  a  gas  at  absolute  temperature  T; 

i>  =  volume  of  same  gas  at  absolute  temperature  t; 
the  proportion  may  be  written 

V:v=T:t          (1) 

EXAMPLE.— If  10,000  cu.  ft.  of  air  at  32°  F.  is  heated  to  60°  F.  in  passing 
through  a  mine,  what  is  the  increased  or  expanded  volume,  the  pressure  remain- 
ing constant? 

SOLUTION.— Here,  F=  10,000,  T  =  460 +32  =  492,  t  =  460 +60  =  520,  and  it 
is  required  to  find  v;  substituting  in  formula  1,  10,000  :  t>  =  492  :  520;  whence, 

v  =  10,OOOX^=  10,569  cu.  ft. 
4y*j 

Relation  Between  Volume  and  Pressure  of  Gases. — The  pressure  remaining 
the  same,  the  volume  of  a  given  weight  of  any  gas  is  inversely  proportional  to  its' 
absolute  pressure.  (Mariotte's,  or  Boyle's  law.) 

Absolute  pressure  is  the  pressure  above  that  of  a  perfect  vacuum  to  which 
a  gas  may  be  subjected  and  is  equal  to  the  pressure  of  the  atmosphere  at  the 
particular  time  and  place  added  to  the  pressure  as  recorded  by  a  gauge  or 
other  instrument.  Thus,  at  sea  level  and  under  ordinary  atmospheric  con- 
ditions, a  gauge  pressure  of  100  Ib.  is  equal  to  an  absolute  pressure  of  114.697  Ib. 
per  sq.  in.  At  a  place  5,000  ft.  above  sea  level,  where  the  average  reading  of 
the  barometer  is,  say,  24.9  in.  corresponding  to  a  pressure  of  12.22  Ib.  per 
sq.  in.,  100  Ib.  gauge  pressure  is  equal  to  112.22  Ib.  absolute. 

If  V  =  volume  of  a  gas  under  an  absolute  pressure  P; 

v  =  volume  of  same  gas  under  an  absolute  pressure  p; 
then,  V :  v=p  :  P          (2) 

EXAMPLE  1. — It  is  estimated  that  the  open  and  abandoned  workings  of  a 
mine  have  a  volume  of  1,000,000  cu.  ft.  Should  the  barometer  fall  from 
29.5  to  29.0  in.,  what  volume  of  air  and  gas  would  be  forced  out  of  the  gob 
and  into  the  airways,  the  temperature  remaining  unchanged? 

SOLUTION. — As  the  barometer  measures  absolute  pressures,  in  this  example, 
the  volumes  are  inversely  proportional  to  the  readings  of  the  barometer. 
Hence,  V  =  1,000,000,  P  =  29.5,  £  =  29.0,  and  it  is  required  to  find  v;  substi- 
tuting in  formula  2,  1,000,000  :  v  =  29.0  :  29.5;  whence, 

»=  1,000,000X^  =  1, 017,250  cu.  ft. 

The  volume  of  gas  and  air  forced  into  the  airways  will  be  17,250  cu.  ft. 

EXAMPLE  2. — When  the  atmospheric  pressure  is  14.7  Ib.  per  sq.  in.,  how 
many  cubic  feet  of  free  air  must  be  compressed  to  a  gauge  pressure  of  80  Ib. 
to  fill  a  cylinder  having  a  capacity  of  20  cu.  ft.,  the  temperature  remaining 
unchanged? 

SOLUTION. — A  gauge  pressure  of  80  Ib.,  under  the  given  conditions,  is  equal 
to  an  absolute  pressure  of  80+14.7  =  94.7  Ib.  Hence,  V  =  20,  P  =  94.7,  p  =  14.7, 
and  it  is  required  to  find  v;  substituting  in  formula  2,  20  :  y  =  14.7  :  94.7; 
whence, 

v  =  20  Xj|^  =  128.84  cu.  ft. 

Relation  Between  Volume,  Temperature,. and  Pressure  of  Gases. — When 
both  the  temperature  and  pressure  of  a  gas  are  changed,  the  change  in  volume 
is  directly  proportional  to  the  change  in  absolute  temperature  (Gay-Lussac's 
law)  and  inversely  proportional  to  the  change  in  absolute  pressure  (Mariotte's 
law).  By  combining  the  formulas  1  and  2,  there  results, 
V:v=Tp:tP  (3) 

EXAMPLE. — A  certain  volume  of  air  measures  100  cu.  ft.  at  32°  F.  and  a 
pressure  of  14.7  Ib.  per  sq.  in.;  what  will  be  the  volume  of  the  air  if  the  temper- 
ature is  increased  to  90°  F.,  and  the  pressure  reduced  to  10  Ib.  per  sq.  in.? 

SOLUTION.— Here,  F=100,  T  =  460+32  =  492,  P  =  14.7,  *  =  460+90  =  550, 


VENTILATION  OF  MINES  841 

£  =  10,  and  it  is  required  to  find  »;  substituting  in  formula  3,  100  :  i>  =  492 
X10  :  550X14.7;  whence, 


Relation  Between  Weight,  Temperature,  and  Pressure  of  Gases.  —  The 

weight  of  1  cu.  ft.  of  a  gas  is  the  reciprocal  of  its  volume  per  pound,  or  W=  -~ 

and  w  =  -,  from  which  V  =  ™  and  v  =  —  .     Substituting  the  values  of  V  and  v 
in  formula  3  and  rearranging,  there  results, 

W:w  =  tP:Tp  (4) 

EXAMPLE.  —  If  1  cu.  ft.  of  carbon  monoxide  weighs  .0781  Ib.  at  32°,  barom- 
eter 29.92  in.,  what  will  be  the  weight  of  the  same  volume  of  gas  at  a  temper- 
ature of  90°,  barometer  28.00  in.? 

SOLUTION.—  Here  J^=.0781,  T  =  460  +  32  =  492,  P  =  29.92,  J  =  460+90 
=  550,  p  =  28.00,  and  it  is  required  to  find  w.  Substituting  in  formula  4, 
.0781  :  w  =  550X29.92  :  492X28.00;  whence, 


Another  method  of  determining  the  weight  of  1  cu.  ft.  of  a  gas  at  any 
temperature  and  pressure  is  given  toward  the  end  of  the  next  section. 

Weight  and  Volume  of  Air  and  Gases.  —  The  weight  of  1  cu.  ft.  of  dry  air 
at  32°  F.  and  a  pressure  of  29.921  in.  of  mercury  or  14.697  Ib.  per  sq.  in.,  is 
.08071  Ib.  avoir.  Although  not  a  true  gas  but  a  mixture  of  gases,  the  weight 
per  cubic  foot  of  air  decreases  as  the  temperature  increases  and  the  pressure 
decreases,  and  vice  versa. 

The  usual  formula  for  finding,  approximately,  the  weight  W  of  1  cu.  ft.  of 
air  when  the  temperature  t,  in  degrees  Fahrenheit,  and  the  height  B  of  the 
barometer,  in  inches,  are  given,  is, 

Tr_1.3273B 
460-H 

The  denominator  of  the  fraction  is  the  absolute  temperature,  and  1.3273 
is  the  weight  of  1  cu.  ft.  of  air  under  a  pressure  of  1  in.  of  mercury  and  at  a 
temperature  of  1°  F.,  absolute  (  —  459°  P.). 

When  the  pressure  P,  in  pounds  per  square  inch,  is  given,  W  may  be  found 
from 

'2  7P 


The  factor  2.7  is  obtained  by  dividing  1.3273  (formula  5)  by  the  weight  of 
1  cu.  in.  of  mercury,  .4912  Ib. 

EXAMPLE  1.  —  What  is  the  weight  of  1  cu.  ft.  of  dry  air  at  90°  F.,  barometer 
28  in.? 

SOLUTION.  —  Substituting  in  formula  5, 


EXAMPLE  2.  —  What  is  the  weight  of  1  cu.  ft.  of  dry  air  at  a  temperature 
of  10°  below  zero,  when  the  pressure  is  10  Ib.  per  sq.  in.? 
SOLUTION.  —  Substituting  in  formula  6, 
2.7X10          27 


When  the  specific  gravity  of  a  gas  is  known,  its  weight  per  cubic  foot  under 
any  conditions  of  temperature  and  pressure  may  be  found  by  first  finding  the 
weight  of  1  cu.  ft.  of  air  under  the  same  conditions,  and  multiplying  this  result 
by  the  specific  gravity  of  the  gas. 

EXAMPLE.  —  The  specific  gravity  of  carbon  monoxide  is  .967;  what  is  the 
weight  of  1  cu.  ft.  of  this  gas  at  90°  and  28  in.? 

SOLUTION.  —  Using  formula  5, 

Tr  =  1  '3273X28X.  967-.  0676  X  Qft7=  nflRi  Ib.  per  cu.  ft. 
This  is  the  same  result  as  was  obtained  in  the  example  illustrating  formula  4. 


842 


VENTILATION  OF  MINES 


VOLUME  AND  WEIGHT  OF  AIR  AT  SEA  LEVEL  AT  DIFFERENT 
TEMPERATURES 


Temperature 
Degrees 

Fahrenheit 

Volume  of 
1  Lb. 
Cubic  Feet 

Weight  of 
1  Cu.  Ft. 
Pound 

Temperature 
Degrees 
Fahrenheit 

!"! 

'  Weight  of 
1  Cu.  Ft. 
Pound 

Temperature 
Degrees 
Fahrenheit 

Volume  of 
1  Lb. 
Cubic  Feet 

Weight  of 
1  Cu.  Ft. 
Pound 

0 

11.583 

.08633 

100 

14.103 

.07091 

260 

18.135 

.05514 

10 

11.834 

.08450 

110 

14.355 

.06967 

270 

18.387 

.05439 

20 

12.086 

.08273 

120 

14.607 

.06846 

280 

18.639 

.05365 

32 

12.390 

.08071 

130 

14.859 

.06730 

290 

18.891 

.05294 

40 

12.590 

.07943 

140 

15.111 

.06618 

300 

19.143 

.05224 

45 

12.712 

.07864 

150 

15.363 

.06509 

310 

19.387 

.05158 

50 

12.843 

.07786 

160 

15.615 

.06041 

320 

19.647 

.05090 

55 

12.969 

.07711 

170 

15.867 

.06302 

330 

19.892 

.05027 

60 

13.095 

.07637 

180 

16.119 

.06204 

340 

20.151 

.04963 

65 

13.221 

.07564 

190 

16.371 

.06108 

350 

20.395 

.04903 

70 

13.347 

.07493 

200 

16.623 

.06016 

360 

20.655 

.04841 

75 

13.473 

.07422 

210 

16.875 

.05926 

370 

20.899 

.04785 

80 

13.599 

.07354 

220 

17.127 

.05839 

380 

21.159 

.04726 

85 

13.725 

.07286 

230 

17.379 

.05751 

390 

21.404 

.04672 

90 

13.851 

.07220 

240 

17.631 

.05672 

400 

21.663 

.04616 

95 

13.977 

.07155 

250 

17.883 

.05592 

450 

22.923 

.043624 

Diffusion  of  Gases. — The  rale  or  velocity  of  diffusion  between  air  and  a  gas, 
or  between  different  gases,  is  inversely  proportional  to  their  specific  gravities  or 
densities.  (Graham's  Law.) 

Diffusion  is  the  gradual  mixing  of  one  gas  with  another  when  bodies  of  them 
are  brought  into  direct  contact  or  when  the  wall  of  the  vessel  containing  them 
is  a  porous  membrane  through  which  they  can  pass.  Diffusion  does  not 
depend  on  stirring  or  mechanical  mixing,  although  assisted  thereby.  Thus, 
when  methane  is  given  off  at  the  floor  of  a  seam,  the  tendency  of  the  gas  to 
rise  owing  to  its  extreme  lightness  greatly  assists  its  rapid  diffusion  by  bringing 
a  greater  number  of  molecules  of  air  and  gas  in  contact  in  a  given  time.  A 
feeder  in  the  roof  or  other  high  point  may  give  off  gas  more  quickly  than 
diffusion  can  take  place,  particularly  where  the  air-current  is  sluggish,  in  which 
case  there  will  be  formed  a  body  of  pure  methane.  Similarly,  an  accumula- 
tion of  blackdamp  may  be  formed  near  the  floor  or  in  some  other  low  place 
where  the  current  is  feeble  and  the  gas  is  given  off  more  rapidly  than  it  can 
diffuse. 

Diffusion  continues  until  the  gases  are  uniformly  mixed,  and  when  so  mixed 
the  gases  cannot  be  separated.  As.  stated  in  Graham's  law,  the  greater  the 
difference  in  the  specific  gravities  of  two  gases,  the  more  rapidly  will  they 
diffuse  or  mix.  Thus,  carbon  dioxide  will  mix  with  air  more  rapidly  than  will 
nitrogen. 

The  rate  of  diffusion  of  one  gas  with  respect  to  another  may  be  found  by 
comparing  their  rates  of  diffusion  with  respect  to  air.  Thus,  the  rate  of 
diffusion  of  carbon  dioxide  with  respect  to  methane  is  .812 -5-1.344  =  .604,  and 
of  oxygen  with  respect  to  hydrogen  is  .949  -7-3.830  =  .248. 

The  volumes  of  the  various  gases  that  will  diffuse  in  the  same  time  are 
proportional  to  their  respective  rates  of  diffusion.  Thus,  1,344  volumes  of 
methane  will  diffuse  in  the  same  time  as  1,000  volumes  of  air  or  812  volumes 
of  carbon  dioxide. 

The  rates  of  diffusion  may  also  be  calculated  by  comparing  the  densities 
of  the  gases  with 'respect  to  hydrogen.  The  density  of  air  and  carbon  dioxide 
are,  respectively,  14.359  and  21.835,  whence  the  rate  of  diffusion  of  carbon 
dioxide  with  respect  to  air  is  Vl4.359-f-21.835=  V^657614  =  .811,  which  agrees 
very  closely  with  the  observed  rate  of  .812. 

In  the  accompanying  table,  it  will  be  noted  that  the  observed  and  theo- 
retical rates  of  diffusion  agree  very  closely,  except  in  the  case  of  hydrogen 
sulphide. 


VENTILATION  OF  MINES 


843 


RATES  OF  DIFFUSION  AND  TRANSPIRATION  OF  GASES  COMPARED 
TO  AIR 


Gas 

Specific 
Gravity 

Rate  of  Diffusion 

Rate  of 
Trans- 
piration 

Theoretical 

Observed 

Hydrogen  

.0694 
.5545 
.9670 
.9674 
1.0000 
1.1054 
1.1817 
1.5291 

3.7965 
1.3428 
1.0169 
1.0166 

.9511 
.9199 
.8087 

3.830 
1.344 
1.015 
1.014 

.949 
.950 
.812 

2.066 
1.639 
1.034 
1.030 
1.000 
.903 
1.458 
1.237 

Methane  

Carbon  monoxide 

Nitrogen  
Air 

Oxygen  
Hydrogen  sulphide  
Carbon  dioxide  

Occlusion  and  Transpiration  of  Gases. — All  coals  in  the  seam  contain 
a  greater  or  less  amount  of  various  gases  that  are  given  off  as  the  coal  face 
is  exposed  in  mining.  It  has  commonly  been  supposed  that  these  gases  were 
occluded,  or  hidden,  in  the  coal  under  great  pressure,  but  there  seems,  reason 
to  doubt  this  as  a  universal  rule  (see  under  Formation  of  Methane).  In  any 
case,  the  escaping  gases  are  not  occluded,  a  term  that  refers  to  the  probable 
condensation  and  perhaps  existence  of  a  gas  in  a  quasi-metallic  state  in  the 
pores  of  a  metal,  as  hydrogen  in  the  pores  of  the  metals  palladium  or  platinum. 
The  conditions  that  have  held  the  gas  in  the  coal  or  adjoining  rocks  are  largely 
closeness  of  grain  in  the  coal  and  imperviousness  of  the  clay  in  the  roof  shales. 
The  pressure  of  the  occluded  gases  is  often  as  high  as  10  to  40  or  more  atmos- 
pheres (see  Properties  and  Sources  of  Methane). 

Transpiration  refers  to  the  more  or  less  steady  outflow  of  gas  from  the 
pores  of  the  coal  at  the  working  face.  The  rate  of  transpiration  of  the  various 
mine  gases,  air  being  the  unit,  is  given  in  the  preceding  table.  Although  the 
relative  rates  are  not  the  same,  the  order  of  the  gases  in  transpiration  is  the 
same  as  in  diffusion,  except  in  the  case  of  the  very  heavy  hydrogen  sulphide 
and  carbon  dioxide.  The  rate  of  transpiration  varies  with  the  pressure  under 
which  the  gas  exists  and  decreases  as  the  temperature  decreases  but  not  in  the 
same  ratio,  and  is  independent  of  the  specific  gravity  of  the  gas. 

The  rates  of  transpiration  is  of  importance  in  determining  the  nature  of  the 
gas  mixtures  found  in  mines.  Thus,  1,639  volumes  of  methane  will  transpire 
in  the  same  time  as  1,237  volumes  of  carbon  dioxide  and  there  is,  thence,  a 
tendency  to  increase  the  proportion  of  the  former  and  decrease  that  of  the 
latter  in  the  airways.  This  difference  in  the  rate  of  transpiration  has  made 
difficult  the  accurate  determination  of  the  different  gases  present  in  different 
coals.  The  principal  occluded  gases  are  methane,  nitrogen,  and  carbon  dioxide. 
In  some  coals,  methane  formed  93%  of  the  occluded  gas;  in  others,  nitrogen 
formed  91%;  while  in  others,  carbon  dioxide  formed  54%.  Oxygen  rarely 
exceeds  4  or  5%  and  is  usually  much  less.  Analyses  of  occluded  gases,  both 
face  and  blowers,  are  given  under  Firedamp. 

The  transpiration  of  gas  from  coal  seams  varies  widely  in  its  nature,  often 
being  accompanied  by  a  sharp  crackling  and  a  hissing  sound;  in  extreme  cases 
the  pressure  is  so  great  as  to  dislodge  the  coal  from  the  face.  Usually,  the 
gases  issue  without  noise  either  from  the  pores  in  a  newly  exposed  working  face , 
or  through  blowers,  which  are  the  exposed  ends  of  larger  openings  or  crevices 
in  the  seam  or  its  containing  rocks  (see  Properties  and  Sources  of  Methane). 

Humidity. — The  amount  of  water,  as  vapor,  that  may  be  contained  in 
a  given  volume  of  air  depends  on  the  temperature,  and  is  greater  at  high  than 
at  low  readings  of  the  thermometer.  When  air  contains  all  the  moisture  it 
can  at  any  given  temperature,  it  is  said  to  be  saturated.  -When  the  temper- 
ature of  saturated  air  is  lowered,  some  of  the  vapor  is  condensed  and  deposited 
upon  surrounding  objects  in  the  form  of  drops  of  water.  When  the  temper- 
ature is  raised,  the  air  is  no  longer  saturated  and  is  capable  of  taking  up  more 
moisture  from  the  mine  workings  until  it  becomes  saturated  at  the  higher 
temperature.  The  gallons  of  water  contained  in  100,000  cu.  ft.  of  saturated 
air  is  given  in  the  following  table. 


844 


VENTILATION  OF  MINES 


GALLONS   OF  WATER  IN   100,000  CU.  FT.  OF  SATURATED  AIR  AT 
TEMPERATURES  FROM   -20°  F.  TO   +100°  F. 


Temperature 
Degrees  F. 

%  $ 
ftQ  «J 
0,0^ 

III 

cTcS 

Temperature  | 
Degrees  F.  | 

8,0  J 

its 

3S% 

13-|  3 

o  o 

Temperature! 
Degrees  F. 

w   1o 
Q<O  <u 
nX&i 

oo'.S 

SOXI 
cS"-"  3 

o  o 

Temperature 
Degrees  F. 

Gallons  per 
100,000 
Cubic  Feet 

Temperature 
Degrees  F. 

b  t? 

a8(S 
§O.H 

SO.Q 
ea  *-"  3 

o  o 

-20 

.284 

5 

1.044 

29 

3.172 

53 

7.751 

77 

17.099 

19 

.298 

6 

1.094 

30 

3.312 

54 

8.023 

78 

17.643 

18 

.315 

7 

1.149 

31 

3.462 

55 

8.306 

79 

18.202 

17 

.336 

8 

1.205 

32 

3.618 

56 

8.592 

80 

18.776 

16 

.354 

9 

1.265 

33 

3.756 

57 

8.891 

81 

19.365 

15 

.373 

10 

1.329 

34 

3.902 

58 

9.199 

82 

19.971 

14 

.395 

11 

1.397 

35 

4.051 

59 

9.516 

83 

20.594 

13 

.416 

12 

1.466 

36 

4.206 

60 

9.843 

84 

21.232 

12 

.440 

13 

1.537 

37 

4.366 

61 

10.179 

85 

21.888 

11 

.462 

14 

1.611 

38 

4.530 

62 

10.525 

86 

22.564 

10 

.488 

15 

1.688 

39 

4.701 

63 

10.880 

87 

23.254 

9 

.514 

16 

1.767 

40 

4.878 

64 

11.249 

88 

23.964 

8 

.541 

17 

1.849 

41 

5.059 

65 

11.626 

89 

24.694 

7 

.568 

18 

1.931 

42 

5.246 

66 

12.015 

90 

25.439 

6 

.569 

19 

2.022 

43 

5.439 

67 

12.415 

91 

26.207 

5 

.633 

20 

2.114 

44 

5.639 

68 

12.824 

92 

26.994 

4 

.666 

21 

2.215 

45 

5.845 

69 

13.248 

93 

27.800 

3 

.704 

22 

2.320 

46 

6.059 

70 

13.686 

94 

28.629 

2 

.743 

23 

2.428 

47 

6.278 

71 

14.132 

95 

29.477 

1 

.782 

24 

2.539 

48 

6.507 

72 

14.594 

96 

30.346 

0 

.823 

25 

2.655 

49 

6.740 

73 

15.066 

97 

31.239 

+  1 

.865 

26 

2.779 

50 

6.979 

74 

15.556 

98 

32.156 

2 

.906 

27 

2.905 

51 

7.229 

75 

16.054 

99 

33.098 

3 

.948 

28 

3.035 

52 

7.487 

76 

16.569 

100 

34.058 

4 

.996 

Relative  humidity,  which  is  often  called  humidity,  is  the  ratio  of  the 
quantity  of  water  vapor  present  to  the  quantity  necessary  to  saturate  the  space 
occupied  by  the  air,  at  the  given  temperature  and  pressure.  When  air  is 
saturated,  its  relative  humidity  is  100%.  At  any  relative  humidity,  the 
amount  of  water  actually  present  in  a  given  volume  of  air  may  be  found  by 
multiplying  the  amount  required  to  saturate  the  air  at  the  specified  temperature 
by  the  relative  humidity. 

EXAMPLE  1. — A  current  of  60,000  cu.  ft.  of  air  a  min.  is  entering  a  mine; 
its  temperature  is  20°  F.  and  humidity  65%.  What  is  the  quantity  of  water 
brought  into  the  mine  in  1  min.,  in  1  hr.,  and  in  1  da.  of  24  hr.? 

SOLUTION. — From  the  preceding  table,  100,000  cu.  ft.  of  saturated  air 
at  20°,  contains  2.114  gal.  of  water.  At  65%  relative  humidity,  this  volume 
of  air  will  contain  2.114 X. 65  =  1.3741  gal.,  and  60,000  cu.  ft.  will  contain 
six-tenths  of  this  quantity,  or  1.374 IX. 6  =  .82446  gal.,  which  is  the  quantity 
of  water  brought  into  the  mine  in  1  min.  In  1  hr.  there  will  be  .82446X60 
=  49.4676  gal.,  and  in  a  24-hr,  da.  there  will  be  49.4676X24  =  1,187.2224  gal. 

EXAMPLE  2. — If,  in  example  1,  the  return  air-current  has  a  temperature 
of  65°  and  a  relative  humidity  of  98%,  what  is  the  quantity  of  water  absorbed 
from  the  mine  workings  in  1  min.,  1  hr.,  and  1  da.? 

SOLUTION. — At  98%  humidity,  60,000  cu.  ft.  of  air  contains  11.626X.98 
X. 6  =  6.83609  gal.  At  20°  F.  and  65%  humidity,  the  same  quantity  of  air 
contains  .82446  gal.  (example  1);  hence,  there  is  absorbed  by  the  air-current 
in  its  passage  through  the  mine,  6.83609 -.82446  =  6.01 143  gal.  a  min.;  6.01143 
X 60  =  360.6858  gal.  an  hr.,  and  360.6858X24  =  8,656.4692  gal.  a  da. 

Psychrometers  or  Hygrometers. — A  psychrometer,  or  hygrometer,  is  an 
instrument  for  measuring  the  quantity  of  aqueous  vapor  in  the  air.  The 
standard  type  involves  the  determination  of  the  temperature  of  evaporation 
and  consists  of  two  similar  thermometers  usually  mounted  on  the  same  frame, 
one  called  the  dry  bulb  and  the  other  the  -wet  bulb.  Below  the  wet  bulb  is  a 
small  jar  for  water.  In  order  to  take  an  observation,  a  small  muslin  sack  is 


VENTILATION  OF  MINES 


845 


fixed  around  the  wet  bulb,  its  end  extending  down  into  the  jar  from  which 
the  water  is  drawn  by  capillary  attraction.  The  thermometers  are  exposed  to 
a  current  of  air  that  has  a  velocity  of  15  ft.  or  more  per  sec.  If  the  relative 
humidity  of  the  air  is  less  than  100%,  that  is,  if  the  air  is  not  saturated,  some 
of  the  water  on  the  muslin  sack  is  evaporated,  a  certain  amount  of  heat  is 
absorbed  by  evaporation,  and  the  temperature  of  the  wet-bulb  thermometer 
is  reduced  to  a  point  at  which  the  amount  of  heat  absorbed  by  evaporation  is 
just  equal  to  that  received  from  the  surrounding  air.  From  the  readings 
of  the  two  thermometers,  by  reference  to  suitable  tables,  the  relative  humidity 
and,  consequently,  the  aqueous  vapor  per  cubic  foot  of  air  may  be  calculated. 

The  sling  psychrometer  is  the  form  in  common  use  in  mines.  It  consists  of 
two  thermometers  mounted  side  by  side  in  a  case  provided  with  a  cover.  The 
instrument  has  a  handle  at  the  top  by  which  it  may  be  given  a  whirling  motion 
to  secure  a  velocity  of  the  wet  bulb  of  15  ft.  a  sec.  or  more.  The  muslin  sack 
is  moistened  at  the  time  of  making  the  observation,  which  is  repeated  until 
the  results  agree. 

The  hygrodeik  is  a  form  of  psychrometer  in  which  the  thermometers  are 
attached  to  a  fan-shaped  wooden  frame,  on  which  are  a  series  of  curves  and 
radial  lines  placed  between  the  thermometers.  By  properly  placing  a  pointer 
suspended  from  the  upper  part  of  the  frame  according  to  the  readings  of  the 
two  thermometers,  the  relative  humidity  may  at  once  be  taken  from  one  of 
the  scales,  thus  obviating  any  calculations. 

In  the  hair  hygrometer,  the  rapid  change  that  takes  place  in  the  length 
of  a  strand  of  hair  with  changes  in  the  amount  of  moisture  in  the  air,  is  utilized 
to  move  a  pointer  by  means  of  a  delicately  adjusted  lever  arm. 

A  hygrograph  is  an  instrument  by  which  the  variations  in  relative  humidity 
are  automatically  recorded.  It  consists  of  a  hair  psychrometer,  the  pointer 
of  which  carries  on  its  end  an  inking  arrangement  so  that  it  can  trace  a  line 
on  section  paper  wrapped  on  a  revolving  cylinder  turned  by  clockwork.  In 
this  way,  a  permanent  and  continuous  record  is  obtained.  The  readings  of 
a  hair  psychrometer  are  not  always  reliable,  and  the  instrument  should  be 
standardized  by  comparison  with  the  regular  wet-bulb  instrument,  at  various 
temperatures  and  degrees  of  saturation. 


MINE  GASES 

ATMOSPHERIC  AND  MINE  AIR 

Atmospheric  Air. — Sir  William  Ramsay  gives  the  following  as  the  com- 
position of  ordinary  air: 

COMPOSITION  OF  PURE  AIR 


Name  of  Gas 

By  Volume 

By  Weight 

Exact 

Approximate 

Exact 

Approximate 

20.941 
78.1221 
.937/ 

20.94 
79.0G 

23.024 
75.5391 
1.437  / 

23.02 
76.98 

Nitrogen  
Argon 

Total     . 

100.000 

100.00 

100.000 

100.00 

In  the  column  headed  Approximate,  the  argon  and  nitrogen  are  considered 
as  one  gas,  as  is  usually  done.  With  the  argon  occur  certain  very  rare  gases 
similar  to  nitrogen  whose  proportions,  by  volume,  Ramsay  estimates  to  be: 
Helium,  .0004%;  krypton,  .028%;  neon,  .0123%;  xenon,  .005%. 

In  addition  to  these  normal  gases,  air  always  contains  a  certain  amount  of 
carbon  dioxide  and  water  vapor,  the  former  averaging  .03  to  .04%,  and  the 
latter  depending  on  the  temperature  and  relative  humidity.  At  certain  times 
and  in  certain  places,  traces  of  ammonia,  oxides  of  nitrogen,  sulphur  dioxide, 
and  even  hydrogen  are  found  in  air.  The  composition  of  the  air  is  constant 
regardless  of  the  altitude. 


846  VENTILATION  OF  MINES 

Mine  Air. — Mine  air  does  not  differ  from  atmospheric  air,  except  that  in 
its  passage  through  the  mine,  the  ventilating  current  gives  up  a  certain  amount 
of  oxygen  to  the  coal  and  to  the  various  processes  of  combustion  (breathing  of 
men  and  animals,  burning  of  lamps,  etc.),  and  receives  a  certain  amount  of 
other  gases  in  place  thereof;  always  carbon  dioxide,  usually  methane,  rarely 
carbon  monoxide,  and  very  rarely  or  in  extremely  minute  amounts,  ethane, 
olefiant  gas,  nitrous  oxide,  sulphur  dioxide,  hydrogen  sulphide,  hydrogen,  and 
possibly  hydrocarbons  higher  than  ethane.  The  carbon  dioxide,  methane, 
and  carbon  monoxide  are  generally  known  as  mine  gases,  as  the  others  are 
found  in  very  small  amounts  or  under  unusual  conditions.  The  constituent 
of  air  that  usually  varies  the  most  between  the  intake  and  the  return  is  the 
absolute  humidity,  meaning  by  this  term,  the  actual  amount  of  water  con- 
tained in  a  given  volume  of  the  air-current.  Regardless  of  the  relative  humidity 
of  the  intake,  that  of  the  return  is  rarely  less  than  90%  and  is  very  commonly 
more  than  this;  further,  this  is  generally  true  in  mines  of  any  size  whatever 
may  be  the  outside  temperature.  That  is,  whether  the  air  enters  at  20°  and 
50%  humidity  or  80°  and  95%  humidity,  it  will  usually  leave  the  mine  with 
a  saturation  of  90%  or  more  at  a  temperature  between  55°  and  65°. 

In  passing  through  well-ventilated  mines,  the  air-current  will  rarely  lose 
more  than  .5  to  .75%  of  oxygen  and  gain  about  the  same  amount  of  carbon 
dioxide  and  methane.  At  the  larger  American  mines,  a  chemist  is  employed 
to  regularly  analyze  the  return  air,  and  any  deficiency  in  oxygen  or  dangerous 
increase  in  carbon  dioxide  and,  more  particularly,  methane  is  promptly  rectified 
by  increasing  the  ventilating  current. 

In  Great  Britain,  the  mine  code  of  1914  provides:  "A  place  shall  not  be 
deemed  to  be  in  a  fit  state  for  working  or  passing  therein  if  the  air  contains  either 
less  than  19%  of  oxygen  or  more  than  li%  of  carbon  dioxide." 

OXYGEN 

Properties  and  Sources. — Oxygen  has  an  atomic  symbol  of  O  and  a  mole- 
cular formula  of  Oz.  It  is  but  slightly  soluble  in  water,  100  volumes  of  which 
take  up  4.11  volumes  of  the  gas  at  32°  and  2.83  volumes  at  68°.  It  is  taste- 
less, odorless,  and  colorless  and  is  the  supporter  of  life  and  combustion.  Its 
chemical  and  physical  constants  have  been  given  in  preceding  tables. 

Oxygen  is  the  most  abundant  element  in  nature,  composing,  by  weight, 
23.02%  of  the  atmosphere,  85.79%  of  all  water,  and  47.17%  of  the  rocks  of 
the  solid  crust  of  the  earth.  It  constitutes  49.85%,  or  practically  one-half,  of 
all  matter  existing  between  the  upper  limits  of  the  earth's  atmosphere  and  the 
lower  depths  of  its  crust.  It  is  not  produced  by  any  of  the  ordinary  chemical 
processes  or  changes  going  on  in  mines,  but  is  absorbed  or  consumed  in  prac- 
tically all  of  them.  Small  amounts  are  given  off  by  the  pores  of  the  coal,  by 
blowers,  etc. 

Effect  of  Oxygen  on  Life. — Oxygen  is  essential  to  life,  forming  in  the  lungs 
with  the  hemoglobin  of  the  blood  an  unstable  chemical  compound  known  as 
oxy hemoglobin,  which  gives  arterial  blood  its  bright  red  color.  In  its  passage 
through  the  body,  the  oxyhemoglobin  parts  with  its  oxygen  and  is  converted 
into  hemoglobin,  which  gives  the  familiar  dark  purple  color  to  venous  blood. 

At  rest,  an  average  man  breathes  sixteen  to  eighteen  times  a  minute  and 
takes  into  the  lungs  at  each  respiration  30.5  cu.  in.  of  air.  When  working 
moderately,  there  will  be  about  twenty-five  respirations  a  minute,  which  may 
be  increased  to  as  many  as  sixty  when  the  work  is  very  violent,  as  in  running. 
Of  the  oxygen  passing  into  the  lungs,  10  to  35%  is  consumed  in  the  processes 
of  the  body,  the  rest  being  exhaled  with  the  nitrogen  inhaled  in  the  air  together 
with  the  carbon  dioxide  formed  in  the  tissues.  Exhaled  breath  contains  from 
2.6  to  6.6%  of  carbon  dioxide,  with  an  average  of  about  4%.  The  proportion 
of  carbon  dioxide  is  less  during  sleep,  although  it  changes  but  little  with  changes 
in  the  amount  of  oxygen  in  the  air,  as  long  as  breathing  is  free. 

The  effect  upon  life  of  diminishing  the  proportion  of  oxygen  in  the  air 
depends  on  whether  its  place  is  taken  by  nitrogen  or  carbon  dioxide.  When 
carbon  dioxide  is  not  present,  the  effects  produced  upon  a  miner  by  a  simple 
deficiency  in  the  percentage  of  oxygen  are  the  same  as  those  produced  by  the 
great  diminution  in  atmospheric  pressure  at  high  altitudes  (Haldane).  Quot- 
ing further  from  Haldane:  A  diminution  (of  oxygen  in  the  air)  from  20.93% 
to  15%  is  by  itself  practically  without  effect  on  men,  though  a  candle  would 
be  instantly  extinguished  in  such  air.  As  the  diminution  increases  further, 
certain  effects  begin,  however,  to  be  produced.  The  first  symptoms  usually 
noticed  are  that  any  great  muscular  exertion  is  less  easy,  and  that  it  is  apt  to 
cause  slight  dizziness  and  unusual  shortness  of  breath.  A  person  not  exerting 


VENTILATION  OF  MINES 


847 


himself  will,  as  a  rule,  not  notice  anything  unusual  until  the  oxygen  percentage 
has  fallen  to  10%.  The  breathing  then  usually  begins  to  become  deeper 
and  more  frequent,  the  pulse  more  frequent,  and  the  face  somewhat  dusky. 
At  7%,  there  is  usually  distinct  panting,  accompanied  by  palpitations,  and  the 
face  becomes  a  leaden  blue  color.  At  the  same  time  the  mind  becomes  con- 
fused and  the  senses  dulled,  although  the  person  breathing  the  air  may  be  quite 
unaware  of  the  fact.  Muscular  power  is  also  greatly  impaired.  At  a  slightly 
lower  percentage,  there  is  complete  loss  of  consciousness  .  .  .  .  In  air 
containing  no  oxygen,  loss  of  consciousness  occurs  within  40  sec.  or  less,  without 
any  previous  warning  symptom  (see  Effect  of  Carbon  Dioxide  on  Life). 

Pure  oxygen  may  be  inhaled  for  a  long  time  without  danger  and  is  fre- 
quently administered  in  cases  of  suffocation,  carbon  monoxide  poisoning,  etc. 

Effect  of  Oxygen  on  Combustion. — As  the  proportion  of  oxygen  in  the  air 
is  lessened,  lamps  burn  more  and  more  dimly  until  they  finally  go  out.  The 
amount  of  oxygen  that  will  sustain  combustion  is  influenced  by  the  amount 
of  moisture  and  carbon  dioxide  present.  Thus,  a  lamp  will  be  extinguished 
sooner  when  the  air  is  moist  and  the  oxygen  has  been  replaced  by  carbon 
dioxide  than  when  the  air  is  dry  and  nitrogen  is  the  only  inert  gas  present. 

A  residual  atmosphere  is  one  that  remains  after  a  flame  burning  in  it  has 
so  reduced  the  amount  of  oxygen  that  it  is  finally  extinguished.  The  following 
table,  from  Clowes  and  the  Bureau  of  Mines,  gives  the  residual  atmospheres 
in  which  flames  of  various  burning  substances  were  finally  extinguished. 

COMPOSITION   OF  RESIDUAL  ATMOSPHERES  THAT  EXTINGUISH 
FLAME 


Flame 

Percentage  Composition  of  Atmosphere 

COi 

02 

Nt 

6.30 
4.35 
2.95 
12.25 
4.90 

2.30 
3.25 
3.00 
3.00 
3.00 

11.70 
14.90 
16.24 
13.35 
11.35 
5.50 
15.60 
13.90 
16.60 
16.50 
15.82 

80.50 
80.75 
80.81 
74.40 
83.75 
94.50 
82.10 
82.85 
80.40 
80.50 
81.18 

Alcohol,  absolute  
Candle  

Carbon  monoxide  
Coal  gas  

Hydrogen  
Methane 

Natural  gas  

Paraffin,  lamp  oil  
Wolf  lamp,  bonneted  

Wolf  lamp,  unbonneted  

Clowes  sums  up  the  results  of  his  experiments  as  follows: 

1.  Wick-fed  flames  require  atmospheres  of  very  similar  composition  to 
extinguish  them;  while  gas-fed  flames  require  atmospheres  of  widely  different 
composition. 

2.  Nitrogen  must  be  added  in  larger  proportion  than  carbon  dioxide  in 
order  to  extinguish  the  same  flame  (see  Effect  of  Carbon  Dioxide  on  Com- 
bustion). 

3.  The  minimum  proportion  of  extinctive  gas  that  must  be  mixed  with  air 
in  order  to  extinguish  a  flame  is  independent  of  the  size  of  the  flame. 

4.  The  composition  of  an  atmosphere  that  will  at  once  extinguish  a  lamp 
placed  in  it  is  not  the  same  as  the  residual  atmosphere  resulting  from  the 
lamp  burning  out  in  pure  air.     In  the  case  of  wick-fed  flames,  however,  the 
difference  is  not  great. 

5.  The  flames  of  candles  and  lamps,  when  they  are  extinguished  by  burn 
ing  in  a  confined  space  of  air,  produce  an  atmopshere  of  almost  identical  com- 
position with  that  of  air  expired  from  the  lungs. 

6.  The  extinctive  atmospheres  produced  by  the  combustion  of  the  flames 
of  candles  and  of  lamps,  and  the  air  expired  from  the  lungs  after  inspiring 
fresh  air,  are  respirable  with  safety. 

7.  The  extinction  of  an  ordinary  candle  or  lamp  flame  is  not  necessarily 
indicative  of  the  unsuitability  of  an  atmosphere  to  maintain  life  when  it  is 
breathed. 


848  VENTILATION  OF  MINES 

Absorption  of  Oxygen  by  Coal. — The  experiments  of  the  Bureau  of  Mines 
and  of  others  show  that  coal  bottled  in  air  under  ordinary  atmospheric  pres- 
sure rapidly  absorbs  oxygen  until,  after  a  few  days,  there  remains  often  only 
1  or  2%  of  oxygen  in  the  free  gas  in  the  bottle.  At  the  same  time  a  certain 
proportion  of  the  oxygen  unites  with  the  substances  in  the  coal  to  form  carbon 
dioxide,  but  this  process,  at  least  during  the  comparatively  short  time  of  the 
experiments  accounts  for  only  a  small  part  of  the  oxygen  entering  the  coal. 

The  effect  of  the  gradual  absorption  of  oxygen  with  the  formation  of 
greater  or  less  amounts  of  carbon  dioxide  is  to  form  blackdamp  with  the 
nitrogen  remaining  in  the  air,  as  explained  under  Blackdamp. 

NITROGEN 

Properties  and  Sources. — Nitrogen  has  an  atomic  symbol  of  2V  and  a 
molecular  formula  of  TVz.  It  is  odorless,  colorless,  and  tasteless,  and  supports 
neither  life  nor  combustion.  In  the  atmosphere,  it  serves  to  dilute  the  oxygen 
and,  in  combinations  like  ammonia,  is  a  source  of  plant  food.  It  is  about 
one-half  as  soluble  in  water  as  oxygen,  100  volumes  of  water  taking  up  2.03  vol- 
umes of  the  gas  at  32°  and  1.40  volumes  at  68°.  The  chemical  and  physical 
constants  of  nitrogen  have  been  given  in  the  preceding  tables. 

Small  quantities  of  nitrogen  are  given  off  by  the  pores  of  the  coal.  It  is 
the  product  of  feeders  and  blowers,  rarely  as  pure  nitrogen,  but  mixed  with 
considerable  amounts  of  carbon  dioxide,  forming  blackdamp.  Feeders  of 
methane,  also,  contain  variable  amounts  of  this  gas.  Small  quantities  may  be 
present  in  the  leakage  from  natural  gas  wells  that  have  been  drilled  and  improp- 
erly cased  through  the  coal.  It  is  found  chiefly,  and  to  the  extent  of  20  to  55%, 
in  the  products  of  combustion  of  explosives;  the  percentage  depending  on  the 
kind  of  explosive  and  the  conditions  under  which  it  is  fired. 

While  composing  79.06%  by  weight  of  the  atmosphere,  nitrogen  constitutes 
but  .03%  of  the  matter  existing  between  the  upper  limit  of  the  atmosphere 
and  the  lower  limit  of  the  earth's  crust.  Owing  to  the  absorption  of  oxygen 
in  the  various  chemical  processes  going  on  in  mines,  the  proportion  of  nitrogen 
in  mine  air  is  usually  greater  than  in  that  at  the  surface. 

Effect  of  Nitrogen  on  Life. — Nitrogen  is  distinctly  negative  in  its  action 
and  is  not  in  any  way  poisonous.  The  effect  of  gradually  increasing  the  .per- 
centage of  nitrogen  or,  what  is  the  same  thing,  decreasing  the  proportion  of 
oxygen  in  mine  air,  is  to  cause  death  by  suffocation  (see  Effect  of  Oxygen  on 
Life). 

Effect  of  Nitrogen  on  Combustion. — Pure  nitrogen  instantly  extinguishes 
combustion  of  any  kind.  Increasing  proportions  of  nitrogen  in  the  air  with 
the  accompanying  decreasing  proportions  of  oxygen  cause  a  flame  to  burn 
with  diminishing  brilliancy  until  it  is  finally  extinguished  (see  Effect  of  Oxygen 
and  Effect  of  Carbon  Dioxide,  Respectively,  on  Combustion). 

Atmospheres  deficient  in  oxygen  and  high  in  nitrogen  and  methane  and, 
commonly,  carbon  dioxide,  are  very  common  in  old  workings.  In  these  old 
workings,  a  lamp  may  not  burn  although  breathing  is  without  discomfort,  but 
if  sufficient  fresh  air  is  mixed  with  these  gob  atmospheres  they  may  become 
highly  explosive;  or  they  may  be  explosive  in  one  part  of  the  workings  and 
not  in  another. 

CARBON  DIOXIDE 

Properties  and  Sources. — Carbon  dioxide,  formerly  known  as  carbonic  acid, 
carbonic-acid  gas,  blackdamp,  chokedamp,  stythe,  etc.,  has  a  formula  of  COz, 
is  colorless  and  odorless,  has  a  slight  acid  taste  especially  when  dissolved  in 
water,  and  is  not  combustible.  It  is  very  soluble  in  water,  100  volumes  taking 
up  179.6  volumes  of  the  gas  at  32°  and  90.1  volumes  at  68°.  The  chemical 
and  physical  constants  are  given  in  preceding  tables. 

Under  ordinary  working  conditions,  carbon  dioxide  is  produced  in  the 
mine  by  the  breathing  of  men  and  animals,  by  the  burning  of  oil,  acetylene, 
gasoline,  and  explosives,  by  the  decay  of  vegetable  and  animal  matter,  and  by 
the  slow  oxidation  of  the  coal.  Small  amounts  of  this  gas  are  produced  by 
feeders  and  blowers  occurring  in  the  roof,  floor,  or  face,  by  transpiration  from 
the  coal  being  mined,  by  escape  from  the  water  of  underground  streams  wherein 
it  has  been  held  under  pressure,  and  by  chemical  reaction  between  water  carry- 
ing carbonates  in  solution  and  acid  minewater.  However,  the  amotint  of 
carbon  dioxide  thus  added  to  the  air  of  a  well-ventilated  mine  is  insignificant 
and  is,  according  to  Haas,  not  over  .02  to  .03%,  so  that  normal  mine  air  should 
not  contain  over  .06  to  .07%  of  this  gas. 


VENTILATION  OF  MINES  849 

Under  unusual  conditions,  carbon  dioxide  is  produced  by  spontaneous 
combustion  of  coal  as  in  gob  fires,  by  mine  fires  of  any  kind,  and  by  explosions 
of  methane  and  coal  dust.  While  it  may  be  formed  by  the  burning  or  explosion 
of  carbon  monoxide,  its  origin  in  this  way  is  highly  improbable,  as  over  13% 
of  monoxide  is  necessary  for  the  purpose. 

Owing  to  its  high  specific  gravity,  carbon  dioxide  naturally  tends  to  collect 
along  the  floor  and  in  dip  workings,  but  this  tendency  is  resisted  by  its  diffusive 
properties,  so  that  the  gas  is  commonly  distributed  uniformly  through  the  air 
of  a  working  place.  When  concentrated  at  the  floor  it  is  because  it  is  given  off 
there  faster  than  diffusion  and  the  ventilating  currents  can  remove  it.  As 
Haldane  states,  warm  air  laden  with  carbon  dioxide  from  breathing  and  burning 
will  keep  at  the  top  of  the  rise. 

Effect  of  Carbon  Dioxide  on  Life. — Carbon  dioxide  is  not  actively  poisonous 
like  carbon  monoxide,  hydrogen  sulphide,  etc.,  in  that  it  does  not  combine  with 
the  hemoglobin  of  the  blood  or  cause  degeneration  of  the  brain  cells  or  the 
like,  but  in  sufficient  quantities  it  does  have  a  toxic  effect.  That  is  to  say, 
atmospheres  in  which  a  deficiency  of  oxygen  is  accompanied  by  a  corresponding 
excess  of  carbon  dioxide  are  more  injurious  than  those  where  the  oxygen 
deficiency  merely  results  in  increasing  the  proportion  of  nitrogen  present. 
Messrs.  Priestly  and  Haldane  explain  this  as  follows:  "  At  ordinary  atmos- 
pheric pressure,  the  breathing  always  regulates  in  such  a  way  as  to  keep  the 
percentage  of  carbonic  acid  (COz)  in  the  air  cells  (alveoli)  of  the  lungs  constant. 
Each  individual  has  his  own  exact  percentage;  but  on  an  average  there  is 
about  5.6%  of  carbonic  acid  in  the  alveolar  air  of  man.  The  regulation  is 
almost  astoundingly  exact  for  each  person. 

"If  air  containing  carbonic  acid  is  breathed,  the  respirations  become 
deeper,  in  such  a  way  that  the  alveolar  carbonic-acid  percentage  still  remains 
practically  the  same,  if  possible.  If,  for  instance,  there  is  2%  of  carbonic 
acid  in  the  air,  the  breathing  will  need  to  be  about  50%  deeper  than  before. 
This  difference  would  not  be  noticed  by  the  person.  If  there  is  5%  of  carbonic 
acid  in  the  air,  it  requires  much  panting  to  keep  the  alveolar  carbonic-acid 
percentage  nearly  constant;  if  there  is  6  or  7%,  it  is,  of  course,  quite  impossible 
to  maintain  a  normal  alveolar  carbonic-acid  percentage,  and  great  distress  is 
produced,  as  the  blood  becomes  abnormally  charged  with  carbonic  acid,  to 
which  the  body  is  exquisitely  sensitive. 

"It  is  carbonic  acid,  and  carbonic  acid  alone,  which  regulates  our  breathing 
under  normal  conditions.  The  supposed  ill  effects  of  a  small  percentage  of 
carbonic  acid  in  the  inspired  air  are  wholly  imaginary,  as  a  very  slight  increase 
in  the  depth  of  breathing  at  once  compensates  for  the  extra  carbonic  acid. 
So  long  as  the  efforts  of  the  lungs  to  adjust  themselves  to  the  change  in  the 
amount  of  carbonic  acid  in  the  air  are  not  attended  with  discomfort,  the  person 
is  in  no  danger." 

The  same  authority  says  that  "carbon  dioxide  produces  no  very  noticeable 
effect  until  it  amounts  to  more  than  3%  (3%  COz  and  97%  air  =  3%  CO*. 
20.4%  Oz,  76.6%  Nz),  which  is  more  than  is  often  met  in  mine  air  just  extinctive 
of  lights.  With  an  increasing  proportion,  the  breathing  becomes  noticeably 
deeper  and  more  frequent;  at  about  5  or  6%  (5%  CO*  and  95%  air  =  5%  COz, 
20%  Oz,  75%  A^),  there  is  marked  panting  accompanied  by  increased  frequency 
of  pulse.  At  about  10%  (10%  COz  and  90%  air  =10%  COz,  18.9%  Oz,  71.1% 
Nz),  there  is  violent  panting,  throbbing,  and  flushing  of  the  face.  Headache 
is  also  produced,  especially  noticeable  on  return  to  fresh  air.  Beyond  10%, 
carbon  dioxide  begins  to  have  a  narcotic  effect,  and  at  25%  (25%  COz  and 
75%  air  =  25%  COz,  15.8%  Oz,  59.2%  Nz}  death  may  occur  after  several  hours; 
but  as  much  as  50%  may  be  breathed  for  some  time  without  fatal  effects,  to 
judge  from  experiments  on  animals." 

In  commenting  upon  a  certain  blackdamp,  Mr.  E.  M.  Chance  says:  "With 
10%  of  oxygen,  the  effects  produced  will  be  more  dangerous  from  the  deficiency 
of  oxygen  than  from  the  4%  of  carbon  dioxide.  In  fact,  the  4%  of  carbon 
dioxide  will  prolong  life  by  creating  deeper  and  more  frequent  respiration. 
In  breathing  atmospheres  containing  2%  or  3%  carbon  dioxide  and,  say, 
10%  or  12%  oxygen,  the  respiration  will  be  better  and  the  man  will  be  more 
resistant  to  the  gas  than  if  he  breathed  the  air  without  the  carbon  dioxide." 

Modern  investigations  show  that  a  certain  amount  of  carbon  dioxide  is 
distinctly  stimulating  to  respiration  and,  in  cases  of  suffocation,  it  is  not 
unusual  to  administer  the  dioxide  at  the  same  time  as  oxygen,  because  the 
increased  depth  of  breathing  through  the  effort  of  the  lungs  to  adjust  themselves 
to  the  proper  alveolar  percentage  of  carbon  dioxide,  naturally  draws  into  them 
more  of  the  desired  oxygen. 
54 


850 


VENTILATION  OF  MINES 


Effect  of  Carbon  Dioxide  on  Combustion. — Strictly,  it  is  the  lack  of  oxygen 
and  not  the  presence  of  carbon  dioxide  or  other  inert  gas  that  causes  a  lamp 
flame  to  dim  and  finally  go  out.  However,  the  experiments  of  Haldane, 
Clowes,  Clement,  and  others  show  that  when  a  loss  of  oxygen  is  accompanied 
by  an  increase  in  carbon  dioxide,  a  flame  is  extinguished  more  quickly  than 
when  a  deficiency  in  oxygen  merely  causes  an  increase  of  nitrogen.  The 
following  table,  abridged  from  Clement,  shows  the  effects  on  the  explosive  range 
of  methane  by  decreasing  percentages  of  oxygen  and  increasing  percentages 
of  carbon  dioxide.  The  explosions  were  made  in  a  steel  explosion  chamber 
by  an  electric  spark  and  are  believed  to  approximate  results  that  would  be 
obtained  in  the  mines.  In  any  case,  the  amount  of  nitrogen  in  the  air  may 
be  found  by  subtracting  from  100%,  the  sum  of  the  percentages  of  oxygen, 
carbon  dioxide  and  methane. 

EXPLOSIVE    RANGE    OF    MIXTURES    OF    METHANE   AND    CARBON 
DIOXIDE 


Atmosphere 
Contains 

Methane 
Explodes 

Atmosphere 
Contains 

Methane 
Explodes 

02 
Per 
Cent. 

C02 
Per 
Cent. 

Lower 
•  Limit 
Per 
Cent. 

Upper 
Limit 
Per 
Cent. 

02 
Per 
Cent. 

C02 
Per 
Cent. 

Lower 
Limit 
Per 
Cent. 

Upper 
Limit 
Per 
Cent. 

19 

5.5 

13.5 

16 

20.0 

6.7 

9.6 

19 

20 

6.4 

16 

30.0 

7.4 

8.1 

19 

50 

8.0 

10.8 

15 

5.9 

9.6 

18 

5.7 

12.8 

15 

16.0 

6.9 

8.7 

18 

20 

6.4 

11.8 

15 

21.0 

7.5 

7.5 

18- 

48 

8.5+ 

10.0 

14 

6.2 

8.2 

17 

5.7 

11.8 

14 

12.5 

7.3 

7.5 

17 

20 

6.4 

10.3 

14 

13.5 

6.9* 

7.2* 

17 

43. 

8.3 

8.7 

13 

6.3 

7.1 

16 

5.8 

10.7 

13 

2.0 

6.6 

6.8 

The  effect  of  increasing  percentages  of  carbon  dioxide,  that  of  the  oxygen 
remaining  unchanged,  is  to  shorten  the  explosive  range  of  methane  by  raising 
the  lower  and  reducing  the  upper  explosive  limit.  Immediately  after  the 
explosive  limits  coincide,  there  is  so  much  carbon  dioxide  present  that  an 
explosion  is  not  possible.  The  lower  the  oxygen  percentage  in  the  air,  the 
less  carbon  dioxide  is  required  to  make  the  atmosphere  inexplosive.  Further, 
the  dioxide  appears  to  be  more  active  in  reducing  the  upper  explosive  limit 
than  in  raising  the  lower  one. 

According  to  J.  F.  Clement,  the  author  of  the  foregoing  table,  the  difference 
in  the  effects  of  carbon  dioxide  and  nitrogen  on  the  explosive  limits  of  methane 
is  due  to  the  marked  difference  in  the  specific  heats  of  the  two  gases.  The 
mean  molecular  heats  of  carbon  dioxide  and  nitrogen  between  0°  and  650°  C. 
are,  respectively,  10.6  and  7.2.  A  given  volume  of  carbon  dioxide  will  absorb, 
therefore,  10.6 -r- 7.2  =  1.47  times  as  much  heat,  practically  50%  more,  as  the 
same  volume  of  nitrogen  while  being  heated  to  650°  C.,  the  ignition  temperature 
of  methane.  An  amount  of  carbon  dioxide  may,  thence,  be  eventually  reached 
where  its  cooling  effect  is  so  great  that  the  temperature  of  the  surrounding  air 
will  be  below  the  ignition  point  of  methane. 

Similar  reasoning  shows  that  the  amount  of  heat  required  to  raise  the 
temperature  of  an  excessive  percentage  of  carbon  dioxide  may  be  so  great 
that  the  products  of  combustion  of  an  oil  flame  may  be  cooled  below  the 
ignition  point  of  the  oil;  and  when  this  is  passed,  the  lamp  goes  out.  As  the 
cooling  is  gradual  as  the  percentage  of  carbon  dioxide  increases,  so  is  the 
diminution  of  the  light  given  out  by  the  lamp,  which  is  proportional  to  the 
rate  of  combustion  of  the  oil.  A  reduction  of  1%  in  the  oxygen  normally  in 

*  Note  that  these  are  burnings  and  not  explosions. 


VENTILATION  OF  MINES  851 

the  air  causes  a  loss  of  30%  jn  the  light  emitted  by  oil  flame.  Clowes  states 
that  when  2%  of  carbon  dioxide  is  present,  the  hydrogen  flame  begins  to  change 
from  reddish  to  pale  blue,  whereas  10%  is  necessary  to  reduce  the  size  of  an 
oil  flame  and  15%  to  extinguish  it.  A  reduction  in  the  oxygen  to  16%  causes 
the  acetylene  flame  to  become  yellow. 

Blackdamp.  —  The  term  blackdamp  is  commonly  applied  by  the  miner  to 
carbon  dioxide  and  by  others  to  a  mixture  of  that  gas  and  air  in  which  the 
proportion  of  carbon  dioxide  is  so  large  that  a  lamp  will  not  burn  in  it. 

Strictly,  there  is  no  such  gas  as  blackdamp,  and  the  term  is  now  used  to 
describe  a  residual  atmosphere,  resulting  from  the  slow  absorption  of  oxygen 
by  the  coal  and  by  the  processes  of  oxidation  always  taking  place  underground. 
Was  it  not  for  the  fact  that  in  these  processes  of  absorption  and  oxidation  a 
certain  amount  of  carbon  dioxide  is  given  off,  the  resulting  mine  atmosphere 
would  be  one  of  pure  nitrogen.  On  this  understanding,  blackdamp  is  mine 
air  deficient  in  oxygen  but  containing  an  excess  of  nitrogen,  with  (usually) 
or  without  carbon  dioxide. 

However,  certain  chemists  like  Haldane  and  those  of  the  Bureau  of  Mines 
regard  blackdamp  as  a  more  or  less  distinct  gaseous  mixture  containing,  on  an 
average,  from  90  to  85%  of  nitrogen  and  10  to  15%  of  carbon  dioxide,  with 
seldom  less  than  5%  or  more  than  20%  of  the  latter.  The  chemical  and 
physical  properties  of  such  a  mixture,  both  by  itself  and  when  associated  with 
air,  will  depend  on  the  relative  proportions  of  the  two  gases.  Thus,  a  black- 
damp  mixture  high  in  carbon  dioxide  will  have  a  much  more  marked  effect 
upon  life  and  combustion  than  when  the  mixture  is  largely  or  entirely  nitrogen; 
pure  blackdamp  is  lighter  than  carbon  dioxide  and  is  lighter  than  air  when  the 
proportion  of  carbon  dioxide  is  less  than  5.25%.  If  a  small  amount  of  methane 
is  associated  with  the  blackdamp,  the  resulting  mixture  will  almost  always  be 
lighter  than  air.  As  illustrating  the  variable  composition  of  blackdamp, 
Haldane  cites  that  at  the  Grotto  del  Cane,  near  Naples,  as  being  pure  carbon 
dioxide  and  that  at  a  metal  mine  in  Colorado  as  being  pure  nitrogen;  between 
these  extremes,  the  two  gases  may  exist  in  any  proportion. 

The  following  analyses  from  Haldane  illustrate  the  composition  of  air  and 
blackdamp  mixtures  and  the  methods  of  computation. 

In  the  first  form,  the  amounts  of  the  gases  are  reported  in  the  ordinary  way; 
in  the  second,  the  oxygen  with  the  proper  amount  of  nitrogen  to  form  air  is 
reported  as  such,  and  the  remainder  of  the  nitrogen  together  with  all  the 
carbon  dioxide  is  reported  as  blackdamp. 

AIR  FROM  OLD  WORKINGS,  HAMSTEAD  COLLIERY 
As  Analyzed  Air-Blackdamp  Ratio 

Oxygen  ...............      3.35  A-  /Oxygen  .........     3.35\    1fim 

Nitrogen  .............    84.03  Air\Nitrogen  ........  12.65  /    lb<UU 

Carbon  dioxide  ........      5.25     T,,     t,jorv,^f  Nitrogen  ........  71.38\    7R  Ro 

Methane  .............      7.33      Blackdamp  \  Carbon  dioxide  ..     5.25  /    76'63 

Carbon  monoxide  .......  04  Methane  ...............      7.33 

Carbon  monoxide  ........  04 

100.00 

100.00 

In  the  preceding  analysis,  the  blackdamp  is  composed  of  93.2%  nitrogen 
and  6.8%  carbon  dioxide. 

AIR  FROM  A  DISUSED  END,  DOLCOATH  TIN  MINE,  CORNWALL 

As  Analyzed  Air-Blackdamp  Ratio 

Oxygen  ...............    17.99  ../Oxygen  .........  17.99"l     Rr  q~ 

Nitrogen  .............    78.83  Air  \  Nitrogen  ........  67.94  /    85'93 

Carbondioxide  .......  .38     Blackdain™  M  14-07 


100.00 


100.00 


In  the  preceding  analysis,  the  blackdamp  is  composed  of  77.6%  nitrogen 
and  22.4%  carbon  dioxide. 

In  the  section  headed  Firedamp  are  numerous  analyses  of  gaseous  mixtures 
given  off  by  the  face,  blowers,  feeders,  etc.,  the  majority  of  which  contain 
blackdamp.  The  constituents  of  these,  and  similar  mixtures,  may  be  combined 
in  the  same  way  as  the  foregoing. 

Haldane's  Blackdamp  Indicator.  —  Haldane's  blackdamp  indicator  is  based 
upon  the  fact  that  the  distance  above  the  bottom  of  a  tube  at  which  a  lighted 


852  VENTILATION  OF  MINES 

taper  is  extinguished  bears  a  constant  relation  to  the  amount  of  oxygen  in  the 
air  or,  conversely,  to  the  amount  of  inert  impurities  present.  The  apparatus 
consists  of  a  glass  tube  7  in.  long  and  |  in.  in  diameter  with  a  vertical  scale  on 
its  face  which  is  graduated  in  percentages  of  blackdamp  and  the  corresponding 
percentages  of  oxygen.  The  blackdamp  graduations  run  from  0  to  10.5%  and 
the  corresponding  oxygen  graduations  from  20.9  to  18.8%.  A  lighted  taper, 
•fg  in.  in  diameter  is  introduced  into  the  bottom  of  the  tube  and  is  moved 
upward  until  it  is  extinguished,  when  the  percentage  of  blackdamp  present  is 
read  directly  from  the  scale.  Since  an  excess  of  moisture  or  of  nitrogen  affects 
the  flame  in  a  similar  way  to  carbon  dioxide,  the  indicator  records  the  sum  of 
the  inert  impurities  in  the  mine  air.  As  methane  elongates  the  flame,  the 
device  is  better  adapted  to  use  in  non-gaseous  mines.  The  instrument  is 
graduated  to  correspond  with  air  saturated  with  moisture  at  64°  F.  (about 
2%  of  moisture)  as  this  is  a  fair  average  of  temperature  and  humidity  con- 
ditions in  mines.  Provided  the  temperature  and  humidity  do  not  vary  greatly 
from  those  just  named,  it  is  found  that  the  indications  of  the  instrument  may 
be  relied  upon  to  within  about  .2%  of  oxygen  and  1%  of  blackdamp.  The 
instrument  may  be  graduated  for  any  other  conditions  of  temperature  and 
humidity. 

Below  18.8%  of  oxygen,  the  taper  will  no  longer  burn  in  the  tube  nor  will 
it  burn  without  it  when  the  oxygen  is  below  18.2%  (13%  of  blackdamp)  unless 
held  horizontally  when  it  will  burn  until  the  oxygen  has  been  reduced  to  about 
17.2%  (18%  of  blackdamp). 

CARBON  MONOXIDE 

Properties  and  Sources. — Carbon  monoxide,  formerly  known  as  carbonic 
oxide,  carbonic-oxide  gas,  and  whitedamp,  has  a  formula  CO,  is  odorless,  color- 
less, and  tasteless,  and  supports  neither  life  nor  combustion.  It  burns  with 
a  bright  bluish  flame  and  is  explosive  when  mixed  with  air  in  the  proper  pro- 
portions. The  gas  is  so  extremely  poisonous  that  its  presence  in  mine  air 
indicates  conditions  that  should  be  investigated  and  remedied  at  once. 

The  burning  of  coal  dust  suspended  in  the  air  or  lodged  on  the  roof,  floor, 
and  ribs,  at  the  time  of  a  mine  explosion,  is  the  greatest  and  most  dangerous 
source  of  carbon  monoxide,  a  gas  that  has  probably  caused  more  deaths, 
certainly  more  at  one  time,  than  have  all  the  other  mine  gases  combined. 

Insignificant  amounts  of  carbon  monoxide  are  given  off  by  certain  coals 
either  because  they  are  occluded  in  the  pores  of  the  seam  or  because  they 
result  from  the  slow  oxidation  of  the  coal.  Rollin  T.  Chamberlain  investigated 
the  gases  given  off  by  coals  when  bottled  in  a  vacuum.  The  gases  from  small 
lumps  from  the  Mansfield  mine,  Carnegie,  Pa.,  contained  .22%  CO  at  the  end 
of  1  mo.;  analyses  made  at  the  end  of  10  and  of  20  da.  showing  none  of  the 
gas.  The  gases  from  Monongah,  W.  Va.,  coal  crushed  to  pass  through  a 
ten-mesh  sieve,  showed  .20%  of  carbon  oxide  for  the  first  6  wk.,  .16%  CO  for 
the  next  10  wk.,  and  2.86%  CO  for  the  final  10  wk.  of  the  half  year  during  which 
the  tests  were  carried  on.  In  these  instances,  the  coal  used  was  the  Pittsburgh, 
or  No.  8,  containing  over  30%  volatile  matter.  It  was  found  that  the  finer 
the  coal,  the  more  gas  was  given  off.  The  amount  of  gas  thrown  into  the  mine 
air  in  this  way  is  top  small  to  be  detected  by  analysis  in  the  return. 

Under  all  conditions  of  working,  gasoline-haulage  motors  produce  gases 
containing  carbon  monoxide.  When  the  carburation  is  poor,  the  proportion  of 
the  gas  is  high  and,  if  the  ventilation  is  defective,  may  be  a  source  of  grave 
danger.  Proper  operation  of  the  motor  and  sufficient  ventilation  will  generally 
prevent  trouble  from  this  cause. 

Carbon  monoxide  may  be  produced  by  the  explosion  of  methane  when 
the  percentage  of  the  latter  gas  in  the  air  is  between  the  limits  of  maximum 
explosibility  and  the  upper  explosive  limit  or  between  9.46  and,  say,  13%. 
The  amount  of  the  gas  thus  produced  increases  as  the  percentage  of  methane 
approaches  the  upper  explosive  limit  (see  Combustion  Products  of  Methane). 

Carbon  monoxide  is  produced  by  the  detonation  of  all  kinds  of  explosives 
in  amounts  ranging  from  2  to  35%  of  the  volume  of  the  gases  resulting  there- 
from, depending  on  the  composition  of  the  explosive,  the  care  used  in  handling 
it,  and  the  conditions  under  which  it  was  fired.  Ordinarily,  under  proper 
conditions  of  management,  the  carbon  monoxide  produced  in  this  way  is  not 
dangerous  and  cannot  be  detected  in  the  return  air. 

The  gases  from  black  powder  exploded  in  a  vacuum  contain  from  2  to  12% 
of  carbon  monoxide,  with  an  average  of  about  6%.  In  mining  operations, 
however,  the  presence  of  coal  dust  will  increase  the  proportion  of  the  gas  to 
18  to  20%  and  to  35%  in  some  cases.  The  proportion  given  off  is  found  to 


VENTILATION  OF  MINES  853 

decrease  as  the  pressure  decreases  and  the  amount  of  moisture  present  increases. 
Haas  states  that  the  gases  from  black  powder  will  yield  on  an  average  18% 
of  the  monoxide,  and  that  1  Ib.  of  powder  will  produce  1  cu.  ft.  of  the  gas. 
Should  12  Ib.  of  powder  be  exploded  in  a  place  6  ft.  X 15  ft.,  and  such  amounts 
are  sometimes  used  in  solid  shooting,  the  gases,  if  confined  within  a  distance 
of  10  ft.  from  the  face,  would  cause  the  air  to  contain  1.33%  of  carbon  monoxide ; 
an  amount  that  would  be  fatal  in  a  few  minutes. 

In  the  case  of  a  standing  shot,  the  cracks  and  crevices  of  the  coal  are  com- 
monly filled  with  a  combustible  gas,  which  is  frequently  ignited  by  the  lamp 
of  a  miner  returning  too  soon  to  the  face.  It  has  commonly  been  supposed 
that  this  gas  is  carbon  monoxide,  but  Mr.  Haas  suggests  that  it  is  probably 
some  hydrocarbon  distilled  from  the  coal  by  the  intense  heat  of  the  explosion, 
and  that  the  monoxide  produced  was  all  burned  immediately  after  the  blast 
was  discharged. 

Some  permissible  explosives,  notably  those  of  the  ammonium  nitrate  class, 
yield  no  carbon  monoxide  when  detonated  in  a  vacuum.  However,  when 
fired  in  the  presence  of  coal  dust,  as  in  a  mine,  they  will  yield  from  6  to  36%  of 
the  gas,  the  higher  figures  being  extreme. 

Abel  and  others  have  shown  that  the  explosion  of  nitroglycerine  does  not 
yield  any  carbon  monoxide,  but  the  tests  of  the  Bureau  of  Mines  indicate  the 
presence  of  as  much  as  28.4%  CO  in  the  gases  from  exploding  40%  strength 
nitroglycerine  dynamite  and  34.6%  in  the  gases  of  the  same  explosive  when 
of  60%  strength.  A  60%  strength  low  freezing  dynamite  yielded  as  much 
as  47.4%  CO,  in  the  gases.  The  explosion  products  from  ammonia  and  gelatine 
dynamites  contain  from  0  to  4%  CO.  However,  when  these  explosives  are 
improperly  used,  that  is,  when  all  or  a  part  of  the  charge  is  burned  and  not 
exploded,  the  amount  of  carbon  monoxide  in  the  gases  is  greatly  increased. 
In  a  test  by  the  Bureau  of  Mines,  the  gases  from  a  40%  strength  gelatine 
dynamite  contained  3%  CO  when  the  explosive  was  detonated  and  13.7%  when 
it  was  burned. 

The  gases  from  selected  permissible  powders  and  dynamites  should  cause 
no  trouble  from  carbon  monoxide  if  the  explosives  are  properly  used  with  detona- 
tors of  ample  strength,  if  the  air  supply  at  the  face  is  good,  and  if  a  reasonable 
time  is  allowed  for  the  gases  to  mix  with  the  air  before  returning  to  the  face 
after  a  shot. 

While  the  Bureau  of  Mines  (Miner's  Circular  14)  states  that  natural  gas 
does  not  contain  carbon  monoxide,  from  which  it  follows  that  the  leakage 
from  an  improperly  cased  well  drilled  through  the  seam  cannot  be  a  source 
of  this  gas,  other  analysts  have  found  from  0  to  .4%  CO  in  natural  gas  from 
Pennsylvania  and  West  Virginia,  from  0  to  .5%  in  that  from  Ohio  and  Indiana, 
and  an  average  of  1%  in  that  from  Kansas. 

Carbon  monoxide  is  invariably  present  in  the  gases  from  gob  fires.  These 
fires  are  caused  by  the  spontaneous  combustion  of  the  coal  through  the  slow 
oxidation  of  piles  of  slack  and  bone  coal  left  behind  in  the  workings  where 
the  air  supply  is  sufficient  to  furnish  the  necessary  oxygen,  but  is  not  great 
enough  to  carry  away  all  the  heat  formed  by  the  chemical  processes  going  on 
(see  under  Spontaneous  Combustion  and  Mine  Fires). 

Should  a  gob  fire  burst  into  flame  through  an  increase  of  the  air  supply,  or 
should  a  fire  in  the  ordinary  sense  start  in  the  timber  or  in  the  coal,  large 
volumes  of  carbon  monoxide  will  be  given  off  because,  in  the  confined  workings 
of  a  mine,  it  is  not  possible  for  there  to  be  enough  air  present  to  furnish  all  the 
oxygen  required  to  burn  the  carbon  to  carbon  dioxide.  Either  a  portion  of  the 
carbon  is  burned  to  the  monoxide  directly,  ir  it  is  burned  to  the  dioxide,  a 
part  or  all  of  which  is  at  once  reduced  to  monoxide.  Numerous  deaths  have 
been  caused  by  the  carbon  monoxide  from  extensive  mine  fires  being  carried 
into  the  workings  in  mines,  where  under  usual  conditions,  the  air  current  was 
ample. 

Effect  of  Carbon  Monoxide  on  Life.— While  perhaps  not  so  poisonous  as 
hydrogen  sulphide  and  nitrogen  dioxide,  carbon  monoxide  is  formed  under  so 
many  more  conditions  and  to  a  so  much  greater  extent  that  it  is  commonly 
considered  the  most  dangerous  of  mine  gases. 

The  poisonous  effect  of  the  gas  is  due  to  its  absorption  by  the  hemoglobin 
of  the  blood  (with  which  it  forms  an  unstable  chemical  compound)  which  has 
200  to  300  times  the  affinity  for  carbon  monoxide  that  it  has  for  oxygen,  and  to 
the  extent  that  the  blood  is  saturated  with  monoxide  to  that  extent  it  cannot 
carry  the  oxygen  required  by  the  tissues.  The  Committee  on  Resuscitation 
from  Mine  Gases  of  the  American  Medical  Association,  in  speaking  of  the 
effects  of  illuminating  gas  which  contains  much  carbon  monoxide,  says;  If  the 


854  VENTILATION  OF  MINES 

amount  of  hemoglobin  combined  with  carbon  monoxide  exceeds  a  figure  between 
60  and  70%,  so  that  only  30  to  40%  is  available  for  the  transportation  of 
oxygen,  and  if  the  patient  has  been  in  this  condition  for  f  hr.  or  more,  degen- 
erative processes  will  have  started  in  the  brain  from  lack  of  oxygen  and  death 
or  serious  nervous  or  mental  impairment  will  certainly  follow.  According  to 
Wabner,  when  the  saturation  reaches  67%  (two-thirds)  death  is  practically 
certain  and  is  inevitable  when  the  saturation  is  79%.  Haldane  says  that  when 
death  occurs  gradually,  the  hemoglobin  is  usually  about  80%  saturated. 

The  absorption  of  carbon  monoxide  by  the  blood  changes  its  color  from 
deep  purple  red  to  a  very  characteristic  pale  or  rose  shade.  This  distinctive 
coloring  is  noticeable  in  the  lips  and  other  parts  of  the  body  where  the  skin 
is  thin,  and  for  this  reason  the  bodies  of  those  who  have  died  from  monoxide 
poisoning  commonly  present  a  very  lifelike  appearance,  entirely  different  from 
the  pallid,  leaden  look  accompanying  death  from  other  causes. 

The  effect  of  carbon  monoxide  is  not  cumulative,  and  for  each  per  cent,  of 
the  gas  in  the  air  there  is  a  fixed  degree  of  saturation  of  the  hemoglobin,  as 
shown  in  the  table  on  page  858.  Thus,  breathing  air  containing  .04%  of 
carbon  monoxide  will  result  in  the  blood  becoming  30%  saturated;  and  indefi- 
nite exposure  will  not  increase  this  degree  of  saturation  unless  the  percentage 
of  the  gas  in  the  air  is  increased.  Nasmith  and  Graham  have  shown  that 
animals  may  be  hardened  to  the  effects  of  carbon  monoxide  so  that  after  several 
weeks'  exposure  to  gradually  increasing  proportions  of  the  gas,  they  are  able  to 
live  in  atmospheres  that  would  kill  them  at  the  outset.  In  the  case  of  man, 
however,  the  inhalation  of  small  amounts  of  this  gas  while  at  work  during 
the  day  does  not  render  him  immune,  as  the  blood  is  purified  at  night  by  breath- 
ing fresh  air. 

Haldane  says,  "The  symptoms  of  carbon-monoxide  poisoning  are  essentially 
the  same  as  those  produced  by  air  deficient  in  oxygen,  and  vary  according  to 
the  degree  of  saturation  reached  by  the  blood.  The  onset  of  the  symptoms  is 
very  insidious,  there  being  only  slight  shortness  of  breath  and  palpitations,  but 
hardly  any  discomfort;  and  the  senses,  power  of  judgment  and  of  movement, 
are  commonly  much  impaired  before  the  person  is  aware  of  anything  being 
wrong.  In  some  cases  there  is  much  excitement,  but  often  there  is  simple 
drowsiness  and  stupidity.  The  symptoms  are,  in  some  respects,  similar  to 
those  produced  by  alcohol.  One  curious  fact  is  that  in  carbon-monoxide,  as  in 
alcoholic,  poisoning  sudden  exposure  to  cool  fresh  air  may  greatly  increase 
the  symptoms.  Death  seems  often  to  be  immediately  brought  about  by 
attempts  to  escape  rapidly  up  inclines,  ladders,  etc."  In  several  instances 
in  American  mines,  the  victims  of  a  dust  explosion  have  been  able  to  make 
their  way  as  much  as  £  mi.  from  their  working  places  before  being  overcome 
by  the  carbon  monoxide  in  the  afterdamp. 

The  rapidity  with  which  carbon  monoxide  will  overcome  a  person  and 
whether  death  or  disablement  will  follow,  depends  on  the  percentage  of  gas  in 
the  air  and  the  length  of  time  it  has  been  breathed,  and  on  the  rapidity  of 
breathing  which,  in  turn,  depends  on  the  violence  of  his  exertions,  and  on 
the  shortage  of  oxygen  or  presence  of  inert  gases  as  carbon  dioxide  in  the 
mine  air.  When  the  blood  is  saturated  with  carbon  monoxide  to  the  extent 
of  50%,  a  man  is  too  weak  to  walk.  As  Haldane  points  out,  the  blood  of  a 
man  will  take  up  about  2  pt.  of  the  monoxide,  and  of  the  gas  inhaled  about 
60%  is  absorbed  by  the  hemoglobin.  A  man  at  rest  inhales  about  10  or  12  pt. 
of  air  a  min.,  and  should  this  air  contain  .10%  CO,  the  absorption  of  the  gas 
would  be  at  the  rate  of  .007  pt.  a  min.,  requiring  2.25  hr.  to  produce  one-half 
saturation  and  total  disability.  A  man  walking  breathes  about  three  times  as 
much  air  as  when  at  rest  and  would  be  disabled  in  1  hr.  or  less,  and  when 
running  in  from  20  to  30  min.  As  50%  saturation  is  the  maximum  with 
.10%  CO,  death  does  not  follow.  Haldane's  experiments  showed  that  with 
.20%  CO  in  the  air,  it  required  70  min.  for  the  blood  of  a  man  at  rest  to  become 
50%  saturated,  and  \  hr.  when  walking.  The  same  degree  of  saturation 
would  probably  be  reached  in  10  to  15  min.  when  running.  Since  the  maximum 
saturation  for  .02^,  CO  is  a  trifle  over  70%,  death  is  practically  certain  if  the 
patient  is  unconscious  when  found  and  degeneration  of  the  brain  cells  has 
set  in.  If  the  air  contains  .30%  CO,  50%  saturation  of  the  blood  and  uncon- 
sciousness will  take  place  in  £  hr.  or  less  when  at  rest,  in  10  to  15  min.  when 
walking  and  proportionately  less  when  running.  If  at  rest,  with  this  per- 
centage of  carbon  monoxide,  the  blood  will  become  fully  saturated  (.30%  CO 
=  80%  saturation)  in  a  little  more  than  $  hr.,  and  death  is  certain.  According 
to  Wabner,  when  there  is  1%  CO  in  the  air,  saturation  will  require  but  5  to 
6  min.,  even  supposing  the  ill-ventilated  place  does  not  already  contain  other 


VENTILATION  OF  MINES  855 

injurious  gases  or  impoverished  air,  which  will  generally  be  the  case  in  the  pit. 
Death,  of  course,  takes  place. 

Haldane  gives  the  following  as  effects  of  percentages  of  carbon  monoxide 
less  than  .10%:  Even  .01%  may  prove  injurious  where  the  oxygen  is  below 
21%  and  where  considerable  quantities  of  carbon  dioxide  are  present,  as  in 
afterdamp;  .02%  will  produce  a  saturation  of  the  blood  to  the  extent  of  20% 
resulting  in  a  slight  tendency  to  dizziness  and  shortness  of  breath  on  exertion; 
with  .05%  giddiness  on  exertion  will  result  after  £  hr.  exposure;  and  with  .07% 
there  will  be  vertigo  on  the  slightest  exertion . 

When  the  air  is  deficient  in  oxygen  or  contains  notable  amounts  of  carbon 
dioxide,  breathing  is  deeper  and  more  frequent  and  a  greater  amount  of  carbon 
monoxide  is  inhaled  and  absorbed  in  a  given  time  than  would  otherwise  be 
the  case.  Such  atmospheres  are  common  after  dust  explosions,  and  members 
of  a  rescue  party  entering  them  are  either  more  quickly  overcome  by  the  same 
percentage  of  gas  or  are  finally  overcome  by  a  less  percentage  than  if  the  air, 
except  for  the  presence  of  the  monoxide,  was  otherwise  normal.  It  must  not 
be  overlooked,  however,  that  members  of  a  rescue  party  have  probably  been 
exposed  for  some  time  to  atmospheres  containing  appreciable  amounts  of 
this  gas,  so  that  when  they  enter  a  place  where  the  content  of  carbon  monoxide 
is  fairly  high,  their  blood  is  already  partly  saturated,  and  they  naturally 
succumb  more  quickly  than  if  entering  from  fresh  air. 

The  percentage  of  this  gas  that  may  be  safely  allowed  as  a  permanent 
constituent  of  mine  air  is  very  low  indeed,  certainly  under  .01%,  as  such  air 
is  commonly  deficient  in  oxygen  and  contains  carbon  dioxide  and  methane 
as  well.  The  maximum  percentage  that  may  be  breathed  for  considerable 
time  without  producing  permanent  injurious  after-effects  is  commonly  placed 
at  .05%.  This  percentage,  although  causing  giddiness  when  working,  results 
in  a  saturation  of  the  blood  not  to  exceed  one-third,  from  which  recovery,  in 
fresh  air,  is  rapid. 

In  severe  cases  of  carbon-monoxide  poisoning,  death  usually  takes  place  in 
a  few  hours,  although  life  may  be  prolonged  for  a  few  days  or  weeks;  but 
recovery  is  not  unknown.  Such  recovery  is  very  slow  and  the  patient  may 
develop  chronic  pains  in  the  head  and  legs,  and  impaired  eyesight  or  dis- 
ordered brain;  and  there  appears  to  exist  a  tendency  to  pneumonia,  etc.  Even 
in  mild  cases,  where  complete  recovery  is  made,  the  process  is  extremely 
slow,  requiring  from  several  hours  to  weeks,  depending  on  the  length  of  expo- 
sure; the  milder  attacks  are  accompanied  by  violent  headaches,  nausea,  and 
vomiting,  and  the  more  severe  ones  by  spasms,  cramps,  and  the  like,  in  addition. 

The  Committee  of  the  American  Medical  Association,  previously  quoted, 
says  further,  "As  hemoglobin  gives  up  carbon  monoxide  very  rapidly  in  atmos- 
pheres free  from  the  gas,  if  the  patient  is  still  breathing  when  discovered,  the 
mere  inhalation  of  fresh  air  without  the  use  of  artificial  respiration  and  the 
administration  of  oxygen  will  restore  him  unless  the  degeneration  of  the  brain 
tissues  has  set  in,  in  which  case  no  amount  of  oxygen  will  prevent  either  death 
or  serious  mental  derangement  should  the  patient  survive.  Owing  to  the  fact 
that  it  is  impossible  to  tell  at  the  time  the  patient  is  discovered  or  for  an  hour 
or  two  afterwards  whether  the  critical  point  (degeneration  of  the  brain  cells) 
has  been  reached,  it  is  of  the  greatest  importance  to  begin  resuscitation  at 
once  and  preferably  by  administering  oxygen,  which  removes  the  monoxide 
five  times  as  fast  as  air  alone."  The  Committee  does  not  recommend  the 
general  use  of  appliances  for  mechanically  stimulating  breathing,  the  suction 
required  to  produce  exhalation  being  very  injurious  to  the  delicate  tissues  of 
the  lungs  and  say  that  the  apparatus  should  be  used  not  longer  than  5  or 
6  min.  at  a  time,  and  should  be  alternated  with  the  manual  method  alone,  or 
in  gas  cases,  combined  with  oxygen  inhalation. 

Explqsibility  of  Carbon  Monoxide. — Carbon  monoxide  will  not  support 
combustion  but  instantly  extinguishes  a  flame  placed  in  it.  It  is,  however, 
explosive  over  a  very  wide  range.  Authorities  differ  as  to  the  explosive 
limits,  but  they  are  generally  taken  to  lie  between  13  and  15.5%  (lower  limit) 
and  75%  (upper  limit)  in  air.  For  complete  combustion-  by  means  of  an 
electric  spark,  Blair  fixes  the  limits  at  16.5  and  75%,  and  Clowes  gives  13  and 
75%  when  the  gas  is  ignited  in  the  ordinary  way  and  from  below  (see  Relative 
Explosibility  of  Methane  and  Other  Gases).  The  equation  for  the  burning 
of  carbon  monoxide  in  air  is  2CO  +  (O2+3.7822V2)  =  2C02+3.7822W,  from  this, 
the  maximum  explosive  point  is  reached  when  there  is  29.45%  of  the  gas 
in  air. 

A  certain  amount  of  moisture  is  necessary  for  the  explosion  of  carbon 
monoxide;  it  is  claimed  as  much  as  5%  for  the  maximum  explosive  effects. 


856  VENTILATION  OF  MINES 

The  reaction  is  a  double  one.  First,  Cp+HzO  =  COz+Hr,  the  hydrogen 
immediately  combining  with  the  oxygen  in  the  air  by  the  action,  2Hz  +  Oz 
=  2HyO.  If  it  is  true  that  carbon  monoxide  enters  into  a  dust  explosion,  which 
appears  doubtful,  in  an  absolutely  dry  mine  an  explosion  of  this  gas  would 
not  be  possible. 

The  explosive  limits  of  whitedamp  mixtures  (air  and  carbon  monoxide) 
may  be  lowered  by  the  addition  of  a  gas  of  a  lower  explosive  limit,  as  methane 
or  hydrogen,  and  this  is  true  even  when  the  percentage  of  the  added  gas  is 
below  its  own  explosive  limit.  Similarly,  the  addition  of  carbon  monoxide 
to  firedamp  mixtures  (air  and  methane)  will  raise  the  higher  explosive  limit  of 
the  last-named  gas. 

Explosions  of  carbon  monoxide  are  very  rare  if  they  occur  at  all,  not  only 
because  the  lower  explosive  limit  is  so  high  but  also  because  such  large  amounts 
of  the  gas  are  usually  accompanied  by  still  larger  amounts  of  nitrogen  or 
carbon  dioxide,  which  so  reduce  the  percentage  of  oxygen  that  there  is  not 
enough  of  it  to  combine  with  the  monoxide  in  explosive  proportions.  Inves- 
tigations appear  to  sustain  the  view  of  Mr.  Haas  that  the  burnings  and  explo- 
sions that  sometimes  follow  the  placing  of  a  lamp  in  the  crevices  of  a  standing 
shot  are  due  not  so  much  to  carbon  monoxide  given  off  by  the  powder  as  to 
hydrocarbons  distilled  from  the  coal  by  the  heat  of  the  explosion. 

Detection  of  Carbon  Monoxide. — Flame  Test. — In  the  laboratory,  for  equal 
percentages,  carbon  monoxide  gives  a  flame  cap  identical  with  that  of  methane. 
The  .30%  which  is  exceedingly  dangerous  is  without  effect  on  the  flame  of 
the  ordinary  safety  lamp  and  the  2%,  which  is  the  limit  of  detection  by  the 
skilled  observer  (very  many  firebosses  cannot  detect  less  than  3%),  will  pro- 
duce unconsciousness  in  30  sec.  or  less  in  one  who  is  running,  as  a  fireboss  on 
his  rounds.  Further,  in  examining  old  workings  where  gob  fires  exist  or  in 
opening  a  mine  that  has  been  sealed  to  extinguish  a  fire,  the  observer  will  have 
been  breathing  for  some  time  air  containing  gradually  increasing  amounts  of 
the  monoxide,  so  that  his  blood  will  be  partly  saturated  and  himself  be  more 
susceptible  to  its  effects  some  time  before  he  reaches  a  point  where  the  gas  will 
show  in  the  safety  lamp.  It  is  unquestionably  true  that  no  observer,  unless 
wearing  some  one  of  the  types  of  rescue  apparatus,  ever  detected  carbon 
monoxide  in  the  mine  with  a  standard  safety  lamp  and  lived  to  describe  his 
observations.  In  the  Clowes  hydrogen  lamp,  .25%  of  CO  gives  a  plainly  visible 
cap  $  in.  in  height,  but  as  Mr.  Clowes  says  it  is  impossible  to  distinguish 
between  the  cap  made  by  the  poisonous  monoxide  and  the  non-poisonous 
methane;  so  that  the  hydrogen  flame  test  is  not  distinctive. 

Potain  and  Drouin  Method. — The  apparatus  employed  by  Potain  and 
Drouain  consisted  of  a  long  tapered  tube  connected  with  a  supply  of  mine  air 
to  be  tested  and  dipping  to  the  bottom  of  an  outer  tube  containing  the  reagent 
composed  of  10  cu.  cm.  of  a  .01%  solution  of  palladium  chloride,  and  two 
drops  of  hydrochloric  acid.  When  the  mine  air  is  drawn  through  the  outer 
tube  by  an  aspirator,  the  reagent  (which  is  about  8  in.  in  depth)  is  discolored 
by  the  palladium  precipitated  by  the  carbon  monoxide  if  present.  The  per- 
centage of  carbon  monoxide  is  determined  by  comparing  the  volume  9f  mine 

air  taken  with  that 


REACTION  OF  CO  ON  PtCU 


Percentage 
of  CO 
in  Air 

Reaction  Visible  After 

Time  in 
which  Paper 
Turns  Black 
Minutes 

Minutes 

Seconds 

.010 

11 

60 

.025 

5 

32 

.050 

3 

16 

.075 

2 

12 

.100 

1 

9 

.250 

44 

6 

.500 

26 

4 

.750 

20 

3 

1.000 

16 

2 

2.000 

15 

2 

of  a  standard  mix- 
ture of  air  and  car- 
bon monoxide  re- 
quired to  produce  an 
equal  discoloration 
in  another  similar 
bulk  of  the  reagent. 
The  method  will  de- 
tect the  presence  of 
.01%  of  CO. 

Simonis  Method. 
— In  the  Simonis 
method,  mine  air 
previously  freed,  if 
necessary,  from  the 
sulphides  of  ammo- 
nia or  hydrogen  by 
passing  through  a 
solution  of  copper 
sulphate  or  sul- 
phuric acid,  is  drawn 


VENTILATION  OF  MINES 


857 


through  a  tube  in  which  is  placed  a  strip  of  paper  saturated  with  the  chloride 
of  either  platinum  or  palladium.  Carbon  monoxide,  if  present,  will  decompose 
the  chloride  and  turn  the  paper  first  brown  and  then  black  in  a  length  of 
time  proportional  to  the  amount  of  gas  present:  .01%  of  CO  being  detectible. 
The  table  gives  the  lengths  of  time  required  by  various  percentages  of  carbon 
monoxide  in  air  to  discolor  and  blacken  the  test  paper  saturated  with  platinum 
chloride  which  is  rather  more  sensitive  than  palladium  chloride.  J.  R.  Camp- 
bell has  modified  the  process  by  placing  a  wet  sponge  in  the  bottom  of  the 
receptacle,  thus  permitting  the  use  of  dry  instead  of  moist  test  papers.  Any 
number  of  papers  may  be  prepared  in  advance  for,  in  use,  they  will  absorb 
enough  moisture  from  the  sponge  to  permit  of  the  reaction.  When  used  in 
the  mine,  air  is  forced  through  the  apparatus  by  a  pump  or  India-rubber 
inflator,  but  fairly  good  results  may  be  obtained  by  merely  exposing  the 
instrument  to  the  mine  air  for  any  desired  length  of  time.  As  little  as  .01% 
of  CO  may  be  thus  detected, 

Use  of  Canaries  or  Mice. — In  recovery  work  after  a  mine  explosion,  the 
existence  of  dangerous  amounts  of  carbon  monoxide  in  the  afterdamp  is  com- 
monly determined  by  the  effect  of  the  gas  upon  mice  or  canaries  carried  in  a 
cage  by  some  one  of  the  exploring  party.  When  advancing  with  the  air,  the 
last  man  should  carry  the  animals,  and  when  moving  against  the  air,  the  first 
man,  so  that  they  may  be  exposed  to  the  air  and  its  effects  on  them  noted 
before  the  men  enter  it.  Canaries  are  preferred  to  mice  as  they  are  more 
sensitive  to  the  action  of  the  gas,  and  their  signs  of  distress  while  perched  are 
more  easily  noted  than  those  of  mice  who  are  apt  to  crouch  in  a  corner  of  the 
cage.  If  a  mouse  is  used,  it  must  be  made  to  move  from  time  to  time  by 
tilting  the  cage,  poking  it  with  a  stick,  etc.,  so  that,  while  moving,  its  symptoms 
may  be  noticed.  The  rate  of  breathing,  number  of  heart  beats,  etc.,  in  a  mouse 
or  canary,  are  so  much  more  rapid  (pulse  about  700  to  1,000  beats  a  min.)  than 
in  a  man,  that  the  effects  of  the  gas  on  them  is  much  more  rapid. 

The  accompanying  table  from  the  Bureau  of  Mines  gives  the  effect  on  mice 
and  canaries  of  varying  percentages  of  carbon  monoxide,  and  should  be  com- 
pared with  the  effect  of  similar  amounts  on  men,  as  previously  given.  Thus, 
when  exposed  to  an  atmosphere  containing  .20%  CO  it  will  require  ?  hr.  for  the 
blood  of  a  man  walking  to  become  50%  saturated,  at  which  stage  the  legs  will 
give  way;  but  a  canary  similarly  exposed  showed  signs  of  distress  in  1.5  min., 
and  fell  from  his  perch  in  5  min.  In  using  canaries  as  guides  to  the  presence 
of  the  monoxide,  certain  facts  must  be  remembered.  In  the  excitement  of 
rescue  work,  the  unskilled  observer  may  entirely  fail  to  note  in  the  canary  the 
preliminary  symptoms  of  poisoning  that  would  be  clear  to  the  trained  man; 

EFFECT  OF  CO  ON  MICE  AND  CANARIES 


Mice 

Canaries 

Per 

Per 

Effect 

Cent. 

Effect 

Cent. 

CO 

CO 

.16 

Very  slight  distress  at  end  of 

.09 

Very  slight  distress  at  end  of 

hour. 

Ihr. 

.20 

Distress    in    8    min.;    partial 

.12 

Weaker  at  end  of   1  hr. 

than 

.31 

collapse  in  15  min. 
Distress  in  4  min.;  collapse  in 

.15 

after  exposure  to  .9% 
Distress  in   3   min.;  fell 

from 

7£  min.;  lost  muscular  pow- 

perch in  18  min. 

er  in  35  min. 

.46 

Distress  in  2  min.;  collapse  in 

.20 

Distress  in   1?  min.;  fell 

from 

4  min. 

perch  in  5  min. 

.57 

Distress  in  1  min.;  collapse  in 

.29 

Fell  from  perch  in  2\  min 

2  min.;  muscular  power  lost 
in  7  min.;  death  in  16  min. 

.77 

Distress  in  1  min.;  muscular 

power  lost  in  6|  min.;  death 

in  12  J  min. 

858 


VENTILATION  OF  MINES 


and  the  ability  of  even  trained  men  to  detect  these  early  symptoms  varies  con- 
siderably. There  is  also  a  marked  difference  in  the  resisting  power  to  carbon- 
monoxide  poisoning  of  canaries,  some  birds  showing  no  more  distress  at  the  end 
of  6  min.  than  others  did  in  2  min.  For  this  reason,  either  a  bird  should  be 
selected  which  previous  tests  has  shown  to  be  sensitive  to  the  gas,  or  several 
birds  should  be  taken  along.  It  would  also  appear  that  small  percentages  of 
carbon  monoxide  (say  .10%)  which  in  the  course  of  1  hr.  or  so  seriously  affect 
men,  are  often  without  any  influence  at  all  on  the  canary.  For  these  reasons, 
while  actual  distress  or  disablement  on  the  part  of  the  bird  are  unfailing  signs 
of  the  presence  of  the  gas,  these  signs  should  net  be  waited  for,  and  the  display 
by  any  member  of  such  symptoms  of  poisoning  as  dizziness,  shortness  of 
breath,  weakness  of  the  legs,  impairment  of  sight,  etc.,  should  lead  to  the 
immediate  withdrawal  of  the  entire  party. 

Blood  Tests. — The  so-called  blood  test,  while  giving  excellent  results  in 
determining  whether  carbon  monoxide  is  or  is  not  present  in  the  air  or  blood,  is 
not  definite  when  the  percentage  of  gas  is  required.  For  this  determination,  a 
chemical  analysis  should  be  made  in  the  regular  way.  To  make  the  blood 
test,  one  to  three  drops  of  blood  secured  from  a  healthy  animal  or  by  pricking 
the  finger  are  shaken  up  with  enough  water  to  make  about  a  1%  solution 
(1  part  of  blood  in  100  of  water).  This  results  in  a  buff-colored  solution,  which 
is  equally  divided  between  two  test  tubes,  which  are  corked.  One  test  tube  is 
set  aside  for  comparison,  and  through  the  cork  of  the  other  are  inserted  two 
glass  tubes,  one  of  which  is  long  enough  to  reach  nearly  to  the  bottom  of  the 
test  tube,  the  end  of  the  other  being  above  the  level  of  the  solution.  A  glass 
bottle  filled  with  the  suspected  air  is  connected  with  the  long  tube  and  suction 
applied  at  the  end  of  the  short  one.  This  will  exhaust  the  air  from  the  bottle 
and  cause  it  to  bubble  up  through  the  test  solution,  which  will  be  colored  a 
distinctive  pink  shade  if  any  carbon  monoxide  is  present.  The  colors  will  be 
more  distinctly  visible  if  the  two  tubes  are  compared  against  a  brightly  lighted 
white  background.  The  same  result  may  be  obtained  by  shaking  one  of  the 
blood  solutions  for  10  min.  or  so  in  a  bottle  containing  the  suspected  air.  The 
presence  of  the  gas  in  the  blood  may  be  told  by  preparing  solutions  of  equal 
strength  (same  quantity  of  blood  and  water)  of  the  blood  of  the  supposedly 
poisoned  person  and  that  of  a  healthy  person  or  animal;  the  latter  for  com- 
parison, as  before. 

To  obtain  an  approximate  idea  of  the  percentage  of  carbon  monoxide  in 
the  air,  Haldane  recommends  the  following:  Prepare  a  solution  of  normal 
blood  and  fill  two  test  tubes  with  it  as  already  described.  Set  one  of  the 
tubes  aside,  and  thoroughly  saturate  the  other  with  illuminating  gas,  which  con- 
tains large  quantities  of  the  monoxide,  by  bubbling  the  gas  through  the  solution 
and  shaking  them  together  for  about  10  min.  This  will  give  a  buff-colored 
solution  containing  no  carbon  monoxide  and  a  pink  solution  saturated  with  it: 
and  these  are  the  two  ends  of  the  scale.  A  mouse  is  exposed  in  the  suspected 
air  in  the  mine  for  from  10  to  15  min.  and  then  killed  in  the  place,  as  its  rembval 
to  fresh  air,  while  alive,  would  greatly  reduce  the  amount  of  the  gas  in  its 
blood  and  thus  invalidate  the  test.  As  much  of  the  mouse's  blood  is  taken  as 
was  required  to  make  the  test  solutions,  and  it  is  diluted  to  the  same  degree. 
By  comparing,  against  a  white  background,  the  color  of  the  mouse-blood 
solution  with  that  of  the  two  test  solutions,  it  can  be  approximately  determined 
if  its  blood  is  jfo,  j&,  etc.,  saturated.  The  amount  of  carbon  monoxide  in  the 
air  can  then  be  determined  from  the  following  table. 

PER  CENT.  OF  CARBON  MONOXIDE  IN  AIR  CORRESPONDING  TO 

VARIOUS  PERCENTAGES  OF  SATURATION  OF  BLOOD 

SOLUTION 


Blood 

Carbon  Monoxide 

Blood 

Carbon  Monoxide 

Saturation 

in  Air 

Saturation 

in  Air 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

10 

.012 

60 

.12 

20 

.025 

70 

.19 

30 

.040 

80 

.30 

40 

.060 

90 

.70 

50 

.080 

VENTILATION  OF  MINES  859 

As  it  is  only  necessary  that  the  test  solution  should  have  a  clearly  perceptible 
color,  one  drop  of  blood  may  be  sufficient.  The  test  may  be  used  to  estimate 
the  amount  of  the  gas  in  the  blood  of  a  person  suffering  from  gas  poisoning,  by 
taking  as  much  blood  from  the  patient  as  was  used  in  making  the  test  solution 
and  diluting  it  to  the  same  degree.  As  noted,  if  the  patient  has  been,  uncon- 
scious for  £  hr.  or  more  and  his  blood  is  found  to  be  over  60%  saturated,  it  is 
more  than  probable  that  degeneration  of  the  brain  cells  has  set  in  and  that  no 
amount  of  oxygen  or  other  respiratory  treatment  would  have  effected  his 
recovery. 

By  measurihg  the  quantity  of  a  normal  solution  of  carmine  that  is  required 
to  color  the  mouse-blood  solution  to  the  same  intensity  as  the  solution  satu- 
rated by  means  of  _  illuminating  gas,  it  is  possible  to  make  a  very  accurate 
quantitative  determination  of  the  amount  of  carbon  monoxide  present.  The 
method,  while  delicate,  is  not  used  to  any  great  extent,  ordinary  methods  by 
absorption  being  preferred. 

Spectroscopic  Methods. — A  portable  pocket  spectroscope  for  the  detection 
of  carbon  monoxide  has  been  devised  by  a  German  firm.  A  sample  of  the 
suspected  air  is  obtained  in  the  ordinary  way  and  to  it  are  added  a  few  drops  of 
a  very  weak  solution  of  blood  which  is  supplied  with  the  instrument.  After 
being  well  shaken  the  blood  solution  is  examined  with  the  spectroscope. 
Whether  CO  is  present  or  not,  two  dark  bands  will  be  seen  in  the  yellow  and 
green  parts  of  the  spectrum  between  the  Frauenhofer  lines  D  and  E,  the 
position  of  which  is  specially  marked  on  the  scale  of  the  spectroscope.  If  no 
carbon  monoxide  is  present  these  bands  will  disappear  on  adding  to  the  original 
solution  a  drop  or  two  of  colorless  ammonium  sulphide  (diluted),  and  in  their 
place  and  between  them  will  appear  one  broad  band  which  shades  off  at  the 
edges.  If  carbon  monoxide  is  present  the  two_  bands  are  but  very  slightly 
altered  in  appearance  by  the  addition  of  ammonium  sulphide  and  they  are  not 
replaced  by  a  single  band.  In  the  one  case  the  oxyhemoglobin  is  decomposed 
by  ammonium  sulphide  and  in  the  other  the  carboxyhemoglobin  is  not  affected 
by  that  reagent. 

METHANE 

Properties  and  Sources. — Methane,  otherwise  known  as  light  carburetted 
hydrogen,  marsh  gas,  firedamp,  or  simply  as  gas,  has  a  formula  CHt,  is  odorless, 
colorless,  tasteless,  and  non-poisonous,  and  will  not  support  life  or  combustion. 
From  the  mining  standpoint,  it  is  the  most  important  member  of  the  paraffin 
series  of  gases  whose  general  formula  is  CnHzn  +2  in  which  n  is  the  number  of 
atoms  of  carbon  in  a  molecule  of  any  one  of  these  gases.  Methane  burns  with 
a  blue  flame  similar  to  that  of  carbon  monoxide,  and  like  that  gas  is  explosive 
when  mixed  with  air  in  the  proper  proportions. 

Methane  is  given  off  by  the  pores  of  the  coal  in  practically  all  mines, 
although  often  in  amounts  that  can  only  be  detected  by  careful  analysis.  Gas 
so  contained  in  the  coal  is  commonly,  but  incorrectly,  spoken  of  as  occluded,  a 
term  strictly  referring  to  gas  absorbed  and  possibly  condensed  in  the  pores  of 
a  metal,  as  hydrogen  in  palladium.  The  amount  of  gas  given  off  by  the  seam 
is  very  variable,  and  depends,  in  a  great  measure,  on  the  opportunity  it  has 
had  to  escape  naturally  from  the  coal.  Thus,  more  gas  may  be  expected  in  the 
inner  workings  than  near  the  outcrop,  in  a  shaft  than  in  a  drift  mine,  and  at 
great  than  at  shallow  depths.  In  the  deep  European  mines,  the  Prussian  Fire- 
damp Commission  found  that  from  357  to  2,400  cu.  ft.  of  methane  are  given 
off  per  ton  of  coal  mined;  and,  in  France,  Chesneau  reports  1,377  cu.  ft.  of  gas 
per  ton  of  coal  mined  at  the  Herin  mine,  Anzin,  and  882  cu.  ft.  at  Ronchamp. 
Similar  figures  for  American  mines  are  not  available,  but  may  be  readily  cal- 
culated when  the  output  of  the  mine  and  the  volume  of  the  air  current  and  its 
content  of  methane  are  known.  Thus,  in  a  mine  producing  1,000  tons  a  day, 
when  the  return  has  a  volume  of  100,000  cu.  ft.  a  min.,  which  contains  .30%  of 
CH4,  the  volume  of  gas  per  ton  of  coal  mined  is  (60 X 24X100,000 X. 003)  -r- 
l,000  =  432cu.  ft. 

Many  coals  continue  to  give  off  gas  for  months  after  being  mined  and 
explosions  of  methane  have  occurred  on  shipboard  by  taking  a  lighted  torch 
into  the  bunkers  where  the  boiler  coal  is  stored.  Samples  of  coal  bottled  in 
a  vacuum  continue  to  give  off  gas  for  from  5  to  1£  yr.,  the  gas  escaping  more 
rapidly  from  finely  crushed  than  from  lump  coal.  The  volume  of  gas  given 
off  by  the  coal  is  much  greater  during  the  first  few  days  after  mining  than 
later.  From  American  coals,  Chamberlain  obtained  a  volume  of  gas  equal 
to  .9  to  2.3  times  that  of  the  sample  before  crushing.  Lump  coal  yielded 
but  .5  to  .9  their  volumes  of  gas  under  similar  conditions.  Analyses  of  the 
gases  given  off  by  coal  will  be  found  under  Firedamp. 


860 


VENTILATION  OF  MINES 


These  so-called  occluded  gases  exist  under  a  pressure  that  is  more  or  less 
proportional  to  the  thickness  of  the  cover  upon  the  coal  and,  according  to 
the  European  investigations  recorded  in  the  accompanying  table,  is  frequently 
as  great  as  10  to  16  atmospheres  (150  to  240  Ib.  per  sq.  in.).  Pressures  over 
40  atmospheres,  or  about  600  Ib.  per  sq.  in.,  have  been  noted.  The  figures 
in  the  second  column  of  the  table  are  the  depths  of  the  boreholes,  or  the  dis- 
tance back  from  the  face  and  in  the  solid  coal  where  the  pressure  was  measured. 

PRESSURE  OF  OCCLUDED  GAS 


Name  of  Mine 

Depth  of  Hole 
Feet 

Pressure 
Pounds 

Elmore  mine,  main  bed  

8.53 

4.36 

Hetton  mine,  Hutton  bed  
Eppleton  mine   Hutton  bed 

8.98 
46.90 

6.96 
36.14 

Balden  mine,  Bensham  bed  
Harris  Navigation  mine 

31.85 
32.80 

71.41 
22.04 

Methyr  Vale  mine  

49.20 

39.67 

Celynen  mine                               .    .      .  .        .    . 

54.48 

68.32 

Harton  mine  (1,214  ft.  deep)  

16.24 

196.30 

Harton  mine                                             .        .    . 

27.55 

230.44 

Harton  mine  

37.13 

294.45 

Methane  is  given  off  by  blowers,  otherwise  known  as  feeders  or  bleeders, 
which  are  streams  or  jets  of  gas  issuing  from  cracks  and  crevices  in  the  coal 
face  or  in  the  floor  or  roof.  These  blowers  seem  to  follow  some  well-defined 
line  of  fracture  in  the  measures  or  some  fissure  or  clay  vein  and,  as  they  fre- 
quently give  off  gas  under  high  pressure  for  many  months,  they  are  probably 
connected  with  some  underlying  reservoir  or  porous  stratum  filled  with  gas. 
In  many  cases,  because  of  the  high  pressure,  the  gas  in  escaping  makes  a 
singing  noise,  which  resembles  the  pattering  of  light  rain  upon  leaves. 

Methane  is  frequently  found  along  the  line  of  clay  veins  and  similar  irregu- 
larities, probably  following  the  line  of  separation  between  the  material  filling 
the  vein  and  the  rocks  through  which  it  cuts.  In  many  cases,  the  gas  is  found 
under  high  pressure  just  after  the  clay  vein  is  pierced,  whereas  none,  or  but 
normal  quantities  are  found  between  it  and  the  crop  line.  Gas  may  be  found 
within  an  area  bounded  by  clay  veins  or  by  the  dykes  of  igneous  rock  common 
in  some  of  the  western  coal  fields.  In  such  cases,  if  the  mine  has  not  hitherto 
generated  gas  and,  consequently,  the  necessary  precautions  to  cope  with  it 
have  not  been  made,  the  sudden  piercing  of  a  clay  vein  or  dyke  and  the  unex- 
pected release  of  large  volumes  of  gas  has  led  to  serious  accidents. 

Sudden  outbursts  of  gas  in  large  quantities  and  under  great  pressure  some- 
times take  place.  These  may  be  caused  by  the  gas  finding  its  way  through 
vertical  crevices  or  cleats  to  cavities  of  considerable  horizontal  extent,  so  that 
the  gas  pressure  is  distributed  over  a  wide  area.  As  the  mine  openings  approach 
such  a  locality,  the  pressure  manifests  itself  by  bursting  the  coal  from  its  posi- 
tion in  the  face  and  throwing  it  into  the  entries,  in  some  cases  completely 
blocking  them.  These  outbursts  are  frequently  preceded  and  accompanied 
by  thunderings  and  poundings,  the  former  for  several  days  before  the  gas 
actually  escapes. 

Whether  the  outbursts  of  gas  so  frequently  accompanying  bumps  (bounces) 
are  a  cause  or  an  effect  of  the  throwing  of  large  masses  of  coal  into  the- workings 
as  a  result  of  a  sudden  rending  of  the  pillars,  is  not  satisfactorily  decided.  The 
weight  of  evidence,  however,  indicates  that  bumps  are  due  to  the  sudden  release 
of  pressure  in  the  overlying  rocks,  and  that  the  shattering  of  the  coal  and 
roof,  and  sometimes  the  floor,  sets  free  the  contained  gas  and  opens  any  pockets 
or  crevices  in  which  it  may  be  stored.  If  pillars  are  left  too  small  or  their 
drawing  has  been  carried  too  far,  the  tendency  to  slowly  and  regularly  settle 
(and  possibly  to  bring  on  a  squeeze)  may  be  resisted  by  a  strong  roof  until 
such  a  time  as  the  limit  of  its  strength  is  reached  when  it  will  suddenly  give 
and  as  suddenly  crush  the  coal  over  an  area  of  a  few  hundred  square  feet  or 
several  acres.  When  the  resistance  becomes  adjusted  to  the  pressure,  the 
crushing  will  cease;  therefore,  unless  the  place  is  entirely  closed,  bumps  may 
be  repeated  in  the  same  or  adjacent  areas  as  the  roof  pressure  accumulates. 
The  outbursts  mentioned  in  the  first  part  of  the  paragraph  produce  results 
similar  to  bumps,  but  on  a  smaller  scale. 


VENTILATION  OF  MINES  861 

In  Belgium,  large  volumes  of  gas  under  very  high  pressure  and  accom- 
panied by  a  peculiar  porous  coal  dust  are  found  in  large  chambers  or  pockets. 
When  a  reservoir  of  this  kind  is  accidentally  tapped  by  a  heading,  an  outrush 
of  large  volumes  of  gas  and  coal  dust  occurs  with  great  suddenness,  filing 
the  workings  immediately,  and  causing  enormous  damage.  Thus,  according 
to  Wabner,  at  the  Agrappe  colliery  in  Belgium,  more  than  500,000  cu.  yd.  of 
gas  and  a  great  mass  of  coal  dust  broke  out  into  a  heading  at  a  depth  of  2,000  ft., 
blocking  up  all  the  workings  and  the  shafts,  and  taking  fire  at  the  pit  mouth 
destroyed  the  head-frame  and  surface  plant.  After  the  first  rush  of  gas  had 
subsided,  violent  explosions  occurred,  completely  closing  the  shafts  and  killing 
or  injuring  112  men.  Similar  explosions  have  occurred  in  other  mines  in 
the  same  country.  The  Belgian  measures  have  been  subjected  to  very  heavy 
horizontal  pressure,  which  has  resulted  in  the  formations  slipping  over  and  past 
one  another,  the  irregular  line  of  fracture  producing  pockets  in  which  the  gas 
accumulated,  and  in  which  pockets  were  large  quantities  of  dust  resulting  from 
the  grinding  of  the  coal  by  the  rock  movement. 

Methane  is  often  released  in  unusual  quantities  from  the  rocks  during 
a  squeeze  or  a  creep,  by  a  heavy  fall  of  roof  or  a  general  breaking  or  settling 
of  the  overburden  accompanying  and  following  pillar  drawing. 

In  some  mining  districts,  the  leakage  under  great  pressure  from  improperly 
cased  oil  and  gas  wells  drilled  through  the  workings,  is  a  source  of  methane 
as  it  constitutes  50%  or  more  of  natural  gas. 

Black  powder  does  not  usually  produce  any  methane  but  many  safety 
(permissible)  powders  and  high  explosives  yield  from  a  trace  to  as  much  as 
5%  of  it  when  exploded  in  the  laboratory.  Analyses  of  the  combustion  pro- 
ducts of  explosives  are  given  on  page  670.  When  used  in  the  mine  in  contact 
with  coal,  and  particularly  when  slack  is  used  for  tamping,  all  powders  yield 
important  amounts  of  methane  (5  to  10%  or  more  of  the  gases  of  combustion), 
which  may  be  in  part  distilled  from  the  coal  by  the  heat  of  the  explosion,  and 
in  part  result  from  chemical  combination  between  the  elements  in  the  powder 
and  those  in  the  coal. 

Methane  is  found  in  the  gases  from  mine  fires  and  in  the  afterdamp  of 
explosions,  where  it  is  distilled  from  the  coal  by  heat. 

Analyses  of  combinations  of  methane  and  various  gases  will  be  found 
under  Firedamp. 

Formation  of  Methane. — Coal  seams  are  formed  by  the  slow  alteration  of 
vegetable  matter  in  the  presence  of  moisture  and  in  the  absence  of  air;  heat 
generated  by  pressure,  commonly  assisting  in  the  process.  The  alteration  has 
resulted  in  the  formation  of  various  hydrocarbons,  the  chief  of  which  is  methane. 
While,  in  the  course  of  ages,  most  of  the  gas  has  escaped  through  the  over- 
lying rocks,  large  quantities  still  remain.  Methane  may  be  formed  wherever 
moist  vegetable  matter  is  protected  from  the  air,  as  in  swamps  and  peat  bogs  and 
the  bottom  of  stagnant  ponds,  where  it  may  be  seen  bubbling  up  through  the 
water;  whence  the  name  marsh  gas.  It  is  suggested  that  methane  is  yet  being 
formed  in  some  seams  where  the  processes  of  alteration  have  not  been  com- 
pleted; but  this  has  not  been  proved. 

All  methane  does  not  originate  in  coal  seams.  It  occurs  in  mines  of  salt 
and  strontia,  in  beds  of  clay  and  sandstone,  invariably  accompanies  the  pro- 
duction of  petroleum,  and  always  forms  the  bulk  of  natural  gas,  even  when 
these  substances  are  found  many  hundreds  of  miles  from  any  coal  field.  In 
mining  regions,  natural  gas  is  often  met  in  sands  (more  or  less  porous  sand- 
stones) several  hundred  to  several  thousand  feet  below  the  lowest  coal  bed. 
These  facts  have  led  Mr.  Haas  to  hold,  for  northern  West  Virginia  at  least,  that 
methane  does  not  originate  in  the  coal,  but  in  the  natural-gas  sands  many 
feet  below.  In  these  deep  sands,  the  natural  gas  is  under  a  pressure  pro- 
portional to  the  depth,  a  pressure  in  many  instances  as  great  as  1,500  Ib.  and 
often  reaching  2,000  to  3,000  Ib.  a  sq.  in.  Because  of  this  pressure,  the  gas 
is  forced  slowly  upwards  and  meeting  the  seam,  is  held  in  the  pores  of  the 
coal.  This  view  of  Mr.  Haas'  explains  why  the  deeper  seams  are  more  gaseous 
than  the  higher  ones,  why  one  mine  in  a  district  may  produce  much  gas  and  its 
neighbor  but  little,  and  why  feeders  from  the  floor  and  bottom  of  the  seam 
are  more  lasting  than  those  from  the  roof  and  the  top  of  the  bed. 

Occurrence  of  Methane  in  Mines. — After  prolonged  exposure,  the  occluded 
methane  is  largely  given  off  by  the  seam  so  that  in  active  workings,  at  least, 
the  gas  is  more  commonly  found  at  or  near  the  face  of  the  rooms  and  entries 
than  nearer  the  drift  mouth  or  the  foot  of  the  shaft.  Unless  diffused  or  removed 
by  the  air-current  as  fast  as  it  escapes,  the  extreme  lightness  of  methane  tends 
to  its  concentration  near  the  roof;  and  in  workings  being  driven  to  the  nse, 


862  VENTILATION  OF  MINES 

and  it  is  commonly  looked  for  there.  When  slowly  given  off  near  the  floor, 
diffusion  will  distribute  it  uniformly  through  the  air  of  the  place;  and  when 
once  mixed  it  will  not  again  separate.  The  same  is  true  of  gas  coming  from 
the  roof,  but  the  diffusion  is  not  so  rapid.  When  issuing  from  the  top,  the  gas 
under  the  influence  of  a  gentle  air-current  will  often  flow  in  a  thin  sheet  or 
layer  next  the  roof,  rising  into  and  remaining  in  any  cracks  or  crevices.  In 
entries,  gas  will  accumulate  behind  any  obstruction  in  the  air;  thus,  it  will  be 
found  at  the  roof  between  the  collars  of  parallel  sets  of  timbers. 

The  volume  and  velocity  of  the  air-current  have  much  to  do  with  the 
concentration  of  gas  in  one  part  or  another  of  the  workings.  In  rooms,  where 
the  air  is  apt  to  be  stagnant,  and  particularly  beyond  the  last  break-through, 
accumulations  of  methane  are  usual.  In  such  places,  the  gas  often  tails  out 
or  tails  back  from  the  face;  that  is,  at  the  face  it  will  extend  down  from  the 
roof  for,  say,  3  ft.  and  thence  gradually  decrease  in  depth  outwards  towards 
the  break-through  where  none  may  be  found.  Bodies  of  what  is  known  as 
standing  gas  will  accumulate  in  old  workings  where  there  is  little  or  no  circu- 
lation of  the  air.  In  some  cases,  the  oxygen  will  be  so  reduced  through  absorp- 
tion by  the  coal  or  the  percentage  of  methane  may  be  so  high  that  an  explosion 
is  not  possible  in  the  old  workings,  but  should  the  gas  escape  into  the  air-current 
an  explosive  mixture  may  result.  Gas  is  very  often  a  source  of  trouble  in  pillar 
drawing,  accumulating  above  the  falls  of  roof  where  it  is  entirely  out  of  reach 
of  the  sluggish  air-currents  which,  possibly,  may  be  circulating  through  the  gob. 
This  pillar  gas  (as  well  as  standing  gas  in  old  workings)  may  be  forced  into  the 
airways  with  disastrous  results  by  a  heavy  fall  of  roof  or  by  the  reduced  at- 
mospheric pressure,  which  is  marked  by  a  fall  of  the  barometer. 

Effect  of  Methane  on  Life. — As  methane  is  not  concerned  with  breathing, 
like  carbon  dioxide,  and  does  not  combine  with  the  hemoglobin  of  the  blood, 
like  carbon  monoxide,  it  is  without  active  effect  on  life.  When  unusually  large 
amounts  are  present,  it  acts  in  the  same  way  as  an  excess  of  nitrogen,  reducing 
the  percentage  of  oxygen  available  for  breathing  which  becomes  more  and  more 
difficult  and  finally  impossible.  Wabner  states  that  methane  produces  suf- 
focation when  constituting  50%  of  the  inhaled  air,  while  Guibal  places  the 
limit  at  33%. 

Explosibility  of  Methane. — Methane,  like  carbon  monoxide,  will  either 
burn  or  explode  when  mixed  in  the  proper  proportions  with  air.  The  temper- 
ature of  ignition  of  methane  is  variously  stated  to  be  650°  C.  (1,202°  F.)  by 
Demanet,  740°  C.  (1,364°  F.)  by  Brunck,  780°  C.  (1,436°  F.)  by  Koehler. 
The  Bureau  of  Mines  gives  the  igniton  temperature  in  air  as  650°  to  750°  C. 
(1,202°  to  1,382°  F.);  and  in  oxygen,  536°  to  700°  C.  (1,033°  to  1,292°  F.). 

The  percentage  of  methane  in  the  air  necessary  to  produce  either  a  burning 
or  an  explosion  depends  on  the  means  taken  to  ignite  the  gas,  on  the  presence 
of  other  combustible  or  inert  gases,  on  the  amount  of  oxygen  and  water  vapor 
in  the  air,  on  the  temperature  and  pressure,  etc.  With  low  percentages  of 
methane,  owing  to  the  cooling  effect  of  a  large  body  of  air,  the  burning  will 
extend  only  a  very  short  distance  from  the  cause  of  ignition,  as  when  the 
gas  is  detected  in  the  flame  of  a  safety  lamp.  As  the  percentage  of  gas  increases, 
the  inflammation  extends  farther  and  farther  from 'its  origin  until  it  entirely 
permeates  the  gaseous  mass.  A  point  is  then  reached  when  the  burning  is 
instantaneous  and  an  explosion  occurs;  this  marks  the  lower  explosive  limit. 
Later,  as  the  percentage  of  gas  increases,  the  maximum  explosive  point  is 
reached.  When  this  is  passed,  the  still  increasing  percentage  of  methane  in  the 
air  is  accompanied  by  explosions  of  less  and  less  violence,  until  the  higher,  or 
upper,  explosive  limit  is  reached.  From  this  point  to  the  upper  inflammable 
limit,  the  phenomena  are  the  same,  but  in  reversed  order,  to  those  leading 
from  the  lower  inflammable  to  the  lower  explosive  limit. 

As  it  is  a  difficult  matter  to  tell  just  when  a  very  rapid  burning  becomes 
an  explosion,  authorities  differ  in  the  values  assigned  to  the  explosive  limits 
of  methane  in  air.  Blair  gives  the  limits  as  6.1%  and  12.8%  for  ignition  by 
an  electric  spark  when  complete  combustion  results.  Doctor  Brunck  states 
that  below  6%  and  above  15%  an  explosion  cannot  take  place.  The  Bureau 
of  Mines  notes  that  5.5%  of  gas  in  air  will  explode,  but  not  with  violence,  and 
that  an  incomplete  burning  sometimes  results  with  as  little  as  4.5%.  Similarly, 
the  Bureau  has  secured  slight  burnings  with  as  much  as  20%  of  methane. 
Clowes  places  the  explosive  limits  at  5  and  13%  when  the  gas  is  ignited  from 
below,  and  at  6  and  11%  when  ignition  is  from  above,  and  remarks  that  the 
lower  figures  (5  and  6%)  represent  the  least  amount  of  gas  that  will  always 
burn,  and  under  certain  conditions  will  explode.  The  maximum  explosive 
point  is  reached  when  the  air  contains  9.46%  of  methane. 


VENTILATION  OF  MINES 


863 


The  determination  of  the  exact  explosive  limits  of  the  gas  is  not  a  matter 
of  first  importance,  that  is,  it  makes  little  difference  in  practical  ventilation 
whether  the  lower  limit  is  5.5  or  7.1%,  as  either  figure  is  far  beyond  the  amount 
that  can  be  tolerated  in  the  presence  of  bituminous-coal  dust,  which  is  com- 
monly fixed  at  not  more  than  1%,  one  of  the  largest  producers  requiring  that 
the  return  air  in  its  mines  shall  not  contain  more  than  .30%  of  methane. 

Methane  can  only  be  ignited  by  a  flame  or  an  electric  arc  and  not  by  dark 
heat  alone,  although  explosions  have  been  attributed,  as  at  the  Belleyue  mine, 
Alberta,  Can.,  to  ignition  of  methane  by  sparks  produced  by  rocks  striking  one 
another  during  a  fall  of  roof.  Sparks  from  the  old-time  flint  mill,  or  wheel,  used 
for  lighting  in  gaseous  mines  are,  also,  believed  to  have  originated  gas  explosions. 

The  explosion  of  methane  is  not  instantaneous  when  it  is  raised  to  the 
ignition  point,  but  requires  an  appreciable  time  interval.  This  fact  is  taken 
advantage  of  in  the  use  of  high  and  permissible  explosives  the  flame  of  which  is 
so  short  that  notwithstanding  its  high  temperature,  it  goes  out  before  it  has 
time  to  ignite  the  gas. 

A  decrease  in  the  pressure  makes  the  gas  less  explosive.  According  to 
Brunck,  a  mixture  of  air  7.5%  of  methane  that  explodes  with  violence  at 
atmospheric  pressure  (30  in.  of  mercury)  cannot  be  made  to  explode  if  the  pres- 
sure is  reduced  to  8  in.  of  mercury.  Similarly,  an  increase  in  pressure  as  well  as 
one  in  temperature  renders  the  gas  more  explosive ;  hence  at  great  depths,  where 
the  barometer  stands  at,  say,  33  to  34  in.  and  the  thermometer  registers  possibly 
100°  F.,  a  lower  percentage  of  gas  will  be  explosive  than  in  surface  workings. 

As  the  other  combustible  gases  have  a  much  wider  explosive  range  (see  table 
below)  and  lower  ignition  temperature  than  methane,  their  presence  in- 
creases the  liability  of  a  firedamp  mixture  to  explode.  On  the  other  hand, 
inert  gases  like  nitrogen  and  carbon  dioxide  by  shortening  the  explosive  range 
of  methane  and  by  their  cooling  effect  on  the  products  of  combustion,  materially 
reduce  the  liability  of  occurrence  of  such  explosions.  The  presence  of  gases 
having  a  maximum  explosive  point  greater  than  that  of  methane  as  well  as 
that  of  inert  gases,  raises  the  maximum  explosive  point  of  firedamp.  Since 
mine  air  is  commonly  deficient  in  oxygen,  the  explosive  limits  of  methane  in  it 
are  usually  higher  than  in  pure  air,  one  authority  placing  them  at  7.14  and 
16.67%,  respectively,  and  another  stating  that  the  maximum  degree  of  explosi- 
bility  is  reached  when  the  methane  is  one-eighth  to  one-ninth  of  the  air,  that 
is,  from  12.5  to  11.1%. 

The  statement  sometimes  made  that  an  addition  of  one-seventh  (14.3%) 
of  carbon  dioxide  to  a  volume  of  air  and  methane  at  its  most  explosive  point 
(CHt,  9.46%;  air,  90.54%)  entirely  prevents  its  explosion  seems  contrary  to 
the  facts  as  the  resulting  mixture,  which  has  the  composition  COz  12.51%, 
Oz  16.60%,  N*  62.61%,  CHt  8.28%,  is  well  within  the  explosive  limits  as  given 
in  the  following  table. 

It  has  been  shown  by  Baker  that  an  explosion  of  gas  is  not  possible  when 
it  and  the  air  are  absolutely  dry,  moisture  playing  the  part  of  a  catalytic  agent, 
as  noted  under  Explosibility  of  Carbon  Monoxide.  However,  the  condition 
of  absolute  dryness  does  not  exist  in  mines  and  cannot  be  brought  about  therein. 

LIMITING  EXPLOSIVE  MIXTURES  OF  VARIOUS  EXPLOSIVE  GASES 
WITH  AIR 


Combustible  Gas  Used 

^Percentage  of  Gas  Mixed 
With  Air 

Method  of 
Kindling 

Lower 
Explosive 
Limit 

Upper 
Explosive 
Limit 

Methane.  .  .  . 

/5 
U 
J6 
19 
9 
6 
13 
4 
3 

13 
11 
29 
22 
55 
72 
75 
22 
82 

Upwards 
Downwards 
Upwards 
Downwards 
Upwards 
Upwards 
Upwards 
Upwards 
Downwards 

Coal  gas,  Nottingham  
Water'  gas  artificial 

Hydrogen  
Carbon  monoxide 

Ethylene,  olefiant  gas  

Acetylene                 .    .    .        

864 


VENTILATION  OF  MINES 


The  above  table  from  Clowes  gives  the  relative  explosibility  of  methane 
and  other  gases.  Clowes  notes  that  the  determination  of  the  limits  for  acetylene 
is  complicated  by  a  somewhat  explosive  separation  of  the  acetylene  itself  into 
its  elements.  The  composition  of  the  coal  gas  was:  Olefins,  5.3%;  hydrogen, 
48.2%;  carbon  monoxide,  6.6%;  methane,  34.2%;  oxygen,  .2%;  nitrogen,  5.5%. 
The  total  combustible  gases  were  94.3%,  inert  gases  5.7%.  The  composition 
of  the  water  gas  was:  Hydrogen,  49.6%;  carbon  monoxide,  40.8%;  carbon 
dioxide,  2.6%;  nitrogen,  7.0%.  The  total  combustible  gases  were  90.4%, 
inert  gases,  9.6%.  Combustion  was  effected  in  tubes,  by  means  of  a  Bunsen 
burner,  the  flame  being  held  both  below  and  above  the  body  of  the  gas.  The 
conditions,  in  the  main,  were  not  unlike  those  that  might  be  met  in  the  mine. 

The  probability  of  an  explosion  is  greatest  in  the  case  of  those  gases  having 
a  wide  explosive  range,  because  it  is  possible  to  form  with  them  a  greater 
number  of  explosive  mixtures.  For  this  reason,  methane  with  an  explosive 
range  of  5  to  8%  is  the  least  dangerous  gas,  and  hydrogen,  with  a  range  of 
67%  is  the  most  dangerous.  Also,  methane  is  less  dangerous  than  the  other 
gases  because  its  temperature  of  ignition  is  higher,  and  it  is  more  slowly  kindled. 
However,  methane  is  in  the  end  the  most  dangerous  gas  from  the  viewpoint  of 
possible  explosions  because  of  its  general  occurrence;  the  other  gases  are  found 
but  rarely  or  in  very  small  amounts,  and  carbon  monoxide,  notwithstanding  its 
wide  range  of  explosibility,  is  dangerous  solely  because  of  its  intensely  poisonous 
properties. 

Firedamp. — Firedamp  originally  meant  the  gas  methane  and  later  was 
modified  to  mean  an  explosive  mixture  of  methane  and  air,  Methane  rarely 
occurs  in  a  pure  state  being  associated  with  small  amounts  of  ethane,  ethylene, 
nitrogen,  etc.,  and  the  word  firedamp  is  now  very  commonly  defined  as  a  mix- 
ture of  explosive  mine  gases,  very  largely  methane  but  often,  if  not  always, 
mixed  with  other  hydrocarbons  and  small  amounts  of  inert  gases.  As,  with 
the  exception  of  the  rare  gas  hydrogen,  all  mine  gases  are  heavier  than  methane, 
the  specific  gravity  of  firedamp  is  higher  than  that  of  pure  methane,  and  may 
reach  above  .7. 

The.  following  analyses,  from  Chamberlain,  are  of  firedamp  given  off  by 
coal  when  bottled  in  a  vacuum. 

COAL    FROM    FACE,  NAOMI    MINE    (GAS    COAL,   PITTSBURGH,  PA., 
DISTRICT) 


Gas 

First 
3  Wk. 

4  Wk. 
Later 

10  Wk. 

Later 

9  Wk. 

Later 

Carbon  dioxide  
Carbon  monoxide                     \ 

1.05 

.83 

.63 

.60 

Olefins  J 
Paraffins                                  .    . 

1.03 
55.39 

.29 
84.96 

.84 
91.39 

1.13 

87.89 

A.    /Oxygen  
Aa  \Nitrogen                        .    . 

.51 
1.91 

.35 
1.32 

.50 
1.89 

.40 
1.51 

Nitrogen,  excess  

40.11 

12.25 

4.75 

-8.47 

Relative  volumes  

100.00 
.21 

100.00 
.20 

100.00 

.28 

100.00 
.21 

COAL  FROM  FACE,  NO.  1  NORTH  SHAFT,  NANTICOKE,  PA. 
(ANTHRACITE) 


Gas 

First 
Week 

Second 
Week 

Third 
Week 

Fourth 
Week 

Carbon  dioxide 

.02 

.17 

Olefins  

.51 

.78 

.87 

.29 

Paraffins.    . 

86.86 

93.99 

94.19 

98.58 

A  •    f  Oxygen 

.04 

.07 

Air  \Nitrogen  
Nitrogen,  excess  

.15 
12.42 

5.23 

4.77 

•  .26 

.80 

Relative  volume  

100.00 
1.22 

100.00 
.99 

100.00 

100.00 

.81 

VENTILATION  OF  MINES 


865 


In  the  preceding  analyses,  by  olefins  is  meant  gases  of  the  type  of  ethylene, 
CzHt,  and  by  paraffins,  gases  of  the  type  of  methane  and  ethane,  CH^  and  CtH6, 
respectively.  In  the  Naomi  analysis,  whatever  carbon  monoxide  may  have 
been  present  is  grouped  with  the  olefins,  and  its  absence  in  the  Nanticoke 
analysis  is  noticeable.  Mr.  Chamberlain  states  that  certain  differences 
observed  in  making  the  analyses  can  be  explained  by  the  presence  of  ethane 
(in  the  paraffins)  in  proportions  of  a  trace  to  four  parts  of  ethane  to  100  parts 
of  methane.  So  far  as  his  tests  went,  the  bituminous  coals  yielded  more  ethane 
than  the  single  sample  of  anthracite  (Nanticoke);  in  fact,  the  analyses  of 
several  anthracite  gases  indicated  that  instead  of  there  being  paraffins  higher 
than  methane,  that  small  amounts  of  hydrogen  were  present. 

The  following  table  gives  the  composition  and  volume  of  gases  (firedamp) 
issuing  from  some  Welsh  coals  when  heated  in  a  vacuum  to  212°  F. 

GASES  ENCLOSED  IN  THE  PORES  OF    COAL    AND  EVOLVED  IN  A 
VACUUM  AT  212°  F. 

(Thomas) 


Quantity 

Name  of  Colliery 

Quality 

COz 

0 

cm 

N 

fecS 

1      § 

iji 

o  fc^ 

*ijj 

f  ft| 

0  p, 

u    w 

Navigation  

Steam 

13.21 

.49 

81.64 

4.66 

250.0 

80 

Dunraven 

Steam 

5.46 

.44 

84.22 

9.88 

218.0 

70 

Cyfarthfa  

Steam 

18.90 

1.02 

67.47 

12.61 

147.0 

47 

Bute  

Steam 

9.25 

.34 

86.92 

3.49 

375.0 

120 

Bonville's  Court  

Anthracite 

2.62 

93.13 

4.25 

555.0 

178 

Watney's. 

Anthracite 

14.72 

84.18 

1.10 

600.0 

192 

Plymouth  Iron  Works 

Bituminous 

36.42 

.80 

62.78 

55.9 

18 

Cwm  Clydach  

Bituminous 

5.44 

1.05 

63.76 

29.75 

55.1 

18 

Bettwys  

Bituminous 

22.16 

6.09 

2.68 

69.07 

24.0 

8 

The  following  table  gives  a  series  of  firedamp  analyses  from  Le  Chatellier, 
some  of  them  being  of  blowers,  others  from  bore  holes,  etc. 

ANALYSES  OF  FIREDAMP 

(Le  Chatellier) 


Locality 

CEt 

C02 

N 

O 

Analyst 

Dunraven  mine,  blowers.  .  .  . 

96.70 

.47 

2.79 

J.  W.  Thomas 

Dunraven  mine,  bore  hole.  . 

96.50 

.44 

3.02 

J.  W.  Thomas 

Garswood  mine. 

84.16 

.86 

12.30 

2.65 

W.  Kellner 

Garswood  mine,  blowers.  .  .  . 

88.86 

.41 

8.90 

1.83 

W.  Kellner 

Glamorgan  mine,  blowers  .  .  . 

93.01 

.27 

5.94 

.78 

.    W.  Kellner 

Dombran  mine,  blowers.  .  .  . 

95.11 

.48 

4.07 

.34 

f  Austrian  Firedamp 

Karwin  mine  

94.59 

.18 

4.48 

.75 

\        Commission 

Karwin  mine,  blowers  

99.10 

.20 

.70 

Hruschau  mine  

79.16 

.19 

17.04 

.61 

Hruschau  mine,  blowers.  .  .  . 

87.93 

.83 

10.25 

.99 

Peters  wald  mine,  blowers.  .  . 

90.00 

.15 

9.25 

.60 

Segen  Gottes  mine  

83.51 

1.17 

15.02 

.30 

Sauer 

Segen  Gottes  mine,  bore  hole 

87.16 

1.11 

11.73 

Sauer 

Liebe  Gottes  mine,  bore  hole 

77.69 

3.77 

18.48 

.06 

Sauer 

The  following  table  from  Schondorrf 
65 


entirely  of  firedamp  from  blowers. 


866 


VENTILATION  OF  MINES 
ANALYSES  OF  FIREDAMP  FROM  BLOWERS 


Locality 

CH* 

CzH6 

H 

COz 

N  +  0 

Bonifacious  mine  at  Kray,  Essen 

90.94 

1.40 

.30 

7  36 

Consolidation  mine  at  Schalk,  Westphalia 
Konig  mine  at  Neunkirchen,  Saarbuck.  .  . 

Oberkirchen  mine  at  Schaumburg  

Cavities  in  the  roof,  Lothringen  mine  at 
Castrop  Westphalia 

89.88 
84.89 
f  60.46 
\  93.66 

27  95 

1.62 
37.64 

.88 

5.84 
2.11 

1  35 

.67 
.65 
2.56 
.63 

45 

3.61 
12.84 

4.80 
70  25 

New  Iserlohn  mine  at  Lawgendren,  West- 
phalia            

/    4.75 
\    4.00 

.06 

.09 

1.34 
.40 

65.00 
95  00 

The  following  analyses  from  Chamberlain  are  of  feeder  gas  from  American 
mines;  the  last  being  that  of  a  gas  issuing  under  high  pressure  from  a  standpipe 
at  Luzerne,  near  Wilkesbarre,  Pa.  In  this  case,  CnHzn,  is  the  general  formula 
for  the  olefin  series  of  gases  of  which  ethylene,  or  olefiant  gas,  is  a  type.  When 
so  used,  the  formula  means  that  the  gases,  while  present,  were  not  separately 
determined.  In  the  same  way,  the  other  paraffin  gases,  of  which  the  general 
formula  is  CnHzn+z,  were  not  determined  but  are  included  with  the  methane. 

ANALYSES  OF  FIREDAMP  FROM  FEEDERS 


Locality 

CH* 

COz 

CO 

CnHzn 

Air 

Nt 

Excess 

Cardiff,  111  

90.42 

2.04 

.20 

6.02 

1.32 

Cardiff,  111  

92.17 

2.39 

£ 

!6 

263 

2  55 

Luzerne,  Pa  

91.31 

1.59 

.04 

.49 

1.10 

4.65 

The  following  series  of  analyses  of  a  firedamp  mixture  that  could  be 
explosive  under  proper  conditions  is  given  by  Mr.  G.  A.  Burrell.  The  analyses, 
made  day  by  day,  show  the  change  in  the  atmosphere  in  an  enclosed  area  in  an 
anthracite  mine,  a  part  of  which  was  sealed  off  to  prevent  entrance  of  a  fire 
in  progress  in  a  neighboring  district.  The  gases  were  not  contaminated  by  the 
products  of  combustion  of  the  fire  as  a  heavy  roof  fall  prevented  the  escape 
of  the  gases  from  the  one  to  the  other,  and  thus  fairly  represent  the  change 
in  mine  air  away  from  the  ventilating  current.  On  the  first  two  days,  there 
was  a  leakage  of  air  into  the  enclosed  area,  and  after  this  was  stopped  the 
change  in  the  imprisoned  air  was  much  more  rapid. 

GASES  FROM  AN  ENCLOSED  AREA  IN  AN  ANTHRACITE  MINE 


Percentage  of 

Sample 
Number 

Date 

COz 

CO 

Oz 

CtH 

Nz 

1 

Oct.  31 

2.2 

15.0 

14.0 

68.8 

2 

Nov.    1 

2.3 

14.6 

18.1 

65.0 

3 

Nov.    2 

2.6 

6.2 

24.2 

67.0 

4 

Nov.    2 

2.9 

5.7 

29.3 

62.1 

5 

Nov.    3 

2.8 

4.1 

34.9 

58.2 

6 

Nov.    6 

2.6 

5.0 

53.0 

41.4 

The  following  analyses  from  Mr.  Austin  King  give  the  composition  of  some 
firedamps  from  the  Connellsville,  Pa.,  bituminous-coal  region.     The  very  large 


VENTILATION  OF  MINES 


867 


amounts  of  ethylene,  carbon  monoxide,  and  hydrogen  in  the  first  two  samples 
is  noticeable.  Mr.  King  also  furnishes  the  following  analyses  of  gases  escaping 
from  bore  holes 'drilled  from  the  surface  to  drain  the  gob. 

ANALYSES  OF  FIREDAMP,  CONNELLSVILLE  REGION 


Samples  Taken  From 

Percentage  of 

C02 

CzHt 

02 

CO 

Fh 

C//4 

Nz 

Drill  hole  in  coal  f 
Crevice  in  roof,  fac 
Return  airway  of  n 

ice 

.30 
1.70 

1.50 
1.30 

1.60 

1.80 
18.40 

1.30 
.90 

7.35 
2.04 

79.60 
63.27 
6.50 

8.25 
28.99 
75.10 

2  main  entry 
lain  entry  .  . 

ANALYSES  OF  GAS  FROM  DRILL  HOLES 

Remarks 

COz 

CzHi 

02 

CO 

H2 

CzH6 

CH* 

Nz 

Hole,  525  ft.  deep. 
Hole,  406  ft.  deep. 
Same,  1  yr.  later  .  . 
Hole,  474  ft.  deep. 

2.50 
5.20 
1.80 
4.60 
6.90 

.10 

10.40 
3.20 
14.90 
4.20 
9.20 

.20 
.40 

1.35 
14.16 

1.60 

11.90 
12.64 
2.20 
8.80 
38.30 

73.85 
78.96 
71.68 
67.52 
48.50 

Firedamp  is  usually  found  in  the  same  relative  positions  in  the  workings  as 
methane.  However,  the  presence  of  large  amounts  of  gas  heavier  than  methane 
may  make  firedamp  heavier  than  air  and  give  it  a  tendency  to  collect  on  the 
floor.  Thus,  a  gaseous  mixture  composed  of  54.1%  of  methane  and  45.9%  of 
carbon  dioxide  has  the  same  weight  as  air.  Any  increase  in  the  percentage  of 
carbon  dioxide  over  45.9  will  make  the  mixture  heavier  than  air  and,  if  diffusion 
is  not  taking  place,  the  firedamp  will  accumulate  on  the  floor. 

Combustion  Products  of  Methane. — When  pure  methane  is  exploded  in 
air  the  reaction  is  Ctf4+2(O2+3.7822V2)  =  CO2+2#2O  +  7.564.ZV2.  The  com- 
position of  the  afterdamp  is  15.1%  COz,  12.3%  vapor  of  water  HzO,  and  72.6% 
Nz.  As  soon  as  the  water  vapor  condenses,  the  remaining  gas  is  a  blackdamp 
with  the  compositioni!7.2%  COz  and  82.8%  Nz.  This  reaction  holds  good  for  all 
burnings  and_  explosions  of  methane  as  long  as  there  is  an  ample  supply  of 
oxygen;  that  is,  from  the  lower  inflammable  limit  (about  5%)  to  the  maximum 
explosive  point  (9.46%). 

_  As  the  percentage  of  methane  in  the  air  rises  above  the  maximum  explosive 
point  and  the  supply  of  oxygen  is  less  than  that  required  for  complete  com- 
bustion, an  increasing  proportion  of  the  methane  is  burned  to  carbon  monoxide 
and  hydrogen,  the  reaction  probably  being  2C#4+ (02+3.782^)  =  2CO  +  4ff2 
+  3.782A/2.  It  is  also  probable  that  portions  of  the  methane  are  burned  to 

PRODUCTS  OF  EXPLOSION  OF  METHANE  IN  AIR 


Percentage  of  Methane  in  Air 


9.46 

10.03 

10.94 

12.00 

Carbon  dioxide  
Carbon  monoxide  
Hydrogen  .... 

15.10 

10.16 
2.13 
1.39 

8.35 
4.47 
3.66 

4.80 
3.90 
3.50 

Water 

12  30 

Nitrogen  . 

72.60 

86.32 

83.52 

82.20 

Methane,  etc  

2.50 

868  VENTILATION  OF  MINES 

carbon  monoxide  without  the  formation  of  hydrogen  by  this  reaction. 
+3(O2+3.782Af2)=2CO-|:4tf2O  +  11.3462V2.  It  is  not  possible  to  determine 
the  percentage  composition  of  the  afterdamp  in  these  cases  as  the  relative 
proportions  of  the  methane  burned  to  carbon  dioxide,  and  to  carbon  monoxide, 
and  hydrogen,  respectively,  cannot  be  known. 

The  first  column  gives  the  composition  of  the  afterdamp  as  calculated  from 
the  reaction  for  complete  combustion.  The  second  and  third  columns  repre- 
sent the  results  of  investigations  by  Mr.  G.  A.  Burrell,  of  the  Bureau  of  Mines. 
The  figures  in  the  fourth  column  are  from  the  French  firedamp  commission 
as  quoted  by  Chamberlain.  The  sums  total  but  96.9%  and  indicate  the 
presence  of  some  unconsumed  methane  and  other  hydrocarbons.  Mr.  Burrell 
notes  that  no  acetylene,  olefin  hydrocarbons,  or  unburned  methane  were  found 
in  the  products  of  combustion. 

The  results  of  the  French  firedamp  commission  in  some  measure  support 
the  contentions  of  Doctor  Broockmann,  of  Bochum,  who,  according  to  Wabner, 
has  shown  that  the  product  of  the  imperfect  combustion  of  methane  is  ethylene 
(olefiant  gas,  CzHt),  and  not  carbon  dioxide.  The  reaction  for  the  explosion 
in  oxygen  would  probably  be  written,  2CHt+02  =  CzH4,+2HzO.  In  dis- 
cussing Doctor  Broockmann's  work,  Chamberlain  says:  A  mixture  of  air 
and  firedamp  containing  from  10.8  to  13.5%  of  marsh  gas  he  found  to  give 
two  separate  flames.  Expecting  to  find  some  carbon  monoxide  formed  as  the 
result  of  the  first  flame,  Broockmann  removed  the  products  of  the  first  com- 
bustion, in  an  exploding  mixture  of  methane  and  air,  before  the  appearance 
of  the  second  flame;  but  in  no  case  found  a  trace  of  carbon  monoxide.  Instead, 
the  heat  of  the  first  combustion  converted  the  unconsumed  methane  into 
acetylene  and  hydrogen.  These  doubtless  furnished  the  fuel  for  the  second 
flame. 

In  the  case  of  the  formation  of  acetylene  and  hydrogen,  the  reaction  for 
explosion  in  oxygen,  would  be,  2CHt+O2  =  C2H2+Hz+2HzO.  From  the 
evidence  in  hand,  it  would  appear  that  the  explosion  of  methane  in  a  deficient 
air  supply,  that  is  when  there  is  more  than  9.46%  methane  in  the  air,  results 
ordinarily  in  the  formation  of  carbon  monoxide  and  hydrogen,  but  that  under 
certain  conditions  some  acetylene  and  olefiant  gas  may  be  formed.  One  of 
these  conditions  for  the  formation  of  ethylene  or  acetylene  would  appear  to 
be  a  percentage  of  methane  approaching  the  upper  explosive  limit. 

Effect  of  Atmospheric  Changes  on  Escape  of  Firedamp. — The  pressure  of 
the  atmosphere  is  not  constant,  but  is  subject  to  fluctuations  depending  on  the 
condition  of  the  atmosphere.  Besides  these,  there  are  fluctuations  that  are 
more  or  less  regular  and  are  called  barometric  variations.  There  is  both  a 
yearly  and  a  diurnal,  or  daily,  variation.  Of  these  two,  the  more  important 
and  the  more  regular  is  the  daily  variation,  in  which  the  barometer  attains  a 
maximum  height  from  9  to  10  o'clock  A.  M.,  and  a  minimum  about  4  o'clock  p.  M. 
Other  maximum  and  minimum  readings  are  obtained  at  10  P.  M.  and  3  A.  M., 
respectively;  but  these  are  not  as  pronounced  as  those  occurring  in  the  day- 
time. The  daily  barometric  variations  range  from  .01  to  .08  in. 

A  reduction  in  atmospheric  pressure  (fall  of  the  barometer)  permits,  or 
tends  to  permit,  an  increase  in  the  outflow  of  gas,  and  an  increase  in  atmospheric 
pressure  (rise  of  the  barometer)  reduces  the  outflow.  Although  at  its  point 
of  escape  face  and  blower  gas  are  but  little  above  atmospheric  pressure,  a 
short  distance  within  the  solid  the  pressure  may  be  from  five  to  forty  or  more 
atmospheres,  whereas  standing  gas  in  old  workings  is  under  atmospheric 
pressure  only.  For  this  reason,  a  change  in  pressure  has  much  more  effect 
on  the  escape  of  gas  from  the  gob  than  from  the  face,  although  the  lengthening 
of  the  flame  of  a  burning  blower  during  periods  of  low  barometer  and  its 
shortening  when  the  barometer  is  high  which  are  due  to  an  increase  and  decrease, 
respectively,  in  the  amount  of  escaping  gas  are  well  known. 

In  connection  with  barometric  fluctuations  the  following  points  should 
be  noted:  Changes  in  the  outflow  of  gas  always  take  place  before  the  corre- 
sponding change  in  the  barometer,  and  from  1  to  6  hr.  in  advance  thereof. 
This  appears  to  be  due  to  the  fact  that  an  air-and-gas  column  is  much  more 
sensitive  to  slight  changes  in  pressure  than  one  of  mercury.  Thus,  the  table 
on  page  838  shows  that  1  in.  of  mercury  =  .491  Ib.  a  sq.  in.  =  876  ft.  of  air,  and 
for  a  given  change  in  the  mercury  column,  the  one  in  the  air  column  is  876  X  12 
=  10,512  times  as  great.  One  reason  for  the  discontinuance  of  the  barometer 
warnings  in  England  was  that  they  did  not  arrive  until  the  danger  was  passed. 
In  an  extensive  country  like  the  United  States,  the  well-known  Daily  Weather 
Maps  of  the  Weather  Bureau  can  be  utilized  in  this  connection.  Thus,  an 
area  of  low  barometer,  say,  in  Arizona,  will  probably  not  reach  Illinois  or 


VENTILATION  OF  MINES  869 

Pennsylvania  for  24  to  36  hr.t  giving  ample  time  to  make  any  necessary  changes 
in  the  ventilation.  The  reason  why  these  maps  have  not  received  extended 
use  is  possibly  due  to  the  facts  that  the  average  American  mine  is  shallow  and 
non-gaseous,  and  provided  with  ample  ventilation. 

Increases  in  the  outflow  of  gas  due  to  working  the  mine  should  not  be 
confused  with  those  due  to  changes  in  atmospheric  pressure.  As  pointed  out 
by  Messrs.  Evans  and  Hutchinson,  the  amount  of  gas  given  off  by  the  face  is 
a  minimum  at  the  beginning  of  the  shift,  increases  to  a  maximum  at  its  end 
and  then  decreases  to  a  minimum  at  the  beginning  of  the  next  morning  shift. 
This  is  due  to  the  fact  that  by  day  fresh  faces  of  coal  are  constantly  being  ex- 
posed, and  does  not  concern  the  escape  of  gas  from  the  gob.  For  the  same 
reason,  a  mine  producing  2,000  or  3,000  tons  a  day  gives  off  more  gas  than 
one  mining  but  1,000  tons.  Rapidity  of  working,  however,  does  not  affect  the 
outflow  of  gas  from  the  gob. 

The  more  rapid  the  change  in  the  barometer,  the  greater  will  be  the  increase 
or  decrease  in  the /outflow  of  gas.  When  the  pressure  falls  a  certain  amount 
and  then  remains  constant  for  some  time,  the  increased  outflow  of  gas  gradu- 
ally diminishes  as  the  pressure  of  the  gas  in  the  coal  adjusts  itself  to  that 
of  the  atmosphere.  The  outflow  does  not  become  as  low  as  before  the  fall 
until  the  pressure  returns  to  its  original  amount.  The  greater  the  pressure  of 
the  gas  in  the  pores  of  the  coal,  the  less  will  be  the  effect  of  atmospheric  changes 
on  its  escape.  Standing  gas  in  old  workings  is  more  dangerous  when  changes 
of  pressure  take  place  than  face  or  blower  gas,  as  large  volumes  of  it  may  be 
forced  into  the  airways. 

Afterdamp.— Strictly  speaking,  afterdamp  and  blackdamp  are  one  and  the 
same  gaseous  mixture  (COz  and  N),  the  one  being  formed  with  extreme  rapidity 
by  the  explosion  of  methane  or  coal  dust  (or  both),  and  the  latter  very  slowly 
by  the  gradual  absorption  of  oxygen  and  the  giving  off  of  carbon  dioxide  by  the 
coal.  Afterdamp,  however,  is  a  convenient  term  in  indicating  that  the  black- 
damp  mixture  it  defines  is  found  after  rather  than  before  an  explosion.  Owing 
to  the  general  insufficiency  of  oxygen  for  complete  cormTustion  and  the  universal 
presence  of  coal  dust  in  mine  workings,  afterdamp  probably  always  contains 
more  or  less  carbon  monoxide,  and  the  presence  of  this  gas  may  be  used  to 
distinguish  it  from  blackdamp  formed  in  the  ordinary  way.  Unfortunately,  it 
is  not  possible  to  give  representative  analyses  of  afterdamp,  because  in  the 
time  between  an  explosion  and  the  arrival  of  a  chemist,  the  mine  atmosphere 
will  have  materially  changed  and  correct  samples  cannot  be  obtained.  Doctor 
Haldane  says  that  afterdamp  may  be  assumed  to  contain  about  80  to  85%  N, 
12  to  14%  O,  4  to  6%  C02,.6  to  1.5%  CO,  together  with  small  amounts  of  SOz, 
HiS,  and  unconsumed  CHi.  Such  an  analysis  indicates,  roughly,  a  composi- 
tion of  62%  air,  38%  blackdamp  composed  of  87%  N  and  13%  CO2,  and  the 
amounts  of  the  other  gases  previously  named,  and  is  a  typical  air-blackdamp 
mixture. 

Afterdamp,  at  least  by  the  time  rescue  parties  arrive  upon  the  scene,  is 
very  rarely  extinctive  of  lights  and  so  must  contain  at  least,  say,  17.5  to  18%  0; 
considerably  more  than  the  figures  given  by  Doctor  Haldane.  Neither  is  the 
atmosphere  always  extinctive  immediately  after  an  explosion  as  is  proved  by 
the  numerous  instances  in  which  the  lamps  of  the  killed  have  been  found 
either  burning  or  exhausted  of  oil. 

Whether  the  breathing  of  afterdamp  results  fatally  or  not  depends  almost 
entirely  on  the  amount  of  carbon  monoxide  present,  for,  except  for  this  gas, 
the  afterdamp  quoted  from  Dr.  Haldane  is  not  necessarily  deadly,  although 
extinctive  of  lights.  In  anthracite  mines,  where  the  dust  is  inert,  carbon 
monoxide  is  derived  from  the  imperfect  combustion  of  methane,  but  in  bitu- 
minous mines  where,  frequently,  no  gas  is  concerned  in. the  explosion,  the 
monoxide  comes  from  the  imperfect  combustion  of  the  carbon  of  the  coal, 
from  the  reduction  of  carbon  dioxide  to  carbon  monoxide  by  incandescent 
carbon  and,  more  likely,  by  the  imperfect  combustion  of  the  various  hydro- 
carbons distilled  from  the  coal  by  the  intense  heat  of  the  explosion.  As  no 
two  explosions  are  alike  in  the  relative  proportions  of  methane  (or  coal  dust) 
and  air  concerned,  so  does  the  amount  of  monoxide  in  the  resultant  afterdamp 
vary  from  amounts  that  are  merely  injurious  to  those  that  are  almost  immedi- 
ately fatal,  Doctor  Haldane's  figure  of  1.5%  probably  well  representing  the 
average  maximum. 

In  some  cases,  depending  on  the  incompleteness  of  the  explosion,  the  after- 
damp will  contain  unburned  methane,  small  amounts  of  hydrogen,  and  possibly 
traces  of  acetylene.  The  oxides  of  nitrogen  may  be  found  in  minute  quantities 
in  afterdamp  as  a  result  of  the  burning  of  explosives  and  if  black  powder  has 


870  VENTILATION  OF  MINES 

been  one  of  these,  traces  of  sulphur  dioxide  and  hydrogen  sulphide  as  well. 
Vapor  of  water  is  always  a  product  of  the  explosion  of  hydrocarbon  gases 
and,  as  stated,  some  moisture  seems  essential  to  the  explosion  of  all  gases. 

Detection  of  Methane. — Some  miners  having  long  familiarity  with  methane 
claim  to  be  able  to  feel  the  presence  of  large  amounts  of  the  gas,  and  others 
attribute  to  it  a  peculiar  odor  and  a  taste  like  apples.  It  is  impossible  to  give 
any  reason  for  these  claims  as  the  pure  gas  is  odorless  and  tasteless  and  its 
effect  on  respiration  is  the  same  as  that  of  nitrogen.  The  claim  that  the  gas 
can  sometimes  be  seen  is  not  altogether  unreasonable,  the  visibility  being  due 
to  the  irregular  refraction  of  the  light  rays  from  a  lamp  while  passing  through 
layers  of  methane  or  of  firedamp  of  varying  densities. 

The  gas  is  universally  detected  in  mine  workings  by  the  use  of  some  form 
of  safety  lamp,  in  rare  cases  a  so-called  mechanical  gas  detector  has  been  used. 
For  accurate  determinations  of  the  methane  content  of  the  return  air  and  the 
control  of  the  ventilation  of  a  mine  as  a  whole,  the  larger  corporations  now 
cause  chemical  analyses  of  the  mine  air  to  be  made  daily  or  more  often  if 
necessary. 

THE  RARER  MINE  GASES 

General  Considerations. — A  number  of  gases,  either  by  reason  of  their 
existence  in  mine  air  being  disputed  or  doubtful,  or  by  their  occurrence  under 
very  unusual  conditions  or  in  such  small  amounts  that  they  can  be  detected 
only  locally  and  not  when  distributed  through  the  ventilating  current,  are 
known  as  the  rarer  mine  gases.  These  gases  are  ethane  and  ethylene  and  the 
higher  members  of  the  paraffin  and  olefin  series  of  gases,  and  hydrogen,  all  of 
which  may  occur  associated  with  methane  in  firedamp;  acetylene,  which  is 
sometimes  found  as  a  combustion  product  of  methane  in  a  deficiency  of  oxygen ; 
hydrogen  sulphide  and  sulphur  dioxide  which  may  be  formed  by  the  burning  of 
certain  explosives,  by  mine  fires,  and  by  certain  natural  chemical  processes; 
and  several  of  the  oxides  of  nitrogen,  which  are  found  in  the  combustion  prod- 
ucts of  various  explosives. 

The  part  that  any  of  these  gases  plays  in  the  general  scheme  of  mine  venti- 
lation is  insignificant,  and  most  of  them  are  of  little  more  than  theoretical 
interest.  Ethane,  ethylene,  and  other  members  of  their  series  are  not  easy 
to  detect,  and  it  is  possible  that  their  more  general  occurrence  will  be  demon- 
strated when  more  accurate  methods  of  analysis  are  employed.  On  the  other 
hand,  many  competent  chemists  doubt  their  existence  in  mine  air  after  special 
and  exhaustive  searches  for  them. 

Ethane  and  Other  Paraffin  Gases. — Ethane,  formula  Czfle,  the  next  higher 
than  methane  in  the  paraffin  series  of  gases  having  the  general  formula 
CnHzn+t,  is  believed  to  be  a  fairly  common  constituent  of  firedamp,  although 
its  presence  is  denied  or  doubted  by  numerous  competent  observers.  The 
Prussian  Firedamp  Commission  reported  a  sample  of  firedamp  containing 
37.62%  of  ethane,  but  the  maximum  noted  in  American  mines  rarely  exceeds 
.25  to  .50%.  Chamberlain  found  from  a  trace  to  4  parts  of  ethane  to  100  parts 
of  methane  in  the  gases  given  off  by  American  coals  when  bottled  in  a  vacuum, 
while  Porter  and  Orvitz  and  Parr  and  Barker  could  find  no  trace  of  it  in  many 
samples  of  coal  from  Illinois  and  other  states,  and  Brunck  (Germany)  and 
Harger  (England)  either  could  not  find  the  gas  or  claim  that  its  existence  has 
not  been  definitely  proved.  As  the  gas  is  formed  under  the  same  natural 
conditions  as  methane,  there  seems  no  good  reason  why  it  should  not  be  found 
in  firedamp.  The  gas  is  given  off  by  the  face  and  by  blowers,  but  it  may 
enter  the  mine  through  leakage  from  wells  of  natural  gas  which  usually  con- 
tains from  3  to  6%  of  ethane  and  as  high  as  16%  in  the  case  of  that  piped  to 
Pittsburgh,  Pa.,  from  the  West  Virginia  fields. 

Ethane  is  odorless,  colorless,  and  tasteless,  is  slightly  heavier  than  air,  and 
is  non-poisonous  but,  like  methane  and  nitrogen,  is  suffocating  in  sufficient 
quantities.  The  gas  is  combustible,  burning  with  a  somewhat  more  brilliant 
flame  than  methane,  and  is  explosive  at  a  lower  temperature  (968°  to  1,166°  F.) 
according  to  the  reaction  2C2#6+7O2  =  4CO2+6.H2O.  The  explosive  range  of 
the  gas  does  not  appear  to  have  been  determined,  but  its  point  of  maximum 
explosibility  in  air  is  fixed  by  Brunck  at  5.6%.  When  present  with  methane, 
it  makes  the  firedamp  mixture  more  easily  explosive,  but  not  to  a  great  extent 
owing  to  the  relative  difference  in  the  amounts  of  the  two  gases. 

Whether  insignificant  amounts  of.  the  next  higher  paraffin  gases,  propane 
CsHs  and  butane  CiHw,  are  or  are  not  associated  with  ethane  in  the  methane 
of  firedamp  is  a  very  much  unsettled  question.  The  chemical  and  physical 
properties  of  these  gases  and  their  effect  on  firedamp  mixtures  are  very  similar 


VENTILATION  OF  MINES  871 

to  those  of  ethane.  In  chemical  analyses,  they  are  commonly  determined  with 
the  methane  or  ethane  and  are  sometimes  reported  as  paraffins. 

Ethylene  and  Other  Olefin  Gases.  —  Ethylene,  otherwise  known  as  ethane, 
and  olefiant  gas,  formula  Ctlh,  is  the  principal  member  of  the  olefin  series  of 
gases  having  the  general  formula  CnHzn.  It  is,  perhaps,  a  rather  more  abun- 
dant constituent  of  some  firedamps  than  ethane,  although  such  a  large  maximum 
as  37.62%  has  not  been  reported  for  it.  Chamberlain  found  .02  to  .26%  of 
ethylene  and  ethylene  and  carbon  monoxide  jointly,  respectively,  in  feeder 
gas  from  Cardiff,  111.,  and  .49%  of  ethylene  in  gas  escaping  from  a  borehole 
near  Wilkes-Barre,  Pa.  Small  amounts  of  ethylene  are  not  uncommon  in 
natural  gas;  it  is  a  usual  constituent  of  producer  and  by-product  coke-oven 
gas,  and  to  its  presence  is  due  the  illuminating  power  of  coal  gas  distilled 
from  coal. 

Ethylene  is  colorless,  has  a  slight  ethereal  odor,  and  is  said  to  have  a 
mild  sweetish  taste.  It  is  a  trifle  lighter  than  air,  is  non-poisonous  although 
suffocating  like  nitrogen  and  methane,  is  combustible,  and  is  explosive  between 
the  limits  of  about  4  and  22%  in  air  according  to  the  reaction  (in  oxygen) 
C2#4+3O2  =  2CO2+2#2O.  The  gas  ignites  and  burns  with  a  very  brilliant 
flame  at  about  1,020°  F.,  its  point  of  maximum  explosibility  being  reached 
when  it  constitutes  5.21%  of  the  air. 

As  with  ethane,  the  tendency  of  ethylene  is  to  increase  the  explosibility 
of  firedamp  mixtures,  but  its  influence  is  not  as  great  as  it  rarely  forms  as 
much  as  1%  of  a  body  of  explosive  gases. 

It  is  possible  that  trifling  amounts  of  propylene,  CsHe,  and  butylene,  CtHs, 
the  next  higher  gases  in  the  olefin  series  are  present  with  ethylene.  If  so,  they 
have  not  been  separately  determined  but  are  included  in  the  ethylene  or  are 
reported  under  the  head  of  olefin  or  CnHin  gases. 

Hydrogen.  —  Hydrogen,  with  an  atomic  symbol  of  H  and  a  molecular  for- 
mula Hz,  is  of  quite  general  occurrence  in  small  quantities  in  mines.  Based 
on  published  analyses,  the  gas  is  not  a  common  constituent  of  face  or  feeder 
gas,  although  Mr.  Austin  King  reports  2.04%  in  the  gases  taken  from  a  crevice 
in  a  mine  roof  and  7.35%  in  the  gases  from  a  hole  drilled  into  the  solid.  From 
a  trace  to  as  much  as  8  or  9%  are  found  in  the  crevices  of  the  coal  face  after 
blasting,  where  it  is  formed  in  part  as  an  incomplete-combustion  product  of 
the  powder  and  in  part  by  distillation  of  the  coal.  It  appears  to  be  always 
present  in  amounts  up  to  2%  or  more  in  the  gases  from  gob  and  ordinary  mine 
fires,  and  is  an  almost  universal  constituent  of  the  afterdamp  of  coal-dust 
explosions  where  it  results  from  distillation  from  the  coal  or  the  incomplete 
combustion  of  methane  and  other-  hydrocarbons.  It  is  found  in  natural  gas 
sometimes  to  the  extent  of  25  to  30%,  commonly  forms  nearly  or  fully  one-half 
of  coal  gas,  and  is  present  in  large  amounts  in  all  types  of  manufactured  gas. 

Hydrogen  is  odorless,  colorless,  and  tasteless,  is  the  lightest  substance 
known,  is  non-poisonous  but  is  suffocating  like  methane,  etc.  It  is  com- 
bustible and  is  explosive  between  the  limits  of  5  and  72%  in  air,  having  the 
greatest  explosive  range  of  any  of  the  true  mine  gases.  It  ignites  at  a  tempera- 
ture between  1,030°  and  1,130°  F.,  and  burns  with  an  almost  colorless  bluish 
flame  and  with  the  production  of  intense  heat,  according  to  the  reaction  (in  oxy- 
gen) 2#2  +  O2  =  2H?O.  As  the  water  vapor  condenses,  the  afterdamp  from  the 
explosion  of  pure  hydrogen  in  air  is  nitrogen  only. 

As  its  explosive  range  is  much  wider  and  it  occurs  so  much  more  frequently 
and  abundantly,  its  effect  in  increasing  the  explosibility  of  firedamp  mixtures 
is  much  more  marked  than  that  of  any  other  gas. 

Acetylene.  —  Acetylene,  formula  C2.H2,  is  the  only  gas  of  the  series  having 
the  general  formula  Cn//2n-2,  that  is  found  in  mines.  It  is  reported  only  as 
a  constituent  of  afterdamp  resulting  from  the  explosion  of  methane  in  a  marked 
deficiency  of  oxygen.  Acetylene,  and  the  next  higher  gas  in  the  same  series, 
allylene  CaH*,  are  minor  constituents  of  coal  gas. 

Acetylene  is  colorless,  tasteless,  and  has  an  ethereal  odor  that  has  by  some 
been  likened  to  that  of  geranium.  It  is  slightly  poisonous  and  is  suffocating. 
It  is  combustible  and  is  explosive  between  the  limits  of  3  and  82%  in  air, 
having,  probably,  the  greatest  explosive  range  of  any  gas.  It  ignites  at  about 
900°  P..  and  burns  with  an  intensely  brilliant  flame  and  much  smoke  except 
in  properly  designed  burners,  according  to  the  reaction  (in  oxygen)  2CzHz+ 


--. 

Hydrogen  Sulphide.—  Hydrogen  sulphide,  formula  H2S,  and  otherwise 
known  as  sulphuretted  hydrogen,  or  stinkdamp,  is  colorless,  has  a  sweetish  taste 
and  a  very  distinctive  odor  of  decayed  eggs,  as  little  as  .01%  in  air  being 
capable  of  detection  by  this  means.  The  gas  is  even  more  poisonous  than 


872  VENTILATION  OF  MINES 

carbon  monoxide,  is  combustible,  and  is  explosive  with  violence  when  present 
to  the  extent  of  12.5%  in  air,  the  point  of  maximum  explosibility  being  reached 
at  14.2%.  The  reaction  for  its  burning  in  oxygen  is  2HzS+3Oz  =  2.H2O  +  2SO2. 

Hydrogen  sulphide  is  produced  in  mines  by  the  burning  of  black  powder 
and  those  of  the  higher  explosives  of  less  than  40%  strength  that  contain 
sulphur  as  a  combustible.  The  amount  of  this  gas  in  powder  smoke  varies  from 
a  trace  to  as  much  as  15  to  20%  or  more,  the  proportion,  in  a  great  measure, 
depending  on  the  amount  of  moisture  present.  It  is  also  formed  by  the  decay 
of  animal  and  vegetable  substances  containing  sulphur,  by  the  action  of  acid 
waters  on  metallic  sulphides  (particularly  iron  pyrites),  by  the  heating  of 
sulphides  in  the  presence  of  moisture  as  in  gob  fires,  by  the  distillation  of  coal 
containing  sulphur  when  the  hydrogen  and  sulphur  unite  directly,  and  by  the 
reducing  action  upon  sulphates  of  bacteria  in  foul  and  stagnant  water.  When 
absorbed  by  water,  the  gas  is  readily  given  off  on  stirring,  and  care  should  be 
taken  not  to  .disturb  a  pool  known  or  supposed  to  contain  it.  Very  small  quanti- 
ties of  the  gas  are  sometimes  found  in  feeder  and  blower  gas,  and  it  is,  at  other 
times,  carried  into  the  mine  in  solution  in  water  from  the  containing  rocks. 

The  gas  is  an  irritant  poison  affecting  the  nostrils  and  other  approaches  to 
the  lungs,  the  eyes,  brain,  and  all  the  tissues,  although,  unless  in  large  amount 
it  does  not  appear  to  effect  a  change  in  the  blood  as  does  carbon  monoxide. 
One  of  the  first  symptoms  of  very  small  amounts  is  irritation  of  the  air-passages 
accompanied  by  an  inflammation  of  the  eyes,  which  feel  as  if  full  of  dust.  In 
larger  amounts,  according  to  Lehmann,  the  gas  causes  nausea,  giddiness,  cold 
skin,  labored  breathing,  irregular  action  of  the  heart,  and  pains  in  the  stomach. 
Death  follows  quickly  after  unconsciousness  (which  comes  very  rapidly  in 
cases  of  hydrogen-sulphide  poisoning),  and  is  frequently  accompanied  by 
delirium,  convulsions,  and  lockjaw.  As  little  as  .05%  will  prove  fatal  if 
breathed  for  some  time,  .07%  in  1  hr.,and  .20%  in  a  few  minutes.  The  after- 
effects of  this  poisoning,  like  those  of  carbon  monoxide,  are  frequently  severe, 
long  continued,  and  even  permanent. 

One  of  the  immediate  effects  of  hydrogen  sulphide  in  dangerous  quantities 
is  a  deadening  of  the  sense  of  smell,  which  ceases  to  be  a  guide  to  the  detection 
of  the  gas.  A  simple  test  for  the  presence  of  this  gas  may  be  made  by  dipping 
a  piece  of  paper  in  acetate  of  lead  (sugar  of  lead) ,  and  allowing  it  to  dry.  Upon 
exposure  to  air  containing  even  a  trace  of  the  gas,  the  paper  is  immediately 
blackened  by  the  formation  of  lead  sulphide. 

Sulphur  Dioxide. — Sulphur  dioxide,  formula  SOz,  appears  to  be  formed 
during  mine  fires  by  the  burning  of  coals  containing  pyrites  by  the  reaction 
(in  oxygen)  4:FeSz+llOz  =  2FezO3,  +  8SOz,  and  possibly  by  the  decomposition 
of  sulphates  previously  formed  by  the  slow  oxidation  of  pyrites  according  to 
the  reaction,  2FeSO4  =  FezO3+SO2+SO3. 

Sulphur  dioxide  is  colorless,  has  a  suffocating  irritating  smell,  and  a  pro- 
nounced taste.  It  is  more  than  twice  as  heavy  as  air  and  is  incombustible, 
sometimes  being  used  instead  of  carbon  dioxide  to  extinguish  mine  fires. 

The  gas  is  very  soluble  in  water  forming,  it  is  believed,  sulphurous  acid  by 
the  reaction  HzO [  +  SOz  =  HzSOs.  As  the  gas  is  absorbed  by  the  moisture  in 
the  throat,  nostrils,  etc.,  it  is  probably  as  sulphurous  acid  and  not  as  sulphur 
dioxide  that  this  gas  acts  on  the  system.  The  gas  appears  to  decompose  the 
red  corpuscles  of  the  blood,  is  fatal  in  extremely  small  amounts,  and  its  symp- 
toms in  producing  irritation  of  the  air-passages,  lungs,  eyes,  etc.,  with  accom- 
panying congestion,  are  similar  to  those  of  hydrogen  sulphide.  However,  much 
smaller  amounts  of  it  than  of  the  sulphide  are  dangerous.  Thus,  Lehmann 
says  that  as  little  as  .001%  produces  some  slight  irritation  of  the  mucuos  mem- 
brane and  respiratory  organs,  which  is  pronounced  when  the  percentage  rises 
to  .003.  In  the  case  of  rabbits,  .04%  causes  congestion  of  the  chest  and 
inflammation  of  the  air-passages  and  eyes,  and  .10%  causes  death  in  a  few 
seconds. 

Nitric  Oxide  and  Nitrogen  Di9xide. — When  high  explosives  containing 
nitroglycerine  and  nitro-substitution  compounds  are  burned  rather  than 
exploded,  they  do  not  yield  carbon  dioxide  and  nitrogen  but  their  gases  of 
combustion  contain  large  quantities  of  carbon  monoxide  and  nitric  oxide,  NO, 
which  latter,  on  contact  with  air  is  at  once  converted  into  the  red  fumes  of 
nitrogen  dioxide  NOz,  by  the  reaction  2NO  +  Oz  =  2NOz.  Haldane  shows  that 
when  nitroglycerine  is  exploded,  the  gases  of  combustion  contain  63.2%  COz 
and  31.6%  Nz,  but  when  burned  in  the  presence  of  its  own  gases,  they  con- 
tained 35.9%  CO  and  48.2%  NO.  Clarence  Hall  found  in  the  gases  resulting 
from  the  burning  of  ordinary  40%  strength  gelatine  dynamite,  13.7%  CO, 
11.3%  NO,  and  .6%  NO2, 


VENTILATION  OF  MINES  873 

The  conditions  causing  the  burning,  all  or  in  part,  of  nitro-explosives 
instead  of  their  detonation,  are  poor  quality  of  the  explosive,  improper  tamp- 
ing, the  use  of  detonators  of  insufficient  strength  of  or  defective  fuses,  and  the 
actual  burning  of  a  quantity  of  the  explosive  by  a  fire  carelessly  started. 

Haldane  claims  that  nitrous  fumes,  NOz,  are  even  more  poisonous  than 
those  of  HzS  and  says  that  no  gas  met  in  mines  is  so  treacherous  in  its  effects. 
These  fumes  act  as  an  irritant  to  the  eyes,  nose,  and  throat  not  dissimilar  to 
that  of  hydrogen  sulphide  and  sulphur  dioxide,  but  whereas  the  after-effect  of 
recovery  from  the  last-named  gas  is  a  temporary  catarrh,  with  nitrous  fumes 
there  is  great  danger  of  intensely  acute  bronchitis,  which  is  often  fatal.  While 
temporary  irritation  and  apparent  recovery  may  be  experienced  at  the  time  of 
exposure,  these  are  frequently  followed  by  the  development  of  bronchitis  in 
a  few  hours  and  this  is  frequently  fatal  in  2  da.  Mice  forced  to  breath  air 
containing  but  .05%  of  thesaifumes  for  1  hr.,  and  which  apparently  recovered, 
died  within  24  hr.  of  bronchitis. 

Nitrous  fumes  are  easily  detected  by  their  smell,  even  when  greatly  diluted, 
and  care  should  be  taken  in  returning  to  the  face  if  this  smell  is  at  all  notice- 
able. Minute  traces  of  the  gas  may  be  detected  by  exposing  in  the  suspected 
air  a  paper  soaked  in  a  solution  of  starch  and  potassium  iodide;  if  any  nitric 
oxide  is  present,  the  starch  is  at  once  turned  blue  by  the  iodine  set  free. 

EFFECT  OF  HEAT  AND  HUMIDITY  ON  MINE  WORKERS 

The  mean  annual  underground  temperature  of  the  mines  of  the  United 
States  is  probably  about  10°  more  than  that  of  the  surface,  and  is  between 
60°  and  65°  F.  The  causes  making  for  this  increase  in  temperature  are  the  heat 
given  off  by  men  and  animals,  by  the  burning  of  lamps,  by  the  oxidation  of 
animal  and  vegetable  substances  (as  the  decay  of  timber),  by  the  slow  oxidation 
of  the  coal,  by  gob  fires  whether  active  or  smoldering,  by  the  detonation  of 
explosives,  and  by  the  interior  heat  of  the  earth.  In  deep  mines,  the  effect 
of  increasing  heat  with  increasing  depth  is  of  prime  importance  in  raising 
underground  temperatures.  Below  the  level  of  no  annual  variation  which,  in 
temperate  climates  is  some  60  ft.  below  the  surface,  the  temperature  increases 
at  a  rate  of  from  1°  F.  in  100  ft.  to  1°  F.  in  60  ft.,  or  about  1°  F.  for  each  80  ft. 
of  descent.  A  mine  1,000  ft.  deep  in  a  region  as  western  Pennsylvania  and 
Ohio,  where  the  mean  annual  temperature  is  about  55°,  may  reasonably  be 

expected  to  have  an  average  temperature  of  55°+  (""HQ )  =67°,  about, 

due  to  the  interior  heat  of  the  earth  alone.  To  this  must  be  added  an  always 
uncertain  amount,  perhaps  as  much  as  2°  to  3°,  for  the  heat  arising  from  the 
other  causes  named. 

Whether  the  temperature  of  the  ventilating  current  will  be  greater  or  less 
than  the  temperature  established  by  the  preceding  conditions  depends  on  its 
initial  temperature  and  its  velocity.  Radiation  from  the  side  walls  is  constant 
but  slow  and  rapid  currents  of  air  will  not  absorb  as  much  heat  as  those  moving 
slowly;  consequently,  at  the  face  or  in  any  tight  place  the  temperature  is 
much,  often  5°  or  10°,  greater  than  on  the  entries  where  the  air  is  circulating 
freely.  Haas  found  that  in  a  certain  mine  entry  4,000  ft.  long,  over  30,000 
B.  T.  U.  a  min.  were  radiated  from  the  sides,  which  is  equivalent  to  the  heat 
derived  from  burning  more  than  1  T.  of  coal  a  day.  In  regard  to  the  initial 
temperature  of  the  air,  Scholz  found  at  certain  mines  in  the  Middle  West  that 
during  summer,  when  the  temperature  outside  averages  85°  F.  for  24  hr.,  with  a 
maximum  of  95°  to  100°,  the  mine  temperatures  fluctuated  between  70°  and  78  ; 
and  that  during  winter,  with  a  temperature  of  40°  to  50°  outside,  the  mine 
temperatures  ranged  from  60°  to  67°,  the  exact  temperature  necessarily  depend- 
ing somewhat  on  the  extent  of  the  mine.  As  the  average  annual  temperature 
of  the  region  in  question  cannot  be  far  from  55°,  it  would  appear  that  at  : 
times  (even  in  winter)  the  temperature  of  the  mine  is  considerably  above  t 
annual  for  the  place. 

As  long  as  the  mine  air  is  dry,  or  relatively  so,  men  can  work  m  temperatures 
as  high  as  90°  and  even  100°  without  much  discomfort  or  impairment  of  health, 
as  the  perspiration  is  rapidly  absorbed  by  the  air-currents.  But  it  has  been 
shown  that,  regardless  of  the  outside  temperature  and  humidity,  the  return 
air  is  usually  saturated  to  the  extent  of  90%  or  more,  except  in  the  and  regions 
of  the  West,  where  the  humidity  may  fall  to  85%.  Haldane  states  that  in 
still  and  moist  air  it  is  hardly  possible  for  men  to  do  continuous  hard  work  at 
temperatures  of.  80°  t->  85°  even  when  stripped  to  the  waist.  At  temperatures 


874  VENTILATION  OF  MINES 

above  90°,  by  the  wet  bulb,  it  is  only  possible  to  work  for  short  periods,  and 
it  becomes  increasingly  difficult  to  remain  in  the  place  even  without  working. 
Haldane  found  that  at  a  temperature  of  93°  in  still  and  saturated  air  and 
doing  practically  no  work,  his  temperature  rose  5°  in  2  hr.  and  was  still  rising 
rapidly  when  he  found  it  necessary  to  go  out. 


SAFETY  AND  OTHER  LAMPS 
PRINCIPLE  AND  ORIGIN  OF  SAFETY  LAMPS 

Description. — In  a  safety  lamp,  the  flame  of  the  burning  illuminant  is  iso- 
lated from  direct  contact  with  the  mine  air  by  a  wire  gauze,  or  a  glass  and  gauze 
cylinder,  which  is  closed  at  the  top  where  it  is  covered  by  a  hood  to  which  is 
attached  a  ring  or  hook  for  carrying.  As  a  further  means  of  isolating  the  flame, 
there  may  be  two  or  more  gauzes  with  an  air  space  between  each,  and  in  prac- 
tically all  lamps  the  outer  gauze  is  surrounded  by  a  shield,  called  a  bonnet, 
which  is  provided  with  perforations  or  slots.  The  various  parts  of  the  lamp 
are  securely  held  together  by  the  necessary  standards  and  screw,  soldered,  or 
riveted  joints. 

Dates  of  Discovery. — The  principle  of  isolating  the  flame  of  the  lamp  was 
evolved  by  Dr.  William  R.  Clanny  in  the  spring  of  1813,  although  his,  the  first 
safety  lamp,  did  not  receive  its  final  and  successful  trial  until  Oct.  16,  1815. 
The  principle  of  the  bonnet  was  demonstrated  on  Nov.  28,  1815,  by  George 
Stephenson;  and  on  Dec.  15  of  the  same  year,  Sir  Humphrey  Davy  announced 
the  use  of  the  wire  gauze. 

Principles  of  the  Safety  Lamp. — Although  the  last  to  be  made  public,  the 
principle  discovered  by  Davy  is  the  first  in  importance.  This  principle  is  that, 
while  a  wire  gauze  of  fine  mesh  entirely  surrounding  the  flame  will  permit  the 
free  entrance  of  air  within  the  lamp,  yet  in  its  outward  passage  through  the 
gauze  the  burning  gas  is  broken  up  into  a  series  of  fine  jets  and  is  so  reduced 
in  temperature  by  the  cool  metal  that  its  flame  is  extinguished  and,  hence, 
cannot  ignite  firedamp  mixtures  outside  the  lamp. 

In  Stephenson's  lamp,  the_  burning  gas  was  extinguished  not  by  a  cool 
metal  gauze,  but  by  bringing  it  in  contact  with  the  inert  products  of  combustion 
that  were  held  in  the  upper  part  of  the  lamp  between  the  bonnet  and  the  gauze. 
While,  in  modern  lamps  the  bonnet  plays  in  a  greater  or  less  degree  the  part 
for  which  it  was  originally  intended,  its  chief  use  is  to  prevent  the  direct  impact 
against  the  gauze  of  air-currents  of  high  velocity  which  might  extinguish  the 
lamp  or,  what  is  more  dangerous,  might  force  the  flame  against  or  through 
the  gauze  and  thus  cause  an  explosion.  When  the  blanketing  effect  of  the 
original  bonnet  is  desired,  it  is  now  generally  accomplished  through  the  use  of 
double  or  triple  gauzes  as  in  the  Marsaut  lamp. 

Safety  lamps  are  not  absolutely  safe  in  the  sense  that  they  may  be  burned 
indefinitely  in  explosive  mixtures  of  gas  and  air.  In  comparison  with  the 
unprotected  candles  that  they  replaced  or  with  modern  open  lights,  they  are 
relatively  safe  in  that  the  warning  of  the  presence  of  a  dangerous  amount  of 
gas  afforded  by  its  burning  within  the  lamp,  gives  the  miner  time  to  withdraw 
before  an  explosion  takes  place. 

Early  Classification  of  Safety  Lamps. — Safety  lamps  were  formerly  divided 
into  two  general  classes,  those  designed  for  testing  for  gas  and  those  intended 
for  working  lamps,  the  construction  of  the  former  being  such  that  they  were 
the  more  sensitive  to  gas.  This  distinction  in  usage  and  construction  is  now 
rarely  made,  and  at  any  particular  mine  the  same  kind  of  lamp  is  commonly 
used  by  fireboss  and  miner  alike.  The  reason  for  this  is  that  none  but  special 
lamps  in  the  hands  of  skilled  observers  can  detect  the  less  than  1  %  of  gas  that 
is  dangerous  in  the  presence  of  explosive  coal  dust.  Such  being  the  case,  there 
is  nothing  to  be  gained  in  providing  a  fireboss  with  a  dangerous  lamp  (all  sen- 
sitive lamps  are  unsafe)  t9  detect  2.5%  of  gas  when  a  safe  lamp  will  detect, 
say,  3%;  as  these  proportions  of  gas  are  equally  dangerous  when  coal  dust  is 
present  and  equally  harmless  when  it  is  not. 

Approved  Safety  Lamps. — An  approved  safety  lamp  possesses  those  features 
•that  a  mining  department  or  legislature  declares  essential  in  lamps  to  be  used 
within  its  jurisdiction.  The  features  considered  essential  vary,  but  both  here 
and  in  Europe,  to  be  approved,  a  lamp  must  have  a  bonnet.  The  Davy  lamp, 
not  being  safe  with  or  without  a  bonnet,  is  not  permitted  in  Europe,  but  is 
allowed  in  a  few  American  states  for  gas  testing,  although  the  number  of  states 
permitting  it  is  decreasing. 


VENTILATION  OF  MINES  875 

SAFETY-LAMP  CONSTRUCTION 

Specifications. — Mr.  J.  W.  Paul  sums  up  the  structural  requirements  of 
safety  lamps  as  follows: 

1.  The  framework  should  be  rigid  and  well  made  so  that  it  will  not  get 
out  of  shape  when  roughly  handled; 

2.  If  the  lamp  has  a  glass  chimney,  the  upright  rods  (standards)  should 
be  of  such  number  and  so  spaced  that  a  straightedge,  or  ruler,  placed  against 
any  two  adjacent  rods  will  not  touch  the  glass; 

3.  If  a  lamp  has  no  bonnet,  the  gauze  should  be  protected  with  rods  in 
the  same  manner  as  the  chimney,  as  indicated  in  2; 

4.  The  lock  should  be  such  as  will  require,  .when  locked,  a  special  device 
for  unlocking; 

5.  The  glass  chimney  should  have  a  smooth  and  even  wall  throughout, 
should  be  of  the  best  quality,  and  should  have  its  ends  ground  truly  parallel 
and  at  right  angles  to  the  axis  of  the  chimney.     The  chimney  should  bear  the 
trade-mark  of  the  manufacturer; 

6.  When  the  lamp  is  assembled  there  should  be  no  openings  between  the 
outside  and  the  interior  of  the  lamp  except  those  in  the  gauze  or  other  heat- 
absorbing  device,  such  as  a  perforated  plate  or  cylinder  in  which  the  size  of 
the  perforations  corresponds  with  that  of  the  gauze  openings; 

7.  The  handle  of  the  lamp  should  be  either  an  open  ring  or  a  hook,  strongly 
made  and  not  easily  bent  in  the  hand; 

8.  The  construction  of  the  lamp  should  be  such  that  its  parts  are  made 
in  standard  uniform  sizes  and  fit  so  intimately  that  should  any  part  be  omitted 
in  assembling  its  absence  would  be  easily  detected  by  the  most  casual  inspection ; 

9.  There  should  be  an  expansion  ring  or  equivalent  device  used  with  the 
glass  chimney  so  that  the  chimney  when  heated  can  expand  without  breaking 
any  part  of  the  lamp;- 

10.  In  the  selection  of  a  safety  lamp,  carefully  examine  each  of  the  dis- 
assembled parts  to  ascertain  defects  or  improper  construction;  if  any  such  is 
discovered,  the  entire  lamp  should  be  rejected. 

Design  of  Safety  Lamps. — As  pointed  out  by  Hughes,  Marsaut  and  others 
have  shown  that  a  certain  relation  should  exist  between  the  volume  contained 
within  a  lamp  and  the  gauze  surface  open  for  the  escape  of  the  products  of 
combustion  resulting  from  an  internal  explosion,  as  experiments  have  proved 
that  the  ignitions  of  explosive  mixtures  outside  the  lamp  by  explosions  within 
it  become  less  frequent  as  the  open  surface  of  the  gauze  is  enlarged. 

Marsaut  also  proved  that:  (1)  A  lamp  of  small  diameter  (such  as  a  Davy) 
does  not  readily  pass  an  explosion,  as  the  volume  of  gas  that  can  be  exploded 
is  insignificant.  (2)  A  lamp  without  a  glass  is  more  secure  against  the  effects 
of  internal  explosions  than  a  lamp  with  a  glass  cylinder,  as  the  latter  confines 
the  gases  at  the  time  of  an  explosion  and  acts  like  a  cannon;  it  is,  therefore, 
advisable  to  reduce  both  the  height  and  the  diameter  of  the  glass.  (3)  A  wire 
gauze  of  conical  shape  is  more  secure  against  the  transmission  of  internal 
explosions  than  is  one  of  cylindrical  shape  and  of  the  same  capacity.  (4)  Gases 
resulting  from  combustion  play,  a  certain  part  in  preventing  external  explo- 
sions and  it  might,  therefore,  not  be  advisable  to  guide  them  by  a  chimney. 
(5)  A  descending  current  of  feed-air  prevents  the  filling  up  of  glass  lamps  with 
an  explosive  mixture,  and  occasions  the  formation  of  an  inexplosive  and  elastic 
cushion  at  the  bottom  of  the  lamp. 

Materials  of  Construction. — With  the  exception  of  the  gauze  and  glass, 
the  various  parts  of  safety  lamps  are  made  of  brass  or,  where  lightness  is 
required,  of  aluminum  or  magnalium.  Where  iron  enters  into  the  construc- 
tion, it  is  usually  in  the  standards  and  hood. 

Safety-Lamp  Gauzes. — The  main  gauze  of  safety  lamps  is  of  28  mesh; 
that  is,  there  are  28  openings  in  1  lin.  in.  or  784  openings  in  1  sq.  in.  If  made 
of  No.  28  (B.  W.  G.)  wire  .014  in.  in  diameter  as  is  usual,  1  sq.  in.  of  the  gauze 
will  be  about  two-thirds  (.6151  sq.  in.)  metal  and  one-third  (.3849  sq.  in.) 
openings.  As  exceptions  to  the  use  of  this  standard  gauze,  those  in  the  Marsaut 
and  Chesneau  lamps  have  934  and  1,264  openings  per  sq.  in.,  respectively. 

Gauzes  are  commonly  made  of  iron  wire,  although  copper  is  sometimes 
used.  The  latter  is  rather  more  durable  than  iron  as  it  does  not  rust  or  burn 
out  so  quickly,  but  it  becomes  hot  and  passes  the  flame  sooner  than  iron  as  it 
has  a  higher  specific  heat. 

The  gauze  cylinder  must  not  exceed  a  certain  size,  which  Davy  fixed  m  his 
original  lamp  as  2  in.  in  diameter  and  7  in.  high  (contents  22  cu.  in.),  otherwise 
the  burning  of  the  large  volume  of  gas  within  it  will  heat  the  gauze,  and  par- 


876  VENTILATION  OF  MINES 

ticularly  the  top,  to  a  point  where  it  will  no  longer  cool  the  flame  sufficiently 
to  prevent  its  igniting  gas  outside  the  lamp.  In  modern  lamps,  the  diameter 
of  the  gauze  is  about  the  same  as  that  of  the  original  Davy,  but  its  height  is 
less  and  varies  from  4  to  5  in.,  as  the  lower  part  is  replaced  with  glass.  In 
lamps  built  on  the  Eloin  principle,  that  is  in  those  lamps  that  take  air  in 
through  ports  below  the  flame  and  are  thence  known  as  underfeed  or  under- 
draft  lamps,  as  all  the  gauze  is  available  for  the  discharge  of  the  combustion 
products,  it  may  be  made  much  smaller  than  in  a  lamp  of  ordinary  construc- 
tion. The  Ashworth-Hepplewhite-Gray  lamp,  Fig.  1,  e,  page  885,  is  an  example 
of  a  lamp  with  a  relatively  small  gauze. 

As  the  top  of  the  gauze  receives  the  full  effects  of  the  flame,  it  is  often 
reinforced  by  what  is  known  as  a  gauze  cap  or  smoke  gauze.  This  consists  of  a 
cylinder  of  standard  gauze  closed  at  the  top,  which  fits  snugly  over  the  main 
gauze  for  about  one- third  its  length.  The  upper  part  of  this  cap  is  sometimes 
crimped  or  indented  so  that  it  may  not  be  pushed  too  far  down  upon  the  main 
gauze  as  it  is  desirable  to  leave  a  small  space  between  the  tops  of  the  two. 

The  gauze  of  the  early  lamps  was  always  cylindrical,  but  in  many  modern 
lamps  it  is  in  the  form  of  a  truncated  cone;  a  shape  commonly  followed  where 
there  is  more  than  one  gauze. 

Safety  Lamp  Glasses. — Although  Clanny  and  Stephenson  used  glass  in 
front  of  their  original  (1815)  lamps  to  increase  the  light-giving  power,  the  pres- 
ent form  of  safety  lamp  in  which  a  glass  cylinder  entirely  surrounds  the  flame 
and  is  surmounted  by  a  cylinder  of  gauze  is  due  to  Dr.  Clanny  who  appears 
to  have  combined  ideas  original  with  both  Davy  and  Stephenson.  In  a  gen- 
eral way,  modern  lamps  may  be  said  to  be  Davy  lamps  in  which  the  lower  por  - 
tion  of  the  gauze  cylinder  is  replaced  with  one  of  glass;  or  to  be  Stephenson 
lamps,  the  perforated  metal  cylinder  being  replaced  by  one  of  gauze. 

Glasses  are  commonly  cylindrical,  but  in  the  Ashworth-Hepplewhite-Gray 
lamp  they  have  the  shape  of  an  upward-tapering  truncated  cone.  This  form 
allows  the  upward  diffusion  of  the  light,  at  least  in  pary,  and  thus  permits  of 
a  closer  inspection  of  the  roof  without  having  recourse  to  the  very  dangerous 
practice  of  turning  the  lamp  on  one  side.  t 

Multiple  Gauzes. — Some  safety  lamps  are  made  with  two  or  even  three 
gauzes,  one  within  the  other,  with  a  small  air  space  between;  and  lamps  so 
made  are  known  as  multiple-gauze  lamps.  The  inner  gauze  is  always  conical 
but  the  outer  gauze  may  be  cylindrical  or  conical  with  a  little  more  slope  than 
the  inner  one  so  that  there  may  be  more  air  space  between  the  gauzes  at  the  top 
than  at  the  bottom.  The  intention  of  multiple  gauzes  is  to  interpose  one  or 
more  curtains  or  screens  of  inert  gases  between  the  flame  of  any  gas  burning 
in  the  lamp  and  the  outside  air.  These  screens  are  formed  by  the  retention 
of  the  products  of  combustion  in  the  spaces  between  the  several  gauzes.  The 
multiple  gauze  is  the  modern  development  of  the  original  Stephenson  prin- 
ciple of  preventing  the  outward  passage  of  the  flame  by  smothering  it  in  inert 
gases,  and  adds  greatly  to  the  safety  of  the  lamp. 

The  effect  of  these  gas  screens  is  to  impede  the  free  upward  and  outward 
passage  of  the  products  of  combustion  simultaneously  reducing  the  amount  of 
oxygen  admitted  to  the  flame  and  the  amount  of  oil  burned  in  a  given  time.  In 
other  words,  they  reduce  the  draft  and  thus  increase  the  tendency  of  the  lamp 
to  smoke  and  diminish  the  illuminating  power.  The  reduction  in  illuminating 
power  increases  with  the  number  of  gauzes.  Thus,  the  Marsaut  lamp,  Fig.  1,  d, 
page  885,  with  three  gauzes  has  an  illuminating  power  20  to  25%  less  than 
the  same  lamp  with  two  gauzes.  In  lamps  admitting  air  on  the  Eloin  principle 
and  which,  in  consequence,  have  a  strong  natural  draft,  the  reduction  in 
illuminating  power  through  the  use  of  multiple  gauzes  is  considerably  less 
than  in  lamps  drafted  in  the  ordinary  way.  With  multiple  gauzes,  the  gauze 
cap  (smoke  gauze)  is  rarely  used. 

Safety-Lamp  Bonnets. — A  bonnet  consists>  of  a  metal  cylinder  entirely  sur- 
rounding the  gauze  of  the  safety  lamp,  and  is  intended  to  prevent  the  direct 
impact  of  air-currents  of  high  velocity  against  the  gauze,  as  explained  under 
Principles  of  the  Safety  Lamp.  The  surface  of  the  bonnet  is  usually  smooth, 
but  in  the  Wolfe  lamp,  Fig.  1,  /,  page  885,  it  is  corrugated.  The  bonnet  is 
perforated  or  slotted  with  a  varying  number  of  holes  arranged  in  various  ways 
and  which  are  designed  to  permit  access  of  air  to  and  egress  of  combustion 
products  from  the  lamp.  In  some  bonnets,  the  slots  are  indented  on  one  side 
or  arranged  on  the  corrugations  (Wolfe  lamp)  so  that  the  air  enters  tangentially 
and  not  directly  against  the  gauze.  In  the  early  Davy  lamp,  the  screening 
effect  of  the  bonnet  was  secured,  but  only  in  part,  by  the  use  of  a  semicircular 
shield  that  could  be  slipped  in  front  of  the  flame  when  moving  against  the  air. 


VENTILATION  OF^  MINES  877 

The  fewer  the  perforations  or  slots,  the  greater  the  blanketing  effect  of 
the  bonnet  and  the  more  nearly  it  approaches  a  series  of  gauzes  in  its  influence 
on  the  circulation  of  air  within  the  lamp  and  on  its  light-giving  power.  Lamps 
with  tight-fitting  bonnets  are  easily  extinguished  when  exposed  in  high  per- 
centages of  gas,  the  flame  being  smothered  by  the  large  volume  of  combustion 
products  held  back  by  the  imperfect  circulation. 

In  the  Ash worth-Hepplewhite- Gray  lamp,  a  double  bonnet  is  used,  and 
double-  and  triple-gauze  lamps  are  always  bonneted  for  general  use  and  com- 
monly so  when  employed  for  gas  testing.  f 

Circulation  of  Air  in  Safety  Lamps. — Air  is  admitted  to  safety  lamps  in  three 
ways. 

In  the  Davy  lamp,  Fig.  1,  a,  page  885,  the  air  enters  at  the  bottom  of  the 
gauze,  which  extends  below  the  top  of  the  wick  tube,  and  the  products  of 
combustion  pass  upwards  and  out  through  the  top  of  the  gauze. 

In  underdraft  lamps  (Eloin  principle)  as  in  Fig.  1,  e,  page  885,  the  air 
enters  below  the  flame  through  gauze-protected  ports,  and  the  products  of 
combustion  follow  the  same  course  as  in  the  Davy  lamp. 

In  the  majority  of  lamps,  Fig.  1,  b,  c,  and  d,  page  885,  the  air  enters  at  the 
base  of  the  gauze  above  the  glass  and  must  pass  downwards  to  the  flame. 

Lamps  of  the  first  two  classes,  in  which  the  air  follows  what  may  be  called 
the  natural  course  (as  in  an  ordinary  chimney)  are  sensitive  to  small  amounts 
of  gas,  are  apt  to  flame  readily,  are  adapted  to  gas  testing  but  not  to  general 
use,  and  are  unsafe  in  air-currents  of  any  but  very  low  velocity  unless  provided 
with  bonnets  or  multiple  gauzes.  When  so  equipped,  underfed  lamps  are  ex- 
cellent for  general  use,  but  are  not  so  sensitive  to  gas  as  otherwise. 

In  the  third  class,  the  air  in  passing  down  to  the  lamp  flame  conflicts  with 
the  ascending  products  of  combustion  with  the  formation  of  eddy  currents, 
which  may  cause  the  lamp  to  flicker  and  smoke,  thus  making  it  less  sensitive 
to  gas  and  decreasing  its  illuminating  power.  In  the  Mueseler  lamp,  Fig.  1,  c, 
page  885,  the  flame  is  surmounted  with  a  conical  sheet-iron  chimney,  which 
increases  the  draft  and  causes  the  air  to  circulate  in  a  natural  course.  Follow- 
ing the  arrows,  the  air  enters  through  the  base  of  the  gauze,  passes  down  beside 
the  chimney  to  the  wick,  and  the  products  of  combustion  pass  up  the  chimney 
and  thence  out  through  the  upper  part  of  the  gauze  (see  Mueseler  lamp).  It 
should  be  noted  that  a  bonnet  or  a  series  of  multiple  gauzes  interferes  with  the 
rapidity  but  not  with  the  direction  of  air  circulation. 

In  order  to  detect  thin  layers  of  gas  near  the  roof  without  the  dangerous 
necessity  of  turning  the  lamp  on  one  side,  of  waving  it  to  and  fro,  or  of  brushing 
the  top  air  down  upon  it  with  a  cap,  several  special  constructions  are  employed. 
In  the  Ashworth-Hepplewhite-Gray  lamp,  the  standards  are  hollow  and  air 
can,  when  needed,  be  drawn  down  through  them  by  closing  the  regular  entrance 
ports  at  the  base  of  the  lamp.  A  device  for  the  same  purpose  that  may  be 
attached  to  ordinary  lamps  consists  of  an  L-shaped  pipe  about  §  in.  in  diameter, 
the  short  arm  of  which  is  attached  to  a  special  port  in  the  lamp  below  the  flame 
while  the  long  arm  projects  upwards  into  the  gas.  An  improvement  on  the 
preceding  is  used  by  Mr.  Joseph  Smith,  general  superintendent  of  the  Stag 
Canon  Fuel  Co.,  at  Dawson,  N.  Mex.  The  device  consists  of  a  small,  double- 
acting  pump  the  discharge  end  of  which  may  be  directly  connected  to  the 
base  of  any  of  the  standard  forms  of  safety  lamps.  By  means  of  a  number  of 
5-ft.  lengths  of  f-in.  gas  pipe  which  may  be  screwed  together  until  their  com- 
bined length  is  sufficient  to  reach  the  top  of  the  highest  falls  and  then  attached 
to  the  suction  end  of  the  pump,  samples  of  air  from  otherwise  inaccessible 
places  may  be  drawn  into  and  through  the  lamp.  For  the  same  purpose 
Sir  William  Garforth  uses  a  rubber  bulb  with  a  strong  metal  nozzle.  In  the 
base  of  the  safety  lamp  is  a  tube  with  a  self-closing  valve.  When  testing  for  gas, 
the  bulb  is  placed  in  a  cavity  in  the  roof  or  other  place  where  gas  is  suspected, 
and  is  filled  with  the  firedamp  by  compression  in  the  usual  way.  The  gas  is  pre- 
vented from  escaping  by  holding  a  finger  over  the  nozzle  and  the  lamp  is  taken  to 
some  safe  place  where  the  end  of  the  buib  is  inserted  in  the  tube  in  the  lamp, 
opening  the  valve  in  so  doing,  when  the  gas  may  be  squeezed  upon  the  flame. 

Wick  Tubes,  Wicks,  Etc. — The  wick  tube  of  a  lamp  may  be  round  or  flat. 
When  flat,  one  side  is  commonly  made  with  one  or  more  grooves  to  reduce  the 
fricti9n  when  the  wick  is  adjusted  in  height  and  to  provide  a  space  for  the  cir- 
culation of  the  air  that  the  oil  may  ascend.  The  top  of  the  tube  should  be 
set  about  £  in.  above  the  base  of  the  glass  for,  if  set  too  low,  the  shadow  cast 
on  the  ground  by  the  body  of  the  lamp  is  increased;  and  if  set  too  high,  the 
amount  of  light  diffused  upwards  is  decreased.  In  many  lamps,  m  one  side  of 
the  wick  tube  is  a  narrow  slot  in  which  the  point  of  the  picker  is  inserted  to 


878  VENTILATION  OF  MINES 

adjust  the  wick.  This  slot  should  be  as  narrow  and  as  short  as  possible,  other- 
wise the  oil  will  be  vaporized  and  possibly  ignited  at  the  side  rather  than  at 
the  top  of  the  tube.  In  some  lamps,  the  wick  remains  stationary  and  the 
height  of  the  flame  is  adjusted  by  raising  or  lowering  a  sheath  that  fits  over  the 
wick  tube;  and,  in  other  lamps,  the  wick  is  contained  in  an  adjustable  sheath 
sliding  within  a  fixed  wick  tube.  In  either  case,  the  sheath  is  adjusted  by 
turning  a  screw  attached  to  the  bottom  of  a  shaft  passing  through  the  oil 
chamber. 

Wicks  are  round  05  flat  to  correspond  with  the  wick  tube.  They  are  made 
of  strands  of  cotton  yarn  very  lightly  twisted  or  plaited  (flat  wicks)  to  form  a 
bulk  but  slightly  greater  than  the  inside  dimensions  of  the  wick  tube.  Wicking 
should  be  thoroughly  dried  before  use,  as  moisture  impedes  the  flow  of  oil  and 
reduces  the  illuminating  power  of  the  flame. 

The  picker  used  for  cleaning  the  wick  should  sweep  the  entire  top  of  the 
wick  tube  with  a  motion  somewhat  inclined  to  the  horizontal. 

Igniters,  or  Relighters,  for  Safety  Lamps. — An  igniter  is  a  device  for  relight- 
ing a  safety  lamp  without  opening  it.  In  the  igniter  commonly  used  with  the 
Wolf  lamp,  the  match  is  a  narrow  strip  of  paraffined  paper  in  which  are  inserted 
small  lumps  of  fulminate  at  intervals  of  about  %  in.  The  coiled  match  is 
contained  in  a  flat  metal  box  inserted  in  a  special  receptacle  in  the  bowl.  The 
igniter  proper  consists  of  a  piece  of  spring  steel  doubled  on  itself,  one  end  of 
which  is  provided  with  fine  teeth  to  engage  the  match.  By  raising  the  rod 
attached  to  the  igniter,  the  teeth  catch  in  the  match  and  push  its  end  slightly 
above  the  level  of  the  wick.  When  the  rod  is  suddenly  pulled  downwards  by 
means  of  the  head  at  the  bottom  of  the  oil  chamber,  the  teeth  of  the  igniter 
explode  one  of  the  fulminate  caps  thus  igniting  the  match,  which  burns  until 
level  with  the  top  of  the  wick  tube.  In  a  similar  igniter,  a  friction  match  is 
held  against  a  feed-screw  by  a  steel  spring.  The  upper  part  of  the  feed-screw 
carries  a  wheel  with  sharp  teeth  that  strike  against  and  ignite  the  match  when 
a  button  on  the  lower  end  of  the  feed-screw  is  turned.  In  other  igniters, 
phosphorus  is  used  in  place  of  fulminate  to  light  the  match. 

Electric  relighters  are  used  in  some  standard  lamps.  Where  light  oils,  as 
naptha,  giving  off  vapors  are  burned,  a  low-tension  current  is  used  to  heat 
to  incandescence  a  platinum  wire  placed  immediately  over  the  wick  tube. 
For  the  heavier  colza  and  seal  oils,  a  series  of  sparks  produced  by  a  high-tension 
current  are  passed  over  the  wick  tube.  The  current  is  taken  into  the  lamp 
through  a  carefully  insulated  conductor  passing  through  the  bowl,  the  body  of 
the  lamp  furnishing  the  return  circuit.  (See  Protector  Lamp  and  Hailwood 
Lamp.) 

The  property  of  alloys  of  cerium  of  sparking  when  brushed  by  a  milled 
wheel  has  been  taken  advantage  of  in  the  design  of  safety-lamp  igniters.  The 
alloy  commonly  employed  is  one  of  iron  and  cerium  which,  when  struck  by  the 
milled  wheel  after  the  manner  of  a  flint  against  steel,  often  throws  off  unburned 
particles  of  metal,  which  may  lodge  against  the  gauze.  If  these  are  subse- 
quently ignited,  sufficient  heat  may  be  developed  to  fire  the  gas  outside  the 
lamp.  To  overcome  this  difficulty,  the  American  Safety  Lamp  Co.  uses  an 
alloy  of  cerium  and  magnesium  and  a  positive  igniting  device.  In  the  older 
igniters  of  this  type,  a  series  of  small  sparks  are  struck  by  turning  the  milled 
wheel  until  the  lamp  is  lit.  In  the  improvement,  a  spring  attached  to  the 
igniter  is  compressed  by  turning  the  head  of  a  stem  projecting  below  the  bowl. 
When  the  tension  of  the  spring  reaches  a  certain  amount,  the  wheel  is  released 
and  revolves  with  such  rapidity  that  the  spark  is  practically  a  continuous 
flame,  which  ignites  the  wick  at  once. 

Many  have  advised  against  the  relighting  of  lamps  in  the  presence  of 
explosive  amounts  of  gas,  and  particularly  so  if  the  lamp  burns  naphtha  because, 
in  a  few  seconds  after  being  extinguished,  the  gauze  may  become  filled  with 
highly  combustible  vapors  that  may  explode  and  pass  the  flame  when  the 
igniter  is  applied.  The  long  series  of  tests  made  with  the  Wolf  lamp  go  to  show 
that  this  claim  is  not  well  founded.  Others  object  to  placing  an  igniting 
device  in  the  hands  of  miners  and  irresponsible  boys  and  hold  that  an  electric 
relighter,  which  can  only  be  applied  at  a  lamp  station,  is  to  be  preferred  to 
other  types. 

Locks  for  Safety  Lamps. — Locks  for  safety  lamps  are  made  on  one  of  three 
general  plans. 

1.  The  lamp  may  be  locked  by  a  screw  pin,  catch,  or  similar  device  that 
may  be  opened  by  a  key.  While  locks  of  this  type  cannot  be  opened  acci- 
dently,  they  may  be  readily  unlocked  by  any  one  even  without  a  key.  This 
form  of  lock  is  now  rarely  used. 


VENTILATION  OF  MINES  879 

2.  The  lock  may  be  constructed  so  that  it  may  be  opened  by  any  one,  but 
any  attempt  to  do  so  extinguishes  the  light  or  is  revealed  in  some  way. 

3.  The  lamp   may  be   locked  by  a  device   operated  by  electricity  or  com- 
pressed air,  and  can  only  be  opened  by  means  of  special  appliances  kept  in  the 
lamp  room  at  the  surface  or  at  a  relighting  station  in  the  mine. 

To  the  second  class  belongs  the  lead-plug  lock.  The  lower  part  of  the 
lamp  is  encircled  with  a  movable  ring  to  which  is  attached  a  hinged  lock  that 
drops  over  a  projecting  lug  on  the  bowl.  A  lead  plug  is  inserted  in  the  lug  and 
is  punched  flat;  the  punch  used  for  the  purpose  stamping  the  latter  or  date 
for  the  day  on  the  lead. 

In  the  "Protector"  lock,  the  wick  tube  is  surrounded  by  a  close-fitting 
collar  of  the  same  height  held  in  place  by  a  steel  pin  (lock  bar)  fastened  by  a 
piece  of  spring  steel.  In  order  to  remove  the  lock  bar,  it  is  necessary  to  unscrew 
the  bowl  to  reach  the  spring,  but  in  so  doing  the  wick  tube  (and  wick)  is  drawn 
down  through  the  collar  and  the  lamp  extinguished.  In  other  locks  of  this 
class,  the  unscrewing  of  the  bowl  brings  into  action  a  cap,  or  extinguisher,  that 
smothers  the  flame. 

In  the  third  class  are  several  magnetic  and  compressed-air  locks.  In  the 
Wolf  lock,  the  tooth  on  the  end  of  a  pawl  pivoted  at  its  center  is  forced  by  a 
spring  into  a  socket  in  the  bowl  when  the  latter  is  screwed  into  place.  To 
unlock  the  lamp,  the  poles  of  a  powerful  horseshoe  magnet  are  applied  to  poles 
in  the  base  ring  of  the  lamp.  The  current  passes  through  the  spring  into 
the  pawl,  which  causes  the  end  opposite  the  tooth  to  move  inwards  thus 
releasing  the  tooth  from  its  socket  and  permitting  the  bowl  to  be  unscrewed. 
When  the  lamp  is  released  from  the  magnet,  the  spring  forces  the  tooth  into 
its  original  position  so  that  when  the  bowl  is  screwed  into  place,  it  is  locked 
automatically. 

In  the  Hailwood  lock,  the  ring  holding  the  glass  is  provided  on  the  under 
side  with  ratchet  teeth  into  which  engages  an  iron  lock-bolt,  which  is  held  in 
an  upright  position  by  a  strong  spring  resting  on  a  movable  iron  guard  plug, 
the  latter  resting  on  a  solid  shoulder  formed  in  a  recess  in  the  bowl.  To 
unlock  the  lamp,  the  nose  of  an  electromagnet  in  which  a  current  is  generated 
by  operating  a  treadle  is  placed  against  the  guard  plug  and  is  pressed  upwards. 
As  soon  as  the  plug  comes  in  contact  with  the  lock-bolt,  it  secures  a  strong 
magnetic  hold  upon  it.  Depressing  the  pedal  draws  down  the  guard  plug  and 
with  it  the  lock-bolt,  releasing  it  from  the  teeth  in  the  glass  ring  and  per- 
mitting the  unscrewing  of  the  bowl.  The  lamp  may  be  locked  automatically  by 
simply  screwing  up  the  bowl. 

To  open  the  ordinary  air  lock,  the  suction  end  of  a  small  air  pump  is  applied 
to  the  mouth  of  the  recess  in  which  the  lock-bolt  fits.  On  operating  the  pump 
by  a  treadle,  the  vacuum  created  draws  the  bolt  outwards  against  the  pressure 
of  the  spring  holding  it  in  place,  and  permits  unscrewing  the  _  bowl.  The 
Hailwood  air-lock  differs  from  the  preceding  in  that  the  positive  pressure 
(not  suction,  or  a  vacuum)  of  compressed  air  is  used  to  force  back  the  bolt. 
In  this  lock,  the  spring  holding  the  bolt  in  place  may  be  made  to  withstand  a 
pressure  as  high  as  250  Ib.  so  that  the  pressure  of  the  air  in  the  power  mains 
is  not  sufficient  to  open  the  lamp. 

Oils  for  Safety  Lamps. — Because  of  their  colorless  sensitive  flame,  alcohol 
and  even  hydrogen  are  burned  in  some  special  forms  of  safety  lamps  designed 
for  the  determina^n  of  small  percentages  of  methane.  Ordinarily,  some  kind 
of  illuminating  oil  is  used  both  in  working  and  in  testing  lamps. 

The  principal  illuminating  oils  of  vegetable  origin  are  pressed  from  the 
seeds  of  the  cotton  and  rape  plants,  the  crude  oil  being  treated  with  acid, 
washed,  etc.,  to  remove  various  mucilaginous  substances  that  would  otherwise 
cake  on  the  wick.  The  purified  or  refined  oils  are  commonly  known  as  winter 
oils  as  their  temperature  of  solidification  is  much  below  that  of  the  crude 

Refined  cottonseed  oil  has  a  specific  gravity  between  .922  and  .926  and 
solidifies  at  from  about  33°  to  50°  F. 

Rape,  or  as  otherwise  called,  colza  oil  is  extracted  from  the  seeds  of  several 
species  of  the  genus  Brassica  of  the  Cruciferas,  or  mustard,  family.  These 
plants  are  extensively  cultivated  in  all  parts  of  the  world,  except  in  the  United 
States,  for  the  illuminating  oils  contained  in  them.  The  species  commonly 
cultivated  are  Brassica  napus,  or  rape,  the  B.  campestris,  or  rutabaga,  and,  to 
a  less  extent,  the  B.  oleracea,  or  cabbage.  The  oils  extracted  from  these  plants 
differ  slightly  in  their  properties  but  are  all  sold  as  rape  or  colza  oil,  the  latte 
name  being  derived  from  the  word  cole,  or  kohl,  meaning  cabbage.  Colza 
oil  has  a  specific  gravity  of  .913  to  .915  and  solidifies  at  about  15°  F.,  con- 


880 


VENTILATION  OF  MINES 


siderably  below  cottonseed  oil.  The  illuminating  power  of  vegetable  oils  is 
low  and  may  be  increased  and  the  incrustation  of  the  wick  decreased  by  the 
addition  of  one-half  their  volume  of  kerosene  (ordinary  coal  oil). 

Whale  and  seal  oil  extracted  from  the  blubber  of  the  respective  animals 
are  largely  used  in  safety  lamps,  but  not  to  the  same  extent  as  lard  oils.  Animal 
oils,  like  vegetable  oils,  do  not  possess  great  illuminating  power,  although  this 
depends  on  their  purity.  The  British  Accidents  in  Mines  Commission  recom- 
mends the  use  of  a  mixture  of  one-third  refined  petroleum  (kerosene)  and 
two-thirds  rape  or  seal  oil  as  being  cheaper  and  having  the  same  illuminating 
power  as  the  best  colza  oil  while  not  forming  such  a  hard  cake  or  crust  on  the 
wick.  The  Commission  considered  seal  as  superior  to  colza  oil  in  maintaining 
a  more  uniform  height  of  flame  for  a  longer  time  without  retrimming. 

Of  the  distillation  products  of  petroleum,  the  so-called  light  oils  are  largely 
used  in  safety  lamps  because  of  their  high  illuminating  power.  The  oils  used 
and  the  temperatures  at  which  they  are  distilled  are,  gasoline  below  140°  F., 
naphtha  between  140°  and  230°  F.,  and  benzine  between  230°  and  302°  F.; 
kerosene,  which  is  distilled  between  302°  and  572°  F.,  is  used  only  when  mixed 
with  non-volatile  animal  and  vegetable  oils. 

As  these  oils  are  highly  volatile,  their  volatility  decreasing  in  the  order 
of  the  temperatures  at  which  they  are  distilled,  their  fumes  have  been  con- 
sidered as  a  source  of  danger,  but  this  has  been  disproved  by  long  and  safe 
use  of  lamps  burning  naphtha  and  by  the  researches  of  Watteyne  and  Stassart 
in  Belgium.  These  gentlemen  found  that  when  benzene  was  used,  there  was 
a  slightly  greater  tendency  of  the  lamps  to  heat  and,  in  some  cases,  of  the 
glasses  to  crack,  but  these  in  no  way  involved  a  passing  of  the  flame  or  a 
deterioration  of  the  lamp.  Their  photometric  observations  showed  that  the 
average  illumination  of  the  best  oil  (animal  or  vegetable)  fed  lamp  was  but 
.4  candlepower  as  opposed  to  .87  candlepower  of  the  benzene-burning  lamp 
with  underfeed  draft.  Special  tests  have  shown  that  the  Wolfe  lamp  burning 
naphtha  or  benzene  is  safe  under  any  conditions  of  use;  thus,  when  the  oil 
vessel  of  a  burning  lamp  was  heated  to  180°  F.,  the  lamp  was  extinguished 
and  without  danger. 

The  illuminating  power  of  safety-lamp  oils  varies  so  widely  according  to  the 
purity  of  the  oil,  the  kind  of  lamp  used,  the  conditions  of  burning,  etc.,  that  it  is 
not  possible  to  give  exact  figures  as  to  their  relative  light-giving  value.  The 
following  figures  are  average  of  many  determinations  of  the  light  power  of 
various  oils  burned  in  a  Clanny  lamp  when  referred  to  a  standard  candle 
burning  120  grains  of  spermaceti  an  hour:  Standard  candle,  1.00;  English 
rape  oil,  .32;  best  quality  colza  oil,  .47;  seal  oil,  .35;  two  parts  of  rape  oil  and 
one  of  kerosene,  .30;  various  grades  and  makes  of  so-called  safety  lamps  oils, 
.51,  .43,  and  .48,  respectively. 

Illuminating  Power  of  Safety  Lamps. — The  illuminating  power  of  a  safety 
lamp  depends  on  the  illuminant  used  and  on  the  construction  of  the  lamp. 
As  its  flame  is  not  surrounded  with  glass,  the  Davy  gives  less  light  than  any 
other  lamp  except  the  Stephenson  and  so  (aside  from  being  unsafe)  is  unsuited 
for  working  purposes. 

RELATIVE  ILLUMINATING  POWER  OF  SAFETY  LAMPS 


Lamp 

Candle- 
power 

Lamp 

Candle- 
power 

Ashworth-Hepplewhite-Gray 
Clanny 

.75 
34 

Hailwood,  burning  naphtha 

1.00 
45 

Davy,  common  
Davy,  Jack  

.15 
.08 

Marsaut,  two  gauzes  
Mueseler,  Belgian  

.55 
.36 

Davy,  in  case  
Evan  Thomas  

.16 
.43 

Mueseler,  English  
Stephenson  

.32 
.10 

Hailwood,  burning  oil  

.67 

Wolf,  burning  naphtha  .... 

1.00 

A  free  circulation  of  air,  which  is  best  secured  by  an  underfeed  draft, 
insures  a  better  supply  of  oxygen,  removes  the  combustion  products  more 
quickly,  and  thus  increases  the  lighting  power  of  the  lamp.  Bonnets  and 
multiple  gauzes  (see  the  two  types  of  Marsaut  lamp  in  the  table)  while  increas- 
ing the  safety  of  the  lamp,  reduce  its  illuminating  power  through  impeding 
the  circulation. 


VENTILATION  OF  MINES  881 

The  table  gives  the  relative  illuminating  power  of  various  safety  lamps 
referred  to  a  standard  candle  (burning  120  gr.  of  spermaceti  an  hour)  as  unity. 
The  oils  used  were  mostly  colza  or  seal  oil,  and  the  results  are  averages  only 
and  are  not  to  be  taken  as  exact  and  absolute. 

According  to  Hughes,  Marsaut  found  that  the  illuminating  power  of  a  lamp 
when  the  oil  chamber  is  made  of  brass  is  but  70%  of  that  of  the  same  lamp 
when  the  chamber  is  made  of  iron,  which  appears  to  be  due  to  the  greater 
heat  conductivity  of  the  brass  by  reason  of  which  the  lamp  bottom  gets  much 
hotter  than  if  it  was  made  of  iron  and  the  oil  becomes  viscous  and  will  not  flow. 

TESTING  FOR  METHANE 

Desirable  Features  in  Lamps  for  Testing  and  for  General  Use. — The  fol- 
lowing are  considered  desirable  features  in  a  safety  lamp  for  gas  testing: 

1.  The  flame  should  be  clear,  steady,  and  free  from   smoke,  that  the  gas 
cap  may  be  more  plainly  observed  and,  to  make  the  indications  afforded  by 
the  cap  of  value,  atmospheric  conditions  should  be  the  same  within  and  without 
the  lamp.     Alcohol  and  naphtha,  particularly  when  burned  in  lamps  with 
underfeed  draft,  afford  a  better  and  less  smoky  flame  than  animal  or  vegetable 
oils  burned  in  a  lamp  drafted  above  the  glass  in  the  ordinary  way,  see  under 
Circulation  of  Air  and  Oils  for  Safety  Lamps. 

2.  A  construction   such   that  when  the  lamp  is  exposed  to  air-currents  of 
high  velocity,  the  flame  will  not  be  blown  against  or  through  the  gauze  to  its 
injury  or  cause  the  ignition  of  gas  outside  the  lamp.     This  is  secured  through 
the  use  of  bonnets,  multiple  gauzes,  etc. 

3.  There  should    be   no  bright  surface  behind  the  flame,  reflections  from 
which  may  interfere  with  the  visibility  of  the  cap.     Secured  by  giving  the  metal 
parts  a  dull  finish,  careful  selection  of  the  glass,  etc. 

4.  Ability  to  detect   thin  layers  of    gas  near  the  roof,  see  Circulation  of 
Air  in  Safety  Lamps. 

5.  A  scale  for  measuring  the  height  of  a  flame  cap  so  as  to  more  accurately 
determine  the  percentage  of  gas  in  the  air.     The  use  of  the  scale  is  based  on  the 
assumption  that  a  cap  of  given  height  always  corresponds  to  a  definite  per- 
centage of  gas  in  the  air.     While  this  may  be  true  in  the  laboratory  where  the 
scale  is  adjusted  to  flames  obtained  by  burning  known  proportions  of  pure 
methane  in  pure  air,  it  is  rarely,  if  ever,  true  in  the  mine  where  deficiency  of 

.oxygen,  the  presence  of  blackdamp  and  coal  dust,  and  varying  conditions  of 
pressure,  temperature,  and  humidity  tend  to  alter  the  cap  for  the  same  per- 
centage of  gas  in  the  air.  That  is,  a  cap,  say,  1  in.  in  height  obtained  in  the 
mine  indicates  a  different  per  cent,  of  gas,  and  usually  a  greater  one,  than  the 
same  cap  in  the  laboratory.  Further,  the  conditions  within  the  lamp  where 
the  air  is  more  or  less  mixed  with  combustion  products  cannot  be  the  same  as 
in  the  mine. 

The  following  are  essential  features  in  lamps  for  general  use,  that  is,  in 
working  lamps: 

1.  The  lamp  should  give  the  maximum  light  consistent  with  safety;  this 
is  secured  by  the  use  of  the  proper  illuminant  and  construction. 

2.  The  lamp  should  be  safe  in  air-currents  of  high  velocity;  this  is  secured 
through  the  use  of  bonnets,  multiple  gauzes,  etc. 

3.  The  lamp  should  be  strong  in  all  its  parts  so  that  it  may  not  be  easily 
broken  through  careless  handling  or  in  minor  accidents,  and  should  be  simple 
in  construction  so  that  it  can  easily  be  taken  apart  for  cleaning  and  as  easily 
assembled  when  it  is  done. 

4.  The  lamp  should  be  capable  of  being  securely  locked  so  that  it  cannot 
be  opened  by  unauthorized  persons  or  at  any  but  some  appointed  place. 

5.  The  lamp  should  not  be  as  sensitive  to  gas  as  one  used  for  testing.     A 
lamp   that  rapidly  fills  with   flame  in  the  presence  of    explosive  mixtures 
and  must  be  as  rapidly  removed  therefrom  to  prevent  the  passage  of  the  flame 
through  the  gauze  or  the  extinction  of  the  light,  requires  constant  watching, 
and  is  unfitted  for  a  working  lamp.     The  same  construction  that  makes  a  lamp 
safe  in  strong  air-currents  also  makes  it  less  sensitive  to  gas. 

6.  The  lamp  should  diffuse  light  upwards  so  that  the  roof  may  be  inspected 
without  turning  the  lamp  on  one  side. 

7.  The  lamp  should  be  provided  with  an  appliance  for  relighting  without 
opening  it.     The  tests  of  Watteyne  and  Stassart  showed  that  the  explosion 
relighter  causes  external  explosions  in  rare  instances,  but  that  the  phosphorus 
igniter  does  not.     It  has  been  demonstrated  that,  as  long  as  the  glass  is  not 
broken,  the  gauze  punctured,  etc.,  internal  relighting  is  safe  provided  a  proper 
igniter  is  used.     • 

56 


882 


VENTILATION  OF  MINES 


Testing  tor  Gas. — When  a  safety  lamp  is  brought  into  an  atmosphere  con- 
taining methane,  the  presence  of  the  gas  is  indicated  by  a  bluish  halo  or  cap 
surrounding  and  surmounting  the  lamp  flame.  The  ordinary  lighting  flame 
of  the  lamp  is  rarely  used  in  gas  testing  as  it  does  not  show  a  cap  but  merely 
an  increase  in  length  in  the  presence  of  methane,  and  this  increase  cannot  well 
be  measured  unless  the  length  of  the  flame  in  fresh  air  is  first  observed.  The 
same  is  true  of  what  is  sometimes  called  an  intermediate  flame  about  one-half 
the  height  of  the  ordinary  flame. 

The  flame  commonly  used  for  testing  is  made  by  screwing  down  the  wick 
until  the  yellow  color  of  the  wick  has  disappeared  and  nothing  but  a  faint 
blue  cap  remains  on  the  burner.  This  is  sometimes  spoken  of  as  a  cap,  cap- 
flame,  blue  cap,  testing  flame,  non-luminous  flame,  etc.,  and  is  from  |  to  J  in. 
high,  depending  on  the  illuminant  used,  type  of  lamp,  etc. 

A  blue  cap,  wholly  or  partially  visible,  and  which  should  not  be  confused 
with  that  due  to  gas,  is  frequently  seen  above  the  testing  flame.  This  is 
commonly  called  the  fuel  cap,  and  has  been  supposed  to  be  due  to  the  burning 
of  the  volatile  products  of  the  lamp  fuel  driven  off  by  the  heat.  Briggs,  how- 
ever, has  shown  that  the  fuel  cap  is  the  outer  of  the  three  layers  or  parts  into 
which  any  flame  may  be  divided,  occurs  with  solid  as  well  as  with  liquid  fuels, 
and  that  it  is  intensified  only  by  the  vapors  given  off  when  the  lamp  is  hot. 
The  fuel  cap  appears  as  a  halo  and,  in  order  not  to  be  deceived  by  it,  the 
observer  should  become  accustomed  to  its  appearance  in  fresh  air. 

To  test  for  methane,  hold  the  lamp  in  an  upright  position  with  one  hand  and 
with  the  other  screening  the  eyes  from  the  body  of  the  flame,  slowly  raise  the 
lamp  toward  the  roof  and  watch  closely  for  the  first  appearance  of  the  cap. 
When  this  is  observed,  the  lamp  should  be  promptly  but  cautiously  drawn 
down,  while  the  distance  of  the  lamp  from  the  roof  is  noted;  this  gives  the 
depth  of  the  gas  in  the  place.  When  sufficient  gas  is  present,  or  the  lamp  is 
raised  too  quickly,  the  entire  gauze  sometimes  fills  with  flame;  a  condition 
known  as  faming.  When  this  occurs,  the  lamp  must  be  handled  with  great 
care.  An  explosion  of  gas  within  the  lamp  is  very  likely  to  take  place  when 
it  is  withdrawn  from  a  body  of  gas  into  fresh  air,  and  this  may  be  communi- 
cated to  the  outside  gas  unless  the  lamp  is  properly  made.  Bonneted  lamps  are 
more  liable  to  internal  explosions  than  those  not  bonneted,  but,  owing  to  the 
restricted  circulation  in  the  lamp,  are  far  less  likely  to  pass  the  flame  to  the 
outside. 

Height  of  Gas  Cap. — With  the  same  lamp,  burning  the  same  illuminant, 
with  the  same  wick,  and  using  the  same  height  of  flame,  as  long  as  the  air  is 
pure  and  is  not  contaminated  with  carbon  dioxide  or  excess  nitrogen,  there 
is  a  fixed  height  of  cap  for  each  per  cent,  of  methane  present.  However, 
if  the  lamp,  illuminant,  wick,  or  height  of  flame  is  changed,  or  if  the  propor- 
tion of  inert  gases  in  the  mine  air  is  varied,  there  will  be  a  change  in  the  height 
of  the  cap  made  by  the  same  percentage  of  gas  so  that,  unless  all  the  condi- 
tions are  constant  or  are  known,  it  is  not  possible  to  tell  whether  a  cap  of  a 
certain  height  is  due  to  the  presence  of,  say,  1  or  2.5%  of  methane.  Prof. 
G.  R.  Thompson,  Leeds  University,  gives  the  following  table  for  the  heights 
of  gas  caps  in  different  lamps,  using  different  oils,  etc. 

HEIGHT  OF  GAS  CAPS  IN  DIFFERENT  LAMPS 


Lamp 
.No. 

Wick  and  Oil  Used 

Percentage  of  Gas 
in  Mixture 

1 

2 

3 

Height  of  Cap, 
Inches 

1 
2 
3 

Circular   wick,    .23   in.   in   diameter,    burning 
paraffin  oil 

.200 

.520 
.175 

.30 

.67 
.50 

0.4 

1.1 
1.0 

Flat  wick,  .65  in.  wide,  burning  naphtha  (boil- 
ing point,  55°C.)  

Flat  wick,  .55  in.  wide,  burning  colza  oil  

The  following  figure  shows  the  height,  in  centimeters  and  in  inches,  of  the 
gas  cap  corresponding  to  various  percentages  of  gas  and  pure  air  as  observed 


VENTILATION  OF  MINES  883 

in  the  naphtha-burning  lamps  now  so  generally  used  for  testing  and  general 
purposes. 

The  gas  cap  in  lamps  like  the  Davy  of  Clanny  burning  sperm  or  colza 
oil  are  so  very  small  and  difficult  to  distinguish  when  the  percentage  of 
methane  is  reduced  to  2.5%,  that  it  is  considered  impossible  for  the  most 
skilled  observer  to  detect  less  than  2%  of  gas  with  these  lamps,  and  3%  is 
about  the  limit  for  the  average  man.  For  small  percentages  of  methane  the 
naphtha  flame  is  much  more  sensitive  than  the  oil,  and  with  it  as  little  as 
1  %  of  gas  may  be  detected. 

To  avoid  adjusting  the  flame  in  each  working  place,  fire  bosses  should 
carry  a  second  lamp  with  normal  flame  or,  better,  may  use  a  storage-battery 
portable  electric  lamp. 


In.  CM 

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2.8    7 

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17° 


2%     3%      4% 


CARE  OF  SAFETY  LAMPS 

Cleaning  Lamps. — The  following  suggestions  in  regard  to  cleaning  standard 
naphtha-burning  safety  lamps  are  selected  from  J.  W.  Paul. 

1.  Each  workman  should  have  his  own  lamp,  marked  with  a  distinctive 
number  corresponding  to  that  on  a  hook  or  the  lamp  rack.     When  a  lamp  is 
turned  in  at  the  end  of  a  shift,  if  it  is  in  bad  condition  or  has  been  tampered 
with,  it  should  be  set  aside  for  later  detailed  examination.     If  the  lamp  is 
returned  in  normal  condition,  it  should  be  unlocked  and  the  bowl,  gauzes, 
and  globe  loosened  and  hung  on  a  rack. 

2.  All  removable  parts  should  be  detached  and  the  fount  sent  to  the  filling 
station,  which  should  be  separated  from  the  lamp  room  by  fireproof  parti- 
tions with  iron  or  steel  drop  doors. 

3.  The  gauze  should  be  brushed  inside  and  out  and  blown,  preferably  with 
compressed  air,  until  all  wires  are  clean,  holes  freed  from  dirt,  etc.    Gauzes 
with  broken  wires,  enlarged  holes,  etc.,  should  be  crushed  and  thrown  aside. 
New  gauzes  should  be  thoroughly  burned  to  remove  the  grease  in  order  to 
prevent  flaming  on  the  outside  in  the  presence  of  an  explosive  mixture  of 
gas  and  air. 

4.  The  glass  should  be  wiped  with  a  damp  and  dried  with  a  clean,  dry 
cloth  until  free  from  all  oil  or  moisture.     Gaskets  should  be  whole,  should 
fit,  and  should  be  free  from  grit  or  dirt. 

5.  The  bonnet  should  be  brushed  until  free  from  soot  or  dust. 

6.  The  lower-ring  gauze  of  underdraft  lamps  should  be  brushed  and  if  holes 
or  broken  wires  are  found,  should  be  discarded  or  sent  to  the  repair  shop.     < 

7.  The  igniter  should  be  tested  to  see  if  it  is  in  working  order,  whether  it  is 
supplied  with  tape  (match),  and  whether  it  fits  in  its  receptacle  "so  that  there 
is  no  unnecessary  opening  from  the  outside  to  the  inside  of  the  lamp. 

8.  Only  enough  gasoline  should  be  used  to  saturate  the  cotton  in  the  bowl, 


884  VENTILATION  OF  MINES 

and  the  outside  thereof  should  be  wiped  clean.  The  use  of  special  filling 
tanks  is  to  be  recommended.  Naphtha  or  gasoline  of  the  best  quality 
should  be  used;  its  specific  gravity  should  be  0.70  to  0.72. 

9.  Before  the  lamp  is  assembled,  the  picker  should  be  in  condition  for  use 
and  should  not  hang  below  the  bottom  of  the  bowl  or  it  may  be  bent. 

10.  After  the  lamp  has  been  assembled  the  wick  should   be  lit,  adjusted 
to  a  low  flame,  and  the  tightness  of  the  joints  tested  by  blowing  against 
them;  leakage  will  be  shown  by  the  wavering  of  the  flame.     Compressed- 
air  coils  in  which  the  lamp  may  be  placed  are  recommended. 

11.  It  is  advisable  to  place  the  lighted  lamp  in  a  testing  box  containing 
an  explosive  atmosphere. 

Assembling  Lamps. — Some  of  the  common  errors  made  in  assembling 
lamps  are:  Leaving  out  one  or  both  gaskets,  or  using  broken  gaskets;  plac- 
ing gaskets  in  underfed  lamps  so  as  to  exclude  the  air  from  below;  leaving 
out  one  of  the  gauzes  in  double-gauze  lamps;  placing  on  top  of  the  glass  an 
expansion  ring  designed  to  be  placed  below  it;  failing  to  screw  up  the  bowl 
sufficiently  to  make  a  tight  fit  between  the  glass  globe  and  the  gaskets; 
leaving  out  the  igniting  device  without  plugging  the  stem  hole;  omitting  the 
deflection  rings  that  prevent  air  from  blowing  directly  into  the  lamp;  omitting 
the  shield  or  bonnet;  using  a  defective  gauze. 

Failure  of  Safety  Lamps. — Aside  from  want  of  atten^n  to  the  precautions 
noted  under  Assembling  Lamps,  other  reasons  for  the  failure  of  safety  lamps, 
that  is,  the  ignition  by  the  lamp  of  the  gas  outside  it  are:  Exposure  to  air 
currents  of  greater  velocity  than  those  for  which  the  lamp  was  designed; 
permitting  the  gas  to  burn  within  the  lamp  until  the  gauze  is  red  hot  and 
its  cooling  property  destroyed;  allowing  the  lamp  to  smoke  until  the  pores 
of  the  gauze  become  clogged  with  soot  which  will  heat  and  possibly  burn,  or 
the  coating  of  the  gauze  with  oil,  grease,  or  coal  dust  with  the  same  result; 
holding  the  lamp  on  one  side  so  that  the  flame  strikes  upon  and  heats  the 
gauze;  allowing  the  glass  to  be  broken  by  water  dropping  on  it  or  in  any 
other  way;  puncturing  the  gauze. 

_  A  little-recognized  cause  of  lamp  failure  is  the  presence  of  fine  and  explo- 
sive dust  in  the  air.  Dust  fine  enough  to  pass  through  the  meshes  of  the 
gauze  may  be  ignited  within  the  lamp,  pass  through  the  gauze  and  ignite 
firedamp  or  dust  mixtures  outside  the  lamp.  Ashworth  found  that  a  Davy 
lamp,  that  would  not  cause  an  external  explosion  in  4.5%  of  gas  when  the 
air  was  moving  370  ft.  per  min.  and  was  free  of  dust,  passed  the  flame  and 
caused  an  explosion  in  10  sec.  when  only  the  ordinary  amount  of  dust  was 
floating  in  the  air. 

Relighting  Stations,  Lamp  Houses,  Etc. — In  large  mines  it  is  customary  to 
have  lamp  stations  with  a  man  in  attendance  to  see  to  the  relighting,  renewal, 
etc.,  of  the  safety  lamps.  These  stations  are  usually  located  at  the  mouth  of 
each  principal  entry  and  are  the  headquarters  of  the  district  fire  boss  when 
not  on  his  rounds. 

Lamp  houses,  where  safety  lamps  are  received  from  and  delivered  to  the 
men  and  where  they  are  cleaned,  repaired,  etc.,  vary  in  size  and  completeness 
of  equipment  depending  upon  the  number  of  lamps  handled  daily  At 
almost  all  mines  it  is  customary  to  store  the  oil  in  a  separate  building  or  in  a 
fireproof  room,  pumping  out  the  daily  requirements  into  one  or  more  filling 
tanks  in  the  lamp  room  proper.  At  large  mines,  the  lamp  room  is  fitted  with 
revolving  brushes  and  a  small  air  compressor  for  cleaning  and  testing  lamps, 
a  gas  testing  box,  etc.  The  system  employed  in  handling  lamps  varies 
widely.  Generally  the  lamps  are  numbered  and,  where  possible,  the  lamp 
number  and  that  of  the  miner's  check  correspond.  Lamps  are  often  turned 
in  merely  by  being  hung  on  a  hook  with  a  number  corresponding  to  that  by 
the  lamp,  to  which  they  are  returned  by  the  lampman  in  time  for  the  morning 
shift.  In  other  cases,  the  lamps  are  placed  in  separate  compartments  in  a 
large  cabinet.  The  compartments  are  sometimes  locked,  each  miner  having 
his  own  key,  and  commonly  are  open  on  the  back  or  lamp  room  side  so  that 
the  lampmen  may  easily  remove  the  lamps  for  cleaning  and  as  easily  return 
them  to  the  right  place.  Not  infrequently,  the  lamps  are  handed  out  per- 
sonally through  a  window  in  the  fashion  of  ordinary  supplies. 

STANDARD  TYPES  OF  SAFETY  LAMPS 

Davy  Lamp. — The  Davy  lamp  (Fig.  1,  a,  page  885)  consists  of  the  usual 
oil  vessel,  or  bowl,  to  which  is  secured  by  three  standards  a  gauze  cylinder 
surmounted  by  a  gauze  cap  (smoke  gauze).  The  cylinder  is  made  of  stand- 
ard wire  gauze,  is  generally  1 J  in.  in  diameter  and,  with  its  cap  is  about  6  in. 


VENTILATION  OF  MINES 


885 


high.  Air  enters  all  around  the  lamp,  below  the  flame,  and  passes  out  at 
the  top  of  the  gauze  as  shown  by  the  arrows.  In  the  fire-boss  Davy,  the  oil 
chamber  is  quite  small  and  the  gauze  does  not  exceed  5  in.  in  height;  in  the 
pocket  Davy,  the  gauze  is  3^  to  4  in.  high. 


Marsaut 

rnj.   i 

Davy   lamps   are   often   provided   with   an   upward-sliding   metal   shield 
encircling  the  gauze  for  two-thirds  of  its  circumference  as  a  protection  in 


886  VENTILATION  OF  MINES 

strong  air  currents.  Owing  to  the  free  admission  of  air  these  lamps  give  a 
good  flame  for  testing  and  are  sensitive  to  gas.  At  one  time  they  were  in 
universal  use  for  gas  testing,  but  they  are  so  very  unsafe  that  their  use  for 
any  purpose  is  prohibited  in  Europe  and  in  most  of  the  United  States.  The 
unbonneted  Davy  will  pass  the  flame  in  air  currents  moving  at  more  than  6  ft. 
per  sec.  or  360  ft.  per  min.  (4  mi.  per  hr.),  a  less  speed  than  that  maintained 
by  the  average  fire  boss  in  making  his  rounds. 

In  the  tin-can  Davy,  the  gauze  was  surrounded  by  a  tin  case  with  a  glass 
window;  later,  the  tin  can  was  replaced  by  a  brass  case  having  an  all-around 
glass  window.  In  the  Jack  Davy,  the  tin  case  was  replaced  by  a  glass  cylin- 
der (either  within  or  without  the  gauze)  reaching  the  entire  length  of  the 
gauze.  In  another  form,  a  low  glass  cylinder,  held  in  place  by  a  spring  or 
screw,  was  made  to  slide  up  or  down  over  the  gauze.  When  provided  with  a 
bonnet  over  the  upper  part  of  the  gauze,  this  last  form  of  Davy  was,  at  one 
time,  very  popular  in  the  United  States.  Some  of  the  numerous  types  of 
bonneted  Davy  lamps  have  withstood  air  velocities  as  high  as  1,200  ft.  per 
min.  (14  mi.  per  hr.)  and  even  more  in  the  case  of  the  tin-can  Davy.  The 
Scotch  Davy  was  distinguished  by  the  greater  diameter  (nearly  3  in.)  of  the 
gauze  which  was  closed  at  the  top  by  a  conical  copper  cap.  The  lamp  was 
provided  with  a  hook  at  the  side,  instead  of  a  ring  at  the  top,  for  carrying, 
and  had  a  flat  wick  with  a  small  shield  beside  it  as  a  protection  against  the 
wind.  Davy  lamps  are  designed  to  burn  animal  or  vegetable  oils  only. 

Stephenson  Lamp. — The  original  Stephenson  lamp  consisted  of  a  glass 
chimney  closed  by  a  perforated  copper  cap  and  surmounted  by  a  perforated 
copper  shield.  The  space  between  the  cap  and  the  shield  filled  with  the 
inert  products  of  combustion  which,  from  lack  of  oxygen,  extinguished  the 
flame  of  any  gas  burning  within  the  lamp  before  it  could  reach  the  outside  air. 

The  more  modern  lamp  of  this  name  resembles  the  Davy  in  appearance 
as  it  uses  the  same  gauze,  but  without  the  gauze  cap.  Instead,  within  the 
main  gauze  is  a  conical  glass  chimney,  closed  at  the  top  with  a  perforated 
copper  cap,  which  may  be  raised  from  the  bottom  so  as  to  admit  air  more 
freely  at  the  base  of  the  flame. 

Stephenson  lamps  are  often  called  Geordie  lamps. 

Clanny  Lamp. — The  original  Clanny  lamp  consisted  of  a  cylindrical  metal 
case  (height  about  3  times  the  diameter)  the  front  of  which  was  replaced  with 
glass  and  in  which  an  ordinary  candle  burned.  Air  was  forced  into  the  lamps 
by  a  bellows,  through  a  water  seal.  The  top  of  the  lamp  was  closed  by  a 
tapering  copper  cap  like  an  inverted  funnel,  the  opening  in  which  was  too 
small  to  permit  passage  of  the  flame. 

The  simplest  form  of  the  modern  Clanny  lamp  is  essentially  a  Davy  lamp 
in  which  the  lower  portion  of  the  gauze  is  replaced  with  a  glass  cylinder 
about  2  in.  high,  as  in  Fig.  1,  b,  page  885.  As  in  all  lamps  where  the  air 
enters  above  the  gauze  (see  arrows),  there  are  conflicting  air  currents  which 
interfere  with  the  formation  of  a  perfect  cap,  cause  a  tendency  to  smoke, 
and  unfit  the  lamp  for  delicate  testing.  The  unbonneted  Clanny  is  not  safe 
in  air  currents  moving  over  8  ft.  per  sec.  or  480  ft.  per  min.  (5£  mi.  per  hr.). 
There  are,  however,  many  forms  of  bonneted  Clanny  lamps,  some  of  which 
are  safe  in  currents  moving  2,000  ft.  or  more  per  min.  (22f  mi.  per  hr.). 

Evan  Thomas  Lamp. — There  are  several  lamps  of  this  name,  all  of  which  are 
modifications  of  the  Clanny.  The  original  Evan  Thomas  lamp  was  of  the  un- 
derdraft  type,  being  provided  with  a  double  steel  bonnet  above  a  double  glass 
chimney.  Air  was  drawn  in  at  the  top,  descended  between  the  bonnets  and 
glasses,  and  entered  the  lamp  below  the  flame  through  gauze- protected  ports. 
The  lamp  was  of  excellent  illuminating  power,  but  the  tendency  of  the  glass 
to  crack  by  the  heat  of  the  gas  burning  within  it  led  to  its  abandonment. 

The  present  lamp  is  a  bonneted  Clanny  with  the  addition  of  a  device  to 
control  the  air,  which  commonly  takes  the  form  shown  in  the  Deflector  Lamp 
Fig.  2.  In  another  form,  a  deflector  ring  placed  around  the  base  of  the  gauze, 
throws  the  entering  air  upward.  The  gauze  is  protected  by  a  very  deep 
gauze  cap  at  the  top  between  which  and  the  top  of  the  bonnet  are  deflectors 
throwing  the  products  of  combustion  downward.  The  result  of  this  con- 
struction is  that  only  a  very  small  part  of  the  gauze  is  exposed  to  the  action 
of  gas  burning  within  trie  lamp  and  the  retention  of  the  products  of  combus- 
tion, on  the  Stephenson  principle,  in  the  upper  part  of  the  lamp,  materially 
adds  to  its  safety  in  explosive  mixtures.  This  last  form  of  lamp  is  said  to 
have  safely  withstood  an  explosive  current  moving  at  the  rate  of  3,200  ft. 
per  min.  (36.3  mi.  per  hr.).  The  lamp  burns  oil  and  gives  a  good  light,  but 
has  a  tendency  to  smoke. 


VENTILATION  OF  MINES 


887 


FIG. 


Deflector  Lamp. — A  deflector  lamp  is,  strictly,  not  a  distinct  type  but  is 
any  one  of  the  standard  lamps  t9  which  is  added  a  device  known  as  a  deflector 
that  is  designed  to  control  the  direction  of  the  air  currents.  As  shown  in  Pie 
2,  where  it  is  applied  to  a  bonneted  two-gauze 
Marsaut  lamp,  the  deflector  consists  of  a  brass 
shield  a  midway  between  the  outer  gauze  and  the 
bonnet  and  about  1 J  in.  high.  About  J  in.  above 
the  top  of  this  shield  is  the  bottom  of  an  angle 
ring  b.  This  ring  fits  closely  to  t'he  gauze,  its  top 
flange  entirely  closing  the  space  between  the  gauze 
and  the  bonnet.  The  air  follows  the  course  shown 
by  the  arrows  and  is  thrown  directly  upon  the 
flame.  As  the  air  is  heated  by  passing  over  the 
warm  deflector  and  gauze,  the  draft,  rate  of  com- 
bustion of  oil  and,  consequently  the  illumination 
are  improved.  The  deflector  is  said  to  fit  the 
lamp  for  burning  in  air  containing  a  much  higher 
percentage  of  carbon  dioxide  than  is  otherwise 
possible. 

Bull's  Eye,  or  Mauchline,  Lamp. — The  bull's 
eye,  or  Mauchline,  lamp  is  a  Clanny  in  which  the 
glass  is  replaced  by  a  metal  cylinder  fitted  up 
like  a  bull's  eye  lantern,  with  a  lense  at  one  end 
and  a  reflector  behind  the  flame  at  the  other.  In 
each  side,  at  the  height  of  the  flame,  is  a  gauze- 
protected  circular  port  through  which  gas  caps 
may  be  observed.  The  lamp  is  not  generally 
bonneted,  throws  a  good  light  directly  ahead  and 
was  designed,  primarily,  for  the  use  of  mine  sur- 
veyors. 

Marsaut  Lamp. — The  Marsaut  lamp.  Fig.  1, 
d,  is  a  Clanny  lamp  with  two  or,  usually,  three 
conical  gauzes  to  afford  protection  against  strong 
air  currents  and,  particularly,  internal  explosions.  The  lamp  has  a  tendency 
to  smoke  and  heats  quickly,  but  the  confinement  of  the  products  of  combustion 
between  the  gauzes,  on  the  Stephenson  principle,  adds  much  to  the  safety 
of  the  lamp.  The  unbonneted  lamp  is  considered  safe  in  air  currents  moving 
not  faster  than  600  ft.  per  min.  (7  mi.  per  hr.).  The  bonneted  Marsaut  is 
one  of  the  safest  of  lamps  and  easily  withstands  velocities  of  3,000  ft.  per 
.  min.  (34  mi.  per  hr.),  and  more.  The  table  on  page  880  shows  that  the  two- 
gauze  lamp  has  about  22  %  more  illuminating  power  than  that  with  three 
gauzes. 

Mueseler  Lamp. — The  Mueseler  Lamp,  Fig.  1,  c,  page  885,  is  a  Clanny 
lamp  with  an  interior  conical  sheet-iron  chimney  which  increases  the  draft, 
separates  the  products  of  combustion  from  the  entering  air,  increases  the 
security  of  the  lamp  against  internal  explosions,  and  decreases  its  tendency 
to  flame.  The  unbonneted  type,  shown  in  the  figure,  may  be  considered 
safe  in  an  air  current  having  a  velocity  not  greater  than  600  ft.  per  min. 
(7  mi.  per  hr.). 

There  are  two  types  of  the  bonneted  Mueseler,  the  Belgian  and  the  English, 
which  differ  only  in  the  dimensions  of  the  chimney.  In  the  former,  which  is 
the  official  or  approved  lamp  in  Belgium,  the  chimney  must  have  a  total 
height  of  4.6  in.  and  must  be  so  placed  that  its  bottom  is  .85  in.  above  the 
top  of  the  wick  tube  and  its  top  3.55  in.  above  the  horizontal  gauze  which, 
surrounding  the  chimney  at  the  level  of  the  top  of  the  glass,  divides  the  upper 
from  the  lower  part  of  the  lamp.  The  object  of  the  horizontal  gauze  is  to 
prevent  any  burning  gas  passing  upwards  between  the  chimney  and  the  main 
gauze.  The  chimney  of  the  English  Mueseler  is  set  higher  above  the  flame 
than  that  of  the  Belgian  and  the  area  of  its  upper  end  is  much  larger.  The 
Belgian  lamp,  in  the  tests  of  the  Royal  Accidents  Commission  (English), 
was  extinguished  without  harm  after  a  few  seconds  exposure  to  explosive 
air  currents  moving  at  the  rate  of  2,880  ft.  per  min.  (32.7  mi.  per  hr.),  while, 
in  every  instance,  the  English  lamp  caused  an  explosion;  in  fact,  the  English 
lamp  failed  when  the  velocity  exceeded  1,000  ft.  per  min.  (11.3  mi.  per  hr.). 
The  Mueseler  lamp  is  sensitive  to  air  currents  striking  it  obliquely,  and  these 
sometimes  blow  the  air  circulating  in  the  lamp  from  its  regular  course  with 
danger  of  an  explosion.  The  lamp  is  easily  extinguished  if  held  at  a  slight 
angle  from  the  vertical  as  the  products  of  combustion  then  pass  upwards 


888  VENTILATION  OF  MINES  . 

between  the  chimney  and  the  gauze  and,  mixing  with  the  entering  air, 
smother  the  flame.  The  statement  that  the  Mueseler  lamp  is  safe  in  air 
currents  moving  100  ft.  per  sec.,  or  68.1  mi.  per  hr.,  seems  hardly  credible. 

Ashworth-Hepplewhite-Gray  Lamp. — The  Ashworth-Hepplewhite-Gray 
lamp,  familiarly  known  as  the  A-H-G  or  as  the  Gray  lamp,  is  shown  in  Fig. 
1,  e,  page  885.  The  lamp  is  a  bonneted  Clanny  with  underdraft,  air  entering 
through  gauze-protected  ports  or  through  a  gauze  ring  entirely  surrounding  the 
lamp  at  and  below  the  level  of  the  flame.  Admission  of  air  to  the  gauze  ring 
or  gas  ports  is  through  the  standards  which  are  hollow.  The  openings  at  the 
top  of  the  standards  are  closed  by  a  plate  which  may  be  revolved  over  them, 
and  those  at  the  base  are  closed  by  slides.  When  used  for  testing,  the  cover 
plate  is  revolved  until  the  tops  of  the  standards  are  open  and  the  bottom 
openings  are  closed  by  slipping  the  slides  down  over  them,  the  air  then 
following  the  course  shown  by  the  arrows.  This  construction  permits  the 
testing  of  thin  layers  of  gas  near  the  roof.  When  used  as  a  working  lamp, 
the  top  openings  are  closed  by  the  cover  plate  and  the  slides  at  the  base  of  the 
standards  are  pushed  up.  In  some  types  of  this  lamp  there  are  three  instead 
of  four  standards,  only  one  of  which  is  hollow,  the  others  being  of  thin  wire 
so  as  not  to  impede  the  light.  The  conical  glass  and  short  conical  gauze 
permit  the  upward  diffusion  of  light.  In  some  cases  the  steel  bonnet  is 
cylindrical  instead  of  as  in  the  figure,  but  it  is  always  closed  by  a  truncated 
cone  which  reduces  the  area  of  the  top  of  the  opening  and  better  controls  the 
circulation  and  prevents  downward  currents.  The  opening  in  this  cone  is 
protected  by  a  perforated  dome  or  cap  which,  in  some  lamps,  is  extended 
downwards  like  an  ordinary  bonnet  to  the  level  of  the  top  of  the  glass.  The 
lamp  is  intended  for  burning  colza  or  similar  oils,  has  high  illuminating  power 
(see  following  table),  is  said  to  be  safe  in  air  currents  traveling  6,000  ft.  per 
min.  (68.1  mi.  per  hr.),  and  is  generally  considered  a  most  excellent  lamp. 

Wolf  Lamp.— Fig.  I,/,  page  885,  shows  the  Wolf  lamp  as  used  in  the  United 
States,  The  lamp  burns  naphtha  or  gasoline  and,  hence,  assisted  by  its  con- 
struction, gives  a  maximum  of  light  and  permits  the  detection  of  small  per- 
centages or  methane.  It  uses  a  magnetic  lock  (see  Locks  for  Safety  Lamps), 
has  an  internal  ignition  device  (see  first  paragraph  on  Igniters,  or  Relight- 
ers) ,  and  has  an  underdraft. 

The  lamp  is  of  the  Clanny  type  with  the  double  conical  gauzes  of  the  Mar- 
saut,  and  usually  has  a  corrugated  bonnet,  the  openings  in  which  are  so  ar- 
ranged that  air  currents  strike  tangentially  and  not  directly  upon  the  gauze. 
Air  for  combustion  enters  through  gauzes  or  a  gauze  ring  at  the  base  of  the 
glass  chimney,  the  openings  being  protected  from  direct  contact  of  air  cur- 
rents by  a  baffle  ring^.  The  wick  is  held  in  a  sheath  moving  within  the  wick  • 
tube  and  may  be  adjusted  by  turning  the  screw  at  the  base  of  the  lamp. 

The  baffle  ring  and  bonnet  are  made  in  various  forms  so  that  the  external 
appearance  of  Wolf  lamps  varies  considerably.  Some  of  these  lamps  have 
the  overdraft  of  the  Clanny;  in  some  the  igniter  box  is  circular;  in  others,  a 
lead  in  place  of  a  magnetic  lock  is  used;  some  are  arranged  to  burn  colza; 
others  burn  alcohol,  have  the  Chesneau  scale  attachment,  and  are  adapted  for 
testing  for  small  percentages  of  gas.  While  such  variations  and  adaptations 
are  common  in  the  lamp  as  used  in  Europe,  they  are  practically  unknown 
in  the  United  States. 

The  Wolf  is  a  most  excellent  lamp,  and  is  safe  in  air  currents  containing 
9  %  of  methane  when  moving  3,600  ft.  per  min.  (41  mi.  per  hr.). 

Protector  Lamp. — The  Protector  lamp  is  not  a  separate  type  but  is  a  modi- 
fied Clanny,  Marsaut,  or  Mueseler  lamp  designed  to  burn  colzaline,  a  light 
oil  obtained  by  the  purification  of  colza;  and  is  provided  with  an  electric 
igniter.  The  wick  tube,  or  burner,  is  double  with  a  narrow  annular  space 
between  the  two  tubes.  In  the  inner  tube  is  a  stationary  cotton  wick  extend- 
ing down  into  the  bowl  which  contains  a  piece  of  sponge  for  absorbing  and  re- 
taining the  oil  fuel.  The  lamp  is  lit  electrically  by  means  of  a  platinum  wire 
connected  to  two  terminals,  one  of  which  is  connected  with  a  contact  on 
the  bottom  of  the  bowl,  the  framework  of  the  lamp  forming  the  return 
circuit.  A  low-tension  current  from  a  battery  is  sufficiently  powerful  to 
heat  the  wire  to  the  ignition  point  of  the  colzaline  vapor,  which,  as  it  forms, 
passes  up  the  annular  space  between  the  inner  and  outer  wick  tubes  and  is 
burned  around  the  head  of  the  stationary  wick.  The  flame  is  regulated  by 
screwing  the  bottom  of  the  lamp  up  or  down,  and  is  extinguished  if  an  at- 
tempt is  made  to  unscrew  the  bottom  completely,  as  explained  under  Locks 
for  Safety  Lamps  (Protector  Lock). 

Hailwood  Lamp. — The  Hailwood  lamp  is  designed  to  burn  naphtha  or 


VENTILATION  OF  MINES  889 

gasoline.  It  is  essentially  a  bonneted  Clanny  lamp  with  the  double  gauze  of 
the  Marsaut  and  an  underdraft  protected  by  a  baffle  ring.  The  lamp  is  pro- 
vided, as  desired,  with  either  the  magnetic  or  the  compressed-air  lock  (de- 
scribed under  Locks  for  Safety  Lamps).  The  lamp  is  relit  in  a  special  gas- 
proof, gauze-protected  chamber  by  means  of  an  electric  spark  which  jumps 
the  gap  between  the  top  of  the  wick  tube  and  the  end  of  an  upright  insulated 
copper  wire  through  which  the  current  enters  the  lamp.  The  wick  tube  is 
flat  and  is  surrounded  by  a  sliding  sheath  by  means  of  which  the  lampman 
may  adjust  the  flame  as  desired  but  which  is  so  arranged  that  it  is  impossible 
for  the  miner  to  raise  the  flame  to  such  a  height  that  it  may  be  drawn  through 
the  gauze.  The  ordinary,  or  burning,  wick  is  fed  with  naphtha  by  a  perma- 
nent feeding  wick  which  extends  down  into  the  bowl  and  which  is  pressed 
against  the  ordinary  wick  by  a  spring.  Owing  to  its  construction  and  to  the 
illuminant  used,  the  lamp  gives  a  most  excellent  light  and  also  permits  the 
detection  of  low  percentages  of  methane.  In  the  Belgian  government  tests 
the  lamp  successfully  withstood  air  currents  containing  8  %  of  methane  when 
moving  900  m.,  or  2,952  ft.,  per  min.  (33.5  mi.  per  hr.),  regardless  of  the 
angle  at  which  the  air  struck  the  lamp. 

The  Hailwood  oil-burning  lamp  differs  in  a  few  details  from  the  naphtha- 
burning  lamp  just  described.  The  picker,  which  is  of  copper  and  through 
which  an  electric  current  may  be  passed,  is  provided  with  two  prongs  or 
arms,  one  of  which  is  used  to  snuff  or  trim  the  lamp  wick  and  the  other  to 
convey  the  current  to  the  wick  tube  when  it  is  desired  to  relight  the  lamp. 
Other  lamps  of  this  name,  designed  more  particularly  for  gas  testing,  are  of 
the  Mueseler  type  but  with  a  glass  instead  of  a  metal  chimney  on  the  back 
and  inner  side  of  which  is  a  piece  of  metal  as  a  background  against  which  to 
better  view  the  gas  caps. 

SPECIAL  TYPES  OF  SAFETY  LAMPS 

Clowes  Hydrogen  Lamp. — The  Clowes  hydrogen  lamp  is  essentially  an 
A-H-G  lamp  with  a  somewhat  taller  chimney  and  an  attached  device  for 
burning  hydrogen.  A  seamless  copper  tube  is  inserted  in  the  bowl  beside 
the  wick  tube  and  is  connected  either  below  or  at  the 
side  of  the  lamp  with  a  small  portable  cylinder  a  (Fig. 
3)  containing  hydrogen.  The  cylinder,  which  is  about 
5  in.  long  and  1  in.  in  dia- 
meter, is  attached  to  the 
lamp  by  the  clip  b  and  the 
screw  e.  In  testing  for  gas, 
the  valve  d  is  opened,  the 
hydrogen  enters  the  lamp 
and  is  ignited  at  the  mouth 
of  its  burner  by  the  oil 
flame,  which  is  then  pulled 
down  by  the  picker  until  it 
is  extinguished.  By  means 
of  the  valve  d,  which  regu- 
lates the  supply  of  hydro- 
gen, the  height  of  the  test- 
ing flame  is  adjusted  until 
its  top  coincides  with  a 
scale  not  shown  in  the 
figure,  the  adjustment  be- 
ing made  in  air  free  from 
methane.  The  scale  con- 
sists of  a  number  of  cross- 
bars in  a  ladder-like  frame 
placed  in  front  of  the  flame. 
The  heights  of  the  cross- 
bars (which  appear  as  dark 
lines  against  the  flame) 
mark  the  heights  of  the  gas 


FIG.  3 


FIG.  4 


caos  corresponding  to  various  percentages  of  pure  methane  burning  in  pure 
air.  The  hydrogena  ttachment  is  designed  to  render  possible  the  detection 
of  1  to  3  %  of  gas;  for  higher  percentages,  the  oil  flame  is  used.  With  i  %  of 
gas  the  cap  is  £  in.  high,  and  with  2  %  of  gas  about  l|  in. 

Stokes  Alcohol  Lamp.— The  Stokes  alcohol  lamp,  Fig.  4,  is  a  modification 
of  the  A-H-G  lamp  in  which  a  small  alcohol  flame  is  introduced  beside  the 


890 


VENTILATION  OF  MINES 


regular  oil  flame.  The  small  alcohol  bowl  a  is  screwed  beneath  the  regular 
oil  bowl  and  is  provided  with  a  long  wick  tube  b.  When  the  screw  plug  c 
is  removed  and  the  alcohol  lamp  screwed  in  place  its  wick  is  lit  by  the  oil 
flame  d  which  is  then  extinguished  by  drawing  down  the  wick  with  the  picker. 
In  other  respects  the  lamp  is  the  same  as  the  Clowes.  The  alcohol  is  not  as 
persistent  as  the  hydrogen  flame  and  is  more  easily  extinguished  in  gas;  on 
the  other  hand,  it  is  more  stable  in  gas  than  the  oil  flame  but  is  more  easily 
blown  out  by  the  wind.  The  lamp  is  designed  to  detect  from  $  to  3  %  of  gas. 
Pieler  Lamp.  —  The  Pieler  lamp,  Fig.  5,  is  essentially  a  Davy  lamp  with 
an  exceptionally  tall  gauze,  and  is  arranged  to  burn  alcohol.  The  flame  is 
surrounded  by  a  short  conical  metal  bonnet  or  shade  reaching  up  about  2  in. 
from  the  bottom  of  the  gauze,  and  into  coincidence  with  the  top  of  which  the 
tip  of  the  lamp  flame  is  brought  by  adjusting  in  fresh  air.  Affixed  to  the 
lamp  standards  is  a  slotted  metal  plate,  each  slot  marking  the  height  of  gas 
cap  corresponding  to  a  certain  percentage  of  pure  gas  in  air.  The  lamp  in 
the  cut  is  designed  to  indicate  percentages  of  gas  from  }  to  1?%,  increasing 


FIG.  5 


FIG.  6 


by  £  %.  When  the  cap  reaches  the  top  of  the  scale  plate,  2  %  of  gas  is  pres- 
ent. The  lamp  illustrated  is  unbonneted.  The  bonneted  Pieler  greatly 
resembles  the  Chesneau  lamp,  Fig.  6,  in  external  appearance,  as  the  scale 
plate  is  replaced  by  a  glass  plate  inserted  in  the  bonnet,  on  which  are  etched 
lines  corresponding  to  the  height  of  the  flame  caps. 

The  Pieler  lamp  is  extensively  used  in  Austria  (where  it  originated)  and 
Germany,  but  it  is  of  limited  application  in  the  United  States.  The  lamp, 
like  all  of  the  Davy  type,  is  unsafe  in  air  currents  of  any  but  low  velocity, 
Beyond  2%  of  gas,  the  lamp  is  useless  as  the  gauze  which  is  Sin.  high  fills 
with  flame.  Where  the  gaseous  conditions  are  unknown,  it  is  advisable  to 
make  a  preliminary  test  with  an  9rdinary  lamp,  as  the  Pieler  is  practically 
certain  to  pass  the  flame  if  placed  in  an  explosive  mixture  of  gas  and  air. 

The  absorptive  power  of  the  cotton,  with  which  the  bowl  of  the  lamp  is 
filled,  is  commonly  great  enough  to  modify  the  height  of  the  flame  cap  and 
consequently^  affect  the  accuracy  of  the[determinations.  Furthermore,  after 
a  determination  has  been  made,  the  heat  remaining  in  the  gauze  assists  in 
the  volatilization  of  the  naturally  volatile  alcohol,  so  that  for  20  to  30  min., 
or  until  it  thoroughly  cools  down,  the  lamp  cannot  be  used  f9r  a  second  test 
as  there  will  be  an  artificial  atmosphere  of  alcohol  vapor  within  the  gauze. 

Chesneau  Lamp.— The  Chesneau  lamp,  Fig.  6,  of  French  origin,  is  a 
bonneted  Clanny  with  underdraft  and  is  designed  to  burn  alcohol.  In  the 


VENTILATION  OF  MINES  891 

figure,  c  is  one  of  the  openings  through  which  air  has  access  to  the  gauze 
ring  surrounding  the  lamp  below  the  wick  tube.  The  cylinder  a  plays 
the  same  part  as  the  conical  shield  in  the  Pieler  lamp,  and  the  lamp  flame, 
when  a  test  is  to  be  made,  is  adjusted  to  the  level  of  its  top,  that  is,  to  the  base 
of  the  main  gauze.  The  gauzes  in  this  lamp  have  1,264  openings  per  sq.  in. 
In  the  front  of  the  bonnet  is  inserted  a  mica  window  d  with  a  scale  on  either 
side.  One  scale  is  graduated  in  millimeters  for  measuring  the  height  of  the 
gas  cap,  and  the  other  is  graduated  in  the  corresponding  percentages  of  gas. 
A  sliding  shield  d  can  be  adjusted  to  the  exact  height  of  the  cap,  thus  per- 
mitting of  much  more  precise  readings. 

The  Chesneau  lamp  is  much  superior  to  the  Pieler  in  that  it  is  safe  in  air 
currents  moving  over  2,000  ft.  per  min.,  and  requires  but  30  to  90  sec.  to 
cool  down  between  tests;  but,  as  in  the  Pieler  lamp,  the  accuracy  of  the  tests 
is  somewhat  interfered  with  by  the  absorptive  power  of  the  cotton  in  the  bowl. 
It  should  be  noted,  however,  in  the  Chesneau  as  in  the  Pieler  lamp  so  long 
as  the  physical  condition  of  the  cotton  is  the  same  as  when  the  lamp  was 
standardized,  its  indications  are  accurate. 

Stuchlick  Acetylene  Safety  Lamp. — The  Stuchlick  acetylene  safety  lamp, 
an  Austrian  invention,  is  essentially  a  Clanny  lamp  designed  to  generate 
and  burn  acetylene  gas.  The  bowl  of  the  lamp  is  double  and  consists  of  an 
outer  carbide  box  in  a  groove  in  which  slides  an  interior  water  vessel,  the 
two  being  connected  by  a  flexible  siphon  tube.  The  water  vessel  can  be 
raised  and  lowered  within  the  carbide  box,  and  is  held  in  position  by  a 
spring  and  screw.  The  lamp,  which  weighs  about  3  lb.,  is  held  together  by 
screwing  on  the  bowl. 

After  the  carbide  box  is  two-thirds  filled  with  calcium  carbide,  the  water 
vessel  is  pushed  down  to  its  lowest  position  and  filled  with  water.  The  lamp 
is  then  assembled.  In  the  lowest  position  of  the  water  box  the  level  of  the 
water  in  it  is  below  that  of  the  opening  into  the  carbide  box,  and  the  genera- 
tion of  acetylene  is  not  possible.  As  the  water  box  is  raised,  water  flows 
through  the  siphon  tube  into  the  carbide  box  and  the  acetylene  then  given 
off  enters  the  burner  through  a  small  pipe  within  the  flexible  tube.  Any 
excess  of  gas  is  carried  back  into  the  water  vessel  and  thence  to  the  open  air, 
the  flexible  pipe,  which  has  a  hydraulic  joint,  acting  as  a  safety  valve.  In 
testing  for  gas,  the  flame  is  adjusted  for  height  by  a  screw  which  moves  the 
gas  nipple  in  the  burner. 

One  per  cent,  of  methane  in  air  is  easily  detected  by  the  green  halo  which 
surrounds  the  acetylene  flame,  which,  in  dangerous  percentages  of  gas,  is 
extinguished  by  the  products  of  combustion.  One-third  pound  of  calcium 
carbide  and  one  filling  of  the  water  box  will  furnish  a  light  for  8  hr.  at  a  less 
cost  than  benzene. 

Tombelaine  Acetylene  Safety  Lamp. — The  Tombelame  lamp  is  an  under- 
draft  and  bonneted  Clanny  with  double  gauzes,  the  inner  of  which  extends 
downward  over  the  flame  similarly  to  the  Mueseler  chimney  so  that  any 
sudden  enlargement  of  the  acetylene  flame  will  not  break  the  glass.  The 
bowl  of  the  lamp  is  double,  the  inner  cylinder  holding  the  carbide  and  the 
outer  the  water.  In  use,  the  inner  cylinder  after  being  filled  with  carbide 
is  screwed  into  place  and  the  bottom  of  the  lamp  placed  in  water  which 
flows  into  the  water  holder  through  openings  designed  for  the  purpose.  The 
amount  of  water  entering  the  carbide  chamber,  the  flow  of  acetylene  to  the 
burner,  and  the  height  of  flame  are  regulated  by  a  thumbscrew  in  the  base 
of  the  lamp.  The  lamp  weighs  1.5  kg.  (3.3  lb.),  has  an  illumination  of  about 
6  c.p.,  and  will  burn  11  hr.,  with  a  slightly  greater  consumption  of  acetylene 
than  the  Stuchlick  lamp. 

GAS  INDICATORS  AND  GAS-SIGNALING  DEVICES 
Use  and  Principles. — Gas  indicators  are  designed  to  more  exactly  deter- 
mine the  amount  of  methane  in  mine  air  than  does  the  ordinary  safety  lamp. 
These  devices  are  based  on  the  use  of  some  one  of  the  well-known  physical  or 
chemical  properties  of  gases,  such  as:  The  difference  in  the  density  or  in  the 
rate  of  diffusion  of  methane  and  air;  the  heat  generated  by  the  burning  ot 
methane  or  the  contraction  in  volume  of  its  products  of  combustion;  the 
increased  brilliancy  of  platinum  or  palladium  wire,  or  their  increased  elec- 
trical resistance  when  heated  in  the  presence  of  methane;  the  absorption  of 
methane  by  platinum  or  palladium  sponge,  etc. 

In  addition  to  the  foregoing  are  colored  glass,  various  chemicals,  loops  ot 
wire,  etc.,  the  use  of  which  is  intended  to  make  more  distinctly  visible  the 
gas  cap  formed  in  the  ordinary  safety  lamp. 


892  VENTILATION  OF  MINES 

While,  in  the  main,  based  upon  correct  principles,  these  devices,  with  few 
exceptions,  have  been  discarded  as  being  too  cumbersome  or  costly;  as 
requiring  top  much  time  or  skill  in  their  manipulation;  or  as  being  inaccurate 
under  practical  mining  conditions  while  meeting  the  perfect  ones  in  the  labora- 
tory. This  last  objection  is  the  most  serious,  and  it  is  clear  that  any  appa- 
ratus which  is  standardized  under  certain  atmospheric  conditions  and  for 
pure  methane  and  pure  air,  as  it  would  be  in  the  laboratory,  cannot  give 
correct  readings  in  the  mine  where  the  atmospheric  conditions  may  be  and 
usually  are  widely  different  and  where,  above  all,  the  air  is  certain  to  be  more 
or  less  deficient  in  oxygen  and  contaminated  with  nitrogen,  carbon  dioxide, 
etc. 

In  a  signaling  device  or  system  numerous  gas  indicators  placed  at  points 
in  the  workings  where  methane  is  apt  to  accumulate  are  electrically  connected 
with  some  central  station,  as  the  superintendent's  office.  When  methane 
is  present,  the  indicators  become  operative,  closing  their  respective  circuits 
and  thus  ringing  bells  or  moving  pointers  at  the  central  station. 

Gas-signaling  systems  have  never  proven  satisfactory.  The  indicators 
fail  for  the  reasons  previously  stated  and,  as  they  are  not  instantaneous  in 
their  action,  never  give  warning  of  gas  until  some  time  after  it  has  accumu- 
lated. They  are  particularly  at  fault  in  that  they  announce  the  presence 
of  gas  only  at  points  where  an  indicator  is  placed  and,  as  it  is  impossible  to 
entirely  cover  the  workings  with  indicators,  a  dangerous  accumulation  of 
gas  may  exist  within  a  few  feet  of  one  of  these  appliances.  Further,  indi- 
cators of  the  type  that  glow  in  the  presence  of  methane  are  dangerous,  even 
when  enclosed  in  safety-lamp  gauze. 

Experience  thus  far  has  shown  that  for  the  detection  of  gas  at  the  face 
nothing  is  better  adapted  than  a  standard  safety  lamp,  and  for  accurate 
percentage  determinations,  chemical  analysis  should  be  relied  upon. 

Liveing  Indicator. — The  Liveing  indicator  consists  of  two  coils  or  spirals 
of  platinum  wire  of  equal  electrical  resistance  enclosed  in  separate  glass- 
ended  cylinders  set  facing  each  other  and  about  4  in.  apart.  One  of  the 
cylinders,  which  is  tightly  sealed,  is  filled  with  pure  air,  and  the  other  is  made 
of  standard  safety-lamp  gauze.  Between  the  spirals  is  a  wedge-shaped 
mirror  for  reflecting  their  image  upward  through  the  small  glass  window  of 
the  box  containing  the  apparatus.  By  applying  suction  (by  the  mouth  or  a 
small  air  pump)  to  the  end  of  a  rubber  tube  attached  to  the  box,  mine  air  is 
drawn  into  the  apparatus  through  another  tube  which  is  made  long  enough 
to  reach  places  not  readily  accessible,  as  cavities  in  the  roof,  etc. 

When  an  electric  current,  generated  by  turning  the  handle  of  a  small 
magneto  placed  in  the  bottom  of  the  box,  is  passed  through  the  spirals  they 
glow  with  equal  intensity,  if  no  methane  is  present.  If,  however,  gas  is 
present,  the  spiral  within  the  gauze  cylinder  will  glow  more  brightly.  The 
mirror  is  then  moved  until  the  images  of  the  two  spirals  as  viewed  through 
the  window  appear  of  equal  intensity,  when  the  percentage  of  gas  may  be 
read  from  a  graduated  scale  over  which  the  mirror  passes. 

Repeated  heating  of  the  gauze-encased  spiral  alters  its  electrical  conduc- 
tivity to  such  an  extent  that  it  soon  becomes  necessary  to  adjust  the  zero 
point  of  the  scale  in  fresh  air  before  a  test  is  made.  This  is  done  by  heating 
up  the  coils  and  shifting  the  mirror  until  the  images  appear  of  equal  bright- 
ness; the  zero  of  the  scale  is  then  made  to  coincide  with  the  position  of  the 
mirror. 

Coquillon's  Indicator. — Coquillon's  indicator  consists  of  a  glass  tube  in 
which  is  a  loop  of  palladium  wire  that  can  be  heated  to  incandescence  by  a 
small  battery  contained  within  the  same  box  as  the  tube.  If  a  measured 
quantity  of  mine  air  containing  methane  is  introduced  into  the  tube  and  the 
electric  current  is  applied,  all  the  gas  will  be  burned  and  the  contraction  in 
volume  of  the  products  of  combustion  is  a  measure  of  the  percentage  of  gas 
present.  This  indicator  is  really  an  apparatus  for  making  a  rapid  analysis 
of  mine  air. 

Le  Chatelier's  Indicator. — Le  Chatelier's  indicator,  while  differing  from 
Coquillon's  in  a  few  minor  details,  is  chiefly  distinct  in  the  use  of  platinum 
for  palladium  wire. 

The  indicators  devised  by  Maurice,  Monier,  and  some  others  are  based 
upon  the  same  principle  as  Le  Chatelier's. 

Turquand's  Indicator. — Turquand's  indicator  consists  of  a  glass  U-tube  of 
fine  bore  about  one-half  filled  with  mercury.  The  ends  of  the  tube  are 
inserted  in  a  metal  block  in  such  a  way  that  there  is  a  small  space  between 
the  top  of  each  arm  of  the  tube  and  the  bottom  of  a  porous  stopper  inserted 


VENTILATION  OF  MINES  893 

in  the  corresponding  holes  in  the  block.  In  one  of  these  spaces  is  an  absorb- 
ent  to  distinguish  between  methane  and  carbon  dioxide,  and  in  the  other  is  a 
coil  of  palladium  wire  that  can  be  made  to  glow  by  passing  an  electric 
current  through  it.  Normally,  the  mercury  stands  at  the  same  level  in  the 
two  arms  of  the  tube,  but  when  methane  or  other  hydrocarbon  gases  that 
are  absorbed  by  hot  palladium  wire  enter  through  the  porous  stopper,  heat 
is  generated  and  the  thread  of  mercury  is  pushed  down  one  leg  and  up  the 
other,  the  difference  in  level  of  the  columns  of  mercury  being  a  measure  of 
the  amount  of  gas  present. 

The  Swan  indicator  is  of  this  type,  but  employs  the  expansion  of  a  column 
of  mercury  by  the  heat  liberated  by  the  absorption  of  methane  by  a  glowing 
platinum  wire,  to  show  the  percentage  of  gas  present  upon  a  graduated  scale. 

Ralph's  Indicator. — Ralph's  indicator  employs  a  differential  galvanometer, 
in  one  coil  of  which  is  a  piece  of  platinum  wire  enclosed  in  standard  safety- 
lamp  gauze  so  that  it  may  safely^  be  exposed  in  air  containing  methane. 
When  no  gas  is  present  and  an  electric  current  is  passedthroughtheapparatus, 
the  needle  or  indicator  of  the  galvanometer  is  not  deflected  as  the  resistance 
of  the  two  coils  is  the  same.  When  methane  is  present,  its  absorption 
by  the  platinum  wire  increases  the  resistance  in  that  coil,  and  the  needle  is 
deflected  by  an  amount  proportional  to  the  percentage  of  gas  in  the  air. 

This  indicator  is  the  basis  of  some  signaling  systems  in  which  the  variation 
in  resistance  is  made  to  extinguish  a  distant  light,  to  place  a  distant  buzzer 
in  action,  etc. 

Garforth-Walker  Indicator. — That  the  amount  of  methane  required  to 
make  a  platinum  wire  glow  when  an  electric  current  is  passed  through  it  is 
proportional  to  the  thickness  of  the  wire  is  made  the  basis  of  an  indicator 
devised  by  Mr.  S.  F.  Walker  for  Sir  William  Garforth.  Several  small  glass 
tubes  are  fixed  inside  the  protecting  glass  of  any  portable  electric  lamp. 
The  tubes  are  arranged  to  be  easily  replaced,  are  enclosed  in  safety-lamp 
gauze,  and  contain  platinum  wire  of  a  gauge  or  thickness  proportional  to 
the  percentage  of  gas  in  air  that  each  particular  tube  is  intended  to  indicate. 
At  the  entrance  to  each  tube  is  a  self-closing_  valve  that  can  be  pushed  open 
by  the  metal  nozzle  of  a  rubber  bulb  which  is  filled  with  the  mine  air  to  be 
tested,  the  insertion  of  the  nozzle  automatically  switching  on  the  current 
to  the  wire.  After  sufficient  time  is  allowed  for  the  wire  to  reach  the  proper 
temperature,  the  contents  of  the  bulb  are  squeezed  out,  the  wire  glowing  if  the 
percentage  of  methane  corresponding  to  the  particular  tube  is  present.  In 
testing,  the  tube  with  the  coarsest  wire,  which  indicates  the  greatest  per- 
centage of  gas,  is  used  first;  if  the  percentage  of  gas  is  not  great  enough  to 
make  this  wire  glow,  tubes  with  successively  finer  wires  are  used  until  one 
is  found  that  is  sensitive  to  the  percentage  of  gas  present.  Palladium 
may  be  used  to  advantage  in  place  of  platinum  wire.  This  apparatus  is  still 
in  the  experimental  stage. 

Ansell's  Indicator. — Ansell's  indicator  consists  of  a  cylindrical  chamber, 
one  side  of  which  is  formed  by  a  movable  diaphragm  of  porous  unglazed 
earthenware  and  the  other  by  a  stationary  graduated  dial  or  plate  to  the 
center  of  which  is  pivoted  a  hand  or  needle,  the  apparatus  somewhat  resem- 
bling an  aneroid  barometer  in  appearance.  When  exposed  to  a  mixture  of 
methane  and  air,  the  gas  diffuses  through  the  porous  diaphragm  more  rapidly 
than  the  air  passes  out,  causing  a  difference  in  pressure  on  the  two  sides  with 
a  resultant  outward  movement  of  the  diaphragm.  By  means  of  mechanism, 
the  motion  of  the  diaphragm  is  made  to  move  the  needle  over  the  circular 
scale  on  the  edge  of  the  dial  on  which  the  percentage  of  methane  may  be 
read  off.  After  making  a  test,  the  needle  must  be  set  back  to  zero  by  expos- 
ing the  apparatus  in  pure  air,  a  process  requiring  considerable  time. 

In  some  indicators  of  this  type  the  diaphragm  is  placed  midway  between 
the  ends,  one  of  which  is  porous  while  the  other  carries  the  scale. 

The  action  of  all  indicators  of  this  type  becomes  absolutely  unreliable  if  a 
deficiency  of  oxygen  or  an  excess  of  carbon  dioxide  or  moisture  or  a  rise  or 
fall  of  temperature  affects  the  density  of  the  air,  as  the  rate  of  diffusion 
is  then  changed  from  that  prevailing  when  the  instrument  was  standardized. 
Clowes  has  shown  that  when  4  %  of  coal  gas  and  3  %  of  methane  was  present, 
the  indicator  showed  but  1.71  %  of  the  latter  gas;  also,  that  when  absolutely 
pure  air  was  heated,  the  indicator  showed  it  to  contain  4  %  of  gas,  and  that 
when  the  same  air  was  cooled  the  indicator  gave  a  minus  reading  of  the  same 
amount. 

The  indicators  devised  by  Libin,  McCutcheon,  Webster,  and  some  others 
are  of  this  type. 


894  VENTILATION  OF  MINES 

William's  Methanometer, — William's  methanometer,  which  resembles  the 
previously  mentioned  Ralph  indicator,  consists  of  a  pair  of  thermo-electric 
couples  connected  with  a  galvanometer.  Each  couple  is  enclosed  in  porous 
material,  that  surrounding  one  of  them  being  impregnated  with  platinum- 
black  to  absorb  methane.  The  couples  may  be  brought  to  the  temperature 
at  which  platinum-black  is  most  sensitive  to  methane  by  means  of  a  battery 
current  and,  if  no  gas  is  present,  the  needle  of  the  galvanometer  remains 
stationary.  If,  however,  gas  exists,  the  temperature  of  the  couple  surrounded 
by  platinum-black  will  be  raised  through  its  absorption  of  methane,  its 
resistance  will  be  changed  and  the  needle  of  the  galvanometer  will  be  deflected 
in  proportion  to  the  amount  of  gas  present.  The  indicator  is  made  in  port- 
able form  for  fire  bosses  and  may  be  used  as  the  basis  of  a  signaling  system 
when  connected  to  the  necessary  wires  for  transmitting  the  indications  of 
the  needle  to  a  distance. 

Aitkin's  Indicator. — In  the  Aitkin  indicator  two  thermometers  are  sus- 
pended side  by  side  in  the  same  frame,  the  bulb  of  one  being  covered  with 
platinum-black  (spongy  platinum).  In  pure  air  the  readings  of  the  ther- 
mometers will  be  the  same,  but  if  methane  is  present  its  absorption  by  the 
platinum-black  causes  a  rise  in  temperature  which  is  indicated  by  the  proper 
thermometer  and  which  is  a  measure  of  the  percentage  of  gas.  The  appara- 
tus is  not  accurate  in  that  the  platinum-black  rapidly  deteriorates  through 
the  absorption  of  moisture  and  through  the  deposition  of  dust  on  its  surface 
and,  further,  because  platinum  is  insensitive  to  low  percentages  of  gas  when 
cold. 

An  indicator  of  this  type  was  at  one  time  attached  to  the  Sussmann  port- 
able electric  lamp. 

Beard-Mackie  Sight  Indicator. — The  Beard- Mackie  sight  indicator  is  a 
device  for  making  visible  and  more  accurately  measuring  the  height  of  the 
caps  made  by  small  percentages  of  gas.  While  it  may  be  applied  to  any 
safety  lamp,  it  is  commonly  used  in  connection  with  the  Davy  or  with  those 
having  an  underdraft.  The  indicator,  which  resembles  a  ladder  in  appear- 
ance, consists  of  two  upright  standards  between  which  are  strung  a  series 
of  fine  wires,  the  lowest  being  of  brass  and  the  others  of  platinum.  The 
standards  are  soldered  to  a  brass  washer  which  fits  over  the  neck  of  the  wick 
tube  or,  better,  which  is  pivoted  so  that  the  indicator  may  be  swung  into 
the  flame  only  when  a  test  is  to  be  made.  The  latter  construction  prevents 
the  sooting  of  the  wires  through  continued  contact  with  the  flame,  which  is 
the  greatest  drawback  to  the  use  of  this  indicator.  In  testing,  the  lamp 
flame  is  adjusted  in  fresh  air  until  the  lowest,  or  standard,  wire  is  just  aglow. 
The  platinum  wires  are  so  spaced  that  when  $  %  of  methane  is  present  the 
lowest  of  them  will  glow,  when  1  %  is  present  both  the  first  and  second,  and 
similarly  up  to  the  last  wire  which  indicates  3  %  of  gas. 

Brigg's  Wire  Loop. — Brigg's  wire  loop  which  is  intended  to  delumine,  or 
remove  the  color  from  the  lamp  flame  in  order  that  the  gas  cap  may  be  more 
distinctly  visible,  may  be  applied  to  any  safety  lamp  and  is  not  patented. 
The  device  consists  of  a  piece  of  22-gauge  copper  wire  bent  into  a  loop,  the 
longer  axis  of  which  is  equal  in  width  to  the  wick  of  the  safety  lamp.  The 
loop  is  supported  upon  an  upright  brass  standard  extending  through  the  lamp 
bowl  so  that  it  may  be  swung  in  or  out  of  the  flame.  In  testing,  the  flame 
is  left  at  its  normal  working  height.  As  soon  as  the  loop  is  swung  into  it  the 
flame,  this,  without  being  reduced  in  size,  loses  its  yellow  color  and  the 
cap,  if  methane  is  present,  in  as  little  as  \  %  of  gas  becomes  visible  and  that 
of  §  %  of  gas  may  be  measured. 

By  dipping  the  loop  in  a  solution  of  chloride  of  zinc  a  green  coloration  is 
imparted  to  the  lamp  flame,  to  the  so-called  fuel  cap  (if  present)  and,  to  a 
less  extent,  to  the  gas  cap.  This  action  improves  the  indications  consider- 
ably, but  the  chloride  of  zinc  soon  burns  off.  The  loop,  however,  sometimes 
gives  a  fairly  strong  green  flame  without  this  treatment,  especially  if  it  has 
not  been  used  for  some  days,  and  it  generally  gives  a  very  faint  one. 

The  flame  may  be  intensified  by  introducing  1  or  \\%  of  carbon  tetra- 
chloride  into  the  lamp  oil  or  naphtha,  at  a  cost  of  roughly  \  c.  a  shift.  The 
tetrachloride  does  not  affect  the  working  flame,  but  when  the  loop  is  moved 
into  it  the  flame  becomes  green  from  the  copper  chloride  and  the  gas  cap, 
if  present,  a  bright  blue  from  the  copper  oxide  formed. 

Cuninghame-Cadbury  Indicator. — In  the  Cuninghame-Cadbury  indicator 
a  small  sheet  of  asbestos  is  secured  on  a  holder  in  much  the  same  way  as  the 
Brigg's  wire  loop  so  that  it  may  be  moved  in  or  out  of  the  normal,  or  but 
"  itly  reduced,  flame  of  the  lamp.  The  asbestos,  which  is  twice  steeped 


VENTILATION  OF  MINES  895 

in  a  strong  solution  of  carbonate  of  soda,  is  placed  about  i  in.  above  the 
wick,  and  enters  the  flame  for  about  two-thirds  the  thickness  of  the  same. 
In  pure  air  a  slight  fuzzy  yellow,  or  orange,  halo  will  appear  around  the  flame 
toward  the  upper  part  of  the  asbestos.  If  methane  is  present,  the  halo  will 
be  surmounted  by  a  yellowish  conical  cap  the  length  and  distinctness  of 
which  depends  on  the  per  cent,  of  gas.  In  some  cases  a  perpendicular  scale 
for  measuring  the  he  ght  of  gas  caps  is  attached  to  the  snuffer  pin  so  that  it 
can  be  temporarily  moved  into  position  when  testing.  It  is  stated  that  the 
use  of  this  device,  which  is  not  patented  and  may  be  attached  to  any  safety 
lamp,  permits  the  detection  of  as  little  as  5  %  of  gas. 

Colored  Glass  Indicators. — In  order  to  cut  off  the  yellow  light  and  thus 
render  the  cap  more  distinctly  visible,  Mr.  A.  L.  Steavenson  suggests  that 
a  sheet  of  blue  glass  be  interposed  between  the  flame  and  the  eye,  or  that  a 
pair  of  blue  glass  spectacles  be  worn  while  testing. 

To  do  away  with  the  reflection  of  the  flame  and  cap  in  the  polished  glass 
of  the  ordinary  safety  lamp  which  often  interferes  with  the  accuracy  of  the 
test,  a  strip  of  dull-surfaced  metal  may  be  placed  back  of  the  flame.  The 
same  result  may  be  obtained  by  making  a  strip  of  soot  or  smoke  down  one 
side  of  the  glass  after  it  has  been  cleaned.  As  an  additional  precaution,  all 
metallic  surfaces,  such  as  the  bowl,  standards,  etc.,  that  can  in  any  way 
reflect  the  flame  may  be  given  a  dull  finish. 

Forbes  Indicator. — The  F9rbes  indicator  consists  9f  a  brass  tube  about  6 
in.  long  in  which  moves  a  piston  the  position  of  which,  in  terms  of  the  per 
cent,  of  methane  in  the  air,  is  indicated  by  a  pointer  and  scale.  In  the 
mouth  of  the  tube  is  fixed  a  tuning  fork  that  makes  512  vibrations  a  second 
and  emits  a  corresponding  sound  when  fresh  air  is  forced  through  the  tube 
by  moving  the  piston.  If  the  density  of  the  air  is  lowered  by  the  presence 
of  methane,  the  length  of  stroke  of  the  piston  and  the  corresponding  yolume 
of  air  required  to  produce  a  note  of  equal  depth  is  not  the  same  as  in  pure 
air,  the  difference  being  measurable  on  the  scale.  In  making  tests  an  al- 
lowance is  necessary  for  changes  in  the  density  of  the  air  due  to  variations 
in  temperature. 

Firedamp  Whistle. — In  the  firedamp  whistle  the  attempt  is  made  to  esti- 
mate the  percentage  of  methane  in  the  air  by  the  difference  in  the  sound 
emitted  by  a  metal  pipe  when  air  currents  of  different  densities  are  blown 
through  it.  When  pure  air  is  used,  the  pipe,  which  is  about  10  in.  long  and 
2£  in.  in  diameter,  emits  a  certain  tone,  but  as  the  density  of  the  mine  air 
decreases  as  the  proportion  of  methane  in  it  increases,  the  tones  become 
higher  and  tremulous.  The  device,  which  is  an  adaptation  of  the  Forbes 
indicator,  can  hardly  be  considered  reliable,  as  changes  in  temperature  and 
pressure,  or  a  deficiency  in  oxygen,  or  an  increase  in  carbon  dioxide  or  nitro- 
gen, will  affect  the  density  of  the  air  as  well  as  changes  in  the  methane 
content. 

Hardy  Indicator. — In  the  Hardy  indicator  there  are  two  separate  pipes, 
alike  in  every  respect,  one  of  which  is  blown  with  pure  air  and  the  other 
with  the  mine  air  to  be  tested.  The  number  of  vibrations  per  second  made 
by  the  pipes  is  made  the  measure  of  the  percentage  of  methane  present. 
The  same  objections  apply  to  this  indicator  as  to  the  Forbes  and  to  the  fire- 
damp whistle. 

Shaw  Gas-testing  Machine. — In  the  Shaw  machine,  a  graduated  beam 
operated  by  a  crank  and  connecting  arm  raises  and  lowers  the  pistons  in 
two  vertical  cylinders  known  as  the  air  and  gas  cylinders,  respectively. 
The  larger,  or  air,  cylinder  is  fixed  in  position,  while  the  smaller,  or  gas, 
cylinder  may  be  shifted  along  a  graduated  slide  in  such  a  way  that  the  length 
of  travel  of  its  piston  and  consequently  the  volume  of  its  discharge  may  be 
varied.  Both  cylinders  discharge  into  a  small  combustion  cylinder  in  front 
of  which  a  gas  jet  is  burning  and  one  end  of  which  is  movable  outward  against 
a  gong.  As  a  preliminary  operation  it  is  necessary  to  determine  the  per- 
centage of  some  readily  available  gas  (as  illuminating  gas)  that  must  be 
mixed  with  pure  air  in  order  to  produce  an  explosion.  To  do  this,  pure  air 
and  pure  illuminating  gas  are  pumped  from  their  respective  cylinders  until 
the  mixture  delivered  to  the  combustion  chamber  is  feebly  explosive  as 
evidenced  by  a  slight  ringing  of  the  gong  when  the  mixture  is  lit  and  exploded 
by  the  gas  jet.  This  requires  several  determinations,  much  shifting  of  the 
gas  cylinder  to  secure  the  proper  ratio  of  gas  to  air,  and  consumes  a  good  deal 
of  time. 

If  mine  air  in  place  of  pure  air  is  pumped  from  the  air  cylinder  into  the 
combustion  chamber,  less  and  less  illuminating  gas  will  be  required  to  make 


896  VENTILATION  OF  MINES 

the  mixture  explosive  as  the  percentage  of  methane  in  the  air  increases.  A 
rubber  bag  containing  mine  air  is  connected  with  the  air  cylinder  and  the 
position  of  the  gas  cylinder  shifted  until  the  mixture  from  the  two  cylinders 
as  delivered  to  the  combustion  chamber  is  of  the  same  explosive  intensity  as 
the  mixture  of  pure  air  and  gas.  From  the  position  of  the  gas  cylinder  in 
either  case  may  be  calculated  the  percentage  of  illuminating  gas  required  to 
produce  an  explosion  both  with  pure  and  with  mine  air.  A  simple  proportion 
then  gives  the  percentage  of  methane  in  the  mine  air. 

This  apparatus  is  bulky,  expensive,  and  slow,  but  at  one  time  had  a 
considerable  following  through  intensive  advertising.  It  is  no  longer  used. 

Hauger  and  Pescheux  Gas-signaling  Apparatus. — In  the  signaling  appara- 
tus devised  by  Hauger  and  Pescheux,  an  extremely  sensitive  balance  carries 
on  one  end  a  tightly  sealed  vessel  of  pure  air  and  on  the  other  a  tray  of  the 
same  area  and  weight  as  the  air  vessel.  If  the  composition  of  the  atmosphere 
is  changed  in  any  way,  its  density  will  vary  according  to  the  percentage  of 
gas  invading  it  and,  as  the  composition  of  the  air  in  the  closed  vessel  is 
unaltered,  the  equilibrium  of  the  balance  will  be  destroyed.  If  the  gases 
invading  the  atmosphere  are  lighter  than  air  the  air  chamber  will  descend, 
but  if  they  are  heavier  than  air  it  will  ascend.  Attached  to  the  beam  is  a 
needle  dipping  in  a  cup  of  mercury  which,  immediately  on  disturbance  of 
the  balance,  closes  an  electric  circuit  that  may  be  made  to  ring  a  bell  or  set 
a  danger  signal  at  any  distance  from  the  apparatus.  To  allow  for  the  dis- 
turbing influences  of  changes  in  atmospheric  temperature  and  pressure,  two 
compensators  are  attached  to  the  beam.  One  of  these  is  an  aneroid  barom- 
eter which  acts  on  a  multiplying  lever  which  in  turn  changes  the  position 
of  a  rider  which  slides  along  a  thread.  To  compensate  for  changes  in  tem- 
perature, a  bimetallic  spiral  is  made  to  act  on  a  lever  which,  in  its  turn,  shifts 
the  position  of  a  rider  on  the  beam. 

Low  Gas-signaling  Apparatus. — The  low  signaling  apparatus  consists  of 
two  wires  arranged  in  V-shape  and  held  in  tension  by  a  bar  and  spring.  One 
wire  is  of  platinum  and  carries  at  short  intervals  lumps  of  spongy  platinum; 
the  other  is  of  iron  and  brass  in  such  proportions  that  its  coefficient  of  expan- 
sion is  the  same  as  that  of  the  platinum  for  equal  changes  of  temperature. 
As  long  as  the  wires  contract  and  expand  equally  they  are  kept  in  tension  by 
the  spring  referred  to,  but  should  the  platinum  wire  sag  by  reason  of  its 
more  rapid  expansion,  an  arrangement  of  springs  and  multiplying  mechanism 
closes  an  electric  circuit  which  may  be  made  to  give  a  determined  signal  at 
any  distance.  When  the  apparatus  is  exposed  to  hydrocarbon  gases  they 
are  absorbed  by  the  spongy  platinum,  the  platinum  wire  is  heated,  expands 
and  sags,  and  rings  the  alarm  as  stated. 

ELECTRIC  SAFETY  LAMPS 

The  ordinary  .safety  lamp  is  subject  to  many  disadvantages,  and  several 
explosions  have  been  traced  to  imperfections  in  these  lamps  or  to  their 
unintentional  breakage.  To  obviate  these  disadvantages  many  varieties 
and  models  of  so-called  electric  safety,  lamps  all  of  which  employ  a  small 
storage  battery,  have  been  devised. 

Such  lamps  must  provide  safety  against  ignition  of  mine  gases,  a  steady 
and  uninterrupted  production  of  light  for  at  least  one  shift  and  should  be  of 
practically  foolproof  construction.  Since  such  lamps  are  exposed  to  ex- 
tremely rough  usage  in  the  hands  of  inexperienced  men,  even  slight  mechan- 
ical or  electrical  weaknesses  may  result  in  a  total  failure  of  the  light  supply. 
Furthermore,  to  guard  against  the  opening  of  the  lamp  while  in  the  mine 
most  such  lamps  are  provided  with  some  means,  such  as  a  lock,  which  pre- 
vents anyone  from  tampering  with  or  dismounting  the  apparatus.  These 
locks  may  be  either  in  the  nature  of  an  ordinary  padlock  or  a  type  of  mag- 
netic lock  such  as  is  often  used  on  naphtha-burning  safety  lamps. 

Points  of  Danger  in  an  Electric  Safety  Lamp. — Experiments  both  in  this 
country  and  in  Germany  have  demonstrated  that  the  only  point  of  danger 
in  a  portable  electric  lamp  is  the  glowing  filament.  Sparks  obtained  by  the 
making  or  breaking  of  the  electric  circuit  are  not  of-  sufficient  strength  to 
ignite  an  explosive  mixture.  It  is  unnecessary,  therefore,  to  provide  against 
sparking  at  the  switch  or  other  connections  between  the  battery  and  the 
lamp.  The  lamp  filament  under  ordinary  conditions  is  enclosed  in  a  vacuum 
bulb,  and  the  danger  of  igniting  mine  gases  is  present  only  when  this  bulb  is 
broken  without  rupturing  the  filament.  Several  methods  may  be  employed 
for  preventing  such  a  contingency.  The  two  most  commonly  used,  however, 
are  a  spring  which  instantly  forces  the  lamp  out  of  its  socket,  thus  instantly 


VENTILATION  OF  MINES  897 

breaking  electrical  connections,  and  a  fuse  which  blows  the  moment  the 
bulb  is  fractured. 

Types  of  Electric  Safety  Lamps. — There  are  two  general  types  of  electric 
safety  lamp.  These  may  be  designated  as  hand  lamps  and  cap  lamps;  the 
former  strongly  resembles  in  appearance  an  oil-burning  safety  lamp,  while 
the  latter  is  modelled  after  the  open-flame  cap  lamp  extensively  employed 
in  this  country.  Although  many  varieties  of  each  have  been  placed  on  the 
market,  all  models  of  the  same  type  strongly  resemble  each  other  and  a 
description  of  one  will  apply  with  only  minor  variations  as  to  constructional 
features  to  all  lamps  of  its  particular  type. 

The  Ceag  Lamp.— The  Ceag  lamp  won  first  prize  in  the  competition  con- 
ducted by  the  British  government  in  1912,  since  which  time  it  has  been 
accepted  by  practically  all  European  governments 
and  has  been  approved  by  the  U.  S.  Bureau  of 
Mines.  This  lamp  is  illustrated  in  Fig.  7.  As 
described  by  Mr.  H.  O.  Swoboda  its  construction 
is  as  follows: 

The  bulb  is  covered  with  a  heavy  glass  dome  D, 
which  is  protected  by  four  heavy  steel  rods  H,  held 
together  by  a  sheet-steel  roof  7.  A  substantial 
hook  is  attached  to  this  roof.  Thus  the  miner  can 
either  stand  the  lamp  on  the  ground  or  hang  it  to 
a  post  in  the  immediate  neighborhood  of  his  work- 
ing place.  The  bottom  part,  made  of  heavy  cor- 
rugated galvanized  sheet  steel,  contains  the  stor- 
age battery.  By  turning  the  upper  part  on  the 
lower  the  miner  can  turn  the  light  on  and  off.  The 
incandescent  lamp  rests  in  a  socket  which  is 
pressed  upward  by  a  spiral  spring  O  against 
another  spring  P  between  the  bulb  and  the  glass 
dome  D,  providing  a  complete  spring  support  and 
preventing  breakage  even  with  the  most  severe 
shock.  Electric  connection  is  established  for  one 
pole  through  the  socket  spring  O  and  for  the  other 
pole  by  another  smaller  spring  E  inside  the  socket 
spring  and  insulated  from  it.  In  case  the  bulb 
breaks  the  socket  spring  pushes  the  socket  up- 
ward, and  as  the  inner  spring  does  not  expand  as 
much  as  the  socket  spring  the  circuit  is  inter- 
rupted. Another  safety  device  has  been  added, 
but  it  is  not  shown  in  this  illustration.  This  con- 
sists of  a  fuse  which  blows  the  moment  the  bulb 
of  the  incandescent  lamp  is  broken.  This  elimi- 
nates the  possibility  of  obtaining  sparks  or  getting 
the  filament  to  glow  in  case  the  miner  should 
attempt  to  push  the  bulb  back  into  its  normal 
position.  It  also  protects  the  battery  from  being 
short-circuited  for  any  length  of  time  in  case  the 
leads  to  the  bulb  have  become  short-circuited  " 
during  the  accident.  FIG,  7 

The  rotating  movement  of  the  upper  part  of  the  lamp  upon  the  lower  is 
limited  by  a  soft-iron  pin  M,  which  acts  as  a  magnetic  lock.  This  pin  can  be 
withdrawn  in  the  charging  room  by  a  strong  electromagnet,  and  when  this 
is  done  the  upper  and  lower  parts  of  the  housing  separate  and  the  battery 
can  be  removed  for  charging.  The  storage  battery  consists  of  a  single  round 
lead  cell  with  concentric  electrodes  inside  a  cylindrical  vessel  A  covered  with 
a  waterproof  lid  of  the  same  material.  The  holes  in  the  terminal  sockets 
contain  bushings  made  of  acidproof  metal  into  which  removable  terminals 
Pi  and  P2  are  fitted.  These  terminals  are  pressed  upward  by  the  terminal 
springs  W\  and  Wi  against  the  contact  segments  K\  and  Kz  of  the  switch, 
carrying  in  this  manner  the  current  to  the  incandescent  lamp.  Terminals 
and  springs  can  be  easily  taken  out  and  cleaned  by  washing  in  warm  water. 
In  charging  storage  batteries  gases  develop  which  must  have  an  oppor- 
tunity to  escape.  It  is  therefore  impossible  to  make  the  cells  air-tight.  An 
ordinary  opening  would  allow  the  acid  to  run  out  in  case  the  cell  were  upset. 
The  center  of  the  cell  is  therefore  equipped  with  a  celluloid  tube  B  which 
communicates  by  means  of  a  small  side  tube  F  with  the  upper  part  of  the 
cell  where  the  gases  collect.  The  gases,  therefore,  may  pass  from  the  cell 
57 


898 


VENTILATION  OF  MINES 


through  the  side  tube  F  and  finally  through  the  center  tube  C  to  the  open, 
while  any  particles  of  acid  will  be  deposited  in  the  cylinder  B.  Even  if  the 
cell  is  turned  upside  down  no  acid  can  escape  and  the  lamps  will  burn  upside 
down  without  leaking. 

The  weight  of  this  lamp  in  standard  size  is  5  Ib.  Its  height,  not  including 
hanger,  is  10J  in.,  while  its  largest  diameter  is  3|  in.  The  lamp  consumes 
0.85  amp.  at  2  volts.  The  battery  has  a  capacity  of  16  amp.-hr.  and  the 
maximum  charging  current  should  not  exceed  2  amp.  This  general  design, 
however,  is  built  in  four  sizes,  ranging  from  1*  to  5  Ib.  in  weight  and  in 
capacities  ranging  from  4  to  16  hr.  for  one  discharge  and  producing  a  light 
ranging  from  0.75  to  3  c.p. 

Special  Forms  of  the  Ceag  Lamp. — A  number  of  modifications  of  the  Ceag 
lamp  have  been  developed.  Lamps  are  made  for  rescue  parties,  cages, 


FIG.  12 

powder  magazines,  shaft  lighting,  shaft  inspection,  loading  places,  blasting; 
also  for  head  and  tail  lamps  of  trips.  The  lamp  shown  in  Fig.  8  is  similar 
to  the  standard  design,  but  has  the  incandescent  lamp  mounted  on  one  side 
and  combined  with  a  reflector  projecting  the  light  in  one  direction.  _  This 
lamp  is  used  for  inspection  and  for  a  head  and  tail  lamp.  It  is  made  in  the 
same  capacities  as  the  standard  lamp. 

The  shaft  lamp  shown  in  Fig.  9  is  arranged  with  an  adjustable  arm  carry- 
ing the  incandescent  lamp  and  is  made  to  furnish  from  8  to  24  c.p.,  burning 
from  7  to  12  hr.  on  one  charge,  according  to  size. 

Fig.  10  is  another  type  of  shaft  lamp  without  the  adjustable  arm.  It  is 
made  for  8  to  12  c.p.  and  to  furnish  light  from  10  to  15  hr.  on  one  charge. 

Fig.  11  is  constructed  to  project  light  downward.  It  is  built  for  from  8  to 
32  c.p.  and  for  a  length  of  discharge  of  from  7  to  15  hr. 

Cap  Lamps. — Naked-flame  cap  lamps  have  ^ng  been  used  in  this  country, 
and  it  is  but  natural  that  the  miner  should  desire  an  electric  lamp  of  similar 
utility.  The  lamps  developed  to  meet  this  demand  are  essentially  of  two 


VENTILATION  OF  MINES 


899 


parts,  the  storage  battery  being  carried  on  the  belt  while  the  lamp  proper  is 
attached  to  the  cap,  the  two  being  connected  by  a  suitable  flexible  cable. 
Such  a  lamp  is  shown  in  Fig.  12,  while  Fig.  13  shows  the  general  principles 
of  construction.  The  incandescent  lamp  bulb  is  mounted  inside  a  parabolic 
reflector  provided  with  a  lens.  A  ball  joint  may  also  be  incorporated  in  the 
design,  permitting  the  wearer  to  direct  the  light  beam  where  it  is  most 
needed.  The  flexible  cable  connecting  the  battery  to  the  lamp  is  heavily 
insulated  and  in  addition  is  armored  at  both  ends  where  the  liability  of 
bending  short  is  the  greatest.  Furthermore,  an  alloy  with  a  low  melting  point 
is  employed  in  this  cable  so  that  in  case  of  accident  to  the  lamp  and  the  pos- 
sible short-circuiting  of  the  battery,  this  alloy  will  melt  and  destroy  the 
short-circuit  before  a  sufficient  temperature  has  been  attained  to  render 
the  ignition  of  mine  gases  possible. 


FIG.  14 

Charging  Stations. — After  a  shift  in  the  mine  an  electric  safety  lamp  must 
be  left  at  the  lamp  house  to  be  cleaned  and  recharged.  Special  charging 
racks  have  been  designed  for  this  purpose,  one  or  more  charging  circuits 
being  employed.  Each  circuit  should  be  equipped  with  a  switch,  a  rheostat 
and  an  ammeter.  The  rheostat  should  be  provided  with  surplus  resistance 
so  that  less  than  a  full  complement  of  cells  may  be  charged.  A  portable 
voltmeter  of  suitable  capacity,  say  3  volts,  should  also  be  provided  so  that 
readings  may  be  taken  on  each  individual  cell.  After  charging,  cleaning  and 
reassembling,  the  lamps  are  placed  in  special  racks  from  which  the  miners 
remove  them  when  starting  a  new  shift. 


900  VENTILATION  OF  MINES 

Electric  charging  stations  or  lamp  houses,  particularly  if  many  lamps  are 
to  be  handled,  follow  the  same  general  principles  of  design  as  do  those  where 
oil-burning  safety  lamps  are  used.  No  special  arrangements  need,  however, 
be  made  for  the  storage  and  handling  of  dangerous  inflammable  oils.  Fig. 
14  shows  a  lamp  house  designed  to  accommodate  4,000  lamps.  It  contains 
a  charging  room  with  20  racks,  three  small  motors  for  buffing  and  cleaning 
and  a  distribution  board  with  a  watt-hour  meter.  There  is  also  a  store 
room  for  receiving  the  lamps  when  they  are  ready  for  service,  and  a  repair 
shop.  A  small  room  is  also  employed  for  a  number  of  ordinary  safety  lamps 
to  be  used  by  the  fire  bosses.  To  secure  reliability  of  service  it  is  essential 
that  care  and  intelligence  be  employed  in  the  maintenance  and  repair  of 
any  electric  safety  lamp. 

ACETYLENE  LAMPS 

Acetylene,  C2H2,  is  formed  by  the  action  of  water  on  calcium  carbide, 
Ca.Cz,  by  the  reaction  CaC2  +  2H2O  =  Ca(OH)2  +  C2H2.  The  calcium 
carbide  is  made  by  fusing  together  lime  and  coke  in  the  electric  furnace. 
Commercial  carbide  frequently  contains  small  amounts  of  calcium  sulphide 
and,  rarely,  minute  traces  of  calcium  phosphide  which  will  form  hydrogen 
sulphide  and  phosphide,  respectively,  with  water.  Both  of  these  gases  are 
extremely  poisonous,  but  their  percentage  in  mine  air,  when  derived  from 
acetylene  lamps,  is  so  insignificant  as  to  be  negligible. 

While  the  carbide  of  magnesium  yields  about  50%  more  acetylene  than 
the  carbide  of  calcium,  it  is  too  costly  for  commercial  use. 

Acetylene  ignites  at  896°F.  and  burns  with  an  extremely  white  flame  to 
carbon  dioxide  and  vapor  of  water,  the  reaction  for  combustion  in  oxygen 
being  2C2H2  +  5O2  =  4CO2  +  2H2O.  When  the  oxygen  content  of  the  air 
is  reduced  to  16%  the  acetylene  flame  becomes  distinctly  yellow,  and  at 
12  to  13  %  of  oxygen  it  is  extinguished. 

The  standard  acetylene,  or  carbide,  lamp  consists  of  a  small  water  tank 
screwed  on  top  of  a  container  which  is  about  half  filled  with  small  lumps  of 
calcium  carbide.  The  inflow  of  water  and,  consequently,  the  production  of 
gas,  is  regulated  by  a  valve  operated  from  the  top  or  the  side  of  the  lamp. 
The  lamp  is  usually  provided  with  a  reflector  behind  the  flame,  and  the  burner 
is  similar  to  that  employed  in  a  jet  for  burning  ordinary  illuminating  gas, 
no  wick  being  used. 

While  there  are  many  shapes  and  sizes  of  acetylene  lamps,  the  common 
form  is  about  4  in.  high  and  weighs,  when  charged,  about  6  oz.  The  average 
consumption  of  carbide  is  about  4  oz.  per  8-hr,  shift  at  a  cost  of  2.5  c.  with 
carbide  at  10  c.  per  Ib.  Mr.  G.  W.  Pfeiffer  gives  the  relative  cost  per  man 
per  shift  for  various  types  of  lamps  at  a  Mexican  mine,  where  the  price  of 
materials  is  greater  than  in  the  United  States,  as:  Mixture  of  coal-  and  lard- 
oil,  6  c.;  miners'  oil,  15 J  c.;  acetylene,  5  c. 

The  Bureau  of  Mines  states  that  ordinary  carbide  lamps  when  fitted  with 
a  reflector  and  with  a  flame  1  to  1J  in.  long  give  a  candlepower  head-on  of 
4.2  to  6.2  and  at  right  angles  to  the  flame  of  .87  to  1.45.  Without  a  reflector, 
the  head-on  candlepower  of  these  lamps  averages  1.9  to  2.15  and  at  right 
angles  1.9.  In  comparison,  the  maximum  average  candlepower  of  miners' 
and  drivers'  oil-burning  lamps  is  stated  to  be  1.4  to  1.9. 

Carbide  should  be  kept  in  tightly  sealed  canisters  and  the  contents  of  the 
container  should  not  be  thrown  at  random  about  the  mine  as  there  will 
usually  be  some  unconsumed  carbide  in  it  which,  in  contact  with  water,  may 
generate  sufficient  acetylene  to  start  a  fire  if  this  gas  should  be  accidentally 
ignited;  special  metal  tanks  should  be  provided  at  convenient  intervals  into 
which  the  exhausted  carbide  may  be  thrown. 


EXPLOSIVE  CONDITIONS  IN  MINES 

In  the  ventilation  of  gaseous  seams,  the  air  current  may  be  rendered 
explosive  by  the  sudden  occurrence  of  any  one  of  a  number  of  circum- 
stances that  cannot  be  anticipated.  Among  these  are  the  following:  (1) 
Derangement  of  the  ventilating  current.  (2)  Sudden  increase  of  gas  due  to 
outbursts,  falls  of  roof,  feeders,  fall  of  barometric  pressure,  etc.  (3)  Pres- 
ence  of  coal  dust  thrown  into  suspension  in  the  air,  in  the  ordinary  working  of 
the  mine,  or  by  the  force  of  blasting  at  the  working  f^ce,  or  by  blown-out, 
or  windy  shots.  (4)  Pressure  due  to  a  heavy  blast,  or  any  concussion  of  the 
air  caused  by  closing  of  doors,  etc.  (5)  Rapid  succession  of  shots  in  close 
workings.  (6)  Accidental  discharges  of  an  explosive  in  a  dirty  atmosphere. 


VENTILATION  OF  MINES  901 

Any  or  all  of  these  causes  may  precipitate  an  explosion  at  any  moment. 
Hence,  the  condition  of  the  air  current  should  be  maintained  far  within  the 
explosive  limit.  The  explosive  conditions  vary  considerably  in  different 
coal  seams.  The  nature  of  the  coal  and  its  enclosing  strata,  its  friability 
and  inflammability,  together  with  the  character  of  its  occluded  gases,  deter- 
mine, to  a  large  extent,  the  explosive  conditions  in  the  seam.  Experience 
in  any  particular  seam  or  district  must  always  be  the  best  guide  and  furnish 
the  best  standard  for  determining  the  exploding  power  of  any  given  lamp 
flame.  For  example,  a  2-in.  flame  may  be  comparatively  safe  in  a  small  mine 
where  the  coal  is  hard  and  not  particularly  inflammable,  while  a  IJ-in.  flame 
cap  would  be  considered  unsafe  in  mines  where  the  conditions  are  more 
favorable  to  the^generation  of  gas  and  formation  of  coal  dust.  The  daily 
output  of  the  mine  and  the  general  care  that  is  enforced  upon  the  miners 
at  the  working  face  are  factors  that  should  always  be  considered  and  taken 
into  serious  account  in  determining  explosive  conditions. 

Derangement  of  Ventilating  Current. — -The  flow  of  the  air  current  must  be 
uniform  and  continuous.  Doors  must  be  kept  closed,  since  the  mere  setting 
open  of  a  door,  for  a  short  period  of  time,  may  be  enough  to  make  an  explo- 
sive condition  possible.  Any  contemplated  change  in  the  current,  by  the 
erection  of  brattices,  air  bridges,  stoppings,  etc.,  should  be  carefully  con- 
sidered before  the  work  is  begun,  and  every  precaution  adopted  to  secure  the 
safety  of  the  men.  Derangement  of  the  current  may  occur  through  a  fall 
of  roof  upon  the  main  airway,  by  which  the  area  of  the  airway  is  reduced, 
which  results  in  the  ^reduction  of  the  quantity  of  air  traversing  the  mine. 
If  this  fall  is  not  noticed  at  once,  serious  results  may  happen.  The  utmost 
vigilance  is  therefore  required  on  the  part  of  fire  bosses  and  all  connected  with 
mine  workings.  The  failure  of  the  ventilating  apparatus  is  another  source 
that  gives  rise  to  the  derangement  of  the  current.  As  a  rule,  furnaces  are 
not  now  employed  for  the  ventilation  of  gaseous  seams.  There  are,  however, 
some  furnaces  in  use  in  such  seams,  and  these  require  constant  attention  lest 
the  fire  should  burn  low.  Upon  any  accident  occurring  to  the  ventilating 
machinery,  notice  should  at  once  be  given  to  the  inside  foreman,  and  the 
men  withdrawn  as  rapidly  as  possible. 

A  sudden  increase  of  gas  may  occur  at  any  time  in  a  gaseous  seam,  owing 
to  an  outburst,  which  suddenly  yields  a  large  volume  of  gas  and  may  render 
the  mine  air  in  that  section  extremely  explosive.  The  men  working  on  the 
return  of  such  a  current  must  be  hastily  withdrawn,  and  all  open  lights 
extinguished.  A  heavy  fall  of  coal  in  the  mine  workings  or  in  the  airways, 
or  the  tapping  of  a  large  gas  feeder,  produces  the  same  effect  in  a  less  degree. 
The  nearer  to  the  face  of  the  workings  the  fall  of  roof  takes  place,  the  more 
liable  it  is  to  be  followed  with  a  large  flow  of  gas,  inasmuch  as  the  gas  near 
the  face  has  not  had  time  to  drain  off,  as  in  the  case  of  old  workings.  This 
fact  is  always  true  in  reference  to  new  workings  in  a  gaseous  seam.  The  gas 
continues  to  flow  freely  for  a  considerable  period,  when  its  flow  gradually 
decreases  until  it  about  ceases.  When  a  large  feeder  has  been  tapped,  it 
may  be  plugged  for  a  time,  if  necessary,  but  the  better  practice  is  to  allow  it 
to  flow  freely  and  diffuse  into  the  air  current,  which  should  be  sufficiently 
increased  to  dilute  the  quantity  of  gas  given  off  and  to  render  it  inexplpsive. 
The  men  upon  the  return  air  should  be  notified.  It  is  dangerous  practice  to 
light  these  feeders. 

When  there  is  a  large  area  of  abandoned  workings  in  the  mine,  any  con- 
siderable fall  of  barometric  pressure  is  usually  followed  by  an  outflow  of  gas 
from  the  gobs  or  waste  places  of  the  mine.  A  fall  of  1  in.  in  5  hr.  represents 
a  very  rapid  decrease  of  barometric  pressure.  At  all  large  collieries  there  is, 
or  should  be,  a  good  standard  barometer  located  upon  the  surface  near  the 
shaft.  In  many  cases,  these  barometers  are  self-recording,  and  are  often 
provided  with  an  automatic  alarm  that  gives  warning  whenever  a  fall  of 
barometric  pressure  occurs.  This  warning  should  at  once  be  conveyed  to 
the  men  in  the  workings,  and  every  precaution  adopted  to  avoid  evil  results. 
The  fact  is  fairly  well  established  that  a  fall  of  atmospheric  pressure  is  not 
followed  by  an  outflow  of  gas  from  the  mine  workings  for  the  space  of,  say, 
3  hr.  after  such  fall  occurs.  This  statement^must  be  regarded  with  caution, 
however,  as  it  largely  depends  on  the  condition  and  extent  of  the  abandoned 
workings.  Where  these  are  full  of  gas,  its  expansion  affects  the  condition  of 
the  airways  much  more  quickly  than  in  cases  where  these  workings  places 
are  partly  ventilated. 

Effect  of  Coal  Dust  in  Mine  Workings. — According  to  the  inflammability 
of  the  coal  the  presence  of  coal  dust  in  a  finely  divided  state  becomes  a 


902  VENTILATION  OF  MINES 

dangerous  factor.  Certain  coals  are  friable  and  easily  reduced  to  fine  dust 
which  in  the  course  of  ordinary  operations  becomes  stirred  up  and  is  sus- 
pended in  the  air.  _  For  a  long  time  it  was  a  much  disputed  question  whether 
the  presence  of  this  dust  was  a  dangerous  factor  unless  some  gas  was  also 
present  in  the  atmosphere.  Evidence  secured  in  numerous  investigations 
following  explosions  that  have  occurred  during  recent  years  have  established 
the  explosibility  of  coal  dust  when  acted  upon  by  a  flame  of  sufficient  inten- 
sity, beyond  the  slightest  doubt.  The  exact  action  of  the  flame  on  such 
dust  is  but  imperfectly  understood,  but  the  action  once  started  is  continuous 
as  long  as  the  explosive  medium  is  available.  Naturally,  quantities  of 
methane  will  greatly^  increase  the  violence,  but  its  presence  is  unnecessary 
to  produce  an  explosion. 

Regarding  the  prevention  or  the  checking  of  gas  and  dust  explosions  the 
Bureau  of  Mines  in  numerous  experiments  has  proved  that  an  explosion 
cannot  originate  from  thoroughly  wet  coal  dust,  but  that  it  is  not  easy  to  wet 
piles  of  coal  dust  even  with  well-humidified  air  currents.  This  is  an  impor- 
tant feature.  When  a  saturated  air  current  passes  through  a  mine  it  dampens 
the  roof,  floor,  and  sides,  but  the  coal  dust  itself  when  in  accumulations 
appears  to  repel  moisture;  even  with  long  exposure  dust  like  that  from  the 
Pittsburgh  seam  takes  up  only  1  or  2  %  of  moisture,  though  the  walls  and  floor 
may  become  damp.  The  surprising  result  of  experiments  makes  it  evident 
that  it  is  necessary  to  remove  coal-dust  accumulations,  so  that,  after  a  pas- 
sageway has  been  well  dampened,  any  particles  of  dust  falling  on  wet  sur- 
faces will  themselves  become  wet.  It  has  been  observed  after  some  dust- 
explosion  disasters  that  the  explosion  has  traversed  entries  in  which  there  was 
standing  water  along  the  bottom,  but  on  the  other  hand  examination  of  the 
benches  and  projections  along  the  sides  of  such  entries  has  disclosed  quantities 
of  dry  dust.  Also  it  has  been  observed  that  timbers  frequently  carry  on 
their  upper  surfaces  quantities  of  dust  sufficient  to  propagate  an  explosion. 
Consequently,  the  Bureau  emphasizes  two  precautions,  namely,  first  remove 
all  accumulations  of  dry  dust  and  then  keep  the  entries  wet  or  use  a  coating  of 
rock  dust.  There  will  then  be  little  danger  of  explosion. 

One  of  the  principal  mediums  for  distributing  coal  dust  about  the  mines 
is  the  mine  car.  It  is  often  loaded  so  high  that  the  coal  strikes  the  timbers 
or  roof  and  is  so  jarred  that  it  falls  to  the  roadway  where  it  is  ground  to  a 
powder  by  men  and  mules.  Tight  cars  should  be  used  wherever  possible. 
Gateless  cars  are  used  in  Europe  except  in  Wales  and  Scotland  and  revolving 
tipples  are  employed  for  dumping  them.  By  proper  arrangement  the  coal 
is  thus  discharged  with  little  breakage.  In  the  case  of  a  downcast  shaft  the 
shaking  screens  in  the  tipple  should  not  be  placed  immediately  adjacent  to 
the  shaft  and  if  they  are  already  near  it,  vacuum  dust  collectors  should  be 
installed  9ver  the  screens  and  chutes. 

Otherwise,  a  large  quantity  of  duat  may  be  drawn  down  the  shaft.  In  a 
certain  mine  in  England  in  which  rock  dust  was  used  to  counteract  the 
danger  of  coal  dust  a  thick  film  of  coal  dust  was  observed  on  top  of  the  rock 
dust,  the  deposit  extending  for  a  distance  of  500  or  600  ft.  from  the  shaft. 
Had  it  not  been  for  the  light-colored  rock  dust  the  deposit  could  not  have 
been  seen.  The  coal  dust  had  been  collecting  for  only  2  mo.  subsequent  to 
the  time  when  the  rock  dust  had  last  been  laid.  This  mine  has  since  put  in 
vacuum  dust  collectors  over  its  screens.  In  many  of  the  recently  built 
European  plants  it  is  the  practice  to  place  the  screening  plant  100  to  200  ft. 
distant  from  the  downcast  shaft. 

The  Bureau  of  Mines  in  Technical  Paper  No.  56  has  outlined  a  number  of 
preventive  methods  to  be  used  in  soft-coal  mines  for  fighting  the  coal-dust 
danger.  Naturally,  there  is  but  one  way  to  prevent  any  coal-dust  explo- 
sions, and  that  is  to  wet  or  wash  down  all  rooms  or  haulageways  where  coal 
dust  is  likely  to  accumulate  and  to  keep  such  places  in  a  moist  condition. 
This  is  often  impossible  and  impractical,  but  the  following  methods  suggested 
by  the  Bureau  of  Mines  are  all  highly  commendable. 

Humidifying  the  Air  Current. — With  the  humidifying  system  the  intake 
air  current  is  so  saturated  or  supersaturated  as  to  carry  the  moisture  into 
the  mine  in  minute  but  constant  quantities  every  minute  of  the  day.  The 
amount  of  water  vapor  that  air  will  carry  or  support  varies  with  its  tempera- 
ture. For  example,  if  3,300  cu.  ft.  of  air  will  support  1  Ib.  of  water  at  freez- 
ing or  32°F.  then  at  62°  it  will  support  3  Ib.  and  a  current  of  air  of  3,300  cu. 
ft.  per  min.  entering  a  mine  at  32°F.  would  absorb  moisture  up  to  its  capacity 
at  62°  or  whatever  the  temperature  may  be.  Thus  ordinarily  the  current  of 
air  takes  up  and  carries  away  20  Ib.  per  min.  or  about  2$  gal.  per  min.,  which 


VENTILATION  OF  MINES 


903 


would  be  over  3,500  gal.  per  day.  This  going  on  for  months  makes  a  mine 
more  and  more  dry.  No  ordinary  sprinkler  system  will  entirely  overcome 
this  for  the  air  will  only  absorb  nK>isture.  As  it  becomes  heated  it  expands 
and  dries.  On  the  other  hand,  moisture  in  saturated  air  entering  a  mine  at  a 
higher  temperature  than  that  within  will  condense  over  the  sides  and  roof 
of  the  haulageways  and  working  places,  thereby  depositing  water  instead  of 
withdrawing  it.  This  principle  seems  to 
be  the  solution  for  the  coal-dust  problem 
from  a  humidifying  standpoint.  In  this 
connection,  the  Colorado  Fuel  and  Iron 
Co.  installed  radiators  and  steam  pipes 
in  the  intake  of  its  coal  mines  in  southern 
Colorado,  the  radiators  to  raise  the  tem- 
perature of  ingoing  air,  and  the  steam 
pipes  to  inject  the  necessary  moisture  in 
the  form  of  steam. 

The  percentage  of  saturation  obtained 
will  depend  upon  the  volume  of  air  en- 
tering the  mine  and  its  temperature,  the 
heating  surface  of  the  radiator  and  the 
amount  of  moisture  supplied.  That  is, 
the  larger  the  volume  and  the  lower  the 
outside  temperature,  the  greater  the 
heating  surface  and  amount  of  moisture 
will  have  to  be  to  give  the  same  results. 

Another  method  of  supplying  a  mine 
with  a  preheated  and  humidified  venti- 
lating air  is  suggested  by  the  operation 
and  tests  of  an  evaporative  condenser 
installed  at  the  central  power  plant  of  a 
group  of  mines  near  Pittsburg,  to  handle  the  exhaust  steam  from  turbo  gen- 
erators. This  suggestion  is  made  in  contradistinction  to  the  steam  jet  and 
steam  coil  heating  method. 

The  condenser  referred  to  for  the  purpose  of  humidifying  air,  consists  of 
a  nest  of  900  vertical,  1^-in.  diameter  copper  tubes,  19_ft.  long,  fixed  top 
and  bottom  in  suitable  headers.  The  tubes  are  housed  in  on  two  sides,  as 


FIG.  1 


ft 

and, 


toPullfopor  from  Condenser  i 
it  to  Mine  for  Ventilation 


Man  way 


Exhaust 


Haulage  Way 


Exhaust 


FIG.  2. — Arrangement  of  Entries, 
Fan  Blowing 


ran  to  Pull  vapor  from 

Condenser  thru  Mine 


Man  way 


FIG.  3. — Arrangement  of  Entries, 
Fan  Exhausting 


shown  in  Fig.  1,  one  side  being  left  open  for  the  admission  of  air,  which  is 
drawn  in  and  around  the  tubes,  by  a  fan  placed  opposite  the  open  side. 
The  vapor  generated  by  the  evaporation  of  water,  with  which  the  tubes 
are  mechanically  wetted,  is  picked  up  by  the  air  as  it  passes  around  the  tubes. 
Where  the  arrangement  of  a  mine's  power  equipment  will  permit,_  it  is 
suggested  that  the  usual  mine  fan  be  made  to  perform  the  double  service  of 


904  VENTILATION  OF  MINES 

drawing  the  air  around  condenser  tubes,  where  it  takes  on  heat  and  moisture 
in  proportion  to  the  work  of  condensation,  as  well  as  through  the  mine 
By  test  performance,  the  amount  of  water  evaporated  per  pound  of  steam, 
condensed  is  approximately  1  Ib.  Figures  2  and  3  will  indicate  the  arrange- 
ment of  the  connections  to  a  condenser,  fan,  and  mine,  when  blowing  or 
exhausting. 

Many  variations  of  the  condenser  as  described  could  be  used  for  the  sug- 
gested purpose,  but  the  evaporative  kind  seems  especially  adapted,  inasmuch 
as  the  air  required  to  maintain  its  efficiency  obtains  its  heat  and  humidity 
in  a  single  operation. 

It  is  conceded  that  cold  air  must  be  heated  and  have  a  sufficient  amount  of 
moisture  given  to  it,  to  prevent  it  from  absorbing  moisture  from  the  mine,  as 
it  gradually  becomes  heated  during  its  passage  through  the  air-courses, 
thereby  increasing  its  moisture-carrying  capacity.  The  assumption  is  made 
that,  if  the  air  supplied  to  a  mine  be  heated  to  the  mine's  normal  temperature, 
and  that  be  also  given  a  high  relative  humidity,  it  will  issue  from  that  mine 
having  practically  the  same  temperature  and  humidity.  It  is  further  as- 
sumed that,  should  it  be  possible  to  sufficiently  heat  and  humidify  the  re- 
quired amount  of  ventilating  air,  somewhat  in  excess  of  the  mine's  normal 
temperature,  and  give  it  a  proportional  burden  of  humidity,  an  amount  of 
moisture  would  be  given  off  by  the  air,  as  its  temperature  is  adjusting  itself 
to  that  of  the  mine.  The  basis  for  the  last  assumption  lies  in  the  nil  effect 
that  any  quantity  of  heat  given  off  by  the  ventilating  air,  so  treated,  would 
have  towards  raising  the  normal  temperature  of  a  mine. 

However,  any  interchange  of  heat  that  might  take  place,  from  air  to  the 
walls  of  a  mine,  would  tend  to  diminish  the  moisture-carrying  capacity  of 
the  air,  and  would  result  in  the  deposit  of  a  certain  amount  of  moisture.  The 
possibility  of  conditioning  sufficient  ventilating  air,  and  the  amount  of 
exhaust  steam  required  to  perform  the  work,  can  be  judged  from  the  result 
of  a  series  of  problems,  the  results  of  which  can  be  displayed  graphically 
by  means  of  curves.  _ 

By  virtue  of  a  suitable  condenser,  the  air  used  as  a  vehicle  to  carry  off 
the  vapor,  equal  to  the  amount  of  water  placed  on  the  tubes  necessary  to 
effect  condensation  within  them,  produces  in  one  operation  a  preheated  and 
humidified  atmosphere.  It  seems  possible  to  adjust  the  degree  of  heat  and 
humidity  imparted  to  air  passing  through  such  a  condenser  to  such  a  degree 
that  the  comfort  of  the  miner  would  in  no  way  be  affected.  By  so  doing, 
however,  it  might  be  necessary  to  forego  some  inches  of  vacuum  which  might 
otherwise  be  available  at  the  engine  in  order  to  maintain  the  adjustment. 
Where  a  sufficient  horsepower  of  exhaust  steam  is  not  at  hand,  the  amount 
of  coal  required  under  a  boiler,  working  at  60  %  efficiency,  to  produce  low- 
pressure  steam  used  in  coils  to  heat  air,  is  approximately  6J  T.  per  24  hr., 
for  a  unit  of  100,000  cu.  ft.  of  ventilating  air  per  min.  In  such  an  arrange- 
ment, it  must  be  understood  that  the  air  is  humidified  by  a  second  operation 
and  does  not  come  into  direct  contact  with  the  steam  formed  in  the  boiler. 

From  a  hygienic  standpoint,  mine  ventilating  air  treated  in  the  manner 
described  would,  to  a  considerable  extent,  bring  about  the  same  results  that 
are  claimed  for  devices  now  being  used  to  condition  air  used  to  ventilate 
public  buildings,  assembly  halls,  and  many  up-to-date  residences. 

Considering  the  many  factors  entering  into  the  successful  operation  of 
such  an  air-tempering  device,  when  adapted  to  the  general  mine  proposition, 
it  is  quite  difficult  to  draw  definite  conclusions;  however,  the  foregoing  matter 
possesses  sufficient  merit  to  warrant  consideration  of  mine  operators. 

Hygrometers. — The  use  of  the  hygrometer  is  in  its  infancy  for  observations 
in  coal  mines  and  while  the  complete  rotary  sling  hygrometer  or  psychrome- 
ter  is  undoubtedly  the  most  accurate  for  obtaining  humidity  readings,  it 
is  too  delicate  an  instrument  to  carry  around  underground.  The  hygrometer 
shown  in  Fig.  4  is  inclosed  in  a  carrying  case  which  converts  it  into  a  pocket 
instrument  that  is  not  liable  to  become  broken  when  carried  about  in  the 
mine.  The  wet  and  dry  thermometers  are  inserted  in  each  side  of  a  split 
cylindrical  case  which  is  readily  closed  or  opened  by  a  handle.  It  is  easy  to 
swing  but  it  is  not  so  quick  as  the  sling  hygrometer.  The  thermometers 
are  mounted  on  springs  to  lessen  the  danger  of  breakage,  and  this,  with  the 
case,  makes  a  handy  arrangement  for  underground  observations. 

Recording  hygrometers,  giving  a  single  record  of  the  relative  humidity 
have  been  in  use  for  a  long  time.  Engineers  have  appreciated  the  distinct 
advantage  of  having  a  record  of  both  the  dry-bulb  temperature  and  the 
wet-bulb  temperature  independently  but  simultaneously  on  the  same  chart. 


VENTILATION  OF  MINES 


905 


Such  an  instrument  has  the  added  advantage  in  the  ease  with  which  its 
accuracy  can  be  checked  with  a  standard  thermometer  at  all  times.  The 
importance  of  proper  conditions  of  temperature  and  humidity  is  being  more 
and  more  appreciated  in  its  effect  on  coal  dust. 

The  recording  hygrometer  illustrated  in  Fig.  6  consists  of  two  sensitive 
bulbs  mounted  in  tandem  back  of  the  case,  the  wet  bulb  being  jacketed  and 
kept  moist  by  maintaining  water  at  a  constant  level  in  a  trough  beneath  the 
bulb.  The  pen  arms  are  attached  directly  to  shafts  concentric  with  the 


FIG.  5 

helical  tube  bulbs.  The  case  is 
mounted  on  a  swivel  bracket  en- 
abling the  swinging  of  the  instru- 
ment at  right  angles  to  the  wall 
or  support,  and  giving  easy  ac- 
cess to  the  inverted  glass  bottle 
serving  as  a  water  reservoir.  It 
is  made  to  cover  ranges  between 
the  freezing  and  boiling  points  of 
water  (32°  to  212°F.  or  0-100°C.). 
The  principle  of  the  construc- 
tion of  the  recording  hygrometers 
is  shown  in  Fig.  5.  In  the  cut  A 
represents  the  reservoir,  the  tube 
B,  the  dry  bulb  which  records  the 
atmospheric  temperature,  and  C 
the  wet  bulb  which  is  covered 
with  a  special  jacket  leading 
down  into  trough  D,  containing 
water.  The  bulb  C  is  always 
cooler  than  B  due  to  the  evap- 
oration of  the  water.  The  evap- 
oration increases  or  diminishes 


FIG.  6.— Recording  Hygrometer          ^ .__  „.   

according  to  the   amount  of  moisture  in  the  air       Tak ing  ^difference 
between  the  two  thermometer  readings  and    consulting  the  table  that  is 


906  VENTILATION  OF  MINES 

explosive  condition  of  the  air  would  necessarily  have  to  be  close  to  the  limit, 
in  order  for  such  a  slight  occurrence  to  precipitate  an  explosion.  The  factor 
of  pressure  as  increasing  the  explosiveness  of  gaseous  mixtures  should  be 
considered  and  constantly  borne  in  mind. 

Rapid  Succession  of  Shots  in  Close  Workings. — It  constantly  happens  that 
two,  three,  or  more  shots  are  fired  by  means  of  fuse  or  touch  squibs  in  a 
single  chamber  or  heading,,  where  the  circulation  of  air  is  not  always  the 
best.  The  practical  effect  is  that  a  considerable  quantity  of  carbonic-oxide 
gas,  CO,  is  produced  by  the  firing  of  the  first  shot,  and  this  gas  does  not  have 
time  to  diffuse  or  become  diluted  by  the  air  current  before  it  is  fired  by  the 
flame  of  the  following  shots.  An  explosion  may  often  be  precipitated  by 
such  an  occurrence,  if  the  workings  are  at  all  dusty.  Two  shots  at  the  most 
are  all  that  should  be  fired  at  one  time  in  a  close  chamber  or  heading. 

Mine  explosions  are  commonly  the  result  of  the  ignition  of  firedamp  with 
an  open  lamp,  or  coal  dust  exploding  after  being  set  in  motion  by  an  explo- 
sion of  gas,  blown  out  shot,  fall  of  roof  or  a  rush  of  air  and  an  electric  arc. 
Numerous  other  cases  of  explosions  are  recorded  but  are  not  in  the  class 
commonly  referred  to  as  mine  explosions. 

Before  the  coal-dust  theory  was  advanced  and  proven,  it  was  believed 
that  wherever  the  greatest  damage  was  done,  was  the  point  where  the 
explosion  originated.  This  is  by  no  means  always  the  case. 

QUANTITY  OF  AIR  REQUIRED  FOR  VENTILATION 

The  quantity  of  air  required  for  the  adequate  ventilation  of  a  mine  cannot 
be  stated  as  a  rule  applicable  in  all  cases.  Regulations  that  would  supply  a 
proper  amount  of  air  for  ventilation  of  a  thick  seam  would  be  found  to  cause 
great  inconvenience  if  applied  without  modification  to  the  workings  in  a 
thin  seam.  Likewise,  the  ventilation  of  an  old  mine  with  extended  workings, 
a  large  area  of  which  has  been  abandoned,  and  in  many  cases  not  properly 
sealed  off,  will  require,  naturally,  a  larger  quantity  of  air  per  capita  than  a 
newly  opened  mine  or  shaft.  The  natural  conditions  existing  in  rise  and 
dip  workings,  with  respect  to  the  gases  that  may  be  liberated  or  generated  in 
those  workings,  call  for  the  modification  of  the  quantity  of  air  required  in 
each  case.  For  example,  dip  workings,  where  mucn  blackdamp  is  generated, 
will  require  a  larger  quantity  of  air,  or  higher  velocity  at  the  working  face, 
to  carry  off  such  damps;  and  rise  workings,  liberating  a  large  amount  of 
•marsh  gas,  will  likewise  require  a  higher  velocity  at  the  working  face.  On 
the  other  hand,  a  reversal  of  these  conditions,  such  as  a  large  quantity  of 
marsh  gas  being  liberated  in  dip  workings,  or  a  similar  amount  of  blackdamp 
being  generated  in  rise  workings,  will  require  a  comparatively  low  velocity 
of  the  air  at  each  respective  working  place. 

Quantity  Required  by  State  Laws. — The  quantity  of  air  required  by  the 
laws  of  the  several  states  is  generally  specified  as  100  cu.  ft.  per  man  per 
min.,  and  in  many  cases  an  additional  amount  of  500  cu.  ft.  per  animal  per 
min.  is  stated.  This  quantity  is  in  no  case  stated  as  the  actual  amount  of 
air  required  for  the  use  of  each  man  or  animal,  but  is  only  the  result  of  experi- 
ence, as  showing  the  quantity  of  air  required  for  the  proper  ventilation  of 
the  average  mine,  based  on  the  number  of  men  and  animals  employed.  The 
number  of  men  employed  in  a  mine  is  an  indication  of  the  extent  of  the  work- 
ing face,  while  the  number  of  animals  employed  is  an  indication  likewise  of 
the  extent  of  the  haulage  roads,  or  the  development  of  the  mine.  These 
amounts  refer  particularly  to  non-gaseous  seams. 

The  Bituminous  Mine  Law  of  Pennsylvania  specifies  that  there  shall  be 
not  less  than  150  cu.  ft.  per  min.  per  person  in  any  mine,  while  200  cu.  ft. 
are  required  in  a  mine  where  firedamp  has  been  detected. 

The  Anthracite  Mine  Law  of  Pennsylvania  specifies  a  minimum  quantity 
of  200  cu.  ft.  per  min.  per  person.  Each  of  these  laws  contains  modifying 
clauses,  which  specify  that  the  amount  of  air  in  circulation  shall  be  sufficient 
to  "dilute,  render  harmless,  and  sweep  away"  smoke  and  noxious  or  dan- 
gerous gases.  Some  mining  companies  specify  the  amount  of  air  that  must 
pass  the  last  breakthrough  and  that  the  breakthrough  shall  not  be  more  than 
a  certain  distance  from  the  face  of  room  or  heading.  One  such  company 
operating  several  mines  in  a  region  where  mine  explosions  are  fairly  frequent 
has  never  had  an  explosion.  Its  rule  is  to  have  12,000  cu.  ft.  of  air  per  min. 
passing  the  last  breakthrough  which  must  not  be  over  100  ft.  from  the  work- 
ing face. 

Quantity  of  Air  Required  for  Dilution  of  Mine  Gases. — To  determine  this 
requires  a  knowledge  of  the  quantity  of  gas  generated  or  liberated  in  the 


VENTILATION  OF  MINES  907 

workings.  The  quantity  of  air  for  dilution  should  be  ample,  and  should  be 
such  as  not  to  permit  the  condition  of  the  current  to  approach  the  explosive 
point.  The  ventilation  should  be  ample  at  the  face. 

Quantity  of  Air  Required  to  Produce  the  Necessary  Velocity  of  Current  at 
the  Face. — This  consideration  modifies  considerably  the  quantity  of  air 
required  for  the  ventilation  of  thick  and  thin  seams.  The  velocity  of  the 
current  is  dependent  not  only  on  the  quantity  of  air  in  circulation,  but  on  the 
area  of  the  air  passage.  This  area  is  quite  small  in  thin  seams,  and  often  very 
large  in  thick  seams.  As  a  result,  the  velocity  is  often  low  at  the  face  of 
thick  seams,  and  insufficient  for  the  proper  ventilation  of  the  face,  although 
the  quantity  of  air  passing  into  such  a  mine  may  be  very  large.  A  certain 
velocity  of  the  current  is  always  required  in  order  to  sweep  away  the  gases. 
This  velocity  depends  on  the  character  of  the  gases  and  the  position  of  the 
workings.  Heavy  damps  are  hard  to  move  from  dip  workings  where  they 
have  accumulated;  and,  likewise,  lighter  damps  accumulating  at  the  face 
of  steep  pitches  are  hard  to  brush  away,  and  the  velocity  of  the  current  in 
these  cases  must  be  equal  to  the  task  of  driving  out  these  gases. 

ELEMENTS  IN  VENTILATION 

The  elements  in  any  circulation  of  air  are  (fl)  horsepower,  or  power  ap- 
plied; (b)  resistance  of  the  airways,  or  mine  resistar.ee,  which  gives  rise  to 
the  total  pressure  in  the  airway;  (c)  velocity  generated  by  the  power  applied 
against  the  mine  resistance. 

Horsepower  or  Power  of  the  Current. — The  power  applied  is  often  spoken 
of  as  the  power  upon  the  air.  It  is  the  effective  power  of  the  ventilating 
motor,  whatever  this  may  be,  including  all  the  ventilating  agencies,  whether 
natural  or  otherwise.  The  power  upon  the  air  may  be  the  power  exerted  by 
a  motive  column  due  to  natural  causes,  or  to  a  furnace,  or  may  be  the 
power  of  a  mechanical  motor.  The  power  upon  the  air  is  always  measured 
in  foot-pounds  per  minute,  which  expresses  the  units  of  work  accomplished 
in  the  circulation. 

Mine  Resistance. — The  resistance  offered  by  a  mine  to  the  passage  of  an 
air  current,  or  the  mine  resistance,  is  due  to  the  friction  of  the  air  rubbing 
along  the  sides,  top,  and  bottom  of  the  air  passages.  This  friction  causes  the 
total  ventilating  pressure  in  the  airway,  and  is  equal  to  it.  Calling  the 
resistance  R,  the  unit  of  ventilating  pressure  (pressure  per  square  foot)  p, 
and  the  sectional  area  of  the  airway  a,  we  have,  R  =  pa;  that  is  to  say,  the 
total  pressure  is  equal  to  the  mine  resistance. 

Velocity  of  the  Air  Current. — Whenever  a  given  power  is  applied  against  a 
given  resistance,  a  certain  velocity  results.  For  example,  if  the  power  u 
(foot-pounds  per  minute)  is  applied  against  the  resistance  pa,  a  velocity  v 
(feet  per  minute)  is  the  result;  and  since  the  total  pressure  pa  moves  at 
the  velocity  v,  the  work  performed  each  minute  by  the  power  applied  is  the 
product  of  the  total  pressure  by  the  space  through  which  it  moves  per 
minute,  or  the  velocity.  Thus,  u  =  (pa)v. 

Relation  of  Power,  Pressure,  and  Velocity. — The  relation  of  these  ele- 
ments of  ventilation  is  not  a  simple  relation.  For  example,  a  given  power 
applied  to  move  air  through  an  airway  establishes  a  certain  resistance  and 
velocity  in  the  airway.  The  resistance  of  the  airway  is  not  an  independent 
factor;  that  is  to  say,  it  does  not  exist  as  a  factor  of  the  airway  independent 
of  the  velocity,  but  bears  a  certain  relation  to  the  velocity.  Power  always 
produces  resistance  and  velocity,  and  these  two  factors  always  sustain  a  fixed 
relation. 

This  relation  is  expressed  as  follows:  The  total  pressure  or  resistance  varies 
as  the  square  of  the  velocity;  i.e.,  if  the  power  is  sufficient  to  double  the 
velocity,  the  pressure  will  be  increased  4  times;  if  the  power  is  sufficient  to 
multiply  the  velocity  3  times,  the  pressure  will  be  increased  9  times.  Thus, 
we  observe  that  a  change  of  power  applied  to  any  airway  means  both  a 
change  of  pressure  and  a  change  of  velocity. 

Again,  since  the  power  is  expressed  by  the  equation  u  =  (pa)v,  and  since 
pa,  or  the  total  pressure,  varies  as  v2,  the  work  varies  as  v3.  From  this  it 
follows  that,  if  the  velocity  is  multiplied  by  2,  and,  consequently,  the  total 
pressure  by  4,  the  work  performed  (pa)v  will  be  multiplied  by  2s  =  8.  We 
thus  learn  that  the  power  applied  varies  as  the  cube  of  the  velocity. 

MEASUREMENT  OF  VENTILATING  CURRENTS 

The  measurement  and  calculation  of  any  circulat9n  in  a  mine  airway 
includes  the  measurement  of  (a)  the  velocity  of  the  air  current,  (b)  of  pres- 


908 


VENTILATION  OF  MINES 


sure,  (c)  of  temperature,  (d)  calculation  of  pressure,  quantity,  and  horsepower 
of  the  circulation. 

These  measurements  should  be  made  at  a  point  in  the  airway  where  the 
airway  has  a  uniform  section  for  some  distance,  and  not  far  from  the  foot  of 
the  downcast  shaft  or  the  fan  drift. 

Measurement  of  Velocity.  —  For  the  purpose  of  mine  inspection,  the  veloc- 
ity of  the  air  current  should  be  measured  at  the  foot  of  the  downcast,  at  the 
mouth  of  each  split  of  the  air  current,  and  at  each  inside  breakthrough,  in 
each  split.  These  measurements  are  necessary  in  order  to  show  that  all  the 
air  designed  for  each  split  passes  around  the  face  of  the  workings. 

The  measurement  of  the  velocity  of  a  current  is  most  conveniently  made 
by  means  of  the  anemometer.  This  instrument  consists  of  a  vane  placed 
in  a  circular  frame  and  having  its  blades  so  inclined  to  the  direction  of  its 
motion  that  1  ft.  of  lineal  velocity  in  the  passing  air  current  will  produce  1 
re  volution  of  the  vane.  These  revolutions  are  recorded  by  means  of  several 
pointers,  each  having  a  separate  dial  upon  the  face  of  the  instrument,  the 
motion  being  communicated  by  a  series  of  gearwheels  arranged  decimally  to 
each  other.  Most  anemometers  are  provided  with  a  large  central  pointer 
that  makes  1  revolution  for  each  100  revolutions  of  the  vane.  The  dial  for 
this  pointer  is  marked  by  100  divisions,  which  record  the  number  of  lineal 
feet  of  velocity.  In  very  accurate  work  with  the  anemometer,  certain  con- 
stants are  used  as  suggested  by  the  instrument  maker,  but  these  constants 
are  of  little  value  in  ordinary  practice  and  are  of  doubtful  value  even  in  more 
accurate  observations. 

The  measurement  of  the  velocity  of  an  air  current  must  necessarily 
represent  only  approximately  the  true  velocity  in  the  airway.  The  air 
travels  with  a  greater  velocity  in  the  center  of  the  airway  ,  and  is  retarded  at 
the  sides,  top,  and  bottom  by  the  friction  of  these  surfaces.  Hence,  the 
air  to  a  large  extent  rolls  upon  these  surfaces,  which  naturally  generates  an 
eddy  at  the  sides  of  airways.  When  measuring  the  air,  the  anemometer 
should  be  held  in  a  position  exactly  perpendicular  to  the  direction  of  the 
current,  and  moved  to  occupy  different  positions  in  the  airway,  being  held 
an  equal  time  in  each  position,  or  it  may  be  moved  continuously  around 
the  margin  of  the  airway,  and  through  the  central  portion. 
The  person  taking  the  observation  should  observe  the  caution 
of  not  obstructing  the  area  of  the  airway  by  his  body,  as  the 
area  is  thereby  reduced,  and  the  velocity  of  the  current  in- 
creased.  The  area  of  the  airway  is  accurately  measured  at 
the  point  where  the  observations  are  taken. 

To  obtain  the  quantity  of  air  passing  (cubic  feet  per  minute)  , 
multiply  the  area  of  the  airway,  at  the  point  where  the  velocity 
is  measured,  by  the  velocity. 

EXAMPLE.  —  The  anemometer  gives  a  reading  of  1,320  ft.  in 
2  min.,  the  height  of  the  airway  is  6  ft.  6  in.,  and  its  average 
width  8  ft.  8  in.  What  volume  of  air  is  passing  in  the  airway 
per  minute? 


6*  X  81  X 


37,180  cu.  ft.  per  min. 


The  measurement  of  the  ventilating  pressure  is  made  by 
means  of  a  water  column  in  the  form  of  a  water  gauge. 

Water  Gauge.  —  The  water  gauge  is  simply  a  glass  U-tube 
open  at  both  ends.  Water  is  placed  in  the  bent  portion  of  the 
tube,  and  stands  at  the  same  height  in  both  arms  of  the  tube 
when  each  end  of  the  tube  is  subjected  to  the  same  pressure. 
If,  however,  one  end  of  the  tube  is  subjected  to  a  greater 
pressure  than  the  other  end,  the  water  will  be  forced  down  in 
FIG.  7  that  arm  of  the  tube,  and  will  rise  a  corresponding  height  in 
the  other  arm,  the  difference  of  level  in  the  two  arms  of  the 
tube  representing  the  water  column  balanced  by  the  excess  of  pressure  to 
which  the  water  in  the  first  arm  is  subjected.  An  adjustable  scale  grad- 
uated in  inches  measures  the  height  of  the  water  column.  The  zero  of  the 
scale  is  adjusted  to  the  lower  water  level,  and  the  upper  water  level  will 
then  give  the  reading  of  the  water  gauge.  One  end  of  the  glass  tube  is 
drawn  to  a  narrow  opening  to  exclude  dust,  while  the  other  end  is  bent  to 
a  right  angle,  and  passing  back  through  the  standard  to  which  the  tube  is 
attached,  is  cemented  into  the  brass  tube  that  passes  through  a  hole  in  the 
partition  or  brattice,  when  the  water  gauge  is  in  use.  The  bend  of  the  tube 


VENTILATION  OF  MINES 


909 


is  contracted  to  reduce  the  tendency  to  oscillation  in  the  height  of  water 
column  (see  Fig.  7). 

When  in  use,  the  water  gauge  must  be  in  a  perpendicular  position.  It  may 
be  placed  upon  a  brattice  occupying  a  position  between  two  airways,  as 
shown  at  A,  Fig.  8.  The  brass  tube  forming  one  end  of  the  water  gange  is 
inserted  in  a  cork,  and  passes  through  a  hole  bored  in  the  brattice.  The 
water  gauge  must  not  be  subjected  to  the  direct  force  of  the  air  current,  as 
in  this  case  the  true  pressure  will  not  be  given.  Fig.  8  shows  the  instrument 
as  occupying  a  position  in  the  breakthrough,  between  two  entries.  It  will 
be  observed  that  the  water  gauge  records  a  difference  of  pressure,  each  end 
of  the  water  gauge  being  subject  to  atmospheric  pressure,  but  one  end  in 
addition  being  subject  to  the  ventilat- 
ing pressure,  which  is  the  difference  of 
pressure  between  the  two  entries.  The 
water  gauge  thus  enables  us  to  measure 
the  resistance  of  the  mine  inbye  from 
its  position  between  two  airways.  If 
placed  in  the  first  breakthrough,  at  the 
foot  of  the  shaft,  it  measures  the  entire 
resistance  of  the  mine,  but  if  placed  at 
the  mouth  of  a  split,  it  measures  only 
the  resistance  of  that  split.  It  never 
measures  the  resistance  outbye  from  its 
position  in  the  mine,  but  always  inbye 
(see  Calculation  of  Pressure). 

Calculation  of  Mine  Resistance. — 
The  mine  resistance  is  equal  to  the 
total  pressure  pa  that  it  causes.  This 
mine  resistance  is  dependent  upon 
three  factors:  (a)  The  resistance  k 
offered  by  1  sq.  ft.  of  rubbing  surface 
to  a  current  having  a  velocity  of  1  ft. 
per  min.  The  coefficient  of  friction  k, 
or  the  unit  of  resistance,  is  the  resist- 
ance offered  by  the  unit  of  rubbing  sur- 
face to  a  current  of  a  unit  velocity.  This  unit  resistance  has  been  variously 
estimated  by  different  authorities  (see  following  table).  The  value  most 
universally  accepted,  however,  is  that  known  as  the  Atkinson  coefficient 
(.0000000217).  (b)  The  mine  resistance,  which  varies  as  the  square  of  the 
velocity,  (c)  The  rubbing  surface.  Hence,  if  we  multiply  the  unit  resist- 
ance by  the  square  of  the  velocity,  and  by  the  rubbing  surface,  we  will 
obtain  the  total  mine  resistance  as  expressed  by  the  formula  pa  =  ksv2. 

TABLE  OF  VARIOUS  COEFFICIENTS  OF  FRICTION  OF  AIR  IN  MINES. 

Pressure  per 

Sq.  Ft.  Decimals 

of  a  Pound. 

J.  J.  Atkinson's  treatise 0000000217 

A.   Devillez  in  Ventilation  des  Mines: 

Forchies  00000000821 1 

Crachet-Picquery 000000008928 

Grand  Baisson 000000008611 

Average  of  2,  3,  and  4 000000008585 

Used  in  Ventilation  des  Mines 000000009511 

Arched  Tunnels 000000002113 

Along  a  working  face  of  coal 

G.  G.  Andre,  Atmosphere  of  Coal  Mines 

Peclet,  Cheminee  (Devillez,  p.  112) 

D.  K.  Clark 

According  to  Goupilliere's  Cours  d'  Exploitation  des  Mines, 


FIG.  8 


000000014266 
.000000022424 
.000000003697 
. 000000002272 


W    Fairlev  00000001 

T    Stanlev   TameV  "  •      .00000000929 

D.  MurgueJ      .      ^  iTf !  1 1-!.!  ; ! !  T!  1! ! ; .; 000000008242 

It  will  be  observed  that  J.  J.  Atkinson's  coefficient  is  greatly  in  excess  of 
any  other,   with  the  exception  of  Andre's.     Fairley's  is  derived  from  an 


910  VENTILATION  OF  MINES 

average  taken  between  Atkinson,  Devillez,  and  Clark,  and,  undoubtedly,  it 
is  an  exceedingly  simple  coefficient  to  work  out  calculations  with,  as  it  will 
save  a  great  mass  of  figures.  James,  in  his  work  on  colliery  ventilation, 
reduces  the  coefficient  still  further  on  the  authority  of  the  Belgian  Mine 
Commission,  but  he  gives  a  most  unwieldy  figure  to  use. 

Atkinson's  figure  is  the  one  most  in  use,  and  if  it  is  too  high,  it  errs  on  the 
side  of  safety,  and  it  is  always  advisable  to  have  plenty  of  spare  ventilating 
capacity  at  a  mine.  For  this  reason,  and  until  a  regular  and  thorough  inves- 
tigation, made  by  a  commission  of  competent  men,  provides  a  standard  coef- 
ficient, we  prefer  to  abide  by  Atkinson's  coefficient,  and  it  is  used  in  all  our 
calculations. 

Calculation  of  Power,  or  Units  of  Work  per  Minute.  —  If  we  multiply  the 
total  pressure  by  the  velocity  (feet  per  minute)  with  which  it  moves,  we 
obtain  the  units  of  work  per  minute,  or  the  power  upon  the  air.  Hence,  u  = 
pav  =  ksv3,  which  is  the  fundamental  expression  for  work  per  minute,  or 
power. 

The  Equivalent  Orifice.  —  This  term,  often  used  in  regard  to  ventilation, 
evaluates  the  mine  resistance,  or,  as  will  be  seen  from  the  equation  given 
below  for  its  value,  expresses  the  ratio  that  exists  between  the  quantity 
of  air  passing  in  an  airway  and  the  pressure  or  water  gauge  that  is  produced 
by  the  circulation.  This  term  was  suggested  by  M.  Daniel  Murgue,  and 
refers  to  the  flow  of  a  fluid  through  an  orifice  in  a  thin  plate,  under  a  given 
head.  The_formula  expressing  the  velocity  of  flow  through  such  an  orifice 
is  v  =  \/2gh>  multiplying  both  members  of  this  equation  by  A,  and  substi- 
tuting for  the  first  member  Av,  its  value  q,  we  have,  after  transposing  and 

correcting  for  vena  contracta,  A  —  -  -         t  in  which  .62  is  the  coefficient 

.&2VWh 

for  the  vena  contracta  of  the  flow.  Reducing  this  to  cubic  feet  per  minute  and 
inches  of  water  gauge  represented  by  *',  we  have,  finally,  the  equation  A  = 

.  0004  X  •  —  —  .     By  this  formula,  Murgue  has  suggested  comparing  the  flow  of 

V  i 

air  through  a  mine  to  the  flow  of  a  fluid  through  a  thin  plate;  since,  in  each 
case,  the  quantity  and  the  head  or  pressure  vary  in  the  same  ratio.  Thus, 
applying  this  formula  to  a  mine,  Murgue  multiplies  the  ratio  of  the  quantity 
of  air  passing  (cubic  feet  per  minute)  and  the  square  root  of  the  water  gauge 
(inches)  by  .0004,  and  obtains  an  area  A,  which  he  calls  the  equivalent 
orifice  of  the  mine. 

Potential  Factor  of  a  Mine.  (Proposed  by  T.  J.  Beard.)  —  Equations  8  and 
27  pages  370^-371,  give,  respectively,  the  pressure  and  the  power  that  will 
circulate  a  given  quantity  of  air  per  minute  in  a  given  airway.  These 
equations  may  be  written  as  equal  ratios,  expressed  in  factors  of  the  current 

and  the    airway,   respectively:   thus,   —  =  —  ,  and  —  =  —  ,  which  show  that 

q*     a3      t     q>     c« 

the  ratio  between  the  pressure  and  the  square  of  the  quantity  it  circulates  in 
any  given  airway  is  equal  to  the  ratio  between  the  power  and  the  cube  of  the 
quantity  it  circulates.     Solving  each  of  these  equations  with  respect  to  q, 
we  have  the  following: 
With  respect  to  pressure, 


With  respect  to  power, 


Hence  we  observe  that,  in  any  airway,  for  a  constant  pressure,  the  quan- 
tity of  air  in  circulation  is  proportional  to  the  expression  a  \/— ;  and,  for  a 

\fes 

a 
constant  power,  the  quantity  is  proportional  to  the  expression     $/— ,  which 

terms  are  called  the  potentials  of  the  mine  with  respect  to  pressure  and 

Q  Q 

power,  respectively;  and  their  values  ~j=  and     a/-  are  the  potentials  of  the 

VP  V" 


VENTILATION  OF  MINES 


911 


THE  FOLLOWING  TABLE  OF  WATER  GAUGES  WILL  BE  FOUND  OF  ASSISTANCE 
IN  CALCULATING  THE  AMOUNT  OF  AIR  REQUIRED  FOR  MINE  WORKINGS  • 

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99.84 

0.70 

6,240 

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32.44 

519.04 

3.55 

32,440 

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6.76 

108.16 

0.75 

6,760 

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32.76 

524.16 

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33.80 

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6.6 

34.32 

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141.44 

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35.36 

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7.3 

37.96 

607.36 

4.19 

37,960 

.150 

2.4 

12.48 

199.68 

1.38 

12,480 

0.378 

7.4 

38.48 

615.68 

4.24 

38,480 

.166 

2.5 

13.00 

208  .  00 

1.44 

13,000 

0.390 

7.5 

39.00 

624.00 

4.30 

39,000 

.181 

2.6 

13.52 

216.32 

1.50 

13,320 

0.409 

7.6 

39.52 

632.32 

4.40 

39,520 

.193 

2.7 

14.04 

224  .  64 

1.56 

14,040 

0.425 

7.7 

40.04 

641.12 

4.45 

40,040 

.213 

2.8 

14.56 

232.96 

1.61 

14,560 

0.441 

7.8 

40.56 

648.96 

4.50 

40,560 

.230 

2.9 

15.08 

241.28 

1.68 

15,080 

0.456 

7.9 

41.08 

657.28 

4.56 

41,880 

.242 

3.0 

15.60 

250.60 

1.72 

15,600 

0.471 

8.0 

41.60 

665.60 

4.52 

41,600 

1.262 

3.1 

16.12 

257.92 

1.80 

16,120 

0.490 

8.1 

42.12 

673.92 

4.68 

42,120 

1.274 

3.2 

16.64 

266.24 

1.84 

16,640 

0.504 

8.2 

42.84 

685.44 

4.70 

42,840 

1.300 

3.3 

17.16 

274  .  56 

1.89 

17,160 

0.520 

8.3 

43.16 

690.56 

4.76 

43,160 

1.308 

3.4 

17.68 

282.88 

1.96 

17,680 

0.536 

8.4 

43.68 

698.88 

4.82 

43,680 

1.320 

3.5 

18.20 

291.20 

2.01 

18,200 

0.551 

8.5 

44.20 

707.20 

4.87 

44.200 

1.340 

3.6 

18.72 

299  .  52 

2.08 

18,720 

0.567 

8.6 

44.72 

715.52 

4.96 

44,720 

1.360 

3.7 

19.24 

307.84 

.13 

19,240 

0.583 

8.7 

45.24 

723.84 

.02 

45,240 

1.370 

3.8 

19.76 

316.16 

.20 

19,760 

0.600 

8.8 

45.76 

732.16 

.08 

45,760 

1.386 

3.9 

20.28 

324.48 

.25 

20,280 

0.614 

8.9 

46.28 

740.48 

.16 

46,280 

1.400 

4.0 

20.80 

332.80 

.30 

20,800 

0.631 

9.0 

46.80 

747.80 

.20 

46,800 

1.415 

4    1 

21.32 

341.12 

.36 

21,320 

0.646 

9.1 

47.32 

758.12 

.25 

47,300 

1.432 

4\2 

21.84 

349.44 

.42 

21,840 

0.661 

9.2 

48.04 

768.64 

.28 

48,040 

1.452 

4.3 

22.36 

357.76 

.46 

22,360 

0.677 

9.3 

48.36 

773.76 

.33 

48,360 

1.465 

4.4 

22.88 

366.08 

.54 

22,880 

0.693 

9.4 

48.88 

782.08 

.43 

48,880 

1.481 

4.5 

23.40 

374.40 

.58 

23,400 

0.709 

9.5 

49.40 

790.40 

.45 

49,400 

1.500 

4.6 

23.92 

382.72 

.65 

23,920 

0.724 

9.6 

49.92 

798.72 

.50 

49,920 

1.513 

4.7 

24.44 

391.04 

.71 

24,440 

0.740 

9.7 

50.44 

807.04 

.60 

50,440 

1.525 

4.8 

24.96 

399  .  36 

.80 

24,960 

0.753 

9.8 

50.96 

815.36 

.66 

50,960 

1.542 

4.9 

25.48 

407  .  68 

.83 

25,480 

0.773 

9.9 

51.48 

823.68 

5.72 

51,480 

1.560 

5.0 

26.00 

416.00 

.87 

26,000 

0.789 

0.0 

52.00 

832.00 

5.74 

52,000 

1.600 

NOTE. — The  table  is  based  on  1  cu.  ft.  of  water  weighing  62.4  Ib. 
umn  of  water  1  in.  in  depth  and  1  sq.  ft.  in  area  equals  5.2  ID. 


A  col- 


912  VENTILATION  OF  MINES 

current  with  respect  to  pressure  and  power,  respectively.  These  factors,  it 
will  be  observed,  evaluate  the  airway,  as  they  determine  the  quantity  of  air 
a  given  pressure  or  power  will  circulate  in  that  airway  (cubic  feet  per  min- 
ute). By  their  use  the  relative  quantitites  of  air  any  given  pressure  or 
power  will  circulate  in  different  airways  are  readily  determined.  The  rule 
may  be  stated  as  follows: 

Rule.  —  For  any  given  pressure  or  power,  the  quantity  of  air  in  circulation  is 
always  proportional  to  the  potential  for  pressure,  or  the  potential  for  power,  as 
the  case  may  be. 

This  rule  finds  important  application  in  splitting  (see  Calculation  of 
Natural  Splitting).  In  all  cases  where  the  potential  is  used  as  a  ratio,  the 
relative  potential  may  be  employed  by  omitting  the  factor  k\  or  it  may  be 
employed  to  obtain  the  pressure  and  power  in  several  splits  by  multiplying 
the  final  result  by  k  (see  Formulas  26,  27,  etc.,  page  914). 

EXAMPLE.  —  20,000  cu.  ft.  of  air  is  passing  in  a  mine  in  which  the  airway 
is  6  ft.  X  8  ft.,  and  10,000  ft.  long,  under  a  certain  pressure;  it  is  required  to 
find  what  quantity  of  air  this  same  pressure  will  circulate  in  a  mine  in  which 
the  airway  is  6  ft.  X  12  ft.,  and  8,000  ft.  long. 

Calculating  the  potential  Xp  with  respect  to  the  pressure  for  each 
of  these  mines,  or  airways,  we  have,  using  the  ^relative  potential, 

/       ,    6XJ  __  =.62845,    and    X2  =  6X12\/-         6X12^I 
2(6  +  8)X  10,000  \2(6  +  12)X8,000 

=  1.1384.  Since  the  ratio  of  the  quantities  is  equal  to  the  ratio  of  the 
potentials  with  respect  to  pressure,  in  these  two  mines,  we  write  the  propor- 


. 
tion  20,000  :  q2  :  :  .62845  :  1.1384,  and  g2  =  .'          =  36,229  cu.  ft. 

,O^o4o 

per  min. 

EXAMPLE.  —  20,000  cu.  ft.  of  air  is  passing  in  a  mine  in  which  the  airway 
is  6  ft.  X  8  ft.,  and  10,000  ft.  long,  under  a  certain  power;  it  is  required  to 
find  what  quantity  of  air  will  be  circulated  by  this  same  power  in  a  mine  in 
which  the  airway  is  6  ft.  X  12  ft.,  and  8,000  ft.  long. 

We  calculate  the  potential  Xu  with  respect  to  power  for  each  of  these 

mines,  using,  as  before,  the  relative  potential.     Thus,  X\ 


=  .  7337,  and  Xz  =  =  1.0905.     Then,  in  this  case,  since  the 

<^/2  (6  + 12)  X  8,000 

ratio  of  the  quantities  is  equal  to  the  ratio  of  the  potentials  with  respect 
to    power,    we     write     the    proportion,     20,000  :  qz  :  :  .7337  :  1.0905,    and 

20,000X1.0905     , 
ff2  = ~~ =  29,726  cu.  ft.  per  mm. 

•  /  uO  / 

The  following  table  will  serve  to  illustrate  the  use  of  the  formulas  em- 

Eloyed  in  these  calculations.  It  will  be  observed  that  there  are  several 
)rmulas  for  quantity,  and  for  velocity,  and  for  work  or  horsepower,  but 
in  each  respective  case  the  several  formulas  are  derived  by  simple  transposi- 
tion of  the  terms  of  the  original  formula,  and  are  tabulated  here  for  conven- 
ience. Choice  must  be  made  in  the  use  of  any  of  these  formulas,  according 
to  the  known  terms  in  each  example.  Thus,  an  example  may  ask:  What 
pressure  will  be  produced  in  passing  a  given  quantity  of  air  thro  gh  a  certain 
mine,  the  size  and  length  of  the  airways  being  given?  We  then  use  the 

formula  p  =  — — .     But  if  the  question  asks  what  quantity  of  air  a  given 


pressure  will  produce  in  this  same  mine,  we  use  the  formula  q=  AnT  X-o. 

It  will  be  observed  that  this  second  formula  is  a  simple  transposition  of  the 
first. 

In  like  manner  the  question  may  be  asked,  what  power  will  produce  a 
certain  quantity  of  air  in  a  certain  airway;  and  the  expression  used,  in  this 

case,  is  «  =  — —.  Or  the  question  may  be  asked,  what  quantity  of  air  will 
be  produced  in  a  given  airway  by  means  of  a  certain  power  or  work  applied 
to  the  airway.  In  this  case  the  formula  used  is  q  =  a^-^-.  If  the  question 
asks  for  the  power  required  to  produce  a  given  velocity  in  a  given  airway, 


VENTILATION  OF  MINES 


913 


the  formula  employed  is  u=ksv*.   ^All  of  these  formulas  are  derived  by  com- 
bining the  simple  formulas  p  = ,  q  =  av,  and  u  =  qp. 

To  illustrate  the  use  of  the  formulas,  we  take  as  an  example  an  under- 
ground road,  5  ft.  wide  by  4  ft.  high,  and  2,000  ft.  in  length,  and  calculate  the 
value  of  each  symbol  or  letter,  assuming  a  velocity  of  500  ft.  per  min. 


Symbol 

Value   of    Symbol 
for  this  Particular 
Example 

Area  of  airway  (5  ft.  X  '4  ft.)  

a 
h 

20  sq.  ft. 
2  959  H    p 

Coefficient  of  frictionf  
Length  of  airway  

k 
I 

.000000021  7  Ib. 
2  000  ft 

Perimeter  of  airway,  2(5  ft.  -f-  4  ft.)  
Pressure  (Ib.  per  sq.  ft.)  .  .  . 

o 
p 

18  ft. 
9  765  Ib 

Quantity  of  air  (cu.  ft.  per  min.)  
Area  of  rubbing  surface  
Units  of  work  per  minute  (power)  
Velocity  (ft.  per  min.)  

Q 
s 
u 

V 

10,000  cu.  ft. 
36,000  sq.  ft. 
97,650  ft.-lb. 
500  ft. 
1  87788  in 

Equivalent  orifice  of  the  mine  

A 

Xu 

2.919  sq.  ft. 
217  16  units 

Potential  for  pressure  
Weight  of  1  cu.  ft.  of  downcast  air  

Xv 

w 
M 

3,200  units 
.  08098  Ib. 
120  5  ft 

Depth  of  furnace  shaft  
Average  temperature  of  the  upcast  column  .  . 
Average  temperature  of  the  downcast  column. 

D 
T 
t 

306.77  ft. 
350°F. 
32°F. 

*  A  horsepower  is  equal  to  33,000  units  of  work. 

t  This  coefficient  of  friction  is  an  invariable  quantity,  and  is  the  same  in 
every  calculation  relating  to  the  friction  of  air  in  mines. 

NOTE. — The  water  gauge  is  calculated  to  five  decimal  places  to  enable  all 
the  other  values  to  be  accurately  arrived  at.  In  practice  it  is  only  read  to 
one  decimal  place. 

FORMULAS 

On  the  right  side  of  each  formula  the  various  calculations,  based  on  the 
example  given,  are  worked  out  in  figures. 


To  Find: 

d 
fc 

Formula 

Specimen  Calculation 

Rubbing  surface 
of    an    airway. 
(Sq.  ft.) 

1 

s  =  lo 

2,000X18  =  36,000  sq.  ft. 

Area  of  an  air- 

.     <7 

10.000 

way.     (Sq.  ft.) 

a~v 

Velocity.        (Ft. 

v      9 

10,000 

per  min.) 

3 

a 

20      • 

\IU 

\/               97'65°                  500ft 

4 

V~\ks 

\.000000021  7X36,000     ' 

\E 

.1           9.765X20 

5 

"-\^ 

u 

\.0000000217X36.000     * 
97,650 

V~pa 

9.765X20     * 

58 


914 


VENTILATION  OF  MINES 


To  Find: 

o 
^ 

Formula 

Specimen  Calculation 

Pressure.       (Lb. 

* 

ksv* 

.0000000217X36,000X5002     0  ?65  lb 

per  sq.  ft.) 

P        a 
ksq* 

.0000000217  X  36,000  X  10,000^ 

P            03 
tt 

203 
=  9.765  lb. 

97,650  ^ 

10 

11 

1  ° 

*     Q 
p  =  Mw 
p  =  5.2» 

*=52 

io;ooo    * 

120.58  X.  08098  =  9.765  lb. 
5.2  X  1.87788  =  9.765  lb. 

10'0002     0-651b 

*    XJ 

q* 

217.163     ' 

/lo.oooy 

P~x7> 

U,200,>       9'76'  lb< 

Water  gauge. 
(In.) 

14 

<=h 

2^5.1^88^ 

0*« 

Resistance  of  an 
airway.  (Total 

15 

1  f* 

pa  =  ksv* 
u 

.0000000217  X  36,000  X  5002  =  195.3  lb. 
97,650 

pressure,  Ib.) 

pa-v 

500 

Quantity.  (Cu. 
ft.  per  rain.) 

17 

1  ^ 

q  =  av 
u 

20  X  500  =  10,000  cu.  ft. 
97'650  =  10000cu   ft 

q~P 

9.765      1  ' 

\/^Vfl 

~J           9.765X20           „ 

q~  \ksXa 

\.0000000217X36.000  A 
=  10,000  cu.  ft. 

on 

^/""va 

^/              97,650 

21 

q~    \ksXa 
ff  =  X«-^ 

\.0000000217X  36,000  A 
=  10,000  cu.  ft. 

217.16X  -^97,650  =  10,000  cu.  ft. 

22 
23 

<7  =  -^/Xp2M 
q  =  XPVp 

-Y/3.20Q2X  97,650  =  10,000  cu.  ft. 
3,200  X  V9.765  =  10,000  cu.  ft. 

Units    of    work 
per  minute,  or 
power    on    the 
air.    (Ft.-lb.  per 
min.) 

24 
25 
26 

07 

u=*avp 
u  =  qp 
u  =  ksv* 

ksq<> 

20X500X9.765  =  97,650  ft.-lb. 
10,000X9.765  =  97,650  ft.-lb. 

.0000000217  X  36,000  X  500* 
=  97,650  ft.-lb. 

.0000000217  X  36,000  X  10,000" 

a3 

203 
=  97,650  ft.-lb. 

VENTILATION  OF  MINES 


915 


To  Find: 

d 
£ 

Formula 

Specimen  Calculation 

Units    of     work 
per  minute,  or 
power    on    the 

28 
oq 

«=/z33,000 

u-£- 

2.959X33,000=97,650  ft.-lb. 
10,0003 

air.  (Ft.-lb.  per 
min.) 

•?(-> 

XU3 

u       Q3 

217.163     y7'0<j( 
10,0003     __nfi 

XS 

3,2002  -97'650  fL-lb- 

•71 

h~         U 

97'650     „ 

"     33,000 

33,000  ~2-959IL  r- 

Power  potential. 

S9 

x*     a 

20 

33 

\/ks 

Xu~  \P 

^/.0000000217X36,000 

^/Io^oo~2    0171flur 

9<1 

\/> 

Xu  =      q 

10-000        n171Gun 

^ 

\X97.650 

Pressure    poten- 
tial      (Units  ) 

•JK 

Xn-a\t°~ 

o0V/                 20 

36 

a  Mks 
Y         q 

\.0000000217X36.000 
=  3,200  units. 

10,000 

VP 

V9-765 

Equivalent    ori- 

37 

A      .0004*7 

.0004  X  10,000  _o910.q   ft 

fice.    (Sq.  ft.) 

Vi 

Vl.  87788 

Motive  column, 

3^ 

A/      7)V     T~l 

?0fi  77  V  35°  "~  32       T'O'ift 

downcast     air. 
(Ft.) 

^X459+r 
A/      * 

77X459  +  350      ] 
9.765 

7# 

.08098  ~UO<5  £t> 

Motive  column, 

M     DV   r~* 

306  77  X35°~32     1937ft 

upcast  air. 
(Ft.) 

X459  +  < 
If      p 

!06<77X459  +  32     198'7ft- 
9-765a10o7f. 

M~w 

.04915     ] 

Variation  of  the  Elements. — In  the  illustration  of  the  foregoing  table,  we 
have  assumed  fixed  conditions  of  motive  column,  as  well  as  fixed  conditions 
in  the  mine  airways.  It  is  often  convenient,  however,  to  know  how  the 
different  elements,  as  velocity  v,  quantity  q,  pressure  p,  power  u,  etc.,  will 
vary  in  different  circulations;  since  we  may,  by  this  means,  compare  the 
circulations  in  different  airways,  or  the  results  obtained  by  applying  different 
pressures  and  powers  to  the  same  airway.  These  laws  of  variation  must 
always  be  applied  with  great  care.  For  example,  before  we  can  ascertain 
how  the  quantity  in  circulation  will  vary  in  different  airways,  we  must 
know  whether  the  pressure  or  the  power  is  constant  or  the  same  for  each 
airway.  The  following  rules  may  always  be  applied: 

For  a  constant  pressure:  v  varies  as  VrS  1  varies  as  a\r  (relative 
potential  for  pressure). 


916  VENTILATION  OF  MINES 

For  a  constant  power  :  v  varies  as  -77=;  q  varies  as     g  •  (relative  potential 


for  power). 

For  a  constant  velocity  :  q  varies  as  a;  p  varies  as  —  ;  u  varies  as  /o. 

c 

For  a  constant  quantity:  v  varies  inversely  as  a;  p  varies  inversely  as  Xu3 
(potential  for  power);  u  varies  inversely  as  Xu3  (potential  for  power)  or 
directly  as  p. 

For   the   same  airway:  The  following  terms  vary  as  each  other:  v,  q, 

VP-  -v^- 

SIMILAR  AIRWAYS 

r  =  length  of  similar  side,  or  similar  dimension 

For  a  constant  pressure  :  v  varies  as   \  j;  q  varies  as  r2X   \y;  r  varies 


as  lv2,  or 

For  a  constant  power:  v  varies  as  -*    ;  q  varies  as  rX  A^'-y;  r  varies  as 

•i 

— ,  or  -\flq3, 

For  a  constant  velocity:  q  varies  as  r2;  p  varies  as  — ;  u  varies  as  lr;  r 

,-    I         u 
varies  as  v  q  *  it  or  r- 

P        I 
For  a  constant  quantity:  v  varies  inversely  as  r2;  p  and  u  vary  inversely  as 


T;  r  vanes  as  —  •         -f  or        -. 

FURNACE  VENTILATION 

P  (motive  column)  varies  as  D;  q  varies  as  \^D 
FAN  VENTILATION 

It  has  been  customary  in  calculations  pertaining  to  the  yield  of  centrifu- 
gal ventilators  to  assume  as  follows:  q  varies  as  n\  p  varies  as  w2;  u  varies 
as  n3. 

More  recent  investigation,  however,  shows  that  when  we  double  the  speed 
we  do  not  obtain  double  the  quantity  of  air  in  circulation;  or,  in  other  words, 
the  quantity  does  not  vary  exactly  as  the  number  of  revolutions  of  the  fan. 
Investigation  also  points  to  the  fact  that  the  efficiency  of  centrifugal  ventila- 
tors decreases  as  the  speed  increases.  To  what  extent  this  is  the  case  has 
not  been  thoroughly  established.  The  variation  between  the  speed  of  a 
fan  and  the  quantity,  pressure,  power,  and  efficiency,  as  calculated  from 
a  large  number  of  reliable  fan  tests,  may  be  stated  as  follows: 

For  the  same  fan,  discharging  against  a  constant  potential:  q  varies  as 
»•".  p  varies  as  n1-'4.  Complement  of  efficiency  (1  —  K)  varies  as  n-425. 

The  efficiency  here  referred  to  is  the  mechanical  efficiency,  or  the  ratio 
between  the  effective  work  qp  and  the  theoretical  work  of  the  fan. 

Quantity  Produced  by  Two  or  More  Ventilators.  —  In  the  development  of 
a  mine,  it  often  happens  that  the  means  used  for  producing  a  ventilating 
current  becomes  inadequate  for  the  production  of  the  quantity  of  air  required 
as  the  extent  of  the  workings  increases.  To  increase  the  circulation,  it  is 
often  proposed  to  duplicate  the  ventilating  apparatus  in  use  by  adding 
another  fan  or  furnace  similar  to  the  one  already  in  operation.  This  means 
an  increase  of  ventilating  power,  which,  of  course,  produces  an  increase  in 
the  quantity  of  air  in  circulation.  Assuming  that  no  change  is  made  in 
the  course  of  the  circulation  of  the  air  through  the  mine,  any  increase  of 
quantity  will  require  an  increase  of  power  in  proportion  to  the  cube  of  the 
ratio  in  which  the  quantity  is  increased,  as  is  shown  by  the  following  com- 
parison of  power  and  quantity  for  a  given  airway: 

If  KI  represents  the  power  on  the  air  for  a  given  airway  when  a  quantity 

<ji  is  circulating,  MI=  8S8L  =     _£    ?1s;  jf  M2  represents  the  power  on  the  air 


VENTILATION  OF  MINES  917 

when  a  quantity  32  is  circulating  through  the  same  airway,  u2  =  —^  = 


As  the  same  airway  is  considered  in  each  case,  k,  s,  and  a  are  the  same  and 

Ul        Ql^ 

by  canceling,  —  =  —  -  or  MI  :  uz  —  qi*  :  qz3;    that  is,  for  the  same  airway,  the 

power  is  proportional  to  the  cube  of  the  quantity,  or  the  ratio  between 
the  powers  for  two  quantities  of  air  equals  the  cube  of  the  ratio  between  the 
quantities.  For  example,  if  the  quantity  is  to  be  doubled,  the  quantity 
ratio  is  then  2  and  the  power  ratio  is  23  =  8.  That  is  to  say,  it  will  require 
eight  times  the  power  to  double  the  quantity  of  air  in  the  same  mine  or 
airway.  This  shows  that  two  fans  of  the  same  size  and  running  at  the  same 
speed  will  not  produce  double  the  quantity  of  air  circulated  by  one  of  these 
fans  alone. 

When  two  or  more  ventilating  motors  are  employed,  it  is  evident  that  the 
total  power  producing  the  circulation  is  equal  to  the  sum  of  the  powers  of 
the  several  motors. 

Now,  calling  the  quantities  produced  by  several  motors  working  separately 
on  the  same  airway  gi,  32,  etc.,  the  powers  of  these  several  motors  MI,  uz,  etc., 
and  the  total  quantity  produced  when  all  the  motors  are  working  together, 

Q>  Q3  (^)=afll3O  +  323(S)  +  etC>  °r>  dividinS  both  members  of  the 
equation  by  —  ,  Q3  =  gi3  +  <723  +  etc.,  and,  finally, 


This  formula  shows  the  quantity  of  air  produced  by  the  combined  action 
of  two  or  more  ventilating  motors  working  on  the  same  mine  or  airway,  and 
which,  when  working  alone,  produce  the  quantities  qi,  32,  etc.,  in  the  same 
mine  or  airway. 

EXAMPLE.  —  A  fan  ventilating  a  certain  mine  is  capable  of  producing 
42,600  cu.  ft.  of  air  when  operated  alone,  and  another  fan  ventilating  the 
same  mine  will  produce  57,400  Cu.  ft.  when  working  alone;  what  quantity 
of  air  will  be  produced  in  this  mine  when  both  fans  are  in  operation,  assuming 
that  the  general  conditions  in  the  mine  remain  the  same? 

SOLUTION.  —  Substituting  the  given  quantities  in  the  formula,  and  calling 
the  unknown  quantity  x,  the  total  quantity  of  air  produced  by  the  com- 
bined action  of  the  two  fans 


x  =  -y/42,6003  +  57,4003  =  64,300  cu.  ft.  per  min. 

The  installation  of  two  fans  side  by  side  at  the  mouth  of  the  same  return 
is  very  unusual,  but  the  installation  of  a  second  fan  called  a  "booster" 
at  some  point  in  the  interior  of  the  workings  is  a  fairly  common  practice. 
Boosters  unquestionably  increase  the  amount  of  air  in  circulation  by  aiding 
the  main  fan  to  overcome  the  frictional  resistances  of  exceptionally  long 
air-courses,  but  their  operation  is  expensive  for  the  reasons  explained.  They 
are  permissible  in  ventilating  headings  that  will  have  but  a  short  life,  or 
even  main  workings  which  are  shortly  to  be  abandoned,  but  should  not  be 
tolerated  as  part  of  the  permanent  eouipment  of  a  mine.  It  is  frequently 
the  case  that  a  booster  is  installed  when  the  cleaning  up  of  the  return  air- 
courses  to  their  proper  normal  width  would  have  permitted  the  main  fan 
to  have  supplied  the  necessary  quantity  of  air,  and  more  cheaply. 


DISTRIBUTION  OF  AIR  IN  MINE  VENTILATION 

When  a  mine  is  first  opened,  the  air  is  conducted  in  a  single  current 
around  the  face  of  all  the  headings  and  workings,  and  returns  again  to  the 
upcast  shaft,  where  it  is  discharged  into  the  atmosphere.  As  the  develop- 
ment of  the  mine  advances,  however,  it  becomes  necessary,  to  divide  the  air 
into  two  or  more  splits  or  currents.  This  division  or  splitting  of  the  air- 
current  is  usually  accomplished  at  the  foot  of  the  downcast,  or  as  soon  as 
possible  after  the  current  enters  the  mine.  There  are  several  reasons  why 


918  VENTILATION  OF  MINES 

the  air  current  should  be  thus  divided.  The  most  important  reason  is 
that  the  mine  is  thereby  divided  into  separate  districts,  each  of  which  has 
its  own  ventilating  current,  which  may  be  increased  or  decreased  at  will. 
Fresh  air  is  thus  obtained  at  the  face  of  the  workings,  and  the  ventilation  is 
under  more  perfect  control.  It  often  happens  that  certain  portions  of  a  mine 
are  more  gaseous  than  others,  and  it  is  necessary  to  increase  the  volume  of 
air  in  these  portions,  which  can  be  readily  accomplished  when  each  district 
has  its  own  separate  circulation.  Again,  the  gases  and  foul  air  are  not 
conducted  from  one  district  to  another,  but  each  district  is  supplied  with 
fresh  air  direct  from  the  main  intake.  Should  an  explosion  occur  in  any 
part  of  the  mine,  it  is  more  apt  to  be  confined  to  one  locality  when  a  mine  is 
thus  divided  into  separate  districts.  Another  consideration  is  the  reduced 
power  necessary  to  accomplish  the  same  circulation  in  the  mine;  or  the 
increased  circulation  obtained  by  the  use  of  the  same  power. 

Requirements  of  Law  in  Regard  to  Splitting. — The  Anthracite  Mine  Law  of 
Pennsylvania  specifies  that  every  mine  employing  more  than  75  persons 
must  be  divided  into  two  or  more  ventilating  districts,  thus  limiting  the 
number  that  are  allowed  to  work  on  one  air  current  to  75  persons.  The 
Bituminous  Mine  Law  of  Pennsylvania  limits  the  number  allowed  to  work 
upon  one  current  to  65  persons,  except  in  special  cases,  where  this  number 
may  be  increased  to  100  persons  at  the  discretion  of  the  mine  inspector. 

Practical  Splitting  of  the  Air  Current. — When  the  air  current  is  divided  into 
two  or  more  branches,  it  is  said  to  be  split.  The  current  may  be  divided  one 
or  more  times;  when  split  or  divided  once,  the  current  is  said  to  be  traveling 
in  two  splits,  each  branch  being  termed  a  split.  The  number  of  splits  in 
which  a  current  is  made  to  travel  is  understood  as  the  number  of  separate 
currents  in  the  mine,  and  not  as  the  number  of  divisions  of  the  current. 

Primary  Splits. — When  the  main  air  current  is  divided  into  two  or  more 
splits,  each  of  these  is  called  a  primary  split. 

Secondary  Splits. — Secondary  splits  are  the  divisions  of  a  primary  split. 

Tertiary  Splits. — Tertiary  splits  result  from  the  division  of  a  secondary 
split. 

Equal  Splits  of  Air. — When  a  mine  is  spoken  of  as  having  two  or  more  equal 
splits,  it  is  understood  to  mean  that  the  length  and  the  size  of  the  separate 
airways  forming  those  splits  are  equal  in  each  case.  It  follows,  of  course, 
from  this  that  the  ventilating  current  traveling  in  each  split  will  be  the 
same,  inasmuch  as  they  are  all  subject  to  the  same  ventilating  pressure. 
When  an  equal  circulation  is  obtained  in  two  or  more  splits  by  the  use  of 
regulators,  these  splits  cannot  be  spoken  of  as  equal  splits. 

IJnequal  Splits  of  Air. — By  this  is  meant  that  the  airways  forming  the 
splits  are  of  unequal  size  or  length.  Under  this  head  we  will  consider  (a) 
Natural  Division  of  the  Air  Current;  (b)  Proportionate  Division  of  the  Air 
Current. 

Natural  Division  of  the  Air  Current. — By  natural  division  of  air  is  meant 
any  division  of  the  air  that  is  accomplished  without  the  use  of  regulators;  or, 
in  other  words,  such  division  of  the  air  current  as  results  from  natural  means. 
If  the  main  air  current  at  any  given  point  in  a  mine  is  free  to  traverse  two 
separate  airways  in  passing  to  the  foot  of  the  upcast  shaft,  and  each  9f  these 
airways  is  free  or  an  open  split,  i.e.,  contains  no  regulator,  the  division  of 
the  air  will  be  a  natural  division.  In  such  a  case,  the  larger  quantity  of  air 
will  always  traverse  the  shorter  split  of  airway.  In  other  words,  an  air  cur- 
rent always  seeks  the  shortest  way  out  of  a  mine.  A  comparatively  small 
current,  however,  will  always  traverse  the  long  split  or  airway. 

Calculation  of  Natural  Splitting. — It  is  always  assumed,  in  the  calculation 
of  the  splitting  of  air  currents,  that  the  pressure  at  the  mouth  of  each  split, 
starting  from  any  given  point,  is  the  same.  Since  this  is  the  case,  in  order 
to  find  the  quantity  of  air  passing  in  each  of.  several  splits  starting  from  a 
common  point,  the  rule  given  under  Potential  Factor  of  a  Mine  is  applied. 
This  rule  may  be  stated  as  fallows: 

The  ratio  between  the  quantity  of  air  passing  in  any  split  and  the  pressure 
Potential  of  that  split  is  the  same  for  all  splits  starting  from  a  common  point. 
Also,  the  ratio  between  the  entire  quantity  of  air  in  circulation  in  the  several 
splits  and  the  sum  of  the  pressure  potentials  of  those  splits  is  Hie  same  as  the 
above  ratio,  and  is  equal  to  the  square  root  of  the  pressure. 

Expressed  as  a  formula,  indicating  the  sum  of  the  pressure  potentials 

(Xi+X2+  etc.)  by  the  expression  SXP,  this  rule  is     ~-  =       =  \/J~.     Hence, 


VENTILATION  OF  MINES  919 

Q2  Q3 

P  =  (ZX  )2  a  U  =  (I.X  )2  exPress  the  pressure  and  power,  respectively, 
absorbed  by  the  circulation  of  the  splits.  These  are  the  basal  formulas  for 
splitting,  from  which  any  of  the  factors  may  be  calculated  by  transposition 
They  will  be  found  illustrated  in  the  table  at  the  end  of  this  section.  We  will 
give  here  two  examples  only,  showing  the  calculation  of  the  natural  division  of 
an  air  current  between  several  splits.  We  have,  from  the  above  formulas 

«-5T,°- 

EXAMPLE.  —  In  a  certain  mine,  an  air  current  of  60,000  cu.  ft.  per  min. 
is  traveling  in  two  splits  as  follows:  Split  A,  6  ft.XS  ft.,  5,000  ft.  lone- 
split  B,  5  ft.XS  ft.,  10,000  ft.  long.  It  is  required  to  find  the  natural  divi- 
sion of  this  air  current. 

Calculating  the  relative  potentials  for  pressure  in  each  split,  we  have 


for  split  A,  Xi  =  48\-  —  =  8888 

' 


for  split  B,  X2  =  40\  __  ™  _  =  .4961 

\2(5  +  8)  10,000 
and  substituting  these  values,  we  have, 


X  60,000  =  38,506  cu.  ft.  per  min.; 

and  32  =  ^1^X60,000  =  21,494  Cu.  ft.  per  min. 

i.oo4y 

EXAMPLE.  —  In  a  certain  mine,  there  is  an  air  current  of  100,000  cu.  ft.  per 
min.  traveling  in  three  splits  as  follows:  Split  A,  6  ft.  X  10  ft.,  8,000  ft.  long; 
split  B,  6  ft.  X  12  ft.,  15,000  ft.  long;  split  C,  5  ft.  X  10  ft.,  6,000  ft.  long.  Find 
the  natural  division  of  this  current  of  air. 

Calculating  the  respective  relative  potentials  with  respect  to  pressure, 
we  have  /  -  ™  - 

for  split  A,  Xi  =  60\  _  —  _  =  .9185; 
\2(6  +  10)  X  8,000 

for  split  B,  X2  =  72\/  _  ^—  _  =  .8314; 
\2(6  +  12)  X  15.000 


for  split  C,  X3  =  5Q\f.  50 =  .8333. 

.    \2(5  + 10)  X 6,000 
"  ils,    we    have    SXP  =  .9185 +  .8314  + 
jing  rule,  we  have 

31  =^g|X  100,000  =  35,556  cu.  ft.  per  min.; 

CO  1  A 

32  =  ^^X100,000  =  32,184  cu.  ft.  per  min.; 
53  =  ^^X100,000  =  32,260  cu.  ft.  per  min. 

A.dOOZ 


.  , 

Adding    these    potentials,    we    have    2XP  =  .9185  +  .  8314  +  .  8333  =«  2.5832. 
Then,  applying  the  foregoing  rule,  we  have 


Total,  100,000 

Proportional  Division  of  the  Air  Current. — It  continually  happens  that 
different  proportions  of  air  are  required  in  the  several  splits  of  a  mine  than 
would  be  obtained  by  the  natural  division  of  the  air  current.  It  is  usually 
the  case  that  the  longer  splits  employ  a  larger  number  of  men,  and  require  a 
larger  quantity  of  air  passing  through  them.  They,  moreover,  liberate  a 
larger  quantity  of  mine  gases,  for  which  they  require  a  larger  quantity  of  air 
than  is  passing  in  the  smaller  splits.  The  natural  division  of  the  air  current 
would  give  to  these  longer  splits  less  air,  and  to  the  shorter  ones  a  larger 
amount  of  air,  which  is  directly  the  reverse  of  what  is  needed.  On  this 
account,  recourse  must  be  had  to  some  means  of  dividing  this  air  propor- 
tionately, as  required.  This  is  accomplished  by  the  use  of  regulators,  of 
which  there  are  two  general  types,  the  box  regulator  and  the  door  regulator. 

Box  Regulator. — This  is  simply  an  obstruction  placed  in  those  airways  that 
would  naturally  take  more  air  than  the  amount  required. .  It  consists  of  a 
brattice  or  door  placed  in  the  entry,  and  having  a  small  shutter  that  can  be 
opened  to  a  greater  or  less  amount.  The  shutter  is  so  arranged  as  to  allow 
the  passage  of  more  or  less  air,  according  to  the  requirements.  The  box 
regulator  is,  as  a  rule,  placed  at  the  end  or  near  the  end  of  the  return  air- 


920  VENTILATION  OF  MINES 

way  of  a  split.  It  is  usually  placed  at  this  point  as  a  matter  of  convenience, 
because,  in  this  positipn,  it  obstructs  the  roads  to  a  less  extent,  the  haulage 
from  the  back  entry  in  this  split  being  carried  over  to  the  main  haulway, 
through  a  crosscut,  before  this  point  is  reached.  The  difficulty,  however, 
can  be  avoided,  in  most  cases,  by  proper  consideration  in  the  planning  of  the 
mine  with  respect  to  haulage  and  ventilation.  The  objection  to  this  form 
of  regulator  is  that,  in  effect,  it  lengthens  the  airway,  or  increases  its  resist- 
ance, making  the  resistance  of  all  the  airways,  per  foot  of  area,  the  same. 
It  is  readily  observed  that,  by  thus  increasing  the  resistance  of  the  mine, 
the  horsepower  of  the  ventilation  is  largely  increased,  for  the  same  circula- 
tion. This  is  an  important  point,  as  it  will  be  found  that  the  power  required 
for  ventilation  is  thus  increased  anywhere  from  50%  to  100%  over  the 
power  required  when  the  other  form  of  regulator  can  be  adopted. 

Door  Regulator. — In  this  form  of  regulator,  which  was  first  introduced  by 
Beard,  the  division  of  the  air  is  made  at  the  mouth  of  the  split.  The  regu- 
lator consists  of  a  door  hung  from  a  point  of  the  rib  between  two  entries, 
and  swung  into  the  current  so  as  to  cut  the  air  like  a  knife.  The  door  is 
provided  with  a  set  lock,  so  that  it  may  be  secured  in  any  position,  to  give 
more  or  less  air  to  the  one  or  the  other  of  the  splits,  as  required.  The  posi- 
tion of  this  regulator  door,  as  well  as  the  position  of  the  shutter  in  the  box 
regulator,  is  always  ascertained  practically  by  trial.  The  door  is  set  so  as 
to  divide  the  area  of  the  airway  proportionate  to  the  work  absorbed  in  the 
respective  splits.  The  pressure  in  any  split  is  not  increased,  each  split 
retaining  its  natural  pressure. 

Calculation  of  Pressure  for  Box  Regulators. — When  any  required  division 
of  the  air  current  is  to  be  obtained  by  the  use  of  box  regulators,  these  are 
placed  in  all  the  splits,  save  one.  This  split  is  called  the  open,  or  free,  split, 

and  its  pressure  is  calculated  in  the  usual  way  by  the  formula  p=  — —  • 

a3 

The  natural  pressure  in  this  open  split  determines  the  pressure  of  the  entire 
mine,  since  all  the  splits  are  subject  to  the  same  pressure  in  this  form  of 
splitting. 

First,  determine  in  which  splits  regulators  will  have  to  be  placed,  in  order 
to  accomplish  the  required  division  of  the  air.  Calculate  the  natural  pres- 
sure, or  pressure  due  to  the  circulation  of  the  air  current,  for  each  split, 

kso^ 
when  passing  its  required  amount  of  air,  using  the  formula  p  =  — — .    The 

split  showing  the  greatest  natural  pressure  is  taken  as  the  free  split.  In  each 
of  the  other  splits,  box  regulators  must  be  placed,  to  increase  the  pressure 
in  those  splits;  or,  in  other  words,  to  increase  the  resistance  of  those  splits 
per  unit  of  area. 

EXAMPLE. — The  ventilation  required  in  a  certain  mine  is: 

split  A,  6  ft. X 9  ft.,    8,000  ft.  long;  40,000  cu.  ft.  per  min. 
split  B,  5  ft.XS  ft.,    6,000  ft.  long;  40,000  cu.  ft.  per  min. 
split  C,  9  ft.X9  ft.,    8,000  ft.  long;  10,000  cu.  ft.  per  min. 
split  D,  6  ft.XS  ft.,  10,000  ft.  long;  30,000  cu.  ft.  per  min. 
In  which  of  these  splits  should  regulators  be  placed,  to  accomplish  the 
required  division  of  air,  and  what  will  be  the  mine  pressure  ? 

Calculating  the  pressure  due  to  friction  in  each  split  when  passing  its 
required  amount  of  air,  we  find, 
for  split  At 

for  split  B,  ^.0000000217X2(5  +  8)6.000X40.000^^^ 
for  split  C,  f..0000000217X2(»+Q)8tOOOX10.000«,L176 

for  split  P^..0000000217X2(6+8)10.000X30.000.,49>45  ^  pef  gq  ft 
483 

Split  B  has  the  greatest  pressure,  and  is  theref9re  the  free  split.  Box 
regulators  are  placed  in  each  of  the  other  splits  to  increase  their  respective 
pressures  to  the  pressure  of  the  free  split  or  the  mine  pressure.  Therefore, 
the  mine  pressure  in  this  circulation  is  84.63  Ib.  per  sq.  ft. 

The  size  of  opening  in  a  box  regulator  is  calculated  by  the  formula  for 
determining  the  flow  of  air  through  an  orifice  in  a  thin  plate  under  a  certain 
head  or  pressure.  The  difference  in  pressure  between  the  two  sides  of  a  box 
regulator  is  the  pressure  establishing  the  flow  through  the  opening,  which 


VENTILATION  OF  MINES  921 

corresponds  to  the  head  h  in  the  formula  v<=^/2gh.  This  regulator  is 
usually  placed  at  the  end  of  a  split  or  airway,  and  since  the  regulator  in- 
creases the  pressure  in  the  lesser  splits  so  as  to  make  it  equal  to  the  pressure 
in  the  other  split,  the  pressure  due  to  the  regulator  will  be  equal  to  the 
ventilating  pressure  at  the  mouth  of  the  split,  less  the  natural  pressure  or 
the  pressure  due  to  friction  in  this  split.  Hence,  when  the  position  of  the 
regulator  is  at  the  end  of  the  split,  the  pressure  due  to  friction  in  the  split  is 

first  calculated  by  the  formula  p  =  ——-,  and  this  pressure  is  deducted  from 

the  ventilating  pressure  of  the  free  or  open  split,  which  gives  the  pressure 
due  to  the  regulator.  This  is  then  reduced  to  inches  of  water  gauge,  and 

substituted  for  i  in  the  formula  A  —  '-  -  .    The  value  of  A  thus  obtained  is 

y» 

the  area  (square  feet)  of  the  opening  in  the  regulator. 

EXAMPLE.—  750,000  cu.  ft.  of  air  is  passing  per  min.  in  a  certain  mine,  in 
two  equal  splits,  under  a  pressure  equal  to  2  in.  of  water  gauge,  and  it  is 
required  to  reduce  the  quantity  of  air  passing  in  one  of  these  splits,  by  a  box 
regulator  placed  at  the  end  of  the  split,  so  as  to  pass  but  15,000  cu.  ft.  per 
min.  in  this  split.  Find  the  area  of  the  opening  in  the  regulator,  assuming 
that  the  ventilating  power  is  decreased  to  maintain  the  pressure  constant 
at  the  mouth  of  the  splits  after  placing  the  regulator.  The  size  and  length 
of  each  split  is  6  ft.  X  10  ft.  and  10,000  ft.  long. 

The  natural  pressure  for  the  split  in  which  the  regulator  is  placed  will  be 

ksq*      .0000000217X2(6  +  10)10,000  X  15,0002     f 
P  =  -£-=-  (6X10)3  -  -  7'233  lb-  Per  "I-  ^ 

7  2*^*^ 
Then,  -^ir^1-4  in>  of  water  gauge  (nearly),  due  to  friction  of  the  air 

" 
current  in  this  split.     And,  2  —  1.4  =  .6  in.  water  gauge  due  to  regulator. 

.00040      .0004X15,000     . 
Finally,  A  =  —   ~  =  —  -  —•  —  -  =  7.746  sq.  ft.,  area  of  opening. 

V-6  V.Q 

Size  of  Opening  for  a  Door  Regulator.  —  The  sectional  area  at  the  regulator 
is  divided  proportionately  to  the  work  to  be  performed  in  the  respective  splits 
according  to  the  proportion  A  i  :  A  2  :  :  u\  :  uz.  Or  since  Ai-\-Az  =  a,  we  have 

Ai  :  a  :  :  u\  :  u\-\-ui,  and  Ai=*  —  -  —  Xa.    This  furnishes  a  method  of  pro- 

UI+U2 

portionate  splitting  in  which  each  split  is  ventilated  under  its  own  natura1 
pressure.  The  same  result  would  be  obtained  by  the  placing  of  the  box 
regulator  at  the  intake  of  any  split,  thereby  regulating  the  amount  of  air 
passing  into  that  split,  but  the  door  regulator  presents  less  resistance  to  the 
flow  of  the  air  current.  The  practical  difference  between  these  two  forms 
of  regulators  is  that  in  the  use  of  the  box  regulator  each  split  is  ventilated 
under  a  pressure  equal  to  the  natural  pressure  of  the  open  or  free  split, 
which  very  largely  increases  the  horsepower  required  for  ventilation  of 
the  mine;  while  in  the  use  of  the  door  regulator  each  split  is  ventilated  under 
its  own  natural  pressure,  and  the  proportionate  division  of  the  air  is  accom- 
plished without  any  increase  of  horsepower.  This  is  more  clearly  ex- 
plained in  the  following  two  paragraphs,  and  the  table  showing  the  com- 
parative horsepowers  of  the  two  methods. 

Calculation  of  Horsepower  for  Box  Regulators.  —  By  the  use  of  the  box 
regulator,  the  pressure  in  all  the  splits  is  made  equal  to  the  greatest  natural 
pressure  in  any  one.  This  split  is  made  the  open  or  free  split,  and  its  natural 
pressure  becomes  the  pressure  for  all  the  splits,  or  the  mine  pressure.  This 
mine  pressure,  multiplied  by  the  total  quantity  of  air  in  circulation  (the  sum 
of  the  quantities  passing  in  the  several  splits),  and  divided  by  33,000,  gives 
the  horsepower  upon  the  air,  or  the  horsepower  of  the  circulation.  Thus, 
in  the  first  example  given  on  page  920,  in  which  for  split  B  the  pressure 
£  =  84.63  lb.  per  sq.  ft.  and  the  total  quantity  of  air  passing  per  minute 
is  12,000  cu.  ft.,  we  have 


Calculation  of  Horsepower  for  Door  Regulators.  —  In  the  use  of  the  door 
regulator,  each  split  is  ventilated  under  its  own  natural  pressure,  and, 
hence,  in  the  calculation  of  the  horsepower  of  such  a  circulation,  the  power 
of  each  split  must  be  calculated  separately,  and  the  sum  of  these  several 


922 


VENTILATION  OF  MINES 


powers  will  be  the  entire  power  of  the  circulation.  For  the  purpose  of 
parison,  we  tabulate  below  the  results  obtained  in  the  application  of 
two  methods  of  dividing  the  air  in  the  above  example 


com- 
these 


Splits 

Natural 
Division 

Required 
Division 

Horsepower 

Door 
Regulator 

Box 
Regulator 

Split  A  ,  6  ft.  X  9  ft.,    8,000  ft.  long  . 
Split  B,  5  ft.  X  8  ft.,    6,000  ft.  long  . 
Split  C,  9ft.X9ft.,    8,000  ft.  long. 
Split  D,  6  ft.  X  8  ft.,  10,000  ft.  long  . 

Totals.  .  . 

28,277 
22,360 
47,423 
21,940 

40,000 
40,000 
10,000 
30,000 

64  .  145 
102.582 
.356 
44.955 

102.582 
102  .  582 
25.645 
76  .  936 

120.000 

120,000 

212.038 

307.745 

SPLITTING  FORMULAS 

The  following  table  of  formulas  will  serve  to  illustrate  the  methods  of 
calculation  in  splitting.     The  example  assumes  the  same  airway  as  that  given 
on  page  912  and  used  to  illustrate  the  table  of  formulas,  pages  913,  914  and 
915  but  the  air  current  is  divided,  as  specified  in  the  table: 
NATURAL  DIVISION 

Primary  Splits.— Split  (1)  =4  ft.XS  ft.,  800  ft.  long.     Split  (2)  =4  ft.XS 
ft.,  1,200  ft.  long. 


To  Find: 


Formula 


Specimen  Calculation 


Potential  for 
pressure. 

35 
41 

P+  etc.). 

(1) 

on  A/                      20                             lOfiO 

U    \.0000000217X  14,400     3>U51 

"f}\l                 20 

~°  \.0000000217X  21,600       ' 
5,060  +  4,131=9,191. 

Natural  divi- 
sion. 

g==^XO. 

(1) 
(2) 

|^|~X  10,000  =  5,505  cu.  ft. 

Or  the  natural  division  may  be  calculated  from  the  pressure  at  the  mouth 
of  the  several  splits  by  using  Formula  (23) ;  thus, 


23 

q  =  XP\/P. 

(1)     5,060  Vl-  1838  =  5,505  cu.  ft. 
(2)      4.131V1-  1838  =  4,495  cu.  ft. 
See  formula  (42). 

t,          Q* 

10,000*    11S3Slb 

(2Xp)2 

9.19P  -1'18' 

u          Q3 

10,0003 

(SXp)2 

9.1912      11>8ti8  units. 

a 

44 

Q=2XPVP. 

9,  191  Vl-1838  =  10,000  cu.  ft. 

45 

Q--<^(2X,)*u. 

-Y/9,1912X  11,838  =  10,  000  cu.  ft. 

Increase  of 
quantity    due 

n     2Xpv 

Q  1  Q1 

V  1O  000      °S  7°°  cu    ft 

to  splitting. 
(Pressure  con- 
stant.) 

4b 

C?=  v  —  -Xg<>. 

Xp-O 

cJ.zUU 

Increase  in 
quantity    due 
to  splitting. 
(Power      con- 
stant.) 

47 

°-'X(GF? 

™  \,Ap_o/ 

10,000  ^/(|^)2  -  20,205  cu.  ft. 

s 


VENTILATION  OF  MINES 


923 


sS 


^ 


2£ 

i^i 


>' 


oo 


-?- 


-^ 


o 


ra 

l-i 


924 


VENTILATION  OF  MINES 


Secondary  Splits.— (1)  4  ft.X5  ft.,  800  ft.  long.  (2)  4  ft.X5  ft.,  500  ft. 
long.  (3)  4  ft.  X  5  ft.,  400  ft.  long.  (4)  4  ft.  X  5  ft.,  300  ft.  long. 

The  calculation  is  often  shortened,  when  many  splits  are  concerned,  by 

using  the  relative  potential,  omitting  the  factor  k;  but  the  final  result  must 

then  be  multiplied  by  k  to  obtain  the  pressure  or  power;  or,  these  factors 

must  be  divided  by  k,  when  finding  the  quantity,  as  m  formulas  (49)  to  (51). 

PROPORTIONATE  DIVISION 

Primary  Splits  (only).— (1)  4  ft.XS  ft.,  800  ft.  long  =  3, 500  cu.  ft.  (2) 
4  ft.  X  5  ft.,  1,200  ft.  long  =  6,500  cu.  ft. 


To  Find: 

o 
fc 

Formula 

Specimen  Calculation 

Pressure  due  to 
friction. 

13 

'-£• 

(1) 
(2) 

3'5°°2      17315  Ib 

5,0602     '  7' 
6'5°°2     «17571b 

4.13P     '             lb> 

To  accomplish  this  division  of  air,  the  pressure  in  split  (1)  must  be  in- 
creased by  means  of  a  regulator  to  make  it  equal  to  the  pressure  in  the 
free  or  open  split  (2),  and,  hence,  the  pressure  due  to  the  regulator  is  equal 
to  the  difference  between  the  natural  pressures  in  these  splits. 


Pressure  due  to 
the    regulator 
in  split  (1). 

53 

,•*„-„. 

2.4757  -  .47845  =  1  .99725  Ib. 

Area      of      the 
opening  in 
regulator. 

37 

00040 

.0004  X  3,500  _22505q   ft 

3  vr' 

A  /1  .99725 

\     5.2 

Secondary  Splits.—  (1)  4  ft.  X  5  ft.,  800  ft.  -  3,500  cu.  ft.     (2)  4  ft.  X  5  ft.  , 
500  ft.  -  6,500  cu.  ft.     (3)  4  ft.  X  5  ft.,  400  ft.  -4,000  cu.  ft.     (4)   4ft.X5ft., 
300  ft.  -  2,500  cu.  ft. 
NOTE.  —  When  using  the  relative  potential,  multiply  the  result  by  k,  to 
obtain  the  pressure,  or  the  power. 

Pressure  due  to 
friction.    Free 
split  —  second- 
pressure. 

13 

^ 

("H    0000000217^--              ^          47S4R  1h 

(-)  .0000000-17^  942g  j    =>  1.0314  Ib. 
/  4,000  \  2 

\1.0541/ 
(  \)    OOOOOOO°17^  ^•bvv  \          OQ1  ^fi  1K 

Since  the  natural  pressure  in  (3)  is  greater  than  that  in  (4),  (3)  is  the  free 
split,  and  its  natural  pressure  is  the  pressure  for  the  secondary  splits.  The 
pressure  for  the  primary  splits  is  then  found  by  first  adding  the  pressures  in 
(2)  and  (3),  and  if  their  sum  is  greater  than  the  natural  pressure  for  (1),  it 
becomes  the  pressure  for  the  primary  splits,  or  the  mine  pressure.  If  the 
natural  pressure  for  (1)  is  the  greater,  this  is  made  the  free  split,  and  its 
natural  pressure  becomes  the  primary  or  mine  pressure.  In  this  case,  the 
secondary  pressure  must  be  increased  by  placing  a  regulator  in  split  (3). 


Prim  a  r  y  o  r 
mine  pressure. 

pi  +  ps 

1.0314  +  .31248  =  1.34388. 

Pressure  due  to 
the  regulators. 

0/+V/-,, 

(4) 
(1) 

.31248  -  .091546  =  .220934  Ib. 
(1.0314  +  .31248)  -.47848 
=  .86540  Ib. 

Areas  of  open- 
ings in  the 
regulators. 

37 

(4) 
(1) 

.0004X2,500     10511._   ft 

-4/.220934 

\     5.2 
.0004  X  3,500  ^34300..,  ft 

^^8654 

VENTILATION  OF  MINES  925 

METHODS   AND  APPLIANCES  IN   THE   VENTILATION 
OF  MINES 

Ascensional  Ventilation.— Every  mine,  as  far  as  practicable,  should  be 
ventilated  upon  the  plan  known  as  ascensional  ventilation.  This  term  refers 
particularly  to  the  ventilation  of  inclined,  seams.  The  air  should  enter  the 
mine  at  its  lowest  point,  as  nearly  as  possible,  and  from  thence  be  conducted 
through  the  mine  to  the  higher  points,  and  there  escape  by  a  separate 
shaft,  if  such  an  arrangement  is  practicable.  Where  the  seam  is  dipping 
considerably  and  is  mined  through  a  vertical  shaft,  the  upcast  shaft  should 
be  located  as  far  to  the  rise  of  the  downcast  shaft  as  possible.  The  intake  air 
is  then  first  conducted  to  the  lowest  point  of  the  dip  workings,  which  it 
traverses  upon  its  way  to  the  higher  workings.  In  the  case  of  aslope 
working  where  a  pair  of  entries  is  driven  to  the  dip,  one  being  used  as  the 
intake  and  the  other  the  return,  there  being  cross-entries  or  levels  driven  at 
regular  intervals  along  the  slope,  the  air  should  be  conducted'at  once  to  the 
inside  workings,  from  which  point  it  returns,  ventilating  each  pair  of  cross- 
entries  from  the  inside,  outwards.  Where  the  development  of  the  cross- 
entries  or  levels  is  considerable,  their  circulation  is  considered  separately, 
and  a  fresh  air  split  is  made  in  the  intake  at  each  pair  of  levels.  In  all 
ventilation,  the  main  point  to  be  observed  is  to  conduct  the  air  current  first 
to  the  inside  workings,  from  whence  it  is  distributed  along  the  working  face 
as  it  returns  toward  the  upcast. 

General  Arrangement  of  Mine  Plan. — Every  mine  should  be  planned  with 
respect  to  three  main  requirements,  viz.:  (a)  haulage;  (b)  drainage;  (c) 
ventilation.  These  requirements  are  so  closely  connected  with  one  another 
that  the  consideration  of  one  of  them  necessitates  a  reference  to  all.  The 
mine  should  be  planned  so  that  the  coal  and  the  water  will  gravitate  towards 
the  opening,  as  far  as  possible.  There  are  many  reasons,  in  the  consideration 
of  non-gaseous  mines,  why  the  haulage  should  be  effected  upon  the  return 
airways.  The  haulage  road  is  always  a  dusty  road,  caused  by  the  traveling 
of  men  and  mules,  as  well  as  by  the  loss  of  coal  in  transit,  which  becomes 
reduced  to  fine  slack  and  powder.  If  the  haulage  is  accomplished  upon  the 
intake  entry  or  air-course,  this  dust  is  carried  continually  into  the  mine  and 
working  places,  which  should  be  avoided  whenever  possible.  When  the 
loaded  cars  move  in  the  same  direction  as  the  return  air,  the  ventilation  of 
the  mine  is  not  as  seriously  impeded.  It  is  often  the  case  that  fewer  doors 
are  required  upon  the  return  airway  than  upon  the  intake,  which  is  a  feature 
favorable  to  haulage  roads.  Again,  in  this  arrangement,  the  hoisting  shaft 
is  made  the  upcast  shaft,  which  prevents  the  formation  of  ice,  and  conse- 
quent delay  in  hoisting  in  the  winter  season.  The  arrangement,  however, 
presupposes  the  use  of  the  force  fan  or  blower,  since  if  a  furnace  or  exhaust 
fan  is  employed,  a  door,  or  probably  double  doors,  would  have  to  be  placed 
upon  the  main  haulage  road  at  the  shaft  bottom,  which  would  be  a  great 
hindrance. 

In  the  ventilation  of  gaseous  mines,  however,  other  and  more  important 
considerations  demand  attention.  The  gaseous  character  of  the  return 
current  prevents  making  the  return  airway  a  haulageway.  In  such  mines, 
the  haulage  should  always  be  accomplished  upon  the  intake  air,  as  any  other 
system  would  often  result  in  serious  consequences.  In  such  gaseous  mines, 
men  and  animals  must  be  kept  off  the  return  airways  as  far  as  this  is 
possible. 

As  far  as  practicable,  ventilation  should  be  accomplished  in  sections 
or  districts,  each  district  having  its  own  split  of  air  from  the  main  intake,  and 
its  own  return  connecting  with  the  main  return  of  the  mine.  Reference 
has  been  made  to  this  under  Distribution  of  the  Air  in  Mine  Ventilation. 
This  splitting  of  the  air  current  is  accomplished  preferably  by  means  of  an 
air  bridge,  either  an  under  crossing  or  an  over  crossing.  There  are,  in 
general,  three  systems  of  ventilation,  with  respect  to  the  ventilating  motor 
employed:  (a)  natural  ventilation:  (b)  furnace  ventilation;  (c)  mechanical 
ventilation. 

Natural  ventilation  means  such  ventilation  as  is  secured  by  natural  means, 
or  without  the  intervention  of  artificial  appliances,  such  as  the  furnace, 
or  any  mechanical  appliances  by  which  the  circulation  of  air  is  maintained. 
In  natural  ventilation,  the  ventilating  motor  or  air  motor  is  an  air  column 
that  exists  in  the  downcast  shaft  by  virtue  of  the  greater  weight  of  the 
downcast  air.  This  air  column  acts  to  force  the  air  through  the  airways 


926  VENTILATION  OF  MINES 

of  the  mine.  An  air  column  always  exists  where  the  intake  and  return 
currents  of  air  pass  through  a  certain  vertical  height,  and  have  different 
temperatures.  This  is  the  case  whether  the  opening  is  a  shaft  or  a  slope; 
since,  in  either  case,  there  is  a  vertical  height,  which  in  part  determines 
the  height  of  air  column.  The  other  factor  determining  the  height  of  air 
column  is  the  difference  of  temperature  between  the  intake  and  return. 
The  calculation  of  the  ventilating  pressure  in  natural  ventilation  is  identical 
with  that  of  furnace  ventilation,  which  is  described  later. 

Ventilation  of  Rise  and  Dip  Workings. — We  have  referred  to  the  air  column 
existing  either  in  vertical  shafts  or  slopes  as  the  motive  column  or  venti- 
lating motor.  Such  an  air  column  will  be  readily  seen  to  exist  in  any  rise 
or  dip  workings  within  the  mine,  and  may  assist  or  retard  the  circulation 
of  the  air  current  through  the  mine.  It  is  this  air  column  that  renders  the 
ventilation  of  dip  workings  easy,  and  that  of  rise  workings  correspondingly 
difficult,  depending,  however,  on  the  relative  temperature  of  the  intake  and 
return  currents;  the  latter  usually  is  the  warmer  of  the  two,  which  gives 
rise  to  the  air  column.  The  influence  of  such  air  columns  must  always  be 
taken  into  account  in  the  calculation  of  any  ventilation.  This  is  often 
neglected. 

The  influence  of  air  columns  in  rise  or  dip  workings,  within  the  mine, 
becomes  very  manifest  where,  from  any  reason,  the  main  intake  current  is 
increased  or  decreased.  For  example,  a  mine  is  ventilated  in  two  splits,  a 
rise  and  a  dip  split;  a  current  of  50,000  cu.  ft.  of  air  is  passing  in  the  main 
airway,  30,000  cu.  ft.  passing  into  the  dip  workings,  and  20,000  into  the  rise 
workings.  A  fall  of  roof  in  the  main  intake  airway,  or  other  cause,  reduces 
the  main  current  from  50,000  to  35,000  cu.  ft.  _  Instead,  now,  of  21,000  cu.  ft. 
going  to  the  dip  workings  and  14,000  to  the  rise  workings,  we  find  that  this 
proportion  no  longer  exists,  but  that  the  dip  workings  are  taking  more  than 
their  proportion  of  air,  and  the  rise  workings  less.  Thus,  the  circulation 
being  decreased  to  35,000  cu.  ft.,  the  dip  workings  will  probably  take  25,000 
cu.  ft.,  and  the  rise  workings 1 10,000  cu.  ft.  On  the  other  hand,  had  the 
intake  current  been  increased  instead  of  decreased,  the  rise  workings  would 
then  take  more  than  their  proportion,  while  the  dip  workings  would  take 
less.  The  reason  for  this  distribution  is  evident;  suppose,  for  example,  the 
intake  or  mine  pressure  is  3  in.  of  water  gauge,  and  in  the  dip  workings 
there  is  §  in.  of  water  gauge  acting  to  assist  ventilation,  while  a  like  water 
gauge  of  |  in.  in  the  rise  workings  acts  to  retard  ventilation.  The  effective 
water  gauge  in  the  dip  workings  is  therefore  3J  in.,  while  the  effective 
water  gauge  in  the  rise  workings  is  2J  in.,  or  they  are  to  each  other  as  7  :  5. 
If,  now,  the  mine  pressure  is  decreased  to,  say,  2  in.,  the  effective  rise  and 
dip  pressure  will  be,  respectively,  2$  in.  and  l£  in.,  or  as  5  :  3.  _  We  observe, 
before  the  decrease,  the  dip  pressure  was  J,  or  1.4,  times  the  rise-  pressure, 
while  after  the  decrease  took  place  in  the  mine  pressure,  the  dip  pressure 
became  £,  or  1.66,  times  the  rise  pressure.  The  relative  quantities  passing  in 
the  dip  split  before  and  after  the  decrease  took  place,  as  compared  with  the 
quantities  passing  in  the  rise  split,  will  be  as  the  \/l-4  :  \/1.66,  showing  an 
increase  of  proportion.  Now,  instead  of  a  decrease  taking  place  in  the  mine 
pressure,  let  us  suppose  it  is  increased,  say,  from  3  in.  to  4  in.  The  effective 
pressures  in  the  dip  and  rise  workings  will  then  be,  respectively,  4£  in. 
and  3 1  in.,  or  they  will  be  to  each  other  as  9  :  7,  instead  of  7  :  5.  Here  we 
observe  that  the  dip  pressure  is  If,  or  1.15,  times  the  rise  pressure,  instead 
of  1.4.  The  relative  quantities,  therefore,  passing  in  the  dip  split,  before 
and  after  the  increase  of  the  mine  pressure,  as  compared  with  the  quantities 
passing  in  the  rise  split,  will  be  in  the  ratio  of  -\/\A  :  \/i.l5f  showing  a 
decrease  of  proportion.  We  observe  that  any  alteration  of  the  mine  pres- 
sure by  which  it  is  increased  or  decreased  does  not  affect  the  inside  dip  or 
rise  columns,  and  hence  the  disproportion  obtains.  In  case  of  a  decrease  of 
the  mine  pressure,  the  dip  workings  receive  more  than  their  proportion 
of  air,  and  in  case  of  an  increase  of  the  mine  pressure,  they  receive  less 
than  their  proportion  of  air. 

Influence  of  Seasons. — In  any  ventilation,  air  columns  are  always  estab- 
lished in  slopes  and  shafts,  owing  to  the  relative  temperatures  of  the  outside 
and  inside  air.  The  temperature  of  the  upcast,  or  return  column,  may  always 
be  assumed  to  be  the  same  as  that  of  the  inside  air.  The  temperature  of  the 
downcast,  or  intake  column,  generally  approximates  the  temperature  of  the 
outside  air,  although,  in  deep  shafts  or  long  slopes,  this  temperature  may  be 
changed  considerably  before  the  bottom  of  the  shaft  or  slope  is  reached,  and 


VENTILATION  OF  MINES  927 

C9nsequently  the  average  temperature  of  the  downcast,  or  intake,  is  often 
different  from  that  of  the  outside  air.  The  difference  of  temperatures  will 
also  vary  with  the  seasons  of  the  year.  In  winter  the  outside  temperature  is 
below  that  of  the  mine,  and  the  circulation  in  shafts  and  slopes  is  assisted 
since  the  return  columns  are  warmer  and  lighter  than  the  intake  columns 
for  the  same  circulation.  In  the  summer  season,  however,  the  reverse  of 
this  is  the  case.  The  course  of  the  air  current  will  thus  often  be  changed 
When  the  outside  temperature  approaches  the  average  temperature  of  the 
mine,  there  will  be  no  ventilation  at  all  in  such  mines,  except  such  as  is 
caused  by  accidental  wind  pressure. 

In  furnace  ventilation  the  temperature  of  the  upcast  column  is  increased 
above  that  of  the  downcast  column  by  means  of  a  furnace.  The  chief 
points  to  be  considered  in  furnace  ventilation  are  in  regard  to  the  arrange- 
ment and  size  of  the  furnace.  Furnace  ventilation  should  not  be  applied  to 
gaseous  seams,  and  in  some  cases  is  prohibited  by  law.  It  is,  however,  in 
use  in  may  mines  liberating  gas.  In  su9h  cases  the  furnace  fire  is  fed  by  a 
current  of  air  taken  directly  from  the  air-course,  sufficient  to  maintain  the 
fire,  and  the  return  current  from  the  mine  is  conducted  by  means  of  a  dumb 
drift,  or  an  inclined  passageway,  into  the  shaft,  at  a  point  from  50  to  100  ft. 
above  the  seam.  At  this  point,  the  heat  of  the  furnace  gases  is  not  sufficient 
for  the  ignition  of  the  mine  gases.  The  presence  of  carbonic-acid  gas  in  the 
furnace  gases  also  renders  the  mine  gases  inexplosive.  In  other  cases 
where  the  dumb  drift  is  not  used,  a  sufficient  amount  of  fresh  air  is  allowed 
to  pass  into  the  return  current  to  insure  its  dilution  below  the  explosive 
point  before  it  reaches  the  furnace. 

Construction  of  a  Mine  Furnace.—  In  the  construction  of  a  mine  furnace,  a 
sufficient  area  of  passage  must  be  maintained  over  the  fire  and  around  the 
furnace  to  allow  the  passage  of  the  air  current  circulating  in  the  mine.  The 
velocity  of  the  current  at  _  the  furnace  should  be  estimated  not  to  exceed 
20  ft.  per  sec.  and  the  entire  area  of  passage  calculated  from  this  velocity. 
Thus,  for  a  current  of  50,000  cu.  ft.  of  air  per  min.,  the  area  of  passage 
through  and  around  the  furnace  should  be  not  less  than 


This  is  a  safe  method  of  calculation,  notwithstanding  the  fact  that  the 
velocity  of  the  air  is  often  much  more  than  20  ft.  per  sec.,  yet  the  volume 
of  the  air  is  largely  increased  owing  to  the  increase  of  temperature. 

The  length  of  the  furnace  bars  is  limited  to  the  distance  in  which  good 
firing  can  be  accomplished,  and  should  not  exceed  5  ft.  The  width  of  the 
grate  will  therefore  determine  the  grate  area.  The  grate  area  must,  in  every 
case,  be  sufficient  for  the  heating  of  the  air  of  the  current  to  a  temperature 
such  as  to  maintain  the  average  temperature  of  the  furnace  shaft  high  enough 
to  produce  the  required  air  column,  or  ventilating  pressure,  in  the  mine. 
The  area  A  of  the  grate  of  the  furnace  is  best  determined  by  the  formula 

A  =  ••       XH.  P.,  in  which  A  •=  grate  area  in  square  feet;  H.  P.  =  horse- 

power of  the  circulation;  and  D  =  depth  of  shaft  in  feet.  The  horsepower 
for  any  proposed  circulation  may  always  be  determined  by  dividing  the 
quantity  9f  air  (cubic  feet  per  minute)  by  the  minex*potential  Xv,  and  cubing 
and  dividing  the  result  by  33,000;  thus 


The  furnace  should  have  proper  cooling  spaces  above  and  at  each  side; 
upon  one  side,  at  least,  should  be  a  passageway  or  manway.  The  furnace 
should  be  located  at  a  point  from  10  to  15  yd.  back  from  the  foot  of  the  shaft, 
at  a  place  in  the  airway  where  the  roof  is  strong.  This  is  well  secured 
by  railroad  iron  immediately  over  the  furnace.  A  good  foundation  is 
obtained  in  the  floor,  and  the  walls  of  the  furnace  carried  up  above  the 
level  of  _the  grate  bars,  when  the  furnace  arch  is  sprung.  If  possible,  a 
full  semicircle  should  be  used  in  preference  to  a  flat  arch.  The  sides  and 
arch  of  the  furnace  should  be  carried  backwards  to  the  shaft;  this  is  neces- 
sary in  order  to  prevent  ignition  of  the  coal.  The  walls  and  arch  are  con- 
structed of  firebrick  a  sufficient  distance  from  the  furnace,  and  afterwards 
of  a  good  quality  of  hard  brick;  the  shaft  is  also  lined  with  brick  or  protected 
by  sheet  iron  a  sufficient  height  to  prevent  the  ignition  of  the  curbing. 

Air  Columns  in  Furnace  Ventilation.  —  As  previously  stated,  natural  ven- 
tilation and  furnace  ventilation  are  identical,  in  so  far  as  in  each  the  venti- 


928  VENTILATION  OF  MINES 

lating  motor  is  an  air  column.  This  air  column  is  an  imaginary  column  of 
air  whose  weight  is  equal  to  the  difference  between  the  weights  of  the  upcast 
and  downcast  columns.  The  upcast  and  downcast  columns  in  furnace 
ventilation  are  sometimes  referred  to  as  the  primary  and  secondary  columns, 
respectively.  The  primary  or  furnace  column  is,  in  nearly  every  case,  a 
vertical  column,  and  consists  of  a  single  air  column  whose  average  tempera- 
ture is  easily  approximated.  According  to  the  manner  of  opening  the 
mine,  whether  by  shaft,  slope,  or  drift,  the  secondary  column  may  be  a 
vertical  column  in  the  shaft,  an  inclined  column  in  the  slope,  or  an  outside 
air  column  in  case  of  a  drift  opening.  Again,  it  is  to  be  observed  that  in 
case  of  a  slope  opening  where  the  top  of  the  furnace  shaft  is  much  higher 
than  the  mouth  of  the  slope,  and  the  dip  of  the  slope  is  considerable,  the 
secondary  column  consists  of  two  columns  of  different  temperatures,  an 
outside  air  column  and  the  slope  column.  These  two  parts  of  the  secondary 
column  must  be  calculated  separately,  and  their  sum  taken  for  the  weight  of 
the  secondary  column.  The  level  of  the  top  of  the  furnace  shaft  determines 
the  top  of  both  the  primary  and  secondary  columns,  whether  these  columns 
are  in  the  outer  air  or  in  the  mine.  The  weight  of  the  upcast  or  primary 
column  is  largely  affected  by  its  gaseous  condition.  For  example,  if  the 
return  current  from  the  mine  is  laden  with  blackdamp  COz,  its  weight  will 
be  much  increased,  since  this  gas  is  practically  1$  times  as  heavy  as  air, 
while,  if  laden  with  marsh  gas,  or  firedamp  mixture,  its  weight  will  be  con- 
siderably reduced.  These  causes  decrease  and  increase,  respectively,  the 
ventilating  pressure  in  the  mine. 

Inclined  Air  Columns.  —  In  a  slope  opening,  the  air  column  is  inclined;  it 
is  none  the  less,  however,  an  air  column,  and  must  be  calculated  in  the  same 
manner  as  a  vertical  column  whose  vertical  height  corresponds  to  the  amount 
of  dip  of  the  slope.    Fig.  9  shows  a  vertical  shaft  and 
a  slope,  the  air  column  in  each  of  these  being  the 
same  for  the  same  temperature.     The  air  column  in 
all  dips  and  rises  must  be  estimated  im  like  manner, 
by  ascertaining  the  vertical  height  of  the  dip. 

Calculation  of  Ventilating  Pressure  in  Furnace 
Ventilation.  —  The  ventilating  pressure  in  the  mine 
FIG.  9  airways,    in   natural   or   in   furnace    ventilation,  is 

caused    by    the    difference    of   the   weights   of  the 

primary  and  secondary  columns.  Air  always  moves  from  a  point  of  higher 
pressure  towards  a  point  of  lower  pressure,  and  this  movement  of  the  air  is 
caused  by  the  difference  between  these  two  pressures.  In  this  calculation 
each  column  is  supposed  to  have  an  area  of  base  of  1  sq.  ft.  Hence,  if  we 
multiply  the  weight  of  1  cu.  ft.  of  air  at  a  given  barometric  pressure,  and 
having  a  temperature  equal  to  the  average  temperature  of  the  column,  by 
the  vertical  height  D  of  the  column,  we  obtain  not  only  the  weight  of  the 
column  but  the  pressure  at  its  base  due  to  its  weight.  Now,  since  the  venti- 
lating pressure  per  square  foot  in  the  airway  is  equal  to  the  difference  of  the 
weights  of  the  primary  and  secondary  columns,  we  write 
/1.3253XB 


459+?  459  +  r 

EXAMPLE.  —  Find  the  ventilating  pressure  in  a  mine  ventilated  by  a 
furnace,  the  temperatures  of  the  upcast  and  downcast  columns  being, 
respectively,  350°F.  and  40°F.,  the  depth  of  the  upcast  and  downcast  shafts 
being  each  600  ft.,  and  the  barometer  30  in. 

Substituting  the  given  values  in  the  above  equation,  we  have 

„-  1.3253X30X600(igJp55-  ^350)  -  18-  32  Ib.  per  sq.  ft. 

Calculation  of  Motive  Column  or  Air  Column.  —  It  is  often  convenient  to 
express  the  ventilating  pressure  P  (pounds  per  square  foot)  in  terms  of  air 
column  or  motive  column  M,  in  feet.  The  height  of  the  air  column  M  is 

equal  to  the  pressure  p  divided  by  the  weight  to  of  1  cu.  ft.  of  air,  or  M  —  —  • 

The  expression  for  motive  column  may  be  written  either  in  terms  of  the 
upcast  air  or  of  the  downcast  air,  the  former  giving  a  higher  motive  column 
than  the  latter  for  the  same  pressure,  since  the  upcast  air  is  lighter  than 
that  of  the  downcast.  As  the  surplus  weight  of  the  downcast  column  of  air 
produces  the  ventilating  pressure,  it  is  preferable  to  write  the  air  column  in 
terms  of  the  d9wncast  air,  or,  in  other  words,  to  consider  the  air  column  as 
being  located  in  the  downcast  shaft,  and  pressing  the  air  downwards  and 


VENTILATION  OF  MINES  929 

through  the  airways  of  the  mine.     If  we  divide  the  expression  previously 
given  for  the  ventilating  pressure  by  the  weight  of  1  cu.  ft.  of  downcast  air 

(     459-Uj — )'   we   obtain  for  the   motive   column,  after  simplifying,  M  = 

\459  + TV  *  ^'  which  is  the  exPress'on  for  motive  column  in  terms  of  the 
downcast  air. 

If,  on  the  other  hand,  we  divide  the  expression  for  the  ventilating  pressure 
by   the   weight   of    1  cu.  ft.   of  upcast  air        '3>   we  obtain  M  = 


(459+l)  * Dt  whic^  is  the  exPression  for  motive  column  in  terms  of  the 
upcast  air. 

Influence  of  Furnace  Stack.— To  increase  the  height  of  the  primary  or 
furnace  column,  a  stack  is  often  erected  over  the  mouth  of  the  furnace  shaft. 
The  effect  of  this  is  to  increase  the  ventilating  pressure  in  the  mine  in  pro- 
portion to  the  increased  height  of  the  primary  column,  and  to  increase  the 
quantity  of  air  passing  in  the  mine  in  proportion  to  the  square  root  of  this 
height.  Thus,  the  square  root  of  the  ratio  of  the  heights  of  the  primary 
column,  before  and  after  the  stack  is  erected,  is  equal  to  the  ratio  of  the 
quantities  of  air  passing  before  and  after  the  erection  of  the  stack.  Or, 
calling  these  quantities  gi  and  52,  and  the  height  of  stack  d,  we  have 

\lD  +  d=,  ^  or      =  \lD  +  d 

MECHANICAL  VENTILATORS 

A  large  number  of  mechanical  ventilators  have  been  invented  and  applied, 
with  more  or  less  success,  to  the  ventilation  of  mines.  The  earliest  type  of 
ventilator  was  the  wind  cowl,  by  which  the  pressure  of  the  wind  at  the  sur- 
face was  brought  to  bear  effectively  upon  the  mine  airways  by  the  action  of 
a  cowl  whose  mouth  could  be  turned  toward  the  wind;  this  was  naturally 
very  unreliable.  The  waterfall  was  also  extensively  applied  at  one  time,  but 
its  application  could  only  be  made  where  there  was  \a  reliable  source  of 
water  supply,  and  where  the  drainage  of  the  mine  could  be  effected  through 
a  tunnel,  or  where'  the  mine  opening  could  be  placed  in  connection  with 
such  a  waterfall  outside  of  the  mine.  Where  these  conditions  are  obtained, 
as  is  the  case  in  some  mountainous  districts,  the  waterfall  is  still  in  use,  as 
it  is  an  effective  means  of  ventilation,  and  is  economical.  Its  application, 
however,  must  be  limited  to  the  ventilation  of  small  mines.  The  steam  jet 
is  another  mechanical  device  for  producing  an  air  current  in  the  mine.  The 
steam  is  allowed  to  issue  from  a  jet  at  the  bottom  of  an  upcast  shaft,  and, 
by  the  force  of  its  discharge,  causes  an  upward  current  in  the  shaft.  Its  use, 
however,  is  very  limited,  and  is  practically  restricted  to  the  ventilation  of 
shafts  while  sinking.  In  this  connection  it  may  be  mentioned,  however, 
that  the  discharged  steam  from  the  mine  pumps,  where  practicable,  may  be 
conducted  into  the  upcast  shaft;  or  the  discharge  pipe  from  the  pumps  may 
be  carried  up  the  upcast  shaft,  its  heat  increasing  the  temperature  of  the 
shaft,  and  thereby  increasing  the  motive  column  and  the  ventilation. 

Fan  Ventilation. — Mechanical  motors  of  this  type  present  two  distinct 
modes  of  action  in  producing  an  air  current:  (a)  by  propulsion  of  the  air; 
and  (6)  by  establishing  a  pressure  due  to  the  centrifugal  force  incident  to 
the  revolution  of  the  fan.  Fans  have  been  constructed  to  act  wholly  on 
one  or  the  other  of  these  principles,  while  others  have  been  constructed  to 
act  on  both  of  these  principles  combined. 

Disk  Fans. — The  action  of  this  type  of  fan  resembles  that  of  a  windmill, 
except  that  in  the  latter  the  wind  drives  the  mill,  while  in  the  former  the 
fan  propels  the  air  or  produces  the  wind.  This  type  of  fan  consists  of  a 
number  of  vanes  radiating  from  a  central  shaft,  and  inclined  to  the  plane  of 
revolution.  The  fan  is  set  up  in  the  passageway  between  the  outer  air  and 
the  mine  airways.  Power  being  applied  to  the  shaft,  the  revolution  of  the 
vanes  propels  the  air,  and  produces  a  current  in  the  airways.  The  fan  may 
force  the  air  through,  or  exhaust  the  air  from,  the  airways,  according  to  the 
direction  of  its  revolution.  This  type  of  fan  is  most  efficient  under  light 
pressures.  It  has  found  an  extensive  application  in  mining  practice,  and  has 
a  large  number  of  devotees,  but  has  been  replaced  to  a  large  degree  in  the 
ventilation  of  extensive  mines.  This  type  of  fan  acts  wholly  by  propulsion. 


930  VENTILATION  OF  MINES 

Centrifugal  fans  include  all  fans  that  act  solely  on  the  centrifugal  principle, 
and  those  that  combine  the  centrifugal  and  propulsion  principles.  The 
action  of  the  fan,  whether  by  centrifugal  force  alone,  or  combined  with 
propulsion,  depends  on  the  form  of  the  fan  blades.  In  this  type  of  fan,  the 
blades  are  all  set  at  right  angles  to  the  plane  of  revolution,  and  not  inclined, 
as  in  the  disk  fan  just  described.  The  blades  may,  however,  be  either  radial 
blades,  sometimes  spoken  of  as  paddle  blades,  or  they  may  be  inclined  to  the 
radius  either  forward  in  the  direction  of  revolution,  or  backward.  When 
the  blades  are  radial,  the  action  of  the  fan  is  centrifugal  only.  The  inclina- 
tion of  the  blades  backward  from  the  direction  of  motion  gives  rise  to  an 
action  of  propulsion,  in  addition  to  the  centrifugal  action  of  the  fan.  The 
blades  in  this  position  may  be  either  straight  blades  in  an  inclined  position, 
as  in  the  original  Guibal  fan,  or  they  may  be  curved  backward  in  the  form 
of  a  spiral,  as  in  the  Schiele  and  Waddle  fans. 

Centrifugal  fans  may  be  (a)  exhaust  fans  or  (b)  force  fans  or  blowers.  In 
each,  the  action  of  the  fan  is  essentially  the  same;  i.e.,  to  create  a  difference 
of  pressure  between  its  intake  or  central  opening,  and  its  discharge  at  the 
circumference.  The  centrifugal  force  developed  by  the  revolution  of  the  air 
between  the  blades  of  the  fan  causes  the  air  within  the  fan  to  crowd  towards 
the  circumference;  as  a  result,  a  rarification  is  caused  at  the  center  and  a 
compression  at  the  circumference,  giving  rise  to  a  difference  of  pressure 
between  the  intake  and  the  discharge  of  the  fan. 

Exhaust  Fans. — If  the  intake  opening  of  the  fan  be  placed  in  connection 
with  the  mine  airways,  and  the  discharge  be  open  to  the  atmosphere,  the 
fan  will  act  to  create  rarefaction  in  the  fan  drift  leading  to  the  mine,  which 
will  cause  a  flow  of  air  through  the  mine  airways  and  into  and  through  the 
fan.  In  this  case,  the  fan^is  exhausting,  its  position  being  ahead  of  the 
current  that  it  produces  in  the  airway.  The  atmospheric  pressure  at 
the  intake  of  the  mine  forces  the  air  or  propels  the  current  toward  the 
depression  in  pressure  existing  in  the  fan  drift  caused  by  the  fan's  action. 

Force  Fans  and  Blowers. — If  the  discharge  opening  of  the  fan  be  placed  in 
connection  with  the  mine  airways,  a  compression  will  result  in  the  fan  drift 
owing  to  the  fan's  action,  and  the  air  will  flow  from  this  point  of  compression 
through  the  airways  of  the  mine,  and  be  discharged  into  the  upcast,  and 
thence  into  the  atmosphere.  The  ventilating  pressure  in  the  case  of  either 
the  exhaust  fan  or  the  force  fan  is  equal  to  the  difference  of  pressure  created 
by  the  fan's  action.  In  the  former  case,  when  the  fan  is  exhausting,  the 
absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure  less 
the  ventilating  pressure,  while  in  the  latter  case,  when  a  fan  is  forcing,  the 
absolute  pressure  in  the  fan  drift  is  equal  to  the  atmospheric  pressure  in- 
creased by  the  ventilating  pressure.  This  gives  rise  to  two  distinct  systems 
of  ventilation,  known  as  (a)  vacuum  system  and  (b)  plenum  system. 

Vacuum  System  of  Ventilation. — In  this  system,  the  ventilation  of  the 
mine  is  accomplished  by  creating  a  decrease  of  pressure  in  the  return  airway 
of  the  mine.  This  decrease  may  be  created  by  the  action  of  an  exhaust  fan, 
as  just  described,  or  by  the  action  of  a  furnace.  In  either  case,  the  absolute 
pressure  in  the  mine  is  below  that  of  the  atmosphere,  or,  we  may  say,  the 
mine  is  ventilated  under  a  pressure  below  the  atmospheric  pressure.  This 
system  has  many  points  of  advantage  over  the  plenum  system,  and  for  years 
was  considered  by  many  the  only  practicable  system  of  ventilation.  Its 
application,  however,  is  controlled  by  conditions  in  the  mine  with  respect  to 
the  gases  liberated,  the  arrangement  cf  the  haulage  system,  etc. 

Plenum  System  of  Ventilation. — In  this  sytem,  the  air  current  is  propelled 
through  the  mine  airways  by  means  of  the  compression  or  ventilating 
pressure  created  at  the  intake  opening  of  the  mine.  This  ventilating  pres- 
sure may  be  established  by  a  fan,  waterfall,  wind  cowl,  or  any  other  me- 
chanical means  at  hand.  In  this  system,  the  absolute  pressure  in  the  mine 
is  above  that  of  the  atmosphere;  or,  as  we  say,  the  mine  is  ventilated  under 
a  pressure  above  the  atmospheric  pressure. 

Comparison  of  Vacuum  and  Plenum  Systems. — No  hard-and-fast  rule  can 
be  made  to  apply  in  every  case,  as  each  system  has  its  particular  advantages. 
In  case  of  a  sudden  stoppage  of  the  ventilating  motor  at  a  mine,  there  is, 
in  the  vacuum  system,  a  rise  of  mine  pressure,  instead  of  a  fall,  and  the 
gases  are  driven  back  into  the  workings  for  a  while,  while,  in  the  plenum 
system,  any  stoppage  of  the  ventilating  motor  is  followed  at  once  by  a  fall  of 
pressure  in  the  mine,  and  mine  gases  expand  more  freely  into  the  passage- 
ways at  the  very  moment  when  their  presence  is  most  dangerous.  This 
point  must  be  carefully  considered  in  the  ventilation  of  deep  workings.  In 


VENTILATION  OF  MINES 


931 


shallow  workings,  the  plenum  system  is  often  advantageous,  especially  if 
there  is  a  large  area  of  abandoned  workings  that  have  a  vent  or  opening  to 
the  atmosphere,  either  through  an  old  shaft  or  through  crevices  extending 
to  the  surface.  Every  crevice  or  other  vent  becomes  a  discharge  opening  by 
which  the  mine  gases  find  their  way  to  the  surface,  and  the  gases  accumu- 
lating in  the  old  workings  are  driven  back  into  the  workings,  and  find  their 
way  to  the  surface  instead  of  being  drawn  into  the  mine  airways,  as  would  be 
the  case  in  an  exhaust  system.  Any  given  fall  of  the  barometer  affects  the 
expansion  of  mine  gases  to  a  less  extent  in  the  plenum  system  than  in  the 
vacuum  system,  but  this  small  advantage  would  not  give  it  considera- 
tion in  determining  between  the  adoption  of  the  one  or  the  other  of  these 
two  systems;  regard  must  be  had,  however,  to  other  conditions  more  vital 
than  this.  In  the  ventilation  of  gaseous  seams,  owing  to  the  necessity  of 
making  the  intake  airway  the  haulage  road,  the  exhaust  system  has  usually 
been  adopted,  as  the  main  road  is  thereby  left  unobstructed  by  doors. 

TYPES  OF  CENTRIFUGAL  FANS 

We  shall  only  mention  the  more  prominent  types  of  fans  that  have  been 
or  are  still  in  use,  giving  the  characteristic  features,  as  nearly  as  possible, 
of  each  fan.  Many  fans  have  been  built,  however,  combining  many  of  the 
features  that  originally  characterized  a  single  type  of  fan. 


FIG.  10 


FIG.  11 


Nasmyth  Fan. — Fig.  10  is  the  original  type  of  fan  representing  straight 
paddle  blades  radiating  from  the  center,  which  is  its  characteristic  feature. 
This  was  probably  the  earliest  attempt  to  apply  the  centrifugal  principle  to 
a  mine  ventilator,  and  although  not  recognized  at  the  time,  the  fan  embodied 
some  of  the  most  essential  principles  in  centrifugal  ventilation.  It  possessed 
certain  disadvantages,  however,  chief  of  which  was  a  contracted  central 
or  intake  opening.  The  blades,  also,  were  straight  throughout  their  entire 
length,  being  normal  both  to 
the  inner  and  outer  circles  of 
the  fan,  and  thus  did  not  pro- 
vide for  receiving  the  air 
without  shock  at  the  throat 
of  the  fan.  The  depth  of 
Nasmyth's  blades  equaled 
one-half  the  radius  of  the  fan, 
which  was,  under  ordinary 
conditions  of  mine  practice, 
far  too  great,  and  gave  the 
fan  a  low  efficiency. 

B  i  r  a  m  '  s     Ventilator. — 
About      1850,      Biram     at- 
tempted to  improve  upon  the 
Nasmyth   ventilator   by   re- 
ducing the  depth  of  blade  so  p        12 
that  it  was  but  one-tenth  of       Wmmma 
the  radius.    The  blades  were 

straight,  as  in  Nasmyth's  ventilator,  but  inclined  backwards  from  the  direc- 
tion of  motion  at  a  considerable  angle.  A  large  number  of  these  blades  were 
employed.  This  fan  was  run  at  a  considerable  speed,  but  proved  very  in- 
efficient. It  depended  more  on  the  effort  of  propulsion  given  to  the  air  than 
on  the  centrifugal  principle,  as  the  depth  of  the  blade  was  as  much  too  small 


932^ 


VENTILATION  OF  MINES 


as  that  of  Nasmyth's  was  too  great.  The  intake  or  central  opening  in  this 
fan  was  as  contracted  as  in  the  former  type.  See  Pig.  11. 

Waddle  Ventilator. — In  this  fan,  Fig.  12,  the  inventor  attempted  to  reen- 
force  the  discharge  pressure  at  the  circumference  against  the  pressure  of  the 
atmosphere.  The  discharge  took  place  all  around  the  entire  circumference 
of  the  fan,  which  was  entirely  opened  to  the  atmosphere.  The  blades  were 
curved  backward  from  the  direction  of  motion  in  spiral  form.  The  width 
of  the  blade  decreased  from  the  throat  toward  the  circumference,  so  as  to 
present  an  inverse  ratio  to  the  length  of  radius.  Thus,  the  area  of  passage 
between  the  fan  blades  was  maintained  constant  from  the  throat  to  the  cir- 
cumference of  the  fan.  The  purpose  of  this  was  to  maintain  the  velocity 
of  the  air  through  the  fan  constant,  and  to  fortify  the  pressure  due  to  the  fan 
against  the  atmospheric  pressure  at  the  point  of  discharge.  The  essential 
features  of  the  Waddle  ventilator  were,  therefore,  curved  blades  tapered 
towards  the  circumference,  and  a  free  discharge  into  the  atmosphere  all 
around  the  circumference.  This,  type  is  the  best  type  of  the  open-running 
fans  having  no  peripheral  casing,  and  discharging  air  into  the  atmosphere  all 
around  the  circumference. 

Schiele  Ventilator. — This  ventilator,  Fig.  13,  was  constructed  on  the  same 
principles  as  the  Waddle  ventilator  just  described,  but  differed  from  the 
latter,  as  the  discharge  was  made  into  a  spiral  chamber  surrounding  the 
fan  and  leading  to  an  expanding  or  eVase1  chimney.  There  was  some  advan- 
tage in  this  feature,  as  it  protected  the  fan  against  the  direct  influence  ofthe 
atmosphere,  and  reduced  the  velocity  of  discharge;  but,  in  each  of  these  fans, 
the  intake  opening  was  contracted,  and  the  depth  of  blade  was  very  great, 
yielding  a  comparatively  low  efficiency. 


FIG.  13 


FIG.  14 


Guibal  Ventilator. — The  next  important  step  in  the  improvement  of  cen- 
trifugal ventilators  was  introduced  by  M.  Guibal,  who  constructed  a  fan, 
Fig.  14,  embodying  the  features  of  the  Nasmyth  ventilator,  with  the  addition 
of  a  casing  built  over  the  fan  to  protect  its  circumference.  This  casing  was, 
however,  a  tight-fitting  casing,  and  as  such,  differed  very  materially  from  the 
Schiele  casing.  In  the  Guibal  fan  the  blades  were  arranged  upon  a  series  of 
parallel  bars  passing  upon  each  side  of  the  center  and  at  some  distance  from 
it.  By  this  construction,  the  blades  were  not  radial  at  their  inner  edge  or 
the  throat  of  the  fan.  They  were  curved,  however,  as  they  approached  the 
circumference  of  the  fan,  sd  as  to  be  normal  or  radial  at  the  circumference. 
The  advantage  of  this  construction  was  to  give  a  strong  skeleton  or  frame- 
work to  the  revolving  parts,  and,  further,  each  blade  was  inclined  to  the 
radius  at  its  inner  extremity,  the  effect  of  which  was  to  receive  the  air  upon 
the  blade  with  less  shock  than  was  the  case  in  the  Nasmyth  ventilator.  The 
intake  or  central  opening,  however,  was  very  contracted,  and  the  tight-fitting 
casing  about  the  circumference  prevented  the  effective  action  of  the  fan 
during  a  considerable  portion  of  its  revolution.  The  fan  was  supplied 
with  an  6vas6  chimney,  which  was  a  feature  of  the  Schiele  fan,  but  vibra- 
tion was  so  strong  that  a  shutter  was  required  at  the  cutoff  below  the  chim- 
ney, to  prevent  it.  This  shutter  was  made  adjustable,  and  is  known  as 
the  Walker  shutter,  having  been  applied  to  the  fan  later. 

The  Guibal  ventilator  presents  some  important  and  valuable  features 
in  the  protecting  cover,  and  in  the  blades  meeting  the  outer  circumference 
radially,  and  in  the  air  being  received  with  less  shock  than  before.  On  the 


VENTILATION  OF  MINES 


933 


whole,  it  has  proved  a  very  efficient  ventilator,  although  much  work  is  lost 
by  reason  of  its  contracted  central  orifice  and  tight  casing,  where  the  same 
is  used. 

Murphy  Ventilator. — Fig.  15  consists  of  twin  fans  supported  on  the  same 
shaft  and  set  a  few  feet  apart.  Each  fan  receives  its  air  on  one  side  only, 
the  openings  being  turned  towards  each  other.  This  ventilator  is  built  with 
a  small  diameter,  and  is  run  at  a  high  speed.  The  blades  are  curved  back- 
wards from  the  direction  of  motion.  The  intake  opening  is  considerably 
enlarged;  a  spiral  casing  generally  surrounds  the  fan,  and  in  every  respect 
this  fan  makes  an 
efficient  high-speed 
ventilator.  It  has  re- 
ceived considerable 
favor  in  the  United 
States,  where  it  has 
been  introduced  into 
a  large  number  of 
mines. 

Capell  Ventilator. 
— Perhaps  none  of 
the  centrifugal  venti- 
lators have  been  as 
little  understood  in 
regard  to  their  princi- 


FlG.  15 


pie  of  action  as  the  Capell  fan.  The  fan  is  constructed  along  the  lines  of  the 
Schiele  ventilator,  but  differs  from  it  in  the  manner  of  receiving  its  intake  air 
and  delivering  the  same  into  the  main  body  of  the  fan.  Here,  and  revolving 
with  it,  is  a  set  of  smaller  supernumerary  blades.  These  blades  occupy  a 
cylindrical  space  within  the  main  body  of  the  fan,  and  are  inclined  to  the 
plane  of  revolution  so  as  to  assist  in  deflecting  the  entering  air  through  small 
ports  or  openings  into  the  main  body  of  the  fan,  where  it  is  revolved  and  is 
discharged  at  the  circumference  into  a  spiral  space  resembling  that  surround- 
ing the  Schiele  fan.  The  larger  blades  of  this  fan  are  curved  backwards  as 
the  Schiele  blades,  but  are  not  tapered  toward  the  circumference.  The  fan 
is  capable  of  giving  a  high  water  gauge,  and  is  efficient  as  a  mine  ventilator. 
The  space  surrounding  the  fan  is  extended  to  form  an  expanding  chimney. 
The  fan  may  be  used  either  as  an  exhaust  fan  or  a  blower.  The  best  results 
in  the  United  States  have  been  obtained  by  blowers.  In  Germany,  where 
this  fan  is  in  general  use,  there  are  no  blowers. 


FIG.  16 


FIG.  17 


Sirocco  Fan. — This  Fig.  17  is  the  original  multi-blade  fan,  having  forwardly 
inclined  blades.  The  blades,  therefore,  act  upon  air  at  rest,  relatively  to 
their  own  path  which  is  at  right  angles  to  that  of  the  incoming  stream. 

Thomas  Chester,  chief  engineer  of  the  American  Blower  Co.  gives  num- 
erous formulas  for  use  in  connection  with  these  fans.  These  are  given  here 
in  detail. 

Sirocco  fan  blades  have  a  forward  inclination;  that  is  to  say  the  outer 
tips  are  in  advance  of  the  inner  edges  in  the  direction  of  rotation  and  in 
consequence  air  is  thrown  off  at  a  higher  velocity  than  the  peripheral  speed. 
This  enhanced  velocity  is  responsible  for  the  remarkable  volumetric  and 


934  VENTILATION  OF  MINES 

manometric  efficiencies  of  the  Sirocco  fan,  these  values  usually  being  around 
250%  and  100%  respectively. 

The  high  mechanical  efficiency  is  due  to  the  following  features: 

1.  Large  inlet  area. 

2.  Uniform  action  over  the  whole  periphery,  due  to  the  large  number  of 
blades. 

3.  Absence  of  whirlpool  or  vortex  motion  of  the  entering  air  before  reach- 
ing the  fan  blades,  thereby  avoiding  the  expenditure  of  power  on  unnec- 
essary work. 

4.  Better  stream  lines,  as  the  air  leaves  blades  tilted  forwards  in  very 
nearly  the  same  path  as  that  already  given  off  by  the  impeller  and 
traveling  towards  the  fan  outlet,  consequently  minimizing  the  power- 
absorbing  eddies  produced  by  conflicting  streams. 

Direct-connected  Engines. — For  large  volumes  of  air  against  ordinary 
resistances  when  using  fans  direct  connected  to  engines  it  is  necessary  to  use 
wheels  of  large  diameters  in  order  to  obtain  the  peripheral  speeds  required. 
This  calls  for  fans  of  special  proportions  as  the  widths  under  these  conditions 
are  usually  less  than  standard.  •/'- 

Other  Drives. — Sirocco  mine  fans  driven  by  belt  or  ropes  or  directly  con- 
nected to  motors  can  be  made  of  standard  proportions  which  means  that  in 
the  case  of  a  single-inlet  fan  the  peripheral  width  is  equal  to  one-third  the 
wheel  diameter  and  a  double-inlet  fan  has  a  peripheral  width  two-thirds  the 
wheel  diameter. 

Method  of  Determining  Fan  Diameter.— The  following  formulae  are  used 
in  designing  these  fans,  the  volume  being  in  cubic  feet  per  minute  and  W.G. 
being  the  mine  resistance  in  inches  of  water. 

,    .5"\volume 
Single-inlet,  diameter  in  inches  equals 


Qf\4 

Double-inlet,  diameter  in  inches  equals  — 


T 

Taking  as  an  example  200,000  cu.  ft.  per  min.  against  3-in.  mine  resistance, 
a  double  inlet  exhauster  being  required,  the  formula  for  a  fan  of  this  type 

R'ves  a  diameter  of  120  in.  and  the  impeller  would  therefore  be  120X80  in. 
npeller  diameters  in  inches  are  in  multiples  of  6  so  that  in  event  of  either 
formula  giving  an  intermediate  diameter  such  as  118  in.,  the  nearest  standard 
size  should  be  taken  which  in  this  case  would  be  120  in. 

To  Ascertain  Fan  Speed  Required. — Having  determined  the  diameter  of 
wheel  needed  the  rotative  speed  can  be  found  as  follows; 

10,800-s/W.G. 

Revolutions  per  minute  *=-r-. = — = — r — 

diameter  in  inches 

Horsepower  Needed. — The  power  consumption  is  arrived  at  in  the  ordi- 
nary manner  by  calculating  the  theoretical  horsepower  or  horsepower  in  the 
air  and  dividing  same  by  the  mechanical  efficiency. 

In  the  example  referred  to  previously  the  horsepower  in  the  air  would  be 

-—r^ —  =  94.5.     With   a   Sirocco  fan   of   this    capacity   the   mechanical 
0,040 
efficiency  could  safely  be  figured  at  75  %  so  that  the  actual  power  consump- 

04  *> 
tion  or  brake  horsepower  would  be  — =^-  =  126. 

.  /  o 

Size  of  Motor. — In  selecting  a  motor  for  work  of  this  character  it  should  be 
borne  in  mind  that  the  actual  mine  resistance  cannot  be  predetermined  with 
absolute  accuracy.  The  resistance  offered  by  a  mine  to  the  flow  of  the  re- 
quired quantity  of  air  may  be  less  than  anticipated,  with  a  consequent 
increase  in  the  volume  handled  by  the  fan  and  a  correspondingly  increased 
power  consumption,  so  that  to  provide  a  margin  of  safety  the  factor  .6  should 

Q4  5 
be  used.     This  would  indicate  that  a  motor  capable  of  developing  —jr-  = 

say  158  B.  H.  P.  should  be  installed. 

Evase  Stack. — The  foregoing  is  based  on  the  supposition  that  the  fan  would 
be  equipped  with  an  evase  stack  and  the  effective  length  in  feet  measured 
along  the  stack  axis  from  the  cutoff  should  be  5  times  the  square  root  of 
the  water  gauge  in  inches.  In  the  example  under  consideration  the  effective 
length  would  be  5^/3  or  say  8  ft. 


VENTILATION  OF  MINES 


935 


=  60\/— 


Maximum  Inlet  Velocity.  —  The  minimum  inlet  area  of  a  Sirocco  fan  is  at 
the  inner  ends  of  the  inlet  cones,  the  diameter  of  each  being  .875  the  wheel 
diameter.  In  the  case  cited  the  minimum  area  would  be  60.1  sq.  ft.  for 
each  inlet  or  a  total  of  120.2  sq.  ft.  The  maximum  inlet  velocity  would 
therefore  be  1  ,660  ft.  per  min. 

Loss  at  Inlets.  —  Due  to  the  right-angle  turn  made  by  the  air  entering  a 
fan  inlet  the  velocity  energy  at  this  point  is  almost  entirely  lost  but  as  the 
velocity  head  would  only  be  .171-in.  W.G.  this  could  be  considered  satisfac- 
tory and  it  would  not  pay  to  increase  the  size  of  fan  to  make  a  reduction  of 
this  loss. 

The  velocity  head  is  the  height  of  a  column  of  water  that  can  be  sup- 
ported by  a  stream  of  air  moving  at  any  given  velocity.  This  can  readily 
be  calculated  by  using  as  a  unit  the  air  velocity  required  to  sustain  1  in. 

of   water.     This   velocity  can   be   figured  from  the  formula 

where  g  is  32.16  the  acceleration  due  to  gravity  and  h  is  the  ratio  between  the 
weight  of  a  cubic  foot  of  water  at  62°F.  and  the  weight  of  a  cubic  foot  of  air 
under  the  conditions  respecting  temperature,  humidity  and  barometric 
pressure  prevailing. 

Standard  Air.  —  United  States  Navy  Department  engineers  figure  on 
standard  air  as  70°F.  and  70%  relative  humidity  and  in  this  condition  at 
sea  level  it  weighs  .07465  Ib.  per  cu.  ft.  Water  at  62°F.  weighs  62.355  Ib. 
per  cu.  ft.  so  that  the  constant  K  for  standard  air  is  4,015  and  an  air  velocity 
of  4,015  ft.  per  min.  would  be  equivalent  to  1-in.  W.G. 

Inlet  Velocities.  —  Taking  the  case  under  consideration  the  velocity  head  or 

equivalent  water  gauge  of  the  air  entering  the  fan  inlets  isf   '   ,  -^  or  .171-in 

\4,015/ 

W.G.  as  previously  stated.  The  equivalent  velocity  head  for  any  require- 
ment can  be  worked  out  by  using  the  constant  K  as  shown  and  the  fol- 
lowing table  gives  the  maximum  inlet  velocities  of  standard  Sirocco  fans 
for  various  resistances  with  the  impeller  diameters  figured  as  recommended. 


Mine  Resistance, 
In. 

Max.  Inlet 
Velocity, 
Ft.  per  Min. 

Mine  Resistance, 
In. 

Max.  Inlet 
Velocity, 
Ft.  per  Min. 

1 

960 

4! 

2,090 

1} 

1,070 

5 

2,140 

H 

1,175 

5} 

2,195 

H 

,270 

5i 

2,250 

2 

,355 

5J 

2,300 

2* 

,440 

6 

2,350 

2J 

,515 

6i 

2,400 

2| 

,590 

6J 

2,445 

3 

,660 

6| 

2,490 

3} 

,730 

7 

2,535 

3* 

,790 

71 

2,580 

3| 

,855 

7* 

2,625 

4 

,920 

7J 

2,670 

4i 

,975 

8 

2,715 

4* 

2,030 

8i 

2,760 

Special  Fans. — Fans  of  standard  proportions  can  be  used  for  all  the  mine 
resistances  given  in  the  above  table  as  the  most  severe  duty  stated  requires 
an  inlet  velocity  of  2,760  ft.  per  min.  which  is  equivalent  to  .47-in.  velocity 
head.  When  large  volumes  of  air  are  to  be  handled  against  high  resistances, 
however,  the  power  reduction  which  can  be  obtained  by  installing  a  larger  and 
more  expensive  fan  than  indicated  by  the  formulae  frequently  justifies  the 
greater  cost  as  each  horsepower  saved  represents  approximately  $100  per 
yr.  Cases  of  this  kind  and  those  involving  fans  for  high  altitudes  should  be 
submitted  to  mine  fan  specialists. 

Equivalent  Orifice. — No  mine  should  be  equipped  with  any  style  of  fan 
having  a  minimum  inlet  area  less  than  twice  the  equivalent  -orifice,  if  any- 
thing like  good  efficiency  is  desired.  The  equivalent  orifice  of  a  mine  varies 


936 


VENTILATION  OF  MINES 


directly  as  the  volume  of  air  passed  per  minute  and  inversely  as  the  square 
root  of  the  resistance,  so  that  with  the  same  mine  conditions  prevailing  the 
equivalent  orifice  remains  the  same  even  with  the  fan  speed  altered  and 
the  volume  increased  or  decreased. 

Reverting  to  the  requirement  of  200,000  cu.  ft.  per  min.  against  3-in.  mine 
resistance  previously  considered,  the  equivalent  orifice  is  found  to  be  46.2 
sq.  ft.  by  using  the  well-known  formula 

T^      •     1             •/=       •                   c     ±      nnn*  ^  v°l'  cu-  ft-  Per  rnin. 
Equivalent  orifice  in  square  feet  =  .0004  X ._         

VW.G. 

In  other  words  a  ventilator  drawing  air  through  an  opening  of  46.2  sq.  ft. 
in  a  thin  plate  would  encounter  just  the  same  resistance  as  when  exhausting 
the  same  volume,  200,000  cu.  ft.  per  min.,  from  a  mine  offering  a  resistance 
of  3-in.  water  gauge. 

As  already  noted  the  fan  selected  for  this  requirement  has  a  minimum 
inlet  area  of  120.2  sq.  ft.  or  2.6  times  the  equivalent  orifice  of  the  mine. 

Murgue's  Formula. — It  will  doubtless  be  instructive  at  this  point  to 
examine  the  equivalent  orifice  equation  developed  by  M.  Daniel  Murgue  as 
given  above.  Using  the  established  value  62  %  as  representing  the  effective 
area  of  an  opening  in  a  thin  plate  allowing  for  vena  contracta,  the  equiva- 
lent orifice  of  46.2  sq.  ft.  is  found  to  have  an  effective  area  of  28.6  sq.  ft. 

Dividing  the  volume,  200,000  cu.  ft.,  by  the  effective  area  28.6  the  velocity 
is  found  to  be  7,000  ft.  per  min.  Using  K  the  constant  for  standard  air  as 
per  U.  S.  Navy  practice  namely  4,015  ft.  per  min.,  the  equivalent  water 
gauge  is  found  by  dividing  the  square  of  the  air  velocity  through  the  effective 
area  of  the  equivalent  orifice  by  the  square  of  the  constant  K 

water  gauge. 

The  small  discrepancy  indicates  that  Murgue  used  a  constant  slightly  higher 
than  4,015ft.  per  min.  so  that  he  evidently  figured  on  air  having  a  little  less 
weight  than  is  considered  standard  by  the  Navy  Department  engineers. 
This  would  readily  be  accounted  for  if  he  assumed  a  higher  relative  humidity 
than  70%. 

Sullivan  Reversible  Fans. — The  Sullivan  fan  is  reversible.  The  opera- 
tion of  reversing  is  secured  in  a  manner  that  is  considered  extraordinarily 
simple  and  safe.  It  is  by  the  use  of  a  steel  hood  swing  by  a  gear  and  pinion 
controlled  by  a  hand  wheel.  This  has  an  advantage  in  that  a  smaller  and 
simpler  housing  is  needed  than  is  commonly  the  case.  The  fan  itself  is  of 
the  multi-blade  pattern  with  the  double  wheel,  a  double  inlet  and  cone- 
shaped  deflectors  for  changing  the  direction  of  the  air  with  minimum  fric- 
tion and  loss  in  power.  They  are  of  relatively  small  diameter  and  of  high 
speed. 

It  must  be  noted  that  the  action  of  the  hopd  is  entirely  independent  of 
that  of  the  fan.  It  hangs  in  bearings  concentric  with  those  of  the  fan  wheel 


FIG.  IS 


VENTILATION  OF  MINES 


937 


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VENTILATION  OF  MINES 


RATINGS.     G-FT.  AND  81-FT.  PANS 


6-ft.  Fan 


Capacity, 
Cu.  Ft.  Air  P.M. 

Water  Gauge,  In. 

i 

* 

I 

1 

li 

U 

1! 

2 

2^ 

3 

3* 

4 

4* 

5 

5* 

6 

10,000 
20,000 

R.P.M. 

90 

105 

119 

134 

148 

163 

178 

192 

221 

251 

280 

309 

338 

367 

396 

42,5 

H.P. 
R.P.M. 

10 

11 

12 

13 

14 

15 

16 

17 

19 

21 

23 

25 

27 

29 

31 

33 

133 

146 

159 

172 

185 

199 

212 

225 

251 

277 

303 

330 

356 

382 

408 

435 

H.P. 

13 

15 

16 

17 

19 

20 

22 

23 

26 

29 

32 

34 

37 

40 

42 

45 

30,000 

R.P.M. 

177 

189 

201 

212 

224 

236 

248 

260 

283 

307 

330 

357 

384 

410 

437 

448 

H.P. 

17 

18 

20 

22 

24 

25 

27 

29 

33 

36 

40 

43 

47 

50 

53 

57 

40,000 

R.P.M. 

220 

231 

241 

252 

262 

273 

284 

294 

315 

337 

358 

379 

400 

421 

442 

463 

H.P. 

20 

22 

24 

26 

29 

31 

33 

35 

39 

44 

48 

52 

56 

61 

66 

69 

50,000 

R.P.M. 

263 

272 

282 

291 

301 

310 

319 

329 

348 

366 

385 

404 

423 

442 

461 

480 

H.P. 

23 

26 

28 

31 

34 

36 

38 

41 

46 

31 

56 

61 

66 

71 

76 

81 

60,000 

R.P.M. 

307 

315 

324 

332 

341 

349 

357 

366 

383 

399 

416 

433 

450 

467 

483 

500 

H.P. 

27 

29 

32 

35 

38 

41 

43 

47 

53 

59 

64 

70 

76 

82 

87 

93 

70,000 

R.P.M. 

3.50 

357 

365 

372 

380 

387 

395 

402 

417 

432 

447 

462 

477 

492 

507 

523 

H.P. 

30 

33 

36 

40 

43 

46 

49 

53 

60 

66 

72 

79 

86 

92 

99 

105 

80,000 

R.P.M. 

393 

400 

406 

413 

420 

427 

433 

440 

453 

467 

480 

494 

507 

520 

534 

548 

H.P. 

33 

37 

40 

44 

48 

51 

54 

59 

66 

74 

80 

88 

96 

103 

110 

117 

90,000 

R.P.M. 

437 

443 

449 

455 

461 

467 

473 

479 

491 

503 

515 

527 

539 

551 

563 

575 

H.P. 

37 

40 

44 

49 

53 

57 

60 

65 

73 

81 

89 

97 

105 

113 

121 

129 

100,000 

R.P.M. 

480 

485 

491 

496 

502 

507 

512 

518 

528 

539 

550 

561 

572 

583 

594 

605 

H.P. 

40 

44 

49 

53 

58 

62 

66 

71 

80 

88 

97 

106 

115 

124 

132  141 

H.  P.  tabulated  are  I.  H.  P.  steam  eng.  dir.  conn,  or  motor  output  belted. 
NOTE. — The  power  ratings  are  shown  in  their  present  form,  rather  than 
as  net  H.  P.  delivered  to  the  fan  shaft,  on  account  of  the  variation  in  efficiency 
with  each  change  in  engine  speed. 


VENTILATION  OF  MINES 


8-ft.  6-in.  Fan 


Capacity, 
Cu.  Ft.  Air  P.M. 

Water  Gauge,  In. 

1 

i 

1 

1 

n 

a 

if 

2 

2* 

3 

3} 

4 

4| 

5 

5i 

6 

25,000 

R.P.M. 

56 

65 

74 

83 

91 

100 

109 

118 

136 

153 

171 

189 

207 

224 

242 

260 

H.P. 

17 

20 

22 

24 

27 

29 

32 

35 

40 

45 

50 

55 

60 

65 

70 

75 

50,000 

R.P.M. 

80 

88 

97 

105 

114 

122 

131 

139 

156 

173 

190 

206 

223 

240 

257 

274 

H.P. 

24 

27 

31 

34 

38 

41 

44 

48 

55 

62 

68 

75 

82 

89 

95 

102 

75,000 

R.P.M. 

104 

112 

119 

127 

134 

142 

150 

157 

172 

188 

203 

218 

233 

248 

264 

279 

H.P. 

31 

35 

40* 

44 

48 

52 

57 

62 

71 

79 

87 

96 

104 

113 

121 

129 

100,000 

R.P.M. 

128 

135 

142 

148 

155 

162 

169 

176 

189 

203 

216 

230 

244 

257 

271 

285 

H.P. 

38 

43 

48 

53 

58 

64 

69 

74 

84 

94 

104 

115 

125 

135 

145 

156 

125,000 

R.P.M. 

152 

158 

164 

170 

176 

182 

189 

195 

207 

219 

231 

244 

256 

268 

280 

292 

H.P. 

45 

51 

57 

63 

69 

75 

81 

87 

99 

111 

123 

135 

147 

159 

171 

183 

150,000 

R.P.M. 

176 

181 

187 

192 

198 

203 

208 

214 

225 

235 

246 

257 

268 

279 

289 

300 

H.P. 

52 

59 

66 

73 

80 

87 

93 

100 

114 

128 

142 

156 

169 

183 

197 

210 

175,000 

R.P.M. 

200 

205 

209 

214 

219 

224 

228 

233 

242 

252 

261 

271 

280 

289 

299 

309 

H.P. 

59 

67 

75 

82 

90 

98 

106 

113 

129 

144 

160 

175 

191 

206 

222 

237 
319 
264 
320 

200,000 

R.P.M. 

224 

228 

232 

236 

240 

245 

249 

253 

261 

269 

277 

286 

294 

302 

310 

H.P. 

66 

75 

83 

92 

100 

109 

118 

126 

143 

161 

178 

195 

212 

229 

247 

225,000 
250.000 

R.P.M. 

248 

251 

254 

257 

260 

264 

267 

270 

276 

282 

288 

295 

301 

307 

313 

H.P. 

73 

83 

92 

102 

111 

121 

130 

140 

159 

178 

197 

216 

235 

254 

273 

291 

R.P.M. 

272 

275 

278 

281 

284 

287 

290 

293 

300 

306 

312 

318 

324 

330 

336 

342 

H.P. 

80 

90 

101 

111 

121 

132 

142 

152 

173 

193 

214 

235 

255 

276297 

318 

H.  P.  tabulated  are  I  H.P.  steam  eng.  dir.  conn,  or  motor  output  belted. 


940 


VENTILATION  OF  MINES 
10- FT.  PAN  RATINGS 


lO-'ft.  Fan 


Capacity, 
Cu.  ft.  Air  P.M. 

Water  Gauge,  In. 

i 

~J 

1 

1 

11 

l* 

if 

2 

2i 

3' 

3} 

4 

*i 

5 

H 

6 

25,000 

R.P.M. 

46 

63 

78 

90 

100 

no 

119 

126 

141 

154 

167 

178 

189 

199 

209 

218 

H.P. 

20 

24 

28 

31 

34 

37 

40 

42 

47 

52 

57 

61 

65 

69 

73 

77 

50,000 

R.P.M. 

52 

69 

82 

93 

103 

112 

121 

128 

144 

157 

169 

180 

192 

202 

212 

221 

H.P. 

24 

30 

34 

38 

42 

46 

50 

54 

61 

68 

74 

80 

86 

92 

98 

104 

75,000 

R.P.M. 

62 

75 

87 

98 

107 

116 

124 

132 

147 

159 

172 

183 

194 

204 

214 

223 

H.P. 

30 

36 

42 

47 

51 

56 

61 

65 

74 

83 

92 

100 

108 

116 

124 

132 

100,000 

R.P.M. 

74 

84 

94 

104 

113 

121 

129 

137 

150 

163 

174 

186 

197 

207 

216:225 

H.P. 

37 

43 

49 

55 

61 

66 

72 

77 

88 

99 

109 

119 

129 

139 

149  159 

,  125,000 

R.P.M. 

90 
44 

97 
50 

103 

113 

121 

129 

136 

143 

156 

167 

178 

190 

200 

210 

219228 

H.P. 

57 

64 

70 

77 

83 

90 

102 

114 

126 

138 

151 

163 

175  188 

150.000 

R.P.M. 

107 

112 

117 

124 

131 

138 

144 

150 

163 

174 

184 

194 

204 

214 

224  232 

H.P. 

51 

58 

65 

73 

80 

88 

95 

102 

117 

131 

45 

159 

173 

187 

201 

214 

175,000 

R.P.M. 

123 

127 

132 

137 

143 

148 

154 

160 

170 

180 

90 

200 

210 

219 

229 

237 

H.P. 

59 

67 

74 

82 

91 

99 

107 

115 

131 

147 

63 

79 

95 

211 

227 

242 

200.000 

R.P.M. 

140 

144 

147 

150 

155 

160 

164 

169 

179 

189 

99 

>08 

217 

226 

235 

243 

H.P. 

66 

75 

83 

92 

101 

110 

119 

128 

146 

174 

82 

200 

217 

235 

53 

271 

225,000 

R.P.M. 

158 

160 

163 

166 

169 

173 

177 

181 

189 

199 

08 

17 

?25 

>34 

42 

249 

H.P. 

73 

83 

93 

102 

112 

121 

131 

141 

161 

81 

01 

20 

240 

60 

79 

299 

250,000 

R.P.M. 

174 

177 

179 

181 

183 

187 

190 

193 

201 

210 

18 

27 

35 

43 

49 

257 

H.P. 

81 

91 

102 

112 

123 

133 

144 

155 

176 

98 

20 

41 

63 

85 

06 

327 

275,000 

R.P.M. 

192 

194 

196 

198 

200 

202 

204 

207 

214 

222 

30 

37 

44 

53 

59265 

H.P. 

88 

100 

111 

123 

134 

145 

157 

168 

182 

215 

39 

62 

86 

10 

33  356 

300,000 

R.P.M. 

209 

211 

212 

213 

215 

217 

219 

223 

228 

235 

40 

47 

55 

262 

68275 

H.P. 

96 

108 

120 

132 

145 

157 

170 

183 

208 

233 

58 

83 

09 

334 

60385 

325,000 
350,000 

R.P.M. 

227 

228 

229 

230 

231 

233 

235 

237 

242 

248 

54 

61 

67 

273 

79,285 

H.P. 
R.P.M. 

103 

117 

130 

143 

156 

170 

183 

96 

223 

251 

79 

05 

32 

360 

87414 

243 

244 

245 

246 

247 

248 

250 

253 

257 

263 

68 

73 

78 

284 

90296 

H.P. 

111 

125 

139 

153 

167 

182 

196 

211 

239 

269 

98 

27 

56 

385 

14443 

H.  P.  tabulated  are  I.  H.  P.  steam  eng.  dir.  conn,  or  motor  output  belted. 


VENTILATION  OF  MINES 


941 


so  that  it  may  be  easily  revolved  without  stopping  the  fan.  The  operation 
is  so  simple  that  anyone  about  a  mine  is  enabled  to  reverse  the  current 
instantly  and  to  know  positively  that  the  operation  is  completed. 

The  foregoing  types  of  fans  are  given  to  show  the  general  designs  that  are 
now  in  use.  There  are  numerous  makes  now  on  the  market,  each  with 
one  or  more  modifications  of  these  general  types.  Most  of  these  produce 
results  worthy  of  investigation.  To  describe  them  all  in  detail  is  impractical 
in  a  pocketbook  of  this  size. 

The  following  table  of  capacities  may  b'e  valuable  to  those  having  installa- 
tions of  the  standard  moderate- speed  fan  as  manufactured  by  Crawford 
and  McCrimmon. 


Diameter 
of  Fan, 
.  Ft. 

Width 
ofBlades, 
In. 

Size  of 
Driving 
Engine 

Revolutions 
per  Minute 

Maximum    Ca- 
pacity, Cubic  Feet 
per  Minute 

8 

32 

5   X10 

180 

25,000  approx. 

10 

40 

6JX12 

150 

40,000  approx. 

12 

48 

8   X13 

150 

65,000  approx. 

14 

48 

8    X16 

150 

75,000  approx. 

15 

60 

10   X20 

120 

90,000  approx. 

16 

60 

10    X20 

120 

100,000  approx. 

18 

72 

10   X24 

100 

150,000  approx. 

20 

84 

12   X24 

100 

200,000  approx. 

The  Position  of  Any  Fan,  Etc.,  whether  used  as  an  exhaust  or  blower, 
should  be  sufficiently  removed  from  the  fan  shaft  or  drift  to  avoid  damage  to 
the  fan  in  case  of  explosion  in  the  mine.  Even  in  non-gaseous  mines,  the  fan 
should  be  located  a  short  distance  back  from  the  shaft  mouth,  to  avoid 
damage  due  to  settlement.  Con- 
nection should  be  made  with  the 
fan  shaft  by  means  of  an  ample 
drift,  which  should  be  deflected 
into  the  shaft  so  as  to  produce 
as  little  shock  to  the  current  as 
possible.  In  case  of  gaseous 
seams,  explosion  doors  should  be 
provided  at  the  shaft  mouth. 
The  ventilator  at  every  large 
mine  should  be  arranged  so  that 
it  may  be  converted  from  an  ex- 
hausting to  a  blowing  fan  at  short 
notice.  This  is  managed  by 
housing  the  central  orifices  or 
intake  of  the  fan  in  such  a  man- 
ner as  to  connect  them  directly 
with  the  fan  drift.  A  large  door 
aft,  Fig.  19,  is  arranged  at  the  foot 
of  the  expanding  chimney,  the 
latter  being  placed  between  the 
fan  and  the  shaft.  This  door, 
when  the  fan  is  exhausting,  is  in 
the  lower  position  aft,  and  then 
forms  a  portion  of  the  spiral 
casing  leading  to  the  chimney. 

When   the  fan  is  blowing,  how-  pIG.  jg 

ever,  the  door  is  swung  upwards 

so  as  to  occupy  the  position  ac,  being  tangent  to  the  cutoff  at  c,  thereby 
closing  the  discharge  into  the  chimney  and  causing  it  to  enter  the  fan  drift 
behind  the  door.  At  the  same  time,  the  positions  of  the  two  doors,  ed  and 
fd,  in  the  fan  drift,  are  changed  to  el  and  fs,  respectively,  to  open  the  fan 
drift  to  the  discharge  from  the  fan,  and  to  close  the  openings  leading  from 
the  fan  drift  to  the  housing  upon  each  side  of  the  fan,  while  another  set  of 
doors  A  A  upon  each  side  of  the  fan,  in  the  housing,  which  were  previously 
closed  tightly,  are  now  set  wide  open  to  admit  the  outside  air  to  the  intake 


942  VENTILATION  OF  MINES 

openings  of  the  fan.  The  fan  is  thus  made  to  draw  its  air  from  the  atmos- 
phere, and  discharge  it  into  the  fan  drift,  instead  of  drawing  its  air  from  the 
fan  drift  and  discharging  into  the  chimney,  as  before. 

The  manometrical  efficiency  of  a  fan  is  the  ratio  between  its  effective  and 
theoretical  pressures.  It  has  been  assumed  that  the  theoretical  pressure  due 

M2  M2X  1.2  X 12 

to  the  fan's  action  is  given  by  the  equation  h  =  — ,  or  *  =  —     '        — ,  u  being, 

as  before,  the  tangential  speed  (feet  per  second),  and  g  the  force  of  gravity 
(32.16);  h  =  head  of  air  column  in  feet;  i  =  water  gauge  in  inches. 

Mechanical  efficiency  is  a  term  applied  to  the  ratio  between  its  effective 
and  theoretical  powers.  In  estimating  the  efficiency  of  a  ventilator,  it  is 
customary,  though  incorrect,  to  estimate  the  theoretical  power  of  the  fan 
from  an  engine  card  taken  from  the  steam  cylinder  of  the  fan  engine.  The 
efficiency  of  the  steam  engine  is  this  confused  with  the  efficiency  of  the 
ventilator.  Mr  Beard  gives  the  following  formula  for  the  theoretical  work 

of    the  fan    per    minute:  U  =  . 001699^-^—  -\/V  R3bn2,  in  which  ra  =  ratio 

7W3 

between  outer  and  inner  diameters  of  fan  (D  —  md),  and  V  =  velocity  (feet 
per  minute)  of  air  in  fan  drift;  R  =  outer  radius  of  fan  blades  (feet);  b  = 
breadth  of  fan  blades  (feet);  n  =  number  of  revolutions  of  fan  per  minute. 
If  we  divide  the  power  upon  the  air,  as  determined  by  the  expression  qp, 
by  the  theoretical  work  given  in  the  last  equation,  we  obtain  the  value  of  the 
coefficient  of  efficiency.  According  to  this  formula  the  efficiency  of  the 
ventilator  changes  with  the  speed,  decreasing  as  the  speed  increases,  but 
not  in  the  same  ratio.  An  expression  for  the  coefficient  of  efficiency  of  a 

163,6002 
ventilator  is  given  by  Beard  as  follows:  K=  X3  2. 

The  factor  c  is  a  constant  of  design  whose  value  may  vary  from  2  to  7,  but 
for  an  ordinary  design,  the  value  c  =  4  may  be  taken.  This  factor  has  refer- 
ence to  the  equipment  of  the  machine  with  respect  to  its  efficiency  for  pass- 
ing an  air  current  through  itself  with  least  resistance.  Thus,  where  the 
ventilator  is  to  be  equipped  with  intake  blades  for  the  deflection  of  the  air  cur 
rent  into  the  machine,  and  with  straight  radial  blades  having  only  a  forward 
curve  at  the  lip  of  the  blade  to  avoid  the  shock  of  the  entering  air  against 
the  revolving  blades,  and  the  spiral  casing  starting  a  short  distance  upon  the 
cutoff  and  extending  uniformly  around  the  circumference  of  the  fan,  the 
value  of  this  constant  may  be  2  or  3.  Where  none  of  these  accessories  to 
the  efficiency  of  the  fan  is  employed,  the  value  of  c  may  be  as  high  as  7. 

FAN  CONSTRUCTION 

Size  of  Central  Orifice. — The  velocity  of  the  intake  should  vary  between 
1,000  ft.  and  1,500  ft.  per  min.,  while  1,200  ft.  may  be  used  for  fan  calcula- 
tions. If  d  =  diameter  of  opening,  and  q  =  quantity  of  air  passing  per 

minute'  d=  \UMOX.7854  f°r  sinele-intake  fans-  and  d=  V2.400X.7S54 
for  double-intake  fans. 

Upon  entering  the  fan  the  air  travels  in  a  radial  direction;  this  change  of 
direction  is  accompanied  by  a  slight  reduction  of  the  velocity,  hence  the 
throat  area  of  the  fan  must  be  slightly  in  excess  of  the  intake  area.  The 
throat  is  the  surface  of  the  imaginary  cylinder  that  has  for  its  two  bases  the 
two  intake  openings  of  the  fan,  and  for  its  length  the  width  of  the  fan,  =• 
•trdb.  [The  throat  area  is  commonly  made  1.25  times  the  total  area  of  the 
intake  orifices,  which  gives  for  breadth  of  blade  b  =  %d  for  double-intake, 
and  b  =  fed  for  single-intake. — Beard.] 

Diameter  of  Fan. — Murgue  assumes  the  tangential  velocity  of  the  blade 
tips  (w)  to  create  a  depression  double  that  due  to  the  velocity  as  expressed 

by   the  equation   H  *» — ,   or  if  the   manometrical   efficiency  =  K,   and  the 

effective  head  produced  =  h,  h  =  KH  =  K~t  or  u=  A/^.     From  this  equa. 

&  H  K 

tion,  the  tangential  velocity  (feet  per  second)  may  be  calculated  for  any 
given  effective  head  h.  This  effective  head  h  is  the  head  of  air  column 
effective  in  producing  the  circulation  in  the  airway.  To  convert  the 
effective  head  of  air  column  into  inches  of  water  gauge  (t),.we  have  h  = 

1  2X12*'     **av*nS  found  the  tangential  speed  required  in  feet  per   second 


VENTILATION  OF  MINES  943 

this  is  multiplied  by  60,  to  obtain  the  speed  in  feet  per  minute,  and  dividing 
this  result  by  the  desired  number  of  revolutions  per  minute,  or  the  desired 
speed  of  the  ventilator,  the  outer  circumference  of  the  fan  blades  is  obtained. 
No  reference  is  made  in  the  equation  to  the  quantity  of  air  in  circulation 
which  is  determined  from  the  equivalent  orifice  of  the  mine  and  of  the  fan 

by  the  equation  V  =  *  -  -  -  12,  in  which  V  =  volume  of  air  (cubic  feet  per 


second);  a  =  equivalent  orifice  of  the  mine;  o  =  the  equivalent  orifice  of  the 
fan.  M.  Murgue  also  uses  the  equation  h=>  —  ~7~»  and  suggests  that 

<fe|ir) 

the  value  of  K  for  any  particular  type  of  machine  should  be  first  decided, 
after  which  the  tangential  speed  required  to  produce  any  given  effective 

head  of  air  column  (A)  is  easily  calculated  for  the  formula  u  =   \~.     The 

breadth  of  the  blade  is  left  largely  to  judgment,  while  this  method  of  cal- 
culation gives  the  same  size  of  fan  for  any  given  effective  head  desired, 
regardless  of  the  quantity  of  air  to  be  circulated,  which  is  the  same  as  saying 
that  the  ventilator  will  present  the  same  efficiency  when  a  large  amount  of 
air  is  crowded  through  its  orifice  of  passage  as  when  a  smaller  amount  of  air 
is  necessary. 

Mr.  Beard  uses  the  following  formulas  for  determining  the  several  dimen- 
sions of  a  ventilating  fan; 

D~       m        3,770  V^. 

xi-v'  ^= 

385.000.000^      . 


(m*-l)n*K\/QV'  *    170m  p 

in  which  m  =  -j,  which  is  the  ratio  between  the  outer  diameter  of  the  fan 
a 

blades  D  and  the  inner  diameter  of  the  blade  d,  which  equals  the  diameter  of 
the  intake  orifice;  b  =  width  of  fan  blade;  e  =  expansion  of  spiral  casing  at 
point  of  cutoff. 

The  other  symbols  stand  for  the  same  quantities  as  previously  indicated. 

Curvature  of  Blades.  —  It  was  at  one  time  supposed  that  the  curvature  of 
the  blades  should  be  such  that  the  radial  passage  of  the  air  current  would 
be  undisturbed  by  the  revolution  of  the  fan;  but  fans  constructed  on  this 
principle  gave  no  adequate  results,  and  the  theoretical  spiral  thus  developed 
was  entirely  abandoned.  A  certain  curvature  of  the  blade  backward, 
however,  is  assumed  by  many  to  increase  the  efficiency  of  the  fan.  This 
has  not  been  proved  in  practice,  but  the  effect  of  the  backward  curvature 
appears  simply  to  necessitate  a  higher  speed  of  revolution  in  the  fan,  in 
order  to  obtain  the  same  results  as  are  obtained  with  radial  blades. 

The  Guibal  blade,  radial  at  its  outer  extremity,  or  normal  to  the  outer 
circumference,  and  curved  forward  in  the  direction  of  motion,  at  its  inner 
extremity,  so  that  the  lip  of  the  blade  approaches  tangency  to  the  throat 
circle,  seems  to  be  an  effective  blade  in  centrifugal  ventilation. 

Tapered  Blades.  —  The  object  of  the  taper  is  to  produce  a  constant  area 
of  passage  from  the  throat  to  the  circumference  of  the  fan,  and  thus  prevent 
the  reduction  of  the  velocity  of  the  current  in  its  passage  through  the  fan. 
This  feature  presents  an  attempt  similar  to  that  attempted  by  the  curva- 
ture of  the  blades,  to  hasten  the  passage  of  the  air  through  the  fan.  It 
has  not  been  proved,  however,  to  have  produced  any  beneficial  result, 
except  in  the  strengthening  of  the  discharge  pressure  against  the  atmos- 
pheric pressure,  in  open-running  fans.  On  the  other  hand,  the  slowing  up 
of  the  air  in  its  passage  through  a  covered  fan  has  by  no  means  been  proved 
a  detriment,  but  is  assumed  by  many  to  be  an  advantage,  inasmuch  as  the 
air  thus  remains  longer  within  the  influence  of  the  fan  blades. 

The  number  of  blades  depends  on  the  size  of  the  fan.  An  increased  num- 
ber strengthens  the  fan's  action  at  the  circumference,  or  supports  the  air  at 
that  point,  and  thus  prevents  the  backlash  or  the  reentry  of  air  into  the  fan, 
due  to  the  eddies  occurring  at  the  circumference  when  the  blades  are  too  far 
apart.  To  a  certain  extent,  the  number  of  blades  is  modified  by  the  speed 


944  VENTILATION  OF  MINES 

of  revolution,  high-speed  motors  requiring  a  somewhat  lesser  number, 
while  low-speed  motors  require  more.  In  any  case,  the  number  of  blades 
should  not  be  so  great  as  to  abnormally  increase  the  resistance  to  the  air 
current.  In  general,  the  distance  upon  the  outer  circumference  from  tip 
to  tip  of  the  fan  blades  should  be  from  2  to  3  times  the  depth  of  the  blade. 
The  spiral  casing  gradually  reduces  the  velocity  of  the  air  and  reduees  the 
shock  incident  to  the  discharge  of  the  air  into  the  atmosphere.  The  spiral 
casing  should  be  so  proportioned  that  the  velocity  of  the  flow  from  the  fan 
blades  will  be  maintained  constant  around  the  entire  circumference,  and 
this  should  not  be  less  than  the  velocity  of  the  blade  tips.  The  expansion  e 
of  the  casing  at  the  cutoff  should  be  such  as  to  provide  a  velocity  of  the 
air  at  this  point  equal  to  the  velocity  of  the  blade  tips,  according  to  the 

equation  e  =  —=—-r,  in  which   D  =  diameter  of  fan;   n  =  number  revolutions 

^  iruno 
per  minute \b  =  breadth  of  fan  blade. 

The  evase  chimney  reduces  the  velocity  of  the  air,  as  it  is  discharged  into 
the  atmosphere,  to  a  minimum.  The  chimney  should  be  sufficiently  high 
to  protect  the  fan  from  the  effect  of  high  winds,  but  should  not  extend  too 
far  above  the  fan  casing,  the  point  of  cutoff  being  situated  below  this,  at 
about  the  level  of  a  tangent  to  the  throat  circle  at  its  lower  side.  - 

High-speed  and  Low-speed  Motors.— The  question  of  speed  of  the  venti- 
lating motor  is  largely  an  open  one,  inasmuch  as  the  same  work  may  be 
performed  by  a  small  ventilator  running  at  a  high  speed  as  is  performed  by 
a  large  ventilator  running  at  a  low  speed. 

It  is  important  to  design  a  mine  ventilator  at  a  speed  such  as  to  admit  of 
its  being  increased  in  case  of  emergency.  If  the  ventilator  has  been  de- 
signed at  a  high  speed,  a  demand  for  an  increase  of  speed  cannot  be  met  as 
readily  as  when  the  ventilator  is  designed  at  a  medium  or  low  speed;  in 
other  words,  the  exigencies  of  mine  ventilation  demand  that  a  ventilator 
shall  be  capable  of  greatly  increased  speed. 

Fan  Tests. — A  large  number  of  fan  tests  have  been  made,  from  time  to 
time,  on  different  types  of  fans  and  under  different  conditions,  with  respect 
to  the  resistance  against  which  the  fan  is  operated,  and  the  quantity  of  air 
required,  and  the  speed  of  the  ventilator.  The  experiments  have  resulted, 
to  a  large  extent,  in  tabulating  a  mass  of  contradictory  data.  The  condi- 
tions that  affect  the  yield  of  the  centrifugal  ventilator  are  so  numerous,  and 
the  tabulation  of  the  necessary  data  has  been  so  often  neglected  in  these 
experiments,  as  to  render  them  practically  useless  for  the  purpose  of  scien- 
tific investigation.  In  conducting  a  reliable  fan  test,  the  following  points 
should  be  observed:  (1)  Take  the  velocity,  pressure,  and  temperature  of 
the  air  at  the  same  point  in  the  airway,  as  nearly  as  practicable.  This 
point  should  be  selected  near  the  foot  of  the  downcast  shaft,  or  in  the  fan 
drift  at  a  suitable  distance  from  the  fan,  to  avoid  oscillations  of  pressure  and 
velocity.  (2)  The  area  of  the  fan  drift  should  be  uniform  for  a  suitable 
distance  in  each  direction  from  the  point  of  observation,  and  this  area 
should  be  carefully  measured.  (3)  Take  the  velocity  readings  at  different 
positions  in  the  airway,  so  as  to  obtain  an  average  reading  over  the  entire 
sectional  area.  Do  not  interpose  the  body  in  this  area  so  as  to  decrease  the 
sectional  area  of  the  airway.  (4)  Take  outside  temperature  of  the  air  and 
the  barometric  pressure  at  the  time  of  making  the  test.  (5)  The  intake  and 
discharge  openings  of  the  fan  should  be  protected  against  wind  pressure. 
(6)  At  least  three  observations  should  be  made,  at  as  many  different  speeds 
of  the  ventilator,  and  the  number  of  revolutions  of  the  fan  carefully  observed 
and  recorded  for  each  observation. 

Mr.  R.  Van  A.  Norris  (Trans.  A.  I.  M.  E.,  vol.  XX,  page  637)  gives  the 
results  of  a  large  number  of  experiments  performed  upon  different  mine 
ventilating  fans.  This  table,  like  ajl  other  tabulated  fan  tests,  shows  a  large 
amount  of  contradictory  data.  The  conclusions  drawn  by  Mr.  Norris  from 
these  tests  are  interesting  and  would  be  given  here  excepting  that  they 
might  be  misleading  if  considered  apart  from  the  description  of  the  experi- 
ments and  the  discussion  leading  up  to  the  conclusions. 

CONDUCTING  AIR  CURRENTS 

Doors. — A  mine  door  is  used  for  the  purpose  of  deflecting  the  air  current 
from  its  course  in  one  entry  so  as  to  cause  it  to  traverse  another  entry,  at  the 
same  time  permitting  the  passage  of  mine  cars  through  the  first  entry.  The 
essential  points  in  the  construction  of  a  mine  door  are  that  it  shall  be  hung 
from  a  strong  door  frame  in  such  a  manner  as  to  close  with  the  current.  The 


MINE  FIRES  945 

door  should  be  hung  so  as  to  have  a  slight  fall.  If  necessary,  canvas  flaps 
may  be  supplied  to  prevent  leakage  around  the  door,  and  particularly  at  the 
bottom.  Double  doors  are  used  on  main  entries  at  the  shaft  bottom,  or  at 
any  point  where  the  opening  of  the  door  causes  a  stoppage  of  the  entire  cir- 
culation of  the  mine.  Such  doors  should  be  placed  a  sufficient  distance 
apart  to  allow'an  entire  trip  of  mine  cars  to  stand  between  them,  so  that  one 
of  the  doors  will  always  be  closed  while  the  other  is  open. 

Stoppings. — Stoppings  are  used  to  close  breakthroughs  that  have  been 
made  through  two  entries,  or  rooms,  for  the  purpose  of  maintaining  the  cir- 
culation as  the  workings  advance;  also  to  close  or  seal  off  abandoned  rooms 
or  working  places.  ^Stoppings  must  be  air-tight  and  substantially  built.  A 
good  form  of  stopping  is  constructed  by  laying  up  a  double  wall  of  slate, 
having  about  8  or  10  in.  of  space  between  the  two  walls.  This  space  is  filled, 
as  the  building  progresses,  with  dirt  taken  from  the  roadways,  or  other  fine 
material.  A  still  better  plan  is  to  build  the  stopping  of  brick  or  concrete. 
Hollow  tile  has  been  used  as  a  material  for  stoppings  and  appears  to  be 
admirably  adapted  to  this  purpose. 

Air  Bridges. — An  air  bridge  is  a  bridge  constructed  for  the  passage  of  air 
across  and  over  another  airway,  this  being  called  an  overcast;  or,  the  cross- 
ing may  be  made  to  pass  under  the  airway,  this  being  called  an  undercast. 
In  almost  every  instance,  overcasts  are  preferable  to  undercasts  for  several 
reasons.  An  undercast  is  liable  to  be  filled  with  water  accumulating  from 
mine  drainage;  it  is  also  liable  to  fill  with  heavy  damps  from  the  mine,  when 
the  ventilation  is  sluggish,  and  to  offer  considerable  resistance  to  the  free 
passage  of  the  air  current.  An  undercast  can  never  be  maintained  as  air- 
tight as  an  overcast,  on  account  of  the  continual  travel  through  the  haul- 
ageway  or  passageway  leading  over  it.  This  continual  passing  over  the 
bridge  causes  a  fine  dust  to  sift  into  the  airway  and  mingle  with  the  air  cur- 
rent. All  these  objections  are  overcome  in  the  construction  of  the  overcast. 

An  air  brattice  is  any  partition  erected  in  an  airway  for  the  purpose  of 
deflecting  the  current.  A  thin  board  stopping  is  sometimes  spoken  of  as  a 
brattice;  but  the  term  applies  more  particularly  to  a  thin  board  or  canvas 
partition  running  the  length  of  an  entry  or  room  and  dividing  it  into  two 
airways,  so  that  the  air  will  be  obliged  to  pass  up  one  side  of  the  partition 
and  return  on  the  other  side  of  the  partition,  thus  sweeping  the  face  of  the 
heading  or  chamber.  Such  a  temporary  brattice  _  is  often  constructed  by 
nailing  brattice  cloth  or  heavy  duck  canvas  to  upright  posts  set  from  4  to  6 
ft.  apart  along  one  side  of  the  entry  a  short  distance  from  the  rib. 

Curtains. — These  are  sometimes  called  canvas  doors.  Heavy  duck,  or 
canvas,  is  hung  from  the  roof  of  the  entry  to  divide  the  air  or  deflect  a 
portion  of  it  into  another  chamber  or  entry.  Curtains  are  thus  used  very 
often  previous  to  setting  a  permanent  door  frame.  They  are  of  much  use 
in  long-wall  work,  or  where  there  is  a  continued  settlement  .of  the  roof, 
which  would  prevent  the  construction  of  a  permanent  door;  also,  in  tempo- 
rary openings  where  a  door  is  not  required. 

MINE  FIRES 

Means  Employed. — There  are  two  general  methods  of  extinguishing  mine 
fires;  namely,  flooding  and  smothering.  It  is  generally  considered  better 
practice  and  cheaper  to  smother  a  fire  than  to  drown  it,  since  m  the  latter 
case  the  water  used  for  quenching  must  be  pumped  out  of  the  mine  after 
the  fire  is  extinguished.  In  cases,  however,  where  sealing  off  cannot  be 
accomplished  or  where  for  any  reason  it  is  not  effective,  flooding  may  be  the 
only  means  of  quenching  the  fire. 

Isolating  the  Section. — Where  fire  exists  in  a  portion  of  a  mine  only  and 
it  is  expedient  to  keep  the  remainder  of  the  mine  in  operation  the  section 
involved  may  be  isolated  by  means  of  a  suitable  dam  or  dams  sufficiently 
strong  to  withstand  the  greatest  head  of  water  that  may  possibly  come  upon 
them.  Such  dams  may  be  built  of  wood  with  clay  or  other  filling  of  brick, 
masonry,  concrete  or  reinforced  concrete.  In  most  mines  it  will  be  found, 
however,  that  the  reinforced  concrete  will  be  the  cheaper  structure  to  build 
if  the  head  of  water  to  be  resisted  is  at  all  high. 

When  all  necessary  dams  have  been  constructed  water  may  be  turned  into 

the  portion  of  the  mine  affected  and  the  fire  thus  effectually  quenched,      i  he 

water  may  be  poured  down  a  regular  mine  opening  such  as  a  slope  or  shaft 

or  one  or  more  bore  holes  may  be  sunk  from  the  surface  for  this  purpose. 

60 


946 


MINE  FIRES 


In  many  instances  a  mixture  of  water  and  clay,  mud,  silt,  culm  or  other  mine 
refuse  may  be  used  for  quenching  fires.  Such  a  flush  (often  called  slush) 
has  the  advantage  of  baking  into  a  more  or  less  solid  mass  under  the  action 
of  the  heat  which  it  encounters  and  is  consequently  preferred  by  many 
engineers. 

Methods  Employed  in  Sealing  off  Fires. — In  the  majority  of  instances 
it  is  not  necessary  to  resort  to  flooding  a  mine,  particularly  if  the  fire  is 
promptly  discovered  and  quick  action  is  taken.  Particularly  in  the  more 

easily  inflamed  bituminous 
coals,  fires  often  originate 
in  the  process  of  shooting 
down.  These,  if  discovered 
promptly,  may  be  sealed  off 
without  seriously  endanger- 
ing the  rest  of  the  mine  or 
any  considerable  loss  in  out- 
put. Fig.  1  shows  a  fire  of 
this  kind  and  the  position  of 
the  necessary  stoppings  for 
sealing  it  off. 

Mining  men  differ  some- 
what as  to  whether  a  fire  of 
this  kind  should  be  first 
sealed  on  the  intake  or  the 
return.  It'is  probable,  how- 
ever, that  in  the  majority  of 
instances  it  is  preferable  to 
seal  up  first  the  intake.  If, 
however,  there  are  several 
openings  to  the  fire  all  of 
which  must  be  closed  and 
through  oversight  or  delay 
the  fire  has  gained  consider- 
able headway  or  if  a  strong 
feeder  of  gas  is  the  primary 
cause  of  such  a  fire,  or  if  the 
sealing  is  to  be  undertaken  a 
considerable  distance  from 
the  fire,  it  might  under  cer- 
tain circumstances  be  wise  to 
seal  the  return  first.  This 
procedure  should  at  least  be 
given  careful  consideration. 


In   fighting   mine   fires  in 
"c  following  points 


general  the 

should  be  kept  in  mind: 
Attack  the  fire  as  soon  after 
its  origin  as  possible,  extin- 
guish it  directly,  that  is,  with 
fire-hose  and  water  if  possi- 
ble, and  if  it  is  safe  to  do  so. 
Never  allow  a  gas  feeder  of 
any  magnitude  discharging 

in  rear  of  the  fire,  that  is,  on  the  intake  side  to  continue  its  discharge  into 
the  air  current  reaching  the  fire,  even  though  this  gas  discharge  may  be 
diluted  far  below  the  explosive  mixture.  If  possible  conduct  the  gas  from 
such  a  feeder  direct  to  the  return.  Erect  all  seals  as  close  to  the  fire  as 
possible.  No  more  air  should  be  allowed  to  reach  the  sealing  point  than  is 
necessary  while  the  work  is  being  done.  What  air  is  carried  to  this  point 
should  be  directed  by  brattice  and  curtains  close  around  the  men.  _  Men 
erecting  a  seal  should  never  raise  their  heads  close  to  the  roof  and  thus  inhale 
an  overdose  of  smoke. 

Stopping  Materials. — The  materials  employed  in  building  a  seal  may  be 
the  same  as  those  used  for  ordinary  stoppings,  that  is,  rock  packs  covered 
with  cement,  mortar  or  even  clay,  brick  walls,  concrete  or  reinforced  con- 
crete, hollow  tile,  etc.  As  a  general  rule,  however,  it  will  be  found  that  a 
double  wooden  partition  with  clay  tamping  between  can  be  built  up  more 
rapidly  than  any  other  type  of  stopping — and  speed  is  important.  A  good 


MINE  FIRES  947 

type  of  stopping  of  this  nature  is  shown  in  Pig.  2.  This  should  be  set  into 
floor,  ribs  and  roof,  and  the  joint  around  the  complete  periphery  made  as 
nearly  air-tight  as  possible  with  clay  tamping.  It  is  frequently  advisable  on 
discovering  a  fire  to  start  a  few  men  to  preparing  the  places  selected  for  the 
various  stoppings  while  others  collect  necessary  material  and  as  soon  as 
possible  begin  the  erection  of  the  first  seal.  The  intake  to  the  fire  should 
be  short-circuited  and  a  careful  watch  kept  upon  the  smoke  as  a  heavy  fall 
of  rock  may  drive  this  smoke  and  the  products  of  combustion  back  onto  the 
workers  unless  they  receive  warning  in  time  to  get  away.  The  materials 
will  consist  of  the  timber  posts,  which  should  be  at  least  6  in.  square  (10  in. 
square  is  preferable),  the  necessary  planking,  brattice  cloth  to  cover  the  entire 
stopping  and  the  clay  or  earth  for  the  filling  and  for  a  daubing  coat  on  the 
outside  if  necessary.  Both  sides  of  the  stopping  should  be  carried  up  simul- 
taneously together  with  the  clay  filling  which  should  be  carefully  tamped  in 
place. 

The  last  stopping  is  always  the  most  difficult  to  build,. and  it  is  frequently 
advantageous  to  here  erect  a  temporary  brattice  inside  the  stopping  proper 
to  keep  back  as  much  as  possible  the  smoke  and  gases  from  combustion. 


FIG.  2 


This  brattice  as  well  as  the  stopping  itself  should  contain  a  section  approxi- 
mately 24X34  in.  which  may  be  afterwards  easily  removed,  allowing  the 
entrance  of  a  fire  boss  or  other  person  to  ascertain  the  condition  of  the 
affected  area.  A  pipe,  say  4  in.  in  diameter,  or  more,  and  provided  with  a 
valve,  should  be  built  into  this  last  stopping  to  allow  the  escape  of  the  heated 
air  in  the  fire  area  (see  Fig.  3).  Otherwise  the  expansion  of  this  air  may 
push  out  one  of  the  stoppings.  Throughout  the  entire  process  of  building 
the  last  stopping  extreme  care  should  be  exercised  that  no  workman  raise 
his  head  into  the  dense  smoke,  thus  inhaling  gas. 

When  all  passages  leading  to  the  fire  have  been  sealed,  the  ventilation  up 
to  the  stopping  should  be  restored,  thus  allowing  the  largest  available  amount 
of  air  to  circulate  to  all  the  working  places  in  that  portion  of  the  mine,  thus 
sweeping  out  the  smoke  and  gases  which  may  have  accumulated  there  while 
the  ventilation  was  restricted.  A  careful  inspection  should  then  be  made  to 
see  that  such  places  are  fit  for  operation.  Near  the  seal  containing  the  escape 
pipe  and  valve  a  canvas  brattice  or  tight  curtain  with  suitable  means  of  en- 
trance should  be  constructed,  so  that  the  gas  coming  through  the  pipe  may 
be  periodically  tested.  This  test  may  be  made  each  evening  after  the  work- 
men have  left  the  mine.  For  the  first  few  days  the  gas  issuing  from  the  pipe 
will  be  afterdamp,  after  which  firedamp  will  begin  to  appear.  The  showing 
of  this  gas  will  get  stronger  from  day  to  day  and  during  the  night  or  at  such 
times  as  no  men  are  at  work  in  the  mines  the  valve  may  be  left  open.  After 
several  days  the  gas  issuing  from  the  pipe  will  be  sufficiently  strong  to  give 
a  cap  on  the  lamp  when  the  latter  is  held  some  distance  from  the  pipe. 
From  the  indication  of  this  gas  it  may  be  judged  when  it  is  advisable  to 
open  the  sealed  area.  This  will  probably  not  exceed  18  days  to  three  weeks 
from  the  time  of  sealing  up,  provided,  of  course,  that  the  fire  was  promptly 
discovered  and  that  only  a  comparatively  small  volume  of  air  exists  in  the 
sealed  area. 

Unsealing  after  the  Fire  is  Out. — In  unsealing  a  supposedly  extinguished 
fire,  it  is  well  to  curtain  off  other  districts  of  the  mine  so  as  to  prevent  the 
escaping  gases  from  reaching  them;  also  to  confine  the  return  from  the  fire 
to  one  air-course.  The  previously  mentioned  manhole  opening  in  the  last 
seal  is  first  broken  open.  During  this  process  there  should  be  no  flame,  not 
even  that  of  a  safety  lamp  in  line  with  the  opening  as  the  gas  emitted  will 
be  strongly  inflammable.  After  this  opening  has  been  made  in  the  return  a 
similar  one  may  be  opened  in  the  intake  and  a  current  of  fresh  air  thus 


948 


MINE  FIRES 


passed  through  the  heretofore  sealed  area.  With  the  air  current  through 
this  fire  area  established,  observers  may  be  stationed  at  intervals  along  but 
outside  of  the  return  at  such  points  that  a  safety  lamp  may  be  pushed  into 
the  return  airway  periodically  to  test  the  air.  These  tests  should  be  made 
at  intervals.  When  no  showing  of  gas  appears  in  the  return  from  the  tire 
area  it  is  time  enough  to  make  a  thorough  inspection  of  the  section  which 
has  been  sealed  up.  When  this  is  found  to  be  safe  for  working,  all  the  stop- 
pings may  be  removed,  the  place  cleaned  up  if  necessary,  fallen  or  burned 
timbering  renewed  and  work  resumed. 


FIG.  3 

Gob  fires  are  due  to  the  spontaneous  ignition  of  coal,  and  are  most  likely 
to  occur  in  pack  walls  and  gobs  where  there  is  an  insufficiency  of  air.  Ample 
ventilation  is  the  best  preventive. 

Spontaneous  Combustion. — According  to  Prof.  Able,  Dr.  Percy,  and  Prof. 
Lewes,  the  causes  of  the  spontaneous  ignition  of  coal  are:  First,  and  chiefly, 
the  condensation  and  absorption  of  oxygen  from  the  air  by  the  coal,  which 
of  itself  causes  heating,  and  this  promotes  the  chemical  combination  of  the 
volatile  hydrocarbons  in  the  coal  and  some  of  the  carbon  itself  with  the 
condensed  oxygen.  This  process  may  be  described  as  self-stimulating,  so 
that,  with  conditions  favorable,  sufficient  heat  may  be  generated  to  cause 
the  ignition  of  portions  of  the  coal.  The  favorable  conditions  are:  A  mod- 
erately high  external  temperature;  a  broken  condition  of  the  coal,  affording 
the  fresh  surfaces  for  absorbing  oxygen;  a  supply  of  air  sufficient  for  the 
purpose,  but  not  in  the  nature  of  a  strong  current  adequate  to  remove  the 
neat;  a  considerable  percentage  of  volatile  combustible  matter  or  an  ex- 


THE  PREPARATION  OF  COAL 


949 


tremely  divided  condition.  Second,  moisture  acting  on  sulphur  in  the  form 
of  iron  pyrites.  The  heating  effect  of  this  second  cause  is  very  small,  and 
it  acts  rather  by  breaking  the  coal  and  presenting  fresh  surfaces  for  the 
absorption  of  oxygen. 

Coal  Storage. — Prof.  Lewes  gives  the  following  recommendations  for  the 
storage  of  coal:  "The  coal  store  should  be  well  roofed  in,  and  have  an  iron 
floor  bedded  in  cement;  all  supports  passing  through  and  in  contact  with 
the  coal  should  be  of  iron  or  brick;  if  hollow  iron  supports  are  used,  they 
should  be  cast  solid  with  cement.  The  coal  must  never  be  loaded  or  stored 
during  wet  weather,  and  the  depth  of  coal  in  the  store  should  not  exceed 
8  ft.,  and  should  only  be  6  ft.  where  possible.  Under  no  condition  must  a 
steam  or  exhaust  pipe  or  flue  be  allowed  in  or  near  any  wall  of  the  store, 
nor  must  the  store  be  within  20  ft.  of  any  boiler,  furnace,  or  bench  of  retorts. 
No  coal  should  be  stored  or  shipped  to  distant  points  until  at  least  a  month 
has  elapsed  since  it  was  brought  to  the  surface.  Every  care  should  be  taken 
during  loading  or  storing  to  prevent  breaking  or  crushing  of  the  coal,  and 
on  no  account  must  a  large  accumulation  of  small  coal  be  allowed.  These 
precautions,  if  properly  carried  out,  would  amply  suffice  to  entirely  do 
away  with  spontaneous  ignition  in  stored  coal  on  land." 

When  the  coal  pile  has  ignited,  the  best  way  to  extinguish  the  fire  is  to 
remove  the  coal,  spread  it  out,  and  then  use  water  on  the  burned  part.  The 
incandescent  portion  is  invariably  in  the  interior,  and  when  the  fire  has 
gained  any  headway  usually  forms  a  crust  that  effectually  prevents  the 
water  from  acting  efficiently.  ________ 

THE  PREPARATION  OF  COAL 


CRUSHING  MACHINERY 

The  object  of  crushing  coal  is  usually  to  reduce  it  in  size  preliminary  to 
washing,  a  better  separation  of  impurities  being  secured  in  the  jig  if  the 
particles  are  of  nearly  the  same  size.  At  the  same  time  the  coal  is  crushed 
the  larger  pieces  of  slate,  sulphur,  etc.,  are  separated  by  the  action  of  the 
machine  from  the  lumps  of 
coal  and  are,  also,  more 
effectively  removed  in  the 
subsequent  washing.  In 
the  case  of  anthracite  coal 
it  is  reduced  in  size  to  meet 
the  requirements  of  trade 
which  changes  in  its  de- 
mands from  time  to  time, 
requiring  a  maximum  of 
stove  sizes  today  and  a 
maximum  of  nut  sizes  to- 
morrow, and  at  no  time 
being  able  to  consume  the 
lump  as  it  comes  from  the 
mines. 

Jaw  crushers,  ball  and 
tube  mills,  stamps,  etc., 
commonly  employed  in 
metallurgical  operations  do 
not  find  a  place  in  coal 
preparation.  Coal  is 
almost  invariably  broken 
down  in  size  by  some  form 
of  rolls,  a  few  forms  of  which  arei  . 

Cracking  Rolls.— This  is  a  general  name  applied  to  rolls  having  t( 
which  are  usually  made  separate  and  inserted.     These  rolls,  Fig.  1,  are  ei 
ployed  for  breaking  the  coal,  the  object  being  to  break  the  material  into 
angular  pieces  with  the  smallest  possible  production  of  very  fine  materia  1. 
The  principal  field  for  cracking  rolls  is  in  the  preparation  of  anthracite  coal, 
and  the  exact  style  or  design  of  the  roll  depends  largely  on  the  physical  con- 
dition of  the  coal  under  treatment.     In  most  cases  the  rolls  are  constructs 
with  an  iron  cylinder  having  steel  teeth  inserted,  the  size,  spacing,  and  form 
of  the  teeth  depending  on  the  size  and  physical  condition  of  the  material  to 
be  broken      Cracking  rolls  vary  from  12  to  48  in.  in  diameter  and  from  24 


pIG_ 


950 


THE  PREPARATION  OF  COAL 


to  36  in.   in  face  width.     The  teeth  of  the  larger  sizes  are  from  3  to  3£  in. 
high,  and  of  the  smaller  1  in.  or  less. 

The  average  practice  in  the  anthracite  regions  of  Pennsylvania  is  to  give 
the  points  of  the  teeth  a  speed  of  about  1,000  ft.  per  min.,  though  the  speed 
in  different  cases  varies  from  750  to  1,200  ft.  per  min.  One  of  the  largest 
anthracite  companies  has  a  standard  roll  speed  of  97.5  R.  P.  M.  for  the  main 
rolls  and  124.5  R.  P.  M.  for  the  pony  rolls.  The  harder  the  coal  the  faster 
the  rolls  can  be  run.  If  run  slow  and  overcrowded,  the  rolls  will  make  more 
culm  than  when  driven  at  a  proper  speed.  One  advan- 
tage of  comparatively  fast  driven  rolls  is  that  the  higher 
speed  has  a  tendency  to  free  the  rolls  by  throwing  out, 
by  centrifugal  force,  any  material  lodged  between  the 
teeth.  In  one  test  it  was  found  that  less  fine  coal  was 
produced  at  800  ft.  per  min.,  but  that  the  rolls  blocked 
at  this  speed  and  hence  had  to  be  driven  1,000  ft.  per 
min. 

In  one  case  a  pair  of  main  rolls  24  in.  in  diameter, 
36  in.  face,  running  at  1,000  ft.  per  min.,  handled  2,500 
T.  of  coal  in  24  hr.    A  pair  of  19  in.  X  24  in .  main  rolls  run 
at  1,000  ft.  per  min.  handled  300  T.  mine  run  in  10  hr. 
A  well-known  maker  of  rolls  for  crushing  bituminous 
coal  gives  a  speed  of  100  to  150  R.  P.  M.,  according  to 
the  output  required,  for  rolls  24  in.  in  diameter  and  33 
in.  long.  .  As  a  rule,  cracking  rolls  are  never  run  up  to 
their  full  capacity,  as  is  the  case  with  crushing  rolls. 
The  form  of  the  teeth  varies  greatly,  but,  as  a  rule,  the  larger  rolls  have 
straight  pointed  teeth  of  the  sparrow-bill  or  some  similar  form,   Pig.  2a. 
The  old  curved,  or  hawk-billed,  teeth,  Fig.  2&,  have  now  gone  almost  wholly 
out  of  use. 

On  small  sized  rolls,  rectangular  teeth  with  a  height  equal  to  one  side  of 
the  square  base  are" frequently  employed,  and  these  may  be  cast  in  segments 
of  manganese  or  chrome  steel. 

Corrugated  rolls  have  teeth  or  corrugations  extending  their  entire  length. 
They  were  first  introduced  by  Mr.  E.  B.  Coxe,  at  Drifton,  Pa.,  but  they 
have  not  come  into  general  use  owing  to  the  fact  that,  while  they  break  some 
coal  fairly  well,  in  most  cases  it  has  been  found  that  a  continuous  edge  causes 
too  much  disintegration  along  its  length,  while  a  point  splits  the  coal  into 
three  or  four  pieces  only,  all  the  cracks 
radiating  from  the  place  where  the  point 
strikes,  thus  producing  very  much  less 
culm.  Another  advantage  possessed  by 
the  toothed  rolls  is  that  if  anything  hard 
passes  through  the  corrugated  roll  and 
breaks  out  a  piece  of  the  corrugation, 
the  entire  roll  is  ruined,  while,  in  the 
case  of  the  toothed  rolls,  any  one  of  the 
teeth  may  be  replaced. 

Disintegrating  rolls  and  pulverizers 
are  sometimes  used  to  reduce  coking  coal 
to  the  size  of  corn  or  rice  before  intro- 
ducing it  into  the  ovens.  One  roll  is 
driven  at  double  the  speed  of  the  other, 
the  slower  roll  acting  as  a  feed-roll,  and 
the  other  as  a  disintegrator.  The  slower 
roll  is  commonly  driven  at  from  1,800  to 
2,000  ft.  per  min.  peripheral  speed,  and 
the  faster  roll  at  from  3,600  to  4,000  ft. 
per  min.  The  teeth  are  always  fine, 
rarely  being  over  f  in.  high.  In  some  cases,  the  inner  roll  is  provided  with 
a  series  of  saw  teeth  from  J  in.  to  |  in.  high  and  haying  about  f-in.  pitch, 
the  individual  teeth  being  set  so  as  to  form  a  slight  spiral  about  the  body  of 
the  roll.  The  other  roll  is  provided  with  teeth  having  their  greatest  dimen- 
sion in  the  direction  of  rotation,  so  that  they  tend  to  cross  the  teeth  on  the 
opposite  roll.  These  teeth  are  also  set  so  as  to  form  a  slight  spiral,  and  thus 
prevent  blocking.  In  other  cases,  the  teeth  on  both  rolls  are  set  in  the  form 
of 


FIG.  3 


Lammers. — For  the  reduction  of  coal,  crushers  employing  hammers  have 
been  used,  Fig.  3.     The  crushing  chamber  is  usually  of  a  circular  or  barrel 


THE  PREPARATION  OF  COAL 


951 


form,  and  the  crushing  is  done  by  means  of  hammers  pivoted  about  a  central 
shaft.  These  swing  out  by  centrifugal  force  and  strike  blows  upon  the  coal 
to  be  broken.  When  it  is  reduced  sufficiently  fine,  it  is  discharged  through 
bars  or  gratings  at  the  lower  portion  of  the  machine.  This  style  of  machinery 
is  usually  employed  in  preparing  coal  for  coke  ovens,  thus  occupying  the  same 
field  as  the  disintegrating  rolls.  A  No.  3  pulverizer  of  this  type  will  crush 
50  to  75  T.  per  hr.  run  of  mine,  down  to  f  in.,  or  it  will  crush  100  T.  per  hr.  of 
slack.  Such  a  machine  occupies  about  8  sq.  ft.  of  floor  space  and  requires 
25  to  30  H.  P.  to  run  it. 

Miscellaneous  Forms  of  Crushers. — Most  crushers  can  be  classed  under 
one  of  the  previous  heads,  but  there  are  some  forms  that  depend  on  the 
material  itself  to  do  the  crushing.  For  instance,  in  the  preparation  of  coal 
for  coke  ovens,  there  has  been  a  combined  crusher  and  separator  invented 
that  may  be  described  as  follows:  A  large  horizontal  drum  or  cylinder, 
provided  with  screen  openings  around  its  periphery,  is  mounted  in  a  hori- 
zontal position.  The  coal  to  be  separated  is  fed  into  one  end  and  is  caught 
by  shelves  or  plates  projecting  radially  into  the  cylinder.  These  lift  the 
material  to  the  upper  side,  from  which  it  falls  by  gravity  and  strikes  the 
bottom,  thus  crushing  the  softer  parts.  The  sulphur  and  slate,  being  harder 
than  the  coal,  are  not  crushed  by  the  same  height  of  fall,  and  hence,  by  a 
proper  adjustment  of  the  diameter  of  the  cylinder,  the  coal  may  be  crushed 
and  discharged  through  the  screen  while  the  slate  and  sulphur  will  pass  out 
at  the  opposite  end  of  the  cylinder. 

SIZING  AND  CLASSIFYING  APPARATUS 
Stationary  Screens,  Grizzlies,  Head-Bars,  or  Platform  Bars. — These  are 

the  various  names  given  to  an  inclined  screen  employed  for  removing  the 

fine  material  from  the  run  of  mine  so  that  only 

the  coarse  portion  will  be  passed  to  the  crushers. 

At  concentrating  works  always  and  sometimes 

at  anthracite  coal  breakers,  the  term  grizzly  is 

employed,  and  a  common  form  is  shown  in  Fig. 

4.     This  is  composed  of  flat  bars  held  apart  by 

cast-iron  washers  through  which  the  bar  bolts 

are  passed  to  hold  the   entire   frame  together. 

Grizzlies  are  usually  placed  at  an  angle  of  from 

45°  to  55°,  and  ordinarily  they  are  from  3  to  6 

ft.  wide  and  from  8  to  12  ft.  long,  the  amount  of 

space  between  the  bars  depending  on  the  size  of  FIG.  4 

the  run-of-mine  material  and  on  its  subsequent 

treatment. 

In  the  anthracite  coal  breakers,  the  terms  platform  bars  or  head-bars  are 

usually  employed,  and  these  bars  are  made  of  H-in.  to  2-in.  round  iron  placed 
at  an  inclination  of  5  in.  to  1  ft.,  the  spacing  depending  on 
the  size  of  coal  it  is  desired  to  make  in  the  breaker. 

A  standard  size  for  a  bituminous  lump  screen  (the  bars 
are  called  a  screen)  for  Ohio,  Pennsylvania,  Indiana,  and 
Illinois  is  12  ft.  long  and  6  ft.  wide  over  the  screen  surface. 
The  screen  consists  of  6  bearing  bars  4  in.  by  |  in.  of  soft 
steel  and  39  steel  screen  bars,  Fig.  5,  with  H  m.  clear  space 
between  bars.  In  Iowa,  the  same  sized  bar  is  used,  but  the 
space  between  the  bars  is  If  in.  In  the  other  Western  and 
Southern  States  there  is  apparently  no  standard. 

Adjustable  Bars. — The  top  of  the  bar  is  cylindrical  and 
projects  beyond  the  web  which  supports  it,  so  that  any 
lump  which  passes  through  the  upper  part  will  fall  freely 
without  jamming.  The  two  ends  of  the  bar  are  V-shaped 
and  fit  into  similarly  shaped  grooves,  so  that  the  bars  can 
be  set  at  distances  from  each  other  varying  with  the  sum 
of  the  width  of  the  bases  of  the  triangles',  the  usual  opening 
being  about  4  in.  These  bars  are  generally  4  ft.  long,  but 
FIG.  5  they  can  be  of  any  size. 

Finger  bars  are  screen  bars  that  are  fixed  at  one  end  only, 

and  the   bars   are   narrower  at  the  lower  end  than  at  the  top,  so  that 

spaces  between  them  are  wider  at  the  bottom  than  at  the  top,  thus  giving 

less  tendency  for  pieces  of  material  to  become  wedged  between  the  bars. 
Movable  or  oscillating  bars  are  screen  bars  that  are  attached  to  eccentrics 

at  their  lower  ends,  the  eccentrics  of  adjoining  bars  being  placed  180   apart. 


952 


THE  PREPARATION  OF  COAL 


This  movement  throws  the  material  forward  and  the  bars  do  not,  therefore 
require  nearly  the  same  inclination  as  fixed  bars. 

Shaking  screens  have  an  advantage  in  that  the  entire  area  of  the  screen 
is  available  for  sizing,  and  hence  a  greater  capacity  can  be  obtained  from  a 
given  area  of  screening  surface.  They  also  occupy  less  vertical  height  than 
a  revolving  screen.  In  coal  breakers  they  are  particularly  applicable  where 
the  coal  is  wet  and  has  a  tendency  to  stick  together.  The  principal  disad- 
vantage of  the  shaking  screen  is  that  the  reciprocating  motion  imparts  a 
vibration  to  the  framing  of  the  building.  For  anthracite  coal,  the  screens 
usually  have  an  angle  or  pitch  of  from  \  in.  to  2  in.  per  ft.,  the  average  being 
about  |  in.  per  ft.  These  screens  are  run  at  from  90  to  280  shakes  per  min., 
the  average  being  about  200  shakes  per  min.  or  100  rev.  per  min.  for  the 
camshaft.  The  throw  of  the  eccentric  or  cam  varies  from  2  in.  to  5  in. 

The  capacities  of  shaking  screens  operating  ®n  anthracite  coal  have  been 
given  as  follows.  The  parties  giving  these  figures  advise  the  use  of  140 
R.  P.  M.  for  the  camshaft. 

For  broken  and  egg  coal,  i  sq.  ft.  per  T.  for  10  hr. 

For  stove  and  chestnut  coal,  $  sq.  ft.  per  T.  for  10  hr. 

For  pea  and  buckwheat  coal,  i  sq.  ft.  per  T.  for  10  hr. 

For  birdseye  and  rice,  1J  sq.  ft.  per  T.  for  10  hr. 

Size  of  Mesh. — The  following  perforations  have  been  adopted  by  two  of 
the  largest  anthracite  coal  companies  as  the  dimensions  for  the  holes  in 
shaking  screens  to  produce  sizes  equivalent  to  those  produced  by  revolving 
screens : 

MESH  FOR  SHAKING  SCREENS 


Kind  of  Coal 

Lehigh  Valley 
Coal  Co. 

Phila.  &  Reading 
Coal  &  Iron  Co. 

Kind  of  Coal 

Round, 
In. 

Round, 
In. 

Square, 
In. 

Steamboat 

4 
3 
2 
1 

.,'.  ' 

«r 

\ 

5 
4 
2| 
2 

'! 

Steamboat. 
Large  broken. 
Small  broken. 
Egg. 
Stove. 
Chestnut. 
Pea. 
Buckwheat. 
Rice. 

Lump  
Broken  

4* 
3J 

I  ,•:::;•; 

Eecr 

Stove  

Chestnut  
Pea  
Buckwheat  
Rice  

Revolving  Screens,  or  Trommels. — The  screen  is  placed  about  the  pe- 
riphery of  a  cylinder  or  frustum  of  a  cone.  The  material  to  be  sized  is  intro- 
duced at  one  end;  the  small  size  passes  through  the  screen,  and  the  other 
size  is  discharged  from  the  other  end.  If  the  form  is  cylindrical,  it  is  neces- 
sary to  place  the  supporting  shaft  on  an  incline  so  that  the  material  will 
advance  towards  the  discharge  end.  The  inclination  of  the  shaft  determines 
the  rapidity  with  which  the  material  will  be  carried  through  the  screen. 
The  advantage  of  the  conical  screen  is  that  the  shaft  is  horizontal  and  hence 
the  bearings  are  simpler.  This  is  a  very  decided  advantage  in  many  plants 
where  the  machinery  must  of  necessity  be  crowded  into  a  minimum  space 
and  be  hard  to  get  at. 

Revolving  screens  are  frequently  jacketed,  that  is,  two  or  more  screens 
are  placed  concentrically  about  the  same  shaft,  the  inmost  one  being  the 
coarsest,  and  each  succeeding  screen  serving  to  make  additional  separations. 
This  method  reduces  the  space  necessary  for  a  given  amount  of  sizing 
machinery.  In  other  cases,  a  long  cylindrical  screen  has  a  coarse  mesh  near 
its  discharge  end  and  finer  mesh  near  the  entrance  end,  thus  making  two  or 
more  through  products  as  well  as  the  overproduct.  The  disadvantage  of 
jacketed  screens  is  that  the  necessarily  slow  speed  of  the  inmost  screen 
reduces  the  capacity  of  the  entire  combination,  so  that  if  rapid  work  is 
essential,  it  is  better  to  use  fairly  large-diameter  screens  placed  one  after  the 
other  in  place  of  jacketed  screens.  Another  disadvantage  is  that,  to  renew 
the  inner  jackets,  it  is  often  necessary  to  remove  the  outer  ones. 


THE  PREPARATION  OF  COAL  953 

The  disadvantages  of  having  two  or  more  sizes  of  wire  cloth  on  one  screen 
are  that  the  fine-meshed  screen  near  the  head  is  worn  out  rapidly,  as  all  the 
material  both  coarse  and  fine  passes  over  it,  while,  when  separate  screens 
are  employed,  each  screen  has  to  deal  with  its  through  or  oversized  prod- 
uct, all  coarser  material  having  been  removed. 

Speed. — The  periphery  of  a  revolving  screen  should  travel  about  200  ft. 
per  min.  In  the  case  of  very  fine  material,  screens  are  sometimes  run 
faster  than  this. 

The  following  have  been  adopted  as  standard  speeds  for  screens  by  one 
of  the  largest  anthracite  coal  companies: 

SPEED  OF  SCREENS 
Rev.  per  Min.  Rev.  per  Min. 

Mud  screens 8.87     Big  screens 8.52 

Counter  mud  screens ....    15 . 49     Pony  screens 10 . 87 

Cast-iron  screens 1 1 . 25     Buckwheat  screens 15 . 30 

Duty  of  Anthracite  Screens. — The  following  table  gives  the  number  of 
square  feet  of  screen  surface  required  for  a  given  duty  in  the  case  of  revolv- 
ing screens  working  upon  anthracite  coal: 


Egg  coal, 
Stove  coal, 
Chestnut  coal, 
Pea  coal, 
Buckwheat  coal, 
Rice  coal, 
Culm, 


T.  per  1  sq.  ft.  per  10  hr. 
T.  per  U  sq.  ft.  per  10  hr. 
T.  per  1£  sq.  ft.  per  10  hr. 
T.  per  2  sq.  ft.  per  10  hr. 
T.  per  2|  sq.  ft.  per  10  hr. 
T.  per  3f  sq.  ft.  per  10  hr. 
T.  per  5  sq.  ft.  per  10  hr. 


These  figures  may  be  reduced  from  20  %  to  30  %  for  very  dry  or  washed 
coal. 

Revolving  Screen  Mesh  for  Anthracite. — A  standard  mesh  for  revolving 
screens  for  sizing  anthracite  coal  was  adopted  some  years  ago,  but  it  is  only 
approximately  adhered  to  and  a  considerable  variation  from  the  standard  is 
found  throughout  the  anthracite  region. 

The  following  are  probably  as  nearly  standard  meshes  for  revolving 
screens  for  sizing  anthracite  coal  as  can  be  given: 

MESH  FOR  SIZING  COAL 
Culm  passes  through  &-in.  mesh 


Birdseye  passes  over 

Buckwheat  passes  over 

Pea  passes  over 

Chestnut  passes  over 

Stove  passes  over  Ij 


-in.  mesh,  and  through  f^-in.  mesh, 
-in.  mesh,  and  through    5-in.  mesh. 


-in.  mesh,  and  through    f-in.  mesh, 
-in.  mesh,  and  through  If-in.  mesh. 


&-in- 
5-in. 
f-in. 

if-in. 


-in.  mesh,  and  through  2  -in.  mesh. 
Egg  passes  over  2  -in.  mesh,  and  through  2f-in.  mesh. 

*  Grate  passes  over  2|-in.  mesh,  and  out  end  of  screen. 

*  Special  grate          passes  over  3  -in.  mesh;  and  out  end  of  screen. 

*  Special  steamboat  passes  over  3  -in.  bars,   and  through  6-in.  bars. 
Hydraulic    Classifiers. — The    separation    of    materials    by    this    class    of 

machinery  depends  upon  the  law  of  equally  falling  bodies,  which  may  be 
stated  as  follows:  Bodies  falling  free  in  a  fluid,  fall  at  a  speed  proportional 
to  their  weight  divided  by  the  resistance.  From  this  it  will  be  seen  that  small 
masses  of  a  heavy  mineral  will  fall  as  rapidly  as  large  masses  of  a  light 
mineral,  owing  to  the  fact  that  the  weight  increases,  as  the  volume  and  the 
resistance  only  as  the  area,  so  that  if  a  quantity  of  iron  pyrites  and  coal  of 
various  sizes  were  introduced  into  water,  it  would  settle  into  approximate 
layers,  each  composed  of  relatively  large  pieces  of  coal  and  relatively  small 
pieces  of  iron  pyrites.  This  same  action  would  be  true  in  the  case  of  any 
minerals  differing  in  specific  gravity. 

The  Jeffrey-Robinson  coal  washer,  Pig.  6,  which  operates  on  the  principle 
of  the  Spitzkasten,  consists  of  a  steel  chamber  B  in  the  form  of  an  inverted 
cone,  inside  of  which  are  projecting  arms  and  stirring  plates  C,  C  revolved 
by  a  driving  gear  A.  The  water  supply  enters  at  the  bottom  from  the  water 
pipe  P  through  perforations  M.  The  coal  is  introduced  through  a  chute  5 
and  is  kept  in  a  continual  state  of  agitation  by  the  current  of  water,  and  being 
lighter  than  the  impurities,  it  passes  out  through  the  overflow  K  onto  the 
conveyors  E,  F  and  through  the  chutes  X,  X,  while  the  water  and  sludge 

*  These  sizes  and  "lump"  size  are  seldom  made,  and  there  is  no  uniformity 
whatever  in  the  sizes  called  by  these  names. 


954 


THE  PREPARATION  OF  COAL 


drain  through  the  hopper  into  the  sludge  tank  G,  whence,  if  necessary,  the 
same  water  can  be  again  pumped  by  the  pulsometer  H  back  into  the  washer. 
(As  mentioned  elsewhere,  it  is  poor  practice  to  use  this  water  over  again 
when  it  is  desired  to  decrease  the  percentage  of  sulphur  in  the  washed 
product  as  greatly  as  possible.) 

The  heavy  impurities  sink  to  the  bottom  into  the  chamber  J  and  when 
this  is  full  the  upper  of  the  two  valves  shown  is  closed  and  the  lower  valve  is 
opened  to  discharge  the  refuse. 

The  following  data  in  regard  to  one  of  these  washers  is  given  by  Mr. 
J.  J.  Ormsbee  in  the  Transactions  of  the  A.  I.  M  E.  These  results  were 
obtained  at  the  Pratt  Mines,  Alabama,  with  a  plant  having  a  nominal 

capacity  of  400  T.  per  day. 
By  washing  slack  that 
passed  between  screen 
bars  placed  \  in.  in  the 
clear,  the  washed  coal  con- 
tained 42  %  less  ash  than 
the  unwashed  coal,  the  re- 
duction in  sulphur  was 
15%,  while  ^  the  volatile 
matter  was  increased  4%, 
and  the  fixed  carbon  5%. 
With  coal  passing  overf-in. 
perforations,  the  results 
were  a  reduction  of  48  %  in 
ash,  15  %  in  sulphur,  and  a 
gain  of  5  %  in  volatile  mat- 
ter and  6  %  fixed  carbon. 
These  results  indicate  that 
the  washer  is  better 
adapted  to  large  sizes  than 
to  fines.  The  amount  of 
water  used  per  ton  of 
washed  coal  was  35.1  gal. 
FIG.  6.  and  the  cost  was  2.25  c. 

per  T.  for  washing  400  T., 

itemized  as  follows:  Labor  at  washer,  $2.00;  labor  at  boiler,  fuel, -etc.,  $4.00; 
repairs  and  supplies,  $3.00;  total,  $9.00. 

The  Scaife  trough  washer  consists  of  a  semicircular  iron  trough  2  ft. 
in  diameter  and  24  ft.  long.  Inside  is  a  series  of  fixed  dams  or  partitions 
that  can  be  made  higher  or  lower,  as  required,  by  means  of  plates.  A  shaft 
running  the  entire  length  of  the  trough  and  turning  in  babbitted  journals 
carries  a  number  of  stirring  arms  or  forks  and  is  given  a  reciprocating  motion 
by  a  connecting  rod  attached  to  a  driving  pulley  at  its  center.  The  coal 
is  fed  with  water  at  the  upper  end  of  the  trough,  and  by  the  action  of  the 
flowing  water  and  the  agitation  of  the  arms,  the  slate,  pyrites,  and  other 
impurities  settle  at  the  bottom  and  are  caught  behind  the  dams,  while  the 
clean  coal  passes  over  the  dams  and  out  at  the  lower  end  of  the  trough. 
When  the  spaces  behind  the  dams  are  filled,  feeding  is  stopped  and  the 
refuse  in  the  dams  quickly  dumped.  This  form  of  washer  is  particularly 
successful  with  coal  mixed  with  fireclay.  One  washer  handles  from  75  to 
100  T.  of  coal  per  day,  and  one  man  can  attend  to  six  washers.  Each 
washer  requires  less  than  1  H.  P.  to  operate  it.  The  larger  the  coal,  the 
greater  must  be  the  slope  and  the  quantity  of  water  used. 

Jigs. — This  is  a  general  term  applied  to  that  class  of  machines  in  which  the 
separation  of  the  mineral  from  the  impurities  takes  place  on  a  screen  or  bed 
of  material  and  is  effected  by  pulsating  up-and-down  currents  of  a  fluid 
medium. 

There  are  a  number  of  different  methods  in  use  for  driving  the  pistons 
that  cause  the  pulsations  of  the  water  in  jigs.  Some  of  these  use  plain 
eccentrics,  giving  the  same  time  to  both  the  up  and  the  down  strokes  of  the 
pistons,  while  others  employ  special  arrangements  of  parts,  which  give  a 
quick  down  stroke  and  a  slow  up  stroke,  thus  allowing  the  water  ample 
time  to  work  its  way  back  through  the  bed  without  any  sucking  action 
from  the  piston.  This  tends  to  make  a  better  separation  in  some  cases  than 
the  use  of  the  plain  eccentrics. 

Stationary  Screen  Jigs. — This  class  is  illustrated  by  Fig.  7,  which  shows  a 
3-compartment  jig.  The  separation  takes  place  on  screens  supported  on 


THE  PREPARATION  OF  COAL 


955 


wooden  frames  g,  and  is  effected  by  moving  the  water  in  each  compartment 
so  that  it  ascends  through  the  screen,  lifting  the  mineral  and  allowing  it  to 
settle  again,  thus  giving  the  material  an  opportunity  to  arrange  itself  accord- 
ing to  the  law  of  equally  falling  particles.  Each  compartment  is  composed 
of  two  separate  parts,  one  containing  the  screen  on  the  support  g  and  the 
other  adjoining  it  and  arranged  so  that  the  piston  in  it  may  impart  the 
necessary  pulsations  to  the  water.  These  pistons  are  equally  loose  fitting 


and  are  operated  by  the  eccentrics  e  on  the  shaft  s.  Jigs  should  be  fed  with 
approximately  sized  material,  when  the  impurities  will  accumulate  near  the 
bottom  on  the  screen  and  the  coal  will  be  carried  over  the  discharge. 

The  Heberle  gate,  Fig.  8,  acts  as  follows:  a  is  a  U-shaped  shield  fastened 
against  the  inside  of  the  jig  and  held  in  place  by  a  band  b,  the  ends  of  which 
are  drawn  down  into  the  form  of  bolts  and  pass  through  the  sides  of  the  jig, 
where  they  are  secured  with  suitable  nuts.  The  shield  a  may  be  raised  or 
lowered  by  loosening  the  band  6.  The  dis- 
charge takes  place  through  the  opening  /  in 
the  side  of  the  jig,  the  size  and  position  of 
the  opening  being  regulated  by  slides  c.  The 
impurities  k  rest  on  the  screen  e  supported  by 
a  grating  d,  while  the  coal  i  occupies  a  higher 
position.  The  shield  a  prevents  the  coal 
from  flowing  out  through  the  opening/,  while 
the  impurities  flow  along  the  screen  and  rise 
to  a  height  somewhat  lower  than  the  top  of 
the  coal  in  the  jig,  when  they  are  discharged 
through  the  opening  /  over  the  spout  h,  as 
shown  at  p.  The  coal  is  usually  discharged 
over  the  dam  at  the  end  of  the  jig. 

Theory  of  Jigging. — By  far  the  most  ex- 
haustive investigations  on  the  theory  of  jig- 
ging carried  on  in  America  are  those  of  Prof. 
Robert  H.  Richards,  of  the  Massachusetts 
Institute  of  Technology,  and  the  greater  part 
of  the  following  theoretical  discussion  is 
based  on  his  several  papers  published  in  the 
Institute  of  Mining  Engineers. 


FIG.  8 
Transactions  of  the  American 


Four  laws  of  jigging  are  given  by  the  several  authorities:  (1)  The  law  of 
equal  settling  particles,  under  free  settling  conditions;  (2)  the  law  of  inter- 
stitial currents,  or  settling  under  hindered  settling  conditions;  (3)  the  law 
of  acceleration;  (4)  the  law  of  suction. 

The  first  of  these  is  the  most  important,  but  the  others  are  elements  that 
cannot  be  disregarded  in  connection  with  jigging. 

Equal  Settling  Particles. — Rittinger  gives  the  following  formulas  to  repre- 
sent the  relation  between  diameter  of  grains  and  rate  of  falling  in  water  for 
irregularly  shaped  grains: 


956 


THE  PREPARATION  OF  COAL 


V  =  2.73\/£>(a  —  1),  for  roundish  grains; 

V  =  2A4\fD(6—  1).  for  average  grains; 

y  =  2.37\/P(g-l).  for  long  grains; 

F  =  1.92V#(«-1),  for  flat  grains, 

in  which   V  =  velocity  in  meters  per  second;  D  =  diameter  of  particles  in 
meters,  and  d  =  specific  gravity  of  the  minerals. 

By  means  of  these  different  formulas,  the  ratios  of  the  diameters  of 
different  particles  that  will  be  equal  settling  in  water  can  be  computed. 
Professor  Richards  has  not  found  these  formulas  to  hold  in  all  cases  in  prac- 
tice, and,  as  the  result  of  elaborate  experiments,  he  gives  the  following  table: 

EQUAL  SETTLING  FACTORS  OR  MULTIPLIERS 

Table  of  equal  settling  factors  or  multipliers  for  obtaining  the  diameter  of 
a  quartz  grain  that  will  be  equal  settling  under  free  settling  conditions  with 
the  mineral  specified. 


£ 

Velocity  in  Inches  per  Second 

1 

if 

• 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

o 

id 

4J  """* 

1 

Author's  Multipliers 

•  1-4      3 

Anthracite  .  . 

1.473 

.500 

.352 

.225 

.213 

.288 

Epidote  

3.380 

1.57 

1.35 

.05 

.13 

1.50 

1.61 

1.56 

1.56 

1.47 

1.45 

Sphalerite.  .  . 
Pyrrhotite.... 

4.046 
4.508 

1.46 
1.73 

.05 
.29 

.17 

.48 

1.62 
2.00 

1.64 
2.22 

1.68 
2.26 

1.66 
2.13 

1.56 

2.08 

1.85 
2.14 

Chalcocite.... 

5.334 

1.90 

.47 

.62 

2.07 

2.28 

2.41 

2.44 

2.17 

2.64 

Arsenopyrite 

5.627 

1.90 

.57 

.89 

2.42 

2.56 

2.72 

2.84 

2.94 

2.82 

Cassiterite..  . 

6.261 

2.11 

.79 

2.00 

2.73 

2.93 

3.03 

3.05 

3.12 

3.32 

Antimony.  .  . 

6.706 

2.71 

.00 

2.00 

2.73 

2.93 

3.03 

2.98 

3.00 

3.48 

Wolframite.  . 

6.937 

2.71 

.83 

2.07 

2.86 

3.04 

3.21 

3.28 

3.26 

3.64 

Galena  

7.856 

2.71 

.83 

2.26 

3.00 

3.42 

3.65 

3.76 

3.75 

4.01 

Copper  

8.479 

2.71 

2.00 

2.36 

3.00 

3.20 

3.58 

3.76 

3.75 

4.56 

Quartz  

2.640 

The  significance  of  the  above  table  is  as  follows:  If  a  piece  of  anthracite 
of  a  certain  size  falls  in  water  with  a  velocity  of  4  in.  per  sec.,  a  piece  of  quartz 
.213  times  the  diameter  of  the  anthracite  will  fall  with  the  same  velocity. 
If  a  piece  of  copper  of  a  certain  size  falls  with  a  velocity  of  7  in.  per  sec.,  a 
piece  of  quartz  3.58  times  as.  large  as  the  copper  will  fall  with  the  same 
velocity. 

Interstitial  Currents,  or  Law  of  Settling  under  Hindered  Settling  Condi- 
tions.— If  d  equals  the  diameter  of  a  falling  particle,  and  D  that  of  the  tube 

in  which  it  falls,  the  larger  the  fraction  ^,  the  greater  will  be  the  retardation 

/ — N.    x~N  or  loss  of  a  velocity  by  the  particle. 

(        J  (       )  When  this  fraction  equals  1,  the  parti- 

V__/OV /  s^-~^  cle  stops.     If,  in  Fig.  9  (a),  the  larger 

©circles  represent  say  particles  of  quartz 
and    the  smaller  circles  equal  settling 
particles  of  galena,  then  if  these  mixed 
fb)  particles    are   settling  together  or  are 

held  in  suspension  by  a  rising  current 
of  water,  each  particle  may  be  consid- 
ered to  be  falling  in  a  tube,  the  walls  of 
which  cpnsist  of  the  surrounding  particles.  Substituting  a  circle  in  each  case 
for  the  imaginary  tube,  we  have  Fig.  9  (b)  representing  the  conditions  for 
galena  and  quartz,  the  outer  circle  in  each  case  representing  the  imaginary 

tube.     Evidently, r  is  much  smaller  for  the  galena  than  for  the  quartz,  and 


x 't» — s 

QUO 
O°O 


(a) 


FIG.  9 


THE  PREPARATION  OF  COAL  957 

it  will  therefore  be  much  less  impeded  in  its  fall  than  the  quartz;  hence,  the 
particles  of  galena  found  adjacent  to  the  particles  of  quartz  will  be  smaller 
than  the  ratio  that  the  law  of  equal  settling  particles  under  free  settling  con- 
ditions would  indicate.  Application  of  this  principle  is  found  when  a  mass  of 
grains  is  subjected  to  a  rising  current  of  sufficient  force  to  rearrange  the 
grains  according  to  their  settling  power  and  the  grains  are  said  to  be  treated 
under  hindered  settling  conditions,  as  on  the  bed  of  a  jig. 

Interstitial  factors,  or  multipliers  for  obtaining  the  diameter  of  the  particle 
of  quartz  that  under  hindered  settling  conditions  will  be  found  adjacent 
to  and  in  equilibrium  with  the  particle  of  the  mineral  specified,  are  the 
following: 

Copper 8.598     Cassiterite . . .   4.698     Pyrrhotite. .   2.808 

Galena 5.842     Arsenopyrite.  3.737     Sphalerite....  2.127 

Wolframite...    5.155     Chalcocite. . .   3.115     Epidote 1.628 

Antimony 4.987     Magnetite...    2.808     Anthracite..      .1782 

These  signify  that,  after  pulsion  has  done  its  work  on  a  jig  bed,  for  exam- 
ple, where  quartz  and  anthracite  are  being  jigged,  the  grains  will  be  so 
arranged  that  the  grains  of  quartz  are  .1782  times  the  diameter  of  the  grains 
of  anthracite  that  are  adjacent  to  and  in  equilibrium  with  them. 

Acceleration. — A  particle  of  galena  that  is  equal  in  settling  to  the  particle  of 
quartz  reaches  its  maximum  velocity  in  perhaps  one-tenth  the  time  required 
by  the  quartz.  The  oft-repeated  pulsations  of  a  jig,  therefore,  give  the 
galena  particles  a  decided  advantage  over  the  quartz,  placing  beside  the 
quartz,  when  equilibrium  is  reached,  a  much  smaller  particle  of  galena  than 
we  should  expect  according  to  the  law  of  equal  settling  particles. 

Suction  acts  to  draw  down  through  the  screen  small  grains,  mainly  of  the 
heavier  mineral,  which  are  distributed  among  large  grains.  It  increases  as 
the  length  of  plunger  stroke,  with  the  difference  in  specific  gravity  of  the  two 
minerals,  and  with  the  diminishing  of  the  thickness  of  the  bed  on  the  sieve, 
whether  of  the  heavier  mineral  only  or  of  both  minerals.  The  law  of  suction 
seems  to  be  that  jigging  is  greatly  hindered  by  strong  suction  where  the  two 
minerals  are  nearly  of  the  same  size,  the  quickest  and  best  work  then  being 
done  with  no  suction;  but  when  the  two  minerals  differ  much  in  size  or 
particles,  the  quartz  being  the  larger,  strong  suction  is  not  only  a  great  advan- 
tage, but  may  be  necessary  to  get  any  separation  at  all.  Experiments  have 
indicated  an  approximate  boundary  between  grains  that  are  helped  and 
those  that  are  hindered  by  suction;  namely,  if  the  diameter  of  the  quartz 
particles  is  equal  to  or  greater  than  3.52  times  the  diameter  of  the  other  min- 
eral particles,  then  separation  is  helped  by  suction;  if  less,  separation  is 
hindered.  This  value  3.52  is  approximate  only,  and  it  will  differ  with  the 
fracture  of  the  quartz  under  consideration;  if  the  quartz  grains  are  much  flat- 
tened, it  will  have  a  large  value. 

Removal  of  Sulphur  from  Coal. — The  object  of  washing  coal  is  to  remove 
the  slate  and  pyrites,  thus  reducing  the  amount  of  ash  and  sulphur.  Many 
forms  of  washers  easily  and  cheaply  reduce  the  slate  from  20  %  in  the  coal  to 
8  %  of  ash  in  the  coke,  but  it  is  much  more  difficult  to  reduce  4  %  of  sulphur  in 
the  coal  to  1  %  or  less  of  sulphur  in  the  coke.  Sulphur  occurs  in  the  coal  in 
three  forms,  as  hydrogen  sulphide,  calcium  sulphate,  and  pyrite.  The 
first  is  volatile  and  is  removed  in  coking,  the  second  cannot  usually  be  re- 
moved by  preliminary  treatment,  and  it  is  the  removal  of  the  third  form  with 
which  washing  has  to  do.  The  presence  of  water  in  the  coke  ovens  appar- 
ently assists  the  removal  of  the  sulphur;  but  wet  coals  require  a  longer  time 
for  coking  than  dry,  and,  therefore,  pyrite  should  be  removed  as  far  as  prac- 
ticable before  charging  the  coal  into  the  coke  ovens.  The  pyrite  in  coal  as 
it  comes  from  the  mine  seems  to  be  in  particles  even  finer  than  those  of  the 
coal  dust.  This  impalpable  powder  or  flour  pyrites  floats  in  air  or  water. 
This  being  the  case,  the  common  practice  of  using  the  water  over  and  over 
again  in  a  washery  cannot  give  the  best  results  in  the  removal  of  sulphur,  as 
some  flour  pyrites  will  be  carried  back  each  time  and  remain  with  the  washed 
coal.  Experiments  made  by  Mr.  C.  C.  Upham.  of  New  York  City,  show  that 
the  critical  size  at  which  an  almost  complete  division  of  the  coal  and  pyrites 
takes  place  varies  with  coals  from  different  districts  and  beds  and  in  laying 
out  coal-washing  plants,  the  proper  fineness  of  crushing  should  be  determim 
beforehand  by  careful  experiment. 


958 


THE  PREPARATION  OF  COAL 


PREPARATION  OF  ANTHRACITE 

Under*  the  well-known  conditions  of  the  anthracite  field,  the  general 
methods  of  preparation  may  be  summarized  under  three  classes:  namely, 
(I)  dry  "preparation;  (II)  dry  and  wet  preparation;  and  (III)  wet  prepara- 
tion; of  which  the  one  to  be  adopted  depends  on  the  quality  of  coal  to  be 
mined. 

Class  I  (Fig.  10)  is  employed  when  the  seams  of  coal  mined  are  dry,  or 
are  practically  free  from  impurities,  or  where  the  benches  of  slate  occurring 
in  the  seams  cleave  free  from  the  coal,  and  may  be  removed  during  hand 
loading,  and  the  run-of-mine  contains  generally  _ not  over  7  or  8%  of  rock 
or  slate,  which  may  be  removed  by  hand-picking  or  by  dry  mechanical 
separators. 


Lump  to  Pocket 
Crusher  Rolls-Break  Lump 
to  St.  Boat  or  Broken 


FIG.  10. 

Class  II  (Fig.  11)  is  employed  when  the  run-of-mine  contains  a  high  per- 
centage of  impurities,  including  rock,  slate,  and  bone.  This  percentage 
may  be  as  high  as  55%,  but  the  run-of-mine  must  contain  large  lumps  of 
pure  coal,  which  can  be  handled  as  a  separate  product,  as  in  the  first  class. 
The  sizes  smaller  than  lump  are  sized  and  cleaned,  using  water  to  wash  the 
product,, to  improve  its  appearance,  and  to  remove  the  impurities  by  jigging. 

Class  III  (Fig.  12)  is  adopted  when  the  run-of-mine  is  high  in  impurities 
and  shows  a  discoloration,  as  is  the  case  near  the  outcrop  of  the  vein,  or 
when  the  entire  product  comes  from  wet,  dirty  seams,  requiring  a  thorough 
washing  to  remove  the  dirt  and  discoloration. 

Class  I  presents  the  ideal  breaker,  with  the  advantages  of  low  costs  of 
installation,  operation,  and  maintenance.  Moreover,  shipments  of  dry  coal 

*  The  Preparation  of  Anthracite,  Paul  Stirling,  E.  M.  in  Trans.,  Amer. 
Inst.  Ming.  Engrs.,  vol.  XLII  (1911). 


THE  PREPARATION  OF  COAL  959 

are  very  desirable  to  the  trade,  as  they  are  free  from  the  risk  of  the  freezing 
of  coal  in  cars,  and  the  subsequent  trouble  of  unloading  it. 

Class  II  retains  to  some  extent  the  advantage  of  dry  coal-shipments,  but 
is  higher  in  first-cost,  operation,  and  maintenance  than  Class  I  or  III. 

Class  III  permits  no  dry  shipments,  and  is  higher  in  first-cost,  operation, 
and  maintenance  than  Class  I. 


CRY  PREPARATION-. 

Pure  Coal 


IG.    11. 

PREPARATION  OF  BITUMINOUS  COAL 

Sizes. — Bituminous  coal  is  not,  as  a  rule,  prepared  with  as  great  care  as  is 
anthracite.  In  some  regions  where  the  coal  is  used  mainly  as  a  domestic 
fuel  and  where  competition  is  strong  the  coal  is  carefully  sized  and  in  many 
instances  the  smaller  grades  are  washed  before  being  sent  to  market.  Un- 
like anthracite  soft  coal  ignites  with  ease  but  has  a  tendency  to  spaul  off 
small  pieces  during  the  process  of  burning.  It  is  therefore  in  most  cases 
unnecessary  to  carry  sizing  to  as  fine  a  point  as  with  hard  coal.  The  grade 
of  bituminous  which  brings  the  highest  price  is  the  lump.  There  appears  to 
be  no  fixed  rule  or  even  well-established  custom  concerning  the  sizes  .into 
which  the  run-of-mine  is  prepared.  In  general  outside  of  southern  Illinois 
not  more  than  four  or  five  grades  are  made.  These  and  their  approximate 
sizes  are  shown  on  the  following  table: 

Through  Over 

Grade  Circular  Circular 

Perforation         Perforation 

Slack f  in. 

Nut 1  5  in.  £  in. 

Egg 4   in.  lj  in. 

Lump 4    in. 

Another  grade  which  has  made  its' appearance  recently  is  called  cobble 
and  is  intermediate  between  the  egg  and  the  lump,  passing  through  a  6-m. 
to  7-in.  circular  opening  and  over  (say)  a  3£-in.  to  4-in.  circular  opening. 


960 


THE  PREPARATION  OF  COAL 


Many  other  grades  such  as  li-in.  lump,  2£-in.  lump,  etc.,  are  prepared  in 
certain  fields.  These  are  produced  either  by  passing  the  coal  over  bar 
screens  or  perforated  shaking  screens.  The  coal  which  passes  over  being 
known  as  the  lump  and  that  which  passes  through  as  slack. 

Method  of  Preparation. — Bituminous  coal  is  usually  sized  on  some  type 
of  shaking  screen,  two  general  varieties  being  in  use:  the  inclined  shaking 


le~.fi 


FIG.  12. 


screen  and  the  horizontal  screen.  The  horizontal  screen  has  only  one 
representative.  This  is  patented  and  is  known  as  the  Marcus.  The  motion 
imparted  to  the  screen  by  means  of  a  special  driving  head  is  a  reciprocation 
back  and  forth  with  a  non-uniform  rapidity,  that  is,  one  stroke  being  made 
more  quickly  than  the  other.  The  coal  is  thus  caused  to  travel  along  the 
screen  and  over  the  perforations  unaided  by  gravity.  This  type  of  screen 
may  be  readily  used  as  a  picking  table  and  possesses  some  other  advantages. 
The  inclined  shaking  screen  which  has  a  uniform  rapidity  of  oscillation  in 
both  directions  is  either  hung  from  above  or  supported  from  below.  If  hung 


THE  PREPARATION  OF  COAL  96i 

from  above,  it  may  be  suspended  either  by  links  or  cpnnecting  rods  which 
pivot  upon  pins  at  either  end  or  may  be  hung  by  flexible  wooden  supports 
rigidly  attached  at  both  top  and  bottom.  If  supported  from  below  it  is 
usually  either  placed  on  rollers  or  carried  by  flexible  wooden  supports 
similar  to  those  used  for  suspension.  Large  screens  sizing  run-of-mine  coal 
into  three  or  four  grades  are  usually  given  a  stroke  of  5  to  6  in.,  the  latter 
being  the  more  common.  The  speed  usually  varies  from  90  to  120  R.  P.  M. 
of  the  driving  shaft  and  the  inclination  of  the  screen  is  usually  about  15° 
but  this  varies  somewhat  with  the  district  where  the  coal  is  produced  on 
account  of  the  means  employed  in  mining  and  the  fracture  of  the  coal. 
Frequently  the  screening  plate  is  not  made  flat  but  in  a  series  of  steps,  each 
one  tending  to  turn  over  the  lumps  of  coal  and  dislodge  any  fines  which  may 
be  riding  thereon.  Such  screens  are  known  as  lip  screens  and  the  perfora- 
tions are  frequently  slots  instead  of  circular  openings.  The  following  table 
shows  the  inclination  of  various  fixed  screens  and  other  apparatus  over  which 
the  coal  may  slide  in  a  tipple: 

Inclination, 

Degrees 

Fixed  lip  chute  screens  for  6-in.  egg  (slot  f  X  H  in.  tapered)        30 
Fixed  lip  chute  screen  for  3-in.  nut  (slot  \  X  I  in.  tapered)        32 

Dump  chute 30 

Standard  bar  screens 28 

Weigh  pan 38 

Mine-run  chute  40  in.  diam.  (circular) 28 

Slack  hopper  and  chute 45 

Screening  Area. — The  area  of  a  shaking  screen  should  be  sufficient  to 
size  the  coal  but  not  so  large  that  the  material  is  needlessly  handled.  The 
area  of  the  various  perforated  plates  does  not  vary  directly  with  the  output 
of  the  mine.  There  is  no  means  of  calculating  the  area  necessary  but  ex- 
perience has  proved  that  the  following  sizes  of  plates  are  ordinarily  well 
adapted  to  a  tipple  handling  1,000  T.  of  coal  per  8-hr,  day  where  this  coal 
is  passed  over  a  bar  screen  or  grizzly  before  reaching  the  shaking  screens: 

lj-in.  round  perforations 96  sq.  ft. 

2J-  to  3-;n.  perforations 96  sq.  ft. 

5-  to  6-in.  circular  perforations 24  sq.  ft. 

If  no  bar  screen  is  employed  the  areas  above  given  should  be  increased  about 
30%. 

Any  screen  designed  to  prepare  2,500  T.  or  more  of  run-in-mine  run  coal 
in  8  hr.  should  be  equipped  with  a  feeder.  The  areas  of  the  screens  of  a  2,500- 
T.  mine  would  be  as  follows: 

l^-in.  circular  perforations 160  sq.  ft. 

2?-  to  3-in.  circular  perforations 160  sq.  ft. 

5-  to  6-in.  circular  perforations 40  sq.  ft. 

The  areas  of  a  screen  plate  for  a  capacity  of  4,000  T.  in  8  hr.  would  be  as 
follows: 

1  J-in.  circular  perforations 190  sq.  ft. 

2|-  to  3-in.  circular  perforations 190  sq.  ft. 

5-  to  6-in.  circular  perforations 40  sq.  ft. 

Shaker  Screens  for  Small  Sizes. — It  is  sometimes  advantageous  when 
handling  large  capacities  to  make  a  double  separation,  that  is,  screen  out 
of  the  run-of-mine  the  egg  coal  and  smaller  in  one  operation  and  then  size 
this  material  into  the  egg,  nut,  slack  and  other  grades  in  a  secondary  process. 
The  chief  difference  in  the  design  of  shaker  screens  for  handling  run-of-mine 
and  those  making  smaller  sizes  is  in  the  pitch  and  speed  of  the  screen.  Small 
coal  screens  need  not  be  given  a  pitch  in  excess  of  H  m.  in  a  foot.  The  speed 
of  such  a  screen  should  be  about  120  R.  P.  M.  of  the  driving  shaft  and  the 
throw  of  the  eccentric  or  crank  should  be  about  3  in.  Such  screens  are 
frequently  used  for  preparing  material  which  will  pass  through  a  2-in. 
circular  opening;  that  which  passes  over  this  opening  being  known  as  2-in. 
lump.  In  such  a  case  the  following  grades  are  made: 

Through  Over 

Name  of  Grade  Circular  Circular 

Perforation         Perforation 

No.  2  nut 2      in.  If     in. 

No.  3  nut H     m.  i    m. 

No.  4  pea I     m.  rs   m. 

Duff &   in.       . 

61 


962  THE  PREPARATION  OF  COAL 

Screen  Feeders. — Two  types  of  screen  feeders  are  in  general  use,  the 
reciprocating  and  the  continuous  feed.  The  reciprocating  feeder  always 
leaves  a  cushion  of  coal  in  the  hopper  for  the  succeeding  dump  to  strike, 
With  this  type  of  feeder,  however,  coal  from  two  or  three  dumps  is  mixed 
in  the  hopper  and  it  is  often  impossible  to  dock  for  impurities.  The  recipro- 
cating pan  of  such  a  feeder  oscillates  longitudinally  at  a  speed  about  60 
R.  P.  M.  of  the  driving  shaft  while  the  stroke  is  usually  about  8  in.  This 
type  of  feeder  subjects  the  coal  to  a  more  or  less  pronounced  grinding  action, 
frequently  causing  unnecessary  degradation. 

The  continuous  feeder  is  a  heavy  steel-plate  apron,  the  plates  being 
usually  beaded.  It  is  provided  with  a  dump  chute  and  hopper  at  one  end 
receiving  the  coal  from  the  weigh  pan  while  the  sides  are  from  2  to  4  ft. 
high  to  prevent  spillage.  With  this  type  of  feeder  it  is  possible  to  thoroughly 
inspect,  each  carload  of  coal  as  it  leaves  the  weigh  pan  and  docking  is  made 
easy  without  delaying  hoisting. 

Tipple  Design. — The  efficiency,  capacity  and  cost  of  sizing  coal  depends  in 
large  measure  upon  the  design  of  the  tipple  and  sizing  apparatus.  As 
reliability  is  .of  greater  importance  than  extreme  efficiency,  simplicity  should 
always  be  sought  in  the  design  of  a  bituminous  preparation  plant.  The 
arrangement  of  such  plants  differs  somewhat  in  different  localities  and  with 
the  wage  agreement  with  the  miners'  organization  if  any  exists.  Taking  the 
most  complicated  case  of  a  shaft  mine,  the  process  and  equipment  is  some- 
what as  follows: 

The  coal  is  delivered  by  self-dumping  cages  to  bar  screens  if  the  mine  is 
operated  on  a  lump  basis  or  to  the  weigh  pan  if  operated  on  a  run-of-mine 
basis.  In  the  former  instance  the  bar  screens  discharge  to  the  weigh  pan  and 
in  the  latter  instance  the  weigh  pan  discharges  to  the  bar  screens.  If 
these  screens  discharge  to  the  weigh  pan  the  screenings  pass  through  and  are 
delivered  by  chute  to  the  shaking  screens  thus  preceding  the  lump  coal. 
This  is  the  better  process  so  far  as  the  shakers  are  concerned  as  a  less  screen- 
ing area  will  be  required.  After  passing  the  shaking  screens  the  lump, 
cobble  if  any,  egg  and  frequently  nut  coal  are  picked  on  separate  picking 
tables.  The  egg  and  lump  are,  however,  frequently  picked  together  before 
final  separation  is  made.  The  larger  sizes  are  delivered  to  railroad  cars  on 
separate  tracks  either  by  telescoping  chutes,  side  shaking  chutes  or  hinged 
loading  booms  of  either  the  apron  or  belt  conveyor  type,  frequently  the 
loading  boom,  or  rather  the  horizontal  portion  of  it,  is  utilized  as  a  picking 
table.  Side  shaking  chutes  for  the  delivery  of  the  larger  sizes  often  contain 
degradation  screens  which  deliver  to  a  conveyor,  which  in  turn  discharges 
the  coal  to  the  head  of  the  sizing  screen  or  to  the  slack  car. 

Washing  Bituminous  Coal. — In  many  localities  bituminous  coal,  particu- 
larly the  smaller  sizes,  is  washed  in  order  to  remove  the  sulphur,  fire  clay, 
slate  and  other  detrimental  material.  While  differing  somewhat  in  detail, 
the  process  as  well  as  the  machinery  employed  is  similar  to  that  employed 
with  anthracite. 

HANDLING  OF  MATERIAL 

Anthracite  Coal. — The  following  may  be  taken  as  average  figures  for  the 
angle  or  grade  of  chutes  for  anthracite  coal,  to  be  used  where  the  chutes  are 
lined  with  sheet  steel:  For  broken  or  egg  coal,  2j  in.  per  ft.;  for  stove  or 
chestnut  coal,  3$  in.  per  ft.;  for  pea  coal,  4i  in.  per  ft.;  for  buckwheat  coal, 
6  in.  per  ft.;  for  rice  coal,  7  in.  per  ft.;  for  culm,  8  in.  per  ft. 

If  the  coal  is  to  start  on  the  chute,  1  in.  per  ft.  should  be  added  to  each  of 
the  above  figures;  while  if  the  chutes  are  lined  with  manganese  bronze  in 
place  of  steel,  the  above  figures  can  be  reduced  1  in.  per  ft.  for  coal  in  mo- 
tion, or  would  remain  as  stated  to  start  the  coal.  When  the  run-of- 
mine  is  to  be  handled,  as  in  the  main  chute,  at  the  head  of  the  breaker,  the 
angle  should  be  not  less  than  5  in.  per  ft.,  or  practically  22 J°  from  the  hori- 
zontal. If  chutes  for  hard  coal  are  lined  with  glass,  the  angle  can  be  re- 
duced from  30%  to  50%,  depending  somewhat  on  the  nature  of  the  coal. 
In  all  cases,  the  flatter  the  coal,  the  steeper  the  angle  must  be,  on  account  of 
the  large  fric^n  surfaces  exp9sed,  compared  with  the  weight  of  the  piece. 
If  chutes  are  lined  with  cast  iron,  the  angle  should  be  about  the  same  as 
that  employed  for  steel,  though  sometimes  a  slightly  greater  angle  is  allowed. 

The  following  tables  are  printed  through  the  courtesy  of  the  Link-Belt 
Engineering  Co.,  Philadelphia,  Pa.; 


THE  PREPARATION  OF  COAL 
WEIGHTS  AND  CAPACITIES  OF  STANDARD  STEEL  BUCKETS 


Weight 

Capacity 

Capacity  of  Elevator. 
100  Ft.  per  Min. 

Number 

Chain 

Size  of 
Bucket,  In. 

of 
Bucket, 

of 
Bucket, 

of 
Draw- 

Lb. 

Lb. 

Lb.  per 

Net  Tons 

ing 

Min. 

per  Hr. 

!  In. 
Dodge  | 

12X   9X1H 
14X    9X1H 
18X    9X11J 
24X    9X1H 

&i 

22  i 
27 
36 

11 
12* 
Id} 

22 

1,100 
1,250 
1,650 
2,200 

33.0 
37.5 
49.5 
66.0 

5,357 
5,357 
5,357 
5.357 

12X10X16J 
18X10X16* 

20 
29 

19 

28* 

1,380 
2,072 

41.4 
62.2 

5,357 
5,357 

24X10X161 

38 

38 

2,760 

82.8 

5,357 

8  in. 
Dodge 

30X10X161 
18X12X16* 

46* 
31 

47* 
33 

3,450 
2,400 

103.5 
72.0 

5.357 
5,357 

•24X12X161 
|30X12X16; 

40 

48 

44 
55 

3,200 
4,000 

96.0 
120.0 

5,357 
5,357 

Buckets  taken  f  full.     Buckets  continuous.     1  Ib.  of  coal  =  34  cu.  in. 

ELEVATING   CAPACITIES  OF  MALLEABLE  IRON  BUCKETS 
Table  gives  tons  (2,000  Ib.)  of  pea  coal  per  hour  at  100  ft.  per  min. 


Buckets 

Ca- 
pacities 

Distance  between  Buckets  in  In. 

Size, 
In. 

Wt., 
Lb. 

Cu. 
In. 

Lb. 

8 

10 

12 

14 

16 

18 

20 

22 

24 

2fX4 
3£X  5 
4X6 
4J-X  7 
5X8 
6  XIO 
7  X12 
7  X14 
10  X18 

0.75 
1.50 
2.00 
2.56 
3.56 
5.47 
8.97 
11.41 

15 

31 
51 

75 
102 
185 
287 
295 

0.48 
0.97 
1.57 
2.33 
3.15 
5.73 
8.90 
9.14 

2.16 
4.36 

7.06 
10.38 

1.73 
3.49 
5.65 
8.39 
11.34 

1.44 
2.91 
4.71 
6.99 
9.45 
17.19 

1.23 

2.49 
4.04 
5.99 
8.10 
14.73 
22.88 

1.08 

2.18 
3.53 
5.19 
7.09 
12.88 
20.02 
20.56 

1.94 
3.14 
4.66 
6.30 
11.46 
17.80 
18.28 

2.83 
4.19 
5.67 
10.31 
16.02 
16.45 

3.81 
5.15 
9.38 
14.56 
14.95 

4.72 
8.59 
13.35 
13.71 

Weight  of  1  cu.  ft.  of  pea  coal  =  53.5  Ib.    32.3  cu.  in.,  or  .0187  cu.  ft.  =  1  Ib. 

CONVEYING  CAPACITIES  OF  PLIGHTS  AT  100  FT.  PER  MIN. 

(Tons  of  Pea  Coal  per  Hour) 


Size  of 
Flight,  In. 

Horizontal 

Inclined 

10° 

20° 

30° 

Every 
16  In. 

Every 
18  In. 

Every 
24  In. 

Lb.  Coal 
per  Flight 

Every 
24  In. 

Every 
24  In. 

Every 
24  In. 

4X10 
4X12 
5X12 
5X15 
6X18 
8X18 
8X20 
8X24 
10X24 

33.75 
42.75 
51.75 
69.75 

30 
38 
46 
62 
80 
120 

22.5 
28.5 
34.5 
46.5 
60.0 
90.0 
105.0 
135.0 
172.5 

15 
19 
23 
31 
40 
60 
70 
90 
115 

18.0 
24.0 
28.5 
40.5 
49.5 
72.0 
84.0 
120.0 
150.0 

14.25 
18.00 
22  .  50 
31.50 
40.50 
57.00 
66.50 
96.00 
120.00 

10.5 
13.5 
16.5 
22.5 
31.5 
48.0 
56.0 
72.0 
90.  Q 

NOTE. — These  ratings  are  for  continuous  feed.     2,000  Ib.  =  1  T. 


964 


THE  PREPARATION  OF  COAL 


HORSEPOWER  FOR  BUCKET  ELEVATORS 


N  =  number  taken  from  table;' 
fif  =  height  of  elevator  in  feet; 
w  =  weight  of  material  in  one  bucket  ; 
distance  apart  of  buckets,  in  inches. 


Revolutions 

Diameter  of  Head-wheels 

Revolu- 
tions 

per 

Minute 

22  In. 

24  In. 

26  In. 

28  In. 

30  In. 

32  In. 

per 

Minute 

10 

.064 

.070 

.075 

.080 

.087 

.093 

10 

12 

.077 

.083 

.090 

.097 

.104 

.111 

12 

14 

.089 

.096 

.106 

.114 

.121 

.130 

14 

16 

.102 

.111 

.121 

.130 

.140 

.148 

16 

18 

.115 

.125 

.136 

.146 

.157 

.167 

18 

20 

.128 

.139 

.151 

.162 

.174 

.186 

20 

22 

.140 

.153 

.166 

.179 

.191 

.204 

22 

24 

.153 

.167 

.181 

.195 

.209 

.223 

24 

26 

.166 

.181 

.196 

.211 

.226 

.242 

26 

28 

.179 

.195 

.211 

.227 

.244 

.260 

28 

30 

.191 

.209 

.226 

.244 

.261 

.279 

30 

32 

.204 

.223 

.241 

.260 

.278 

.297 

32 

34 

.217 

.237 

.256 

.276 

.296 

.316 

34 

36 

.230 

.251 

.271 

.292 

.313 

.334 

36 

38 

.242 

.265 

.287 

.309 

.331 

.353 

38 

40 

.255 

.279 

.302 

.325 

.348 

.372 

40 

PITCH  AT  WHICH  ANTHRACITE  COAL  WILL  RUN,  IN  INCHES  PER  FOOT 


Sheet  Iron 

Cast 
Iron 

Glass 

Glass 

Kind  of  Coal 

Start 
on 

Con- 
tinue 

Start 
on 

Start 
on 

Con- 
tinue 

Start 
on 

Con- 
tinue 

Dry 

Wet 

Broken  slate  

5 

4 

5 

3 

3 

Dry  egg  slate  
Dry  stove  slate  

5 
5 

4 
4 

5 
5 

3 
3 

3 
3 

Dry  chestnut  slate  5 

4 

5 

3J 

3 

Broken  coal  

fr 

?- 

Egg  coal  3 
Stove  coal  4 

3 
41 

3 

4 

2j 
3 

2\ 
21 

2f 

2* 

If 

2J 

Chestnut  coal           .  /£. 

4 

41 

h 

4. 

3 

Bl 

8 

2* 

Pea  coal  

5 

5 

«j 

3 
3 

2\ 
3^ 

3 
3 

If 

Buckwheat  No.  1  

Buckwheat  No.  2  

3 

3J 

3 

3i 

Buckwheat  No.  3  

4 

Si 

7 

*4 

Buckwheat  No.  4  |  ... 

4 

4 

4 

4? 

THE  PREPARATION  OF  COAL 


965 


HORSEPOWERS  FOR  COAL  CONVEYORS  (COAL  INCLUDED) 
Speed,  1C  i  ft.  per  min.     Conveyors,  100  ft.  long.    Standard  steel  troughs. 


•s 
s 

CO 

Size  of 

Flights," 
In. 

Horizontal 

In- 
clined 

d 

'rt 
J3 
0 

i 

CO 

Size  of 
Flights, 
In. 

Horizontal 

In- 
clined 

JM 
atf 

sjt 

i 

16  In. 
between 
Flights 

1-1  j£  be 

sji 

a 
»"»  *" 

o"o 

4X10 
4X12 
5X12 
5X15 
6X18 

O»  h^OOOO  K5 

2 
3* 
4f 

05  mi**  oo  oo 

s, 
•g 

q 

d 

5X15 
6X18 
8X18 
8X20 
8X24 
10X24 

4 
5 

7 
8 

3* 

5 
6 

7 
8 

10 
111 

14 

HORIZONTAL  PRESSURE  EXERTED  BY  BITUMINOUS  COAL  AGAINST  VERTICAL 
RETAINING  WALLS  PER  FOOT  OF  LENGTH 

I 

Surface  horizontal 
r . 
Surface  sloping  ' 

Angle  of  repose 

d  =  height  of  wall  in  feet  or  ab 


35° 


BITUMINOUS 


49 

Horizontal 
Surface, 

Sloping 
Surface, 

Horizontal 
Surface, 

Sloping 
Surface, 

fc-t 

bm 

be 

P^H 

bm 

be 

d 

c 

J 

^j 

- 

Q 

.O 

^ 

j 

X 

-  S 

£&H 

~  $ 

£fo 

^ 

—i  £ 

gfe 

~  ® 

£plH 

a 

CTj    3 

3      • 

rt  3 

3  ^ 

o. 

rt  3 

^  +^ 

d  d 

^  4_T 

Q 

*l 

W    "1 

If 

^1 

£  8 

£  0 

Q 

£ 

|| 

O   w 

r         0) 
£ 

£    * 

-> 

H 

-) 

H-J 

1 

6.4 

6.4 

10 

10 

26 

4,305 

325 

6,760 

510 

2 

25.0 

19.0 

40 

30 

27 

4,641 

338 

7,290 

530 

3 

57.0 

32.0 

90 

50 

28 

4.993 

350 

7,840 

550 

4 

102.0 

45.0 

160 

70 

29 

5,358 

363 

8,410 

570 

5 

159.0 

57.0 

250 

90 

30 

5,733 

376 

9,000 

590 

6 

229.0 

70.0 

360 

110 

31 

6,122 

389 

9,610 

610 

7 

312.0 

83.0 

490 

130 

32 

6,523 

401 

10,240 

630 

8 

407.0 

96.0 

640 

150 

33 

6.935 

414 

10,890 

650 

9 

516.0 

108.0 

810 

170 

34 

7,362 

427 

11,560 

670 

10 

637.0 

121.0 

1,000 

190 

35 

7,778 

440 

12.250 

690 

11 

770.0 

134.0 

1,210 

210 

36 

8,253 

452 

12.960 

710 

12 

917.0 

146.0 

1,440 

230 

37 

8,754 

465 

13.690 

730 

13 

1,076.0 

159.0 

1,690 

250 

38 

9,193 

478 

14,440 

750 

14 

1,248.0 

172.0 

1,960 

270 

39 

9,682 

490 

15,210 

770 

15 

1,433.0 

185.0 

2,250 

290 

40 

10,192 

503 

16,000 

790 

16 

1,630.0 

197.0 

2,560 

310 

41 

10,669 

516 

16,810 

810 

17 

1,840.0 

210.0 

2,890 

330 

42 

11.236 

529 

17,640 

830 

18 

2,063.0 

223.0 

3,240 

350 

43 

11,797 

541 

18,490 

850 

19 

2,298.0 

236.0 

3,610 

370 

44 

12,331 

554 

19,360 

870 

20 

2,548.0 

248.0 

4,000 

390 

45 

12,968 

567 

20,250 

890 

21 

2,809.0 

261.0 

4,410 

410 

46 

13,478 

580 

21.160 

910 

22 

3,083.0 

274.0 

4,840 

430 

47 

14,100 

592 

22,090 

930 

23 

3,369.0 

287.0 

5,290 

450 

48 

14,679 

605 

23,040 

950 

24 

3,669.0 

299.0 

5,760 

470 

49 

15,275 

618 

24,010 

970 

25 

3,981.0 

312.0 

6,250 

490 

50 

15,925 

631 

25,000 

990 

Wp.it/ht  of  coal  =  47  Ib.  ner  cu.  ft. 


966 


THE  PREPARATION  OF  COAL 


HORIZONTAL  PRESSURE  EXERTED  BY  ANTHRACITE  COAL  AGAINST  VERTICAL 
RETAINING  WALLS  PER  FOOT  OF  LENGTH 

9.78<f2 
=   9.78(2d-l) 


Surface  horizontal 

Surface  sloping  < 

Angle  of  repose 

d  =  height  of  wall  in  feet. 


14.22  (2d-l) 
27° 


ANTHRACITE 


Horizontal 

Sloping 

Horizontal 

Sloping 

£ 

Surface, 

Surface, 

£ 

Surface, 

Surface, 

P-I 

bm 

be 

PH 

bm 

be 

a 

C 

£ 

0 

j>£ 

D 

-M 

'i 

0 

«£ 

Oj  ry 

*& 

*t«  3 

"oj  3 

W  ** 

^ 

*c3  a 

a  ^ 

32 

*S+r 

I 

•   ll 

II 

*! 

l| 

c 

11 

IJ 

el. 

PH 

<()  4) 
C^  O 

2 

9.78 
39.12 

9.78 
29.34 

14.22 
56.88 

14.22>26 
42.66[27 

6,611.1 
7,129.5 

498.78 
518.35 

9,612.8 
10,366.0 

725.21 
753  .  67 

3 

88.02 

48.90 

127.98 

71.1028 

7,667.6 

537.90 

11,149.0 

782.10 

4 

156.48 

68.46 

227  .  52 

99.54 

29 

8,225.0 

557.46 

11,988.0 

810.54 

5 

244  .  50 

88.02 

355.50 

127.98 

30 

8,802.0 

577.01 

12,797.0 

839  .  00 

6 

352.08 

107.58 

511.92 

156.4231 

9,398.5 

596.59 

13,655.0 

867.41 

7 

479.22 

127.14 

696.78 

184.86 

32 

10,015.0 

616.14 

14,561.0 

895.86 

8 

625.92 

146.70 

910.08 

213.30 

33 

10,650.0 

635.70 

15,486.0 

924  .  30 

9 

792.18 

166.26 

1,151.82 

241.74 

34 

11,306.0 

655.26 

16,439.0 

952.70 

10 

978.00 

185.82 

1,422.00 

270.18 

35 

11,980.0 

674.81 

17,420.0 

981.19 

11 

1,183.38 

205.38 

1,720.62 

298.62 

36 

12,675.0 

694.39 

18,429.0 

1,009.60 

12 

1,408.32 

224.94 

2,047.68 

327.06 

37 

13,389.0 

713.94 

19,467.0 

1,038.10 

13 

1,652.82 

244.50 

2,403.18 

355.50 

38 

14,123.0 

733.50 

20,533.0 

1,066.50 

14 

1,916.88 

264.06 

2,787.12 

383.94 

39 

14,875.0 

753.07 

21,629.0 

1,095.00 

15 

2,200.50 

283.62 

3,199.50 

412.38 

40 

15,648.0 

772.63 

22,752.0 

1,123.40 

16 

2,503.68 

303.18 

3,640.32 

440.82 

41 

16,440.0 

792.20 

23,904.0 

1,151.80 

17 

2,826.42 

322.74 

4,109.56 

469.26 

42 

17,252.0 

811.74 

25,084.0 

1,180.30 

18 

3,168.72 

342.30 

4,607.28 

497.70 

43 

18,083.0 

830.73 

26,293.0 

1,208.70 

19 

3,530.58 

361.86 

5,133.42 

526.14 

44 

18,934.0 

850.86 

27,530.0 

1,237.20 

20 

3,912.00 

381.42 

5,688.00 

554  .  58 

45 

19,804.0 

870.41 

28,793.0 

1,265.60 

21 

4,313.00 

400.98 

6,271.00 

583  .  26 

46 

20,695.0 

889.99 

30,090.0 

1,294.00 

22 

4,733.50 

420.54 

6,882  .  50 

611.46 

47 

21,605.0 

909  .  54 

31,412.0 

1,322.30 

23 

5,173.70 

440.10 

7,522.50 

639.90J48 

22,533.0 

929.10 

32,763.0 

1,350.90 

24 

5.633.30 

459.67 

8,190.70 

668.35 

49 

23,482.0 

948.66 

34,143.0 

1,379.40 

25!6ill2.60 

479.22 

8,887.50 

696.7950 

24,450.0 

968.21 

35,550.0 

1,407.90 

COST  OF  UNLOADING  COAL 

Coal  is  generally  unloaded  from  railroad  cars  into  the  hold  of  a  vessel  by 
some  form  of  unloader,  which  usually  raises  the  car  bodily  and  dumps  it 
directly  into  the  hold  of  the  vessel.  In  this  way  the  cost  of  unloading  has 
been  reduced  to  a  very  small  figure,  and  the  speed  of  unloading  greatly 
increased.  The  cost  of  unloading  is  given  by  the  makers  of  the  Brownhoist 
as  varying  from  2j  c.  per  T.  up  to  4£  c.  per  T.;  deducting  in  each  case  2  c.  for 


THE  PREPARATION  OF  COAL 


967 


trimming  the  coal  in  the  vessel,  the  actual  cost  of  loading  varies  from  i  c.  to 
2j  c.  per  T.,  depending  on  the  conditions.  Along  the  Lakes  it  is  customary 
to  pay  a  premium  of  |  c.  per  T.  to  all  connected  with  the  loading,  for  all  coal 
loaded  in  excess  of  2,500  T.  per  day  and  1,800  T.  per  night.  The  Brownhoist 
has  a  guaranteed  capacity  of  at  least  300  T.  per  hr.,  but  this  has  been  greatly 
exceeded  in  practice.  The  McMyler  end  dump  has  a  record  of  4.65  T.  per 
min.,  and  the  McMyler  side  dump  of  8.41  T.  per  min.  These  figures  apply  to 
the  lake  cities  of  the  U.  S. 

The  C.  W.  Hunt  Co.,  West  New  Brighton,  N.  Y.,  gives  the  following 
figures  for  handling  coal  along  the  Atlantic  seaboard:  The  cost  of  shoveling 
coal  by  hand  in  the  hold  of  the  vessel  into  ordinary  iron  buckets  is  about  6  to 
7  c.  per  T.  of  2,000  lb.;  the  cost  for  iron  ore,  phosphate  rock,  or  sand,  about 
10  %  less.  The  cost  of  shoveling  coal  and  hoisting  it  out  of  vessel  to  the 
wharf  with  an  ordinary  hoist  with  manila  rope  is  12  to  13  c.  per  T.,  so  that 
the  hoisting  costs  about  the  same  as  the  shoveling.  The  cost  for  both 
shoveling  and  hoisting  with  a  steam  engine  is  10  to  11  c.  per  T.  The  cost 
when  using  a  steam  shovel  or  grab  bucket  for  taking  up  coal  out  of  the  vessel 
varies  greatly  in  different  classes  of  vessels,  but  usually  runs  from  about  1  $  to 
5  c.  per  T.,  averaging  about  3  c.  After  the  coal  is  hoisted,  it  can  be  carried 
into  storage  with  an  automatic  railway  or  other  efficient  plant,  at  a  cost  of 
about  1  to  1£  c.  per  T.  For  great  distances,  a  cable  railway  or  a  conveyor  can 
be  used,  which  handles  the  material  about  as  cheaply  as  for  short  distances, 
but  the  cost  of  plant  is  greatly  increased. 

In  unloading  anthracite  from  cars  on  a  trestle  into  pockets  or  on  the 
ground,  the  loss  on  all  sizes  is  2  to  3  %  when  the  coal  is  not  resized;  when  it  is 
resized  the  loss  is  8£  to  9%. 

The  cost  of  stocking  and  unloading  anthracite  by  the  Dodge  system  is 
given  by  Mr.  Piez,  as  follows: 


Year 

fj 

xpense, 
n.  Cents. 

0>   o3   to 
M  P,t! 
*     -  <U 

£15U 

h 

'ftO<_w 

C  t£  cj 

3.S  k 

per  Ton. 

1 

£ 

»Ia4?«! 

Wo 

fiS 

•3 

Bj 

.2  to 

.* 

^    O  "*  "£H 

Q;  " 

H               -4 

O  TTH      d 

a  C! 

3.0 

•a| 

jCtfiJU 

,§1 

l3^ 

3«£ 

S 

^ 

ft  ^ 

CO 

$ 

1895... 
1896  
1897  

.87 
.78 
.69 

.29 
.30 
.32 

.97 

.82 
.62 

2.67 
2.19 
1.88 

.78 
.90 
.97 

.25 
.27 
.16 

5.83 
5.26 
4.64 

BRIQUETING 

Machines  Employed. — Fuel,  fuel  dust,  and  other  products  may  be  bri- 
queted  by  a  number  of  different  styles  of  machines,  but  all  these  may  be 
divided  into  two  classes,  briquet  and  eggette  machines.  The  eggette  ma- 
chines have  a  pair  of  rollers,  the  faces  of  which  are  provided  with  semisphencal 
or  semiovoid  depressions.  The  material  that  is  fed  between  these  rolls 
crowds  into  the  openings  of  the  two  rolls,  thus  forming  small  nodules.  In 
material  is  mixed  with  a  suitable  binder  before  being  fed  to  the  rolls,  and  the 
eggsttes  are  received  on  any  suitable  form  of  traveling  belt  or  chute  and 
removed  for  drying  or  storage.  This  style  of  machine  has  not  been  used 


J.I1LU     WlUCil     l/IIC    IllctLClldl    10    v^i  w  vv  uvu.*  j.  j-j.^    **.i      «-w*  -v*-.     »    ^- —     j 

being  fed  into  the  mold  or  subsequently  by  some  form  of  plunger.  For  some 
materials,  common  brick  machines,  such  as  are  used  in  the  manufacture  ol 
building  brick,  are  employed,  while  in  others  special  f9rms  are  necessary. 

Briqueting  of  Fuel. — Fuel  briquets  have  not  come  into  general  use  in  the 
United  States  for  two  reasons:  (1)  on  account  of  the  great  amount  of  cheap 
fuel  available,  which  has  prevented  the  utilization  of  culm,  coal  dust  etc.; 
and  (2)  on  account  of  the  lack  of  or  high  price  of  suitable  bonding  material. 
This  latter  condition  is  now  being  removed  by  the  introduction  of  byproduc 
coke  ovens,  from  which  supplies  of  coal  tar  can  be  obtained.  Aside  from  peat 
and  certain  kinds  of  brown  coal,  and  possibly  some  caking  coals,  it  is  neces- 


968 


THE  PREPARATION  OF  COAL 


sary  to  employ  a  binder  in  the  making  of  any  fuel  briquets.  This  is  especially 
true  in  the  case  of  anthracite  coal.  The  present  tendency  is  to  employ  no 
in9rganic  bonding  materials,  as  they  increase  the  ash.  The  material  to  be 
briqueted  should  be  as  clean  and  free  from  dirt  or  slate  as  possible,  and  the 
particles  should  be  of  practically  uniform  size,  the  most  satisfactory  product 
being  from  coal  crushed  to  about  |  in.  cube  size.  The  coal  must  be  thor- 
oughly mixed  with  bonding  material  and  then  subjected  to  a  heavy  pressure. 
One  advantage  claimed  for  briquets  is  that  they  can  be  made  of  such  a  form 
as  to  occupy  less  space  than  the  original  fuel.  The  French  navy  has  found 
it  possible  to  store  10%  more  briquets  than  coal  in  a  given  space,  and  also 
that  the  loss  by  breakage  and  pulverization  is  very  much  less.  Under  favora- 
ble conditions,  fuel  can  be  briqueted  for  20  c.  per  T.,  and  the  following 
are  some  of  the  advantages  claimed  for  these  briquets:  They  are  sound 
throughout  and  will  not  decrepitate  while  burning,  thus  reducing  the  loss  by 
fine  material  working  through  the  grates.  The  binder  if  properly  selected, 
renders  the  briquets  practically  waterproof,  so  that  they  are  not  injured  if 
kept  in  storage,  do  not  evolve  combustible  gases,  nor  ignite  from  spontaneous 
combustion.  There  is  no  fine  material  mixed  with  the  briquets,  and  hence  a 
more  uniform  fire  can  be  maintained  with  them. 

Briqueting  of  Flue  Dust. — Flue  dust  from  iron  blast  furnaces  has  been  suc- 
cessfully briqueted  in  a  number  of  instances.  One  firm  employs  a  common 
brick  machine,  making  bricks  2?  in.  X4£  in.  X9  in.  With  this  machine, 
they  mix  the  flue  dust  with  3  %  of  lime  and  3  %  of  cement,  the  lime  acting  as 
a  flux  in  the  furnace.  These  machines  work  with  comparatively  light  pres- 
sure. When  regular  briqueting  machines,  producing  round  bricks  and 
employing  high  pressures  are  employed,  no  cement  need  be  used,  the  flue  dust 
being  mixed  with  4  %  to  6  %  of  lime.  The  flue  dust  is  first  carefully  screened 
from  hard  lumps  and  then  mixed  warm  with  milk  of  lime  in  a  mixer,  after 
which  it  is  put  through  the  press,  and  the  briquets  are  then  placed  in  drying 
ovens  and  subjected  to  heat  from  the  gases  of  a  boiler  or  furnace  plant, 
the  temperature  not  to  exceed  300°F.  For  moderate  sized  briquets,  about 
6  hours'  drying  is  sufficient.  Just  before  the  briquets  are  quite  dry,  they 
are  loaded  into  barrels  and  taken  direct  to  the  blast  furnace,  with  as  little 
handling  as  possible.  The  results  have  been  very  satisfactorily  compared 
with  the  ore  replaced.  The  flue  dust  itself  frequently  contains  30  %  to  40  % 
metallic  iron  and  more  or  less  carbonaceous  matter.  It  is  also  stated  that  at 
a  large  furnace  plant  the  cost  of  making  and  handling  should  not  exceed 
$1  per  T. 

Another  firm,  figuring  on  a  basis  of  130  T.  per  24  hr.,  and  using  3%  lime 
in  the  solution,  gave  the  following  figures: 

4  T.  lime,  $3.00  per  T $12 . 00 

2  machine  tenders  (day  and  night),  12  hr.  at  $2.50.        5.00 

2  laborers  (day  and  night),  12  hr.  at  $1.75 3 . 50 

Oil  and  waste 2 . 00 

Wear  on  machinery 1 .  50 

Interest  on  cost  of  plant 1 . 00   $25  . 00 

This  is  less  than  20  c.  per  T.     This  estimate  does  not  take  into  considera- 
tion the  cost  of  power,  which  would  be  about  35  H.P.,  nor  does  it  take  into 
consideration  hauling  of  material  to  plant  and  removing  of  briquets. 
CUBIC  FEET  OCCUPIED  BY  2,000  POUNDS  OF  VARIOUS  COALS 
(Link-Belt  Engineering  Co.,  Philadelphia,  Pa.} 


Varieties 


Broken  |  Egg  |  Stove  |  Chestnut |  Pea 


Lackawanna,  anthracite 

37.10 
37.30 
37.55 
38.05 
34.90 
34.95 
33.30 
34.65 
35.35 
35.45 

36.65 
36.95 
37.25 
37.70 
34.85 
34.35 
33.80 
34.20 
35.20 
34.95 

34.90 
36.35 
37.55 
37.25 
34.75 
33.75 
33.55 
33.80 
34.60 
34.35 

34.35 
36.35 
37.25 
37.25 
34.70 
34.00 
32.55 
33.55 
33.30 
33.70 

37.25 
37.50 
38.50 
38.50 
36.90 
36.90 
33.05 
35.20 
34.95 
35.50 

Garfield  red  ash,  anthracite  
Lykens  Valley,  anthracite.. 

Shamokin,  anthracite  

Plymouth  red  ash,  anthracite  
Wilkes-Barre,  anthracite  
Lehigh,  anthracite  
Lorberry  anthracite 

Scranton,  anthracite  
Pittston,  anthracite  

Cumberland,  bituminous  136.65 
Clearfield,  bituminous  33.55 

Pocahontas,  bituminous  
American  cannel,  bituminous  .  . 
English  cannel,  bituminous  

34.00 
41.50 
42.30 

New  River,  bituminous  40.  15 

SAFETY  AND  FIRST  AID 


SAFETY  AND  FIRST  AID 

The  following  directions  for  first  aid  to  the  injured  were  prepared  by  Dr. 
George  H.  Halberstadt  of  Pottsville,  Pa.,  Surgeon  for  the  Philadelphia  & 
Reading  Coal  and  Iron  Co.  They  cover  in  a  concise  manner  the  principles 
of  the  excellent  detailed  instructions  that  have  resulted  in  the  great  efficiency 
of  the  P.  &  R.  G.  and  I.  Co.'s  first-aid  corps. 

RULES  FOR  FIRST-AID  CORPS 

1.  The  work  is  limited  to  first  aid. 

2.  In  all  serious  cases  summon  a  doctor.     On  his  arrival,  if  requested,  give 
him  all  possible  assistance. 

3.  Keep  your  presence  of  mind  and  do  not,  by  your  manner,  indicate  to  the 
patient  the  seriousness  of  the  injury. 

4.  Examine  the  mouth  and  remove  any  foreign  substance. 

5.  In  all  serious  injuries  cut  off  the  clothing  to  properly  inspect  and  dress 
wounds.     For  slight  injuries  begin  removal  of  the  clothing  from  the  sound 
side,  and  tp  replace  it  begin  on  the  injured  side. 

6.  Place  the  patient  in  a  comfortable  position,  preferably  on  his  back. 

7.  When  vomiting  occurs  turn  the  patient  on  his  side,  neck  extended  and 
head  low,  so  that  the  vomited  material  will  not  enter  the  wind  pipe. 

8.  Never  attempt  to  wash  or  cleanse  a  wound;  do  not  touch  ft  with  the 
fingers;  cover  up  quickly  every  wound  with  sterile  dressing  and  secure  this 
with  a  clean  bandage.     This  will  prevent  infection  and  blood  poisoning.    The 
old  common  practice  of  applying  a  chew  of  tobacco  to  stop  bleed- 
ing, and  the  use  of  handkerchiefs  or  pieces  torn  from  clothing  in 
binding  up  open  wounds  is  a  source  of  serious  danger. 

9.  Do  not  handle  the  part  of  the  dressing  that  will  come  into 
contact  with  the  wound. 

10.  Stop  severe  hemorrhage  from  arms  and 
legs    with    a    tourniquet    applied    above    the 
wound,    then   apply  sterile  dressings  securely* 
held  with  bandage.      If  the  dressings  control 
the  hemorrhage,  loosen  tourniquet  but  leave 
it    in    position  to  be  retightened  if  necessary; 
always  watch  for  secondary  hemorrhage. 

A  tourniquet  may  be  made  of  the  material 
contained  in  a  first-aid  cabinet  or  a  handker- 
chief can  be  used.  Lay  a  firm  and  even  com- 
press or  pad  over  the  artery  if  you  can  readily 
locate  it.  The  artery  in  the  thigh  runs  along 
the  inner  side  of  the  muscle  in  front  near  the  p  i 

bone,  as  shown  by  a  dotted  line  on  Fig.  1.  A 
little  above  the  knee  it  passes  to  the  back  of  the  bone.  In  case  of  injuries  at 
or  above  the  knee,  apply  the  compress  higher  up,  on  the_inner  side  of  the 
thigh,  along  the  line  of  the  artery,  as  for  instance,  at  the  point  P.  When  the 
leg  is  injured  below  apply  the  compress  at  the  back  of  the  thigh  just  above 
the  knee  at  P,  Fig.  2.  The  artery  in  the  arm  runs  down  the  inner  side  of 
the  large  muscle  in  front,  quite  close  to  the  bone  as  shown  in  Fig.  3.  Lower 
down  it  is  further  forward,  towards  the  bend  of  the  elbow.  It  is  most  easily 

compressed    a   little    above  the  middle  at  P. 

In  all  cases  apply  the  tourniquet  as  close  above 

the  wound  as  possible. 

Tie  the  cloth  or  the   handkerchief   around 

the  limb,  covering  the  compress,  put  a  bit  of 

stick  between  the  bandage  and  the  limb  and 
•  twist  it  as  in  Fig.  4.  until  it  is  just  tight  enough 

to  stop  the  bleeding,  then  put  one  end  of  the 

stick  under  the  handkerchief  as  shown  in  Fig. 

5  to  prevent  untwisting. 
FlG.  3  11.    Check  bleeding  from  all  parts  of  the 

body  by  dressings  and  bandages.     Both  roller 

and  triangular  bandages  are  used  in  first-aid  work.  The  roller  bandages  are 
made  of  various  widths,  and  5  yd.  long.  Triangular  bandages  as  furnished 
in  first-aid  equipments  are  triangular  pieces  of  cotton  cloth,  measuring  4 
ft.  2  in.  on  the  base,  and  2  ft.  9  in.  on  the  sides.  Similar  bandages  can  be 
made  by  cutting  a  yard  of  muslin  diagonally.  The  advantages  of  triangular 


FIG.  2 


970  SAFETY  AND  FIRST  AID 

bandages  are:  they  can  be  folded  to  make  bandages  of  any  desired  width,  and 
can  also  be  used  as  slings.  Triangular  bandages  furnished  in  first-aid  outfits 
have  illustrations  printed  on  them  showing  their  application  to  different 
parts  of  the  body. 

12.  Cover  up  every  injured  person  with  blankets,  regardless  of  the  weather. 
Use  hot-water  bottles  and  an  ambulance  stove,  when  necessity  requires 
them.     When  hot-water  bottles  are  used  always  have  clothing  or  woolen 
blankets  between  them  and  the  patient. 

13.  Do  not,  under  any  circumstances,  use  the  so-called  antiseptic  lotions, 

salves,  balsams,  or  any  material  that  is  likely  to 
infect  the  wound. 

14.  Splint  every  injury  from  toe  to  hip  and 
from  fingers  to  shoulders.     Always  support  fore- 
arm with  sling. 

15.  Notify  at  once  the  patient's  family  or  the 
hospital  of  the  character  of  the  injury  and  prob- 
able time  of  arrival  at  destination. 

Shock. — Shock  accompanies  all  serious  acci- 
dents. The  skin  is  cold  and  clammy;  the  pulse 
is  weak,  rapid  and  often  intermittent;  the  breath- 
ing irregular;  vomiting  and  retching  are  common; 
eyelids  naif  open;  pupils  dilated;  and  there  may 
be  any  degree  of  insensibility.  Check  hemorrhage 
at  once.  Cover  patient  with  blankets  and  sur- 
round him  with  hot-water  bottles.  The  hot-water 
bottles  must  not  come  into  contact  with  the  skin, 
FIG.  4  FIG.  5  have  a  layer  of  blanket  or  clothing  intervene. 

When  able  to  swallow  give  hot  black  coffee  or  a 

half  teaspoqnful  of  aromatic  spirits  of  ammonia  in  a  half  tumbler  of  water. 
Alcoholic  stimulants  should  not  be  given  unless  ordered  by  the  doctor.  If 
vomiting  occurs,  turn  patient  on  his  side  and  see  that  no  vomited  material 
is  left  in  the  mouth.  When  the  injury  is  to  the  skull  give  no  stimulants. 

Burns  and  Scalds. — Remove  clothing  with  knife  or  scissors.  Do  not 
break  the  blisters.  Cover  with  picric  acid  gauze;  this  with  a  layer  of  cotton 
and  secure  with  bandage.  A  solution  of  baking  soda,  one  tablespoonful  to 
a  quart  of  boiled  water,  may  be  applied  on  gauze,  if  picric  acid  gauze  is  not 
at  nand. 

Heat  Prostration  and  Heat  Exhaustion. — In  heat  prostration,  the  face  is 
flushed,  the  skin  dry  and  hot,  pulse  may  be  rapid  or  slow,  and  the  heat  of  the 
body  excessive;  and  patient  may  be  unconscious.  Remove  patient  to  a  cool 
place,  loosen  the  clothing,  lessen  the  heat  of  the  body  and  head  by  cold 
applications. 

In  heat  exhaustion,  the  face  is  pale,  the  skin  cold  and  clammy,  breathing 
shallow,  pulse  weak  and  rapid.  Loosen  the  clothing,  apply  heat  to  the 
surface  of  the  body,  and  when  able  to  swallow,  give  hot  black  coffee  or  tea. 
Convulsions. — Lay  patient  on  back,  loosen  clothing,  place  blanket  or 
coat  under  his  head.  Do  not  attempt  to  resist  the  convulsive  efforts ; 
stand  by  and  protect  him  from  doing  injury  to  himself.  If  he  is  biting  his 
tongue,  force  a  stick  between  his  back  teeth  and  release  it. 

Artificial  Respiration. — This  is  administered  for  drowning,  for  electric 
shocks,  suffocation  by  smoke,  illuminating  gas  or  any  mine  gas. 

The  Schaefer  Method. — Lay  the  subject  on  his  belly,  with  arms  extended 
as  straight  forward  as  possible,  as  shown  in  Fig.  6,  and  with  face  to  one  side 
so  that  the  nose  and  mouth  are  free  for  breathing.  Let  an  assistant  draw 
forward  the  subject's  tongue.  If  possible,  avoid  so  laying  the  subject  that 
any  burned  or  injured  places  are  pressed  upon.  Do  not  permit  bystanders  to 
crowd  around  and  shut  off  the  fresh  air. 

Kneel  straddling  the  subject's  thighs  and  facing  his  head;  rest  the  palms 
of  your  hands  on  his  loins  (on  the  muscles  of  the  small  of  the  back),  with 
thumbs  nearly  touching  each  other  (Fig.  6)  and  with  fingers  spread  over  the 
lowest  ribs. 

With  arms  held  straight  (Fig.  7),  swing  forward  slowly  so  that  the  weight 
of  your  body  is  gradually  brought  to  bear  upon  the  subject.  This  operation, 
which  should  take  from  2  to  3  sec.,  must  not  be  violent  or  internal  organs 
may  be  injured.  The  lower  part  of  the  chest  and  also  the  abdomen  are 
thus  compressed,  and  the  air  is  forced  out  of  the  lungs. 

Now  immediately  swing  backward  so  as  to  remove  the  pressure,  but 
leave  your  hands  in  place,  thus  returning  to  the  position  shown  in  Fig.  6. 


SAFETY  AND  FIRST  AID 


971 


Through  their  elasticity,  the  chest  walls  expand  and  the  lungs  are  thus 
supplied  with  fresh  air. 

After  2  sec.  swing  forward  again.  Thus  repeat  deliberately  12  to  15  times 
a  minute  the  double  movement  of  compression  and  release;  a  complete 
respiration  in  4  or  5  sec.  If  a  watch  or  clock  is  not  visible,  follow  the  natural 
rate  of  your  own  deep  breathing;  swing  forward  with  each  expiration,  and 
backward  with  each  inspiration.  While  this  is  being  done,  an  assistant 
should  loosen  any  tight  clothing  about  the  subject's  neck,  chest,  or  waist. 


FIG. 


Continue  artificial  respiration,  if  necessary,  2  hr.  or  longer  without  inter- 
ruption until  natural  breathing  is  restored,  or  until  a  physician  arrives. 
Even  after  natural  breathing  begins  carefully  watch  that  it  continues.  If 
it  stops,  start  artificial  respiration  again.  During  the  period  of  operation, 
keep  the  subject  warm  by  applying  a  proper  covering  and  by  laying  beside 
his  body  bottles  or  rubber  bags  filled  with  warm  (not  hot)  water.  The  atten- 
tion to  keeping  the  subject  warm  should  be  given  by  an  assistant  or  assistants. 


FIG.  7 

The  Sylvester  Method. — Loosen  clothing.  Place  the  patient  on  his  back 
with  folded  coat  under  the  shoulders  to  extend  the  neck.  Kneel  at  his  head. 
Grasp  the  forearms  "just  below  the  elbows  with  each  hand.  To  expand  the 
chest,  draw  the  arms  outwards  and  upwards  to  the  sides  of  the  head,  as  in  Fig. 
8.  To  expel  the  air  from  the  chest,  bring  patient's  arms  to  sides  and  front 
of  chest  as  in  Fig.  9,  and  exert  firm  compression  on  lower  border  of  ribs. 
This  should  be  done  15  times  a  minute.  The  tongue,  when  the  patient  is  in 
this  condition,  may  drop  back.  The  mouth  can  be  pried  open  with  a  stick, 
and  the  tongue  drawn  forwards  with  the  fingers  covered  with  a  handkerchief. 


972 


SAFETY  AND  FIRST  AID 


With  either  method  of  artificial  respiration  the  administration  of  oxygen 
can  be  given  at  the  same  time.  The  tube,  preferably,  is  placed  in  the  nose. 
If  the  Draeger  pulmotor  is  at  hand,  the  mask  can  be  adjusted  to  the  face  and 
used  synchronously  with  artificial  respiration,  or  the  pulmotor  may  be  used 
alone. 

Treatment  for  Electrical  Shock. — An  accidental  electric  shock  usually 
does  not  kill  at  once,  but  may  only  stun  the  victim  and  for  a  while  stop  his 
breathing.  The  shock  is  not  likely  to  be  immediately  fatal,  because: 


FIG.  8 

(A)  The  conductors  may  make  only  a  brief  and  imperfect  contact  with 
the  body.     . 

(B)  The  skin,  unless  it  is  wet,  offers  high  resistance  to  the  current. 
Hope  of  restoring  the  victim  lies  in  prompt  and  continued  use  of  artificial 

respiration.     The  reasons  for  this  statement  are: 

(A)  The  body  continuously  depends  on  an  exchange  of  air,  as  shown  by 
the  fact  that  we  must  breath  in  and  out  about  15  times  a  minute. 


FIG.  9 

(B)  If  the  body  is  not  thus  repeatedly  supplied  with  air,  suffocation  occurs. 

(C)  Persons  whose  breathing  has  been  stopped  by  electric  shock  have  been 
restored  after  artificial  respiration  has  been  continued  for  approximately 
2  hr. 

Rescue  from  Electrical  Contact. — Break  the  circuit  immediately. 

1.  With  a  single  quick  motion  separate  the  victim  from  the  live  conductor. 
In  so  doing  avoid  receiving  a  shock  yourself.  Many  have,  by  their  care- 
lessness, received  injury  in  trying  to  disconnect  victims  of  shock  from  live 
conductors. 


SAFETY  AND  FIRST  AID  973 

Observe  the  following  precautions: 

(A)  Use  a  dry  coat,  a  dry  rope,  a  dry  stick  or  board,  or  any  other  dry  non- 
conductor to  move  either  the  victim  or  the  wire,  so  as  to  break  the  electrical 
contact.     Beware   of   using   metal   or   any   moist   material.     The    victim's 
loose  clothing,  if  dry,  may  be  used  to  pull  him  away;  do  not  touch  the  sole 
or  heels  of  his  shoes  while  he  remains  in  contact;  the  nails  are  dangerous. 

(B)  If  the  body  must  be  touched  by  your  hands,  be  sure  to  cover  them  with 
rubber  gloves,  mackintosh,  rubber  sheeting  or  dry  cloth;  or  stand  on  a  dry 
board  or  on  some  other  insulating  surface.     If  possible,  use  only  one  hand. 

If  the  victim  is  conducting  the  current  to  the  ground,  and  is  convulsively 
clutching  the  live_conductor,  it  may  be  easier  to  shut  off  the  current  by  lifting 
him  than  by  leaving  him  on  the  ground  and  trying  to  break  his  grasp. 

2.  Open  the  nearest  switch,  if  that  is  the  quickest  way  to  break  the  circuit. 

3.  If  necessary  to  cut  a  live  wire,  use  an  ax  or  a  hatchet  with  a  dry  wooden 
handle,  or  properly  insulated  pliers. 

After  release  from  contact  get  patient's  face  or  hand  in  contact  with 
ground,  so  as  to  discharge  any  retained  current.  Summon  a  doctor  at  once. 
Immediately  begin  artificial  respiration  by  the  Schaeferpr  Sylvester  methods. 

Fractures. — Fractures  of  bones  can  be  divided  into  simple  and  compound. 
The  simple  fracture  is  a  break  of  the  bone  without  an  opening  to  the  surface 
of  the  skin.  A  compound  fracture  is  a  break  of  the  bone  with  an  opening  to 
the  surface  of  the  skin.  Fractures  of  the  bones  of  the  arms  and  legs  can 
usually  be  detected  by  the  position  the  limb  assumes,  and  the  loss  of  power 
and  control  over  the  limb.  The  limb  should  be  straightened  gently  by  pulling 
on  the  foot  or  hand  firmly,  and  fixed  in  position  by  padded  splints,  securely 
fastened  with  bandages. 

In  compound  fractures  do  not  attempt  to  replace  a  protruding  bone.  Cover 
the  wound  with  sterile  dressings  and  then  apply  splints.  Fractures  of  the 
bones  of  the  head  and  body  should  be  fastened  with  dressings  and  bandages. 

In  the  absence  of  regular  splints,  straight  pieces  of  wood  of  proper  length, 
well  padded  can  be  used  in  emergencies. 

Dislocations. — Dress  all  dislocations  of  joints  in  the  position  they  assume 
with  bandages  drawn  only  sufficiently  tight  to  render  the  transportation  of 
the  patient  less  painful. 

Drowning. — After  removal  from  the  water,  elevate  patient's  hips,  shake 
him  gently  and  press  on  chest  as  in  Shafer  method  for  about  2  min.  to 
allow  the  water  to  run  out  of  chest.  The  mouth  should  be  cleansed  and  arti- 
ficial respiration  continued  for  an  hour  or  more.  The  patient's  body  should 
be  warmed  by  the  application  of  hot-water  bottles. 

Foreign  Body  in  Eye. — Have  patient  face  the  light.  Examine  the  eye, 
when  the  foreign  body  is  not  imbedded,  remove  it  with  a  clean  handkerchief 
or  gauze.  Evert  the  upper  lid  by  taking  hold  of  the  lashes,  have  patient 
look  down  and  apply  pressure  with  stick  to  skin  of  upper  lid.  The  under 
surface  of  the  upper  lid  is  where  most  loose  foreign  bodies  are  found.  Do  not 
try  to  scrape  off  imbedded  foreign  bodies.  If  a  foreign  body  cannot  be 
removed  without  scraping  wait  for  a  physician.  Do  not  use  cocaine. 

Foreign  Bodies  in  Throat. — Stand  patient  on  his  feet  and  head  and  a  few 
smart  blows  on  back  will  usually  dislodge  foreign  body. 

Foreign  Body  in  Nose. — If  it  cannot  be  blown  out  by  patient,  summon  a 

Foreign  Body  in  Ear,  Insects,  Etc. — A  teaspoonful  of  water  or  olive  oil 
will  drown  an  insect.  Hardened  wax  better  be  removed  by  a  doctor. 

METHOD  OF  MOVING  INJURED  PERSONS 

One  Bearer. — To  lift  patient  erect:  Turn  patient  on  his  face.  The 
bearer  steps  astride  body,  facing  towards  head,  with  hands  in  arm  pits,  he 
lifts  the  patient  to  his  knees,  then  clasping  hands  over  abdomen  he  lifts 
him  to  his  feet.  He  then  with  left  hand  seizes  patient's  left  wrist  (Fig.  10), 
drawing  left  arm  about  his  (the  bearer's)  neck  holds  it  against  his  lett  chest, 
the  patient's  left  side  resting  against  his  body  and  supports  him  with  his 
right  arm  about  the  waist. 

To  Place  Patient  Across  the  Back.— The  bearer  with  his  left  hand  seizes 
the  right  wrist  of  the  patient  (Fig.  11)  and  draws  the  arm  over  his  head 
and  down  upon  his  left  shoulder,  then  shifting  himself  in  front,  stoops  and 
clasps  the  right  thigh  with  his  right  arm  placed  between  the  legs,  his  right 
hand  seizing  the  patient's  right  wrist;  lastly,  he,  with  the  left  hand  grasps  the 
patient's  left  hand  and  steadies  it  against  his  side,  when  he  rises. 

To  place  patient  across  shoulder:  The  bearer  clasps  his  hands  about  the 


974 


SAFETY  AND  FIRST  AID 


patient's  waist,  shifts  himself  to  the  front,  facing  him,  and  stooping  places  his 
right  shoulder  against  the  abdomen;  he  passes  his  right  hand  and  arm  be- 
tween the  thighs  (Fig  12),  securing  the  right  thigh,  and  with  his  left  grasps 


FIG.  12 


FIG.  13 


the  patient's  right  hand,  bringing  it  from  behind  under  his  (bearer's)  left 
armpit,  when,  the  wrist  being  firmly  grasped  by  his  right  hand  he  rises.  This 
position  leaves  the  left  hand  free. 

In  lowering  patient  from  these  positions  the  motions  are  reversed.     Should 
a  patient  be  injured  in  such  a  manner  as  to  require  these  motions  to  be 


SAFETY  AND  FIRST  AID  975 

conducted  from  his  right  side,  instead  of  left,  as  laid  down,  the  change  is 
simply  one  of  hands,  the  motions  proceed  as  directed,  substituting  right  for 
left,  and  vice  versa. 

By  Two  Bearers. — Bearers  face  each  other  on  right  and  left  of  patient 
Raise  patient  to  sitting  posture,  clasp  hands  behind  patient's  back,  while  the 
other  hands  are  passed  under  patient's  thighs  and  fingers  interlocked  as  in 
Fig.  13.  Athird  bearer  can  support  the  legs. 

By  Three  Bearers. — Lay  patient  on  back;  the  bearers  kneel  on  knees 
nearest  the  patient's  feet.  Pass  arms  under  shoulders,  hips  and  knees 
Raise  patient  to  bearers'  knees;  bearers  rise  and  carry  patient  facing  them 
in  elbows.  To  lower  patient  to  litter,  reverse  movements. 

Emergency  Supplies. — Accidents  very  commonly  happen  where  supplies 
are  not  available  for  proper  treatment  of  injuries.  In  such  cases  make- 
shifts may  be  devised  from  material  at  hand.  Splints  may  be  made  from 


FIG.  14 

strips  of  bark  removed  from  a  post;  by  splitting  a  post  or  cap;  from  the 
staves  of  nail  or  spike  kegs;  from  powder  kegs  cut  in  strips  with  an  ax,  and 
even  thin  and  long  pieces  of  slate,  sprags,  etc.  Bandages  for  holding  splints 
in  place  may  be  improvised  from  clothing  torn  into  strips. 

A  very  common  form  of  emergency  stretcher  is  made  from  two  coats  as 
shown  in  Fig.  14.  The  sleeves  of  two  coats  are  turned  inside  out  and  the 
coats  placed  on  the  ground  with  their  lower  edges  touching.  A  pole  or  long 
drill  is  placed  through  the  sleeves  on  each  side,  the  coats  are  buttoned  up  and 
the  buttoned  side  turned  down.  This  stretcher  is  commonly  made  by  one 
man  grasping  a  drill  in  either  hand,  and  his  companion  pulling  his  coat  off 
over  his  head.  Stretchers  may  be  made  from  doors,  plank  nailed  together, 
etc.,  but  the  coat-stretcher  described  above  is  probably  the  easiest  and 
quickest  to  make  and  the  most  comfortable  for  the  injured  person. 


MINE  SAFETY 

Safety  First. — Although  the  motto  of  "safety  first"  has  been  generally 
adopted  by  many  American'  coal  mining  firms  it  may  or1  may  not  have  a  real 
significance.  Unless  this  or  a  similar  motto  is  to  be  strictly  lived  up  to  it  is 
better  not  adopted.  The  chief  cause  of  mining  accidents  is  of  course  falls  of 
roof  and  coal.  These  can  be  guarded  against  only  by  vigilance,  care  and  an 
adequate  amount  of  carefully  placed  timber. 

Systematic  Timbering. — The  roofs  of  mines  differ  widely  from  one  field  to 
another  and  even  frequently  in  different  mines  of  the  same  field  or  even  in 
different  portions  of  the  same  mine.  Experience  has  demonstrated  that  it 
is  often  safer  to  set  an  excess  of  timbers,  that  is,  more  than  is  deemed  neces- 
sary under  the  existing  conditions  than  to  trust  to  the  judgment  of  even 
experienced  men.  The  spacing  of  such  timbering  will  vary  considerably 
throughout  different  fields  but  will  in  the  main  bear  a  considerable  resem- 
blance to  Fig.  1  which  has  proved  eminently  successful  in  the  prevention 
of  accidents  in  the  Pocahontas  field  of  West  Virginia.  No  props  or  timbers 
as  a  general  rule  should  ever  be  set  without  cap  pieces. 

Adequate  Supervision. — Experience  has  proved  that  to  attain  the  greatest 
measure  of  safety  to  the  mine  workers  adequate  supervision  must  be  given  to 
each  working  face.  For  this  purpose  one  assistant  mine  foreman  (sometimes 
called  face  foreman  or  roof  inspector)  should  be  employed  for  each  20  to  40 
men,  this  number  varying  somewhat  with  natural  conditions  and  with  the 
area  over  which  the  miners  are  scattered.  The  fundamental  idea  of  employ- 
ing the  assistant  mine  foreman  is  that  he  shall  be  able  to  visit  each  working 
face  within  the  territory  intrusted  to  his  care  at  least  twice  during  each 
shift.  It  is  his  duty  whenever  he  sees  a  dangerous  condition  of  any  kind, 


976 


MINE  SAFETY 


whether  from  loose  coal,  loose  roof,  inadequate  timbering  or  what  not,  not 
only  to  instruct  the  workmen  in  that  place  to  rectify  the  condition  at  once 
but  to  himself  remain  until  the  dangerous  condition  has  been  rendered 
absolutely  safe. 

The  Premium  System  and  Company  Rules. — In  order  to  encourage  the 
foremen  and  assistant  foremen  to  be  constantly  on  the  alert  for  danger  and 
dangerous  practices  and  to  see  to  it  that  the  laws  of  the  state  and  the  rules  of 
the  company  are  implicitly  obeyed,  one  plan  which  has  been  adopted  is  a 
premium  system  arranged  on  a  merit  and  demerit  basis  so  that  the  official 

who  has  a  clean  record,  that 
is,  one  without  a  serious  or 
fatal  accident,  is  paid  a  bonus 
at  the  end  of  the  month.  If 
this  record  is  clean  for  six 
months  a  special  bonusis  paid 
which  continues  monthly  as 
long  as  the  record  is  clean. 
The  United  States  Coal  & 
Coke  Co.,  with  works  in  Mc- 
Dowell County  W.  Va.,  which 
js  has  adopted  this  system  with 
"  marked  success,  furnishes 
each  foreman  and  assistant 
foreman  with  a  book  of  in- 
structions which  he  is  sup- 
posed to  carry  at  all  times 
and  which  contains  the  rules 
of  the  company  which  he  is 
expected  to  see  obeyed. 
Although  many  of  these  rules 
may  be  considered  as  being 
applicable  only  to  the  field  in 
question  several  of  the  more 
important  ones  are  here 
given.  Doubtless  many 
others  will  suggest  them- 
selves to  wide  awake  officials 
operating  in  other  localities. 
The  last  breakthrough  of 
every  pair  of  headings, 
whether  working  or  not, 
must  have  at  least  12,000 
cu.  ft.  of  air  per  min.  passing 
through  it. 

Assistant  foremen  must 
examine  each  working  place 
in  their  district,  and  mark 
each  place  visited  with  date 
of  month  before  allowing  men 


Where  cars  nlder 
this  one  are  used: 
clearances  must  be  kept- 
the  same. 

Where  necessary,  fempora 
posts  must  be  Set  to 
protect  loaders  rrftite 
^loading  out 
^-.  If  any  additional 
%  posts  arereauired 


FIG.   1 


to  enter  them.    Each  idle  place  must  also  be  examined  each  day  and  a  record 
of  the  examination  must  be  made  daily  in  the  book  provided  for  this  purpose. 

When  the  fan  has  been  stopped  for  1  hr.  or  more  for  any  reason,  all  places 
must  be  thoroughly  examined  by  assistant  foremen  before  allowing  men  to 
enter  them  and  a  record  of  the  examination  must  be  made  in  the  record  book. 
All  permanent  brattices  must  be  built  of  incombustible  material,  con- 
crete preferred. 

_  Air  measurements  must  be  made  weekly  and  be  recorded  in  the  book  pro- 
vided for  that  purpose. 

Assistant  foremen  must  carry  Pieler  testing  lamps  when  making  examina- 
tions, and  all  final  tests  for  gas  must  be  made  with  this  lamp.  When  an 
ordinary  safety  lamp  will  not  detect  gas,  try  the  Pieler  lamp. 

The  presence  of  dust,  as  well  as  gas,  must  be  noted  in  the  record  book. 

Dust  must  not  be  allowed  to  accumulate  in  working  places  nor  anywhere 
in  the  mine. 

All  dusty  places  on  haulage  roads  must  be  sprinkled  daily. 

No  charge  of  any  explosive  in  any  hole  shall  exceed  2  Ib. 

Assistant  foremen  must  not  fire  any  shot  that  is  improperly  drilled, 
drilled  on  the  solid,  or  improperly  tamped. 


MINE  SAFETY 


977 


An  assistant  foreman  must  not  fire  any  shot  within  3  hr.  after  detecting  gas 
in  any  place  in  his  district. 

Where  more  than  one  shot  is  to  be  fired  in  any  place,  one  shot  only  shall  be 
charged,  tamped  and  fired,  and  an  examination  of  the  place  must  be  made 
before  firing  the  second  or  following  shots.  Only  one  shot  shall  be  fired  at  a 
time.  Assistant  foremen  must  carefully  examine  working  places  after  shoot- 
ing before  allowing  work  to  begin. 


Ail  trolley  frogs  are  to  be  placed  directly  aboys 
point  where,  irjside  of  .curvzd  rait,  /s  &rrom 
inside  of  main  line  rait. 

FIG.  2 

No  explosives  except  flameless  explosives  approved  by  the  U.  S.  Bureau  of 
Mines  shall  be  used. 

If  necessary,  water  dust  at  working  face  before  shooting. 

Shots  must  be  fired  by  battery  and  not  from  machine  or  trolley  wire. 

All  haulage  roads  on  which  more  than  one  car  is  hauled  per  trip  shall  be 
at  least  5  ft.  high  above  the  rail,  and  there  shall  be  at  least  2$  ft.  clearance 
between  any  part  of  a  car,  and  the  side  of  the  heading  at  all  places. 


—  ?C  --.. 


t. X' 


300  Ft.  Radius,  Hangers  6'F'rom  Track 


250  ft.  Radius, Hangers  6'Frotn  Track 


J50  Ft.  Rad'ius ,  Hangers  6From  Trac 


100  F+.  Radius,  Hangers  6  From  Track 
FIG.  3 

All  rash,  slate,  etc.,  is  to  be  kept  cleaned  off  haulage  roads. 

Permanent  track  must  be  bonded  as  it  is  laid. 

Where  any  dangerous  slate  is  found,  an  assistant  foreman  must  take  it 
down  at  once  before  work  is  done  near  it  or  anyone  or  any  trip  allowed  to 
pass  under  it. 

Loaders  must  post  their  working  places.     Proper  arrangement  and  placing 
of  caps,  posts,  etc.,  is  shown  on  standard  plan  which  must  be  strictly  followed. 
Posts  must  be  set  in  straight  lines  and  be  vertical.     Cap  pieces  must  be 
wedged  tightly  against  roof  with  wedge  between  post  and  cap. 
62 


978 


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MINE  SAFETY 


Assistant  foremen  must 
not  O.  K.  nor  allow  any 
place  to  be  cut  where 
posts  are  more  than  6  it. 
from  the  face  at  the  bot- 
tom. 

No  permanent  timber- 
ing will  be  allowed  on 
haulage  roads  ^  unless 
under  special  instruc- 
tions from  the  general 
superintendent. 

Loaders  must  clean  up 
slate  falls  in  their  work- 
ing places,  and  must  be 
paid  extra  for  this  work. 
The  general  arrange- 
ment of  hangers,  etc., 
for  trolley  wire  is  shown 
on  accompanying  plans 
(see  Figs.  2,  3,  4  and  5) 
which  must  be  strictly 
followed. 

^  .        Trolley    wire  must  be 
^g£   hung  6  in.  outside  of  rail 
^iu,o    and    must    be    as  nearly 
1 5      parallel  to  it,  both  hori- 
zontally and  vertically  as 
it  can  be. 

Feeder  cables  must  be 
supported  at  intervals  of 
20  ft.   on    barn   hangers 
and  special  "  Gem  "  insu- 
lators.    Cables  are  to  be 
.     placed   12  in.   outside  of  trolley  lines, 
**     and  must  be  connected  to  them  at  in- 
£    tervals  of  200  ft.       Cables   must    be 
£    properly  dead  ended  with  cable  clamps 
and  insulated  turn  buckles. 

All  insulated  cables  and  wires  must 
be  kept  free  from  grounds,  same  as 
bare  wires. 

All  men  must  be  checked  in  and  out 
of  the  mine  each  day. 

All   work  excepting  such  repairs  as 
cannot  be  done  while  operating  or  at 
night  must  be  suspended  on  Sundays. 
No  machinery  of  any  kind  must  be 
allowed  to  operate  unless  all  gears  and 
dangerous  portions  are  fully  guarded. 
Safeguarding      Machinery.  —  The 
second  greatest  cause  of  accidents  in 
&i  coal    mines    results    directly  or  indi- 
^S>5  rectly    from    machinery,    mechanical 
PJJ  devices,     electrical    conductors,     etc. 
;£^  Although  there  are  many  exceptions, 
;5z  accidents    with    machinery   generally 
;5°  arise  from  one  or  more  of  five  causes: 
£g       (o)   Falls   from   ladders,  platforms, 
!<*<  runways,  etc.,  around  machines. 
'=  =       (6)   Coming  into  contact  with  mov- 
*  =.  ing  machine  parts. 
zo       (c)   Electric  shocks. 
r  5       W  The  failure  of  a  machine  part. 
££       (e)   Mismanipulation   of  hand-oper- 
zo  ated  controlling  devices  (valves,  levers, 
0:=  switches,  etc.). 
<<       The  remedy  for  the[class  of  accidents 


MINE  SAFETY 


979 


under  (a)  is  simple  and  if 
carefully  executed,  quite 
effective.  Ladders,  stag- 
ings, platforms,  runways, 
etc.,  should  be  made 
abundantly  strong  to 
carry  any  weight  which 
may  be  placed  upon 
them;  ample  railings 
should  be  provided  on  all 
platforms,  stairways, 
etc.,  and  non-slipping 
feet  on  movable  ladders. 
Coming  into  contact 
with  moving  elements  of 
machines  is  a  prolific 
source  of  mining  acci- 
dent. When  buying  new 
machinery  it  is  wise  to 
specify  that  such  ma- 
chines should  be  properly 
safeguarded  before  deliv- 
ery. Particularly  danger- 
ous are  explosed  gear 
trains,  revolving  l)olt 
heads,  set  screws,  splines, 
open  keyways  and  the 
like.  Such  machine  parts 
should  be  eliminated  so 
far  as  possible,  e.g., 
ordinary  square-head  set 
screws  should  be  replaced 
with  hollow  flush-head 
set  screws.  In  addition, 
revolving  or  moving  dan- 
gerous machine  parts 
should  be  thoroughly 
guarded.  Guards  for 
machine  parts  or  ma- 
chines in  general  may  be 
of  many  materials  and 
many  types  of  construc- 
tion. Wooden  guards 
are  vastly  better  than 
none.  Pipe  or  structural 
shape  railings  _  have  a 
legitimate  application  in 
safeguarding  belts,  silent 
chains  and  the  like. 
Probably  the  most  satis- 
factory guards  are,  how- 
ever, constructed  of  a 
structural  shape  frame- 
work over  which  heavy 
woven  wire  or  expanded 
metal  is  placed.  _  Such 
guards  are  shown  in  Figs. 
6,  7,  8,  9  and  10.  Some 
firms  have  constructed 
quite  efficient  guards  as 
well  as  some  presenting  a 
respectable  appearance 
from  worn-out  perforated 
plates  used  on  shaker 
screens.  For  this  pur- 
pose, however,  the  per- 
forations should  not  ex- 
ceed about  2 5  in.  in  diam- 


980 


MINE  SAFETY 


Experience  has  proved 
o  which  access  is  neces- 


eter  as  a  larger   opening  may  admit  a  man's  hand. 

that  it  is  better  to  make  the  guarding  of  machinery  to  wnicn  access  is  neces- 
sary for  oiling,  etc.,  a  little  difficult  of  removal  rather  than  extremely  easy 
to  take  apart.  If  it  is  too  easily  removed,  it  may  not  be  replaced. 

Protecting  from  Electricity.— Generally  speaking  an  air  gap  of  sufficient 
width  is  a  sure  protection  against  electric  shocks.  The  only  safe  way  in 
which  to  treat  an  electrical  conductor,  regardless  of  insulation  or  the  voltage 
carried,  is  to  consider  it  as  if  it  carried  a  high  potential  and  was  devoid  of  all 
insulation.  Trolley  wires  may  be  portected  from  accidental  contact  by 
trolley  guard  boards,  a  good  type  of  which  is  shown  in  Fig.  5.  In  all  locations 
where  men  may  pass  under  such  wires  during  the  day's  work,  as  at  turnouts, 
such  boards  should  always  be  placed. 

The  failure  of  machine  parts  is  an  accident  which  it  is  difficult  to  antici- 
pate. There  is  practically  no  means  of  determining  the  existence  of  a  flaw  in 
a  welded  pipe  or  a  cold  shut  in  a  cast  fitting.  The  danger  from  the  failure  of 


FIGS.  6  TO  8 


such  parts  is  in  many  instances  quite  as  much  from  the  release  of  the  fluid 
carried  (steam,  air,  hot  water,  etc.),  as  from  flying  fragments.  In  certain 
instances  breaking  parts,  dangerous  in  themselves,  may  be  rendered  harmless 
by  the  installation  of  proper  shields  or  retainers.  Probably  the  best  known 
of  such  devices  are  water  glass  protectors  on  boilers  and  safety  collars  on 
emery  wheels. 

Preventing  Mismanipulation  of  Controlling  Devices. — Many  machines, 
machine  parts  and  electrical  equipment  cause  accidents  through  mismanipu- 
lation.  Among  these  might  be  mentioned  overwinds,  the  closing  of  electric 
circuits  while  men  are  repairing  parts  thereof;  the  unintentional  opening  of 
valves  allowing  steam  or  hot  water  to  enter  boilers  in  which  repair  men  are  at 
work,  and  the  like.  Overwinds  may  be  prevented  by  reliable  overwind  pre- 
ventors  or  regulating  devices  attached  to  the  engine  which  will  not  allow  a 
safe  speed  to  be  exceeded  or  the  landing  to  be  passed.  Many  such  devices 
are  on  the  market.  Switches  controlling  electric  circuits  should  be  provided 
with  means  for  locking  them  open,  the  key  being  carried  by  the  chief  repair 
man.  In  the  case  of  such  circuits  as  trolleys  or  the  cables  feeding  them  an 
additional  precaution  consists  in  placing  an  intentional  temporary  short 
circuit,  e.g.,  a  crowbar,  mine  drill,  piece  of  wire,  etc.,  between  the  trolley  and 
the  rail  a  few  yards  away  from  the  repair  men  in  the  direction  of  the  power 
supply.  Valves  leading  to  the  interior  of  boilers,  feed-water  heaters  and  the 
like  wherein  repairs  are  being  made  should  either  be  locked  in  the  closed  posi- 
tion by  means  of  a  chain  and  padlock  or  some  other  means  should  be  taken 


Tfghfener  Pulle 
ttotor  Pulley -- 


981 


DETAILS  OF6UARD 
FIG.  10 


982  MINE  SAFETY 

which  will  render  it  impossible  for  either  steam  or  hot  water  to  be  turned  in 
upon  them. 

The  foregoing  are  only  a  few  suggestions  of  the  many  means  which  may  be 
employed  to  insure  the  safety  of  workers  around  coal  mines.  Many  others 
will  doubtless  suggest  themselves  and  be  found  advisable  to  install  under 
specific  circumstances. 

Safety  Practices  of  the  H.  C.  Frick  Coke  Co.— In  the  proceedings  of  the 
American  Institute  of  Mining  Engineers,  vol.  51,  page  345,  Thomas  W. 
Dawson  gives  the  following  r6sum6  of  the  safety  practices  employed  by  the 
H.  C.  Frick  Coke  Co.  These  are  all  well  worthy  of  careful  consideration  by 
the  official  who  really  wishes  to  make  his  mines  as  safe  as  possible. 

Every  official  and  foreman  of  the  company  is  continually  impressed  with 
the  fact  that  "safety"  should  be  the  first  consideration,  and  all  officials  and 
their  subordinates  are  brought  together  as  one  great  committee  on  safety. 
Pamphlets  showing  the  duties  of  the  miner  and  the  manner  in  which  he  may 
protect  himself  from  danger  and  giving  safety  regulations  for  those  working 
around  machinery  have  been  printed  and  generally  distributed.  Permanent 
danger  signs  are  placed  wherever  there  is  the  least  possibility  of  an  accident. 
When  men  are  working  in  shafts,  the  "  Men  in  Shaft"  sign  is  placed  so  that 
no  accident  can  be  caused  by  mistake  in  moving  cages.  A  similar  sign  is 
placed  on  hoisting  engines  and  other  machinery  when  it  is  being  repaired. 
When  workmen  are  cleaning  or  making  repairs  to  the  inside  of  a  boiler,  a 
"Man  in  the  Boiler"  sign  is  displayed  outside  and  the  steam  valve  for  this 
boiler  is  locked  and  the  key  carried  by  one  of  the  men  until  the  work  is 
completed.  When  coke-drawing  machines  are  being  repaired  or  cleaned,  the 
"Do  Not  Move"  sign  is  placed  on  the  controller  and  the  trolley  wheel  is 
locked  and  the  key  carried  by  one  of  the  repair  men  until  the  work  is  finished. 
"No  Clearance"  signs  are  conspicuously  displayed  at  all  points  about  the 
plants  where  there  is  no  clearance  for  a  man  between  moving  cars  and  ob- 
structions of  any  character.  Bridge  guards  and  overhead  warning  signs  are 
placed  wherever  needed. 

In  the  mines,  guide  signs  in  various  languages  are  posted  at  road  junctions 
and  on  traveling  ways,  indicating  the  safest  way  out  of  the  mine. 

All  machinery  is  safely  guarded.  These  guards  include  locking  devices 
for  handwheels  of  valves,  safety  locks  for  electric  switches,  guards  for  water 
gauges;  safety  gaskets  to  be  inserted  in  steam  blow-off  and  feed- water  con- 
nections when  cleaning  and  repairing  boilers;  safety  locking  device  for  self- 
dumping  cages;  soap  lubrication  for  air  compressors;  wagon  guard  and 
dumping  platform  for  swing-gate  mine  cars;  spooling  device  for  tail  ropes  on 
haulages;  stiles  or  protected  crossings  over  rope  and  sheaves  where  necessary 
for  men  to  pass;  improved  safety  catch  for  cages;  device  for  positively 
rectifying  wagon  catches  on  car  hauls;  self-closing  hinges  for  shaft  gates ;  steel 
galleries  for  runways  over  boilers,  and  safety  platforms  for  operating  electric 
larries.  "Do  Not  Touch  "  signs  are  used  about  electric  wires,  indicating  vol- 
tage of  ^current;  and  "Do  Not  Pass  Under"  signs  are  used  where  there  is 
danger  in  passing  underneath  structures.  Steel  doors  are  provided  to  drop 
over  shafts  which  have  wooden  head  frames  or  coal  bins  above  them,  should 
these  wooden  structures  catch  fire.  The  company  has  originated  a  device 
for  automatically  controlling  high-pressure  air  compressors.  When  the  tem- 
perature of  the  discharge  air  in  the  pipe  reaches  a  predetermined  point, 
showing  that  the  pressure  is  excessively  high,  it  acts  on  the  thermometer  and 
recording  device,  thus  closing  an  electric  circuit  and  energizing  a  solenoid. 
This  moves  over  a  tripping  device,  which  opens  the  pilot  valve,  releasing  the 
steam  pressure  on  one  side  of  the  regulating  piston.  Thereby  the  valve  on 
the  steam  feed  pipe  is  automatically  closed,  shutting  off  the  steam  and 
stopping  the  compressor. 

All  hoisting  engines  are  equipped  with  an  automatic  overwinding  device, 
which  acts  directly  on  the  engine,  cutting  off  the  steam  and  applying  the 
brakes. 

When  it  is  necessary  to  clean  the  sump  at  the  bottom  of  the  shaft,  the 
cages  are  hoisted  to  a  clearance  height  and  secured  by  iron  pins,  through  holes 
in  the  guides;  these  pins  are  attached  to  the  guides  by  chains,  which  prevent 
their  removal  when  not  in  use. 

At  the  surface  landings  of  all  shaft  mines,  a  device  is  installed  which  pre- 
vents the  gates  from  being  opened  when  the  cage  is  not  in  position  at  the 
landing.  All  hoisting  compartments  of  shafts  are  lined  at  the  cage  ends. 
All  cages  and  safety  catches  are  periodically  inspected,  tested,  and  a  written 
report  made  of  the  inspection.  In  no  case  is  a  hoisting  rope  kept  in  service 


MINE  SAFETY  983 

longer  than  2\  yr.,  even  though  apparently  safe  and  in  good  condition.  Fre- 
quent inspection  of  air  shafts  must  be  made  to  keep  them  open  and  free  at 
all  times  from  ice  and  other  obstructions.  A  fire  boss  must  make  this  exami- 
nation and  travel  either  up  or  down  such  shaft  once  each  day,  the  mine  fore- 
men once  each  two  weeks,  and  the  superintendent  once  a  month. 

The  company's  rules  require  that  in  mines  generating  explosive  gas  not  less 
than  500  cu.  ft.  of  air  per  min.  per  person  employed  in  the  mine  shall  be 
provided  at  the  intake  and  this  must  be  so  distributed  that  there  will  not  be 
less  than  300  cu.  ft.  per  min.  per  person  employed  in  each  split  at  the  working 
faces.  No  mine  shall  have  at  the  intake  less  than  300  cu.  ft.  of  air  per  min. 
per  person  employed,  and  at  the  working  places  at  least  150  cu.  ft.  per  min. 
per  person  employed.  Measurements  of  air  supplied  are  carefully  made  and 
reported  to  the  general  office  once  each  week.  Local  officials  at  mines  gen- 
erating gas  are  required  to  keep  air  up  to  the  working  faces  and  to  such  other 
places  where  explosive  gas  might  be  encountered.  At  a  number  of  the  larger 
and  more  recent  plants,  the  ventilating  fan  is  operated  by  two  engines,  one 
on  each  end,  and  either  of  them  powerful  enough  to  operate  the  fan  in  case  of 
failure  of  the  other.  All  ventilating  systems  in  the  mines  are  ascensional. 

The  Clowes  hydrogen  test  lamp  is  used  in  all  mines  generating  gas,  for 
testing  purposes.  Samples  of  air  are  taken  in  gaseous  mines  and  sent  in 
copper  cans  to  the  company's  laboratory,  where  they  are  analyzed.  The 
results  of  the  analyses  are  reported  to  the  general  office  and  to  the  mine.  If 
these  show  a  percentage  of  explosive  gas  which  might  have  been  detected  by 
the  Clowes  lamp,  the  party  making  the  test  and  reporting  no  gas  is  required 
to  make  an  explanation. 

Boreholes  are  frequently  drilled  from  the  surface  to  release  any  dangerous 
accumulations  of  explosive  gas  in  the  gob,  where  these  cannot  be  remoyed  by 
the  mine  ventilation.  Shot  firers  have  been  employed  to  do  all  blasting  by 
battery,  and  inspect  all  places  where  shots  have  been  fired  to  see  that  there  is 
no  fire  or  other  danger  thereafter.  Only  the  safest  permissible  explosives  are 
used,  and  all  tamping  is  done  with  clay. 

All  safety-lamp  mines  are  examined  on  Sundays,  holidays  and  lay-off  days, 
and  all  mines  which  have  been  idle  for  more  than  two  consecutive  days  are 
examined  before  operations  are  renewed.  In  the  larger  mines,  wherever 
safety  lamps  are  used,  auxiliary  escapeways  are  provided.  In  some  instances 
these  are  stair  shafts  from  the  surface  to  the  mine,  placed  in  the  active  work- 
ing sections,  and  used  also  for  additional  ventilation.  In  other  cases,  means 
of  escape  are  provided  by  having  connections  between  mines,  which  are  closed 
by  double  iron  doors.  Frequent  examinations  are  made  to  see  that  these 
doors  are  always  in  condition  for  use.  Where  coal  dust  occurs,  a  system  of 
pipes  and  a  supply  of  water  under  sufficient  head  and  all  necessary  appliances 
are  provided  to  dampen  thoroughly  the  floor,  sides,  and  roof  of  all  parts  of 
dry  mines. 

On  rope  haulage,  a  device  is  provided  for  disengaging  the  rope  from  the  trip 
as  soon  as  it  is  given  slack.  Brakes  are  provided  for  all  mine  cars  and  2^  ft. 
clearance  is  provided  on  all  haulageways  on  one  side;  this  side  being  indicated 
by  a  wide  whitewashed  strip  on  the  rib.  _ 

Systematic  timbering  systems  are  demised  and  strictly  followed.  Printed 
regulations  cover  the  system  of  timbering  in  rooms,  headings,  and  in  rib  and 
pillar  drawing;  these  are  worked  out  to  suit  conditions  at  the  various  mines. 
Timbering  is  not  set  without  caps  or  cross-bars. 

All  mines  have  complete  mine-telephone  systems.  Stables,  pump  rooms, 
haulage-engine  rooms,  shaft  bottoms,  underground  offices  and  all  such  places 
where  men  might  congregate  are  of  fireproof  construction  and  are  kept  clean 
and  neat.  No  open  lights  are  allowed  in  any  building.  Cans  are  provided 
for  the  reception  of  oily  waste,  grease,  small  quantities  of  oil,  etc.  All 
electric  wiring  is  carefully  inspected  twice  each  year.  All  bare  power  lines 
underground  and  on  the  surface  are  properly  guarded  for  their  entire  length 
by  a  neat  wooden  guard,  so  as  to  prevent  the  workman  or  his  tools  from  com- 
ing in  contact  with  the  same.  For  the  same  reason,  trolley  wires  for  coke- 
drawing  machines  are  placed  at  a  sufficient  height  to  make  contact  with  tools 
unlikely.  A  system  of  checking  men  in  and  out  of  the  workings  is  maintained 
at  all  of  the  mines.  All  abandoned  places  in  the  mines  are  fenced  off. 

The  company  employs  four  mine  inspectors,  one  of  them  acting  as  cruet. 
It  is  the  duty  of  these  men  to  visit  each  mine  and  thoroughly  inspect  it  at 
least  once  every  60  days.  When  an  accident  occurs  in  or  about  any  mine, 
the  chief  mine  inspector  promptly  visits  the  scene  of  the"  accident,  gathers  all 
of  the  data  he  can  relative  thereto  and  makes  a  sketch  of  the  surroundings. 


984  MINE  SAFETY 

This  sketch  is  put  into  permanent  form,  blueprinted  and  sent  to  each  mine 
with  a  circular  letter,  giving  a  full  account  of  the  accident  and  making  sug- 
gestions for  the  prevention  of  similar  ones.  This  is  discussed  at  the  meeting 
of  the  local  officials  at  each  plant.  Once  each  week,  the  superintendent  of 
each  plant  and  his  subordinates  meet  and  discuss  mine  conditions  and  opera- 
tions in  general  and  especially  matters  pertaining  to  the  safety  of  their 
employees.  The  discussions  of  these  meetings  are  reported  to  the  General 
Superintendent  each  week.  General  meetings  are  held  at  stated  intervals  at 
the  general  office,  which  are  attended  by  the  superintendent  of  each  plant  and 
.heads  of  departments. 

Projections  for  mine  workings  are  made  far  in  advance  of  the  actual  work, 
and  the  haulage  and  ventilating  problems  are  planned  so  that  when  the  mine 
is  developed  the  best  system  is  in  use.  Specifications  are  written  for  each 
mine,  stating  where  and  how  the  mining  is  to  be  done.  The  officials  of  the 
company  make  detailed  inspections  at  intervals,  insuring  that  their  instruc- 
tions and  the  best  methods  are  actually  followed. 

A  safety  committee  of  three  or  four  men  is  appointed  at  each  mine,  which 
inspects  periodically  the  working  places,  roadways,  ventilation  and  any  other 
things  which  in  its  opinion  might  be  the  cause  of  an  accident.  The  com- 
mittee reports  in  writing  to  the  superintendent  of  the  mine,  who  forwards  the 
same  to  the  general  office.  These  suggestions  are  immediately  acted  upon 
and  all  dangers  reported,  should  there  be  any,  are  removed  as  quickly  as 
possible.  .  Three  rescue  and  first-aid  stations  are  maintained  at  the  different 
plants  of  the  company,  which  are  fully"  equipped  with  the  best  apparatus  and 
accessories  obtainable.  About  400  men  have  been  thoroughly  trained  and 
qualified  in  both  rescue  and  first-aid  work,  local  contests  being  held  by  the 
different  teams  at  various  times. 

Emergency  hospitals,  fully  equipped,  have  been  provided  at  a  number  of 
the  largest  mines. 

Tests  are  made  frequently  for  gas  above  roof  falls  in  gobs.  Work  is 
prohibited  in  any  place  in  which  gas  is  found,  until  after  it  has  been  removed. 
Mine  inspectors  instruct  all  new  employees  about  the  dangers  of  their  work. 

MINE-RESCUE  WORK 

Mine-rescue  work  is  usually  understood  to  mean  the  rescue  of  men  or  the 
recovery  of  bodies  after  a  mine  explosion,  mine  fire  or  other  disaster.  In  the 
case  of  explosions  or  fires  it  implies  the  use  of  so-called  rescue  apparatus 
consisting  of  oxygen  helmets,  mouth-breathing  apparatus,  etc. 

Organization. — The  organization  for  mine-rescue  work  will  differ  so 
widely  with  local  conditions  that  but  little  may  be  said  on  the  subject  in  a 
book  of  this  kind.  Careful  preparation  and  training  of  a  rescue  crew  here 
means  everything.  While  rescue  work  may  be  undertaken  by  untrained 
men  it  is  necessarily  much  slower  and  more  dangerous  than  where  a  well- 
trained,  well-disciplined  and  thoroughly  reliable  team  of  helmet  men  are  at 
hand.  As  to  the  selection,  organization  and  training  of  a  helmet  crew  the  U. 
S.  Bureau  of  Mines  has  done  much  valuable  work  along  this  line,  and  every 
mine  or  group  of  mines  under  one  management  should  avail  itself  of  the  in- 
struction, training  and  advice  of  the  mine-rescue  experts  on  the  various 
mine-rescue  cars  maintained  by  the  government.  At  least  four  helmets  and 
preferably  six  should  be  available  at  all  times  for  immediate  use,  and  the 
organization  of  the  team  should  be  such  that  not  more  than  half  its  members 
should  be  underground  at  any  one  time,  that  is,  with  a  rescue  team  contain- 
ing 12  men,  6  should  at  all  times  be  available  for  instant  call  to  service,  and 
at  least  4  of  these  should  be  thoroughly  familiar  with  the  underground  work- 
ings. All  should  be  men  of  good  physique,  sound  heart  and  of  known  re- 
liability, nerve  and  coolness. 

First  Steps  after  a  Disaster. — It  is  extremely  important  that  immediately 
upon  the  occurrence  of  a  mine  disaster,  such  as  an  explosion,  that  the  proper 
steps  toward  rescue  be  taken  promptly.  Here  again  much  will  depend  upon 
circumstances  and  local  conditions,  but  in  a  general  sense  the  following  is 
necessary.  Call  the  helmet  men  together,  summon  aid  from  nearby  mines, 
summon  the  nearest  government  mine-rescue  car.  It  is  important  that 
exploration  work  start  as  promptly  as  possible.  Consequently  the  helmet 
men  should  precede  all  others  into  the  mine.  There  are  two  other  important 
considerations  which  require  careful  attention;  the  ventilation  must  be 
restored  as  quickly  as  possible  and  the  means  of  communicating  with  the 
underground  workings  must  be  kept  intact  or  repaired  immediately.  If  the 
mine  is  a  shaft  operation  the  hoisting  cages  if  damaged  should  be  repaired  as 


MINE  SAFETY  935 

quickly  as  possible  or  if  this  is  out  of  the  question  a  temporary  means  of  rais- 
ing and  lowering  men  and  material  must  be  had.  For  this  purpose  some 
mines  keep  on  hand  an  emergency  cage  so  that  if  the  regular  cages  are  put 
out  of  commission,  men  at  least  may  still  be  raised  and  lowered  by  the 
emergency  apparatus. 

Reversing  the  Air  Current. — An  explosion  usually  causes  more  or  less 
havoc  with  the  underground  ventilating  system,  that  is,  brattices  are  fre- 
quently destroyed,  stoppings  broken  down,  etc.  There  is  a  wide  diversity  of 
opinion  among  engineers  and  mine  men  in  general  concerning  the  advisability 
of  reversing  the  air  current,  that  is,  changing  a  blowing  fan  to  an  exhauster  and 
vice  versa  after  a  mine  disaster.  This  is  a  question,  the  expediency  of  which 
had  better  be  thought  out  before  the  explosion  occurs,  or  in  any  instance  the 
current  should  not  be  reversed  without  due  and  careful  consideration.  Men 
attempting  to  find  their  way  out  of  the  mine  after  a  disaster  are  apt  to  be 
guided  largely  by  the  air  current  flowing.  They  are  in  utter  darkness  unless 
of  course  they  be  provided  with  safety  lamps  or  electric  lamps  and  will 
naturally  move  against  the  air  current.  If  this  current  is  reversed  it  will  in 
many  instances  drive  the  foul  and  poisonous  gases  resulting  from  the  explo- 
sion directly  upon  them.  There  may  however  be  instances  wherein  it  would 
be  advisable  to  reverse  the  current. 

The  Work  of  Recovery. — Mine-rescue  and  recovery  work  requires  above 
all  else  a  strong  and  careful  leader.  This  leader  should  if  possible  be  known 
at  least  by  reputation  to  all  the  men  engaged  in  the  work.  He  should  be  a 
man  whom  all-  can  respect  and  trust. 

After  it  has  been  ascertained  that  the  fan  is  in  working  order  and  at  work 
(an  auxiliary  fan  may  be  used  if  necessary),  and  a  means  of  access  to  the 
mine  is  established,  the  helmet  men  with  their  mice,  canaries  or  qther  means  of 
testing  the  gas  may  enter  the  mine.  These  men  are  to  the  main  body  of  the 
rescuers  what  the  scouts  are  to  an  army — inlarge  measure  at  least  they  con- 
stitute the  department  of  security  and  information.  Their  work  will  be  to 
explore  the  mine,  ascertain  the  presence  of  dangerous  gas  and  bring  to  a 
point  of  safety  any  living  men  that  may  be  found.  Unhelmeted  men  should 
follow  them,  restoring  the  ventilation  as  they  go.  This  usually  requirestthe 
building  of  a  considerable  amount  of  temporary  bratticework  and  stoppings 
and  material  therefor  (boards,  plank,  posts,  canvass,  nails,  spikes,  etc.) 
must  be  provided.  No  one  should  be  allowed  to  enter  the  mine  merely 
through  curiosity.  Whoever  enters  should  be  immediately  put  to  work. 
The  person  directing  recovery  work  may  do  so  either  from  the  surface,  the 
foot  of  the  shaft  or  some  other  convenient  point,  communicating  with  his 
various  lieutenants  either  by  word  of  mouth,  by  telephone  if  possible  or  in 
some  instances  by  messenger  at  frequent  intervals. 

The  person  directing  rescue  and  recovery  work  should  be  careful  in  his 
selection  of  lieutenants.  The  ventilation  apparatus  is  perhaps  the  most 
important  of  all  machinery.  It  must  be  kept  going,  or  if  a  shutdown  is 
absolutely  necessary,  this  must  be  anticipated,  a  sufficient  amount  of  time  to 
allow  all  men,  helmeted  as  well  as  unhelmeted  to  be  withdrawn,  from  the  mine 
before  the  air  current  is  actually  stopped.  It  is  well  therefore  to  place  an 
experienced  man  at  the  fan,  whose  sole  duty  it  shall  be  to  keep  it  in  opera- 
tion. If  necessary,  this  man  should  have  all  the  helpers  he  may  require. 
The  hoisting  apparatus  is  also  important,  but  if  possible  the  regular  hoist  man 
should  stick  to  his  post.  There  should  be  appointed  a  gang  whose  duty 
should  be  to  secure  and  bring  to  the  mouth  of  the  mine  the  materials  neces- 
sary for  bratticing.  If  the  mine  is  electrically  lighted  a  competent  electrician 
with  a  requisite  number  of  helpers  should  be  put  to  work  repairing  or  estab- 
lishing lighting  conditions.  The  brattice  men  fol^wing  the  helmet  crew 
should  be  under  an  experienced  brattice  builder  who  is  competent  to  see  that 
the  work  is  done  properly  and  rapidly;  in  many  instances  also  a  man  with 
such  assistance  as  he  may  need  may  be  employed  to  transport  the  various 
materials  from  the  mine  entrance  to  the  point  where  they  are  needed. 
Furthermore,  since  mine  rescue  work  usually  lasts  for  several  hours  or  even 
days  a  commissary  department  should  be  established  so  that  food  such  as 
sandwiches,  hot  soup  and  particularly  hot  coffee  may  be  served  to  the  men 
at  work  at  regular  intervals  and  the  coffee  whenever  they  desire  it.  Men 
skilled  in  first  aid  as  well  as  physicians  should  also  be  on  hand  to  give  prompt 
and  efficient  treatment  to  any  men  that  may  be  found  alive.  The  helmet 
men  will  of  course  remove  few  if  any  dead  bodies  so  long  as  there  is  even  hope 
of  finding  living  people  in  the  mine.  Once  a  man  is  found  alive  he  should  be 
promptly  taken  to  a  point  where  at  least  reasonably  pure  air  is  available. 


986 


MINE  SAFETY 


In  selecting  his  lieutenants  heading  the  various  gangs  or  groups   of  men 
above  mentioned,  the"  man  in  charge  should  use  careful  discretion  and  dele- 


ate to  each  subordinate  the  work  with  which  that  particular  man  is  most 
familiar.  Thus  a  mine  official  of  even  high  standing  such  as  a  superintendent 
might  be  given  a  job  of  caging  at  the  ground  landing  if  he  were  known  to 
have  had  successful  previous  experience  at  that  kind  of  work.  The  man  in 
charge  of  the  transporting  of  material  from  the  shaft  bottom  to  the  point  of 
use  might  be  a  mine  superintendent  or  he  might  be  a  motor  boss,  depending 
on  his  previous  experience  in  the  transportation  department.  The  main  idea 
is  that  every  man  in  charge  of  a  gang  should  know  the  work  which  he  is 
called  upon  to  do,  know  it  well  and  be  a  person  that  can  be  depended  upon. 
The  success  of  mine-rescue  work,  that  is,  the  recovery  of  living  men,  will  often 
depend  much  upon  the  coolness,  good  judgment  and  persistence  of  the  man 
or  men  in  charge  of  this  work.  The  careful  mine  official  will  therefore  think 
out  and  decide  many  possible  mine-rescue  problems  before  the  actual  time  of 
disaster  arrives.  _ 

MINE-RESCUE  APPARATUS 

Mine-rescue  apparatus,  so-called,  is  of  two  general  types:  (a)  breathing 
apparatus,  used  by  the  rescue  crew,  and  (b)  resuscitation  apparatus  used  by 
or  rather  on  the  people.  recovered. 

Breathing  Apparatus.  —  There  are  two  types  of  breathing  apparatus  in 
general  use  in  the  United  States.  These  are  known  respectively  as  helmet 
apparatus  and  mouth-breathing  apparatus.  The  helmet  apparatus  consists 
or  a  metal  helmet  which  may  be  strapped  over  the  face  and  be  rendered  air- 
tight by  an  inflatable  gasket  which  fits  under  the  chin  and  extends  upwards 
completely  encircling  the  front  portion  of  the  head  or  by  other  means. 


PIG.  1 

The  rear  portion  of  the  head  is  protected  by  a  leather  apron.  The  mouth- 
breathing  apparatus  is  exactly  similar  except  that  in  place  of  the  helmet  a 
mouthpiece  which  is  provided  with  a  device  to  close  the  nostrils  of  the  nose 
is  strapped  onto  the  head.  The  oxygen  containers,  pipes,  breathing  bag  and 
regenerator  are  at  least  similar  if  not  identical  in  the  two  types  and  sometimes 
are  made  interchangeable. 

The  operation  of  the  instrument  is  simple  and  may  be  readily  understood 
from  the  diagrammatic  drawing  Fig.  1.  The  oxygen  tanks  A  A  are  connected 
together  and  the  flow  of  oxygen  is  regulated  by  the  valve  B.  Opening  this 
valve  allows  the  compressed  oxygen  in  the  tanks  to  flow  to  the  pressure 
gauge  C  and  to  the  reducing  valve  D,  which  is  fitted  with  a  safety  valve  E. 
The  oxygen  is  reduced  to  a  predetermined  pressure  in  the  regulating  valve 
and  next  passes  to  the  injector  F.  It  then  flows  through  the  pipe  G  to  the 
inhalation  compartment  of  breathing  bag  H  and  from  thence  to  the  mouth- 
piece or  helmet.  After  being  exhaled  from  the  lungs  the  gas  passes  to  a 


MINE  SAFETY 


987 


second  compartment  or  exhalation  bag  /  which  is  part  and  parcel  of  the 
inhalation  bag  but  separated  therefrom  by  a  partition.  From  here  it  passes 
through  the  pipe  J  to  the  regenerator.  This  is  provided  with  potash  in  a 
granular  form  which  is  arranged  in  wire  gauze  trays  around  which  the  exhaled 
oxygen  passes  and  from  which  the  carbon  dioxide  is  absorbed  by  the  chem- 
ical. It  then  passes  through  the  pipe  K  to  the  injector  where  it  is  reoxygen- 
ated  and  again  passed  to  the  breathing  bag  //  to  be  inhaled.  Under  ordinary 
conditions  the  oxygen  tanks  contain  sufficient  compressed  oxygen  for  2  hr. 
of  hard  work.  A  smaller  regenerator  is  sometimes  employed  for  practice 
work  in  the  smoke. room,  thus  reducing  the  cost  of  each  practice.  When  the 
mouth-breathing  apparatus  is  used,  it  is  advisable  to  supply  the  wearer  with 
smoke  goggles  to  protect  the  eyes  in  case  work  is  being  done  in  any  gas  which 
would  tend  to  irritate  them. 

The  operation  of  the  helmet  is  practically  the  same  as  that  of  the  mouth- 
breathing  apparatus  above  described  except  that  the  helmet  is  substituted 
in  place  of  the  mouthpiece.  The  mouth-breathing  .  —- 

apparatus  is  somewhat  lighter  and  simpler 'both  in 
construction  and  operation  than  is  the  helmet.  The 
helmet,  however,  possesses  the  advantage  of  allowing 
the  wearer  to  talk  with  his  companions  which  is  diffi- 
cult, if  not  impossible,  with  the  mouth-breathing 
apparatus. 

Oxygen  for  use  with  mine-rescue  apparatus  may  be 
purchased  in  large  cylinders  from  whence  it  may  be 
transferred  to  the  small  cartridges  of  the  breathing 
apparatus  by  means  of  a  suitable  hand  pump.  Such 
pumps  are  usually  made  double-acting  and  will  com- 
press the  oxygen  in  the  small  tanks  to  approximately 
120  atmospheres. 

Self  Rescuer. — A  small  type  of  breathing  apparatus 
for  use  in  noxious  or  poisonous  gases  and  holding  a 
charge  of  oxygen  sufficient  for  30  min.  work  is  known 
as  ^  the  self  rescuer.  This  apparatus  is  compact, 
weighs  about  6J.£  lb.,  can  be  quickly  adjusted  to  the 
wearer  and  does  not  require  previous  training.  This 
apparatus  is  shown  diagramatically  in  Fig.  2.  Here 
5  represents  the  oxygen  cylinder,  U  the  closing  valve, 
P  the  potash  or  regenerating  cartridge,  A  the  breath- 
ing bag,  L  the  respiration  pipe  which  is  provided  with 
the  rubber  mouthpiece  M.  The  apparatus  is  sus- 
pended by  a  strap  around  the  neck  while  a  canvas 
apron  fastened  around  the  waist  holds  the  apparatus 
in  place.  The  exhaled  air  flows  through  the  respira- 
tion pipe  L  into  the  regenerator  P  where  it  is  subjected  to  the  action  of 
the  carbon-dioxide-absorbihg  chemicals.  Freed  from  the  products  of  respira- 
tion the  air  enters  the  breathing  bag  A  where  a  fresh  oxygen  supply  is  pro- 
vided from  the  cylinder  S.  The  regenerated  air  is  again  drawn  through 
the  potash  cartridge  where  it  is  once  more  subjected  to  purification  and 
is  inhaled  through  the  pipe  L.  Care  must  be  taken  with  any  of  these  instru- 
ments to  provide  fresh  potash  cartridges  for  regenerating  the  air.  Fresh 
cartridges  when  shaken  will  rattle,  spent  ones  will  not. 

Resuscitation  Apparatus. — In  cases  of  partial  asphyxiation  from  poisonous 
gas  or  drowning,  severe  electric  shock,  etc.,  a  means  of  compelling  the  patient 
to  breathe  is  necessary.  This  may  be  supplied  either  by  artificial  respiration 
according  to  the  Schaefer  or  Sylvester  method  or  by  some  variety  of  re- 
suscitation apparatus.  One  of  the  simplest  of  resuscitation  apparatuses  is 
shown  in  Fig.  3  and  is  known  as  the  lungmotor.  This  may  be  arranged  to 
administer  either  atmospheric  air  only  or  atmospheric  air  enriched  with  oxy- 
gen either  from  a  charged  tank  or  an  oxygen  generator,  or  pure  9xygen  from 
the  same  source.  The  lungmotor  consists  of  two-air  pumps  which  are  oper- 
ated simultaneously  but  which  are  connected  together  only  by  the  two  flexi- 
ble tubes  leading  to  the  face  mask.  After  the  face  mask  has  been  adjusted 
and  strapped  in  place  and  the  adjustment  for  the  size  of  the  patient  made 
by  turning  the  pin  A  so  as  to  give  the  proper  length  of  stroke  to  the  two 
pumps  the  handle  of  the  machine  is  simply  worked  up  and  down  at  the  normal 
rapidity  of  breathing;  the  operator  may  judge  this  from  his  own  respiration. 
Air  is  thus  gently  but  positively  forced  into  and  withdrawn  from  the  patient's 
lungs,  the  lungs  meanwhile  being  maintained  at  their  normal  inflation.  In 


FIG.  2 


MINE  SAFETY 


FIG.  4 


NATURAL  SINES  AND  COSINES  989 

case  it  is  desired  to  administer  to  the  patient  an  atmosphere  richer  in  oxygen 
than  atmospheric  air  a  charged  tank  of  oxygen  or  an  oxygen  generator  may 
be  connected  to  the  nipple  C  which  forms  the  oxygen  inlet.  An  adjustment 
of  the  mixing  valve  B  renders  it  possible  to  administer  all  air,  all  oxygen,  or 
any  desired  mixture^of  the  two.  This  apparatus  is  light,  positive  in  action, 
easily  portable  and  is  not  dependent  for  operation  upon  a  supply  of  oxygen 
either  compressed  in  tanks  or  generated  as  required. 

Another  type  of  apparatus  which  has  been  used  to  a  considerable  extent 
is  known  as  the  pulmotor.  The  motive  power  for  this  machine  is  the  oxygen 
compressed  in  the  cylinder  C  (see  Fig.  4).  When  the  valve  V  is  opened  the 
full  pressure  of  the  oxygen  in  the  tank  is  exerted  upon  valve  D.  _  It  is  here 
reduced  to  75  Ib.  per  sq.  in.  and  at  this  pressure  passes  to  the  injector  5. 
Here  the  oxygen  is  fed  at  the  rate  of  £  cu.  ft.  per  min.  through  the  tube  L. 
The  injector  is  so  arranged,  'however,  that  while  accomplishing  this  function 
it  will  create  a  suction  through  a  line  connected  to  the  outside  air,  thus 
drawing  in  a  large  volume  of  atmospheric  air,  mixing  it  with  the  oxygen  and 
forcing  it  through  tube  E  to  the  lungs,  which  are  represented  by  the  bag  at 
the  bottom  of  the  figure.  This  action  continues  until  the  lungs  are  inflated 
to  a  measured  amount.  There  being  no  valve  or  other  obstruction  to 
prevent,  this  increase  of  pressure  acts  through  the  tube  A  which  leads  to  the 
bellows  B.  As  soon  as  the  pressure  attains  .29  Ib.  per  sq.  in.  this  pressure 
forces  the  head  of  the  bellows  outward  reversing  the  pulmotor  valve  L 
through  the  medium  of  a  tension  spring.  The  suction  action  of  the  nozzle 
5  is  now  cut  off  from  the  outside  circuit  and  is  carried  through  the  return  air 
tube  A  which  is  connected  through  the  face  mask  to  the  lungs.  Air  from  the 
lungs  is  thus  exhausted  to  the  outside  air  until  a  proper  vacuum  amounting 
to  .37  Ib.  per  sq.  in.  is  developed  in  the  lungs,  when  the  bellows  contracts 
under  the  action  of  the  vacuum  throwing  the  valve  back  to  its  original  posi- 
tion and  starting  the  cycle  of  operations  over  again.  This  action  proceeds  at 
the  rate  of  from  14  to  18  strokes  per  min. 

The  entire  equipment,  including^  several  sizes  of  face  masks,  is  packed  in  a 
wooden  carrying  case  for  convenience  in  transportation.  This  apparatus 
has  the  advantage  of  being  automatic  in  action  but  is  somewhat  complicated. 
It  has,  however,  been  used  to  a  wide  extent  and  with  considerable  success. 


TABLE  OF  NATURAL  SINES,  COSINES, 
TANGENTS,  AND  COTANGENTS 


EXPLANATION 

Given  an  angle,  to  find  its  sine,  cosine,  tangent,  and  cotangent 

To  find  the  sine,  cosine,  tangent,  and  cotangent  of  37°  24',  look  in  the  table 
of  natural  sines  along  the  tops  of  the  pages,  and  find  37°.  Glancing  down  the 
left-hand  column  marked  ('),  until  24  is  found,  find  opposite  this  24  in  the 
column  marked  sine  and  headed  37°,  the  number  .60738;  then  .60738  = 
sin  37°  24'.  Similarly,  find  in  the  column  marked  cosine  and  headed  37°, 
the  number  .79441,  which  corresponds  to  cos  37°  24'.  So,  also,  find  in  the 
column  marked  tangent  and  headed  37°,  and  opposite  24',  the  number 
.76456;  and  in  the  column  marked  cotangent  and  headed  37°,  and  opposite 
24',  the  number  1.30795. 

In  most  of  the  tables  published,  the  angles  run  only  from  0  to  45  at  the 
heads  of  the  columns;  to  find  an  angle  greater  than  45°,  look  at  the  bottom  oj 
the.  page  and  glance  upwards,  using  the  extreme  right-hand  column  to  find 
minutes,  which  begin  with  0  at  the  bottom  and  run  upwards,  1,  2,  3,  etc., 

To  find  the  sine  of  77°  43',  look  along  the  bottom  of  the  tables  until  the 
column  marked  sine  and  marked  77°  is  found.  Glancing  up  the  column  of 
minutes  on  the  right  until  43'  is  found,  find  opposite  43'  in  the  column  marked 
sine  at  the  bottom  and  marked  77°,  the  number  .97711;  this  is  the  sine  of 
77°  43'.  Similarly,  the  cosine,  tangent,  and  cotangent  may  be  found. 

To  find  the  sine,  cosine,  tangent,  or  cotangent  of  an  angle  whose  exact 
value  is  not  given  in  the  table: 


f 

990  NATURAL  SINES  AND  COSINES 

Rule. — Find  in  the  table  the  sine,  cosine,  tangent,  or  cotangent  corresponding 
to  the  degrees  and  minutes  of  the  angle.  For  the  seconds,  find  the  difference  of 
the  values  of  the  sine,  cosine,  tangent,  or  cotangent  taken  from  the  table  between 
which  the  seconds  of  the  angle  fall;  multiply  this  difference  by  a  fraction  whose 
numerator  is  the  number  of  seconds  in  the  given  angle  and  whose  denominator 
is  60. 

//  sine  or  tangent,  add  this  correction  to  the  value  first  found;  if  cosine  or 
cotangent,  subtract  the  correction. 

EXAMPLE. — Find  the  sine,  cosine,  tangent,  and  cotangent  of  56°  43'  17". 

SOLUTION.— Sin  56°  43'  =  .83597.  Sin  56°  44'  =  .83613.  As  56°  43'  17" 
is  greater  than  56°  43'  and  less  than  56°  44',  the  value  of  the  sine  of  the  angle 
lies  between  .83597  and  .83613;  the  difference  equals  .83613  -  .83597  = 
.00016;  multiplying  this  by  the  fraction  JJ,  .00016  X  H  =  .00005,  nearly, 
which  is  to  be  added  to  .83597,  the  value  first  found,  or  .83597  +  .00005  = 
.83602.  Hence,  sin  56°  43'  17"  =  .83602. 

Cos  56°  43'  =  .54878;  cos  56°  44'  =  .54854;  the  difference  equals  .54878 
—  .54854  =  .00024,  and  .00024  X  II  =  .00007,  nearly.     Now,  as  the  cosine 
is  desired,  this  correction  must  be  subtracted  from  cos  56°  43',  or  .54878; 
subtraction,  .54878  -  .00007  =  .54871.     Hence,  cos  56°  43'  17"  =  .54871. 
Given  the  sine,  cosine,  tangent,  or  cotangent,  to  find  the  angle  corresponding 

If  the  sine  of  an  angle  is  .47486;  what  is  the  angle?  Consulting  the  table 
of  natural  sines,  glance  down  the  columns  marked  sine  until  .47486  is  found, 
opposite  21'  in  the  left-hand  column  and  under  the  column  headed  28°. 
Therefore,  the  angle  whose  sine  =  .47486  is  28°  21',  or  sin  28°  21'  =  .47486. 

To  find  the  angle  corresponding  to  a  given  sine,  cosine,  tangent,  or  co- 
tangent whose  exact  value  is  not  contained  in  the  table: 

Rule. — Find  the  difference  of  the  two  numbers  in  the  table  between  which  the 
given  sine,  cosine,  tangent,  or  cotangent  falls,  and  use  the  number  of  parts  in 
this  difference  as  the  denominator  of  a  fraction. 

Find  the  difference  between  the  number  belonging  to  the  smaller  angle  and  the 
given  sine,  cosine,  tangent,  or  cotangent,  and  use  the  number  of  parts  in  the  dif- 
ference just  found  as  the  numerator  of  the  ftaction  just  mentioned.  Multiply 
this  fraction  by  60,  and  the  result  will  be  the  number  of  seconds  to  be  added  to  the 
smaller  angle. 

EXAMPLE. — Find  the  angle  whose  sine  equals  .57698. 

SOLUTION. — Looking  in  the  table  of  natural  sines,  in  the  column  marked 
sine,  it  is  found  between  .57691  =  sin  35°  14'  and  .57715  =  35°  15'.  The 
difference  between  them  is  .57715  -  .57691  =  .00024,  or  24  parts.  The 
difference  between  the  sine  of  the  smaller  angle,  or  sine  35°  14'  =  .57691, 
and  the  given  sine,  or  .57698,  is  .57698  —  .57691  =  .00007,  or  7  parts. 

Then,  /4  X  60  =  17.5",  and  the  angle  =  35°  14'  17.5",  or  sin  35°  14'  17.5" 
=  .57698. 

The  cosecant  of  an  angle  is  equal  to  the  reciprocal  of  its  sine,  and  the 
secant  is  equal  to  the  reciprocal  of  its  cosine.  Hence,  to  multiply  a  quantity 


by  the  cosecant,  divide  it  by  the  sine;  or,  to  divide  it  by  the  cosecant,  multi- 
ply it  by  the  sine.  Similarly,  to  multiply  a  quantity  by  the  secant  of  an 
angle,  divide  it  by  the  cosine;  or,  to  divide  it  by  the  secant,  multiply  it  by 


NATURAL  SINES  AND  COSINES 


991 


/ 

fl 

P 

1 

0 

2 

0 

5 

0 

4 

0 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.00000 

1. 

.01745 

.99985 

.03490 

.99939 

.05234 

.99863 

.06976 

.99756 

60 

1 

.00029 

1. 

.01774 

.99984 

.03519 

.99938 

.05263 

.99861 

.07005 

.99754 

59 

2 

.00058 

.01803 

.99984 

.03548 

.99937 

.05292 

.99860 

.07034 

.99752 

58 

3 

.00087 

.01832 

.99983 

.03577 

.99936 

.05321 

.99858 

.07063 

.99750 

57 

4 

.00116 

.01862 

.99983  " 

.03606 

.99935 

.05350 

.99857 

.07092 

.99748 

56 

5 

.00145 

.01891 

.99982 

.03635 

.99934 

.05379 

.99855 

.07121 

.99746 

55 

6 

.00175 

.01920 

.99982 

.03664 

.99933 

.05408 

.99854 

.07150 

.99744 

54 

7 

.00204 

.01949 

.99981 

.03693 

.99932 

.05437 

.99852 

.07179 

.99742 

53 

8 

.00233 

.01978 

.99980 

.03723 

.99931 

.05466 

.99851 

.07208 

.99740 

52 

9 

.00262 

.02007 

.99980 

.03752 

.99930 

.05495 

.99849 

.07237 

.99738 

51 

10 

.00291 

.02036 

.99979 

.03781 

.99929 

.05524 

.99847 

.07266 

.99736 

50 

11 

.00320 

.99999 

.02065 

.99979 

.03810 

.99927 

.05553 

.99846 

.07295 

.99734 

49 

12 

.00349 

.99999 

.02094 

.99978 

.03839 

.99926 

.05582 

.99844 

.07324 

.99731 

48 

13 

.00378 

.99999 

.02123 

.99977 

.03868 

.99925 

.05611 

.99842 

.07353 

.99729 

47 

14 

.00407 

.99999 

.02152 

.99977 

.03897 

.99924 

.05640 

.99841 

.07382 

.99727 

46 

15 

.00436 

.99999 

.02181 

.99976 

.03926 

.99923 

.05669 

.99839 

.07411 

.99725 

45 

16 

.00465 

.99999 

.02211 

.99976 

.03955 

.99922 

.05698 

•99838 

.07440 

.99723 

44 

17 

.00495 

.99999 

.02240 

.99975 

.03984 

.99921 

.05727 

.99836 

.07469 

.99721 

43 

18 

.00524 

.99999 

.02269 

.99974 

.04013 

.99919 

.05756 

.99834 

.07498 

.99719 

42 

19 

.00553 

.99998 

.02298 

.99974 

.04042 

.99918 

.05785 

.99833 

.07527 

.99716 

41 

20 

.00582 

.99998 

.02327 

.99973 

.04071 

.99917 

.05814 

.99831 

.07556 

.99714 

40 

21 

.00611 

.99998 

.02356 

.99972 

.04100 

.99916 

.05844 

.99829 

.07585 

.99712 

39 

22 

.00640 

.99998 

.02385 

.99972 

.04129 

.99915 

.05873 

.99827 

.07614 

.99710 

38 

23 

.00669 

.99998 

.02414 

.99971 

.04159 

.99913 

.05902 

.99826 

.07643 

.99708 

37 

24 

.00698 

.99998 

.02443 

.99970 

.04188 

.99912 

.05931 

.99824 

.07672 

.99705 

36 

25 

.00727 

.99997 

.02472 

.99969 

.04217 

.99911 

.05960 

.99822 

.07701 

.99703 

35 

26 

.00756 

.99997 

.02501 

.99969 

.04246 

.99910 

.05989 

.99821 

.07730 

.99701 

34 

27 

.00785 

.99997 

.02530 

.99968 

.04275 

.99909 

.06018 

.99819 

.07759 

33 

28 

.00814 

.99997 

.02560 

.99967 

.04304 

.99907 

.06047 

.99817 

.07788 

[99696 

32 

29 

.00844 

.99996 

.02589 

.99966 

.04333 

.99906 

.06076 

.99815 

.07817 

.99694 

31 

30 

.00873 

.99996 

.02618 

.99966 

.04362 

.99905 

.06105 

.99813 

.07846 

.99692 

30 

31 

.00902 

.99996 

.02647 

.99965 

.04391 

.99904 

.06134 

.99812 

.07875 

.99689 

29 

32 

.00931 

.99996 

.02676 

.99964 

.04420 

.99902 

.06163 

.99810 

.07904 

.99687 

28 

33 

.00960 

.99995 

.02705 

.99963 

.04449 

.99901 

.06192 

.99808 

.07933 

.99685 

27 

34 

.00989 

.99995 

.02734 

.99963 

.04478 

.99900 

.06221 

.99806 

.07962 

.99683 

26 

35 

.01018 

.99995 

.02763 

.99962 

.04507 

.99898 

.06250 

.99804 

.07991 

.99680 

25 

36 

.01047 

.99995 

.02792 

.99961 

.04536 

.99897 

.06279 

.99803 

.08020 

.99678 

24 

37 

.01076 

.99994 

.02821 

.99960 

.04565 

.99896 

.06308 

.99801 

.08049 

.99676 

23 

38 

.01105 

.99994 

.02850 

.99959 

.04594 

.99894 

.06337 

.99799 

.08078 

.99673 

22 

39 

.01134 

.99994 

.02879 

.99959 

.04623 

.99893 

.06366 

.99797 

.08107 

.99671 

21 

40 

.01164 

.99993 

.02908 

.99958 

.04653 

.99892 

.06395 

.99795 

.08136 

.99668 

20 

41 

.01193 

.99993 

.02938 

.99957 

.04682 

.99890 

.06424 

.99793 

.08165 

.99666 

19 

42 

.01222 

.99993 

.02967 

.99956 

.04711 

.99889 

.06453 

.99792 

.08194 

.99664 

18 

43 

.01251 

.99992 

.02996 

.04740 

.99888 

.06482 

.99790 

.08223 

.99661 

17 

44 

.01280 

.99992 

.03025 

;99954 

.04769 

.99886 

.06511 

.99788 

.08252 

.99659 

16 

45 

.01309 

.99991 

.03054 

.99953 

.04798 

.99885 

.06540 

.99786 

.08281 

.99657 

15 

46 

.01338 

.99991 

.03083 

.99952 

.04827 

.99883 

.06569 

.99784 

.08310 

.99654 

14 

47 

.01367 

.99991 

.03112 

.99952 

.04856 

[99882 

.06598 

.99782 

.08339 

.99652 

13 

48 

.01396 

.99990 

.03141 

.99951 

.04885 

.06627 

.99780 

.08368 

.99649 

12 

49 

.01425 

.99990 

.03170 

.99950 

.04914 

[99879 

.06656 

.99778 

.08397 

.99647 

11 

50 

.01454 

.99989 

.03199 

.99949 

.04943 

.99878 

.06685 

.99776 

.08426 

.99644 

10 

51 

.01483 

.99989 

.03228 

.99948 

.04972 

.99876 

.06714 

.99774 

.08455 

.99642 

52 

.01513 

.99989 

.03257 

.99947 

.05001 

.99875 

.06743 

.99772 

.08484 

.99639 

53 

.01542 

.99988 

.03286 

.99946 

.05030 

.99873 

.06773 

.99770- 

.08513 

.99637 

54 

.01571 

.99988 

.03316 

.99945 

.05059 

.99872 

.06802 

.99768 

.08542 

.99635 

55 

.01600 

.99987 

.03345 

.99944 

.05088 

.99870 

.06831 

.99766 

.08571 

.99632 

56 

.01629 

.99987 

.03374 

.99943 

.05117 

.99869 

.06860 

.99764 

.08600 

.99630 

57 

.01658 

.99986 

.03403 

.99942 

.05146 

.99867 

.06889 

.99762 

.08629 

.99627 

58 

.01687 

.99986 

.03432 

.99941 

.05175 

.99866 

.06918 

.99760 

.08658 

.99625 

59 

.01716 

.99985 

.03461 

.05205 

.99864 

.06947 

.99758 

.08687 

.99622 

60 

.01745 

.99985 

.03490 

!99939 

.05234 

.99863 

.06976 

.99756 

.08716 

.99619 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

/ 

81 

>° 

« 

;° 

81; 

0 

8( 

)° 

8£ 

0 

992 


NATURAL  SINES  AND  COSINES 


5° 

6° 

70 

8° 

9° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.08716 

.99619 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

60 

1 

.08745 

.99617 

.10482 

.99449 

.12216 

.99251 

.13946 

.99023 

.15672 

.98764 

59 

2 

.08774 

.99614 

.10511 

.99446 

.12245 

.99248 

.13975 

.99019 

.15701 

.98760 

58 

3 

.08803 

.99612 

.10540 

.99443 

.12274 

.99244 

.14004 

.99015 

.15730 

.98755 

57 

4 

.08831 

.99609 

.10569 

.99440 

.12302 

.99240 

.14033 

.99011 

.15758 

.98751 

56 

5 

.08860 

.99607 

.10597 

.99437 

.12331 

.99237 

.14061 

.99006 

.15787 

.98746 

55 

6 

.08889 

.99604 

.10626 

.99434 

.12360 

.99233 

.14090 

.99002 

.15816 

.98741 

54 

7 

.08918 

.99602 

.10655 

.99431 

.12389 

.99230 

.14119 

.98998 

.15845 

.98737 

53 

8 

.08947 

.99599 

.10684 

.99428 

.12418 

.99226 

.14148 

.98994 

.15873 

.98732 

52 

9 

.08976 

.99596 

.10713 

.99424 

.12447 

.99222 

.14177 

.98990 

.15902 

.98728 

51 

10 

.09005 

.99594 

.10742 

.99421 

.12476 

.99219 

.14205 

.98986 

.15931 

.98723 

50 

11 

.09034 

.99591 

.10771 

.99418 

.12504 

.99215 

.14234 

.98982 

.15959 

.98718 

49 

12 

.09063 

.99588 

.10800 

.99415 

.12533 

.99211 

.14263 

.98978 

.15988 

98714 

48 

13 

.09092 

.99586 

.10829 

.99412 

.12562 

.99208 

.14292 

.98973 

.16017 

.98709 

47 

14 

.09121 

.99583 

.10858 

.99409 

.12591 

.99204 

.14320 

.98969 

.16046 

.98704 

46 

15 

.09150 

.99580 

.10887 

.99406 

.12620 

.99200 

.14349 

.98965 

.16074 

.98700 

45 

16 

.09179 

.99578 

.10916 

.99402 

.12649 

.99197 

.14378 

.98961 

.16103 

.98695 

44 

17 

.09208 

.99575 

.10945 

.99399 

.12678 

.99193 

.14407 

.98957 

.16132 

.98690 

43 

18 

.09237 

.99572 

.10973 

.99396 

.12706 

.99189 

.14436 

.98953 

.16160 

.98686 

42 

19 

.09266 

.99570 

.11002 

.99393 

.12735 

.99186 

.14464 

.98948 

.16189 

.98681 

41 

20 

.09295 

.99567 

.11031 

.99390 

.12764 

.99182 

.14493 

.98944 

.16218 

.98676 

40 

21 

.09324 

.99564 

.11060 

.99386 

.12793 

.99178 

.14522 

.98940 

.16246 

.98671 

39 

22 

.09353 

.99562 

.11089 

.99383 

.12822 

.99175 

.14551 

.98936 

.16275 

.98667 

38 

23 

.09382 

.99559 

.11118 

.99380 

.12851 

.99171 

.14580 

.98931 

.16304 

.98662 

37 

24 

.09411 

.99556 

.11147 

.99377 

.12880 

.99167 

.14608 

.98927 

.16333 

.98657 

36 

26 

.09440 

.99553 

.11176 

.99374 

.12908 

.99163 

.14637 

.98923 

.16361 

.98652 

35 

26 

.09469 

.99551 

.11205 

.99370 

.12937 

.99160 

.14666 

.98919 

.16390 

.98648 

34 

2T 

.09498 

.99548 

.11234 

.99367 

.12966 

.99156 

.14695 

.98914 

.16419 

.98643 

33 

28 

.09527 

.99545 

.11263 

.99364 

.12995 

.99152 

.14723 

.98910 

.16447 

.98638 

32 

29 

.09556 

.99542 

.11291 

.99360 

.13024 

.99148 

.14752 

.98906 

.16476 

.98633 

31 

30 

.09585 

.99540 

.11320 

.99357 

.13053 

.99144 

.14781 

.98902 

.16505 

.98629 

30 

31 

.09614 

.99537 

.11349 

.99354 

.13081 

.99141 

.14810 

.98897 

.16533 

.98624 

29 

32 

.09642 

.99534 

.11378 

.99351 

.13110 

.99137 

.14838 

.98893 

.16562 

.98619 

S8 

33 

.09671 

.99531 

.11407 

.99347 

.13139 

.99133 

.14867 

.98889 

.16591 

.98614 

27 

34 

.09700 

.99528 

.11436 

.99344 

.13168 

.99129 

.14896 

.98884 

.16620 

.98609 

26 

35 

.09729 

.99526 

.11465 

.99341 

.13197 

.99125 

.14925 

.98880 

.16648 

.98604 

25 

36 

.09758 

.99523 

.11494 

.99337 

.13226 

.99122 

.14954 

.98876 

.16677 

.98600 

24 

37 

.09787 

.99520 

.11523 

.99334 

.13254 

.99118 

.14982 

.98871 

.16706 

.98595 

23 

33 

.09816 

.99517 

.11552 

.99331 

.13283 

.99114 

.15011 

.98867 

.16734 

.98590 

22 

39 

.09845 

.99514 

.11580 

.99327 

.13312 

.99110 

.15040 

.98863 

.16763 

.98585 

21 

40 

.09874 

.99511 

.11609 

.99324 

.13341 

.99106 

.15069 

.98858 

.16792 

.98580 

20 

41 

.09903 

.99508 

.11638 

.99320 

.13370 

.99102 

.15097 

.98854 

.16820 

.98575 

19 

42 

.09932 

.99506 

.11667 

.99317 

.18399 

.99098 

.15126 

.98849 

.16849 

.98570 

18 

43 

.09961 

.99503 

.11696 

.99314 

.13427 

.99094 

.15155 

.98845 

.16878 

.98565 

17 

44 

.09990 

.99500 

.11725 

.99310 

.13456 

.99091 

.15184 

.98841 

.16906 

.98561 

16 

15 

.10019 

.99497 

.11754 

.99307 

.13485  . 

.99087 

.15212 

.98836 

.16935 

.98556 

15 

46 

.10048 

.99494 

.11783 

.99303 

.13514 

.99083 

.15241 

.98832 

.16964 

.98551 

14 

47 

.10077 

.99491 

.11812 

.99300 

.13543 

.99079 

.15270 

.98827 

.16992 

.98546 

13 

48 

.10106 

.99488 

.11840 

.99297 

.13572 

.99075 

.15299 

.98823 

.17021 

.98541 

12 

49 

.10135 

.99485 

.11869 

.99293 

.13600 

.99071 

.15327 

.98818 

.17050 

.98536 

11 

50 

.10164 

.99482 

.11898 

.99290 

.13629 

.99067 

.15356 

.98814 

.17078 

.98531 

10 

51 

.10192 

.99479 

.11927 

.99286 

.13658 

.99063 

.15385 

.98809 

.17107 

.98526 

9 

52 

.10221 

.99476 

.11956 

.99283 

.13687 

.99059 

.15414 

.98805 

.17136 

.98521 

8 

53 

.10250 

.99473 

.11985 

.99279 

.13716 

.99055 

.15442 

.98800 

.17164 

.98516 

7 

54 

.10279 

.99470 

.12014 

.99276 

.13744 

.99051 

.15471 

.98796 

.17193 

.98511 

6 

55 

.10308 

.99467 

.12043 

.99272 

.13773 

.99047 

.15500 

.98791 

.17222 

.98506 

5 

56 

.10337 

.99464 

.12071 

.99269 

.13802 

.99043 

.15529 

.98787 

.17250 

.98501 

4 

57 

.10366 

.99461 

.12100 

.99265 

.13831 

.99039 

.15557 

.98782 

.17279 

.984% 

3 

58 

.10395 

.99458 

.12129 

.99262 

.13860 

.99035 

.15586 

.98778 

.17308 

.98491 

2 

59 

.10424 

.99455 

.12158 

.99258 

.13889 

.99031 

.15615 

.98773 

.17336 

.98486 

60 

.10453 

.99452 

.12187 

.99255 

.13917 

.99027 

.15643 

.98769 

.17365 

.98481 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

1 

84° 

83° 

82° 

81° 

80° 

NATURAL  SINES  AND  COSINES 


993 


/ 

1 

[)° 

1 

1° 

1 

2° 

1 

3° 

1 

4° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.17365 

.98481 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

60 

1 

.17393 

.98476 

.19109 

.98157 

.20820 

.97809 

.22523 

.97430 

.24220 

.97023 

59 

2 

.17422 

.98471 

.19138 

.98152 

.20848 

.97803 

.22552 

.97424 

.24249 

.97015 

58 

3 

.17451 

.98466 

.19167 

.98146 

.20877 

.97797 

.22580 

.97417 

.24277 

.97008 

57 

4 

.17479 

.98461 

.19195 

.98140 

.20905 

.97791 

.22608 

.97411 

.24305 

.97001 

56 

5 

.17508 

.98455 

.19224 

.98135 

.20933 

.97784 

.22637 

.97404 

.24333 

.96994 

55 

6 

.17537 

.98450 

.19252 

.98129 

.20962 

.97778 

.22665 

.97398 

.24362 

.96987 

54 

7 

.17565 

.98445 

.19281 

.98124 

.20990 

.97772 

.22693 

.97391 

.24390 

.96980 

53 

8 

.17594 

.98440 

.19309 

.98118 

.21019 

.97766 

.22722 

.97384 

.24418 

.96973 

52 

9 

.17623 

.98435 

.19338 

.98112 

.21047 

.97760 

.22750 

.97378 

.24446 

.96966 

51 

10 

.17651 

.98430 

.19366 

.98107 

.21076 

.97754 

.22778 

.97371 

.24474 

.96959 

50 

11 

.17680 

.98425 

.19395 

.98101 

.21104 

.97748 

.22807 

.97365 

.24503 

.96952 

49 

12 

.17708 

.98420 

.19423 

.98096 

.21132 

.97742 

.22835 

.97358 

.24531 

.96945 

48 

13 

.17737 

.98414 

.19452 

.98090 

.21161 

.97735 

.22863 

.97351 

.24559 

.96937 

47 

14 

.17766 

.98409 

.19481 

.98084 

.21189 

.97729 

.22892 

.97345 

.24587 

.96930 

46 

15 

.17794 

.98404 

.19509 

.98079 

.21218 

.97723 

.22920 

.97338 

.24615 

.96923 

45 

16 

.17823 

.98399 

.19538 

.98073 

.21246 

.97717 

.22948 

.97331 

.24644 

.96916 

44 

17 

.17852 

.98394 

.19566 

.98067 

.21275 

.97711 

.22977 

.97325 

.24672 

.96909 

43 

18 

.17880 

.98389 

.19595 

.98061 

.21303 

.97705 

.23005 

.97318 

.24700 

.96902 

42 

19 

.17909 

.98383 

.19623 

.98056 

.21331 

.97698 

.23033 

.97311 

.24728 

.96894 

41 

20 

.17937 

.98378 

.19652 

.98050 

.21360 

.97692 

.23062 

.97304 

.24756 

.96887 

40 

21 

.17966 

.98373 

.19680 

.98044 

.21388 

.97686 

.23090 

.97298 

.24784 

.96880 

39 

22 

.17995 

.98368 

.19709 

.98039 

.21417 

.97680 

.23118 

.97291 

.24813 

.96873 

38 

23 

.18023 

.98362 

.19737 

.98033 

.21445 

.97673 

.23146 

.97284 

.24841 

.96866 

87 

24 

.18052 

.98357 

.19766 

.98027 

.21474 

.97667 

.23175 

.97278 

.24869 

.96858 

36 

25 

.18081 

.98352 

.19794 

.98021 

.21502 

.97661 

.23203 

.97271 

.24897 

.96851 

35 

26 

.18109 

.98347 

.19823 

.98016 

.21530 

.97655 

.23231 

.97264 

.24925 

.96844 

34 

27 

.18138 

.98341 

.19851 

.98010 

.21559 

.97648 

.23260 

.97257 

.24954 

.96837 

33 

28 

.18166 

.98336 

.19880 

.98004 

.21587 

.97642 

.23288 

.97251 

.24982 

.96829 

32 

29 

.18195 

.98331 

.19908 

.97998 

.21616 

.97636 

.23316 

.97244 

.25010 

.96822 

31 

30 

.18224 

.98325 

.19937 

.97992 

.21644 

.97630 

.23345 

.97237 

.25038 

.96815 

30 

31 

.18252 

.98320 

.19965 

.97987 

.21672 

.97623 

.23373 

.97230 

.25066 

.96807 

29 

32 

.18281 

.98315 

.19994 

.97981 

.21701 

.97617 

.23401 

.97223 

.25094 

.96800 

28 

33 

.18309 

.98310 

.20022 

.97975 

.21729 

.97611 

.23429 

.97217 

.25122 

.96793 

27 

34 

.18338 

.98304 

.20051 

.97969 

.21758 

.97604 

.23458 

.97210 

.25151 

.96786 

26 

35 

.18367 

.98299 

.20079 

.97963 

.21786 

.97598 

.23486 

.97203 

.25179 

.96778 

25 

36 

.18395 

.98294 

.20108 

.97958 

.21814 

.97592 

.23514 

.97196 

.25207 

.96771 

24 

37 

.18424 

.98288 

.20136 

.97952 

.21843 

.97585 

.23542 

.97189 

.25235 

.96764 

23 

38 

.18452 

.98283 

.20165 

.97946 

.21871 

.97579 

.23571 

.97182 

.25263 

.96756 

22 

39 

.18481 

.98277 

.20193 

.97940 

.21899 

.97573 

.23599 

.97176 

.25291 

.96749 

21 

40 

.18509 

.98272 

.20222 

.97934 

.21928 

.97566 

.23627 

.97169 

.25320 

.96742 

20 

41 

.18538 

.98267 

.20250 

.97928 

.21956 

.97560 

.23656 

.97162 

.25348 

.96734 

19 

42 

.18567 

.98261 

.20279 

.97922 

.21985 

.97553 

.23684 

.97155 

.25376 

.96727 

18 

43 

.18595 

.98256 

.20307 

.97916 

.22013 

.97547 

.23712 

.97148 

.25404 

.96719 

17 

44 

.18624 

.98250 

.20336 

.97910 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

16 

45 

.18652 

.98245 

.20364 

.97905 

.22070 

.97534 

.23769 

.97134 

.25460 

.96705 

15 

46 

.18681 

.98240 

.20393 

.97899 

.22098 

.97528 

.23797 

.97127 

.25488 

.96697 

14 

47 

.18710 

.98234 

.20421 

.97893 

.22126 

.97521 

.23825 

.97120 

.25516 

.96690 

13 

48 

.18738 

.93229 

.20450 

.97887 

.22155 

.97515 

.23853 

.97113 

.25545 

.96682 

12 

49 
50 

.18767 
.18795 

.98223 
.98218 

.20478 
.20507 

.97881 
.97875 

.22183 
.22212 

.97508 
.97502 

.23882 
.23910 

.97106 
.97100 

.25573 
.25601 

.96675 
.96667 

11 
10 

51 
62 
53 

.18824 

.18852 
.18881 

.98212 
.98207 
.98201 

.20535 
.20563 
.20592 

.97869 
.97863 
.97857 

.22240 
.22268 
.22297 

.97496 
.97489 
.97483 

.23938 
.23966 
.23995 

.97093 
.97086 
.97079 

.25629 
.25657 
.25685 

.96660 
.96653 
.96645 

9 

54 

.18910 

.98196 

.20620 

.97851 

.22325 

.97476 

.24023 

.97072 

.25713 

.96638 

55 

.18938 

.98190 

.20649 

.97845 

.22353 

.97470 

.24051 

.97065 

.25741 

.96630 

56 

.18967 

.98185 

.20677 

.97839 

.22382 

.97463 

.24079 

.97058 

.25769 

.96623 

57 

18995 

.98179 

.20706 

.97833 

.22410 

.97457 

.24108 

.97051 

.25798 

.96615 

58 
69 

.19024 
19052 

.98174 
.98168 

.20734 
.20763 

.97827 
.97821 

.22438 
.22467 

.97450 
.97444 

.24136 
.24164 

.97044 
.97037 

.25826 
.25854 

.96608 
.96600 

60 

.19081 

.98163 

.20791 

.97815 

.22495 

.97437 

.24192 

.97030 

.25882 

.96593 

Oosia* 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

l 

7t 

P 

11 

i° 

77 

o 

76 

o 

75 

3 

63 


994 


NATURAL  SINUS  AND  COSINES 


15° 

16° 

17° 

18° 

19° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.25882 

.96593 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

60 

1 

.25910 

.96585 

.27592 

.96118 

.29265 

.95622 

.30929 

.95097 

.32584 

.94542 

59 

2 

.25938 

.96578 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94533 

58 

3 

.25966 

.96570 

.27648 

.96102 

.29321 

.95605 

.30985 

.95079 

.32639 

.94523 

57 

4 

.25994 

.96562 

.27676 

.96094 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

56 

5 

.26022 

.96555 

.27704 

.96086 

.29376 

.95588 

.81040 

.95061 

.32694 

.94504 

55 

6 

.26050 

.96547 

.27731 

.96078 

.29404 

.95579 

.31068 

.95052 

.32722 

.94495 

54 

7 

.26079 

.96540 

.27759 

.96070 

.29432 

.95571 

.31095 

.95043 

.32749 

.94485 

53 

8 

.26107 

.96532 

.27787 

.96062 

.29460 

.95562 

.31123 

.95033 

.32777 

.94476 

52 

9 

.26135 

.96524 

.27815 

.96054 

.29487 

.95554 

.31151 

.95024 

.32804 

.94466 

51 

10 

.26163 

.96517 

.27843 

.96046 

.29515 

.95545 

.31178 

.95015 

.32832 

.94457 

50 

11 

.26191 

.96509 

.27871 

.96037 

.29543 

.96536 

.31206 

.95006 

.32859 

.94447 

49 

12 

.26219 

.96502 

.27899 

.96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13- 

.26247 

.96494 

.27927 

.96021 

.29599 

.95519 

.31261 

.94988 

.32914 

.94428 

47 

14 

.26275 

.96486 

.27955 

.96013 

.29626 

.95511 

.31289 

.94979 

.32942 

.94418 

46 

15 

.26303 

.96479 

.27983 

.96005 

.29654 

.95502 

.31316 

.94970 

.32969 

.94409 

45 

16 

.26331 

.96471 

.28011 

.95997 

.29682 

.95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

.26359 

.96463 

.28039 

.95989 

.29710 

.95485 

.31372 

.94952 

.33024 

.94390 

43 

18 

.26387 

.96456 

.28067 

.95981 

.29737 

.95476 

.81399 

.94943 

.33051 

.94380 

42 

19 

.26415 

.96448 

.28095 

.95972 

.29765 

.95467 

.81427 

.94933 

.33079 

.94370 

41 

20 

.26443 

.96440 

.28123 

.95964 

.29793 

.95459 

.31454 

.94924 

.33106 

.94361 

40 

21 

.26471 

.96433 

.28150 

.95956 

.29821 

.95450 

.31482 

.94915 

.83134 

.94351 

39 

22 

.26500 

.96425 

.28178 

.95948 

.29849 

.95441 

.31510 

.94906 

.33161 

.94342 

38 

23 

.26528 

.96417 

.28206 

.95940 

.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.26556 

.96410 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

25 

.26584 

.96402 

.28262 

.95923 

.29932 

.95415 

.31593 

.94878 

.33244 

.94313 

35 

26 

.26612 

.96394 

.28290 

.95915 

.29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.26640 

.96386 

.28318 

.95907 

.29987 

.95398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.26668 

.96379 

.28346 

.95898 

.30015 

.95389 

.31675 

.94851 

.33326 

.94284 

32 

29 

.26696 

.96371 

.28374 

.95890 

.30043 

.95380 

.31703 

.94842 

.33353 

.94274 

31 

30 

.26724 

.96363 

.28402 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

.94264 

30 

31 

.26752 

.96355 

.28429 

.95874 

.30098 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.26780 

.96347 

.28457 

.95865 

.30126 

.95354 

.31786 

.94814 

.33436 

.94245 

28 

33 

.26808 

.96340 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

.94235 

27 

34 

.26836 

.96332 

.28513 

.95849 

.30182 

.95337 

.31841 

.94795 

.33490 

.94225 

26 

35 

.26864 

.96324 

.28541 

.95841 

.30209 

.95328 

.31868 

.94786 

.33518 

.94215 

25 

36 

.26892 

.96316 

.28569 

.95832 

.30237 

.95319 

.31896 

.94777 

.33545 

.94206 

24 

37 

.26920 

.96308 

!28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

23 

38 

.26948 

.96301 

.28625 

.95816 

.30292 

.95301 

.31951 

.94758 

.33600 

.94186 

22 

39 

.26976 

.96293 

.28652 

.95807 

.30320 

.95293 

.31979 

.94749 

.33627 

.94176 

21 

40 

.27004 

.96285 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

.94167 

20 

41 

.27032 

.96277 

.28708 

.95791 

.30376 

.95275 

.32034 

.94730 

.33682 

.94157 

19 

42 

.27060 

.96269 

.28736 

.95782 

.30403 

.95266 

.32061 

.94721 

.33710 

.94147 

18 

43 

.27088 

.96261 

.28764 

.95774 

.30431 

.95257 

.32089 

.94712 

.33737 

.94137 

17 

44 

.27116 

.96253 

.28792 

.95766 

.30459 

.95248 

.32116 

.94702 

.33764 

.94127 

16 

45 

.27144 

.96246 

.28820 

.95757 

.30486 

.95240 

.82144 

.94693 

.33792 

.94118 

15 

46 

.27172 

.96238 

.28847 

.95749 

.30514 

.95231 

.32171 

.94684 

.33819 

.94108 

14 

47 

.27200 

.96230 

.28875 

.95740 

.30542 

.95222 

.32199 

.94674 

.33846 

.94098 

13 

48 

.27228 

.96222 

.28903 

.95732 

.30570 

.95213 

.32227 

.94665 

.33874 

.94088 

12 

49 

.27256 

.96214 

.28931 

.95724 

.30597 

.95204 

.32254 

.94656 

.33901 

.94078 

11 

50 

.27284 

.96206 

.28959 

.95715 

.30625 

.95195 

.32282 

.94646 

.33929 

.94068 

10 

51 

.27312 

.96198 

.28987 

.95707 

.30653 

.95186 

.32309 

.94637 

.33956 

.94058 

9 

52 

.27340 

.96190 

.29015 

.95698 

.30680 

.95177 

.32337 

.94627 

.33983 

.94049 

8 

53 

.27368 

.96182 

.29042 

.95690 

.30708 

.95168 

.32364 

.94618 

.34011 

.94039 

7 

54 

.27396 

.96174 

.29070 

.95681 

.30736 

.95159 

.32392 

.94609 

.34038 

.94029 

6 

55 

.27424 

.96166 

.29098 

.95673 

.30763 

.95150 

.82419 

.94599 

.34065 

.94019 

5 

56 

.27452 

.96158 

.29126 

.95664 

.30791 

.95142 

.32447 

.94590 

.34093 

.94009 

4 

57 

.27480 

.96150 

.29154 

.95656 

.30819 

.95133 

.82474 

.94580 

.34120 

.93999 

3 

58 

.27508 

.96142 

.29182 

.95647 

.30846 

.95124 

.32502 

.94571 

.34147 

.93989 

2 

59 

.27536 

.96134 

.29209 

.95639 

.30874 

.95115 

.32529 

.94561 

.34175 

.93979 

1 

60 

.27564 

.96126 

.29237 

.95630 

.30902 

.95106 

.32557 

.94552 

.34202 

.93969 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

74° 

73° 

72° 

71° 

70° 

/ 

NATURAL  SINES  AND  COSINES 


995 


/ 

20° 

21° 

22° 

23° 

24° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.34202 

.93969 

.35837 

.93358 

.37461 

.92718 

.39073 

.92050 

.40674 

.91355 

60 

1 

.34229 

.93959 

.35864 

.93348 

.37488 

.92707 

.39100 

.92039 

.40700 

.91843 

59 

2 

.34257 

.93949 

.35891 

.93337 

.37515 

.92697 

.39127 

.92028 

.40727 

.91331 

58 

3 

.34284 

.93939 

.35918 

.93327 

.37542 

.92686 

.39153 

.92016 

.40753 

.91319 

57 

4 

.34311 

.93929 

.35945 

.93316 

.37569 

.92675 

.39180 

.92005 

.40780 

.91307 

56 

5 

.34339 

.93919 

.35973 

.93306 

.37595 

.92664 

.39207 

.91994 

.40806 

.91295 

55 

6 

.34366 

.93909 

.36000 

.93295 

.37622 

.92653 

.39234 

.91982 

.40833 

.91283 

54 

7 

.34393 

.93899 

.36027 

.93285 

.37649 

.92642 

.39260 

.91971 

.40860 

.91272 

53 

8 

.34421 

.93889 

.36054 

.93274 

.37676 

.92631 

.39287 

.91959 

.40886 

.91260 

52 

9 

.34448 

.93879 

.36081 

.93264 

.37703 

.92620 

.39314 

.91948 

.40913 

.91248 

51 

10 

.34475 

.93869 

.36108 

.93253 

.37730 

.92609 

.39341 

.91936 

.40939 

.91236 

50 

11 

.34503 

.93859 

.36135 

.93243 

.37757 

.92598 

.39367 

.91925 

.40966 

.91224 

49 

12 

.34530 

.93849 

.36162 

.93232 

.37784 

.92587 

.39394 

.91914 

.40992 

.91212 

48 

13 

.34557 

.93839 

.36190 

.93222 

.37811 

.92576 

.39421 

.91902 

.41019 

.91200 

47 

14 

.34584 

.93829 

.36217 

.93211 

.37838 

.92565 

.39448 

.91891 

.41045 

.91188 

46 

15 

.34612 

.93819 

.36244 

.93201 

.37865 

.92554 

.39474 

.91879 

.41072 

.91176 

45 

16 

.34639 

.93809 

.36271 

.93190 

.37892 

.92543 

.39501 

.91868 

.41098 

.91164 

44 

17 

.34666 

.93799 

.36298 

.93180 

.37919 

.92532 

.39528 

.91856 

.41125 

.91152 

43 

18 

.34694 

.93789 

.36325 

.93169 

.37946 

.92521 

.39555 

.91845 

.41151 

.91140 

42 

19 

.34721 

.93779 

.36352 

.93159 

.37973 

.92510 

.39581 

.91833 

.41178 

.91128 

41 

20 

.34748 

.93769 

.36379 

.93148 

.37999 

.92499 

.39608 

.91822 

.41204 

.91116 

40 

21 

.34775 

.93759 

.36406 

.93137 

.38026 

.92488 

.39635 

.91810 

.41231 

.91104 

39 

22 

.34803 

.93748 

.36434 

.93127 

.38053 

.92477 

.39661 

.91799 

.41257 

.91092 

38 

23 

.84830 

.93738 

.36461 

.93116 

.38080 

.92466 

.39688 

.91787 

.41284 

.91080 

37 

24 

.34857 

.93728 

.36488 

.93106 

.38107 

.92455 

.39715 

.91775 

.41310 

.91068 

36 

25 

.34884 

.93718 

.36515 

.93095 

.38134 

.92444 

.39741 

.91764 

.41337 

.91056 

35 

26 

.34912 

.93708 

.36542 

.93084 

.38161 

.92432 

.39768 

.91752 

.41363 

.91044 

34 

27 

.34939 

.93698 

.36569 

.93074 

.38188 

.92421 

.39795 

.91741 

.41390 

.91032 

33 

28 

.34966 

193688 

.36596 

.93063 

.38215 

.92410 

.39822 

.91729 

.41416 

.91020 

32 

29 

.34993 

.93677 

.36623 

.93052 

.38241 

.92399 

.39848 

.91718 

.41443 

.91008 

31 

30 

.35021 

.93667 

.36650 

.93042 

.38268 

.92388 

.39875 

.91706 

.41469 

.90996 

30 

31 

.35048 

.93657 

.36677 

.93031 

.38295 

.92377 

.39902 

.91694 

.41496 

.90984 

29 

32 

.35075 

.93647 

.36704 

.93020 

.38322 

.92366 

.39928 

.91683 

.41*22 

.90972 

28 

33 

.35102 

.93637 

.36731 

.93010 

.38349 

.92355 

.39955 

.91671 

.41549 

.90960 

27 

34 

.35130 

.93626 

.36758 

.92999 

.38376 

.92343 

.39982 

.91660 

.41575 

.90948 

26 

35 

.35157 

.93616 

.36785 

.92988 

.38403 

.92332 

.40008 

.91648 

.41602 

.90936 

25 

36- 

.35184 

.93606 

.36812 

.92978 

.38430 

.92321 

.40035 

.91636 

.41628 

.90924 

24 

37 

.35211 

.93596 

.36839 

.92967 

.38456 

.92310 

.40062 

.91625 

.41655 

.90911 

23 

38 

.35239 

.93585 

.36867 

.92956 

.38483 

.92299 

.40088 

.91613 

.41681 

.90899 

22 

39 

.35266 

.93575 

.36894 

.92945 

.38510 

.92287 

.40115 

.91601 

.41707 

.90887 

21 

40 

.35293 

.93565 

.36921 

.92935 

.38537 

.92276 

.40141 

.91590 

.41734 

.90875 

20 

41 

.35320 

.93555 

.36948 

.92924 

.38564 

.92265 

.40168 

.91578 

.41760 

.90863 

19 

42 

.35347 

.93544 

.36975 

.92913 

.38591 

.92254 

.40195 

.91566 

.41787 

.90851 

18 

43 

.35375 

.93534 

.37002 

.92902 

.38617 

.92243 

.40221 

.91555 

.41813 

.90839 

17 

44 

.35402 

.93524 

.37029 

.92892 

.38644 

.92231 

.40248 

.91543 

.41840 

.90826 

16 

45 

.35429 

.93514 

.37056 

.92881 

.38671 

.92220 

.40275 

.91531 

.41866 

.90814 

15 

46 

.35456 

.93502 

.37083 

.92870 

.92209 

.40301 

.91519 

.41892 

.90802 

14 

47 

.35484 

.93493 

.37110 

.92859 

138725 

.92198 

.40328 

.91508 

.41919 

.90790 

13 

48 

.35511 

.93483 

.37137 

.92849 

.38752 

.92186 

.40355 

.91496 

.41945 

.90778 

12 

49 

.35538 

.93472 

.37164 

.92838 

.38778 

.92175 

.40381 

.91484 

.41972 

.90766 

11 

50 

.35565 

.93462 

.37191 

.92827 

.38805 

.92164 

.40408 

.91472 

.41998 

.90753 

10 

51 

.35592 

.93452 

.87218 

.92816 

.38832 

.92152 

.40434 

.91461 

.42024 

.90741 

9 

52 

.35619 

.93441 

.37245 

.92805 

.92141 

.40461 

.91449 

.42051 

.90729 

8 

53 

.35647 

.93431 

.37272 

.92794 

.38886 

.92130 

.40488 

.91437 

.42077 

.90717 

7 

54 

.35674 

.93420 

.87299 

.92784 

[38912 

.92119 

.40514 

.91425 

.42104 

.90704 

6 

55 

.35701 

.93410 

.37326 

.92773 

.38939 

.92107 

.40541 

.91414 

.42130 

.90692 

5 

56 

.35728 

.93400 

.37353 

.92762 

.38966 

.92096 

.40567 

.91402 

.42156 

.90680 

4 

57 

.35755 

.93389 

.37380 

.92751 

.38993 

.92085 

.40594 

.91390 

.42183 

.90668 

3 

58 

35782 

.93379 

.37407 

.92740 

.39020 

.92073 

.40621 

.91378 

.42209 

.90655 

2 

59 
60 

.35810 
.35837 

.93368 
.93358 

.37434 
.37461 

.92729 
.92718 

.39046 
.39073 

.92062 
.92050 

.40647 
.40674 

.91366 
.91355 

.42235 
.42262 

.90643 
.90631 

1 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

t 

69° 

68° 

67° 

66° 

65° 

NATURAL  SINES  AND  COSINES 


/ 

2 

3° 

2 

6° 

2 

7° 

2 

8° 

2 

9° 

f 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.42262 

.90631 

.43837 

.89879 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

60 

1 

.42288 

.90618 

.43863 

.89867 

.45425 

.89087 

.46973 

.88281 

.48506 

.87448 

59 

2 

.42315 

.90606 

.43889 

.89854 

.45451 

.89074 

.46999 

.88267 

-.-48532 

.87434 

58 

.42341 

.90594 

.43916 

.89841 

.45477 

.89061 

.47024 

.88254 

.48557 

.87420 

57 

.42367 

.90582 

.43942 

.89828 

.45503 

.89048 

.47050 

.88240 

.48583 

.87406 

56 

.42394 

.90569 

.43968 

.89816 

.45529 

.89035 

.47076 

.88226 

.48608 

.87391 

55 

.42420 

.90557 

.43994 

.89803 

.45554 

.89021 

.47101 

.88213 

.48634 

.87377 

54 

.42446 

.90545 

.44020 

.89790 

.45580 

.89008 

.47127 

.88199 

.48659 

.87363 

53 

8 

.42473 

.90532 

.44046 

.89777 

.45606 

.88995 

.47153 

.88185 

.48684 

.87349 

52 

9 

.42499 

.90520 

.44072 

.89764 

.45632 

.88981 

.47178 

.88172 

.48710 

.87335 

51 

10 

.42525 

.90507 

.44098 

.89752 

.45658 

.88968 

.47204 

.88158 

.48735 

.87321 

50 

11 

.42552 

.90495 

.44124 

.89739 

.45684 

.88955 

.47229 

.88144 

.48761 

.87306 

49 

12 

.42578 

.90483 

.44151 

.89726 

.45710 

.88942 

.47255 

.88130 

.48786 

.87292 

48 

13 

.42604 

.90470 

.44177 

.89713 

.45736 

.88928 

.47281 

.88117 

.48811 

.87278 

47 

14 

.42631 

.90458 

.44203 

.89700 

.45762 

.88915 

.47306 

.88103 

.48837 

.87264 

46 

15 

.42657 

.90446 

.44229 

.89687 

.45787 

.88902 

.47332 

.88089 

.48862 

.87250 

45 

16 

.42683 

.90433 

.44255 

.89674 

.45813 

.47358 

.88075 

.48888 

.87235 

44 

17 

.42709 

.90421 

.44281 

.89662 

.45839 

!88875 

.47383 

.88062 

.48913 

.87221 

43 

18 

.42736 

.90408 

.44307 

.89649 

.45865 

.88862 

.47409 

.88048 

.48938 

.87207 

42 

19 

.42762 

.90396 

.44333 

.89636 

.45891 

.47434 

.88034 

.48964 

.87193 

41 

20 

.42788 

.90383 

.44359 

.89623 

.45917 

!88835 

.47460 

.88020 

.48989 

.87178 

40 

21 

.42815 

.90371 

.44385 

.89610 

.45942 

.88822 

.47486 

.88006 

.49014 

.87164 

39 

22 

.42841 

.90358 

.44411 

.89597 

.45968 

.88808 

.47511 

.87993 

.49040 

.87150 

38 

23 

.42867 

.90346 

.44437 

.89584 

.45994 

.88795 

.47537 

.87979 

.49065 

.87136 

37 

24 

.42894 

.90334 

.44464 

.89571 

.46020 

.88782 

.47562 

.87965 

.49090 

.87121 

36 

25 

.42920 

.90321 

.44490 

.89558 

.46046 

.88768 

.47588 

.87951 

.49116 

.87107 

35 

26 

.42946 

.90309 

.44516 

.89545 

.46072 

.88755 

.47614 

.87937 

.49141 

.87093 

34 

27 

.42972 

.90296 

.44542 

.89532 

.46097 

.88741 

.47639 

.87923 

.49166 

.87079 

.33 

28 

.42999 

.90284 

.44568 

.89519 

.46123 

.88728 

.47665 

.87908 

.49192 

.87064 

32 

29 

.43025 

.90271 

.44594 

.89506 

.46149 

.88715 

.47690 

.87896 

.49217 

.87050 

31 

30 

.43051 

.90259 

.44620 

.89493 

.46175 

.88701 

.47716 

.87882 

.49242 

.87036 

30 

31 

.43077 

.90246 

.44646 

.89480 

.46201 

.88688 

.47741 

.87868 

.49268 

.87021 

29 

82 

.43104 

.90133 

.44672 

.89467 

.46226 

.88674 

.47767 

.87854 

.49293 

.87007 

28 

33 

.43130 

.90221 

.44698 

.89454 

.46252 

.88661 

.47793 

.87840 

.49318 

.86993 

27 

34 

.43156 

.90208 

.44724 

.89441 

.46278 

.88647 

.47818 

.87826 

.49344 

.86978 

26 

35 

.43182 

.90196 

.44750 

.89428 

.46304 

.88634 

.47844 

.87812 

.86964 

25 

36 

.43209 

.90183 

.44776 

.8941-5 

.46330 

.88620 

.47869 

.87798 

.49394 

.86949 

24 

87 

.43235 

.90171 

.44802 

.89402 

.46355 

.88607 

.47895 

.87784 

.49419 

.86935 

23 

38 

.43261 

.90158 

.44828 

.89389 

.46381 

.88593 

.47920 

.87770 

.49445 

.86921 

22 

39 

.43287 

.90146 

.44854 

•:89376 

.46407 

.88580 

.47946 

.87756 

.49470 

.86906 

21 

40 

.43313 

.90133 

.44880 

.89363 

.46433 

.88566 

.47971 

.87743 

.49495 

.86892 

20 

41 

.43340 

.90120 

.44906 

.89350 

.46458 

.88553 

.47997 

.87729 

.49521 

.86878 

19 

42 

.43366 

.90108 

.44932 

.89337 

.46484 

.88539 

.48022 

.87715 

.49546 

.86863 

18 

43 

.43392 

.90095 

.44958 

.89324 

.46510 

.88526 

.48048 

.87701 

.49571 

.86849 

17 

44 

.43418 

.90082 

.44984 

.89311 

.46536 

.88512 

.48073 

.87687 

.49596 

.86834 

16 

45 

.43445 

.90070 

.45010 

.89298 

.46561 

.88499 

.48099 

.87673 

.49622 

.86820 

15 

46 

.43471 

.90057 

.45036 

.89285 

.46587 

.88485 

.48124 

.87659 

.49647 

.86805 

14 

47 

.43497 

.90045 

.45062 

.89272 

.46613 

.88472 

.48150 

.87645 

.49672 

.86791 

13 

48 

.43523 

.90032 

.45088 

.89259 

.46639 

.88458 

.48175 

.87631 

.49697 

.86777 

12 

49 

.43549 

.90019 

.45114 

.89245 

.46664 

.88445 

.48201 

.87617 

.49723 

.86762 

11 

50 

.43575 

.90007 

.45140 

.89232 

.46690 

.88431 

.48226 

.87603 

.49748 

.86748 

10 

51 

.43602 

.89994 

.45166 

.89219 

.46716 

.88417 

.48252 

.87589 

.49773 

.86733 

9 

52 

.43628 

.89981 

.45192 

.89206 

.46742 

.88404 

.48277 

.87575 

.49798 

.86719 

8 

53 

.43654 

.89968 

.45218 

.89193 

.46767 

.88390 

.48303 

.87561 

.49824 

.86704 

7 

54 

.43680 

.89956 

.45243 

.89180 

.46793 

.88377 

.48328 

.87546 

.49849 

.86690 

6 

55 

.43706 

.89943 

.45269 

.89167 

.46819 

.88363 

.48354 

.87532 

.49874 

.86675 

5 

56 

.43733 

.89930 

.45295 

.89153 

.46844 

.88349 

.48379 

.87518 

.49899 

.86661 

4 

67 

.43759 

.89918 

.45321 

.89140 

.46870 

.88336 

.48405 

.87504 

.49924 

.86646 

8 

58 

.43785 

.89905 

.45347 

.89127 

.46896 

.88322 

.48430 

.87490 

.49950 

.86632 

2 

59 

.43811 

.89892 

.45373 

.89114 

.46921 

.88308 

.48456 

.87476 

.49975 

.86617 

1 

60 

.43837 

.89879 

.45399 

.89101 

.46947 

.88295 

.48481 

.87462 

.50000 

86603 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

9 

64 

0 

63 

0 

62 

0 

61 

0 

60 

0 

/ 

NATURAL  SINES  AND  COSINES 


30° 

31° 

32° 

33° 

34° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.50000 

.86603 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

60 

1 

.50025 

.86588 

.51529 

.85702 

.53017 

.84789 

.54488 

.83851 

.55943 

.82887 

59 

2 

.50050 

.86573 

.51554 

.85687 

.53041 

.84774 

.54513 

.83835 

.55968 

.82871 

58 

3 

.50076 

.86559 

.51579 

.85672 

.53066 

.84759 

.54537 

.83819 

.55992 

.82855 

57 

4 

.50101 

.86544 

.51604 

.85657 

.53091 

.84743 

.54561 

.83804 

.56016 

.82839 

56 

5 

.50126 

.86530 

.51628 

.85642 

.53115 

.84728 

.54586 

.83788 

.56040 

.82822 

55 

6 

.50151 

.86515 

.51653 

.85627 

.53140 

.84712 

.54610 

.83772 

.56064 

.82806 

54' 

7 

.50176 

.86501 

.51678 

.85612 

.53164 

.84697 

.54635 

.83756 

.56088 

.82790 

53 

8 

.50201 

.86486 

.51703 

.85597 

.53189 

.84681 

.54659 

.83740 

.56112 

.82773 

52 

9 

.50227 

.86471 

.51728 

.85582 

.53214 

.84666 

.54683 

.83724 

.56136 

.82757 

51 

10 

.50252 

.86457 

.51753 

.85567 

.53238 

.84650 

.54708 

.83708 

.56160 

.82741 

50 

11 

.50277 

.86442 

.51778 

.85551 

.53263 

.84635 

.54732 

.83692 

.56184 

.82724 

49 

12 

.50302 

.86427 

.51803 

.85536 

.53288 

.84619 

.54756 

.83676 

.56208 

.82708 

48 

13 

.50327 

.86413 

.51828 

.85521 

.53312 

.84604 

.54781 

.83660 

.56232 

.82692 

47 

14 

.50352 

.86398 

.51852 

.85506 

.53337 

.84588 

.64805 

.83645 

.56256 

.82675 

46 

15 

.50377 

.86384 

.51877 

.85491 

.53361 

.84573 

.54829 

.83629 

.56280 

.82659 

45 

16 

.50403 

.86369 

.51902 

.85476 

.53386 

.84557 

.54854 

.83613 

.56305 

.82643 

44 

17 

.50428 

.86354 

.51927 

.85461 

.53411 

.84542 

.54878 

.83597 

.56329 

.82626 

43 

18 

.50453 

.86340 

.51952 

.85446 

.53435 

.84526 

.54902 

.83581 

.56353 

.82610 

42 

19 

.50478 

.86325 

.51977 

.85431 

.53460 

.84511 

.54927 

.83565 

.56377 

.82593 

41 

20 

.50503 

.86310 

.52002 

.85416 

.53484 

.84495 

.54951 

.83549 

.56401 

.82577 

40 

21 

.50528 

.86295 

.52026 

.85401 

.53509 

.84480 

.54975 

.83533 

.56425 

.82561 

89 

22 

.50553 

.86281 

.52051 

.85385 

.53534 

.84464 

.54999 

.83517 

.56449 

.82544 

88 

23 

.50578 

.86266 

.52076 

.85370 

.53558 

.84448 

.55024 

.83501 

.56473 

.82528 

37 

24 

.50603 

.86251 

.52101 

.85355 

.53583 

.84433 

.55048 

.83485 

.66497 

.82511 

36 

25 

.50628 

.86237 

.52126 

.85340 

.53607 

.84417 

.55072 

.83469 

.56521 

.82495 

35 

26 

.50654 

.86222 

.52151 

.85325 

.53632 

.84402 

.55097 

.83453 

.56545 

.82478 

34 

27 

.50679 

.86207 

.52175 

.85310 

.53656 

.84386 

.55121 

.83437 

.56569 

.82462 

33 

28 

.50704 

.86192 

.52200 

.85294 

.53681 

.84370 

.55145 

.83421 

.56593 

.82446 

32 

29 

.50729 

.86178 

.52225 

.85279 

.53705 

.84355 

.55169 

.83405 

.66617 

.82429 

31 

30 

.50754 

.86163 

.52250 

.85264 

.53730 

.84339 

.65194 

.83389 

.56641 

.82413 

SO 

31 

.50779 

.86148 

.52275 

.85249 

.53754 

.84324 

.55218 

.83373 

.56665 

.82396 

29 

32 

.50804 

.86133 

.52299 

.85234 

.53779 

.84308 

.65242 

.83356 

.56689 

.82380 

28 

33 

.50829 

.86119 

.52324 

.85218 

.53804 

.84292 

.55266 

.83340 

.56713 

.82363 

27 

34 

.50854 

.86104 

.52349 

.85203 

.53828 

.84277  ' 

.55291 

.83324 

.56736 

.82347 

26 

35 

.50879 

.86089 

.52374 

.85188 

.53853 

.84261 

.55315 

.83308 

.56760 

.82330 

25 

36 

.50904 

.86074 

.52399 

.85173 

.53877 

.84245 

.55389 

.83292 

.56784 

.82314 

24 

37 

.50929 

.86059 

.52423 

.85157 

.53902 

.84230 

.55363 

.83276 

.56808 

.82297 

23 

38 

.50954 

.86045 

.52448 

.85142 

.53926 

.84214 

.55388 

.83260 

.56832 

.82281 

22 

39 

.50979 

.86030 

.52473 

.85127 

.53951 

..84198 

.55412 

.83244 

.56856 

.82264 

21 

40 

.51004 

.86015 

.52498 

.85112 

.53975 

.84182 

.65436 

.83228 

.56880 

.82248 

20 

41 

.51029 

.86000 

.52522 

.85096 

.54000 

.84167 

.55460 

.83212 

.56904 

.82231 

19 

42 

.51054 

.85985 

.52547 

.85081 

.54024 

.84151 

.55484 

.83195 

.56928 

.82214 

18 

43 

.51079 

.85970 

.52572 

.85066 

.54049 

.84135 

.55509 

.83179 

.56952 

.82198 

17 

44 

.51104 

.85956 

.52597 

.85051 

.54073 

.84120 

.55533 

.83163 

.56976 

.82181 

16 

45 

.51129 

.85941 

.52621 

.85035 

.54097 

.84104 

.55557 

.83147 

.57000 

.82165 

15 

46 

.51154 

.85926 

.52646 

.85020 

.54122 

.84088 

.55581 

.83131 

.57024 

.82148 

14 

47 

.51179 

.85911 

.52671 

.85005 

.54146 

.84072 

.55605 

.83115 

.57047 

.82132 

13 

48 

.51204 

.85896 

.52696 

.84989 

.54171 

.84057 

.55630 

.83098 

.57071 

.82115 

12 

49 

.51229 

.85881 

.52720 

.84974 

.54195 

.84041 

.55654 

.83082 

.57095 

.82098 

11 

50 

.51254 

.85866 

.52745 

.84959 

.54220 

.84025 

.55678 

.83066 

.57119 

.82082 

10 

51 

.51279 

.85851 

.52770 

.84943 

.54244 

.84009 

.65702 

.83050 

.57143 

.82065 

9 

52 

.51304 

.85836 

.52794 

.84928 

.54269 

.83994 

.55726 

.83034 

.57167 

.82048 

8 

53 

.51329 

.85821 

.52819 

.84913 

.54293 

.83978 

.55750 

.83017 

.57191 

.82032 

7 

54 

.51354 

.85806 

.52844 

.84897 

.54317 

.83962 

.55775 

.83001 

.57215 

.82015 

6 

55 

.51379 

.85792 

.52869 

.84882 

.54342 

.83946 

.55799 

.82985 

.57238 

.81999 

5 

56 

.51404 

.85777 

.52893 

.84866 

.54366 

.83930 

.55823 

.82969 

.57262 

.81982 

4 

57 

.61429 

.85762 

.52918 

.84851 

.54391 

.83915 

.55847 

.82953 

.57286 

.81965 

8 

58 

.51454 
.51479 

.85747 
.85732 

.52943 
.62967 

.84836 
.84820 

.54415 
.54440 

.83899 
.83883 

.55871 
.65895 

.82936 
.82920 

.57310 
.57334 

.81949 
.81932 

2 

60 

.51504 

.85717 

.52992 

.84805 

.54464 

.83867 

.55919 

.82904 

.57358 

31915 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

59° 

58° 

57° 

56° 

65° 

998 


NATURAL  SINES  AND  COSINES 


f 

35° 

36° 

37° 

38° 

39° 

/ 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.57358 

.81915 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

T  

.77715 

60 

1 

.57381 

.81899 

.58802 

.80885 

.60205 

.79846 

.61589 

.78783 

.62955 

.77696 

59 

2 

.57405 

.81882 

.58826 

.80867 

.60228 

.79829 

.61612 

.78765 

.62977 

.77678 

58 

3 

.57429 

.81865 

•  .58849 

.80850 

.60251 

.79811 

.61635 

.78747 

.63000 

.77660 

57 

4 

.57453 

.81848 

.58873 

.80833 

.60274 

.79793 

.61658 

.78729 

.63022 

.77641 

56 

5 

.57477 

.81832 

.58896 

.80816 

.60298 

.79776 

.61681 

.78711 

.63045 

.77623 

55 

6 

.57501 

.81815 

.58920 

.80799 

.60321 

.79758 

.61704 

.78694 

.63068 

.77605 

54 

1 

.57524 

.81798 

.58943 

.80782 

.60344 

.,79741 

.61726 

.78676 

.63090 

.77586 

53 

8 

.57548 

.81782 

.58967 

.80765 

.60367 

.79723 

.61749 

.78658 

.63113 

.77568 

52 

9 

.57572 

.81765 

.58990 

.80748 

.60390 

.79706 

.61772 

.78640 

.63135 

.77550 

51 

10 

.57596 

.81748 

.59014 

.80730 

.60414 

.79688 

.61795 

.78622 

.63158 

.77531 

60 

11 

.57619 

.81731 

.59037 

.80713 

.60437 

.79671 

.61818 

.78604 

.63180 

.77513J 

49 

12 

.67643 

.81714 

.59061 

.80696 

.60460 

.79653 

.61841 

.78586 

.63203 

.77494 

48 

13 

.67667 

.81698 

.59084 

.80679 

.60483 

.79635 

.61864 

.78568 

.63225 

.77476 

47 

14 

.57691 

.81681 

.59108 

.80662 

.60506 

.79618 

.61887 

.78550 

.63248 

.77458 

46 

15 

.57715 

.81664 

.59131 

.80644 

.60529 

.79600 

.61909 

.78532 

.63271 

.77439 

45 

16 

.67738 

.81647 

.59154 

.80627 

.60553 

.79583 

.61932 

.78514 

.63293 

.77421 

44 

17 

.57762 

.81631 

.59178 

.80610 

.60576 

.79565 

.61955 

.784*96 

.63316 

.77402 

43 

18 

.57786 

.81614 

.59201 

.80593 

.60599 

.79547 

.61978 

.78478 

.63338 

.77384 

42 

19 

.57810 

.81597 

.59225 

.80576 

.60622x 

.79530 

.62001 

.78460 

.63361 

.77366 

41 

20 

.57833 

.81580 

.59248 

.80558 

.60645 

.79512 

.62024 

.78442 

.63383 

.77347 

40 

21 

.57857 

.81563 

.59272 

.80541 

.60668 

.79494 

.62046 

.78424 

.63406 

.77329 

39 

22 

.57881 

.81546 

.59295 

.80524 

.60691 

.79477 

.62069 

.78405 

.63428 

.77310 

38 

23 

.57904 

.81530 

.59318 

.80507 

.60714 

.79459 

.62092 

.78387 

.63451 

.77292 

37 

24 

.57928 

.81513 

.59342 

.80489 

.60738 

.79441 

.62115 

.78369 

.63473 

.77273 

36 

25 

.67952 

.81496 

.59365 

.80472 

.60761 

.79424 

.62138 

.78351 

.63496 

.77255 

35 

26 

.57976 

.81479 

.59389 

.80455 

.60784 

.79406 

.62160 

.78333 

.63518 

.77236 

34 

27 

.57999 

.81462 

.69412 

.80438 

.60807 

.79388 

.62183 

.78315 

.63540 

.77218 

33 

28 

.68023 

.81445 

.59436 

.80420 

.60830 

.79371 

.62206 

.78297 

.63563 

.77199 

32 

29 

.58047 

.81428 

.59459 

.80403 

.60853 

.79353 

.62229 

.78279 

.63585 

.77181 

31 

30 

.58070 

.81412 

.59482 

.80386 

.60876 

.79335 

.62251 

.78261 

.63608 

.77162 

30 

31 

.58094 

.81395 

.59506 

.80368 

.60899 

.79318 

.62274 

.78243 

.63630 

.77144 

29 

32 

.58118 

.81378 

.59529 

.80351 

.60922 

.79300 

.62297 

.78225 

.63653 

.77125 

28 

33 

.58141 

.81361 

.59552 

.80334 

.60945 

.79282 

.62320 

.78206 

.63675 

.77107 

27 

34 

.58165 

.81344 

.59576 

.80316 

.60968 

.79264 

.62342 

-.78188 

.63698 

.77088 

26 

35 

.58189 

.81327 

.59599 

.80299 

.60991 

.79247 

.62365 

.78170 

.63720 

.77070 

25 

36 

.58212 

.81310 

.59622 

.80282 

.61015 

.79229 

.62388 

.78152 

.63742 

.77051 

24 

37 

.58236 

.81293 

.59646 

.80264 

.61038 

.79211 

.62411 

.78134 

.63765 

.77033 

23 

38 

.68260 

.81276 

.59669 

.80247 

.61061 

.79193 

.62433 

.78116 

.63787 

.77014 

22 

39 

.58283 

.81259 

.59693 

.80230 

.61084 

.79176 

.62456 

.78098 

.63810 

.76996 

21 

40 

.58307 

.81242 

.59716 

.80212 

.61107 

.79158 

.62479 

.78079 

.63832 

.76977 

20 

41 

.58330 

.81225 

.59739 

.80195 

.61130 

.79140 

.62502 

.78061 

.63854 

.76959 

19 

42 

.58354 

.81208 

.59763 

.80178 

.61153 

.79122 

.62524 

.78043 

.63877 

.76940 

18 

43 

.58378 

.81191 

.59786 

.80160 

.61176 

.79105 

.62547 

.78025 

.63899 

.76921 

17 

44 

.58401 

.81174 

.59809 

.80143 

.61199 

.79087 

.62570 

.78007 

.63922 

.76903 

16 

45 

.58425 

.81157 

.59832 

.80125 

.61222 

.79069 

.62592 

.77988 

.63944 

.76884 

15 

46 

.58449 

.81140 

.59856 

.80108 

.61245 

.79051 

.62615 

.77970 

.63966 

.76866 

14 

47 

.68472 

.81123 

.59879 

.80091 

.61268 

.79033 

.62638 

.77952 

.63989 

.76847 

13 

48 

.68496 

.81106 

.59902 

.80073 

.61291 

.79016 

.62660 

.77934 

.64011 

.76828 

12 

49 

.58519 

.81089 

.59926 

.80056 

.61314 

.78998 

.62683 

.77916 

.64033 

.76810 

11 

50 

.58543 

.81072 

.59949 

.80038 

.61337 

.78980 

.62706 

.77897 

.64056 

.76791 

10 

51 

.58567 

.81055 

.59972 

.80021 

.61360 

.78962 

.62728 

.77879 

.64078 

.76772 

9 

52 

.58590 

.81038 

.59995 

.80003 

.61383 

.78944 

.62751 

.77861 

.64100 

.76754 

8 

53 

.58614 

.81021 

.60019 

.79986 

.61406 

.78926 

.62774 

.77843 

.64123 

.76735 

7 

54 

.58637 

.81004 

.60042 

.79968 

.61429 

.78908 

.62796 

.77824 

.64145 

.76717 

6 

55 

.58661 

.80987 

.60065 

.79951 

.61451 

.78891 

.62819 

.77806 

.64167 

.76698 

5 

56 

.58684 

.80970 

.60089 

.79934 

.61474 

.78873 

.62842 

.77788 

.64190 

.76679 

4 

57 

.58708 

.80953 

.60112 

.79916 

.61497 

.78855 

.62864 

.77769 

.64212 

.76661 

3 

68 

.58731 

.80936 

.60135 

.79899 

.61520 

.78837 

.62887 

.77751 

.64234 

.76642 

2 

59 

.58755 

.80919 

.60158 

.79881 

.61543 

.78819 

.62909 

.77733 

.64256 

.76623 

1 

60 

.58779 

.80902 

.60182 

.79864 

.61566 

.78801 

.62932 

.77715 

.64279 

.76604 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

/ 

64° 

53° 

52° 

51° 

50° 

/ 

NATURAL  SINES  AND  COSINES 


1 

40° 

41° 

42° 

43° 

44° 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

0 

.64279 

.76604 

.65606 

.75471 

.66913 

.74314 

.68200 

.73135 

.69466 

.71934 

60 

1 

.64301 

.76586 

.65628 

.75452 

.66935 

.74295 

.68221 

.73116 

.69487 

.71914 

59 

2 

.64323 

.76567 

.65650 

.75433 

.66956 

.74276 

.68242 

.73096 

.69508 

.71894 

58 

3 

.64346 

.76548 

.65672 

.75414 

.66978 

.74256 

.68264 

.73076 

.69529 

.71873 

57 

4 

.64368 

.76530 

.65694 

.75395 

.66999 

.74237 

.68285 

.73056 

.69549 

.71853 

56 

5 

.64390 

.76511 

.65716 

.75375 

.67021 

.74217 

.68306 

.73036 

.69570 

.71833 

55 

6 

.64412 

.76492 

.65738 

.75356 

.67043 

.74198 

.68327 

.73016 

.69591 

.71813 

54 

7 

.64435 

.76473 

.65759 

.75337 

.67064 

.74178 

.68349 

.72996 

.69612 

.71792 

53 

8 

.64457 

.76455 

.65781 

.75318 

.67086 

.74159 

.68370 

.72976 

.69633 

.71772 

52 

9 

.64479 

.76436 

.65803 

.75299 

.67107 

.74139 

.68391 

.72957 

.69654 

.71752 

51 

10 

.64501 

.76417 

.65825 

.75280 

.67129 

.74120 

.68412 

.72937 

.69675 

.71732 

50 

11 

.64524 

.76398 

.65847 

.75261 

.67151 

.74100 

.68434 

.72917 

.69696 

.71711 

49 

12 

.64546 

.76380 

.65869 

.75241 

.67172 

.74080 

.68455 

.72897 

.69717 

.71691 

48 

13 

.64568 

.76361 

.65891 

.75222 

.67194 

.74061 

.68476 

.72877 

.69737 

.71671 

47 

[4 

.64590 

.76342 

.65913 

.75203 

.67215 

.74041 

.68497 

.72857 

.69758 

.71650 

46 

15 

.64612 

.76323 

.65935 

.75184 

.67237 

.74022 

.68518 

.72837 

.69779 

.71630 

45 

16 

.64635 

.76304 

.65956 

.75165 

.67258 

.74002 

.68539 

.72817 

.69800 

.71610 

44 

17 

.64657 

.76286 

.65978 

.75146 

.67280 

.73983 

.68561 

.72797 

.69821 

.71590 

43 

18 

.64679 

.76267 

.66000 

.75126 

.67301 

.73963 

.68582 

.72777 

.69842 

.71569 

42 

19 

.64701 

.76248 

.66022 

.75107 

.67323 

.73944 

.68603 

.72757 

.69862 

.71549 

41 

20 

.64723 

.76229 

.66044 

.75088 

.67344 

.73924 

.68624 

.72737 

.69883 

.71529 

40 

21 

.64746 

.76210 

.66066 

.75069 

.67366 

.73904 

.68645 

.72717 

.69904 

.71508 

39 

22 

.64768 

.76192 

.66088 

.75050 

.67387 

.73885 

.68666 

.72697 

.69925 

.71488 

38 

23 

.64790 

.76173 

.66109 

.75030 

.67409 

.73865 

.68688 

.72677 

.69946 

.71468 

37 

24 

.64812 

.76154 

.66131 

.75011 

.67430 

.73846 

.68709 

.72657 

.69966 

.71447 

36 

25 

.64834 

.76135 

.66153 

.74992 

.67452 

.73826 

.68730 

.72637 

.69987 

.71427 

35 

26 

.64856 

.76116 

.66175 

.74973 

.67473 

.73806 

.68751 

.72617 

.70008 

.71407 

34 

27 

.64878 

.76097 

.66197 

.74953 

.674951 

.73787 

.68772 

.72597 

.70029 

.71386 

33 

28 

.64901 

.76078 

.66218 

.74934 

.67516 

.73767 

.68793 

.72577 

.70049 

.71366 

32 

29 

.64923 

.76059 

.66240 

.74915 

.67538 

.73747 

.68814 

.72557 

.70070 

.71345 

31 

30 

.64945 

.76041 

.66262 

.74896 

.67559 

.73728 

.68835 

.72537 

.70091 

.71325 

30 

31 

.64967 

.76022 

.66284 

.74876 

.67580 

.73708 

.68857 

.72517 

.70112 

.71305 

29 

32 

.64989 

.76003 

.66306 

.74857 

.67602 

.73688 

.68878 

.72497 

.70132 

.71284 

28 

33 

.65011 

.75984 

.66327 

.74838 

.67623 

.73669 

.68899 

.72477 

.70153 

.71264 

27 

34 

.65033 

.75965 

.66349 

.74818 

.67645 

.73649 

.68920 

.72457 

.70174 

.71243 

26 

35 

.65055 

.75946 

.66371 

.74799 

.67666 

.73629 

.68941 

.72437 

.70195 

.71223 

25 

36 

.65077 

.75927 

.66393 

.74780 

.67688 

.73610 

.68962 

.72417 

.70215 

.71203 

24 

37 

.65100 

.75908 

.66414 

.74760 

.67709 

.73590 

.68983 

.72397 

.70236 

.71182 

23 

38 

.65122 

.75889 

.66436 

.74741 

.67730 

.73570 

.69004 

.72377 

.70257 

.71162 

22 

39 

.65144 

.75870 

.66458 

.74722 

.67752 

.73551 

.69025 

.72357 

.70277 

.71141 

21 

40 

.65166 

.75851 

.66480 

.74703 

.67773 

.73531 

.69046 

.72337 

.70298 

.71121 

20 

41 

42 

.65188 
.65210 

.75832 

.75813 

.66501 
.66523 

.74683 
.74664 

.67795 
.67816 

.73511 
.73491 

.69067 
.69088 

.72317 

.72297 

.70319 
.70339 

.71100 
.71080 

19 

18 

43 
44 

45 

.65232 
.65254 
.65276 

.75794 
.75775 
.75756 

.66545 
.66566 

.66588 

.74644 
.74625 
.74606 

.67837 
.67859 
.67880 

.73472 
.73452 
.73432 

.69109 
.69130 
.69151 

.72277 
.72257 
.72236 

.70360 
.70381 
.70401 

.71059 
.71039 
.71019 

17 
16 

15 

46 
47 
48 
49 
50 

.65298 
.65320 
.65342 
.65364 
.65386 

.75738 
.75719 
.75700 
.75680 
.75661 

.66610 
.66632 
.66653 
.66675 
.66697 

.74586 
.74567 
.74548 
.74528 
.74509 

.67901 
.67923 
.67944 
.67965 
.67987 

.73413 
.73393 
.73373 
.73353 
.73333 

.69172 
.69193 
.69214 
.69235 
.69256 

.72216 
.72196 
.72176 
.72156 
.72136 

.70422   .70998 
.70443   .70978 
.70463  .70957 
.70484  .70937 
.70505  .70916 

14 
13 
12 
11 
10 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

.65408 
.65430 
.65452 
.65474 
.65496 
.65518 
.65540 
.65562 
.65584 
.65606 

.75642 
.75623 
.75604 
.75585 
.75566 
.75547 
.75528 
.75509 
.75490 
.75471 

.66718 
.66740 
.66762 
.66783 
.66805 
.66827 
.66848 
.66870 
.66891 
.66913 

.74489 
.74470 
.74451 
.74431 
.74412 
.74392 
.74373 
.74353 
.74334 
.74314 

.68008 
.68029 
.68051 
.68072 
.68093 
.68115 
.68136 
.68157 
.68179 
.68200 

.73314 
.73294 
.73274 
.73254 
.73234 
.73215 
.73195 
.73175 
.73155 
.73135 

.69277 
.69298 
.69319 
.69340 
.69361 
.69382 
.69403 
.69424 
.69445 
.69466 

.72116 
.72095 
.72075 
.72055 
.72035 
.72015 
.71995 
.71974 
.71954 
.71934 

.70525 
.70546 
.70567 
.70587 
.70608 
.70628 
.70649 
.70670 
.70690 
.70711 

.70896 
.70875 
.70855 
.70834 
.70813 
.70793 
.70772 
.70752 
.70731 
.70711 

0 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

Cosine 

Sine 

t 

49° 

48° 

47° 

46° 

45° 

1000 


NATURAL  TANGENTS  AND  COTANGENTS 


f 

0 

> 

V 

> 

2 

J 

3 

9 

'1 

9  • 

f 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.00000 

Infln. 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

60 

1 

.00029 

3437.75 

.01775 

56.3506 

.03521 

28.3994 

.05270 

18.9755 

.07022 

14.2411 

59 

2 

.00058 

1718.87 

.01804 

55.4415 

.03550 

28.1664 

.05299 

18.8711 

.07051 

14.1821 

58 

3 

.00087 

1145.92 

.01833 

54.5613 

.03579 

27.9372 

.05328 

18.7678 

.07080 

14.1235 

57 

4 

.00116 

859.436 

.01862 

53.7086 

.03609 

27.7117 

.05357 

18.6656 

.07110 

14.0655 

56 

5 

.00145 

687.549 

.01891 

52.8821 

.03638 

27.4899 

.05387 

18.5645 

.07139 

14.0079 

55 

6 

.00175 

572.957 

.01920 

52.0807 

.03667 

27.2715 

.05416 

18.4645 

.07168 

13.9507 

54 

7 

.00204 

491.106 

.01949 

51.3032 

.03696 

27.0566 

.05445 

18.3655 

.07197 

13.8940 

53 

8 

.00233 

429.718 

.01978 

50.5485 

.03725 

26.8450 

.05474 

18.2677 

.07227 

13.8378 

52 

9 

.00262 

381.971 

.02007 

49.8157 

.03754 

26.6367 

.05503 

18.1708 

.07256 

13.7821 

51 

10 

.00291 

343.774 

.02036 

49.1039 

.03783 

26.4316 

.05533 

18.0750 

.07285 

13.7267 

50 

11 

.00320 

312.521 

.02066 

48.4121 

.03812 

26.2296 

.05562 

17.9802 

.07314 

13.6719 

49 

12 

.00349 

286.478 

.02095 

47.7395 

.03842 

26.0307 

.05591 

17.8863 

.07344 

13.6174 

48 

13 

.00378 

264.441 

.02124 

47.0853 

.03871 

25.8348 

.05620 

17.7934 

.07373 

13.5634 

47 

14 

.00407 

245.552 

.02153 

46.4489 

.03900 

25.6418 

.05649 

17.7015 

.07402 

13.5098 

46 

15 

.00436 

229.182 

.02182 

45.8294 

.03929 

25.4517 

.05678 

17.6106 

.07431 

13.4566 

45 

16 

.00465 

214.858 

.02211 

45.2261 

.03958 

25.2644 

.05708 

17.5205 

.07461 

13.4039 

44 

17 

.00495 

202.219 

.02240 

44.6386 

.03987 

25.0798 

.05737 

17.4314 

.07490 

13.3515 

43 

18 

.00524 

190.984 

.02269 

44.0661 

.04016 

24.8978 

.05766 

17.3432 

.07519 

13.2996 

42 

19 

.00553 

180.932 

.02298 

43.5081 

.04046 

24.7185 

.05795 

17.2558 

.07548 

13.2480 

41 

20 

.00682 

171.885 

.02328 

42.9641 

.04075 

24.5418 

.05824 

17.1693 

.07578 

13.1969 

40 

21 

.00611 

163.700 

.02357 

42.4335 

.04104 

24.3675 

.05854 

17.0837 

.07607 

13.1461 

39 

22 

.00640 

156.259 

.02386 

41.9158 

.04133 

24.1957 

.05883 

16.9990 

.07636 

13.0958 

38 

23 

.00669 

149.465 

.02415 

41.4106 

.04162 

24.0263 

.05912 

16.9150 

.07665 

13.0458 

37 

24 

.00698 

143.237 

.02444 

40.9174 

.04191 

23.8593 

.05941 

16.8319 

.07695 

12.9962 

36 

25 

.00727 

137.507 

.02473 

40.4358 

.04220 

23.6945 

.05970 

16.7496 

.07724 

12.9469 

35 

26 

.00756 

132.219 

.02502 

39.9655 

.04250 

23.5321 

.05999 

16.6681 

.07753 

12.8981 

34 

27 

.00785 

127.321 

.02531 

39.5059 

.04279 

23.3718 

.06029 

16.5874 

.07782 

12.8496 

33 

28 

.00815 

122.774 

.02560 

39.0568 

.04308 

23.2137 

.06058 

16.5075 

.07812 

12.8014 

32 

29 

.00844 

118.540 

.02589 

38.6177 

.04337 

23.0577 

.06087 

16.4283 

.07841 

12.7536 

31 

30 

.00873 

114.589 

.02619 

38.1885 

.04366 

22.9038 

.06116 

16.3499 

.07870 

12.7062 

30 

31 

.00902 

110.892 

.0?648 

37.7686 

.04395 

22.7519 

.06145 

16.2722 

.07899 

12.6591 

29 

32 

.00931 

107.426 

.02677 

37.3579 

.04424 

22.6020 

.06175 

16.1952 

.07929 

12.6124 

28 

33 

.00960 

104.171 

.02706 

36.9560 

.04454 

22.4541 

.06204 

16.1190 

.07958 

12.5660 

27 

34 

.00989 

101.107 

.02735 

36.5627 

.04483 

22.3081 

.06233 

16.0435 

.07987 

12.5199 

26 

35 

.01018 

98.2179 

.02764 

36.1776 

.04512 

22.1640 

.06262 

15.9687 

.08017 

12.4742 

25 

36 

.01047 

95.4895 

.02793 

35.8006 

.04541 

22.0217 

.06291 

15.8945 

.08046 

12.4288 

24 

37 

.01076 

92.9085 

.02822 

35.4313 

.04570 

21.8813 

.06321 

15.8211 

.08075 

12.3838 

23 

38 

.01105 

90.4633 

.02851 

35.0695 

.04599 

21.7426 

.06350 

15.7483 

.08104 

12.3390 

22 

39 

.01135 

88.1436 

.02881 

34.7151 

.04628 

21.6056 

.06379 

15.6762 

.08134 

12.2946 

21 

40 

.01164 

85.9398 

.02910 

34.3678 

.04658 

21.4704 

.06408 

15.6048 

.08163 

12.2505 

20 

41 

.01193 

83.8435 

.02939 

34.0273 

.04687 

21.3369 

.06437 

15.5340 

.08192 

12.2067 

19 

42 

.01222 

81.8470 

.02968 

33.6935 

.04716 

21.2049 

.06467 

15.4638 

.08221 

12.1632 

18 

43 

.01251 

79.9434 

.02997 

33.3662 

.04745 

21.0747 

.06496 

15.3943 

.08251 

12.1201 

17 

44 

.01280 

78.1263 

.03026 

33.0452 

.04774 

20.9460 

.06525 

15.3254 

.08280 

12.0772 

16 

45 

.01309 

76.3900 

.03055 

32.7303 

.04803 

20.8188 

.06554 

15.2571 

.08309 

12.0346 

15 

46 

.01338 

74.7292 

.03084 

32.4213 

.04833 

20.6932 

.06584 

15.1893 

.08339 

11.9923 

14 

47 

.01367 

73.1390 

.03114 

32.1181 

.04862 

20.5691 

.06613 

15.1222 

.08368 

11.9504 

13 

48 

.01396 

71.6151 

.03143 

31.8205 

.04891 

20.4465 

.06642 

15.0557 

.08397 

11.9087 

12 

49 

.01425 

70.1533 

.03172 

31.5284 

.04920 

20.3253 

.06671 

14.9898 

.08427 

11.8673 

11 

50 

.01455 

68.7501 

.03201 

31.2416 

.04949 

20.2056 

.06700 

14.9244 

.08456 

11.8262 

10 

51 

.01484 

67.4019 

.03230 

30.9599 

.04978 

20.0872 

.06730 

14.8596 

.08485 

11.7853 

9 

52 

.01513 

66.1055 

.03259 

30.6833 

.05007 

19.9702 

.06759 

14.7954 

.08514 

11.7448 

8 

53 

.01542 

64.8580 

.03288 

30.4116 

.05037 

19.8546 

.06788 

14.7317 

.08544 

11.7045 

54 

.01571 

63.6567 

.03317 

30.1446 

.05066 

19.7403 

.06817 

14.6685 

.08573 

11.6645 

55 

.01600 

62.4992 

.03346 

29.8823 

.05095 

19.6273 

.06847 

14.6059 

.08602 

11.6248 

56 

.01629 

61.3829 

.03376 

29.6245 

.05124 

19.5156 

.06876 

14.5438 

.08632 

11.5853 

57 

.01658 

60.3058 

.03405 

29.3711 

.05153 

19.4051 

.06905 

14.4823 

.08661 

11.5461 

58 

.01687 

59.2659 

.03434 

29.1220 

.05182 

19.2959 

.06934 

14.4212 

.08690 

11.5072 

59 

.01716 

58.2612 

.03463 

28.8771 

.05212 

19.1879 

.06963 

14.3607 

.08720 

11.4685 

60 

.01746 

57.2900 

.03492 

28.6363 

.05241 

19.0811 

.06993 

14.3007 

.08749 

11.4301 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

8 

9° 

8! 

3° 

8 

7° 

8 

5° 

8 

5° 

NATURAL  TANGENTS  AND  COTANGENTS 


1001 


5 

0 

6 

o 

7 

0 

8 

Q 

9 

o 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

.08749 

11.4301 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

60 

.08778 

11.3919 

.10540 

9.48781 

.12308 

8.12481 

.14084 

7.10038 

.15868 

6.30189 

59 

.08807 

11.3540 

.10569 

9.46141 

.12338 

8.10536 

.14113 

7.08546 

.15898 

6.29007 

58 

.08837 

11.3163 

.10599 

9.43515 

.12367 

8.08600 

.14143 

7.07059 

.15928 

6.27829 

57 

.08866 

11.2789 

.10628 

9.40904 

.12397 

8.06674 

.14173 

7.05579 

.15958 

6.26655 

56 

.08895 

11.2417 

.10657 

9.38307 

.12426 

8.04756 

.14202 

7.04105 

.15988 

6.25486 

55 

.08925 

11.2048 

.10687 

9.35724 

.12456 

8.02848 

.14232 

7.02637 

.16017 

6.24321 

54 

.08954 

11.1681 

.10716 

9.33155 

.12485 

8.00948 

.14262 

7.01174 

.16047 

6.23160 

53 

.08983 

11.1316 

.10746 

9.30599 

.12515 

7.99058 

.14291 

6.99718 

.16077 

6.22003 

52 

.09013 

11.0954 

.10775 

9.28058 

.12544 

7.97176 

.14321 

6.98268 

.16107 

6.20851 

51 

10 

.09042 

11.0594 

.10805 

9.25530 

.12574 

7.95302 

.14351 

6.96823 

.16137 

6.19703 

50 

11 

.09071 

11.0237 

.10834 

9.23016 

.12603 

7.93438 

.14381 

6.95385 

.16167 

6.18559 

49 

12 

.09101 

10.9882 

.10863 

9.20516 

.12633 

7.91582 

.14410 

6.93952 

.16196 

6.17419 

48 

13 

.09130 

10.9529 

.10893 

9.18028 

.12662 

7.89734 

.14440 

6.92525 

.16226 

6.16283 

47 

14 

.09159 

10.9178 

.10922 

9.15554 

.12692 

7.87895 

.14470 

6.91104 

.16256 

6.15151 

46 

15 

.09189 

10.8829 

.10952 

9.13093 

.12722 

7.86064 

.14499 

6.89688 

.16286 

6.14023 

45 

16 

.09218 

10.8483 

.10981 

9.10646 

.12751 

7.84242 

.14529 

6.88278 

.16316 

6.12899 

44 

17 

.09247 

10.8139 

.11011 

9.08211 

.12781 

7.82428 

.14559 

6.86874 

.16346 

6.11779 

43 

18 

.09277 

10.7797 

.11040 

9.05789 

.12810 

7.80622 

.14588 

6.85475 

.16376 

6.10664 

42 

19 

.09306 

10.7457 

.11070 

9.03379 

.12840 

7.78825 

.14618 

6.84082 

.16405 

6.09552 

41 

20 

.09335 

10.7119 

.11099 

9.00983 

.12869 

7.77035 

.14648 

6.82694 

.16435 

6.08444 

40 

21 

.09365 

10.6783 

.11128 

8.98598 

.12899 

7.75254 

.14678 

6.81312 

.16465 

6.07340 

39 

22 

.09394 

10.6450 

.11158 

8.96227 

.12929 

7.73480 

.14707 

6.79936 

.16495 

6.06240 

38 

23 

.09423 

10.6118 

.11187 

8.93867 

.12958 

7.71715 

.14737 

6.78564 

.16525 

6.05143 

37 

24 

.09453 

10.5789 

.11217 

8.91520 

.12988 

7.69957 

.14767 

6.77199 

.16555 

6.04051 

36 

25 

.09482 

10.5462 

.11246 

8.89185 

.13017 

7.68208 

.14796 

6.75838 

.16585 

6.02962 

35 

26 

.09511 

10.5136 

.11276 

8.86862 

.13047 

7.66466 

.14826 

6.74483 

.16615 

6.01878 

34 

27 

.09541 

10.4813 

.11305 

8.84551 

.13076 

7.64732 

.14856 

6.73133 

.16645 

6.00797 

33 

28 

.09570 

10.4491 

.11335 

8.82252 

.13106 

7.63005 

.14886 

6.71789 

.16674 

5.99720 

32 

29 

.09600 

10.4.172 

.11364 

8.79964 

.13136 

7.61287 

.14915 

6.70450 

.16704 

5.98646 

31 

30 

.09629 

10.3854 

.11394 

8.77689 

.13165 

7.59575 

.14945 

6.69116 

.16734 

5.97576 

30 

31 

.09658 

10.3538 

.11423 

8.75425 

.13195 

7.57872 

.14975 

6.67787 

.16764 

5.96510 

29 

32 

.09688 

10.3224 

.11452 

8.73172 

.13224 

7.56176 

.15005 

6.66463 

.16794 

5.95448 

28 

33 

.09717 

10.2913 

.11482 

8.70931 

.13254 

7.54487 

.15034 

6.65144 

.16824 

5.94390 

27 

34 

.09746 

10.2602 

.11511 

8.68701 

.13284 

7.52806 

.15064 

6.63831 

.16854 

5.93335 

26 

35 

.09776 

10.2294 

.11541 

8.66482 

.13313 

7.51132 

.15094 

6.62523 

.16884 

5.92283 

25 

36 

.09805 

10.1988 

.11570 

8.64275 

.13343 

7.49465 

.15124 

6.61219 

.16914 

5.91236 

24 

37 

.09834 

10.1683 

.11600 

8.62078 

.13372 

7.47806 

.15153 

6.59921 

.16944 

5.90191 

23 

38 

.09864 

10.1381 

.11629 

8.59893 

.13402 

7.46154 

.15183 

6.58627 

.16974 

5.89151 

22 

39 

.09893 

10.1080 

.11659 

8.57718 

.13432 

7.44509 

.15213 

6.57339 

.17004 

5.88114 

21 

40 

.09923 

10.0780 

.11688 

8.55555 

.13461 

7.42871 

.15243 

6.56055 

.17033 

5.87080 

20 

41 

.09952 

10.0483 

.11718 

8.53402 

.13491 

7.41240 

.15272 

6.54777 

.17063 

5.86051 

19 

42 

.09981 

10.0187 

.11747 

8.51259 

.13521 

V.  39616 

.15302 

6.53503 

.17093 

5.85024 

18 

43 

.10011 

9.98931 

.11777 

8.49128 

.13550 

7.37999 

.15332 

6.52234 

.17123 

5.84001 

17 

44 

.10040 

9.96007 

.11806 

8.47007 

.13580 

7.36389 

.15362 

6.50970 

.17153 

5.82982 

16 

45 

.10069 

9.93101 

.11836 

8.44896 

.13609 

7.34786 

.15391 

6.49710 

.17183 

5.81966 

15 

46 

.10099 

9.90211 

.11865 

8.42795 

.13639 

7.33190 

.15421 

6.48456 

.17213 

5.80953 

14 

47 

.10128 

9.87338 

.11895 

8.40705 

.13669 

7.31600 

.15451 

6.47206 

.17243 

5.79944 

13 

48 

.10158 

9.84482 

.11924 

8.38625 

.13698 

7.30018 

.15481 

6.45961 

.17273 

5.78938 

12 

49 

.10187 

9.81641 

.11954 

8.36555 

.13728 

7.28442 

.15511 

6.44720 

.17303 

5.77936 

11 

50 

.10216 

9.78817 

.11983 

8.34496 

.13758 

7.26873 

.15540 

6.43484 

.17333 

5.76937 

10 

51 

.10246 

9.76009 

.12013 

8.32446 

.13787 

7.25310 

.15570 

6.42253 

.17363 

5.75941 

9 

52 

.10275 

9.73217 

.12042 

8.30406 

.13817 

7.23754 

.15600 

6.41026 

.17393 

5.74949 

8 

53 

.10305 

9.70441 

.12072 

8.28376 

.13846 

7.22204 

.15630 

6.39804 

.17423 

5.73960 

7 

54 

.10334 

9.67680 

.12101 

8.26355 

.13876 

7.20661 

.15660 

6.88587 

.17453 

5.72974 

55 

.10363 

9.64935 

.12131 

8.24345 

.13906 

7.19125 

.15689 

6.37374 

.17483 

5.71992 

56 

.10393 

9.62205 

.12160 

8.22344 

.13935 

7.17594 

.15719 

6.36165 

.17513 

5.71013 

57 

.10422 

9.59490 

.12190 

8.20352 

.13965 

7.16071 

.15749 

6.34961 

.17543 

5.70037 

58 

.10452 

9.56791 

.12219 

8.18370 

.13995 

7.14553 

.15779 

6.33761 

.17573 

5.69064 

59 

.10481 

9.54106 

.12249 

8.16398 

.14024 

7.13042 

.15809 

6.32566 

.17603 

5.68094 

60 

.10510 

9.51436 

.12278 

8.14435 

.14054 

7.11537 

.15838 

6.31375 

.17633 

5.67128 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

o  ang 

f 

' 

8 

4° 

& 

J° 

8 

2° 

8 

L° 

8 

0° 

1002 


NATURAL  TANGENTS  AND  COTANGENTS 


t 

1( 

)° 

1 

L° 

1 

y> 

1, 

5° 

3 

40 

/ 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.17633 

5.67128 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

60 

.17663 

5.66165 

.19468 

5.13658 

.21286 

4.69791 

.23117 

4.32573 

.24964 

4.00582 

59 

.17693 

5.65205 

.19498 

5.12862 

.21316 

4.69121 

.23148 

4.32001 

.24995 

4.00086 

58 

.17723 

5.64248 

.19529 

5.12069 

.21347 

4.68452 

.23179 

4.31430 

.25026 

3.99592 

57 

.17753 

5.63295 

.19559 

5.11279 

.21377 

4.67786 

.23209 

4.30860 

.25056 

3.99099 

56 

.17783 

5.62344 

.19589 

5.10490 

.21408 

4.67121 

.23240 

4.80291 

.25087 

3.98607 

55 

.17813 

5.61397 

.19619 

5.09704 

.21438 

4.66458 

.23271 

4.29724 

.25118 

3.98117 

54 

.17843 

5.60452 

.19649 

5.08921 

.21469 

4.65797 

.23301 

4.29159 

.25149 

3.97627 

53 

8 

.17873 

5.59511 

.19680 

5.08139 

.21499 

4.65138 

.23332 

4.28595 

.25180 

3.97139 

52 

9 

.17903 

5.58573 

.19710 

5.07360 

.21529 

4.64480 

.23363 

4.28032 

.25211 

3.96651 

51 

10 

.17933 

5.57638 

.19740 

5.06584 

.21560 

4.63825 

.23393 

4.27471 

.25242 

3.96165 

50 

11 

.17963 

5.56706 

.19770 

5.05809 

.21590 

4.63171 

.23424 

4.26911 

.25273 

3.95680 

49 

12 

.17993 

5.55777 

.19801 

5.05037 

.21621 

4.62518 

.23455 

4.26352 

.25304 

3.95196 

48 

13 

.18023 

5.54851 

.19831 

5.04267 

.21651 

4.61868 

.23485 

4.25795 

.25335 

3.94713 

47 

14 

.18053 

5.53927 

.19861 

5.03499 

.21682 

4.61219 

.23516 

4.25239 

.25366 

3.94232 

46 

15 

.18083 

5.53007 

.19891 

5.02734 

.21712 

4.60572 

.23547 

4.24685 

.25397 

3.93751 

45 

16 

.18113 

5.52090 

.19921 

5.01971 

.21743 

4.59927 

.23578 

4.24132 

.25428 

3.93271 

44 

17 

.18143 

5.51176 

.19952 

5.01210 

.21773 

4.59283 

.23608 

4.23580 

.25459 

3.92793 

43 

18 

.18173 

5.50264 

.19982 

5.00451 

.21804 

4.58641 

.23639 

4.23030 

.25490 

3.92316 

42 

19 

.18203 

5.49356 

.20012 

4.99695 

.21834 

4.58001 

.23670 

4.22481 

.25521 

3.91839 

41 

20 

.18233 

5.48451 

.20042 

4.98940 

.21864 

4.57363 

.23TOO 

4.21933 

.25552 

3.91364 

40 

21 

.18263 

5.47548 

.20073 

4.98188 

.21895 

4.56726 

.23731 

4.21387 

.25583 

3.90890 

39 

22 

.18293 

5.46648 

.20103 

4.97438 

.21925 

4.56091 

.23762 

4.20842 

.25614 

3.90417 

38 

23 

.18523 

5.45751 

.20133 

4.96690 

.21956 

4.55458 

.23793 

4.20298 

.25645 

3.89945 

37 

24 

.18353 

5.44857 

.20164 

4.95945 

.21986 

4.54826 

.23823 

4.19756 

.25676 

3.89474 

36 

25 

.18384 

5.43966 

.20194 

4.95201 

.22017 

4.54196 

.23854 

4.19215 

.25707 

3.89004 

35 

26 

.18414 

5.43077 

.20224 

4.94460 

.22047 

4.53568 

.23885 

4.18675 

.25738 

3.88536 

34 

27 

.18444 

5.42192 

.20254 

4.93721 

.22078 

4.52941 

.23916 

4.18137 

.25769 

3.88068 

33 

28 

.18474 

5.41309 

.20285 

4.92984 

.22108 

4.52316 

.23946 

4.17600 

.25800 

3.87601 

32 

29 

.18504 

6.40429 

.20315 

4.92249 

.22139 

4.51693 

.23977 

4.17064 

.25831 

3.87136 

31 

30 

.18534 

5.39552 

.20345 

4.91516 

.22169 

4.51071 

.24008 

4.16530 

.25862 

3.86671 

30 

31 

.18564 

5.38677 

.20376 

4.90785 

.22200 

4.50451 

.24039 

4.15997 

.25893 

3.86208 

29 

32 

.18594 

5.37805 

.20406 

4.90056 

.22231 

4.49832 

.24069 

4.15465 

.25924 

3.85745 

28 

33 

.18624 

5.36936 

.20436 

4.89330 

.22261 

4.49215 

.24100 

4.14934 

.25955 

3.85284 

27 

34 

.18654 

5.36070 

.20466 

4.88605 

.22292 

4.48600 

.24131 

4.14405 

.25986 

3.84824 

26 

35 

.18684 

5.35206 

.20497 

4.87882 

.22322 

4.47986 

.24162 

4.13877 

.26017 

3.84364 

25 

36 

.18714 

5.34345 

.20527 

4.87162 

.22353 

4.47374 

.24193 

4.13350 

.26048 

3.83906 

24 

37 

.18745 

5.33487 

.20557 

4.86444 

.22383 

4.46764 

.24223 

4.12825 

.26079 

3.83449 

23 

38 

.18775 

5.32631 

.20588 

4.85727 

.22414 

4.46155 

.24254 

4.12301 

.26110 

3.82992 

22 

39 

.18805 

5.31778 

.20618 

4.85013 

.22444 

4.45548 

.24285 

4.11778 

.26141 

3.82537 

21 

40 

.18835 

5.30928 

.20648 

4.84300 

.22475 

4.44942 

.24316 

4.11256 

.26172 

3.82083 

20 

41 

.18865 

5.30080 

.20679 

4.83590 

.22505 

4.44338 

.24347 

4.10736 

.26203 

3.81630 

19 

42 

.18895 

5.29235 

.20709 

.22536 

4.43735 

.24377 

4.10216 

.26235 

3.81177 

18 

43 

.18925 

5.28393 

.20739 

4182175 

.22567 

4.43134 

.24408 

4.09699 

.26266 

3.80726 

17 

44 

.18955 

5.27553 

.20770 

4.81471 

.22597 

4.42534 

.24439 

4.09182 

.26297 

3.80276 

16 

45 

.18986 

5.26715 

.20800 

4.80769 

.22628 

4.41936 

.24470 

4.08666 

.26328 

3.79827 

15 

46 

.19016 

5.25880 

.20830 

4.80068 

.22658 

4.41340 

.24501 

4.08152 

.26359 

3.79378 

14 

47 

.19046 

5.25048 

.20861 

4.79370 

.22689 

4.40745 

.24532 

4.07639 

.26390 

3.78931 

13 

48" 

.19076 

5.24218 

.20891 

4.78673 

.22719 

4.40152 

.24562 

4.07127 

.26421 

3.78485 

12 

49 

.19106 

5.23391 

.20921 

4.77978 

.22750 

4.39560 

.24593 

406616 

.26452 

3.78040 

11 

50 

.19186 

5.22566 

.20952 

4.77286 

.22781 

4.38969 

.24624 

4.06107 

.26483 

3.77595 

10 

51 

.19166 

5.21744 

.20982 

4.76595 

.22811 

4.38381 

.24655 

4.05599 

.26515 

3.77152 

9 

52 

.19197 

5.20925 

.21013 

4.75906 

.22842 

4.37793 

.24686 

4.05092 

.26546 

3.76709 

8 

53 

.19227 

5.20107 

.21043 

4.75219 

.22872 

4.37207 

.24717 

4.04586 

.26577 

3.76268 

7 

54 

.19257 

5.19293 

.21073 

4.74534 

.22903 

4.36623 

.24747 

4.04081 

.26608 

3.75828 

6 

55 

.19287 

5.18480 

.21104 

4.73851 

.22934 

4.36040 

.24778 

4.03578 

.26639 

3.75388 

5 

56 

.19317 

5.17671 

.21134 

4.73170 

.22964 

4.35459 

.24809 

4.03076 

.26670 

3.74950 

4 

57 

.19347 

5.16863 

.21164 

4.72490 

.22995 

4.34879 

.24840 

4.02574 

.26701 

3.74512 

3 

58 

.19378 

5.16058 

.21195 

4.71813 

.23026 

4.34300 

.24871 

4.02074 

.26733 

3.74075 

2 

59 

.19408 

5.15256 

.21225 

4.71137 

.23056 

4.33723 

.24902 

4.01576 

.26764 

3.73640 

1 

60 

.19438 

5.14455 

.21256 

4.70463 

.23087 

4.33148 

.24933 

4.01078 

.26795 

3.73205 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

1 

7< 

19 

7! 

5° 

T 

r° 

H 

)° 

7 

5° 

t 

NATURAL  TANGENTS  AND  COTANGENTS 


1003 


11 

>° 

If 

>° 

H 

o 

1* 

*° 

1 

9° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.S6795 

3.73205 

.28675 

3.48741 

.30573 

3.27085 

.32492 

3.07768 

.34433 

2.90421 

60 

1 

.26826 

3.72771 

.28706 

3.48359 

.30605 

3.26745 

.32524 

3.07464 

.34465 

2.90147 

59 

2 

26857 

3.72338 

.28738 

3.47977 

.30637 

3.26406 

.32556 

3.07160 

.34498 

2.89873 

58 

3 

.26888 

3.71907 

.28769 

3.47596 

.30669 

3.26067 

.32588 

3.06857 

.34530 

2.89600 

57 

4 

.26920 

3.71476 

.28800 

3.47216 

.30700 

3.25729 

.32621 

3.06554 

.34563 

2.89327 

56 

5 

.26951 

3.71046 

.28832 

3.46837 

.30732 

3.25392 

.32653 

3.06252 

.34596 

2.89055 

55 

.26982 

3.70616 

.28864 

3.46458 

.30764 

3.25055 

.32685 

3.05950 

.34628 

2.88783 

54 

7 

.27013 

3.70188 

.28895 

3.46080 

.30796 

3.24719 

.32717 

3.05649 

.34661 

2.88511 

53 

8 

.27044 

3.69761 

.28927 

3.45703 

.30828 

3.24383 

.32749 

3.05349 

.34693 

2.88240 

52 

9 

.27076 

3.69335 

.28958 

3.45327 

.30860 

3.24049 

.32782 

3.05049 

.34726 

2.87970 

51 

10 

.27107 

3.68909 

.28990 

3.44951 

.30891 

3.23714 

.32814 

3.04749 

.34758 

2.87700 

50 

11 

.27138 

3.68485 

.29021 

3.44576 

.30923 

3.23381 

.32846 

3.04450 

.34791 

2.87430 

49 

12 

.27169 

3.68061 

.29053 

3.44202 

.30955 

3.23048 

.32878 

3.04152 

.34824 

2.87161 

48 

13 

.27201 

3.67638 

.29084 

3.43829 

.30987 

3.22715 

.32911 

3.03854 

.34856 

2.86892 

47 

14 

.27232 

3.67217 

.29116 

3.43456 

.31019 

3.22384 

.32943 

3.03556 

.34889 

2.86624 

46 

15 

.27263 

3.66796 

.29147 

3.43084 

.31051 

3.22053 

.32975 

3.03260 

.34922 

2.86356 

45 

16 

.27294 

3.66376 

.29179 

3.42713 

.31083 

3.21722 

.33007 

3.02963 

.34954 

2.86089 

44 

17 

.27326 

3.65957 

.29210 

3.42343 

.31115 

3.21392 

.33<T40 

3.02667 

.34987 

2.85822 

43 

18 

.27357 

3.65538 

.29242 

3.41973 

.31147 

3.21063 

.33072 

3.02372 

.35020 

2.85555 

42 

19 

.27388 

3.65121 

.29274 

3.41604 

.31178 

3.20734 

.33104 

3.02077 

.35052 

2.85289 

41 

20 

.27419 

3.64705 

.29305 

3.41236 

.31210 

3.20406 

.33136 

3.01783 

.35085 

2.85023 

40 

21 

.27451 

3.64289 

.29337 

3.40869 

.31242 

3.20079 

.33169 

3.01489 

.35118 

2.84758 

39 

22 

.27482 

3.63874 

.29368 

3.40502 

.31274 

3.19752 

.33201 

3.01196 

.35150 

2.84494 

38 

23 

.27513 

3.63461 

.29400 

3.40136 

.31306 

3.19426 

.33233 

3.00903 

.35183 

2.84229 

37 

24 

.27545 

3.63048 

.29432 

3.39771 

.31338 

3.19100 

.33266 

3.00611 

.35216 

2.83965 

36 

25 

.27576 

3.62636 

.29463 

3.39406 

.31370 

3.18775 

.33298 

3.00319 

.35248 

2.83702 

35 

26 

.27607 

3.62224 

.29495 

3.39042 

.31402 

3  18451 

.33330 

3.00028 

.35281 

2.83439 

34 

27 

.27638 

3.61814 

.29526 

3.38679 

.31434 

3.18127 

.33363 

2.99738 

.35314 

2.83176 

33 

28 

.27670 

3.61405 

.29558 

3.38317 

.31466 

3.17804 

.33395 

2.99447 

.35346 

2.82914 

32 

29 

.27701 

3.60996 

.29590 

3.37955 

.31498 

3.17481 

.33427 

2.99158 

.35379 

2.82653 

31 

80 

.27732 

3.60588 

.29621 

3.37594 

.31530 

3.17159 

.33460 

2.98868 

.35412 

2.82391 

30 

31 

.27764 

3.60181 

.29653 

3.37234 

.31562 

3.16838 

.33492 

2.98580 

.35445 

2.82130 

29 

82 

.27795 

3.59775 

.29685 

3.36875 

31594 

3.16517 

.33524 

2.98292 

.35477 

2.81870 

28 

33 

.27826 

3.59370 

.29716 

3.36516 

.31626 

3.16197 

.33557 

2.98004 

.35510 

2.81610 

27 

84 

.27858 

3.58966 

.29748 

3.36158 

.31658 

3.15877 

.33589 

2.97717 

.35543 

2.81350 

26 

35 

.27889 

3.58562 

.29780 

3.35800 

.31690 

3.15558 

.33621 

2.97430 

.35576 

2.81091 

25 

36 

.27921 

3.58160 

.29811 

3.35443 

.31722 

3.15240 

.33654 

2.97144 

.35608 

2.80833 

24 

37 

.27952 

3.57758 

.29843 

3.35087 

.31754 

3.14922 

.33686 

2.96858 

.35641 

2.80574 

23 

38 

.27983 

3.57357 

.29875 

3.34732 

.31786 

3.14605 

.33718 

2.96573 

.35674 

2.80316 

29 

89 

.28015 

3.56957 

.29906 

3.34377 

.31818 

3.14288 

.33751 

2.96288 

.35707 

2.80059 

21 

40 

.28046 

3.56557 

.29938 

3.34023 

.31850 

3.13972 

.33783 

2.96004 

.35740 

2.79802 

20 

41 

.28077 

3.56159 

.29970 

3.33670 

.31882 

3.13656 

.33816 

2.95721 

.35772 

2.79545 

19 

42 

.28109 

3.55761 

.30001 

3.33317 

.31914 

3.13341 

.33848 

2.95437 

.35805 

2.79289 

18 

43 

.28140 

3.55364 

.30033 

3.32965 

.31946 

3.13027 

.33881 

2.95155 

.35838 

2.79033 

17 

44 

.28172 

3.54968 

.30065 

3.32614 

.31978 

3.12713 

.33913 

2.94872 

.35871 

2.78778 

16 

45 

.28203 

3.54573 

.30097 

3.32264 

.32010 

3.12400 

.33945 

2.94591 

.35904 

2.78523 

15 

46 

.28234 

3.54179 

.30128 

3.31914 

.32042 

3.12087 

.33978 

2.94309 

.35937 

2.78269 

14 

47 

.28266 

3.53785 

.30160 

3.31565 

.32074 

3.11775 

.34010 

2.94028 

.35969 

2.78014 

n 

48 

.28297 

3.53393 

.30192 

3.31216 

.32106 

3.11464 

.34043 

2.93748 

.36002 

2.77761 

12 

49 

.28329 

3.53001 

.30224 

3.30868 

.32139 

3.11153 

.34075 

2.93468 

.36035 

2.77507 

11 

50 

.28360 

3.52609 

.30255 

3.30521 

.32171 

3.10842 

.34108 

2.93189 

.36068 

2.77254 

10 

51 

52 

.28391 
28423 

3.52219 
3  51829 

.30287 
.30319 

3.30174 
3.29829 

.32203 
.32235 

3.10532 
3.10223 

.34140 
.34173 

2.92910 
2.92632 

.36101 
.36134 

2.77002 
2.76750 

9 

8 

53 
54 

.28454 
.28486 

3.51441 
3  51053 

.30351 
.30382 

3.29483 
3.29139 

.32267 
.32299 

3.09914 
3.09606 

.34205 
.34238 

2.92354 
2.92076 

.36167 
.36199 

2.76498 
2.76247 

55 
56 

.28517 
.28549 

3.50666 
3  50279 

.30414 
.30446 

3.28795 
3.28452 

.32331 
.32363 

3.09298 
3.08991 

.34270 
.34303 

2.91799 
2.91523 

.36232 
.36265 

2.75996 
2.75746 

57 
58 

.28580 
.28612 

3.49894 
3  49509 

.30478 
.30509 

3.28109 
3.27767 

.32396 
.32428 

3.08685 
3.08379 

.34335 
.34368 

2.91246 
2.90971 

.36298 
.36331 

2.75496 
2.75246 

59 
60 

!28643 
.28675 

3.49125 
3.48741 

.30541 
.30573 

3.27426 
3.27085 

.32460 
.32492 

3.08073 
3.07768 

.34400 
.34433 

2.90696 
2.90421 

.86364 
.36397 

2.74997 
2.74748 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

7 

40 

7 

3° 

7 

2° 

7 

1° 

7 

[)° 

1004 


NATURAL  TANGENTS  AND  COTANGENTS 


f 

2( 

)° 

2] 

L° 

2 

J° 

2 

J° 

2 

40 

f 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

.36397 

2.74748 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

60 

.36430 

2.74499 

.38420 

2.60283 

.40436 

2.47302 

.42482 

2.35395 

.44558 

2.24428 

59 

.36463 

2.74251 

.38453 

2.60057 

.40470 

2.47095 

.42516 

2.35205 

.44593 

2.24252 

58 

.364% 

2.74004 

.38487 

2.59831 

.40504 

2.46888 

.42551 

2.35015 

.44627 

2.24077 

57 

.36529 

2.73756 

.38520 

2.59606 

.40538 

2.46682 

.42585 

2.34825 

.44662 

2.23902 

56 

.36562 

2.73509 

.38553 

2.59381 

.40572 

2.46476 

.42619 

2.34636 

.44697 

2.23727 

55 

.36595 

2.73263 

.38587 

2.59156 

.40606 

2.46270 

.42654 

2.34447 

.44732 

2.23553 

54 

7 

.36628 

2.73017 

.38620 

2.58932 

.40640 

2.46065 

.42688 

2.34258 

.44767 

2.23378 

53 

8 

.36661 

2.72771 

.38654 

2.58708 

.40674 

2.45860 

.42722 

2.34069 

.44802 

2.23204 

52 

9 

.36694 

2.72526 

.38687 

2.58484 

.40707 

2.45655 

.42757 

2.33881 

.44837 

2.23030 

51 

10 

.36727 

2.72281 

.38721 

2.58261 

.40741 

2.45451 

.42791 

2.33693 

.44872 

2.22857 

50 

11 

.36760 

2.72036 

.38754 

2.58038 

.40775 

2.45246 

.42826 

2.33505 

.44907 

2.22683 

49 

12 

.36793 

2.71792 

.38787 

2.57815 

.40809 

2.45043 

.42860 

2.33317 

.44942 

2.22510 

48 

13 

.36826 

2.71548 

.38821 

2.57593 

.40843 

2.44839 

.42894 

2.83130 

.44977 

2.22337 

47 

14 

.36859 

2.71305 

.38854 

2.57371 

.40877 

2.44636 

.42929 

2.32943 

.45012 

2.22164 

46 

15 

.36892 

2.71062 

.38888 

2.57150 

.40911 

2.44433 

.42963 

2.32756 

.45047 

2.21992 

45 

16 

.36925 

2.70819 

.38921 

2.56928 

.40945 

2.44230 

.42998 

2.32570 

.45082 

2.21819 

44 

17 

.36958 

2.70577 

.38955 

2.56707 

.40979 

2.44027 

.43032 

2.32383 

.45117 

2.21647 

43 

18 

.86991 

2.70335 

.38988 

2.56487 

.41013 

2.43825 

.43067 

2.32197 

.45152 

2.21475 

42 

19 

.37024 

2.70094 

.39022 

2.56266 

.41047 

2.43623 

.43101 

2.32012 

.45187 

2.21804 

41 

20 

.37057 

2.69853 

.39055 

2.56046 

.41081 

2.43422 

.43136 

2.31826 

.45222 

2.21132 

40 

21 

.37090 

2.69612 

.39089 

2.55827 

.41115 

2.43220 

.43170 

2.31641 

.45257 

2.20961 

39 

22 

.37123 

2.69371 

.39122 

2.55608 

.41149 

2.43019 

43205 

2.31456 

.45292 

2.20790 

38 

23 

.37157 

2.69131 

.39156 

2:55389 

.41183 

2.42819 

.43239 

2.31271 

.45327 

2.20619 

37 

24 

.37190 

2.68892 

.39190 

2.55170 

.41217 

2.42618 

.43274 

2.31086 

.45362 

2.20449 

36 

25 

.37223 

2.68653 

.39223 

2.54952 

.41251 

2.42418 

.43308 

2.30902 

.45397 

2.20278 

35 

26 

.37256 

2.68414 

.39257 

2.54734 

.41285 

2.42218 

.43343 

2.30718 

.45432 

2.20108 

34 

27 

.37289 

2.68175 

.39290 

2.54516 

.41319 

2.42019 

.43378 

2.30534 

.45467 

2.19938 

33 

28 

.37322 

2.67937 

.39324 

2.54299 

.41353 

2.41819 

.43412 

2.30351 

.45502 

2.19769 

32 

29 

.37355 

2.67700 

.39357 

2.54082 

.41387 

2.41620 

.43447 

2.30167 

.45538 

2.19599 

31 

30 

.37388 

2.67462 

.39391 

2.53865 

.41421 

2.41421 

.43481 

2.29984 

.45573 

2.19430 

30 

31 

.37422 

2.67225 

.39425 

2.53648 

.41455 

2.41223 

.43516 

2.29801 

.45608 

2.19261 

29 

32 

.37455 

2.66989 

.39458 

2.53432 

.41490 

2.41025 

.43550 

2.29619 

.45643 

2.19092 

28 

33 

.37488 

2.66752 

.39492 

2.53217 

.41524 

2.40827 

.43585 

2.29437 

.45678 

2.18923 

27 

34 

.37521 

2.66516 

.39526 

2.53001 

.41558 

2.40629 

.43620 

2.29254 

.45713 

2.18755 

26 

35 

.37554 

2.66281 

.39559 

2.52786 

.41592 

2.40432 

.43654 

2.29073 

.45748 

2.18587 

25 

36 

.37588 

2.66046 

.39593 

2.52571 

.41626 

2.40235 

.43689 

2.28891 

.45784 

2.18419 

24 

37 

.37621 

2.65811 

.39626 

2.52357 

.41660 

2.40038 

.43724 

2.28710 

.45819 

2.18251 

23 

38 

.37654 

2.65576 

.39660 

2.52142 

.41694 

2.39841 

.43758 

2.28528 

.45854 

2.18084 

22 

39 

.37687 

2.65342 

.39694 

2.51929 

.41728 

2.39645 

.43793 

2.28348 

.45889 

2.17916 

21 

40 

.37720 

2.65109 

.39727 

2.51715 

.41763 

2.39449 

.43828 

2.28167 

.45924 

2.17749 

20 

41 

.37754 

2.64875 

.39761 

2.51502 

.41797 

2.39253 

.43862 

2.27987 

.45960 

2.17582 

19 

42 

.37787 

2.64642 

.39795 

2.51289 

.41831 

2.39058 

.43897 

2.27806 

.45995 

2.17416 

18 

43 

.37820 

2.64410 

.39829 

2.51076 

.41865 

2.38863 

.43932 

2.27626 

.46030 

2.17249 

17 

44 

.37853 

2.64177 

.39862 

2.50864 

.41899 

2.38668 

.43966 

2.27447 

.46065 

2.17083 

16 

45 

.37887 

2.63945 

.398% 

2.50652 

.41933 

2.38473 

.44001 

2.27267 

.46101 

2.16917 

15 

46 

.37920 

2.63714 

.39930 

2.50440 

.41968 

2.38279 

.44036 

2.27088 

.46136 

2.16751 

14 

47 

.37953 

2.63483 

.39%3 

2.50229 

.42002 

2.38084 

.44071 

2.26909 

.46171 

2.16585 

13 

48 

.37986 

2.63252 

.39997 

2.50018 

.42036 

2.37891 

.44105 

2.26730 

.46206 

2.16420 

12 

49 

.38020 

2.63021 

.40031 

2.49807 

.42070 

2.37697 

.44140 

2.26552 

.46242 

2.16255 

11 

50 

.38053 

2.62791 

.40065 

2.49597 

.42105 

2.37504 

.44175 

2.26374 

.46277 

2.16090 

10 

51 

.38086 

2.62561 

.40098 

2.49386 

.42139 

2.37311 

.44210 

2.26196 

.46312 

2.15925 

9 

52 

.38120 

2.62332 

.40132 

2.49177 

.42173 

2.37118 

.44244 

2.26018 

.46348 

2.15760 

8 

53 

.38153 

2.62103 

.40166 

2.48967 

.42207 

2.36925 

.44279 

2.25840 

.46383 

2.155% 

54 

.38186 

2.61874 

.40200 

2.48758 

.42242 

2.36733 

.44314 

2.25663 

.46418 

2.15432 

55 

.38220 

2.61646 

.40234 

2.48549 

.42276 

2.36541 

.44349 

2.25486 

.46454 

2.15268 

56 

.38253 

2.61418 

.40267 

2.48340 

.42310 

2.36349 

.44384 

2.25309 

.46489 

2.15104 

57 

.38286 

2.61190 

.40301 

2.48132 

.42345 

2.36158 

.44418 

2.25132 

.46525 

2.14940 

58 

.38320 

2.60963 

.40335 

2.47924 

.42379 

2.35967 

.44453 

2.24956 

.46560 

2.14777 

£9 

.38353 

2.60736 

.40369 

2.47716 

.42413 

2.35776 

.44488 

2.24780 

.46595 

2.14614 

1 

60 

.38386 

2.60509 

.40403 

2.47509 

.42447 

2.35585 

.44523 

2.24604 

.46631 

2.14451 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

6< 

)° 

61 

$° 

6' 

70 

6( 

)° 

6 

5° 

/ 

NATURAL  TANGENTS  AND  COTANGENTS 


1005 


2J 

)° 

2 

5° 

2 

7° 

2. 

3° 

2 

9° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.46631 

2.14451 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80405 

60 

.46666 

2.14288 

.48809 

2.04879 

.50989 

1.96120 

.53208 

1.87941 

.55469 

1.80281 

59 

.46702 

2.14125 

.48845 

2.04728 

.51026 

1.95979 

.53246 

1.87809 

.55507 

1.80158 

58 

.46737 

2.13963 

.48881 

2.04577 

.51063 

1.95838 

.53283 

1.87677 

.55545 

1.80034 

57 

.46772 

2.13801 

.48917 

2.04426 

.51099 

1.95698 

.53320 

1.87546 

.55583 

1.79911 

56 

.46808 

2.13639 

.48953 

2.04276 

.51136 

1.95557 

.53358 

1.87415 

.55621 

1.79788 

55 

.46843 

2.13477 

.48989 

2.04125 

.51173 

1.95417 

.53395 

1.87283 

.55659 

1.79665 

54 

.46879 

2.13316 

.49026 

2.03975 

.51209 

1.95277 

.53432 

1.87152 

.55697 

1.79542 

53 

.46914 

2.13154 

.49062 

2.03825 

.51246 

1.95137 

.53470 

1.87021 

.55736 

1.79419 

52 

.46950 

2.12993 

.49098 

2.03675 

.51283 

1.94997 

.53507 

1.86891 

.55774 

1.79296 

51 

10 

.46985 

2.12832 

.49134 

2.03526 

.51319 

1.94858 

.53545 

1.86760 

.55812 

1.79174 

50 

11 

.47021 

2.12671 

.49170 

2.03376 

.51356 

1.94718 

.53582 

1.86630 

.55850 

1.79051 

49 

12 

.47056 

2.12511 

.49206 

2.03227 

.51393 

1.94579 

.53620 

1.86499 

.55888 

1.78929 

48 

13 

.47092 

2.12350 

.49242 

2.03078 

.51430 

1.94440 

.53657 

1.86369 

.55926 

1.78807 

47 

14 

.47128 

2.12190 

.49278 

2.02929 

.51467 

1.94301 

.53694 

1.86239 

.55964 

1.78685 

46 

15 

.47163 

2.12030 

.49315 

2.02780 

.51503 

1.94162 

.53732 

1.86109 

.56003 

1.78563 

45 

16 

.47199 

2.11871 

.49351 

2.02631 

.51540 

1.94023 

.53769 

1.85979 

.56041 

1.78441 

44 

17 

.47234 

2.11711 

.49387 

2.02483 

.51577 

1.93885 

.53807 

1.85850 

.56079 

1.78319 

43 

18 

.47270 

2.11552 

.49423 

2.02335 

.51614 

1.93746 

.53844 

1.85720 

.56117 

1.78198 

42 

19 

.47305 

2.11392 

.49459 

2.02187 

.51651 

1.93608 

.53882 

1.85591 

.56156 

1.78077 

41 

20 

.47341 

2.11233 

.49495 

2.02039 

.51688 

1.93470 

.53920 

1.85462 

.56194 

1.77955 

40 

21 

.47377 

2.11075 

.49532 

2.01891 

.51724 

1.93332 

.53957 

1.85333 

.56232 

1.77834 

39 

22 

.47412 

2.10916 

.49568 

2.01743 

.51761 

1.93195 

.53995 

1.85204 

.56270 

1.77713 

38 

23 

.47448 

2.10758 

.49604 

2.01596 

.51798 

1.93057 

.54032 

1.85075 

.56309 

1.77592 

37 

24 

.47483 

2.10600 

.49640 

2.01449 

.51835 

1.92920 

.54070 

1.84946 

.56347 

1.774U 

36 

25 

.47519 

2.10442 

.49677 

2.01302 

.51872 

1.92782 

.54107 

1.84818 

.56385 

1.77351 

35 

26 

.47555 

2.10284 

.49713 

2.01155 

.51909 

1.92645 

.54145 

1.84689 

.56424 

1.77230 

34 

27 

.47590 

2.10126 

.49749 

2.01008 

.51946 

1.92508 

.54183 

1.84561 

.56462 

1.77110 

33 

28 

.47626 

2.09969 

.49786 

2.00862 

.51983 

1.92371 

.54220 

1.84433 

.56501 

1.76990 

32 

29 

.47662 

2.09811 

.49822 

2.00715 

.52020 

1.92235 

.54258 

1.84305 

.56539 

1.76869 

31 

30 

.47698 

2.09654 

.49858 

2.00569 

.52057  - 

1.92098 

.54296 

1.84177 

.56577 

1.76749 

30 

31 

.47733 

2.09498 

.49894 

2.00423 

.52094 

1.91962 

.54333 

1.84049 

.56616 

1.76629 

29 

32 

.47769 

2.09341 

.49931 

2.00277 

.52131 

1.91826 

.54371 

1.83922 

.56654 

1.76510 

28 

33 

.47805 

2.09184 

.49967 

2.00131 

.52168 

1.91690 

.54409 

1.83794 

.56693 

1.76390 

27 

34 

.47840 

2.09028 

.50004 

1.99986 

.52205 

1.91554 

.54446 

1.83667 

.56731 

1.76271 

26 

35 

.47876 

2.08872 

.50040 

1.99841 

.52242 

1.91418 

.54484 

1.83540 

.56769 

1.76151 

25 

36 

.47912 

2.08716 

.50076 

1.99695 

.52279 

1.91282 

.54522 

1.83413 

.56808 

1.76032 

24 

37 

.47948 

2.08560 

.50113 

1.99550 

.52316 

1.91147 

.54560 

1.83286 

.56846 

1.75913 

23 

38 

.47984 

2.08405 

.50149 

1.99406 

.52353 

1.9101-2 

.54597 

1.83159 

.56885 

1.75794 

22 

39 

.48019 

2.08250 

.50185 

1.99261 

.52390 

1.90876 

.54635 

1.83033 

.56923 

1.75675 

21 

40 

.48055 

2.08094 

.50222 

1.99116 

.52427 

1.90741 

.54673 

1.82906 

.56962 

1.75556 

20 

41 

.48091 

2.07939 

.50258 

1.98972 

.52464 

1.90607 

.54711 

1.82780 

.57000 

1.75437 

19 

42 

.48127 

2.07785 

.50295 

1.98828 

.52501 

1.90472 

.54748 

1.82654 

.57039 

1.75319 

18 

43 

.48163 

2.07630 

.50331 

1.98684 

.52538 

1.90337 

.54786 

1  .82528 

.57078 

1.75200 

17 

44 

.48198 

2.07476 

.50368 

1.98540 

.52575 

1.90203 

.54824 

1.82402 

.57116 

1.75082 

16 

45 

.48234 

2.07321 

.50404 

1.98396 

.52613 

1.90069 

.54862 

1.82276 

.57155 

1.74964 

15 

46 

.48270 

2.07167 

.50441 

1.98253 

.52650 

1.89935 

.54900 

1.82150 

.57193 

1.74846 

14 

47 

.48306 

2.07014 

.50477 

1.98110 

.52687 

1.89801 

.54938 

1.82025 

.57232 

1.74728 

13 

48 

.48342 

2.06860 

.50514 

1.97966 

.52724 

1.89667 

.54975 

1.81899 

.57271 

1.74610 

12 

49 

.48378 

2.06706 

.50550 

1.97823 

.52761 

1.89533 

.55013 

1.81774 

.57309 

1.74492 

11 

50 

.48414 

2.06553 

.50587 

1.97681 

.52798 

1.89400 

.55051 

1.81649 

.57348 

1.74375 

10 

51 

.48450 

2.06400 

.50623 

1.97538 

.52836 

1.89266 

.55089 

1.81524 

.57386 

1.74257 

52 

.48486 

2.06247 

.50660 

1.97395 

.52873 

1.89133 

.55127 

1.81399 

.57425 

1.74140 

53 

.48521 

2.06094 

.50696 

1.97253 

.52910 

1.89000 

.55165 

1.81274 

.57464 

1.74022 

54 

.48557 

2.05942 

.50733 

1.97111 

.52947 

1.88867 

.55203 

1.81150 

.57503 

1.73905 

55 

.48593 

2.05790 

.50769 

1.96969 

.52985 

1.88734 

.55241 

1.81025 

.57541 

1.73788 

56 

.48629 

2.05637 

.50806 

1.96827 

.53022 

1.88602 

.55279 

1.80901 

.57580 

1.73671 

57 

.48665 

2.05485 

.50843 

1  .96685 

.53059 

1.88469 

.55317 

1.80777 

.57619 

1.73555 

58 

.48701 

2.05333 

.50879 

1.96544 

.53096 

1.88337 

.55355 

1.80653 

.57657 

1.73438 

59 

.48737 

2.05182 

.50916 

1.96402 

.53134 

1.88205 

.55393 

1.80529 

.57696 

1.73321 

60 

.48773 

2.05030 

.50953 

1.96261 

.53171 

1.88073 

.55431 

1.80405 

.57735 

1.73205 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

1 

64 

0 

K 

\° 

6S 

O 

61 

0 

• 

)° 

t 

1006 


NATURAL  TANGENTS  AND  COTANGENTS 


30° 

31° 

32° 

33° 

34° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.57735 

1.73205 

.60086 

1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

60 

1 

.57774 

1.73089 

.60126 

1.66318 

.62527 

1.59930 

.64982 

1.53888 

.67493 

1.48163 

59 

2 

.57813 

1.72973 

.60165 

1.66209 

.62568 

1.59826 

.65024 

1.53791 

.67536 

1.48070 

58 

3 

.57851 

1.72857 

.60205 

1.66099 

.62608 

1.59723 

.65065 

1.53693 

.67578 

1.47977 

57 

4 

.57890 

1.72741 

.60245 

1.65990 

.62649 

1.59620 

.65106 

1.53595 

.67620 

1.47885 

56 

5 

.57929 

1.72625 

.60284 

1.65881 

.62689 

1.59517 

.65148 

1.53497 

.67663 

1.47792 

55 

6 

.57968 

1.72509 

.60324 

1.65772 

.62730 

1.59414 

.65189 

1.53400 

.67705 

1.47699 

54 

7 

.58007 

1.72393 

.60364 

1.65663 

.62770 

1.59311 

.65231 

1.53302 

.67748 

1.47607 

53 

8 

.58046 

1.72278 

.60403 

1.65554 

.62811 

1.59208 

.65272 

1.53205 

.67790 

1.47514 

52 

9 

.58085 

1.72163 

.60443 

1.65445 

.62852 

1.59105 

.65314 

1.53107 

.67832 

1.47422 

51 

10 

.58124 

1.72047 

.60483 

1.65337 

.62892 

1.59002 

.65355 

1.53010 

.67875 

1.47330 

50 

11 

.58162 

1.71932 

.60522 

1.65228 

.62933 

1.58900 

.65397 

1.52913 

.67917 

1.47238 

49 

12 

.58201 

1.71817 

.60562 

1.65120 

.62973 

1.58797 

.65438 

1.52816 

.67960 

1.47146 

48 

13 

-.58240 

1.71702 

.60602 

1.65011 

.63014 

1.58695 

.65480 

1.52719 

.68002 

1.47053 

47 

14 

.58279 

1.71588 

.60642 

1.64903 

.63055 

1.58593 

.65521 

1.52622 

.68045 

1.46962 

46 

15 

.58318 

1.71473 

.60681 

1.64795 

.63095 

1.58490 

.65563 

1.52525 

.68088 

1.46870 

45 

16 

.58357 

1.71358 

.60721 

1.64687 

.63136 

1.58388 

.65604 

1.52429 

.68130 

1.46778 

44 

17 

.58396 

1.71244 

.60761 

1.64579 

.63177 

1.58286 

.65646 

1.52332 

.68173 

1.46686 

43 

18 

.58435 

1.71129 

.60801 

1.64471 

.63217 

1.58184 

.65688 

1.52235 

.68215 

1.46595 

42 

19 

.58474 

1.71015 

.60841 

1.64363 

.63258 

1.58083 

.65729 

1.52139 

.68258 

1.46503 

41 

20 

.58513 

1.70901 

.60881 

1.64256 

.63299 

1.57981 

.65771 

1.52043 

.68301 

1.46411 

40 

21 

.58552 

1.70787 

.60921 

1.64148 

.63340 

1.5787J9 

.65813 

1.51946 

.68343 

1.46320 

39 

22 

.58591 

1.70673 

.60960 

1.64041 

.63380 

1.57778 

.65854 

1.51850 

.68386 

1.46229 

38 

23 

.58631 

1.70560 

.61000 

1.63934 

.63421 

1.57676 

.65896 

1.51754 

.68429 

1.46137 

37 

24 

.58670 

1.70446 

.61040 

1.63826 

.63462 

1.57575 

.65938 

1.51658 

.68471 

1.46046 

36 

25 

.58709 

1.70332 

.61080 

1.63719 

.63503 

1.57474 

.65980 

1.51562 

.68514 

1.45955 

35 

26 

.58748 

1.70219 

.61120 

1.63612 

.63544 

1.57372 

.66021 

1.51466 

.68557 

1.45864 

34 

27 

.58787 

1.70106 

.61160 

1.63505 

.63584 

1.57271 

.66063 

1.51370 

.68600 

1.45773 

33 

28 

.58826 

1.69992 

.61200 

1.63398 

.63625 

1.57170 

.66105 

1.51275 

.68642 

1.45682 

32 

29 

.58865 

1.69879 

.61240 

1.63292 

.63666 

1.57069 

.66147 

1.51179 

.68685 

1.45592 

31 

30 

.58905 

1.69766 

.61280 

1.63185 

.63707 

1.56969 

.66189 

1.51084 

.68728 

1.45501 

30 

31 

.58944 

1.69653 

.61320 

1.63079 

.63748 

1.56868 

.66230 

1.50988 

.68771 

1.45410 

29 

32 

1.69541 

.61360 

1.62972 

.63789 

1.56767 

.66272 

1.50893 

.68814 

1.45320 

28 

33 

.'59022 

1.69428 

.61400 

1.62866 

.63830 

1.56667 

.66314 

1.50797 

.68857 

1.45229 

27 

34 

.59061 

1.69316 

.61440 

1.62760 

.63871 

1.56566 

.66356 

1.50702 

.68900 

1.45139 

26 

35 

.59101 

1.69203 

.61480 

1.62654 

.63912 

1.56466 

.66398 

1.50607 

.68942 

1.45049 

25 

36 

.WHO 

1.69091 

.61520 

1.62548 

.63953 

1.56366 

.66440 

1.50512 

.68985 

1.44958 

24 

37 

.59179 

1.68979 

.61561 

1.62442 

.63994 

1.56265 

.66482 

1.50417 

.69028 

1.44868 

23 

88 

.59218 

1.68866 

.61601 

1.62336 

.64035 

1.56165 

.66524 

1.50322 

.69071 

1.44778 

22 

39 

.59258 

1.68754 

.61641 

1.62230 

.64076 

1.56065 

.66566 

1.50228 

.69114 

1.44688 

21 

40 

.59297 

1.68643 

.61681 

1.62125 

.64117 

1.55966 

.66608 

1.50133 

.69157 

1.44598 

20 

41 

.59336 

1.68531 

.61721 

1.62019 

.64158 

1.55866 

.66650 

1.50038 

.69200 

1.44508 

19 

42 

.59376 

1.68419 

.61761 

1.61914 

.64199 

1.55766 

.66692 

1.49944 

.69243 

1.44418 

18 

43 

.59415 

1.68308 

.61801 

1.61808 

.64240 

1.55666 

.66734 

1.49849 

.69286 

1.44329 

17 

44 

.59454 

1.68196 

.61842 

1.61703 

.64281 

1.55567 

.66776 

1.49755 

.69329 

1.44239 

16 

45 

.59494 

1.68085 

.61882 

1.61598 

.64322 

1.55467 

.66818 

1.49661 

.69372 

1.44149 

15 

46 

.59533 

1.67974 

.61922 

1.61493 

.64363 

1.55368 

.66860 

1.49566 

.69416 

1.44060 

14 

47 

.59573 

1.67863 

.61962 

1.61388 

.64404 

1.55269 

.66902 

1.49472 

.69459 

1.43970 

13 

48 

.59612 

1.67752 

.62003 

1.61283 

.64446 

1.55170 

.66944 

1.49378 

.69502 

1.43881 

12 

49 

.59651 

1.67641 

.62043 

1.61179 

.64487 

1.55071 

.66986 

1.49284 

.69545 

1.43792 

11 

50 

.59691 

1.67530 

.62083 

1.61074 

.64528 

1.54972 

.67028 

1.49190 

.69588 

1.43703 

10 

51 

.59730 

1.67419 

.62124 

1.60970 

.64569 

1.54873 

.67071 

1.49097 

.69631 

1.43614 

9 

52 

.59770 

1.67309 

.62164 

1.60865 

.64610 

1.54774 

.67113 

1.49003 

.69675 

1.43525 

8 

53 

.59803 

1.67198 

.62204 

1.60761 

.64652 

1.54675 

.67155 

1.48909 

.69718 

1.43436 

7 

54 

.59849 

1.67088 

.62245 

1.60657 

.64693 

1.54576 

.67197 

1.48816 

.69761 

1.43347 

6 

55 

.59888 

1.66978 

.62285 

1.60553 

.64734 

1.54478 

.67239 

1.48722 

.69804 

1.43258 

5 

56 

.59928 

1.66867 

.62325 

1.60449 

.64775 

1.54379 

.67282 

1.48629 

.69847 

1.43169 

4 

57 

.59967 

1.66757 

.62366 

1.60345 

.64817 

1.54281 

.67324 

1.48536 

.69891 

1.43080 

3 

58 

.60007 

1.66647 

.62406 

1.60241 

.64858 

1.54183 

.67366 

1.48442 

.69934 

1.42992 

2 

59 

.60046 

1.66538 

.62446 

1.60137 

.64899 

1.54085 

.67409 

1.48349 

.69977 

1.42903 

1 

60 

.60086 

1.66428 

.62487 

1.60033 

.64941 

1.53986 

.67451 

1.48256 

.70021 

1.42815 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

t 

59° 

58° 

57° 

5b° 

55° 

t 

NATURAL  TANGENTS  AND  COTANGENTS 


1007 


* 

o 

36 

o 

37 

0 

38 

o 

3 

3° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.70021 

1.42815 

.72654 

1.37638 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

60 

1 

.70064 

1.42726 

.72699 

1.37554 

.75401 

1.32624 

.78175 

1.27917 

.81027 

1.23416 

59 

2 

.70107 

1.42638 

.72743 

1.37470 

.75447 

1.32544 

.78222 

1.27841 

.81075 

1.23343 

58 

3 

.70151 

1.42550 

.72788 

1.37386 

.75492 

1.32464 

.78269 

1.27764 

.81123 

1.23270 

57 

4 

.70194 

1.42462 

.72832 

1.37302 

.75538 

1.32384 

.78316 

1.27688 

.81171 

1.23196 

56 

5 

.70238 

1.42374 

.72877 

1.37218 

.75584 

1.32304 

.78363 

1.27611 

.81220 

1.23123 

55 

6 

.70281 

1.42286 

.72921 

1.37134 

.75629 

1.32224 

.78410 

1.27535 

.81268 

1.23050 

54 

7 

.70325 

1.42198 

.72966 

1.37050 

.75675 

1.32144 

.78457 

1.27458 

.81316 

1.22977 

53 

8 

.70368 

1.42110 

.73010 

1.36967 

.75721 

1.32064 

.78504. 

1.27382 

.81364 

1.22904 

52 

9 

.70412 

1.42022 

.73055 

1.36883 

.75767 

1.31984 

.78551 

1.27306 

.81413 

1.22831 

51 

10 

.70455 

1.41934 

.73100 

1.36800 

.75812 

1.31904 

.78598 

1.27230 

.81461 

1.22758 

50 

11 

.70499 

1.41847 

.73144 

1.36716 

.75858 

1.31825 

.78645 

1.27153 

.81510 

1.22685 

49 

12 

.70542 

1.41759 

.73189 

1.36633 

.75904 

1.31745 

.78692 

1.27077 

.81558 

1.22612 

48 

13 

.70586 

1.41672 

.73234 

1.36549 

.75950 

1.31666 

.78739 

1.27001 

.81606 

1.22539 

47 

14 

.70629 

1.41584 

.73278 

1.36466 

.75996 

1.31586 

.78786 

1.26925 

.81655 

1.22467 

46 

15 

.70673 

1.41497 

.73323 

1.36383 

.76042 

1.31507 

.78834 

1.26849 

.81703 

1.22394 

45 

16 

.70717 

1.41409 

.73368 

1.36300 

.76088  ' 

1.31427 

.78881 

1.26774 

.81752 

1.22321 

44 

17 

.70760 

1.41322 

.73413 

1.36217 

.76134 

1.31348 

.78928 

1.26698 

.81800 

1.22249 

43 

18 

.70804 

1.41235 

.73457 

1.36134 

.76180 

1.31269 

.78975 

1.26622 

.81849 

1.22176 

42 

19 

.70848 

1.41148 

.73502 

1.36051 

.76226 

1.31190 

.79022 

1.26546 

.81898 

1.22104 

41 

20 

.70891 

1.41061 

.73547 

1  35968 

.76272 

1.31110 

.79070 

1.26471 

.81946 

1.22031 

40 

21 

.70935 

1.40974 

.73592 

1.35885 

.76318 

1.31031 

.79117 

1.26395 

.81995 

1.21959 

39 

22 

.70979 

1.40887 

.73637 

1.35802 

.76364 

1.30952 

.79164 

1.26319 

.82044 

1.21886 

38 

23 

.71023 

1.40800 

.73681 

1.35719 

.76410 

1.30873 

.79212 

1.26244 

.82092 

1.21814 

37 

24 

.71066 

1.40714 

.73726 

1.35637 

.76456 

1.30795 

.79259 

1  .26169 

.82141 

1.21742 

36 

25 

.71110 

1.40627 

.73771 

1.35554 

.76502 

1.30716 

.79306 

1.26093 

.82190 

1.21670 

35 

26 

.71154 

1.40540 

.73816 

1.35472 

.76548 

1.30637 

.79354 

1  .26018 

.82238 

1.21598 

34 

27 

.71198 

1.40454 

.73861 

1.35389 

.76594 

1.30558 

.79401 

1.25943 

.82287 

1.21526 

33 

28 

.71242 

1.40367 

.73906 

1.35307 

.76640 

1.30480 

.79449 

1.25867 

.82336 

1.21454 

32 

29 

.71285 

1.40281 

.73951 

1.35224 

.76686 

1.30401 

.79496 

1.25792 

.82385 

1.21382 

31 

30 

.71329 

1.40195 

.73996 

1.35142 

.76733 

1.30323 

.79544 

1.25717 

.82434 

1.21310 

80 

31 

.71373 

1.40109 

.74041 

1.35060 

.76779 

1.30244 

.79591 

1.25642 

.82483 

1.21238 

29 

32 

.71417 

1.40022 

.7-40*6 

1.34978 

.76825 

1.30166 

.79639 

1.25567 

.82531 

1.21166 

28 

33 

.71461 

1.39936 

.74181 

1.34896 

.76871 

1.30087 

.79686 

1.25492 

.82580 

1.21094 

27 

34 

.71505 

1.39850 

.74176 

1.34814 

.76918 

1  .30009 

.79734 

1.25417 

.82629 

1.21023 

26 

35 

.71549 

1.39764 

.74221 

1.34732 

.  .76964 

1.29931 

.79781 

1.25343 

.82678 

1.20951 

25 

36 

.71593 

1.39679 

.74267 

1.34650 

.77010 

1.29853 

.79829 

1.25268 

.82727 

1.20879 

24 

37 

.71637 

1.39593 

.74312 

1  .84568 

.77057 

1.29775 

.79877 

1.25193 

.82776 

1  .20808 

23 

38 

.71681 

1.39507 

.74357 

1.34487 

.77103 

1.29696 

.79924 

1.25118 

.82825 

1.20736 

22 

39 

.71725 

1.39421 

.74402 

1.34405 

.77149 

1.29618 

.79972 

1.25044 

.82874 

1.20665 

21 

40 

.71769 

1.39336 

.74447 

1.34323 

.77196 

1.29541 

.80020 

1.24969 

.82923 

1.20593 

20 

41 

.71813 

1.39250 

.74492 

1.34242 

.77242 

1.29463 

.80067 

1.24895 

.82972 

1.20522 

19 

42 

.71857 

1.39165 

.74538 

1.34160 

.77289 

1.29385 

.80115 

1.24820 

.83022 

1.20451 

18 

43 

.71901 

1.39079 

.74583 

1.34079 

.77335 

1.29307 

.80163 

1.24746 

.83071 

1.20379 

17 

44 

.71946 

1.38994 

.74628 

1.33998 

.77382 

1.29229 

.80211 

1.24672 

.83120 

1.20308 

16 

45 

.71990 

1.38909 

.74674 

1.33916 

.77428 

1.29152 

.80258 

1.24597 

.83169 

1.20237 

15 

46 

.72034 

1.38824 

.74719 

1.33835 

.77475 

1.29074 

.80306 

1.24523 

.83218 

1.20166 

14 

47 

.72078 

1.38738 

.74764 

1.33754 

.77521 

1.28997 

.80354 

1.24449 

.83268 

1.20095 

13 

48 

.72122 

1.38653 

.74810 

1.33673 

.77568 

1.28919 

.80402 

1.24375 

.83317 

1.20024 

12 

49 

.72167 

1.38568 

.74855 

1.33592 

.77615 

1.28842 

.80450 

1.24301 

.83366 

1.19953 

11 

50 

.72211 

1.38484 

.74900 

1.33511 

.77661 

1.28764 

.80498 

1.24227 

.83415 

1.19882 

10 

51 

.72255 

1.38399 

.74946 

1.33430 

.77708 

1.28687 

.80546 

1.24153 

.83465 

1.19811 

9 

52 

.72299 

1.38314 

.74991 

1.33349 

.77754 

1.28610 

.80594 

1.24079 

.83514 

1.19740 

8 

53 

.72344 

1.38229 

.75037 

1.33268 

.77801 

1.28533 

.80642 

1.24005 

.83564 

.19669 

1 

54 

.72388 

1.38145 

.75082 

1.33187 

.77848 

1.28456 

.80690 

1.23931 

.83613 

.19599 

6 

55 

.72432 

1.38060 

.75128 

1.33107 

.77895 

1.28379 

.80738 

1.23858 

.83662 

.19528 

5 

56 

.72477 

1.37976 

.75173 

1.33026 

.77941 

1.28302 

.80786 

1.23784 

.83712 

.19457 

4 

57 

.72521 

1.37891 

.75219 

1.32946 

.77988 

1.28225 

.80834 

1.23710 

.83761 

.19387 

3 

58 

.72565 

1.37807 

.75264 

1.32865 

.78035 

1.28148 

.80882 

1.23637 

.83811 

.19316 

2 

59 

.72610 

1.37722 

.75310 

1.32786 

.78082 

1.28071 

.80930 

1.23563 

.83860 

.19246 

1 

60 

.72654 

1.37638 

.75355 

1.32704 

.78129 

1.27994 

.80978 

1.23490 

.83910 

1.19175 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

t 

5 

4° 

5 

J° 

5 

>° 

51 

L° 

5 

0° 

f 

1008 


NATURAL  TANGENTS  AND  COTANGENTS 


4C 

o 

41 

0 

ti 

JO 

42 

o 

4 

1° 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

0 

.83910 

1.19175 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

60 

.83960 

1.19105 

.86980 

1.14969 

.90093 

.10996 

.93306 

1.07174 

.96625 

1  .03493 

59 

.84009 

1.19035 

.87031 

1.14902 

.90146 

.10931 

.93360 

1.07112 

.96681 

1.03433 

58 

.84059 

1.18964 

.87082 

1.14834 

.90199 

1.10867 

.93415 

1.07049 

.96738 

1.03372 

57 

.84108 

1.18894 

.87133 

1.14767 

.90251 

.10802 

.93469 

1.06987 

.96794 

1.03312 

56 

.84158 

1.18824 

.87184 

1.14699 

.90304 

1.10737 

.93524 

1.06925 

.96850 

1.03252 

55 

.84208 

1.18754 

.87236 

1.14632 

.90357 

1.10672 

.93578 

1.06862 

.96907 

1.03192 

54 

.84258 

1.18684 

.87287 

1.14565 

.90410 

1.10607 

.93633 

1.06800 

.96963 

1.03132 

53 

.84307 

1.18614 

.87338 

1.14498 

.90463 

.10543 

.93688 

1.06738 

.97020 

1.03072 

52 

.84357 

1.18544 

.87389 

1.14430 

.90516 

.10478 

.93742 

1.06676 

.97076 

1.03012 

51 

10 

.84407 

1.18474 

.87441 

1.14363 

.90569 

.10414 

.93797 

1.06613 

.97133 

1.02952 

50 

11 

.84457 

1.18404 

.87492 

1.14296 

.90621 

.10349 

.93852 

1.06551 

.97189 

1.02892 

49 

12 

.84507 

1.18334 

.87543 

1.14229 

.90674 

.10285 

.93906 

1.06489 

.97246 

1.02832 

48 

13 

.84556 

1.18264 

.87595 

1.14162 

.90727 

.10220 

.93961 

1.06427 

.97302 

1.02772 

47 

14 

.84606 

1.18194 

.87646 

1.14095 

.90781 

.10156 

.94016 

1.06365 

.97359 

1.02713 

46 

15 

.84656 

1.18125 

.87698 

1.14028 

.90834, 

.10091 

.94071 

1.06303 

.97416 

1.02653 

45 

16 

.84706 

1.18055 

.87749 

1.13961 

.90887 

.10027 

.94125 

1.06241 

.97472 

1.02593 

44 

17 

.84756 

1.17986 

.87801 

1.13894 

.90940 

1.09963 

.94180 

1.06179 

.07529 

1.02533 

43 

18 

.84806 

1.17916 

.87852 

1.13828 

.90993 

1.09899 

.94235 

1.06117 

.97586 

1.02474 

42 

19 

.84856 

1.17846 

.87904 

1.13761 

.91046 

1.09834 

.94290 

1.06056 

.97643 

1.02414 

41 

20 

.84906 

1.17777 

.87955 

1.13694 

.91099 

1.09770 

.94345 

1.05994 

.97700 

1.02355 

40 

21 

.84956 

1.17708 

.88007 

1.13627 

.91153 

1.09706 

.94400 

1.05932 

.97756 

1.02295 

39 

22 

.85006 

1.17638 

.88059 

1.13561 

.91206 

1.09642 

.94455 

1.05870 

.97813 

1.02236 

38 

23 

.85057 

1.17569 

.88110 

1.13494 

.91259 

1.09578 

.94510 

1.05809 

.97870 

1.02176 

37 

24 

.85107 

1.17500 

.88162 

1.13428 

.91313 

1.09514 

.94565 

1.05747 

.97927 

1.02117 

36 

25 

.85157 

1.17430 

.88214 

1.13361 

.91366 

1.09450 

.94620 

1.05685 

.97984 

1.02057 

35 

26 

.85207 

1.17361 

.88265 

1.13295 

.91419 

1.09386 

.94676 

1.05624 

.98041 

1.01998 

34 

27 

.85257 

1.17292 

.88317 

1.13228 

.91473 

1.09322 

.94731 

1.05562 

.98098 

1.01939 

33 

28 

.85308 

1.17223 

.88369 

1.13162 

.91526 

1.09258 

.94786 

1.05501 

.98155 

1.01879 

32 

29 

.85358 

1.17154 

.88421 

1.13096 

.91580 

1.09195 

.94841 

1  .05439 

.98213 

1.01820 

31 

30 

.85408 

1.17085 

.88473 

1.13029 

.91633 

1.09131 

.94896 

1.05378 

.98270 

1.01761 

30 

31 

.85458 

1.17016 

.88524 

1.12963 

.91687 

1.09067 

.94952 

1.05317 

.98327 

1.01702 

29 

32 

.85509 

1.16947 

.88576 

1.12897 

.91740 

1.09003 

.95007 

1.05255 

.98384 

1.01642 

28 

33 

.85559 

1.16878 

.88628 

1.12831 

.91794 

1.08940 

.95062 

1.05194 

.98441 

1.01583 

27 

34 

.85609 

1.16809 

.88680 

1.12765 

.91847 

1.08876 

.95118 

1.05133 

.98499 

1.01524 

26 

35 

.85660 

1.16741 

.88732 

1.12699 

.91901 

1.08813 

.95173 

1.05072 

.98556 

1.01465 

25 

36 

.85710 

1.16672 

.88784 

1.12633 

.91955 

1.08749 

.95229 

1.05010 

.98613 

1.01406 

24 

37 

.85761 

1.16603 

.88836 

1.12567 

.92008 

1.08686 

.95284 

1.04949 

.98671 

1.01347 

23 

38 

.85811 

1.16535 

.88888 

1.12501 

.92062 

1.08622 

.95340 

1.04888 

.98728 

1.01288 

22 

39 

.85862 

1.16466 

.88940 

1.12435 

.92116 

1.08559 

.95395 

1.04827 

.98786 

1.01229 

21 

40 

.85912 

1.16398 

.88992 

1.12369 

.92170 

1.08496 

.95451 

1.04766 

.98843 

1.01170 

20 

41 

.85963 

1.16329 

.89045 

1.12303 

.92224 

1.08432 

.95506 

1.04705 

.98901 

1.01112 

19 

42 

.86014 

1.16261 

.89097 

1.12238 

.92277 

1.08369 

.95562 

1.04644 

.98958 

1.01053 

18 

43 

.86064 

1.16192 

.89149 

1.12172 

.92331 

1.08306 

.95618 

1.04583 

.99016 

1.00994 

17 

44 

.86115 

1.16124 

.89201 

1.12106 

.92385 

1.08243 

.95673 

1.04522 

.99073 

1.00935 

16 

45 

.86166 

1.16056 

.89253 

1.12041 

.92439 

1.08179 

.95729 

1.04461 

.99131 

1.00876 

15 

46 

.86216 

1.15987 

.89306 

1.11975 

.92493 

1.08116 

.95785 

1.04401 

.99189 

1.00818 

14 

47 

.86267 

1.15919 

.89358 

1.11909 

.92547 

1.08053 

.95841 

1.04340 

.99247 

1.00759 

13 

48 

.86318 

1.15851 

.89410 

1.11844 

.92601 

1.07990 

.95897 

1.04279 

.99304 

1.00701 

12 

49 

.86368 

1.15783 

.89463 

1.11778 

.92655 

1.07927 

.95952 

1.04218 

.99362 

1.00642 

11 

50 

.86419 

1.15715 

.89515 

1.11713 

.92709 

1.07864 

.96008 

1.04158 

.99420 

1.00583 

10 

51 

.86470 

1.15647 

.89567 

1.11648 

.92763 

1.07801 

.96064 

1.04097 

.99478 

1.00525 

9 

52 

.86521 

1.15579 

.89620 

1.11582 

.92817 

1.07738 

.96120 

1.04036 

.99536 

1.00467 

8 

53 

-86572 

1.15511 

.89672 

1.11517 

.92872 

1.07676 

.96176 

1.03976 

.99594 

1.00408 

7 

54 

•86623 

1.15443 

.89725 

1.11452 

.92926 

1.07613 

.96232 

1.03915 

.99652 

1.00350 

6 

55 

86674 

1.15375 

.89777 

1.11387 

.92980 

1.07550 

.96288 

1.03855 

.99710 

1.00291 

5 

56 

86725 

1.15308 

.89830 

1.11321 

.93034 

1.07487 

.96344 

1.03794 

.99768 

1.00233 

4 

57 

.86776 

1.15240 

.89883 

1.11256 

.93088 

1.07425 

.96400 

1.03734 

.99826 

1.00175 

3 

58 

.86827 

1.15172 

.89935 

1.11191 

.93143 

1.07362 

.96457 

1.03674 

.99884 

1.00116 

2 

59 

.86878 

1.15104 

.89988 

1.11126 

.93197 

1.07299 

.96513 

1.03613 

.99942 

1.00058 

1 

60 

.86929 

1.15037 

.90040 

1.11061 

.93252 

1.07237 

.96569 

1.03553 

1.00000 

1.00000 

0 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

Cotang 

Tang 

/ 

t 

4< 

>° 

4$ 

*° 

4' 

1° 

4( 

•o 

4 

5° 

LOGARITHMIC  TABLES 


1009 


LOGARITHMIC  TABLES 

To  Find  the  Logarithmic  Sine,  Cosine,  Tangent,  or  Cotangent  of  an  Angle 
From  0°  to  45°. — In  the  table  entitled  Logarithms  of  Trigonometric  Functions, 
find  the  number  of  degrees  at  the  top  of  the  page,  and  the  number  of^minutes 
in  the  left-hand  column  headed  (') ;  opposite  the  latter,  and  under  the  proper 
head,  find  the  desired  logarithmic  sine,  cosine,  tangent,  or  cotangent. 

To  Find  the  Logarithmic  Sine,  Cosine,  Tangent,  or  Cotangent  of  an  Angle 
From  45°  to  90°. — In  the  table  entitled  Logarithms  of  Trigonometric  Func- 
tions, find  the  number  of  degrees  at  the  bottom  of  the  page,  and  the  number 
of  minutes  in  the  right-hand  column  headed  (') ;  opposite  the  latter,  and 
above  the  proper  head,  find  the  desired  logarithmic  sine,  cosine,  tangent,  or 
cotangent. 

To  Find  the  Logarithmic  Functions  for  an  Angle  Containing  Degrees,  Min- 
utes, and  Seconds. — Find  the  logarithm  for  the  degrees  and  minutes  in  the 
manner  just  given,  then  from  the  column  headed  d.  take  the  number  next 
below  the  logarithm  thus  found;  under  the  heading  P.P.,  find  a  column 
headed  by  this  number,  and  find  in  this  column  the  number  opposite  the  given 
number  of  seconds;  add  it  to  the  logarithm  already  found  for  the  degrees 
and  minutes.  If  the  exact  number  of  seconds  is  not  given  under  P.P.,  the 
proper  values  may  be  found  by  interpolating  between  the  values  given. 
As  the  differences  in  the  column  headed  d.  represent  differences  correspond- 
ing to  60  sec.,  the  amount  to  be  added  after  the  logarithm  of  the  degrees 
and  minutes  has  been  found  may  be  obtained  by  multiplying  the  difference 
by  the  number  of  seconds,  and  dividing  the  result  by  60. 

The  columns  headed  Cpl.  S.  and  Cpl.  T.  on  pages  1028  to  1030  can  be  used 
to  find  logarithms  of  angles  including  seconds  less  than  3°  and  greater  than  86°. 
Reduce  the  degrees,  minutes,  and  seconds  to  seconds,  and  use  the  following 
formulas,  substituting  for  Cpl.  S  and  Cpl.  T.  the  values  given  in  the  table, 
and  for  S.  and  T.,  the  difference  between  10  and  Cpl.  S.  and  Cpl.  T.  as  given. 

For  angles  less  than  4°,  log  sin  a  =  log  a"  +  S.;  log  tang  a  =  log  a" 
+  T.;  log  cotg  a  =  Cpl.  log  a"  +  Cpl.  T.  =  Cpl.  log  tang  «;  log  a"  =  log 
sin  a  +  Cpl.  S.  =  log  tang  a  +  Cpl.  T.  =  Cpl.  log  cotg  a  +  Cpl.  T. 

For  angles  greater  than  86°,  log  cos  a  =  log  (90°  —  a")  +  S.:  log  c6tg  a 
=  log  (90°  -  a")  +  T.;  log  tang  a  =  Cpl.  log  (90°  -  a")  +  Cpl.  T.  =  Cpl. 
log  cotg  a;  log  (90°  -  a")  =  log  cos  a  +  Cpl.  S.  =  log  cotg  a  +  Cpl.  T. 
=  Cpl.  log  tang  a  +  Cpl.  T. 

COMMON  LOGARITHMS  OF  NUMBERS 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

0 

20 

30  103 

40 

60  206 

60 

77  815 

80 

90  309 

no  nno 

21 

32  222 

41 

61  278 

61 

78  533 

81 

90849 

o   an  im 

22 

34  242 

4?, 

62  325 

62 

79  239 

82 

91  381 

3 
4 

5 

47  712 
60  206 
69  897 

23 
24 
25 

36  173 
38021 
39  794 

43 
44 
45 

63  347 
64  345 
65  321 

63 
64 
65 

79  934 
80  618 
81  291 

83 
84 
85 

91  908 
92  428 
92  942 

77  815 
84  510 

26 

27 

41  497 
43  136 

46 
47 

66  276 
67  210 

66 
67 

81  954 
82  607 

86 
87 

93  450 
93  952 

9 

90  309 
95424 

28 
29 

44  716 
46  240 

48 
49 

68  124 
69020 

68 
69 

83  251 
83  885 

88 
89 

94  448 
94  939 

in 

00  000 

30 

47  712 

50 

69  897 

70 

84510 

90 

95424 

11 

12 
13 
14 
15 
16 
17 
18 
19 

04  139 
07  918 
11  394 
14  613 
17  609 
20  412 
23  045 
25  527 
27  875 

31 
32 
33 
34 
35 
36 
37 
38 
39 

49136 
50  515 
51  851 
53148 
54407 
55  630 
56820 
57  978 
59  106 

51 
52 
53 
54 
55 
56 
57 
58 
59 

70  757 
71  600 
72  428 
73  239 
74  036 
74  819 
75  587 
76  343 
77085 

71 
72 
73 
74 
75 
76 
77 
78 
79 

85  126 
85  733 
86  332 
86  923 
87  506 
88081 
88649 
89  209 
89  763 

91 
92 
93 
94 
95 
96 
97 
98 
99 

95  904 
96  379 
96  848 
97  313 
97772 
98  227 
98  677 
99  123 
99564 

20 

30103 

40 

60  206 

60 

77815 

80 

90309 

100 

00000 

1010 


LOGARITHMS 


N. 

L.  0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

too 

101 
102 
103 
104 
105 
106 
107 
108 
109 

110 

111 

112 
113 
114 
115 
116 
117 
118 
119 

120 

121 
122 
123 
124 
125 
126 
127 
128 
129 

130 

131 
132 
133 
134 
135 
136 
137 
138 
139 

140 

141 
142 
143 
144 
145 
146 
147 
148 
149 

150 

00  000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

8 
9 

a 
i 

i 

2 
3 
4 
5 
I 
7 
8 
1 

1 
•> 
1 
4 
8 
6 
7 
8 
9 

1 
2 
3 
4 
5 
i 

7 
8 
9 

44 

4.4 

8.8 
13.2 
17.6 
22.0 
26.4 
30.8 
35.2 
39.6 

41 

4.1 

8.2 
12.3 
16.4 
20.5 
24.6 
28.7 
32.8 
36.9 

38 

3.8 
7.6 
11.4 
15.2 
19.0 
22.8 
26.6 
80.4 
34.2 

35 

3.5 
7.0 
10.5 
14.0 
17,5 
21.0 
24.5 
28.0 
31.5 

32 

3.2 
6.4 
9.6 

12.8 
16.0 
19.2 
22.4 
25.6 
28.8 

43| 

4.3 

8.6 
12.9 
17.2 
21.5 
25.8 
30.1 
34.4 
38.7 

40 

4.0 
8.0 
12.0 
16.0 
20.0 
24.0 
28.0 
82.0 
36.0 

37 

3.7 

7.4 
11.1 
14.8 
18.5 
22.2 
25.9 
296 
33.3 

34 

3.4 

6.8 
10.2 
13.6 
17.0 
20.4 
23.8 
27.2 
30.6 

31 

3.1 

6.2 
9.3 
12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

42 

4.2 

8.4 
12.6 
16.8 
21.0 
25.2 
29.4 
33.6 
37.8 

39 

3.9 
7.8 
11.7 
15.6 
19.5 
23.4 
27.3 
31.2 
35.1 

36 

3.6 

7.2 
10.8 
14.4 
18.0 
21.6 
25.2 
28.8 
32.4 

33 

3.3 

6.6 
9.9 
13.2 
16.5 
19.8 
23.1 
26.4 
29.7 

30 

3.0 
6.0 
9.0 
12.0 
15.0 
18.0 
21.0 
24.0 
27.0 

432 
860 
01  284 
703 
02  119 
531 
938 
03  342 
743 

475 
903 
326 
745 
160 
572 
979 
383 
782 

518 
945 

368 
787 
202 
612 
*019 
423 
822 

561 
988 
410 
828 
243 
653 
*060 
463 
862 

258 

604 
*030 
452 
870 
284 
694 
*100 
503 
902 

297 

647 
*072 
494 
912 
325 
735 
*141 
543 
941 

336 

689 
*115 
536 
953 
366 
776 
*181 
583 
981 

376 

732 
*157 
578 
995 
407 
816 
*222 
623 
*021 

415 

775 
*199 
620 
*036 
449 
857 
*262 
663 
*060 

817 
*242 
662 
*078 
490 
898 
*302 
703 
*100 

04139* 

179 

218 

454 

->493 

532 
922 
05308 
690 
06070 
446 
819 
07  188 
555 

571 
961 
346 
729 
108 
483 
856 
225 
591 

954 

610 
999 
385 
767 
145 
521 
893 
262 
628 

650 
*038 
423 
805 
183 
558 
930 
298 
664 

689 
*077 
461 
843 
221 
595 
967 
335 
700 

727 
*115 
500 
881 
258 
633 
*004 
372 
737 

766 
*154 
538 
918 
296 
670 
*041 
408 
773 

805 
*192 
576 
956 
333 
707 
*078 
445 
809 

844 
*231 
614 
994 
371 
744 
*115 
482 
846 

883 
*269 
652 
*032 
408 
781 
*151 
518 
882 

918 

990 

350 
707 
*061 
412 
760 
106 
449 
789 
126 

*027 

*063 

422 

778 
*132 
482 
830 
175 
517 
857 
193 

528 

*099 

458 
814 
*167 
517 
864 
209 
551 
890 
227 

*135 

493 
849 
*202 
552 
899 
243 
585 
924 
261 

*171 

529 
884 
*237 
587 
934 
278 
619 
958 
294 

628 

*207 

*243 

08  279 
636 
991 
09  342 
691 
10037 
380 
721 
11  059 

314 
672 
*026 
377 
726 
072 
415 
755 
093 

386 
743 
*096 
447 
795 
140 
483 
823 
160 

565 
920 
*272 
621 
968 
312 
653 
992 
327 

661 

600 
955 
*307 
656 
*003 
346 
687 
*025 
361 

394 

428 

461 

494 

561 

594 

694 

727 
12  057 
385 
710 
13033 
354 
672 
988 
14  301 

760 
090 
418 
743 
066 
386 
704 
*019 
333 

793 
123 
450 
775 
098 
418 
735 
*051 
364 

675 

983 
290 
594 
897 
197 
495 
791 
085 
377 

826 
156 
483 
808 
130 
450 
767 
*082 
395 

860 
189 
516 
840 
162 
481 
799 
*114 
426 

737 

893 
222 
548 
872 
194 
513 
830 
*145 
457 

768 

926 

254 
581 
905 
226 
545 
862 
*176 
489 

959 

287 
613 
937 
258 
577 

*208 
520 

992 
320 
646 
969 
290 
609 
925 
*239 
551 

*024 
352 
678 
*001 
322 
640 
956 
*270 
582 

613 

644 

706 

*014 
320 
625 
927 
227 
524 
820 
114 
406 

799 

*106 
412 
715 
*017 
316 
613 
909 
202 
493 

829 

*137 
442 
746 
*047 
346 
643 
938 
231 
522 

860 

891 

*198 
503 
806 
*107 
406 
702 
997 
289 
580 

922 
15  229 
534 
836 
16  137 
435 
732 
17  026 
319 

953 
259 
564 
866 
167 
465 
761 
056 
348 

*045 
351 
655 
957 
256 
554 
850 
143 
435 

*076 
381 
685 
987 
2S6 
584 
879 
173 
464 

*168 
473 
776 
*077 
376 
673 
967 
260 
551 

609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS 


1011 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

F 

.] 

P. 

ISO 

17  609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

151 
152 
153 
154 
155 
156 
157 
158 
159 

898 
18  184 
469 
752 
19  033 
312 
590 
866 
20  140 

926 
213 
498 
780 
061 
340 
618 
893 
167 

955 
241 
526 
808 
089 
368 
645 
921 
194 

984 
270 
554 
837 
117 
396 
673 
948 
•222 

*013 
298 
583 
865 
145 
424 
700 
976 
249 

*041 
327 
611 
893 
173 
451 
728 
*003 
276 

*070 
355 
639 
921 
201 
479 
756 
*030 
303 

*099 
384 
667 
949 
229 
507 
783 
*058 
330 

*127 
412 
696 
977 
257 
535 
811 
*085 
358 

*156 
441 
724 
*005 
285 
562 
838 
*112 
385 

8 
9 

2 

2 
5 
8 
11 
14 
17 
20 
28 
26 

9 

.9 
.8 
.7 
.6 
.5 
.4 
.3 
.2 
.1 

28 

2.8 
5.6 
8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

656 

161 
162 
163 
164 
165 
166 
167 
168 
169 

683 
952 
21  219 
484 
748 
22  Oil 
272 
531 
789 

710 
978 
245 
511 
775 
037 
298 
557 
,814 

737 
*005 
272 
537 
801 
063 
324 
583 
840 

763 
*032 
299 
564 
827 
089 
350 
608 
866 

790 
*059 
325 
590 
854 
115 
376 
634 
891 

817 
*085 
352 
617 
880 
141 
401 
660 
917 

844 
*112 
378 
643 
906 
167 
427 
686 
943 

871 
*139 
405 
669 
932 
194 
453 
712 
968 

898 
*165 
431 
696 
958 
220 
479 
737 
994 

925 
*192 
458 
722 
985 
246 
505 
763 
*019 

2 
8 
4 
6 
6 
1 
8 
9 

2 

2 
5 
8 
10 
13 
16 
18 
21 
24 

7 

.7 
4 
1 
8 
5 
2 
9 
6 
3 

26 

2.6 
5.2 
7.8 
10.4 
13.0 
15.6 
18.2 
20.8 
23.4 

170 

23  045 

070 

096 

121 

147 

172 

198 

223 

249 

274 

171 
172 
173 
174 
175 
176 
177 
178 
179 

300 
553 
805 
24  055 
304 
551 
797 
25  042 
285 

325 
578 
830 
080 
329 
576 
822 
066 
310 

350 
603 
855 
105 
353 
601 
846 
091 
334 

376 
629 
880 
130 
378 
625 
871 
115 
358 

401 
654 
905 
155 
403 
650 
895 
139 
382 

426 
679 
930 
180 
428 
674 
920 
164 
406 

452 
704 
955 
204 
452 
699 
944 
188 
431 

477 
729 
980 
229 
477 
724 
969 
212 
455 

502 
754 
*005 
254 
502 
748 
993 
237 
479 

528 
779 
*030 
279 
527 
773 
*018 
261 
503 

1 
2 

8 

4 
6 

6 

T 
8 
tl 

2 

5 

! 
l( 
15 
lc 

r 

2( 

21 

5 

.5 
.0 
.5 
.0 
.5 
.0 
.5 
.0 
.5 

180 

527 

551 

575 

600 

624 

648 

672 

696 

720 

744 

181 
182 
183 
184 
185 
186 
187 
188 
189 

768 
26  007 
245 
482 
717 
951 
27  184 
416 
646 

792 
031 
269 
505 
741 
975 
207 
439 
669 

816 
055 
293 
529 
764 
998 
231 
462 
692 

840 
079 
316 
553 
788 
*021 
254 
485 
715 

864 
102 
340 
576 

811 
*045 
277 
508 
738 

888 
126 
364 
600 
834 
*068 
300 
531 
761 

912 
150 
387 
623 
858 
*091 
323 
554 
784 

935 
174 
411 
647 
881 
*114 
346 
577 
807 

959 
198 
435 
670 
905 
*138 
370 
600 
830 

983 
221 
458 
694 
928 
*161 
393 
623 
852 

2 

2 
4 
7 
9 
12 
14 
16 
19 
21 

4 

4 

8 
2 
6 
0 
4 
8 
2 
6 

23 

2.3 
4.6 
6.9 
9.2 
11.5 
13.8 
16.1 
18.4 
20.7 

190 

875 

898 

921 

944 

967 

989 

*012 

*035 

*058 

*081 

191 
192 
193 
194 
195 
196 
197 
198 
199 

28  103 
330 
556 
780 
29  003 
226 
447 
667 
885 

126 
353 
578 
803 
026 
248- 
469 
688 
907 

149 

375 
601 
825 
048 
270 
491 
710 
929 

171 
398 
623 
847 
070 
292 
513 
732 
951 

194 
421 
646 
870 
092 
314 
535 
754 
973 

217 
443 
668 
892 
115 
336 
557 
776 
994 

240 
466 
691 
914 
137 
358 
579 
798 
*016 

262 
488 
713 
937 
159 
380 
601 
820 
*038 

285 
511 
735 
959 
181 
403 
623 
842 
*060 

307 
533 
758 
981 
203 
425 
645 
863 
*081 

9 

2 

2 
4 
6 
8 
11 
13 
15 
17 
19 

2 

2 
4 

6 
8 
0 
2 
4 
6 
8 

21 

2.1 

4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
18.9 

200 

30103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

I 

> 

1012 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

200 

201 
202 
203 
204 
205 
206 
207 
208 
209 

210 

211 
212 
213 
214 
215 
216 
217 
'218 
219 

220 

221 
222 
223 
224 
225 
226 
227 
228 
229 

230 

231 

232 
233 
234 
235 
236 
237 
238 
239 

240 

241 
242 
243 
244 
245 
246 
247 
248 
249 

250 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

J 

1   2 
2   4 
3   6 
4   8 
5  11 
6  13 
7  15 
8  17 
9  19 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 

2 
3 
4 

5 
6 
7 
8 
9 

7 
8 
9 

2   21 

.2   2.1 
.4   4.2 
.6   6.3 
.8   8.4 
.0  10.5 
.2  12.6 
.4  14.7 
.8  16.8 
.8  18.9 

20 

2.0 
4.0 
6.0 
8.0 
10.0 
12.0 
14.0 
16.0 
18.0 

19 

1.9 
3.8 
5.7 
7.6 
9.5 
11.4 
13.3 
15.2 
17.1 

18 

1.8 
3.6 
5.4 
7.2 
9.0 
10.8 
12.6 
14.4 
16.2 

17 

1.7 
34 
5.1 
6.8 
8.5 
10.2 
11.9 
13.6 
15.3 

320 
535 
750 
963 
31  175 
387 
597 
806 
32015 

341 
557 
771 
984 
197 
408 
618 
827 
035 

363 
578 
792 
*006 
218 
429 
639 
848 
056 

384 
600 
814 
*027 
239 
450 
660 
869 
077 

406 
621 
835 
*048 
260 
471 
681 
890 
098 

428 
643 
856 
*069 
281 
492 
702 
911 
118 

•449 
664 
878 
*091 
302 
513 
723 
931 
139 

471 
685 
899 
*112 
323 
534 
744 
952 
160 

492 
707 
920 
*133 
345 
555 
765 
973 
181 

514 

728 
942 
*154 
366 
576 
785 
994 
201 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 

428 
634 
838 
33  041 
244 
445 
646 
846 
34044 

449 
654 
858 
062 
264 
465 
666 
866 
064 

469 
675 
879 
082 
284 
486 
686 
885 
084 

490 
695 
899 
102 
304 
506 
706 
905 
104 

510 
715 
919 
122 
325 
526 
726 
925 
124 

531 
736 
940 
143 
345 
546 
746 
945 
143 

552 
756 
960 
163 
365 
566 
766 
965 
163 

572 
777 
980 
183 
385 
586 
786 
985 
183 

593 
797 
*001 
203 
405 
606 
806 
*005 
203 

613 
818 
*021 

626 
826 
*025 
223 

242 

262 

459 
655 
850 
044 
238 
430 
622 
813 
*003 

282 

479 

674 
869 
064 
257 
449 
641 
832 
*021 

301 

321 

341 

537 
733 
928 
122 
315 
507 
698 
889 
*078 

361 

557 
753 
947 
141 
334 
526 
717 
908 
*097 

380 

400 

420 

439 
635 
830 
35  025 
218 
411 
603 
793 
984 

498 
694 
889 
083 
276 
468 
660 
851 
*040 

518 
713 
908 
102 
295 
488 
679 
870 
*059 

677 
772 
967 
160 
353 
545 
736 
927 
*116 

596 
792 
986 
180 
372 
564 
755 
946 
*135 

324 

511 
698 
884 
*070 
254 
438 
621 
803 
985 

616 
811 
*005 
199 
392 
583 
774 
965 
*154 

342 

36  173 

192 

380 
568 
754 
940 
125 
310 
493 
676 
858 

211 

399 
586 
773 
959 
144 
328 
511 
694 
876 

229 

248 

267 

286 

305 

361 
549 
736 
922 
37  107 
291 
475 
658 
840 

418 
605 
791 
977 
162 
346 
530 
712 
894 

436 
624 
810 
996 
181 
365 
548 
731 
912 

455 
642 
829 
*014 
199 
383 
566 
749 
931 

474 
661 
847 
*033 
218 
401 
585 
767 
949 

493 
680 
866 
*051 
236 
420 
603 
785 
967 

530 
717 
903 
*088 
273 
457 
639 
822 
*003 

38  021 

039 

057 

075 

093 

112 

130 

148 

166 

184 

202 
382 
561 
739 
917 
39  094 
270 
445 
620 

220 
399 
578 
757 
934 
111 
287 
463 
637 

238 
417 
596 
775 
952 
129 
305 
480 
655 

829 

256 
435 
614 
792 
970 
146 
322 
498 
672 

846 

3 

274 
453 
632 
810 
987 
164 
340 
515 
690 

292 
471 
650 
828 
*005 
182 
358 
533 
707 

310 
489 
668 
846 
*023 
199 
375 
550 
724 

328 
507 
686 
863 
*041 
217 
393 
&68 
742 

915 

346 
525 
703 
881 
*058 
235 
410 
585 
759 

364 
543 

721 
899 
*076 
252 

428 
602 

777 

950 

794 

811 

863 

881 

898 

933 

N. 

L.O 

1 

2 

4 

5 

6 

7 

8 

9 

P.P. 

-  LOGARITHMS 


1013 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

250 

251 

252 
253 
254 
255 
256 
257 
258 
259 

260 

261 
262 
263 
264 
265 
266 
267 
268 
269 

270 

271 
272 
273 
274 
275 
276 
277 
278 
279 

280 

281 
282 
283 
284 
285 
286 
287 
288 
289 

290 

291 
292 
293 
294 
295 
296 
297 
298 
299 

300 

39  794 

811 

829 

846 

863 

*037 
209 
381 
552 
722 
892 
*061 
229 
397 

564 

881 

898 

915 

933 

950 

8 
9 

7 
8 
9 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

18 

1.8 
3.6 

5.4 
7.2 
9.0 
10.8 
12.6 
14.4 
16.2 

17 

1.7 
3.4 
5.1 
6.8 
8.5 
10.2 
11.9 
13.6 
15.3 

16 

1.6 
3.2 
4.8 
6.4 
8.0 
9.6 
11.2 
12.8 
14.4 

15 

1.5 
3.0 
4.5 
6.0 
7,5 
9.0 
10.5 
12.0 
13.5 

14 

1.4 
2  8 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 

967 
40  140 
312 
483 
654 
824 
993 
41  162 
330 

985 
157 
329 
500 
671 
841 
*010 
179 
347 

*002 
175 
346 
518 
688 
858 
*027 
196 
363 

*019 
192 
364 
535 
705 
875 
*044 
212 
380 

*054 
226 
398 
569 
739 
909 
*078 
246 
414 

*071 
243 
415 
586 
756 
926 
*095 
263 
430 

597 

*088 
261 
432 
603 
773 
943 
*111 
280 
447 

614 

*106 
278 
449 
620 
790 
960 
*128 
296 
464 

*123 
295 
466 
637 
807 
976 
*145 
313 
481 

647 

497 

514 

531 

697 
863 
*029 
193 
357 
521 
684 
846 
*008 

169 

547 

714 
880 
*045 
210 
374 
537 
700 
862 
*024 

581 

631 

664 
830 
996 
42  160 
325 
488 
651 
813 
975 

681 
847 
*012 
177 
341 
504 
667 
830 
991 

731 
896 
*062 
226 
390 
553 
716 
878 
*010 

747 
913 
*078 
243 
406 
570 
732 
894 
*056 

217 

377 
537 
696 
854 
*012 
170 
326 
483 
638 

764 
929 
*095 
259 
423 
586 
749 
911 
*072 

780 
946 
*111 
275 
439 
602 
765 
927 
*088 

797 
963 
*127 
292 
455 
619 
781 
943 
*104 

265 

814 
979 
*144 
308 
472 
635 
797 
959 
*120 

281 

43  136 

152 

185 

201 

233 

393 
553 
712 
870 
*028 
185 
342 
498 
654 

249 

297 
457 
616 
775 
933 
44091 
248 
404 
560 

313 
473 
632 
791 
949 
107 
264 
420 
576 

731 

329 
489 
648 
807 
965 
122 
279 
436 
592 

747 

345 
505 
664 
823 
981 
138 
295 
451 
607 

361 
521 
680 
838 
996 
154 
311 
467 
623 

409 
569 
727 
886 
*044 

201 
358 
514 
669 

425 
584 
743 
902 
*059 
217 
373 
529 
685 

441 
600 
759 
917 
*075 
232 
389 
545 
700 

855 

716 

762 

917 
071 
225 
378 
530 
682 
834 
984 
135 

285 

778 

932 
086 
240 
393 
545 
697 
849 
*000 
150 

300 

793 

809 

824 

840 

871 
45  025 
179 
332 
484 
637 
788 
939 
46090 

886 
040 
194 
347 
500 
652 
803 
954 
105 

902 
056 
209 
362 
515 
667 
818 
969 
120 

948 
102 
255 
408 
561 
712 
864 
*015 
165 

963 
117 
271 
423 
576 
728 
879 
*030 
180 

979 
133 
286 
439 
591 
743 
894 
*045 
195 

994 
148 
301 
454 
606 
758 
909 
*060 
210 

*010 
163 
317 
469 
621 
773 
924 
*075 
225 

240 

255 

404 
553 
702 
850 
997 
144 
290 
436 
582 

270 

315 

464 
613 
761 
909 
*056 
202 
349 
494 
640 

330 

345 

359 

374 

389 
538 
687 
835 
982 
47  129 
276 
422 
567 

419 
568 
716 
864 
*012 
159 
305 
451 
596 

434 
583 
731 
879 
*026 
173 
319 
465 
611 

756 

449 

598 
746 
894 
*041 
188 
334 
480 
625 

479 
627 
776 
923 
*070 
217 
363 
509 
654 

494 
642 
790 
938 
*085 
232 
378 
524 
669 

813 

509 
657 
805 
953 
*100 
246 
392 
538 
683 

523 
672 
820 
967 
*114 
261 
407 
553 
698 

712 

727 

741 

770 

784 

799 

828 

842 

9 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

P.P. 

1014 


LOGARITHMS 


N. 

L.O 

1 

727 

871 
015 
159 
302 
444 
586 
728 
869 
*010 

2 

741 

3 

756 

4 
770 

5 

784 

6 

7 

8 

9 

P.P. 

300 

301 
302 
303 
304 
305 
306 
307 
308 
309 

310 

311 
312 
313 
314 
315 
316 
317 
318 
319 

320 

321 
322 
323 
324 
325 
326 
327 
328 
329 

330 

331 
332 
333 
334 
335 
336 
337 
338 
339 

340 

341 
342 
343 
344 
345 
346 
347 
348 
349 

350 

47  712 

799 

813 

828 

842 

986 
130 
273 
416 

558 
700 
841 
982 
*122 

8 
9 

1 
2 

8 
9 

1 
2 
3 
4 

5 
6 

7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

15 

1.5 
3.0 
4.5 
6.0 
7.5 
9.0 
10.5 
12.0 
13.5 

14 

1.4 

2.8 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 

13 

1.3 
2.6  • 
3.9 
5  2 
6.5 
7.8 
9,1 
10.4 
11,7 

12 

1.2 
2.4 
3.6 
4.8 
6.0 
7.2 
8.4 
9.6 
10.8 

857 
48  001 
144 
287 
430 
572 
714 
855 
9% 

885 
029 
173 
316 
458 
601 
742 
883 
*024 

900 
044 
187 
330 
473 
615 
756 
897 
*038 

914 
058 
202 
344 
487 
629 
770 
911 
*052 

929 
073 
216 
359 
501 
643 
785 
926 
*066 

943 
087 
230 
373 
515 
657 
799 
940 
*080 

958 
101 
244 
387 
530 
671 
813 
954 
*094 

972 
116 
259 
401 
544 
686 
827 
968 
*108 

49  136 

150 

164 

178 

192 

206 

220 

234 

374 
513 
651 
790 
927 
*065 
202 
338 
474 

610 

248 

388 
527 
665 
803 
941 
*079 
215 
352 
488 

262 

276 
415 
554 
693 
831 
969 
50  106 
243 
379 

290 
429 
568 
707 
845 
982 
120 
256 
393 

304 
443 
582 
721 
859 
996 
133 
270 
406 

542 

318 
457 
596 
734 
872 
*010 
147 
284 
420 

332 
471 
610 

748 
886 
*024 
161 
297 
433 

569 

346 

485 
624 
762 
900 
*037 
174 
311 
447 

360 
499 
638 
776 
914 
*051 
188 
325 
461 

596 

402 
541 
679 
817 
955 
*092 
229 
365 
501 

637 

515 

529 

556 

583 

623 

651 
786 
920 
51  055 
188 
322 
455 
587 
720 

664 
799 
934 
068 
202 
335 
468 
601 
733 

678 
813 
947 
081 
215 
348 
481 
614 
746 

691 
826 
961 
095 
228 
362 
495 
627 
759 

705 
840 
974 
108 
242 
375 
508 
640 
772 

718 
853 
987 
121 
255 
388 
521 
654 
786 

732 
866 
*001 
135 
268 
402 
534 
667 
799 

745 
880 
*014 
148 
282 
415 
548 
680 
812 

759 
893 
*028 
162 
295 
428 
561 
693 
825 

772 
907 
*041 
175 
308 
441 
574 
706 
838 

851 

865 

878 

891 

904 

917 

930 

943 

957 

970 

983 
52  114 
244 
375 
504 
634 
763 
892 
53  020 

996 
127 
257 
388 
517 
647 
776 
905 
033 

*009 
140 
270 
401 
530 
660 
789 
917 
046 

*022 
153 
284 
414 
543 
673 
802 
930 
058 

*035 
166 
297 
427 
556 
686 
815 
943 
071 

*048 
179 
310 
440 
569 
699 
827 
956 
084 

*061 
192 
323 
453 

582 
711 
840 
969 
097 

*075 
205 
336 
466 
595 
724 
853 
982 
110 

*088 
218 
349 
479 
608 
737 
866 
994 
122 

*101 
231 
362 
492 
621 
750 
879 
*007 
135 

148 

161 

173 

186 

199 

212 

224 

237 

250 

263 

275 
403 
529 
656 
782 
908 
54  033 
158 
283 

288 
415 
542 
668 
794 
920 
045 
170 
295 

301 
428 
555 
681 
807 
933 
058 
183 
307 

314 
441 
567 
694 
820 
945 
070 
195 
320 

444 

326 
453 
580 
706 
832 
958 
083 
208 
332 

456 

339 

466 
593 
719 
845 
970 
095 
220 
345 

469 

352 
479 
605 
732 
857 
983 
108 
233 
357 

481 

364 
491 
618 
744 
870 
995 
120 
245 
370 

494 

377 
504 
631 
757 
882 
*008 
133 
258 
382 

390 
517 
643 
769 
895 
*020 
145 
270 
394 

407 

419 

432 

506 

518 

VN. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS 


1015 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

350 

351 
352 
353 
354 
355 
356 
357 
358 
359 

360 

361 
362 
363 
364 
365 
366 
367 
368 
369 

370 

54  407 

419 

432 

555 
679 
802 
925 
047 
169 
291 
413 
534 

444 

456 

469 

481 

494 

506 

518 

i 

2 
3 
4 
5 
6 
7 
8 
9 

1 

2 
3 
4 
5 
6 
7 
8 
9 

8 
9 

1 

2 

13 

1.3 
2.6 
3.9 
5.2 
6.5 
7.8 
9.1 
10.4 
11.7 

12 

1.2 
2.4 
3.6 
4.8 
6.0 
7.2 
8.4 
9.6 
10.8 

II 

1.1 

2.2 
3.3 
4.4 
5.5 
6.6 
7.7 
8.8 
9.9 

10 

1.0 
2,0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9,0 

531 
654 

777 
900 
55  023 
145 
267 
388 
509 

543 

667 
790 
913 
035 
157 
279 
400 
522 

568 
691 
814 
937 
060 
182 
303 
425 
546 

580 
704 
827 
949 
072 
194 
315 
437 
558 

593 
716 
839 
962 
084 
206 
328 
449 
570 

605 
728 
851 
974 
096 
218 
340 
461 
582 

703 

617 
741 
864 
986 
108 
230 
352 
473 
594 

630 
753 
876 
998 
121 
242 
364 
485 
606 

727 

642 
765 
888 
*011 
133 
255 
376 
497 
618 

630 

642 

654 

666 

678 

691 

715 

739 

751 
871 
991 
56  110 
229 
348 
467 
585 
703 

763 
883 
*003 
122 
241 
360 
478 
597 
714 

775 

895 
*015 
134 
253 
372 
490 
608 
726 

844 

787 
907 
*027 
146 
265 
384 
502 
620 
738 

855 

799 
919 
*038 
158 
277 
396 
514 
632 
750 

867 

811 
931 
*050 
170 
289 
407 
526 
644 
761 

823 
943 
*062 
182 
301 
419 
538 
656 
773 

835 
955 
*074 
194 
312 
431 
549 
667 
785 

847 
967 
*086 
205 
324 
443 
561 
679 
797 

914 

859 
979 
*098 
217 
336 
455 
573 
691 
808 

926 

*043 
159 
276 
392 
507 
623 
738 
852 
967 

820 

832 

879 

891 

902 

371 
372 
373 
374 
375 
376 
377 
378 
379 

380 

381 
382 
383 
384 
385 
386 
387 
388 
389 

390 

391 
392 
393 
394 
395 
396 
397 
398 
399 

400 

937 
57  054 
171 
287 
403 
519 
634 
749 
864 

949 
066 
183 
299 
415 
530 
646 
761 
875 

961 
078 
194 
310 
426 
542 
657 
772 
887 

972 
089 
206 
322 
438 
553 
669 
784 
898 

*013 

984 
101 
217 
334 
449 
565 
680 
795 
910 

*024 

996 
113 
229 
345 
461 
576 
692 
807 
921 

*008 
124 
241 
357 
473 
588 
703 
818 
933 

*019 
136 
252 
368 
484 
600 
715 
830 
944 

*031 
148 
264 
380 
496 
611 
726 
841 
955 

978 

990 

104 
218 
331 
444 
557 
670 
782 
894 
*006 

*001 

*035 

*047 

*058 

*070 

184 
297 
410 
524 
636 
749 
861 
973 
*084 

*081 

58092 
206 
320 
433 
546 
659 
771 
883 
995 

115 
229 
343 
456 
569 
681 
794 
906 
*017 

127 
240 
354 
467 
580 
692 
805 
917 
*028 

138 
252 
365 
478 
591 
704 
816 
928 
*040 

151 

149 
263 
377 
490 
602 
715 
827 
939 
*051 

161 

274 
388 
501 
614 

726 
838 
950 
*062 

172 

286 
399 
512 
625 
737 
850 
961 
*073 

195 
309 
422 
535 
647 
760 
872 
984 
*095 

59  106 

118 

129 

140 

162 

173 

284 
395 
506 
616 
726 
835 
945 
*054 
163 

184 

195 

306 
417 
528 
638 
748 
857 
966 
*076 
184 

207 

218 
329 
439 
550 
660 
770 
879 
988 
60  097 

229 
340 
450 
561 
671 
780 
890 
999 
108 

240 
351 
461 
572 
682 
791 
901 
*010 
119 

228 

251 
362 

472 
583 
693 
802 
912 
*021 
130 

262 
373 
483 
594 
704 
813 
923 
*032 
141 

273 
384 
494 
605 
715 
824 
934 
*043 
152 

295 
406 
517 
627 
737 
846 
956 
*065 
173 

318 
428 
539 
649 
759 
868 
977 
*086 
195 

304 

206 

217 

239 

249 

260 

5 

271 

282 

293 

N. 

L.O 

1 

2 

3 

4 

6 

7 

•8 

9 

P.P. 

1016 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

400 

60  206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

401 
402 
403 
404 
405 
406 
407 
408 
409 

314 
423 
531 
638 
746 
853 
959 
61  066 
172 

325 
433 
541 
649 
756 
863 
970 
077 
183 

336 
444 
552 
660 
767 
874 
981 
087 
194 

347 

455 
563 
670 
778 
885 
991 
098 
204 

358 
466 
574 
681 
788 
895 
*002 
109 
215 

369 
477 
584 
692 
799 
906 
*013 
119 
225 

379 
487 
595 
703 
810 
917 
*023 
130 
236 

390 
498 
606 
713 
821 
927 
*034 
140 
247 

401 
509 
617 
724 
831 
938 
*045 
151 
257 

412 
520 
627 
735 
842 
949 
*055 
162 
268 

l 

2 

II 

1.1 
2.2 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

4 

4.4 

411 
412 
413 
414 
415 
416 
417 
418 
419 

384 
490 
595 
700 
805 
909 
62014 
118 
221 

395 
500 
606 
711 
815 
920 
024 
128 
232 

405 
511 
616 
721 
826 
930 
034 
138 
242 

416 
521 
627 
731 
836 
941 
045 
149 
252 

426 
532 
637 
742 
847 
951 
055 
159 
263 

437 
542 
648 
752 
857 
962 
066 
170 
273 

448 
553 
658 
763 
868 
972 
076 
180 
284 

458 
563 
669 
773 
878 
982 
086 
190 
294 

469 
574 
679 
784 
888 
993 
097 
201 
304 

479 
584 
690 
794 
899 
*003 
107 
211 
315 

6 

7 
8 
9 

M 

7.7 
8.8 
9.9 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

421 

422 
423 
424 
425 

426 
427 
428 
429 

428 
531 
634 
737 
839 
941 
63  043 
144 
246 

439 
542 
644 
747 
849 
951 
053 
155 
256 

449 
552 
655 
757 
859 
961 
063 
165 
266 

459 
562 
665 
767 
870 
972 
073 
175 
276 

469 
572 
675 

778 
880 
982 
083 
185 
286 

480 
583 
685 
788 
890 
992 
094 
195 
296 

490 
593 
696 
798 
900 
*002 
104 
205 
306 

500 
603 
706 
808 
910 
*012 
114 
215 
317 

511 
613 
716 
818 
921 
*022 
124 
225 
327 

521 
624 
726 
829 
931 
*033 
134 
236 
337 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
70 
8.0 
9.0 

430 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 

431 
432 
433 
434 
435 
436 
437 
438 
439 

448 
548 
649 
749 
849 
949 
64  048 
147 
246 

458 
558 
659 
759 
859 
959 
058 
157 
256 

468 
568 
669 
769 
869 
969 
068 
167 
266 

478 
579 
679 
779 
879 
979 
078 
177 
276 

488 
589 
689 
789 
889 

088 
187 
286 

498 
599 
699 
799 
899 
998 
098 
197 
296 

508 
609 
709 
809 
909 
*008 
108 
207 
306 

518 
619 
719 
819 
919 
*018 
118 
217 
316 

528 
629 
729 
829 
929 
*028 
128 
227 
326 

538 
639 
739 
839 
939 
*038 
137 
237 
335 

1 

2 
3 

9 

0.9 
1,8 

2.7 

440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

5 

4.5 

441 
442 
443 
444 
445 
446 
447 
448 
449 

444 
542 
640 
738 
836 
933 
65  031 
128 
225 

454 
552 
650 
748 
846 
943 
040 
137 
234 

464 
562 
660 
758 
856 
953 
050 
147 
244 

473 

572 
670 
768 
865 
963 
060 
157 
254 

483 
582 
680 
777 
875 
972 
070 
167 
263 

493 
591 
689 
787 
885 
982 
079 
176 
273 

503 
601 
699 
797 
895 
992 
089 
186 
283 

513 
611 

709 
807 
904 
*002 
099 
196 
292 

523 
621 
719 
816 
914 
*011 
108 
205 
302 

532 
631 
729 
826 
924 
*021 
118 
215 
312 

7 
8 
9 

6.3 
7.2 
8.1 

450 

321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

P. 

LOGARITHMS 


1017 


N. 

L.O 

1 

331 

427 
523 
619 
715 
811 
906 
*001 
096 
191 

2 

341 

3 

4 

5 

6 

379 

475 
571 
667 
763 
858 
954 
*049 
143 
238 

7 

8 

^9 

408 

P.P. 

450 

451 
452 
453 
454 
455 
456 
457 
458 
459 

460 

461 
462 
463 
464 
465 
466 
467 
468 
469 

470 

471 
472 
473 
474 

475 
476 
477 
478 
479 

480 

481 

482 
483 
484 
485 
486 
487 
488 
489 

490 

491 
492 
493 
494 
495 
496 
497 
498 
499 

500 

65  321 

350 

360 

369 

389 

398 

i 

2 
3 
4 

5 
6 

7 
8 
9 

1 

2 
3 
4 

I 

1 

2 
3 
4 
5 
6 
7 
8 
9 

10 

1.0 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 

9 

0.9 

» 

3.6 
4.5 

5.4 
6.3 
7.2 
8.1 

8 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2  ' 

418 
514 
610 
706 
801 
896 
992 
66  087 
181 

437 
533 
629 
725 
820 
916 
*011 
106 
200 

447 
543 
639 
734 
830 
925 
*020 
115 
210 

456 
552 
648 
744 
839 
935 
*030 
124 
219 

466 
562 
658 
753 
849 
944 
*039 
134 
229 

323 

485 
581 
677 
772 
-868 
963 
*058 
153 
247 

495 
591 
686 
782 
877 
973 
*068 
162 
257 

504 
600 
696 
792 
887 
982 
*077 
172 
266 

361 

276 

285 

295 

389 
483 
577 
671 
764 
857 
950 
043 
136 

304 

398 
492 
586 
680 
773 
867 
960 
052 
145 

314 

332 

342 

351 

370 
464 
558 
652 
745 
839 
932 
67  025 
117 

380 
474 
567 
661 
755 
848 
941 
034 
12? 

408 
502 
596 
689 
783 
876 
969 
062 
154 

417 
511 
605 
699 
792 
885 
978 
071 
164 

427 
521 
614 

708 
801 
894 
987 
080 
173 

265 

436 
530 
624 
717 
811 
904 
997 
089 
182 

445 
539 
633 
727 
820 
913 
*006 
099 
191 

455 
549 
642 
736 
829 
922 
*015 
108 
201 

210 

219 

228 

321 
413 

504 
596 
688 
779 
870 
961 
052 

142 

237 

330 
422 
514 
605 
697 
788 
879 
970 
061 

247 

256 

274 

284 

293 

385 
477 
569 
660 
752 
843 
934 
*024 
115 

302 
394 
486 
578 
669 
761 
852 
943 
68  034 

311 

403 
495 
587 
679 
770 
861 
952 
043 

339 
431 
523 
614 
706 
797 
888 
979 
070 

348 
440 
532 
624 
715 
806 
897 
988 
079 

357 
449 
541 
633 

724 
815 
906 
997 
088 

367 
459 
550 
642 
733 
825 
916 
*006 
097 

376 

468 
560 
651 
742 
834 
925 
*015 
106 

124 

133 

151 

160 

169 

178 

187 

196 

205 

215 
305 
395 
485 
574 
664 
753 
842 
931 

224 
314 
404 
494 
583 
673 
762 
851 
940 

233 
323 
413 
502 
592 
681 
771 
860 
949 

242 
332 
422 
511 
601 
690 
780 
869 
958 

251 
341 
431 
520 
610 
699 
789 
878 
966 

260 
350 
440 
529 
619 
708 
797 
886 
975 

269 
359 
449 
538 
628 
717 
806 
895 
984 

278 
368 
458 
547 
637 
726 
815 
904 
993 

287 
377 
467 
556 
646 
735 
824 
913 
*002 

296 
386 
476 
565 
655 
744 
833 
922 
*011 

69  020 

028 

037 

046 

055 

064 

073 

082 

090 

099 

108 
197 
285 
373 
461 
548 
636 
723 
810 

117 

205 
294 
381 
469 
557 
644 
732 
819 

126 
214 
302 
390 
478 
566 
653 
740 
827 

135 

223 
311 
399 
487 
574 
662 
749 
836 

144 

232 
320 
408 
496 
583 
671 
758 
845 

152 
241 
329 
417 
504 
592 
679 
767 
854 

940 

161 
249 
338 
425 
513 
601 
688 
775 
862 

949 

170 
258 
346 
434 
522 
609 
697 
784 
871 

179 
267 
355 
443 
531 
618 
705 
793 
880 

188 
276 
364 
452 
539 
627 
714 
801 
888 

897 

906 

914 

923 

932 

958 

966 

975 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

1018 


'LOGARITHMS 


N. 

L.O 

1 

.  2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

500 

501 

502 
503 
504 
505 
506 
507 
508 
509 

510 

511 
512 
513 
514 
515 
516 
517 
518 
519 

520 

521 
522 
523 
524 
525 
526 
527 
528 
529 

530 

531 
532 
533 
534 
535 
536 
537 
538 
539 

540 

541 

542 
543 
544 
545 
546 
547 
548 
549 

550 

69  897 

906 

914 

*001 
088 
174 
260 
346 
432 
518 
603 
689 

923 

*010 
096 
183 
269 
355 
441 
526 
612 
697 

932 

*018 
105 
191 
278 
364 
449 
535 
621 
706 

940 

949 

*036 
122 
209 
295 
381 
467 
552 
638 
723 

958 

*044 
131 
217 
303 
389 
475 
561 
646 
731 

966 

975 

l 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 

2 
3 
4 
5 
6 
7 
8 
9 

9 

0.9 
1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 

-£» 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 

7 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
56 
6.3 

984 
70  070 
157 
243 
329 
415 
501 
586 
672 

992 
079 
165 
252 
338 
424 
509 
595 
680 

*027 
114 
200 
286 
372 
458 
544 
629 
714 

*053 
140 
226 
312 
398 
484 
569 
655 
740 

*062 
148 
234 
321 
406 
492 
578 
663 
749 

757 

766 

774 

783 

868 
952 
037 
122 
206 
290 
374 
458 
542 

791 

876 
961 
046 
130 
214 
299 
383 
466 
550 

634 

717 
800 
883 
966 
049 
132 
214 
296 
378 

460 

542 
624 
705 
787 
868 
949 
*030 
111 
191 

272 

800 

885 
969 
054 
139 
223 
307 
391 
475 
559 

808 

893 
978 
063 
147 
231 
315 
399 
483 
567 

817 

902 
986 
071 
155 
240 
324 
408 
492 
575, 

825 

910 
995 
079 
164 
248 
332 
416 
500 
584 

834 

842 
927 
71  012 
096 
181 
265 
349 
433 
517 

600 

851 
935 
020 
105 
189 
273 
357 
441 
525 

859 
944 
029 
113 
198 
282 
366 
450 
533 

919 
*003 
088 
172 
257 
341 
425 
508 
592 

609 

692 
775 
858 
941 
024 
107 
189 
272 
354 

617 

700 
784 
867 
950 
032 
115 
198 
280 
362 

625 

709 
792 
875 
958 
041 
123 
206 
288 
370 

642 

650 

659 

667 

675 

759 
842 
925 
*008 
090 
173 
255 
337 
419 

684 
767 
850 
933 
72  016 
099 
181 
263 
346 

725 
809 
892 
975 
057 
140 
•222 
304 
387 

734 
817 
900 
983 
066 
148 
230 
313 
395 

742 
825 
908 
991 
074 
156 
239 
321 
403 

750 
834 
917 
999 
082 
165 
247 
329 
411 

428 

436 

518 
599 
681 
762 
843 
925 
*006 
086 
167 

247 

444 

452 

469 

477 

558 
640 
722 
803 
884 
965 
*046 
127 
207 

485 

493 

501 

509 
591 
673 
754 
835 
916 
997 
73  078 
159 

239 

526 
607 
689 
770 
852 
933 
*014 
094 
175 

534 
616 
697 
779 
860 
941 
*022 
102 
183 

550 
632 
713 
795 
876 
957; 
*038 
119 
199 

567 
648 
730 
811 
892 
973 
*054 
135 
215 

575 
656 
738 
819 
900 
981 
*062 
143 
223 

583 
665 
746 
827 
908 
989 
*070 
151 
231 

312 

255 

263 

280 

288 

296 

304 

320 
400 
480 
560 
640 
719 
799 
878 
957 

328 
408 
488 
568 
648 
727 
807 
886 
965 

336 
416 
496 
576 
656 
735 
815 
894 
973 

344 
424 
504 
584 
664 
743 
823 
902 
981 

352 
432 
512 
592 
672 
751 
830 
910 
989 

360 
440 
520 
600 
679 
759 
838 
918 
997 

368 
448 
528 
608 
687 
767 
846 
926 
*005 

376 
456 
536 
616 
695 
775 
854 

*013 

384 
464 
544 
624 
703 
783 
862 
941 
*020 

099 

392 
472 
552 
632 
711 
791 
870 
949 
*028 

74  036 

044 

052 

060 

3 

068 

076 

084 

092 

107 

N. 

L.O 

1 

2 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS 


1019 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

550 

74  036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

551 

552 
553 
554 
555 
556 
557 
558 
559 

115 
194 
273 
351 
429 
507 
586 
663 
741 

123 
202 
280 
359 
437 
515 
593 
671 
749 

131 

210 
288 
367 
445 
523 
601 
679 
757 

139 

218 
296 
374 
453 
531 
609 
687 
764 

147 
225 
304 
382 
461 
539 
617 
695 
772 

155 
233 
312 
390 
468 
547 
624 
702 
780 

162 
241 
320 
398 
476 
554 
632 
710 
788 

170 

249 
327 
406 
484 
562 
640 
718 
796 

178 
257 
335 
414 
492 
570 
648 
726 
803 

186 
265 
343 
421 
500 
578 
656 
733 
811 

560 

819 

827 

834 

842 

850 

858 

865 

873. 

881 

889 

561 
562 
563 
564 
565 
566 
567 
568 
569 

896 
974 
75  051 
128 
205 
282 
358 
435 
511 

904 
981 
059 
136 
213 
289 
366 
442 
519 

912 
989 
066 
143 
220 
297 
374 
450 
526 

920 

997 
074 
151 
228 
305 
381 
458 
534 

927 
*005 
082 
159 
236 
312 
389 
465 
542 

935 
*012 
089 
166 
243 
320 
397 
473 
549 

943 

*020 
097 
174 
251 
328 
404 
481 
557 

950 
*028 
105 
182 
259 
335 
412 
488 
565 

958 
*035 
113 
189 
266 
343 
420 
496 
572 

966 
*043 
120 
197 
274 
351 
427 
504 
580 

0.8 
1.6 
2.4 
3.2 
4.0 
4.8 
5.6 
6.4 
7.2 

570 

587 

595 

603 

610 

618 

626 

633 

641 

648 

656 

571 
572 
573 
574 
575 
576 
577 
578 
579 

664 
740 
815 
891 
967 
76  042 
118 
193 
268 

671 
747 
823 
899 
974 
050 
125 
200 
275 

679 
75-5 
831 
906 
982 
057 
133 
208 
283 

686 
762 
838 
914 
989 
065 
140 
215 
290 

694 
770 
846 
921 
997 
072 
148 
223 
298 

702 
778 
853 
929 
*005 
080 
155 
230 
305 

709 
785 
861 
937 
*012 
087 
163 
238 
313 

717 
793 
868 
944 
*020 
095 
170 
245 
320 

724 
800 
876 
952 
*027 
103 
178 
253 
328 

732 
808 
884 
959 
*035 
110 
185 
260 
335 

580 

343 

350 

358 

365 

373 

380 

388 

395 

403 

410 

7 

581 

582 
583 
584 
585 
586 
587 
588 
589 

418 
492 
567 
641 
716 
790 
864 
938 
77  012 

425 
500 
574 
649 
723 
797 
871 
945 
019 

433 

507 
582 
656 
730 
805 
879 
953 
026 

440 
515 

589 
664 
738 
812 
886 
960 
034 

448 
522 
597 
671 
745 
819 
893 
967 
041 

455 
530 
604 
678 
753 
827 
901 
975 
048 

462 
537 
612 
686 
760 
834 
908 
982 
056 

470 
545 
619 
693 
768 
842 
916 
989 
063 

477 
552 
626 
701 
775 
849 
923 
997 
070 

485 
559 
634 
708 
782 
856 
930 
*004 
078 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
8  5.6 
9  6.3 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144 

151 

591 
592 
593 
594 
595 
596 
597 
598 
599 

159 
232 
305 
379 
452 
525 
597 
670 
743 

166 
240 
313 
386 
459 
532 
605 
677 
750 

173 
247 
320 
393 
466 
539 
612 
685 
757 

181 
254 
327 
401 
474 
546 
619 
692 
764 

188 
262 
335 
408 
481 
554 
627 
699 
772 

195 
269 
342 
415 
488 
561 
634 
706 
779 

203 
276 
349 
422 
495 
568 
641 
714 
786 

210 
283 
357 
430 
503 
576 
648 
721 
793 

217 
291 
364 
437 
510 
583 
656 
728 
801 

225 
298 
371 
444 
517 
590 
663 
735 
808 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

1020 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

r 

.P. 

600 

77  815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

601 
602 
603 
604 
605 
606 
607 
608 
609 

887 
960 
78  032 
104 
176 
247 
319 
390 
462 

895 
967 
039 
111 
183 
254 
326 
398 
469 

902 
974 
046 
118 
190 
262 
333 
405 
476 

909 
981 
053 
125 
197 
269 
340 
412 
483 

916 
988 
061 
132 
204 
276 
347 
419 
490 

924 
996 
068 
140 
211 
283 
355 
426 
497 

931 
*003 
075 
147 
219 
290 
362 
433 
504 

938 
*010 
082 
154 
226 
297 
369 
440 
512 

945 
*017 
089 
161 
233 
305 
376 
447 
519 

952 
*025 
097 
168 
240 
312 
383 
455 
526 

i 

2 

8 

0.8 
1.6 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

4 

3.2 

611 
612 
613 
614 
615 
616 
617 
618 
619 

604 
675 
746 
817 
888 
958 
79  029 
099 
169 

611 

682 
753 
824 
895 
965 
036 
106 
176 

618 
689 
760 
831 
902 
972 
043 
113 
183 

625 
696 
767 
838 
909 
979 
050 
120 
190 

633 
704 
774 
S45 
916 
986 
057 
127 
197 

640 
711 
781 
852 
923 
993 
064 
134 
204 

647 
718 
789 
859 
930 
*000 
071 
141 
211 

654 
725 
796 
866 
937 
*007 
078 
148 
218 

661 
732 
803 
873 
944 
*014 
085 
155 
225 

668 
739 
810 
880 
951 
*021 
092 
162 
232 

6 
7 
8 
9 

4.8 
5.6 
6.4 
7.2 

620 

239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

621 
622 
623 
624 
625 
626 
627 
628 
629 

309 
379 
449 
518 
588 
657 
727 
796 
865 

316 
386. 
456 
525 
595 
664 
734 
803 
872 

323 
393 
463 
532 
602 
671 
741 
810 
879 

330 
400 
470 
539 
609 
678 
748 
817 
886 

337 
407 
477 
546 
616 
685 
754 
824 
893 

344 
414 

484 
553 
623 
692 
761 
831 
900 

351 
421 
491 
560 
630 
699 
768 
837 
906 

358 
428 
498 
567 
637 
706 
775 
844 
913 

365 
435 
505 
574 
644 
713 
782 
851 
920 

372 
442 
511 
581 
650 
720 
789 
858 
927 

9 

7 

0.7 
1.4 
2.1 
2.8 
3.5 
4.2 
4.9 
5.6 
6.3 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

631 
632 
633 
634 
635 
636 
637 
638 
639 

80  003 
072 
140 
209 
277 
346 
414 
482 
550 

010 
079 
147 
216 
284 
353 
421 
489 
557 

017 
085 
154 
223 
291 
359 
428 
496 
564 

024 
092 
161 
229 
298 
366 
434 
502 
570 

030 
099 
168 
236 
305 
373 
441 
509 
577 

037 
106 
175 
243 
312 
380 
448 
516 
584 

044 
113 
182 
250 
318 
387 

591 

051 
120 

188 
257 
325 
393 
462 
530 
598 

058 
127 
195 
264 
332 
400 
468 
536 
604 

065 
134 
202 
271 
339 
407 
475 
543 
611 

1 
2 
3 

6 

0.6 
1.2 

1.8 

640 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

5 

3.0 

641 
642 
643 
644 
645 
646 
647 
648 
649 

686 
754 
821 
889 
956 
81  023 
090 
158 
224 

693 
760 
828 
895 
963 
030 
097 
164 
231 

699 
767 
835 
902 
969 
037 
104 
171 
238 

706 
774 
841 
909 
976 
043 
111 
178 
245 

713 
781 
848 
916 
983 
050 
117 
184 
251 

720 
787 
855 
922 
990 
057 
124 
191 
258 

726 
794 
862 
929 
996 
064 
131 
198 
265 

733 
801 
868 
936 
003 
070 
137 
204 
271 

740 
808 
875 
943 
010 
077 
144 
211 
278 

747 
814 
882 
949 
*017 
084 
151 
218 
285 

7 
8 
9 

4.2 
4.8 
5.4 

650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

LOGARITHMS 


1021 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

650 

81  291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

651 
652 
653 
654 
655 
656 
657 
658 
659 

358 
425 
491 
558 
624 
690 
757 
823 
889 

365 
431 
498 
564 
631 
697 
763 
829 
895 

371 
438 
505 
571 
637 
704 
770 
836 
902 

378 
445 
511 
578 
644 
710 
776 
842 
908 

385 
451 
518 

584 
651 
717 
783 
849 
915 

391 
458 
525 
591 
657 
723 
790 
856 
921 

398 
465 
531 
598 
664 
730 
796 
862 
928 

405 
471 
538 
604 
671 
737 
803 
869 
935 

411 
478 
544 
611 
677 
743 
809 
875 
941 

418 
485 
551 
617 
684 
750 
816 
882 
948 

660 

954 

961 

968 

974 

981 

987 

994 

*000 

*007 

*014 

661 
662 
663 
664 
665 
666 
667 
668 
669 

82  020 
086 
151 
217 
282 
347 
413 
478 
543 

027 
092 
158 
223 
289 
354 
419 
484 
549 

033 
099 
164 
230 
295 
360 
426 
491 
556 

040 
105 
171 
236 
302 
367 
432 
497 
562 

046 
112 
178 
243 
308 
373 
439 
504 
569 

053 
119 
184 
249 
315 
380 
445 
510 
575 

060 
125 
191 
256 
321 
387 
452 
517 
582 

066 
132 
197 
263 
328 
393 
458 
523 
588 

073 
138 
204 
269 
334 
400 
465 
530 
595 

079 
145 
210 
276 
341 
406 
471 
536 
601 

1  0.7 
2   1.4 
3  2.1 
4  2.8 
5  3.5 
6  4.2 
7   4.9 
8   5.6 
9  6.3 

670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 

671 
672 
673 
674 
675 
676 
677 
678 
679 

672 
737 
802 
866 
930 
995 
83  059 
123 
187 

679 
743 
808 
872 
937 
*001 
065 
129 
193 

685 
750 
814 
879 
943 
*008 
072 
136 
200 

692 
756 
821 
885 
950 
*014 
078 
142 
206 

698 
763 
827 
892 
956 
*020 
085 
149 
213 

705 
769 
834 
898 
963 
*027 
091 
155 
219 

711 
776 
840 
905 
969 
*033 
097 
161 
225 

718 
782 
847 
911 
975 
*040 
104 
168 
232 

724 
789 
853 
918 
982 
*046 
110 
174 
238 

730 
795 
860 
924 
988 
*052 
117 
181 
245 

680 

251 

257 

264 

270 

276 

283 

289 

296 

302 

308 

6 

681 
682 
683 
684 
685 
686 
687 
688 
689 

315 
378 
442 
506 
569 
632 
696 
759 
822 

321 

385 
448 
512 
575 
639 
702 
765 
828 

327 
391 
455 
518 
582 
645 
708 
771 
835 

334 
398 
461 
525 
588 
651 
715 
77£ 
841 

340 
404 
467 
531 
594 
658 
721 
784 
847 

347 
410 
474 
537 
601 
664 
727 
790 
853 

353 
417 
480 
544 
607 
670 
734 
797 
860 

359 
423 
487 
550 
613 
677 
740 
803 
866 

366 
429 
493 
556 
620 
683 
746 
809 
872 

372 
436 
499 
563 
626 
689 
753 
816 
879 

1  0.6 
2   1.2 
3   1.8 
4  2.4 
5  3.0 
6  3.6 
7   4.2 
8  4.8 
9  5.4 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 

691 
692 
693 
694 
695 
696 
697 
698 
699 

948 
84  Oil 
073 
136 
198 
261 
323 
386 
448 

954 

017 
080 
142 
205 
267 
330 
392 
454 

960 
023 
086' 
148 
211 
273 
336 
398 
460 

967 
029 
092 
155 
217 
280 
342 
404 
466 

973 

036 
098 
161 
223 
286 
348 
410 
473 

979 
042 
105 
167 
230 
292 
354 
417 
479 

985 
048 
111 
173 
236 
298 
361 
423 
485 

992 
055 
117 
180 
242 
305 
367 
429 
491 

998 
061 
123 
186 
248 
311 
373 
435 
497 

004 
067 
130 
192 
255 
317 
379 
442 
504 

700 

510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

1022 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.P. 

700 

84  510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

701 
702 
703 
704 
705 
706 
707 
708 
709 

572 
634 
696 
757 
819 
880 
942 
85  003 
065 

578 
640 
702 
763 
825 
887 
948 
009 
071 

584 
646 
708 
770 
831 
893 
954 
016 
077 

590 
652 
714 
776 
837 
899 
960 
022 
083 

597 
658 
720 
782 
844 
905 
967 
028 
089 

603 
665 
726 
788 
850 
911 
973 
034 
095 

609 
671 
733 
794 
856 
917 
979 
040 
101 

615 
677 
739 
800 
862 
924 
985 
046 
107 

621 
683 
745 
807 
868 
930 
991 
052 
114 

628 
689 
751 
813 
874 
936 
997 
058 
120 

i 

2 

7 

0.7 
1.4 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

3 
4 

2.1 

2.8 

711 
712 
713 
714 
715 
716 
717 
718 
719 

187 
248 
309 
370 
431 
491 
552 
612 
673 

193 
254 
315 
376 
437 
497 
558 
618 
679 

199 
260 
321 
382 
443 
503 
564 
625 
685 

205 
266 
327 
388 
449 
509 
570 
631 
691 

211 
272 
333 
394 
455 
516 
576 
637 
697 

217 
278 
339 
400 
461 
522 
582 
643 
703 

224 
285 
345 
406 
467 
528 
588 
649 
709 

230 
291 
352 
412 
473 
534 
594 
655 
715 

236 
297 
358 
418 
479 
540 
600 
.661 
721 

242 
303 
364 
425 
485 
546 
606 
667 
727 

5 
6 
7 
8 
9 

3.5 
4.2 
4.9 
5.6 
6.3 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

721 
722 
723 
724 
725 
726 
727 
728 
729 

794 
854 
914 
974 
86  034 
094 
153 
213 
273 

800 
860 
920 
980 
040 
100 
159 
219 
279 

806 
866 
926 
986 
046 
106 
165 
225 
285 

812 
872 
932 
992 
052 
112 
171 
231 
291 

818 
878 
938 
998 
058 
118 
177 
237 
297 

824 
884 
944 
*004 
064 
124 
183 
243 
303 

830 
890 
950 
*010 
070 
130 
189 
249 
308 

836 
896 
956 
*016 
076 
136 
195 
255 
314 

842 
902 
962 
*022 
082 
141 
201 
261 
320 

848 
908 
968 
*028 
088 
147 
207 
267 
326 

1 
2 
3 
4 
5 
6 
7 
8 
9 

6 

0.6 
1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 
732 
733 
734 
735 
736 
737 
738 
739 

392 
451 
510 
570 
629 
688 
747 
806 
864 

398 
457 
516 
576 
635 
694 
753 
812 
870 

404 
463 
522 
581 
641 
700 
759 
817 
876 

410  ' 
469 
528 
587 
646 
705 
764 
823 
882 

415 
475 
534 
593 
652 
711 
770 
829 
888 

421 
481 
540 
599 
658 
717 
776 
835 
894 

427 
487 
546 
605 
664 
723 
782 
841 
900 

433 
493 
552 
611 
670 
729 
788 
847 
906 

439 
499 
558 
617 
676 
735 
794 
853 
911 

445 
504 
564 
623 

682 
741 
800 
859 
917 

1 
2 
3 

5 

0.5 
1.0 
1.5 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

4 

5 

2.0 
2.5 

741 
742 
743 
744 
745 
746 
747 
748 
749 

982 
87  040 
099 
157 
216 
274 
332 
390 
448 

988 
046 
105 
163 
221 
280 
338 
396 
454 

994 
052 
111 
169 
227 
286 
344 
402 
460 

999 
058 
116 
175 
233 
291 
349 
408 
466 

*005 
064 
122 
181 
239 
297 
355 
413 
471 

*011 
070 
128 
186 
245 
303 
361 
419 
477 

*017 
075 
134 
192 
251 
309 
367 
425 
483 

*023 
081 
140 
198 
256 
315 
373 
431 
489 

*029 
087 
146 
204 
262 
320 
379 
437 
495 

*035 
093 
151 
210 
268 
326 
384 
442 
500 

6 
7 
8 
9 

3.5 
4.0 
45 

750 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P. 

P. 

LOGARITHMS 


1023 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

750 

87  50 

512 

518 

523 

529 

535 

541 

547 

552 

558 

751 
752 
753 
754 
755 
756 
757 
758 
759 

564 
622 
67 
737 
795 
852 
910 
967 
88024 

570 
628 
685 
743 
800 
858 
915 
973 
030 

576 
633 
691 
749 
806 
864 
921 
978 
036 

581 
639 
697 
754 
812 
869 
927 
984 
041 

587 
645 
703 
760 
818 
875 
933 
990 
047 

593 
651 
708 
766 
823 
881 
938 
996 
053 

599 
656 
714 
772 
829 
887 
944 
*001 
058 

604 
662 
720 
777 
835 
892 
950 
*007 
064 

610 
668 
726 
783 
841 
898 
955 
*013 
070 

616 
674 
731 
789 
846 
904 
961 
*018 
076 

760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 

761 

762 
763 
764 
765 
766 
767 
788 
769 

138 
195 
252 
309 
366 
423 
480 
536 
593 

144 

201 
258 
315 
372 
429 
485 
542 
598 

150 
207 
264 
321 
377 
434 
491 
647 
604 

156 
213 
270 
326 
383 
440 
497 
553 
610 

161 
218 
275 
332 
389 
446 
502 
559 
615 

167 
224 
281 
338 
395 
451 
508 
564 
621 

173 
230 
287 
343 
400 
457 
513 
570 
627 

178 
235 
292 
349 
406 
463 
519 
576 
632 

184 
241 
298 
355 
412 
468 
525 
581 
638 

190 
247 
304 
360 
417 
474 
530 
587 
643 

6 

1  0.6 

2   1.2 
3   1.8 
4   2.4 
5  3.0 
6  3.6 
7   4.2 
8  4.8 
9  5.4 

770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

771 
Til 
773 
774 
775 
776 
777 
778 
779 

705 
762 
818 
874 
930 
986 
89  042 
098 
154 

711 
767 
824 
880 
936 
992 
048 
104 
159 

717 
773 
829 
885 
941 
997 
053 
109 
165 

722 
779 
835 
891 
947 
*003 
059 
115 
170 

728 
784 
840 
897 
953 
*009 
064 
120 
176 

734 
790 
846 
902 
958 
*014 
070 
126 
182 

739 
795 
852 
908 
964 
*020 
076 
131 
187 

745 
801 
857 
913 
969 
*025 
081 
137 
193 

750 
807 
863 
919 
975 
*031 
087 
143 
198 

756 
812 
868 
925 
981 
*037 
092 
148 
204 

780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

5 

781 
782 
783 
784 
785 
786 
787 
788 
789 

265 
321 
376 
432 
487 
542 
597 
653 
708 

271 

326 
382 
437 
492 
548 
603 
658 
713 

276 
332 
387 
443 
498 
553 
609 
664 
719 

282 
337 
393 
448 
504 
559 
614 
669 
724 

287 
343 
398 
454 
509 
564 
620 
675 
730 

293 
348 
404 
459 
515 
570 
625 
680 
735 

298 
354 
409 
465 
520 
575 
631 
686 
741 

304 
360 
415 
470 
526 
581 
636 
691 
746 

310 
365 
421 
476 
531 
586 
642 
697 
752 

315 
371 
426 
481 
537 
592 
647 
702 
757 

1   0.5 
2   1.0 
3  1.5 
4  2.0 
5  2.5 
6  3.0 
7   3.5 
8  4.0 
9  j  4.5 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 

792 
793 
794 
795 
7% 
797 
798 
799 

818 
873 
927 
982 
90  037 
091 
146 
200 
255 

823 
878 
933 
988 
042 
097 
151 
206 
260 

829 
883 
938 
993 
048 
102 
157 
211 
266 

834 
889 
944 
998 
053 
108 
162 
217 
271 

840 
894 
949 
*004 
059 
113 
168 
222 
276 

845 
900 
955 
*009 
064 
119 
173 
227 
282 

851 
905 
960 
*015 
069 
124 
179 
233 
287 

856 
911 
966 
020 
075 
129 
184 
238 
293 

862 
916 
971 
026 
080 
135 
189 
244 
298 

867 
922 
977 
*031 
086 
140 
195 
249 
304 

800 

309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

1024 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

347 

8 

352 

9 

P.P. 

800 

801 

802 
803 
804 
805 
806 
807 
808 
809 

810 

811 
812 
813 
814 
815 
816 
817 
818 
819 

820 

821 
822 
823 
824 
825 
826 
827 
828 
829 

830 

831 
832 
833 
834 
835 
836 
837 
838 
839 

840 

841 

842 
843 
844 
845 
846 
847 
848 
849 

850 

90  309 

314 

320 

325 

331 

336 

342 

358 

6 

1   0.6 
2   1.2 
3   1.8 
4   2.4 
5  3.0 
6  3.6 
7   4.2 
8   4.8 
9   5.4 

5 

1  0.5 
2   1.0 
3   1.5 
4  2.0 
5  2.5 
6  3.0 
7   3.5 
8  4.0 
9   4.6 

363 
417 
472 
526 
580 
634 
687 
741 
795 

369 
423 
477 
531 
585 
639 
693 
747 
800 

374 

428 
482 
536 
590 
644 
698 
752 
806 

488 
542 
596 
650 
703 
757 
811 

385 
439 
493 
547 
601 
655 
709 
763 
816 

390 
445 
499 
553 
607 
660 
714 
768 
822 

396 
450 
504 
558 
612 
666 
720 
773 
827 

881 

401 
455 
509 
563 
617 
671 
725 
779 
832 

407 
461 
515 
569 
623 
677 
730 
784 
838 

412 
466 
520 
574 
628 
682 
736 
789 
843 

897 

849 

854 

907 
961 
014 
068 
121 
174 
228 
281 
334 

859 

913 
966 
020 
073 
126 
180 
233 
286 
339 

865 

918 
972 
025 
078 
132 
185 
238 
291 
344 

870 

875 

929 
982 
036 
089 
142 
196 
249 
302 
355 

886 

891 

902 
956 
91  009 
062 
116 
169 
222 
275 
328 

924 
977 
030 
084 
137 
190 
243 
297 
350 

934 
988 
041 
094 
148 
201 
254 
307 
360 

940 
993 
046 
100 
153 
206 
259 
312 
365 

945 

998 
052 
105 
158 
212 
265 
318 
371 

950 
*004 
057 
110 
164 
217 
270 
323 
376 

429 

381 

387 

392 

397 

403 

408 

413 

418 

424 

434 
487 
540 
593 
645 
698 
751 
803 
855 

440 
492 
545 
598 
651 
703 
756 
808 
861 

445 
498 
551 
603 
656 
709 
761 
814 
866 

450 
503 
556 
609 
661 
714 
766 
819 
871 

455 
508 
561 
614 
666 
719 
772 
824 
876 

461 
514 

566 
619 
672 

724 
777 
829 
882 

466 
519 

572 
624 
677 
730 

782 
834 
887 

471 

524 
577 
630 
682 
735 
787 
840 
892 

477 
529 
582 
635 
687 
740 
793 
845 
897 

482 
535 
587 
640 
693 
745 
798 
850 
903 

908 

913 

918 

924 

976 
028 
080 
132 
184 
236 
288 
340 
392 

929 

981 
033 
085 
137 
189 
241 
293 
345 
397 

934 

939 

944 

950 

955 

960 
92  012 
065 
117 
169 
221 
273 
324 
376 

965 
018 
070 
122 
174 
226 
278 
330 
381 

433 

971 
023 
075 
127 
179 
231 
283 
335 
387 

438 

986 
038 
091 
143 
195 
247 
298 
350 
402 

991 
044 
096 
148 
200 
252 
304 
355 
407 

459 

997 
049 
101 
153 
205 
257 
309 
361 
412 

464 

*002 
054 
106 
158 
210 
262 
314 
366 
418 

469 

*007 
059 
111 
163 
215 
267 
319 
371 
423 

428 

443 

449 

454 

474 

480 
531 
583 
634 
686 
737 
788 
840 
891 

485 
536 
588 
639 
691 
742 
793 
845 
896 

947 

490 
542 
593 
645 
696 
747 
799 
850 
901 

495 

547 
598 
650 
701 
752 
804 
855 
906 

957 

500 
552 
603 
655 
706 
758 
809 
860 
911 

962 

505 
557 
609 
660 
711 
763 
814 
865 
916 

511 

562 
614 
665 
716 
768 
819 
870 
921 

973 

516 
567 
619 
670 
722 
773 
824 
875 
927 

978 

521 

572 
624 
675 
727 
778 
829 
881 
932 

526 
578 
629 
681 
732 
783 
834 
886 
937 

942 

952 

967 

983 

988 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

LOGARITHMS 


1025 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

'.P. 

850 

92  942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

851 
852 
853 
854 
855 
856 
857 
858 
859 

993 
93  044 
095 
146 
197 
247 
298 
349 
399 

998 
049 
100 
151 
202 
252 
303 
354 
404 

*003 
054 
105 
156 
207 
258 
308 
359 
409 

*008 
059 
110 
161 
212 
263 
313 
364 
414 

*013 
064 
115 
166 
217 
268 
318 
369 
420 

*018 
069 
120 
171 
222 
273 
323 
374 
425 

*024 
075 
125 
176 
227 
278 
328 
379 
430 

*029 
080 
131 
181 
232 
283 
334 
384 
435 

*034 
085 
136 
186 
237 
288 
339 
389 
440 

*039 
090 
141 
192 
242 
293 
344 
394 
445 

i 

2 

6 

0.6 
1.2 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

4 

2.4 

861 

862 
863 
864 
865 
866 
867 
868 
869 

500 
551 
601 
651 
702 
752 
802 
852 
902 

505 
556 
606 
656 
707 
757 
807 
857 
907 

510 
561 
611 
661 
712 
762 
812 
862 
912 

515 

566 
616 
666 
717 
767 
817 
867 
917 

520 
571 
621 
671 

722 
772 
822 
872 
922 

526 
576 
626 
676 
727 
777 
827 
877 
927 

531 
581 
631 
682 
732 
782 
832 
882 
932 

536 
586 
636 

687 
737 
787 
837 
887 
937 

541 
591 
641 
692 
742 
792 
842 
892 
942 

546 
596 
646 
697 
747 
797 
847 
897 
947 

6 

7 

9 

3.6 

4.2 

4.8 
5.4 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

871 
872 
873 
874 
875 
876 
877 
878 
879 

94  002 
052 
101 
151 
201 
250 
300 
349 
399 

007 
057 
106 
156 
206 
255 
305 
354 
404 

012 
062 
111 
161 
211 
260 
310 
359 
409 

017 
067 
116 
166 
216 
265 
315 
364 
414 

022 
072 
121 
171 
221 
270 
320 
369 
419 

027 
077 
126 
176 
226 
275 
325 
374 
424 

032 
082 
131 
181 
231 
280 
330 
379 
429 

037 
086 
136 
186 
236 
285 
335 
384 
433 

042 
091 
141 
191 
240 
290 
340 
389 
438 

047 
096 
146 
196 
245 
295 
345 
394 
443 

1 

2 
3 
4 
5 
6 
7 
8 
9 

0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
4.5 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

881 
882 
883 
884 
885 
886 
887 
888 
889 

498 
547 
596 
645 
694 
743 
792 
841 
890 

503 
552 
601 
650 
699 
748 
797 
846 
895 

507 
557 
606 
655 
704 
753 
802 
851 
900 

512 
562 
611 
660 
709 
758 
807 
856 
905 

517 
567 
616 
665 
714 
763 
812 
861 
910 

522 
571 
621 
670 
719 
768 
817 
866 
915 

527 
576 
626 
675 
724 
773 
822 
871 
919 

532 
581 
630 
680 
729 
778 
827 
876 
924 

537 
586 
635 
685 
734 
783 
832 
880 
929 

542 
591 
640 
689 
738 
787 
836 
885 
934 

1 
2 
3 

4 

0.4 
0.8 
1.2 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

5 

2.0 

891 
892 
893 
894 
895 
896 
897 
898 
899 

988 
95  036 
085 
134 
182 
231 
279 
328 
376 

993 
041 
090 
139 
187 
236 
284 
332 
381 

998 
046 
095 
143 
192 
240 
289 
337 
386 

*002 
051 
100 
148 
197 
245 
294 
342 
390 

*007 
056 
105 
153 
202 
250 
299 
347 
395 

*012 
061 
109 
158 
207 
255 
303 
352 
400 

*017 
066 
114 
163 
211 
260 
308 
357 
405 

*022 
071 
119 
168 
216 
265 
313 
361 
410 

*027 
075 
124 
173 
221 
270 
318 
366 
415 

*032 
080 
129 
177 
226 
274 
323 
371 
419 

7 
8 
9 

2.8 
3.2 
3.6 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

P. 

05 


1026 


LOGARITHMS 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

900 

901 

902 
903 
904 
905 
906 
907 
908 
909 

910 

911 
912 
913 
914 
915 
916 
917 
918 
919 

920 

.  921 

922 
923 
924 
925 
926 
927 
928 
929 

930 

931 
932 
933 
934 
935 
936 
937 
938 
939 

940 

941 
942 
943 
944 
945 
946 
947 
948 
949 

950 

95  424 

429 

434 

439 

444 

448 

453 

501 
550 
598 
646 
694 
742 
789 
837 
885 

458 

463 

468 

5 

1  0.5 
2   1.0 
3  1.5 
4  2.0 
5  2.5 
6  3.0 
7   3.5 
8  4.0 
9  4.5 

4 

1  0.4 
2   0.8 
3   1.2 
4  1.6 
5  2.0 
6  2.4 
7   2.8 
8  3.2 
9  3.6 

472 
521 
569 
617 
665 
713 
761 
809 
856 

904 

477 
525 
574 
622 
670 
718 
766 
813 
861 

482 
530 
578 
626 
674 
722 
770 
818 
866 

487 
535 
583 
631 
679 
727 
775 
823 
871 

492 
540 

588 
636 
684 
732 
780 
828 
875 

923 

497 
545 
593 
641 
689 
737 
785 
832 
880 

506 
554 
602 
650 
698 
746 
794 
842 
890 

511 
559 
607 
655 
703 
751 
799 
847 
895 

516 
564 
612 
660 
708 
756 
804 
852 
899 

909 

957 
*004 
052 
099 
147 
194 
242 
289 
336 

914 

961 
*009 
057 
104 
152 
199 
246 
294 
341 

918 

966 
*014 
061 
109 
156 
204 
251 
298 
346 

928 

933 

938 

985 
*033 
080 
128 
175 
223 
270 
317 
365 

942 

947 

995 
*042 
090 
137 
185 
232 
280 
327 
374 

421 

952 
999 
96  047 
095 
142 
190 
237 
284 
332 

971 
*019 
066 
114 
161 
209 
256 
303 
350 

976 
*023 
071 
118 
166 
213 
261 
308 
355 

980 
*028 
076 
123 
171 
218 
265 
313 
360 

990 
*038 
085 
133 
180 
227 
275 
322 
369 

379 

384 

431 
478 
525 
572 
619 
666 
713 
759 
806 

388 

393 

398 

445 
492 
539 

586 
633 
680 

727 
774 
820 

402 

450 
497 
544 
591 
638 
685 
731 
778 
825 

407 

454 

501 
548 
595 
642 
689 
736 
783 
830 

412 

459 
506 
553 
600 
647 
694 
741 
788 
834 

881 

417 

464 
511 
558 
605 
652 
699 
745 
792 
839 

886 

426 
473 
520 
567 
614 
661 
708 
755 
802 

435 
483 
530 
577 
624 
670 
717 
764 
811 

440 
487 
534 
581 
628 
675 
722 
769 
816 

468 
515 
562 
609 
656 
703 
750 
797 
844 

848 

853 

858 

862 

867 

872 

876 

890 

895 
942 
988 
97  035 
081 
128 
174 
220 
267 

900 
946 
993 
039 
086 
132 
179 
225 
271 

904 
951 
997 
044 
090 
137 
183 
230 
276 

909 
956 
*002 
049 
095 
142 
188 
234 
280 

327 

914 
960 
*007 
053 
100 
146 
192 
239 
285 

918 
965 
*011 
058 
104 
151 
197 
243 
290 

923 
970 
*016 
063 
109 
155 
202 
248 
294 

928 
974 
*021 
067 
114 
160 
206 
253 
299 

932 
979 
*025 
072 
118 
165 
211 
257 
304 

937 
984 
*030 
077 
123 
169 
216 
262 
308 

313 

317 

322 

331 

336 

340 

345 

350 

354 

359 
405 
451 
497 
543 
589 
635 
681 
727 

364 
410 
456 
502 
548 
594 
640 
685 
731 

777 

368 
414 
460 
506 
552 
598 
644 
690 
736 

782 

373 
419 
465 
511 
557 
603 
649 
695 
740 

377 

424 
470 
516 
562 
607 
653 
699 
745 

382 
428 
474 
520 
566 
612 
658 
704 
749 

387 
433 
479 
525 
571 
617 
663 
708 
754 

391 
437 
483 
529 
575 
621 
667 
713 
759 

396 
442 
488 
534 
580 
626 
672 
717 
763 

400 
447 
493 
539 
585 
630 
676 
722 
768 

772 

786 

791 

4 

795 

800 

6 

804 

809 

813 

N. 

L.O 

1 

2 

3 

5 

7 

8 

9 

P.P. 

LOGARITHMS 


1027 


N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

950 

7  772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

951 
952 
953 
954 
955 
956 
957 
958 
959 

818 
864 
909 
955 
98  000 
046 
091 
137 
182 

823 
868 
914 
959 
005 
050 
096 
141 
186 

827 
873 
918 
964 
009 
055 
100 
146 
191 

832 
877 
923 
968 
014 
059 
105 
150 
195 

836 
882 
928 
973 
019 
064 
109 
155 
200 

841 
886 
932 
978 
023 
068 
114 
159 
204 

845 
891 
937 
982 
028 
073 
118 
164 
209 

850 
896 
941 
987 
032 
078 
123 
168 
214 

855 
900 
946 
991 
037 
082 
127 
173 
218 

859 
905 
950 
996 
041 
087 
132 
177 
223 

960" 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

5 

961 
962 
963 
964 
965 
966 
967 
968 
969 

272 
318 
363 
408 
453 
498 
543 
588 
632 

277 
322 
367 
412 
457 
502 
547 
592 
637 

281 
327 
372 
417 
462 
507 
552 
597 
641 

286 
331 
376 
421 
466 
511 
556 
601 
646 

290 
336 
381 
426 
471 
516 
561 
605 
650 

295 
340 
385 
430 
475 
520 
565 
610 
655 

299 
345 
390 
435 
480 
525 
570 
614 
659 

304 
349 
394 
439 
484 
529 
574 
619 
664 

308 
354 
399 
444 
489 
534 
579 
623 
668 

313 

358 
403 
448 
493 
538 
583 
628 
673 

1  0.5 
2   1.0 
3  1.5 
4  2.0 
5  2.5 
6  3.0 
7  3.5 
8  4.0 
9  4.5 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

971 
972 
973 
974 
975 
976 
977 
978 
979 

722 
767 
811 
856 
900 
945 
989 
99034 
078 

726 
771 
816 
860 
905 
949 
994 
038 
083 

731 
776 
820 
865 
909 
954 
998 
043 
087 

735 
780 
825 
869 
914 
958 
*003 
047 
092 

740 
784 
829 
874 
918 
963 
*007 
052 
096 

744 
789 
834 
878 
923 
967 
*012 
056 
100 

749 
793 
838 
883 
927 
972 
*016 
061 
105 

753 

798 
843 
887 
932 
976 
*021 
065 
109 

758 
802 
847 
892 
936 
981 
*025 
069 
114 

762 
807 
851 
896 
941 
985 
*029 
074 
118 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

4 

981 
982 
983 
984 
985 
986 
987 
988 
989 

167 
211 
255 
300 
344 
388 
432 
476 
520 

171 

216 
260 
304 
348 
392 
436 
480 
524 

176 
220 
264 
308 
352 
396 
441 
484 
528 

180 
224 
269 
313 
357 
401 
445 
489 
533 

185 
229 
273 
317 
361 
405 
449 
493 
537 

189 
233 
277 
322 
366 
410 
454 
498 
542 

193 
238 
282 
326 
370 
414 
458 
502 
546 

198 
242 
286 
330 
374 
419 
463 
506 
550 

202 
247 
291 
335 
379 
423 
467 
511 
555 

207 
251 
295 
339 
383 
427 
471 
515 
559 

2  0.8 
3  1.2 
4  1.6 
5  2.0 
6  2.4 
7  2.8 
8  8.2 
9  3.6 

990 

564 

568 

572 

577 

581 

585 

590 

594 

599 

603 

991 
992 
993 
994 
995 
996 
997 
998 
999 

607 
651 
695 
739 
782 
826 
870 
913 
957 

612 
656 
699 
743 
787 
830 
874 
917 
961 

616 
660 
704 
747 
791 
835 
878 
922 
965 

621 
664 
708 
752 
795 
839 
883 
926 
970 

625 
669 
712 
756 
800 
843 
887 
930 
974 

629 
673 
717 
760 
804 
848 
891 
935 
978 

634 
677 
721 
765 
808 
852 
896 
939 
983 

638 
682 
726 
769 
813 
856 
900 
944 
987 

642 
686 
730 
774 
817 
861 
904 
948 
991 

647 
691 
734 
778 
822 
865 
909 
952 
996 

1000 

00  000 

004 

009 

013 

017 

022 

026 

030 

035 

039 

N. 

L.O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

1028  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

0° 


It 

/ 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.c. 

L.  Cotg. 

L.Cos. 

o 
60 
120 
180 
240 

0 
1 
2 
3 
4 

6.46373 
6.76476 
6.94085 
7.06579 

30103 
17609 
12494 
QfiQI 

5.31443 
5.31443 
5.31443 
5.31443 

5.31443 
5.31443 
5.31443 
5.31442 

6.46373 
6.76476 
6.94085 
7.06579 

30103 
17609 
12494 

QfiQI 

3.53627 
3.23524 
3.05915 
2.93421 

0.00000 
0.00000 
0.00000 
0.00000 
0.00000 

60 

59 
58 
57 
56 

300 
360 
420 
480 
540 

5 
6 
7 
8 
9 

7.16270 

7.24188 
7.30882 
7.36682 
7.41797 

7918 
6694 
5800 
5115 
4576 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31442 
5.31442 
5.31442 
5.31442 
5.31442 

7.16270 
7.24188 
7.30882 
7.36682 
7.41797 

7918 
6694 
5800 
5115 
4576 

2.83730 
2.75812 
2.69118 
2.63318 
2.58203 

0.00000 
0.00000 
0.00000 
0.00000 
0.00000 

55 
54 
53 
52 
51 

600 
660 
720 
780 
840 

10 

11 
12 
13 
14 

7.46373 
7.50512 
7.54291 
7.57767 
7.60985 

4139 
3779 
3476 
3218 
2997 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31442 
5.31442 
5.31442 
5.31442 
5.31442 

7.46373 
7.50512 
7.54291 
7.57767 
7.60986 

4139 
3779 
3476 
3219 
2996 

2.53627 
2.49488 
2.45709 
2.42233 
2.39014 

0.00000 
0.00000 
0.00000 
0.00000" 
0.00000 

50 

49 
48 
47 
46 

900 
960 
1020 
1080 
1140 

15 
16 
17 
18 
19 

7.63982 
7.66784 
7.69417 
7.71900 
7.74248 

2802 
2633 
2483 
2348 
9997 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31442 
5.31442 
5.31442 
5.31442 
5.31442 

7.63982 
7.66785 
7.69418 
7.71900 
7.74248 

2803 
2633 
2482 
2348 

OOOQ 

2.36018 
2.33215 
2.30582 
2.28100 
2.25752 

0.00000 
0.00000 
9.99999 
9.99999 
9.99999 

45 
44 
43 
42 
41 

1200 
1260 
1320 
1380 
1440 

20 

21 
22 
23 
24 

7.76475 
7.78594 
7.80615 
7.82545 
7.84393 

2119 
2021 
1930 
1848 
1773 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31442 
5.31442 
5.31442 
5.31442 
5.31442 

7.76476 
7.78595 
7.80615 
7.82546 
7.84394 

2119 
2020 
1931 
1848 
1773 

2.23524 
2.21405 
2.19385 
2.17454 
2.15606 

9.99999 
9.99999 
9.99999 
9.99999 
9.99999 

40 

39 
38 
37 
36 

1500 

1560 
1620 
1680 
1740 

25 
26 
27 
28 
29 

7.86166 
7.87870 
7.89509 
7.91088 
7.92612 

1704 
1639 
1579 
1524 
1472 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31442 
5.31442 
5.31442 
5.31442 
5.31441 

7.86167 
7.87871 
7.89510 
7.91089 
7.92613 

1704 
1639 
1579 
1524 
1473 

2.13833 
2.12129 
2.10490 
2.08911 
2.07387 

9.99999 
9.99999 
9.99999 
9.99999 
9.99998 

35 
34 
33 
32 
31 

1800 
1860 
1920 
1980 
2040 

30 

31 
32 
33 
34 

7.94084 
7.95508 
7.96887 
7.98223 
7.99520 

1424 
1379 
1336 
1297 

-lOKQ 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31441 
5.31441 
5.31441 
5.31441 
5.31441 

7.94086 
7.95510 
7.96889 
7.98225 
7.99522 

1424 
1379 
1336 
1297 

IOCQ 

2.05914 
2.04490 
2.03111 
2.01775 
2.00478 

9.99998 
9.99998 
9.99998 
9.99998 
9.99998 

30 

29 
28 
27 
26 

2100 
2160 
2220 
2280 
2340 

35 
36 
37 
38 
39 

8.00779 
8.02002 
8.03192 
8.04350 
8.05478 

1223 
1190 
1158 
1128 
1100 

5.31443 
5.31443 
5.31443 
5.31443 
5.31443 

5.31441 
5.31441 
5.31441 
5.31441 
5.31441 

8.00781 
8.02004 
8.03194 
8.04353 
8.05481 

1223 
1190 
1159 
1128 
110ft 

1.99219 
1.97996 
1.96806 
1.95647 
1.94519 

9.99998 
9.99998 
9.99997 
9.99997 
9.99997 

25 
24 
23 
22 
21 

2400 
2460 
2520 
2580 
2640 

40 

41 
42 
43 

44 

8.06578 
8.07650 
8.08696 
8.09718 
8.10717 

1072 
1046 
1022 
999 
Q7fi 

5.31443 
5.31444 
5.31444 
5.31444 
5.31444 

5.31441 
5.31440 
5.31440 
5.31440 
5.31440 

8.06581 
8.07653 
8.08700 
8.09722 
8.10720 

1072 
1047 
1022 
998 

1.93419 
1.92347 
1.91300 
1.90278 
1.89280 

9.99997 
9.99997 
9.99997 
9.99997 
9.999% 

20 

19 
18 
17 
16 

2700 
2760 
2820 
2880 
2940 

45 
46 

47 
48 
49 

8.11693 
8.12647 
8.13581 
8.14495 
8.15391 

954 
934 
914 

896 
877 

5.31444 
5.31444 
5.31444 
5.31444 
5.31444 

5.31440 
5.31440 
5.31440 
5.31440 
5.31440 

8.11696 
8.12651 
8.13585 
8.14500 
8.15395 

955 
934 
915 

895 

070 

1.88304 
1.87349 
1.86415 
1.85500 
1.84605 

9.99996 
9.99996 
9.99996 
9.999% 
9.999% 

15 
14 
13 
12 
11 

3000 
3060 
3120 
3180 
3240 

50 

51 
52 
53 

54 

8.16268 
8.17128 
8.17971 
8.18798 
8.19610 

860 
843 
827 
812 
7Q7 

5.31444 
5.31444 
5.31444 
5.31444 
5.31444 

5.31439 
5.31439 
5.31439 
5.31439 
5.31439 

8.16273 
8.17133 
8.17976 
8.18804 
8.19616 

860 
843 
828 
812 

1.83727 
1.82867 
1.82024 
1.81196 
1.80384 

9.99995 
9.99995 
9.99995 
9.99995 
9.99995 

10 

9 
8 
7 
6 

3300 
3360 
3420 
3480 
3540 

55 
56 
57 
58 
59 

8.20407 
8.21189 
8.21958 
8.22713 
8.23456 

782 
769 
755 
743 
730 

5.31444 
5.31444 
5.31445 
5.31445 
5.31445 

5.31439 
5.31439 
5.31439 
5.31438 
5.31438 

8.20413 
8.21195 
8.21964 
8.22720 
8.23462 

782 
769 
756 
742 

70A 

1.79587 
1.78805 
1.78036 
1  77280 
1.76538 

9.99994 
9.99994 
9.99994 
9.99994 
9.99994 

5 
4 
3 
2 
1 

3600 

60 

8.24186 

5.31445 

5.31438 

8.24192 

1.75808 

9.99993 

0 

L.  Cos. 

d. 

L.cotg. 

d.c. 

L.  Tang. 

L.  Sin. 

i 

89° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
1° 


1029 


II 

' 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

3600 
3660 
3720 
3780 
3840 

0 

1 
2 
3 
4 

8.24186 
8.24903 
8.25609 
8.26304 
8.26988 

717 
706 
695 
684 
673 

5.31445 
5.31445 
5.31445 
5.31445 
5.31445 

5.31438 
5.31438 
5.31438 
5.31438 
5.31437 

8.24192 
8.24910 
8.25616 
8.26312 
8.269% 

718 
706 
696 
684 
673 

1.75808 
1.75090 
1.74384 
1.73688 
1.73004 

9.99993 
9.99993 
9.99993 
9.99993 
9.99992 

60 

59 
58 
57 
56 

3900 
3960 
4020 
4080 
4140 

5 
6 
7 
8 
9 

8.27661 
8.28324 
8.28977 
8.29621 
8.30255 

663 
653 
644 
634 
fi24 

5.31445 
5.31445 
5.31445 
5.31445 
5.31445 

5.31437 
5.31437 
5.31437 
5.31437 
5.31437 

8.27669 
8.28332 
8.28986 
8.29629 
8.30263 

663 
654 
643 
634 
625 

1.72331 
1.71668 
1.71014 
1.70371 
1.69737 

9.99992 
9.99992 
9.99992 
9.99992 
9.99991 

55 
54 
53 
52 
51 

4200 
4260 
4320 
4380 
4440 

10 

11 
12 
13 
14 

8.30879 
8.31495 
8.32103 
8.32702 
8.33292 

616 
608 
599 
590 

5.31446 
5.31446 
5.31446 
5.31446 
5.31446 

5.31437 
5.31436 
5.31436 
5.31436 
5.31436 

8.30888 
8.31505 
8.32112 
8.32711 
8.33302 

617 
607 
599 
591 

KOt 

1.69112 
1.68495 
1.67888 
1.67289 
1.66698 

9.99991 
9.99991 
9.99990 
9.99990 
9.99990 

50 

49 

48 
47 
46 

4500 
4560 
4620 
4680 
4740 

15 
16 
17 
18 
19 

8.33875 
8.34450 
8.35018 
8.35578 
8.36131 

575 
568 
560 
553 

•vt? 

5.3144& 
5.31446 
531446 
5.31446 
5.31446 

5.31436 
5.31435 
5.31435 
5.31435 
5.31435 

8.33886 
8.34461 
8.35029 
8.35590 
8.36143 

575 
568 
561 
553 
546 

1.66114 
1.65539 
1.64971 
1.64410 
1.63857 

9.99990 
9.99989 
9.99989 
9.99989 
9.99989 

45 
44 
43 
42 
41 

4800 
4860 
4920 
4980 
5040 

20 

21 
22 
23 
24 

8.36678 
8.37217 
8.37750 
8.38276 
8.38796 

539 
533 
526 
520 

5.31446 
5.31447 
5.31447 
5.31447 
5.31447 

5.31435 
5.31434 
5.31434 
5.31434 
5.31434 

8.36689 
8.37229 
8.37762 
8.38289 
8.38809 

540 
533 
527 
520 

r-M 

1.63311 
1.62771 
1.62238 
1.61711 
1.61191 

9.99988 
9.99988 
9.99988 
9.99987 
9.99987 

40 

39 
38 
37 
36 

5100 
5160 
5220 
5280 
5340 

25 
26 

27 
28 
29 

8.39310 
8.39818 
8.40320 
8.40816 
8.41307 

508 
502 
496 
491 

5.31447 
5.31447 
5.31447 
5.31447 
5.31447 

5.31434 
5.31433 
5.31433 
5.31433 
5.31433 

8.39323 
8.39832 
8.40334 
8.40830 
8.41321 

509 
502 
496 
491 
486 

1.60677 
1.60168 
1.59666 
1.59170 
1.58679 

9.99987 
9.99986 
9.99986 
9.99986 
9.99985 

35 
34 
33 
32 
31 

5400 
5460 
5520 
5580 
5640 

30 

31 
32 
33 
34 

8.41792 
8.42272 
8.42746 
8.43216 
8.43680 

480 
474 
470 
464 

5.31447 
5.31448 
5.31448 
5.31448 
5.31448 

5.31433 
5.31432 
5.31432 
5.31432 
5.31432 

8.41807 
8.42287 
8.42762 
8.43232 
8.43696 

480 
475 
470 
464 
460 

1.58193 
1.57713 
1.57238 
1.56768 
1.56304 

9.99985 
9.99985 
9.99984 
9.99984 
9.99984 

30 

29 
28 
27 
26 

5700 
5760 
5820 
5880 
5940 

35 
36 
37 
38 
39 

8.44139 
8.44594 
8.45044 
8.45489 
8.45930 

455 
450 
445 
441 

AQC 

5.31448 
5.31448 
5.31448 
5.31448 
5.31449 

5.31431 
5.31431 
5.31431 
5.31431 
5.31431 

8.44156 
8.44611 
8.45061 
8.45507 
8.45948 

455 
450 
446 
441 
437 

1.55844 
1.55389 
1.54939 
1.54493 
1.54052 

9.99983 
9.99983 
9.99983 
9.99982 
9.99982 

25 
24 
23 
22 
21 

6000 
6060 
6120 
6180 
6240 

40 

41 
42 
43 
44 

8.46366 
8.46799 
8.47226 
8.47650 
8.48069 

433 
427 
424 
419 

5.31449 
5.31449 
5.31449 
5.31449 
5.31449 

5.31430 
5.31430 
5.31430 
5.31430 
5.31429 

8.46385 
8.46817 
8.47245 
8.47669 
8.48089 

432 
428 
424 
420 
416 

1.53615 
1.53183 
1.52755 
1.52331 
1.51911 

9.99982 
9.99981 
9.99981 
9.99981 
9.99980 

20 

19 
18 
17 
16 

6300 
6360 
6420 
6480 
6540 

45 

46 
47 
48 
49 

8.48485 
8.48896 
8.49304 
8.49708 
8.50108 

411 

408 
404 
400 

5.31449 
5.31449 
5.31450 
5.31450 
5.31450 

5.31429 
5.31429 
5.31428 
5.31428 
5.31428 

8.48505 
8.48917 
8.49325 
8.49729 
8.50130 

412 
408 
404 
401 
397 

1.51495 
1.51083 
1.50675 
1.50271 
1.49870 

9.99980 
9.99979 
9.99979 
9.99979 
9.99978 

15 
14 
13 
12 
11 

6600 
6660 
6720 
6780 
6840 

50 

51 

52 
53 

54 

8.50504 
8.50897 
8.51287 
8.51673 
8.52055 

393 
390 
386 

382 

5.31450 
5.31450 
5.31450 
5.31450 
5.31450 

5.31428 
5.31427 
5.81427 
5.31427 
5.31427 

8.50527 
8.50920 
8.51310 
8.51696 
8.52079 

393 
390 
386 
383 
380 

1.49473 

1.49080 
1.48690 
1.48304 
1.47921 

9.99978 
9.99977 
9.99977 
9.99977 
9.99976 

10 

9 
8 
7 
6 

6900 
6960 
7020 
7080 
7140 

55 
56 
57 
58 
59 

8.52434 
8.52810 
8.53183 
8.53552 
8.53919 

376 
373 
369 
367 

5.31451 
5.31451 
5.31451 
5.31451 
5.31451 

5.31426 
5.31426 
5.31426 
5.31425 
5.31425 

8.52459 
8.52835 
8.53208 
8.53578 
8.53945 

376 
373 
370 
367 
363 

1.47541 
1.47165 
1.46792 
1.46422 
1.46055 

9.99976 
9.99975 
9.99975 
9.99974 
9.99974 

5 
4 
3 
2 
1 

7200 

60 

8.54282 

5.31451 

5.31425 

8.54308 

1.45692 

9.99974 

0 

L.  Cos. 

d. 

L.Cotg. 

d.c. 

L.  Tang. 

L.  Sin. 

88° 


1030  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

2° 


If 

/ 

L.  Sin. 

d. 

Cpl.  S. 

Cpl.  T. 

L.  Tang. 

d.c. 

L.  Cotg 

L.  Cos. 

7200 
7260 
7320 
7380 
7440 

0 

1 
2 
3 
4 

8.54282 
8.54642 
8.54999 
8.55354 
8.55705 

360 
357 
355 
351 
349 

5.31451 
5.31451 
5.31452 
5.31452 
5.31452 

5.31425 
5.31425 
5.31424 
5.31424 
5.31424 

8.54308 
8.54669 
8.55027 
8.55382 
8.55734 

361 
358 
355 
352 
040 

1.45692 
1.45331 
1.44973 
1.44618 
1.44266 

9.99974 
9.99973 
9.99973 
9.99972 
9.99972 

60 

59 
58 
57 
56 

7500 
7560 
7620 
7680 
7740 

5 
6 

7 
8 
9 

8.56054 
8.56400 
8.56743 
8.57084 
8.57421 

346 
343 
341 
337 
336 

5.31452 
5.31452 
5.31452 
5.31453 
5.31453 

5.31423 
5.31423 
5.31423 
5.31422 
5.31422 

8.56083 
8.56429 
8.56773 
8.57114 
8.57452 

346 
344 
341 

338 

qofi 

1.43917 
1.43571 
1.43227 
1.42886 
1.42548 

9.99971 
9.99971 
9.99970 
9.99970 
9.99969 

55 
54 
53 
52 
51 

7800 
7860 
7920 
7980 
8040 

10 

11 
12 
13 
14 

8.57757 
8.58089 
8.58419 
8.58747 
8.59072 

332 
330 
328 
325 
323 

5.31453 
5.31453 
5.31453 
5.31453 
5.31454 

5.31422 
5.31421 
5.31421 
5.31421 
5.31421 

8.57788 
8.58121 
8.58451 
8.58779 
8.59105 

333 
330 
328 
326 
323 

1.42212 
1.41879 
1.41549 
1.41221 
1.40895 

9.99969 
9.99968 
9.99968 
9.99967 
9.99967 

50 

49 
48 
47 
46 

8100 
8160 
8220 
8280 
8340 

15 
16 
17 
18 
19 

8.59395 
8.59715 
8.60033 
8.60349 
8.60662 

320 
318 
316 
313 
311 

5.31454 
5.31454 
5.31454 
5.31454 
5.31454 

5.31420 
5.31420 
5.31420 
5.31419 
5.31419 

8.59428 
8.59749 
8.60068 
8.60384 
8.60698 

321 
319 
316 
314 

1.40572 
1.40251 
1.39932 
1.39616 
1.39302 

9.99967 
9.99966 
9.99966 
9.99965 
9.99964 

45 
44 
43 
42 
41 

8400 
8460 
8520 
8580 
8640 

20 

21 
22 
23 
24 

8.60973 
8.61282 
8.61589 
8.61894 
8.62196 

309 
307 
305 
302 
301 

5.31455 
5.31455 
5.31455 
5.31455 
5.31455 

5.31418 
5.31418 
5.31418 
5.31417 
5.31417 

8.61009 
8.61319 
8.61626 
8.61931 
8.62234 

310 
307 
305 
303 
qni 

1.38991 
1.38681 
1.38374 
1.38069 
1.37766 

9.99964 
9.99963 
9.99963 
9.99962 
9.99962 

40 

39 
38 
37 
36 

8700 
8760 
8820 
8880 
8940 

25 

26 

27 
28 
29 

8.62497 
8.62795 
8.63091 
8.63385 
8.63678 

298 
296 
294 
293 
290 

5.31455 
5.31456 
5.31456 
5.31456 
5.31456 

5.31417 
5.31416 
5.31416 
5.31416 
5.31415 

8.62535 
8.62834 
8.63131 
8.63426 
8.63718 

299 
297 
295 
292 
291 

1.37465 
1.37166 
1.36869 
1.36574 
1.36282 

9.99961 
9.99961 
9.99960 
9.99960 
9.99959 

35 
34 
33 
32 
31 

9000 
9060 
9120 
9180 
9240 

30 

31 
32 
33 
34 

8.63968 
8.64256 
8.64543 
8.64827 
8.65110 

288 
287 
284 
283 
281 

5.31456 
5.31456 
5.31457 
5.31457 
5.31457 

5.31415 
5.31415 
5.31414 
5.31414 
5.31413 

8.64009 
8.64298 
8.64585 
8.64870 
8.65154 

289 
287 
285 
284 

001 

1.35991 
1.35702 
1.35415 
1.35130 
1.34846 

9.99959 
9.99958 
9.99958 
9.99957- 
9.99956 

30 

29 
28 
27 
26 

9300 
9360 
9420 
9480 
9540 

35 
36 
37 
38 
39 

8.65391 
8.65670 
8.65947 
8.66223 
8.66497 

279 
277 
276 
274 
272 

5.31457 
5.31457 
5.31458 
5.31458 
5.31458 

5.31413 
5.31413 
5.31412 
5.31412 
5.31412 

8.65435 
8.65715 
8.65993 
8.66269 
8.66543 

280 
278 
276 
274 
273 

1.34565 
1.34285 
1.34007 
1.33731 
1.33457 

9.99956 
9.99955 
9.99955 
9.99954 
9.99954 

25 
24 
23 
22 
21 

9600 
9660 
9720 
9780 
9840 

40 

41 
42 
43 
44 

8.66769 
8.67039 
8.67308 
8.67575 
8.67841 

270 
269 
267 
266 

oco 

5.31458 
5.31458 
5.31459 
5.31459 
5.31459 

5.31411 
5.31411 
5.31410 
5.31410 
5.31410 

8.66816 
8.67087 
8.67356 
8.67624 
8.67890 

271 
269 
268 
266 

net 

1.33184 
1.32913 
1.32644 
1.32376 
1.32110 

9.99953 
9.99952 
9.99952 
9.99951 
9.99951 

20 

19 
18 
17 
16 

9900 
9960 
10020 
10080 
10140 

45 
46 
47 
48 
49 

8.68104 
8.68367 
8.68627 
8.68886 
8.69144 

263 
260 
259 
258 
256 

5.31459 
5.31459 
5.31460 
5.31460 
5.31460 

5.31409 
5.31409 
5.31408 
5.31408 
5.31408 

8.68154 
8.68417 
8.68678 
8.68938 
8.69196 

263 
261 
260 
258 
°57 

1.31846 
1.31583 
1.31322 
1.31062 
1.30804 

9.99950 
9.99949 
9.99949 
9.99948 
9.99948 

15 
14 
13 
12 
11 

10200 
10260 
10320 
10380 
10440 

SO 

51 
52 
53 
54 

8.69400 
8.69654 
8.69907 
8.70159 
8.70409 

254 
253 
252 
250 
249 

5.31460 
5.31460 
5.31461 
5.31461 
5.31461 

5.31407 
5.31407 
5.31406 
5.31406 
5.31405 

8.69453 
8.69708 
8.69962 
8.70214 
8.70465 

255 
254 
252 
251 

1.30547 
1.30292 
1.30038 
1.29786 
1.29535 

9.99947 
9.99946 
9.99946 
9.99945 
9.99944 

10 

9 

8 
7 
6 

10500 
10560 
10620 
10680 
10740 

55 
56 
57 
58 
59 

8.70658 
8.70905 
8.71151 
8.71395 
8.71638 

247 
246 
244 
243 
242 

5.31461 
5.31461 
5.31462 
5.31462 
5.31462 

5.31405 
5.31405 
5.31404 
5.31404 
5.31403 

8.70714 
8.70962 
8.71208 
8.71453 
8.71697 

248 
246 
245 
244 

1.29286 
1.29038 
1.28792 
1.28547 
1.28303 

9.99944 
9.99943 
9.99942 
9.99942 
9.99941 

5 
4 
3 
2 
1 

10800 

60 

8.71880 

5.31462 

5.31403 

8.71940 

1.28060 

9.99940 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.C. 

L.  Tang. 

L.  Sin. 

' 

87° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


1031 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

I 

>.  P. 

0 

1 

2 
3 
4 

8.71880 
8.72120 
8.72359 
8.72597 
8.72834 

240 
239 
238 
237 
235 

8.71940 

8.72181 
8.72420 
8.72659 
8.72896 

241 

239 
239 
237 
oqc 

1.28060 
1.27819 
1.27580 
1.27341 
1.27104 

9.99940 
9.99940 
9.99939 
9.99938 
9.99938 

60 

59 
58 
57 
56 

6 
7 
8 
9 

238 

23.8 
27.8 
31.7 
35.7 

234 

23.4 
27.3 
31.2 
35.1 

229 

22.9 
26.7 
30.5 
34.4 

5 
6 

7 
8 
9 

8.73069 
8.73303 
8.73535 
8.73767 
8.73997 

234 
232 
232 
230 
229 

8.73132 
8.73366 
8.73600 
8.73832 
8.74063 

234 
234 
232 
231 

OOQ 

1.26868 
1.26634 
1.26400 
1.26168 
1.25937 

9.99937 
9.99936 
9.99936 
9.99935 
9.99934 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

39.7 
79.3 
119.0 
158.7 
198.3 

39.0 
78.0 
117.0 
156.0 
195.0 

38.2 
76.3 
114.5 
152.7 
190.8 

10 
11 

12 
13 
14 

8.74226 
8.74454 
8.74680 
8.74906 
8.75130 

228 
226 
226 
224 
223 

8.74292 
8.74521 
8.74748 
8.74974 
8.75199 

229 
227 
226 
225 
224 

1.25708 
1.25479 
1.25252 
1.25026 
1.24801 

9.99934 
9.99933 
9.99932 
9.99932 
9.99931 

50 

49 
48 
47 
46 

6 
7 
8 
q 

225 

22.5 
26.3 
30.0 
338 

220 

22.0 
25.7 
29.3 
33  0 

216 
21.6 
25.2 
28.8 
324 

15 
16 
17 
18 
19 

8.75353 
8.75575 
8.75795 
8.76015 
8.76234 

222 
220 
220 
219 
217 

8.75423 
8.75645 
8.75867 
8.76087 
8.76306 

222 
222 
220 
219 
21  Q 

1.24577 
1.24355 
1.24133 
1.23913 
1.23694 

9.99930 
9.99929 
9.99929 
9.99928 
9.99927 

45 
44 
43 
42 
41 

10 
20 
30 
40 
50 

37.5 
75.0 
112.5 
150.0 

187.5 

36.7 
73.3 
110.0 
146.7 
183.3 

36.0 
72.0 
108.0 
144.0 
180.0 

20 

21 
22 
23 
24 

8.76451 
8.76667 
8.76883 
8.77097 
8.77310 

216 
216 
214 
213 
212 

8.76525 
8.76742 
8.76958 
8.77173 

8.77387 

217 
216 
215 
214 

010 

1.23475 
1.23258 
1.23042 
1.22827 
1.22613 

9.99926 
9.99926 
9.99925 
9.99924 
9.99923 

40 

39 
38 
37 
36 

6 
7 
8 
Q 

212 

21.2 
24.7 
28.3 
31  8 

208 

20.8 
24.3 
27.7 
31  2 

204 

20.4 
23.8 

27.2 
30  6 

25 
26 
27 
28 
29 

8.77522 
8.77733 
8.77943 
8.78152 
8.78360 

211 

210 
209 
208 
208 

8.77600 
8.77811 
8.78022 
8.78232 
8.78441 

211 
211 
210 
209 

OAQ 

1.22400 
1.22189 
1.21978 
1.21768 
1.21559 

9.99923 
9.99922 
9.99921 
9.99920 
9.99920 

35 
34 
33 
32 
31 

10 
20 
30 
40 
50 

35.3 
70.7 
106.0 
141.3 
176.7 

34.7 
69.3 
104.0 
138.7 
173.3 

34.0 
68.0 
102.0 
136.0 
170.0 

30 

31 
32 
33 
34 

8.78568 
8.78774 
8.78979 
8.79183 
8.79386 

206 
205 
204 
203 

909 

8.78649 
8.78855 
8.79061 
8.79266 
8.79470 

206 
206 
205 
204 

1.21351 
1.21145 

1.20939 
1.20734 
1.20530 

9.99919 
9.99918 
9.99917 
9.99917 
9.99916 

30 

29 
28 
27 
26 

6 
7 
8 

201 

20.1 
23.5 
26.8 

197 

19.7 
23.0 
26.3 

193 

19.3 
22.5 
25.7 

35 
36 
37 
38 
39 

8.79588 
8.79789 
8.79990 
8.80189 
8.80388 

201 
201 
199 
199 

8.79673 
8.79875 
8.80076 
8.80277 
8.80476 

202 
201 
201 
199 

1.20327 
1.20125 
1.19924 
1.19723 
1.19524 

9.99915 
9.99914 
9.99913 
9.99913 
9.99912 

25 
24 
23 
22 
21 

9 
10 
20 
30 
40 
50 

33.5 
67.0 
100.5 
134.0 
167  5 

32.8 
65.7 
98.5 
131.3 
164  2 

32.2 
64.3 
96.5 
128.7 
160.8 

40 

41 
42 
43 
44 

8.80585 
8.80782 
8.80978 
8.81173 
8.81367 

197 
196 
195 
194 

1QO 

8.80674 
8.80872 
8.81068 
8.81264 
8.81459 

198 
196 
196 
195 
194 

1.19326 
1.19128 
1.18932 
1.18736 
1.18541 

9.99911 
9.99910 
9.99909 
9.99909 
9.99908 

20 

19 
18 
17 
16 

6 

7 
8 

189 

18.9 
22.1 
25.2 

185 

18.5 
21.6 
24.7 

181 

18.1 
21.1 

24.1 

45 
46 
47 
48 
49 

8.81560 
8.81752 
8.81944 
8.82134 
8.82324 

192 
192 
190 
190 
IRQ 

8.81653 
8.81846 
8.82038 
8.82230 
8.82420 

193 
192 
192 
190 
190 

1.18347 
1.18154 
1.17962 
1.17770 
1.17580 

9.99907 
9.99906 
9.99905 
9.99904 
9.99904 

15 
14 
13 
12 
11 

9 

10 
20 
30 
40 
50 

28.4 
31.5 
63.0 
94.5 
126.0 
157  5 

27.8 
30.8 
61.7 
92.5 
123.3 
154  2 

27.2 
30.2 
60.3 
90.5 
120.7 
150.8 

50 

51 
52 
53 
54 

8.82513 
8.82701 
8.82888 
8.83075 
8.83261 

188 
187 
187 
186 

-IQC 

8.82610 
8.82799 
8.82987 
8.83175 
8.83361 

189 
188 
188 
186 
186 

1.17390 
1.17201 
1.17013 
1.16825 
1.16639 

9.99903 
9.99902 
9.99901 
9.99900 
9.99899 

10 

9 
8 

7 
6 

6 

7 
8 

4 

0.4 
0.5 
0.5 

3   2 

3.3  0.2 
0.4  0.2 
3.4  0.3 

1 

0.1 
0.1 

0.1 

55 
56 
57 
58 
59 

8.83446 
8.83630 
8.83813 
8.83996 
8.84177 

184 
183 
183 
181 

8.83547 
8.83732 
8.83916 
8.84100 
8.84282 

185 
184 
184 
182 
182 

1.16453 
1.16268 
1.16084 
1.15900 
1.15718 

9.99898 
9.99898 
9.99897 
9.99896 
9.99895 

5 
4 
3 
2 
1 

9 

10 
20 
30 
40 

0.6 
0.7 
1.3 
2.0 

2.7 

3.5  0.3 
3.5  0.3 
1.0  0.7 
1.5  1.0 
2.0  1.3 
j  K.  17 

0.2 
0.2 
0.3 
0.5 
0.7 
0  8 

60 

8.84358 

8.84464 

1.15536 

9.99894 

0 

i 

L.  Cotg. 

d,c. 

L.Tang. 

L.  Sin. 

' 

1 

».  P. 

86° 

1032 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


1 

L.  Sin. 

d. 

L.Tang 

d.c 

L.  Cotg 

L.  Cos. 

1 

>.  P. 

0 

1 

2 
3 
4 

8.84358 
8.84539 
8.84718 
8.84897 
8.85075 

181 
179 

179 
178 
177 

8.84464 
8.84646 
8.84826 
8.85006 
8.85185 

182 
180 
180 
179 
178 

1.15536 
1.15354 
1.15174 
1.14994 
1.14815 

9.99894 
9.99893 
9.99892 
9.99891 
9.99891 

60 

59 
58 
57 
56 

6 

7 
8 
9 

181 

18.1 
21.1 
24.1 
27.2 

179 

17.9 
20.9 
23.9 
26.9 

177 

17.7 
20.7 
23.6 
26.6 

5 
6 

7 
8 
9 

8.85252 
8.85429 
8.85605 
8.85780 
8.85955 

177 
176 
175 
175 
•170 

8.85363 
8.85540 
8.85717 
8.85893 
8.86069 

177 
177 
176 
176 

1.14637 
1.14460 
1.14283 
1.14107 
1.13931 

9.99890 
9.99889 
9.99888 
9.99887 
9.99886 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

30.2 
60.3 
90.5 
120.7 
150.8 

29.8 
59.7 
89.5 
119.3 
149.2 

29.5 
59.0 
88.5 
118.0 
147.5 

10 

11 
12 
13 
14 

8.86128 
8.86301 
8.86474 
8.86645 
8.86816 

173 
173 
171 
171 
171 

8.86243 
8.86417 
8.86591 
8.86763 
8.86935 

174 
174 
172 
172 
171 

1.13757 
1.13583 
1.13409 
1.13237 
1.13065 

9.99885 
9.99884 
9.99883 
9.99882 
9.99881 

SO 

49 
48 
47 
46 

6 

7 
8 
q 

175 

17.5 
20.4 
23.3 
26.3 

173 

17.3 
20.2 
23.1 
260 

171 

17.1 
20.0 
22.8 
257 

15 
16 
17 
18 
19 

8.86987 
8.87156 
8.87325 
8.87494 
8.87661 

169 
169 
169 
167 
168 

8.87106 
8.87277 
8.87447 
8.87616 
8.87785 

171 
170 
169 
169 
168 

1.12894 
1.12723 
1.12553 
1.12384 
1.12215 

9.99880 
9.99879 
9  99879 
9.99878 
9.99877 

45 
44 
43 
42 
41 

10 
20 
30 
40 
50 

29.2 
58.3 
87.5 
116.7 
145.8 

28.8 
57.7 
86.5 
115.3 
144.2 

28.5 
57.0 
85.5 
114.0 
142.5 

20 

21 
22 
23 
24 

8.87829 
8.87995 
8.88161 
8.88326 
8.88490 

166 
166 
165 
164 
1fi4 

8.87953 
8.88120 
8.88287 
8.88453 
8.88618 

167 
167 
166 
165 
165 

1.12047 
1.11880 
1.11713 
1.11547 
1.11382 

9.99876 
9.99875 
9.99874 
9.99873 
9.99872 

40 

39 
38 
37 
36 

6 

7 
8 

i) 

168 

16.8 
19.6 
22.4 
25  2 

166 

16.6 
19.4 
22.1 
24  Q 

164 

16.4 
19.1 
21.9 
24  fi 

25 
26 
27 
28 
29 

8.88654 
8.88817 
8.88980 
8.89142 
8.89304 

163 
163 
162 
162 
160 

8.88783 
8.88948 
8.89111 
8.89274 
8.89437 

165 
163 
163 
163 
161 

1.11217 
1.11052 
1.10889 
1.10726 
1.10563 

9.99871 
9.99870 
9.99869 
9.99868 
9.99867 

35 
34 
33 
32 
31 

10 
20 
30 
40 
50 

28.0 
56.0 
84.0 
112.0 
140.0 

27.7 
55.3 
83.0 
110.7 
138.3 

27.3 
54.7 
82.0 
109.3 
136.7 

30 

31 
32 
33 
34 

8.89464 
8.89625 
8.89784 
8.89943 
8.90102 

161 
159 
159 
159 
158 

8.89598 
8.89760 
8.89920 
8.90080 
8.90240 

162 
160 
160 
160 
159 

1.10402 
1.10240 
1.10080 
1.09920 
1.09760 

9.99866 
9.99865 
9.99864 
9.99863 
9.99862 

30 

29 
28 
27 
26 

6 

7 
8 

162 

16.2 
18.9 
21.6 

159 

15.9 
18.6 
21.2 

157 

15.7 
18.3 
20.9 

35 
36 
37 
38 
39 

8.90260 
8.90417 
8.90574 
8.90730 
8.90885 

157 
157 
156 
155 

IKK 

8.90399 
8.90557 
8.90715 
8.90872 
8.91029 

158 
158 
157 
157 
156 

1.09601 
1.09443 
1.09285 
1.09128 
1.08971 

9.99861 
9.99860 
9.99859 
9.99858 
9.99857 

25 
24 
23 
22 
21 

10 
20 
30 
40 
fiO 

27.0 
54.0 
81.0 
108.0 
135.0 

26.5 
53.0 
79.5 
106.0 
1325 

26.2 
52.3 
78.5 
104.7 
1308 

40 

41 
42 
43 
44 

8.91040 
8.91195 
8.91349 
8.91502 
8.91655 

155 
154 
153 
153 
152 

8.91185 
8.91340 
8.91495 
8.91650 
8.91803 

155 
155 
155 
153 
154 

1.08815 
1.08660 
1.08505 
1.08350 
1.08197 

9.99856 
9.99855 
9.99854 
9.99853 
9.99852 

20 

19 
18 
17 
16 

6 

7 
8 

155 

15.5 
18.1 
20.7 

153 

15.3 
17.9 
20.4 

151 

15.1 
17.6 
20.1 

45 

46 
47 
48 
49 

8.91807 
8.91959 
8.92110 
8.92261 
8.92411 

152 
151 
151 
150 

-icjrv 

8.91957 
8.92110 
8.92262 
8.92414 
8.92565 

153 

152 
152 
151 

1.08043 
1.07890 
1.07738 
1.07586 
1.07435 

9.99851 
9.99850 
9.99848 
9.99847 
9.99846 

15 
14 
13 
12 
11 

9 
10 
20 
30 
40 
rn 

23.3 
25.8 
51.7 
77.5 
103.3 
129  2 

23.0 
25.5 
51.0 
76.5 
102.0 
127  5 

•22.7 
25.2 
50.3 
75.5 
100.7 
125  8 

50 

51 
52 
53 
54 

8.92561 
8.92710 
8.92859 
8.93007 
8.93154 

149 
149 
148 
147 
147 

8.92716 
8.92866 
8.93016 
8.93165 
8.93313 

150 
150 
149 
148 
149 

1.07284 
1.07134 
1.06984 
1.06835 
1.06687 

9.99845 
9.99844 
9.99843 
9.99842 
9.99841 

10 

9 

8 
7 
6 

6 
7 
8 

149 

14.9 
17.4 
19.9 

147 

14.7 
17.2 
19.6 

1 
0.1 
0.1 
0.1 

55 
56 
57 
58 
59 

8.93301 
8.93448 
8.93594 
8.93740 
8.93885 

147 
146 
146 
145 
145 

8.93462 
3.93609 
8.93756 
8.93903 
8.94049 

147 
147 
147 
146 
146 

1.06538 
1.06391 
1.06244 
1.06097 
1.05951 

9.99840 
9.99839 
9.99838 
9.99837 
9.99836 

5 
4 
3 
2 
1 

9 
10 
20 
30 
40 

22.4 
24.8 
49.7 
74.5 
99.3 

22.1 
24.5 
49.0 
73.5 

98.0 

0.2 
0.2 
0.3 
0.5 
0.7 

60 

8.94030 

8.94195 

1.05805 

9.99834 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

' 

P 

P. 

85C 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


1033 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

F 

.P. 

0 

1 

2 
3 
4 

8.94030 
8.94174 
8.94317 
8.94461 
8.94603 

144 
143 
144 
142 
143 

8.94195 
8.94340 
8.94485 
8.94630 
8.94773 

145 
145 
145 
143 
144 

1.05805 
1.05660 
1.05515 
1.05370 
1.05227 

9.99834 
9.99833 
9.99832 
9.99831 
9.99830 

60 

59 
58 
57 
56 

6 

7 
8 
9 

145 

14.5 
16.9 
19.3 
21.8 

143 
14.3 
16.7 
19.1 
21.5 

141 
14.1 
16.5 

18.8 
21.2 

5 
6 
7 
8 
9 

8.94746 
8.94887 
8.95029 
8.95170 
8.95310 

141 
142 
141 
140 
140 

8.94917 

8.95060 
8.95202 
8.95344 
8.95486 

143 
142 
142 
142 
141 

1.05083 
1.04940 
1.04798 
1.04656 
1.04514 

9.99829 
9.99828 
9.99827 
9.99825 
9.99824 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

24.2 
48.3 
72.5 
96.7 
120.8 

23.8 
47.7 
71.5 
95.3 
119.2 

23.5 
47.0 
70.5 
94.0 
117.5 

10 

11 
12 
13 
14 

8.95450 
8.95589 
8.95728 
8.95867 
8.96005 

139 
139 
139 
138 
-100 

8.95627 
8.95767 
8.95908 
8.96047 
8.96187 

140 
141 
139 
140 
138 

1.04373 
1.04233 
1.04092 
1.03953 
1.03813 

9.99823 
9.99822 
9.99821 
9.99820 
9.99819 

50 

49 
48 
47 
46 

6 
7 
8 
9 

139 

13.9 
16.2 
18.5 
20.9 

138 

13.8 
16.1 
18.4 
20.7 

136 
13.6 
15.9 
18.1 
20.4 

15 
16 
17 
18 
19 

8.96143 
8.96280 
8.96417 
8.96553 
8.96689 

137 
137 
136 
136 

8.96325 
8.96464 
8.96602 
8.96739 
8.96877 

139 
138 
137 
138 
136 

1.03675 
1.03536 
1.03398 
1.03261 
1.03123 

9.99817 
9.99816 
9.99815 
9.99814 
9.99813 

45 
44 
43 
42 
41 

10 
20 
30 
40 
50 

23.2 
46.3 
69.5 
92.7 
115.8 

23.0 
46.0 
69.0 
92.0 
115.0 

22.7 
45.3 
68.0 
90.7 
113.3 

20 

21 
22 
23 
24 

8.96825 
8.96960 
8.97095 
8.97229 
8.97363 

135 
135 
134 
134 

8.97013 
8.97150 
8.97285 
8.97421 
8.97556 

137 
135 
136 
135 
135 

1.02987 
1  02850 
1.02715 
1.02579 
1.02444 

9.99812 
9.99810 
9.99809 
9.99808 
9.99807 

40 

39 
38 
37 
36 

6 
7 
8 
q 

135 

13.5 
15.8 
18.0 
203 

133 

13.3 
15.5 
17.7 
20.0 

131 

13.1 
15.3 
17.5 
19.7 

25 
26 
27 
28 
29 

8.97496 
8.97629 
8.97762 
8.97894 
8.98026 

133 
133 
132 
132 

8.97691 
8.97825 
8.97959 
8.98092 
8.98225 

134 
134 
133 
133 

•100 

1.02309 
1.02175 
1.02041 
1.01908 
1.01775 

9.99806 
9.99804 
9.99803 
9.99802 
9.99801 

35 
34 
33 
32 
31 

10 
20 
30 
40 
50 

22.5 
45.0 
67.5 
90.0 
112.5 

22.2 
44.3 
66.5 
88.7 
110.8 

21.8 
43.7 
65.5 
87.3 
109.2 

30 

31 
32 
33 
34 

8.98157 
8.98288 
8.98419 
8.98549 
8.98679 

131 
131 
130 
130 

8.98358 
8.98490 
8.98622 
8.98753 
8.98884 

132 
132 
131 
131 
131 

1.01642 
1.01510 
1.01378 
1.01247 
1.01116 

9.99800 
9.99798 
9.99797 
9.99796 
9.99795 

30 

29 
28 
27 
26 

6 

7 
8 
9 

129 

129 
15.1 
17.2 
19  4 

128 

12.8 
14.9 
17.1 
19  2 

126 

12.6 
14.7 
16.8 
18  9 

35 
36 
37 
38 
39 

8.98808 
8.98937 
8.99066 
8.99194 
8.99322 

129 
129 

128 
'128 

8.99015 
8.99145 
8.99275 
8.99405 
8.99534 

130 
130 
130 
129 

128 

1.00985 
1.00855 
1.00725 
1.00595 
1.00466 

9.99793 
9.99792 
9.99791 
9.99790 
9.99788 

25 
24 
23 
22 
21 

10 
20 
30 
40 
50 

21.5 
43.0 
64.5 
86.0 
107.5 

21.3 
42.7 
64.0 
85.3 
106.7 

21.0 
42.0 
63.0 
84.0 
105.0 

40 

41 
42 
43 
44 

8.99450 
8.99577 
8.99704 
8.99830 
8.99956 

127 
127 
126 
126 

8.99662 
8.99791 
8.99919 
9.00046 
9.00174 

129 

128 
127 
128 
197 

1.00338 
1.00209 
1.00081 
0.99954 
0.99826 

9.99787 
9.99786 
9.99785 
9.99783 
9.99782 

20 

19 
18 
17 
16 

6 

7 
8 

125 

12.5 
14.6 
16.7 
18  8 

123 

12.3 
14.4 
16.4 
18  5 

122 

12.2 
14.2 
16.3 
18  3 

45 

46 
47 
48 
49 

9.00082 
9.00207 
9.00332 
9.00456 
9.00581 

125 
125 
124 
125 

9.00301 
9.00427 
9.00553 
9.00679 
9.00805 

126 
126 
126 
126 

0.99699 
0.99573 
0.99447 
0.99321 
0.99195 

9.99781 
9.99780 
9.99778 
9.99777 
9.99776 

15 
14 
13 
12 
11 

10 
20 
30 
40 
50 

20.8 
41.7 
62.5 
83.3 
104.2 

20.5 
41.0 
61.5 
82.0 
102.5 

20.3 
40.7 
61.0 
81.3 
101.7 

50 

51 
52 
53 
54 

9.00704 
9.00828 
9.00951 
9.01074 
9.01196 

124 
123 
123 
122 

9.00930 
9.01055 
9.01179 
9.01303 
9.01427 

125 
124 
124 
124 

-IrtO 

0.99070 
0.98945 
0.98821 
0.98697 
0.98573 

9.99775 
9.99773 
9.99772 
9.99771 
9.99769 

10 

9 
8 
7 
6 

6 

7 
8 

121 

12.1 
14.1 
16.1 

120 

12.0 
14.0 
16.0 

1 

0.1 
0.1 
0.1 

55 
56 
57 
58 
59 

w 

9.01318 
9.01440 
9.01561 
9.01682 
9.01803 
9.01923 

122 
121 
121 
121 
120 

9.01550 
9.01673 
9.01796 
9.01918 
9.02040 
9.02162 

123 
123 
122 
122 
122 

0.98450 
0.98327 
0.98204 
0.98082 
0.97960 
0.97838 

9.99768 
9.99767 
9.99765 
9.99764 
9.99763 
9.99761 

5 
4 
3 
2 
1 
0 

10 
20 
3C 
40 
5C 

20.2 
40.3 
60.E 
80.1/ 
100.8 

• 

20.C 
40.C 
60.C 
80.( 
100.( 

r-p  — 

0.2 
0.3 
0.5 
»  0.7 
)  0.8 

L.  COS. 

rt 

L.  Cotg 

(1,0 

L.Tang 

L.  Sin. 

1034 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 


I 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

P 

P. 

0 

1 

2 
3 
4 

9.01923 
9.02043 
9.02163 
9.02283 
9.02402 

120 
120 
120 
119 

9.02162 
9.02283 
9.02404 
9.02525 
9.02645 

121 
121 
121 
120 

0.97838 
0.97717 
0.97596 
0.97475 
0.97355 

9.99761 
9.99760 
9.99759 
9.99757 
9.99756 

60 

59 

58 
57 
56 

6 

7 
8 
9 

121 

12.1 
14.1 
16.1 
18.2 

120 

12.0 
14.0 
16.0 
18.0 

113 
11.9 
13.9 
15.9 
17.9 

5 
6 
7 
8 
9 

9.02520 
9.02639 
9.02757 
9.02874 
9.02992 

119 
118 
117 
118 

9.02766 
9.02885 
9.03005 
9.03124 
9.03242 

119 
120 
119 
118 

0.97234 
0.97115 
0.96995 
0.96876 
0.96758 

9.99755 
9.99753 
9.99752 
9.99751 
9.99749 

55 
54 
53 
52 
61 

10 
20 
30 
40 
50 

20.2 
40.3 
60.5 
80.7 
100.8 

20.0 
40.0 
60.0 
80.0 
100.0 

19.8 
39.7 
59.5 
79.3 
99.2 

10 
11 
12 
13 
14 

9.03109 
9.03226 
9.03342 
9.03458 
9.03574 

117 
116 
116 
116 

9.03361 
9.03479 
9.03597 
9.03714 
9.03832 

118 
118 
117 
118 

0.96639 
0.96521 
0.96403 
0.96286 
0.96168 

9.99748 
9.99747 
9.99745 
9.99744 
9.99742 

60 

49 
48 
47 
46 

6 

7 
8 

118 

11.8 
13.8 
15.7 

117 

11.7 
13.7 
16.6 

116 
11.6 
13.5 
15.5 

15 
16 
17 
18 
19 

9.03690 
9.03805 
9.03920 
9.04034 
9.04149 

115 
115 
114 
115 

9.03948 
9.04065 
9.04181 
9.04297 
9.04413 

117 
116 
116 
116 

0.96052 
0.95935 
0.95819 
0.95703 
0.95587 

9.99741 
9.99740 
9.99738 
9.99737 
9.99736 

45 
44 
43 
42 
41 

10 
20 
30 
40 
50 

19.7 
39.3 
59.0 
78.7 
98.3 

19.5 
39.0 
58.5 
78.0 
97.5 

19.3 
38.7 
58.0 
77.3 
96.7 

20 

21 
22 
23 
24 

9.04262 
9.04376 
9.04490 
9.04603 
9.04715 

114 
114 
113 
112 

9.04528 
9.04643 
9.04758 
9.04873 
9.04987 

115 
115 
115 
114 

0.95472 
0.95357 
0.95242 
0.95127 
0.95013 

9.99734 
9.99733 
9.99731 
9.99730 
9.99728 

40 
39 
38 
37 
36 

6 

7 
8 

115 

11.5 
13.4 
15.3 

114 
11.4 
13.3 
15.2 

113 
11.3 
13.2 
15.1 

25 
26 
27 
28 
29 

9.04828 
9.04940 
9.05052 
9.05164 
9.05275 

112 
112 
112 
111 

9.05101 
9.05214 
9.05328 
9.05441 
9.05553 

113 
114 
113 
112 

0.94899 
0.94786 
0.94672 
0.94559 
0.94447 

9.99727 
9.99726 
9.99724 
9.99723 
9.99721 

35 
34 
33 
32 
31 

9 
10 

20 
30 
40 
50 

17.3 
19.2 
38.3 
57.5 
76.7 
958 

17.1 
19.0 
38.0 
57.0 
76.0 
950 

17.0 
18.8 
37.7 
56.5 
75.3 
942 

30 

31 
32 
33 
34 

9.05386 
9.05497 
9.05607 
9.05717 
9.05827 

111 
110 
110 
110 
no 

9.05666 
9.05778 
9.05890 
9.06002 
9.06113 

112 
112 
112 
111 

0.94334 
0.94222 
0.94110 
0.93998 
0.93887 

9.99720 
9.99718 
9.99717 
9.99716 
9.99714 

30 

29 
28 
27 
26 

6 
7 
8 

112 

11.2 
13.1 
14.9 

III 

11.1 
13.0 
14.8 

110 
11.0 

12.8 
14.7 

35 
36 
37 
38 
39 

9.05937 
9.06046 
9.06155 
9.06264 
9.06372 

109 
109 
109 
108 

9.06224 
9.06335 
9.06445 
9.06556 
9.06666 

111 
110 
111 
110 

0.93776 
0.93665 
0.93555 
0.93444 
0.93334 

9.99713 
9.99711 
9.99710 
9.99708 
9.99707 

25 
24 
23 
22 

21 

9 
10 
20 
30 
40 

16.8 
18.7 
37.3 
56.0 

74.7 

16.7 
18.5 
37.0 
55.5 
74.0 

16.5 
18.3 
36.7 
55.0 
73.3 

40 

41 
42 
43 
44 

9.06481 
9.06589 
9.06696 
9.06804 
9.06911 

108 
107 
108 
107 

9.06775 
9.06885 
9.06994 
9.07103 
9.07211 

110 
109 
109 
108 

-IAQ 

0.93225 
0.93115 
0.93006 
0.92897 
0.92789 

9.99705 
9.99704 
9.99702 
9.99701 
9.99699 

20 

19 
18 
17 
16 

6 
7 
8 

109 

10.9 
12.7 
14.5 

108 

10.8 
12.6 
14.4 

107 

10.7 
12.5 
14.3 

45 
46 

47 
48 
49 

9.07018 
9.07124 
9.07231 
9.07337 
9.07442 

106 
107 
106 
105 
Iftfi 

9.07320 
9.07428 
9.07536 
9.07643 
9.07751 

108 
108 
107 
108 
1O7 

0.92680 
0.92572 
0.92464 
0.92357 
0.92249 

9.99698 
9.99696 
9.99695 
9.99693 
9.99692 

15 
14 
13 
12 
11 

9 
10 
20 
30 
40 

16.4 
18.2 
36.3 
54.5 
72.7 

16.2 
18.0 
36.0 
54.0 
72.0 

16.1 
17.8 
35.7 
53.5 
71.3 

50 

51 
52 
53 
54 

9.07548 
9.07653 
9.07758 
9.07863 
9.07968 

105 
105 
105 
105 
104 

9.07858 
9.07964 
9.08071 
9.08177 
9.08283 

106 
107 
106 
106 
106 

0.92142 
0.92036 
0.91929 
0.91823 
0.91717 

9.99690 
9.99689 
9.99687 
9.99686 
9.99684 

10 

9 
8 

7 
6 

50 

6 

7 
8 

90.8 

106 

10.6 
12.4 
14.1 

90.0 

105 

10.5 
12.3 
14.0 

89.2 

104 

10.4 
12.1 
13.9 

55 
56 
57 

58 
59 

9.08072 
9.08176 
9.08280 
9.08383 
9.08486 

104 
104 
103 
103 
103 

9.08389 
9.08495 
9.08600 
9.08705 
9.08810 

106 
105 
105 
105 
104 

0.91611 
0.91505 
0.91400 
0.91295 
0.91190 

9.99683 
9.99681 
9.99680 
9.99678 
9.99677 

5 
4 
3 
2 
1 

9 

10 
20 
30 
40 

15.9 
17.7 
35.3 
53.0 
70.7 

15.8 
17.5 
35.0 
52.5 
70.0 

15.6 
17.3 
34.7 
52.0 
69.3 

60 

9.08589 

9.08914 

0.91086 

9.99675 

0 

50 

88.3 

87.5 

86.7 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

/ 

P. 

P. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
7° 


1035 


1 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

P. 

P. 

0 

1 

2 
3 
4 

9.08589 
9.08692 
9.08795 
9.08897 
9.08999 

103 
103 
102 
102 
102 

9.08914 
9.09019 
9.09123 
9.09227 
9.09330 

105 
104 
104 
103 
104 

0.91086 
0.90981 
0.90877 
0.90773 
0.90670 

9.99675 
9.99674 
9.99672 
9.99670 
9.99669 

60 

59 
58 
57 
56 

6 

7 
8 
g 

105 

10.5 
12.3 
14.0 
15  8 

104 

10.4 
12.1 
13.9 
15  6 

103 

10.3 
12.0 
13.7 
15  5 

5 

6 
7 
8 
9 

9.09101 
9.09202 
9.09304 
9.09405 
9.09506 

101 
102 
101 
101 
100 

9.09434 
9.09537 
9.09640 
9.09742 
9.09845 

103 
103 
102 
103 
102 

0.90566 
0.90463 
0.90360 
0.90258 
0.90155 

9.99667 
9.99666 
9.99664 
9.99663 
9.99661 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

17.5 
35.0 
52.5 
70.0 
87.5 

17.3 
34.7 
52.0 
69.3 
86.7 

17.2 
34.3 
51.5 
68.7 
85.8 

10 

11 
12 
13 
14 

9.09606 
9.09707 
9.09807 
9.09907 
9.10006 

101 
100 
100 
99 
100 

9.09947 
9.10049 
9.10150 
9.10252 
9.10353 

102 
101 
102 
101 
101 

0.90053 
0.89951 
0.89850 
0.89748 
0.89647 

9.99659 
9.99658 
9.99656 
9.99655 
9.99653 

50 

49 
48 
47 
46 

6 
7 
8 
g. 

102 

10.2 
11.9 
13.6 
15  3 

101 

10.1 
11.8 
13.5 

-ico 

100 

10.0 
11.7 
13.3 
15  0 

15 
16 

17 
18 
19 

9.10106 
9.10205 
9.10304 
9.10402 
9.10501 

99 
99 
98 
99 

QQ 

9.10454 
9.10555 
9.10656 
9.10756 
9.10856 

101 
101 
100 
100 

100 

0.89546 
0.89445 
0.89344 
0.89244 
0.89144 

9.99651 
9.99650 
9.99648 
9.99647 
9.99645 

45 
44 
43 
42 
41 

10 

20 
30 
40 
50 

17.0 
34.0 
51.0 
68.0 
85,0 

16.8 
33.7 
50.5 
67.3 

84,?, 

16.7 
33.3 
50.0 
66.7 
83.3 

20 

21 
22 
23 
24 

9.10599 
9.10697 
9.10795 
9.10893 
9.10990 

98 
98 
98 
97 
97 

9.10956 
9.11056 
9.11155 
9.11254 
9.11353 

100 
99 
99 
99 
99 

0.89044 
0.88944 
0.88845 
0.88746 
0.88647 

9.99643 
9.99642 
9.99640 
9.99638 
9.99637 

40 

39 
38 
37 
36 

9 

6   9 
7  11 
8  13 

)   9 

9   9 
6  11 
2  13 

J 

8 
4 

1 

25 
26 
27 
28 
29 

9.11087 
9-11184 
S.11281 
9.11377 
9.11474 

97 
97 
96 

97 

9.11452 
9.11551 
9.11649 
9.11747 
9.11845 

99 
98 
98 
98 

0.88548 
0.88449 
0.88351 
0.88253 
0.88155 

9.99635 
9.99633 
9.99632 
9.99630 
9.99629 

35 
34 
33 
32 
31 

: 
4 

1 

0  16 
!0  33 
10  49 
LO  66 
)0  82 

5  16 
0  32 
5  49 
0  65 
5  81 

3 

7 
0 
3 

7 

30 

31 
32 
33 
34 

9.11570 
9.11666 
9.11761 
9.11857 
9.11952 

96 
95 
96 
95 

9.11943 
9.12040 
9.12138 
9.12235 
9.12332 

97 
98 
97 
97 

0.88057 
0.87960 
0.87862 
0.87765 
0.87668 

9.99627 
9.99625 
9.99624 
9.99622 
9.99620 

30 

29 
28 
27 
26 

6 
7 
8 

97 

9.7 
11.3 
12.9 

96 

9.6 
11.2 
12.8 

95 

9.5 
11.1 

12.7 

35 
36 
37 
38 
39 

9.12047 
9.12142 
9.12236 
9.12331 
9.12425 

95 
94 
95 
94 
Q4 

9.12428 
9.12525 
9.12621 
9.12717 
9.12813 

97 
96 
96 
96 
96 

0.87572 
0.87475 
0.87379 
0.87283 
0.87187 

9.99618 
9.99617 
9.99615 
9.99613 
9.99612 

25 
24 
23 
22 
21 

9 
10 
20 
30 
40 
50 

14.6 
16.2 
32.3 

48.5 
64.7 
808 

14.4 
16.0 
32.0 
48.0 
64.0 
800 

14.3 
15.8 
31.7 
47.5 
63.3 
79.2 

40 

41 
42 
43 
44 

9.12519 
9.12612 
9.12706 
9.12799 
9.12892 

93 
94 
93 
93 

9.12909 
9.13004 
9.13099 
9.13194 
9.13289 

95 
95 
95 
95 

QT 

0.87091 
0.86996 
0.86901 
0.86806 
0.86711 

9.99610 
9.99608 
9.99607 
9.99605 
9.99603 

20 

19 
18 
17 
16 

6 

7 
8 

94 

9.4 
11.0 
12.5 

93 

9.3 
10.9 
12.4 

92 

9.2 
10.7 
12.3 

45 
46 
47 

48 
49 

9.12985 
9.13078 
9.13171 
9.13263 
9.13355 

93 
93 
92 
92 

9.13384 
9.13478 
9.13573 
9.13667 
9.13761 

94 

95 
94 
94 

QO 

0.86616 
0.86522 
0.86427 
0.86333 
0.86239 

9.99601 
9.99600 
9.99598 
9.99596 
9.99595 

15 
14 
13 
12 
11 

9 

10 
20 
30 
40 

14.1 
15.7 
31.3 
47.0 
62.7 

70  0 

14.0 
15.5 
31.0 
46.5 
62.0 
77  5 

13.8 
15.3 
30.7 
46.0 
61.3 
76  7 

50 

51 
52 
53 

54 

9.13447 
9.13539 
9.13630 
9.13722 
9.13813 

92 
91 
92 
91 
Q1 

9.13854 
9.13948 
9.14041 
9.14134 
9.14227 

94 
93 
93 
93 
93 

0.86146 
0.86052 
0.85959 
0.85866 
0.85773 

9.99593 
9.99591 
9.99589 
9.99588 
9.99586 

10 

9 
8 
7 
6 

6 

7 
8 

91 

9.1 
10.6 
12.1 

90 

9.0 
10.5 
12.0 

2 

0.2 
0.2 
0.3 

55 
56 
57 
58 
59 

9.13904 
9.13994 
9.14085 
9.14175 
9.14266 

90 
91 
90 
91 

9.14320 
9.14412 
9.14504 
9.14597 
9.14688 

92 
92 
93 
91 
92 

0.85680 
0.85588 
0.85496 
0.85403 
0.85312 

9.99584 
9.99582 
9.99581 
9.99579 
9.99577 

5 
4 
3 
2 
1 

9 
10 
20 
30 
40 

13.V 
15.2 
30.3 
45.5 
60.7 

13.5 
15.0 
30.0 
45.0 
60.0 

0.3 
0.3 
0.7 
1.0 
1.3 
1  7 

60 

9.14356 

9.14780 

0.8522C 

9.99575 

0 

L.  Cos 

d. 

L.  Cotg 

d.c 

L.Tang 

L.  Sin 

r 

i 

'.  P. 

82 

1036 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
8° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

P. 

P. 

0 

1 

2 
3 
4 

9.14356 
9.14445 
9.14535 
9.14624 
9.14714 

89 
90 
89 
90 

9.14780 
9.14872 
9.14963 
9.15054 
9.15145 

92 
91 
91 
91 

Q-l 

0.85220 
0.85128 
0.85037 
0.84946 
0.84855 

9.99575 
9.99574 
9.99572 
9.99570 
9.99568 

60 

59 
58 
57 
56 

6 

7 
8 
9 

9 

9 
10 
VI 
Y\ 

2 

.2 
.7 
.3 

H 

9 

9 
10 
12 
IS* 

1 
.1 
.6 

.1 

7 

90 

9.0 
10.5 
12.0 
13  5 

5 

6 
7 
8 
9 

9.14803 
9.14891 
9.14980 
9.15069 
9.15157 

88 
89 
89 
88 

88 

9.15236 
9.15327 
9.15417 
9.15508 
9.15598 

91 
90 
91 
90 
90 

0.84764 
0.84673 
0.84583 
0.84492 
0.84402 

9.99566 
9.99565 
9.99563 
9.99561 
9.99559 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

u 

30 
4(j 
61 

7C 

& 

.1 
.0 
.3 
*.? 

15 

30 
45 
GO 

75 

.2 
.3 
.5 
.7 

.8 

15.0 
30.0 
45.0 
60.0 
75.0 

10 

11 
12 
13 
14 

9.15245 
9.15333 
9.15421 
9.15508 
9.15596 

88 
88 
87 
88 

9.15688 
9.15777 
9.15867 
9.15956 
9.16046 

89 
90 
89 
90 

CQ 

0.84312 
0.84223 
0.84133 
0.84044 
0.83954 

9.99557 
9.99556 
9.99554 
9.99552 
9.99550 

50 

49 
48 
47 
46 

6 

7 
8 

8 
8 

10 
11 
V 

9 

.9 
.4 
.9 

8 

8 
10 
11 
1° 

8 

.8 
.3 
.7 
2 

15 
16 
17 
18 
19 

9.15683 
9.15770 
9.15857 
9.15944 
9.16030 

87 
87 
87 
86 

oa 

9.16135 
9.16224 
9.16312 
9.16401 
9.16489 

89 
88 
89 
88 

CO 

0.83865 
0.83776 
0.83688 
0.83599 
0.83511 

9.99548 
9.99546 
9.99545 
9.99543 
9.99541 

45 
44 
43 
42 
41 

'*   ' 

' 

0 
>0 
50 
10 
>0 

14 
20 
44 

59 
74 

.8 
.7 
.5 
.3 
.2 

14 

21 
44 

f)S 

73 

.7 
.3 
.0 
.7 
.3 

20 

21 
22 
23 
24 

9.16116 
9.16203 
9.16289 
9.16374 
9.16460 

87 
86 
85 
86 

85 

9.16577 
9.16665 
9.16753 
9.16841 
9.16928 

88 
88 
88 
87 
88 

0.83423 
0.83335 
0.83247 
0.83159 
0.83072 

9.99539 
9.99537 
9.99535 
9.99533 
9.99532 

40 

39 
38 
37 
36 

6 

7 
8 

Q 

8 
8 

10 
11 
1° 

7 

.7 
.2 
.0 

8 

•8 
10 
11 
-it 

6 

.6 
.0 
.5 
q 

25 
26 
27 
28 
29 

9.16545 
9.16631 
9.16716 
9.16801 
9.16886 

86 
85 
85 
85 
84 

9.17016 
9.17103 
9.17190 
9.17277 
9.17363 

87 
87 
87 
86 
87 

0.82984 
0.82897 
0.82810 
0.82723 
0.82637 

9.99530 
9.99528 
9.99526 
9.99524 
9.99522 

35 
34 
33 
32 
31 

•  \ 

10 

20 
W 
40 
V) 

14 
21 
43 
58 
72 

.5 
.0 
.5 
.0 

5 

14 

2J- 

43 
57 
71 

.3 
.7 
.0 
.3 

.7 

30 

31 
32 
33 
34 

9.16970 
9.17055 
9.17139 
9.17223 
9.17307 

85 
84 
84 
84 

84 

9.17450 
9.17536 
9.17622 
9.17708 
9.17794 

86 
86 
86 
86 
86 

0.82550 
0.82464 
0.82378 
0.82292 
0.82206 

9.99520 
9.99518 
9.99517 
9.99515 
9.99513 

30 

29 
28 
27 
26 

G 

7 
8 

8 
8 

1 
11 

5 

.5 
.9 
.3 

8 
1 

S 
11 

4 
.4 

.8 
.2 

35 
36 
37 
38 
39 

9.17391 
9.17474 
9.17558 
9.17641 
9.17724 

83 
84 
83 
83 
83 

9.17880 
9.17965 
9.18051 
9.18136 
9.18221 

85 
86 
85 
85 
85 

0.82120 
0.82035 
0.81949 
0.81864 
0.81779 

9.99511 
9.99509 
9.99507 
9.99505 
9.99503 

25 
24 
23 
22 
21 

y 

10 
20 
*) 
40 
"i() 

J^ 
14 
2^ 
42 
5t 
9) 

.8 
.2 
.3 
.5 
.7 
g 

1. 
14 
'2k 

41 

5e 

7f 

.6 
.0 
.0 
.0 
.0 

o 

40 

41 
42 
43 
44 

9.17807 
9.17890 
9.17973 
9.18055 
9.18137 

83 
83 
82 
82 
83 

9.18306 
9.18391 
9.18475 
9.18560 
9.18644 

85 
84 
85 

84 
84 

0.81694 
0.81609 
0.81525 
0.81440 
0.81356 

9.99501 
9.99409 
9.99497 
9.99495 
9.99494 

20 

19 

18 
17 
16 

6 

7 
8 

8 
1 
1 

11 

3 

.3 

.7 
.1 

8 
8 

8 

K 

2 

.2 
.6 
.9 

45 

46 
47 
48 
49 

9.18220 
9.18302 
9.18383 
9.18465 
9.18547 

82 
81 
82 
82 
81 

9.18728 
9.18812 
9.18896 
9.18979 
9.19063 

84 
84 
83 
84 
83 

0.81272 
0.81188 
0.81104 
0.81021 
0.80937 

9.99492 
9.99490 
9.99488 
9.99486 
9.99484 

15 
14 
13 
12 
11 

y 

10 
20 
30 
10 
jO 

n 
i: 

27 
41 

55 
6° 

.0 

.8 
.7 
.5 
.3 

0 

11 

i! 

27 
41 
54 

fi< 

.3 
.7 
.3 
.0 

.7 

q 

50 

51 
52 
53 
54 

9.18628 
9.18709 
9.18790 
9.18871 
9.18952 

81 
81 
81 
81 
81 

9.19146 
9.19229 
9.19312 
9.19395 
9.19478 

83 
83 
83 
83 

CO 

0.80854 
0.80771 
0.80688 
0.80605 
0.80522 

9.99482 
9.99480 
9.99478 
9.99476 
9.99474 

10 

9 

8 
7 
6 

6 

7 
8 

8 
i 

c 

K 

1 
LI 

.5 

.8 

8 

i 

! 

If 

0 

.0 
.3 

.7 

2 

0.2 
0.2 
0.3 

55 
56 
57 
58 
59 

9.19033 
9.19113 
9.19193 
9.19273 
9.19353 

80 
80 
80 
80 
80 

9.19561 
9.19643 
9.19725 
9.19807 
9.19889 

82 
82 
82 
82 

CO 

0.80439 
0.80357 
0.80275 
0.80193 
0.80111 

9.99472 
9.99470 
9.99468 
9.99466 
9.99464 

5 
4 
3 

2 

1 

9 

10 
20 
30 
40 

r_ 

lc 
27 
4( 

5^ 

.2 
.5 
.0 
.5 
.0 

11 

i; 

2f 
4C 
53 

.0 
.3 

.7 
.0 
.3 

0.3 
0.3 
0.7 
1.0 
1.3 

60 

9.19433 

9.19971 

0.80029 

9.99462 

0 

50 

6/ 

.0 

6f 

./ 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

i 

P. 

P. 

81° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS      1037 
9° 


L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

P. 

P 

0 

1 

2 
3 
4 

9.19433 
9.19513 
9.19592 
9.19672 
9.19751 

80 
79 
80 
79 
7Q 

9.19971 
9.20053 
9.20134 
9.20216 
9.20297 

82 
81 
82 
81 

0.80029 
0.79947 
0.79866 
0.79784 
0.79703 

9.99462 
9.99460 
9.99458 
9.99456 
9.99454 

60 

59 
58 
57 
56 

6 

7 
8 

8 

I 
r 

1C 

2 

.2 

.6 
.9 

8 
I 

c 

1C 

1 

.1 
.5 
.8 

80 

8.0 
9.3 
10.7 

5 
6 
7 
8 
9 

9.19830 
9.19909 
9.19988 
9.20067 
9.20145 

79 
79 
79 

78 
78 

9.20378 
9.20459 
9.20540 
9.20621 
9.20701 

81 
81 
81 
80 

0.79622 
0.79541 
0.79460 
0.79379 
0.79299 

9.99452 
9.99450 
9.99448 
9.99446 
9.99444 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

IS 

27 
41 
54 
«• 

.7 
.3 

.0 

.7 
3 

IS 
27 
4C 
54 
6' 

.5 
.0 
.5 
.0 
5 

13.3 
26.7 
40.0 
53.3 
66.7 

10 
11 
12 
13 

14 

9.20223 
9.20302 
9.20380 
9.20458 
9.20535 

79 

78 
78 
77 
78 

9.20782 
9.20862 
9.20942 
9.21022 
9.21102 

80 
80 
80 
80 

0.79218 
0.79138 
0.79058 
0.78978 
0.78898 

9.99442 
9.99440 
9.99438 
9.99436 
9.99434 

50 

49 
48 
47 
46 

6 

7 
8 

7 

Q 

10 

J 
9 
2 
5 

7 

7 
9 
10 

8 
.8 
.1 
.4 

15 
16 
17 

18 
19 

9.20613 
9.20691 
9.20768 
9.20845 
9.20922 

78 
77 

77 
77 
77 

9.21182 
9.21261 
9.21341 
9.21420 
9.21499 

79 
80 
79 
79 

0.78818 
0.78739 
0.78659 
0.78580 
0.78501 

9.99432 
9.99429 
9.99427 
9.99425 
9.99423 

45 
44 
43 
42 
41 

] 
I 
| 

4 
£ 

0 
0 
0 
0 
iO 

13 
26 
39 
52 
fir> 

2 
3 

5 

7 

s 

13 
2f 
39 
52 
6ri 

.7 
.0 
.0 
.0 
.0 

o 

20 

21 
22 
23 
24 

9.20999 
9.21076 
9.21153 
9.21229 
9.21306 

77 
77 
76 
77 
76 

9.21578 
9.21657 
9.21736 
9.21814 
9.21893 

79 
79 
78 
79 

0.78422 
0.78343 
0.78264 
0.78186 
0.78107 

9.99421 
9.99419 
9.99417 
9.99415 
9.99413 

40 

39 
38 
37 
36 

6 

7 
8 

7 

7 
9 
10 

1 

1 
0 
3 

7 

7 
8 
10 

6 
.6 
.9 
.1 

25 
26 
27 
28 
29 

9.21382 
9.21458 
9.21534 
9.21610 
9.21685 

76 
76 
76 

75 
7fi 

9.21971 
9.22049 
9.22127 
9.22205 
9.22283 

78 
78 
78 
78 

0.78029 
0.77951 
0.77873 
0.77795 
0.77717 

9.99411 
9.99409 
9.99407 
9.99404 
9.99402 

35 
34 
33 
32 
31 

] 

! 
S 

I 

f 

9 
0 
0 
0 
0 

Q 

11 
12 

25 
38 
51 
61 

b 
8 
7 
5 
3 

0 

li 
12 

25 

38 
50 
6'} 

.4 

.7 
.3 
.0 
.7 
3 

30 

31 
32 
33 
34 

9.21761 
9.21836 
9.21912 
9.21987 
9.22062 

75 
76 
75 
75 

9.22361 
9.22438 
9.22516 
9.22593 
9.22670 

77 
78 
77 
77 

0.77639 
0.77562 
0.77484 
0.77407 
0.77330 

9.99400 
9.99398 
9.99396 
9.99394 
9.99392 

30 

29 
28 
27 
26 

6 

7 
8 

7 

7 
8 
10 

) 

5 
8 
0 

7 
7 
8 
9 

4 
.4 
.6 
.9 

35 
36 
37 
38 
39 

9.22137 
9.22211 
9.22286 
9.22361 
9.22435 

74 
75 
75 
74 
74 

9.22747 
9.22824 
9.22901 
9.22977 
9.23054 

77 
77 
76 
77 

0.77253 
0.77176 
0.77099 
0.77023 
0.76946 

9.99390 
9.99388 
9.99385 
9.99383 
9.99381 

25 
24 
23 
22 
21 

1 
1 
1 
4 

9 
0 
•0 
0 
0 
o 

11 

12 
25 
37 
50 

fi° 

3 

5 
0 

5 
0 

r. 

11 
12 
24 

37 
49 
fi1 

.1 
.3 
.7 
.0 
.3 
7 

40 
41 
42 
43 
44 

9.22509 
9.22583 
9.22657 
9.22731 

9.22805 

74 
74 
74 
74 
70 

9.23130 
9.23206 
9.23283 
9.23359 
9.23435 

76 

77 
76 
76 

0.76870 
0.76794 
0.76717 
0.76641 
0.76565 

9.99379 
9.99377 
9.99375 
9.99372 
9.99370 

20 

19 
18 
17 
16 

6 

7 
8 

7. 

7 
8 
9 

J 

3 
5 

7 

7 
7 
8 
9 

2 

.2 
.4 
.6 

45 
46 
47 
48 
49 

9.22878 
9.22952 
9.23025 
9.23098 
9.23171 

74 
73 
73 
73 

9.23510 
9.23586 
9.23661 
9.23737 
9.23812 

76 

75 
76 
75 

0.76490 
0.76414 
0.76339 
0.76263 
.0.76188 

9.99368 
9.99366 
9.99364 

15 
14 
13 
12 
11 

1 
2 
3 
4 

9 
0 
0 
0 
0 

11 
12 
24 
36 

48. 

0 
2 
3 
5 

7 

10 
12 
24 

36 

48 

.8 
0 
0 
0 
0 

50 

51 
52 
53 
54 

9.23244 
9.23317 
9.23390 
9.23462 
9.23535 

73 

73 
72 
73 

79 

9.23887 
9.23962 
9.24037 
9.24112 
9.24186 

75 
75 
75 
74 

0.76113 
0.76038 
0.75963 
0.75888 
0.75814 

9.99357 
9.99355 
9.99353 
9.99351 
9.99348 

10 

9 

8 
7 
6 

5 

6 
7 

8 

0 

60. 

71 

7.1 
8.3 
9.5 

8 

0 
0 
0 

GO 

3 

.3 
.4 
.4 

0 

2 

0.2 
0.2 
0.3 

55 
56 
57 
58 
59 

9.23607 
9.23679 
9.23752 
9.23823 
9.23895 

72 
73 

71 
72 

79 

9.24261 
9.24335 
9.24410 
9.24484 
9.24558 

74 

75 
74 
74 

74. 

0.75739 
0.75665 
0.75590 
0.75516 
0.75442 

9.99346 
9.99344 
9.99342 
9.99340 
9.99337 

5 
4 
3 

2 

1 

9 
10 

20 
30 
40 

1 
1 

2 
3 
4 

0.7 
1.8 
3.7 
5.5 
7.3 

0 
0 

1 
1 

2 

.5 
.5 
.0 
.5 
.0 

0.3 
0.3 
0.7 
1.0 
1.3 

60 

9.23967 

9.24632 

0.75368 

9.99335 

0 

50 

5 

9.2 

2 

.5 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

' 

P. 

P 

80° 


1038 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
10° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

P.P. 

0 

1 

2 
3 
4 

9.23967 
9.24039 
9.24110 
9.24181 
9.24253 

72 
71 
71 

72 

9.24632 
9.24706 
9.24779 
9.24853 
9.24926 

74 
73 

74 
73 

0.75368 
0.75294 
0.75221 
0.75147 
0.75074 

9.99335 
9.99333 
9.99331 
9.99328 
9.99326 

60 

59 
58 
57 
56 

6 
7 
8 
9 

74 

7.4 
8.6 
9.9 
11  1 

73 

7.3 

8.5 

9.7 
11  0 

5 

6 
7 
8 
9 

9.24324 
9.24395 
9.24466 
9.24536 
9.24607 

71 
71 
70 
71 

9.25000 
9.25073 
9.25146 
9.25219 
9.25292 

73 
73 
73 
73 
73 

0.75000 
0.74927 
0.74854 
0.74781 
0.74708 

9.99324 
9.99322 
9.99319 
9.99317 
9.99315 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50 

12.3 
24.7 
37.0 
49.3 
61.7 

12.2 
24.3 
36.5 
48.7 
60.8 

10 

11 
12 
13 
14 

9.24677 
9.24748 
9.24818 
9.24888 
9.24958 

71 
70 
70 
70 
70 

9.25365 
9.25437 
9.25510 
9.25582 
9.25655 

72 
73 
72 
73 
72 

0.74635 
0.74563 
0.74490 
0.74418 
0.74346 

9.99313 
9.99310 
9.99308 
9.99306 
9.99304 

50 

49 
48 
47 
46 

6 

7 
8 

g 

72 

7.2 

8.4 
9.6 
10  8 

71 
7.1 

8.3 
9.5 

10  7 

15 
16 
17 
18 
19 

9.25028 
9.25098 
9.25168 
9.25237 
9.25307 

70 
70 
69 
70 

9.25727 
9.25799 
9.25871 
9.25943 
9.26015 

72 
72 
72 
72 
71 

0.74273 
0.74201 
0.74129 
0.74057 
0.73985 

9.99301 
9.99299 
9.99297 
9.99294 
9.99292 

45 
44 
43 
42 
41 

10 
20 
30 
40 
50 

12.0 
24.0 
36.0 
48.0 
600 

11.8 
23.7 
35.5 
47.3 
59.2 

20 

21 
22 
23 
24 

9.25376 
9.25445 
9.25514 
9.25583 
9.25652 

69 
69 
69 
69 

fiQ 

9.26086 
9.26158 
9.26229 
9.26301 
9.26372 

72 
71 
72 
71 

0.73914 
0.73842 
0.73771 
0.73699 
0.73628 

9.99290 
9.99288 
9.99285 
9.99283 
9.99281 

40 

39 
38 
37 
36 

6 

7 
8 

70 

7.0 
8.2 
9.3 

69 

6.9 
8.1 
9.2 

25 
26 

27 
28 
29 

9.25721 
9.25790 
9.25858 
9.25927 
9.25995 

69 
68 
69 
68 

fiS 

9.26443 
9.26514 
9.26585 
9.26655 
9.26726 

71 
71 
70 
71 
71 

0.73557 
0.73486 
0.73415 
0.73345 
0.73274 

9.99278 
9.99276 
9.99274 
9.99271 
9.99269 

35 
34 
33 
32 
31 

10 
20 
30 
40 
50 

11.7 
23.3 
35.0 
46.7 
583 

10.4 
11.5 
23.0 
34.5 
46.0 
575 

30 

31 
32 
33 
34 

9.26063 
9.26131 
9.26199 
9.26267 
9.26335 

68 
68 
68 
68 
68 

9.26797 
9.26867 
9.26937 
9.27008 
9.27078 

70 
70 
71 
70 
70 

0.73203 
0.73133 
0.73063 
0.72992 
0.72922 

9.99267 
9.99264 
9.99262 
9.99260 
9.99257 

30 

29 
28 
27 
26 

6 

7 
.   8 

68 

6.8 
7.9 
9.1 

67 

6.7 
7.8 
8.9 

35 
36 
37 
38 
39 

9.26403 
9.26470 
9.26538 
9.26605 
9.26672 

67 
68 
67 
67 
fi7 

9.27148 
9.27218 
9.27288 
9.27357 
9.27427 

70 
70 
69 

70 

0.72852 
0.72782 
0.72712 
0.72643 
0.72573 

9.99255 
9.99252 
9.99250 
9.99248 
9.99245 

25 
24 
23 
22 
21 

9 
10 
20 
30 
40 

CA 

10.2 
11.3 
22.7 
34.0 
45.3 

Kfi  7 

10.1 
11.2 
22.3 
33.5 
44.7 

CC  Q 

40 

41 
42 
43 
44 

9.26739 
9.26806 
9.26873 
9.26940 
9.27007 

67 
67 
67 
67 
fifi 

9.27496 
9.27566 
9.27635 
9.27704 
9.27773 

70 
69 
69 
69 
fiO 

0.72504 
0.72434 
0.72365 
0.72296 
0.72227 

9.99243 
9.99241 
9.99238 
9.99236 
9.99233 

20 

19 
18 
17 
16 

6 

7 
8 

66 

6.6 

7.7 
8.8 

65 

6.5 

7.6 
8.7 

45 
46 

47 
48 
49 

9.27073 
9.27140 
9.27206 
9.27273 
9.27339 

67 
66 
67 
66 
66 

9.27842 
9.27911 
9.27980 
9.28049 
9.28117 

69 
69 
69 
68 
fiQ 

0.72158 
0.72089 
0.72020 
0.71951 
0.71883. 

9.99231 
9.99229 
9.99226 
9.99224 
9.99221 

15 
14 
13 
12 
11 

9 

10 
20 
30 
40 

9.9 
11.0 
22.0 
33.0 
44.0 

9.8 
10.8 
21.7 
32.5 
43.3 

50 

51 
62 
53 
54 

9.27405 
9.27471 
9.27537 
9.27602 
9.27668 

66 
66 
65 
66 
66 

9.28186 
9.28254 
9.28323 
9.28391 
9.28459 

68 
69 
68 
68 
68 

0.71814 
0.71746 
0.71677 
0.71609 
0.71541 

9.99219 
9.99217 
9.99214 
9.99212 
9.99209 

10 

9 
8 
7 
6 

6 

7 
8 

3 

0.3 
0.4 
0.4 

2 

0.2 
0.2 
0.3 

55 
56 
57 
58 
59 

9.27734 
9.27799 
9.27864 
9.27930 
9.27995 

65 
65 
66 
65 

9.28527 
9.28595 
9.28662 
9.28730 
9.28798 

68 
67 
68 

68 

f\7 

0.71473 
0.71405 
0.71338 
0.71270 
0.71202 

9.99207 
9.99204 
9.99202 
9.99200 
9.99197 

5 
4 
3 
2 
1 

9 
10 
10 
30 
40 

0.5 
0.5 
1.0 
1.5 
2.0 

0.3 
0.3 
0.7 
1.0 
1.3 

60 

9.28060 

9.28865 

0.71135 

9.99195 

0 

50 

2.5 

1.7 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

/ 

P.  P 

79° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
11° 


' 

L.  Sin. 

d. 

L.  Tang. 

d.  c.  JL.  Cotg. 

L.  Cos. 

P.P. 

0 

1 

3 
4 

9.28060 
9.28125 
9.28190 
9.28254 
9.28319 

65 
65 
64 
65 
65 

64 
64 
65 

8 

64 
64 
63 
64 
64 
63 
63 
64 
63 
63 
63 
63 
63 
62 
63 
62 
63 
62 
62 
63 
62 
62 
61 
62 
62 
61 
62 
61 
62 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
61 
60 
60 
60 
60 
59 
60 
60 
59 
60 

9.28865 
9.28933 
9.29000 
9.29067 
9.29134 

68 
67 
67 
67 
67 

67 
•67 
67 

if 

66 
67 
66 
66 
66 
66 
66 
66 
66 
65 
66 
65 
65 
66 
65 
65 
66 
65 
65 
64 
65 
64 
65 
64 
64 
65 
64 
64 
64 
64 
63 
64 
63 
64 
63 
64 
63 
63 
63 
63 
63 
63 
63 
62 
63 
62 
63 
62 
62 
62 

0.71135 
0.71007 
0.71000 
0.70933 
0.70866 

9.99195 
9.99192 
9.99190 
9.99187 
9.99185 

60 

59 
58 
57 
56 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 

7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

68 

6.8 
7.9 
9.1 
10.2 
11.3 
22.7 
34.0 
45.3 
56.7 

66 

6.6 
7.7 
8.8 
9.9 
11.0 
22.0 
33.0 
44.0 
55.0 

64 

6.4 
7.5 
8.5 
9.6 
10.7 
21.3 
32.0 
42.7 
53.3 

62 

6.2 
7.2 
8.3 
9.3 
10.3 
20.7 
31.0 
41.3 
51.7 

60 

6.0 
7.0 
8.0 
9.0 
10.0 
20.0 
30.0 
40.0 
50.0 

3 

0.3 
0.4 
0.4 
0.5 
0.5 
1.0 
1.5 
2.0 
2.5 

67 

6.7 
7.8 
8.9 
10.1 
11.2 
22.3 
33.5 
44.7 
55.8 

65 

6.5 
7.6 
8.7 
9.8 
10.8 
21.7 
3L.5 
43.3 
54.2 

63 

6.3 
7.4 
8.4 
9.5 
10.5 
21.0 
31.5 
42.0 
52.5 

61 

6.1 
7.1 
8.1 
9.2 
10.2 
20.3 
30.5 
40.7 
50.8 

59 

5.9 
6.9 
7.9 
8.9 
9.8 
19.7 
29.5 
39.3 
49.2 

2 

0.2 
0.2 
0.3 
0.3 
0.3 
0.7 
1.0 
1.3 
1.7 

5 

6 

7 
8 
9 

9.28384 
9.28448 
9.28512 
9.28577 
9.28641 

9.29201 
9.29268 
9.29335 
9.29402 
9.29468 

0.70799 
0.70732 
0.70665 
0.70598 
0.70532 

9.99182 
9.99180 
9.99177 
9.99175 
9.99172 

55 
54 
53 
52 
51 

10 

11 
12 
13 
14 

9.28705 
9.28769 
9.28833 
9.28896 
9.28960 

9.29535 
9.29601 
9.29668 
9.29734 
9.29800 

0.70465 
0.70399 
0.70332 
0.70266 
0.70200 

9.99170 
9.99167 
9.99165 
9.99162 
9.99160 

50 

49 
48 
47 
46 

15 
16 
17 
18 
19 

9.29024 
9.29087 
9.29150 
9.29214 
9.29277 

9.29866 
9.29932 
9.29998 
9.30064 
9.30130 

0.70134 
0.70068 
0.70002 
0.69936 
0.69870 

9.99157 
9.99155 
9.99152 
9.99150 
9.99147 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

9.29340 
9.29403 
9.29466 
9.29529 
9.29591 

9.30195 
9.30261 
9.30326 
9.30391 
9.30457 

0.69805 
0.69739 
0.69674 
0.69609 
0.69543 

9.99145 
9.99142 
9.99140 
9.99137 
9.99135 

40 

39 
38 
37 
36 

25 
26 
27 
28 
29 

9.29654 
9.29716 
9.29779 
9.29841 
9.29903 

9.30522 
9.30587 
9.30652 
9.30717 
9.30782 

0.69478 
0.69413 
0.69348 
0.69283 
0.69218 

9.99132 
9.99130 
9.99127 
9.99124 
9.99122 

35 
34 
33 
32 
31 

30 

31 
32 
33 
34 

9.29966 
9.30028 
9.30090 
9.30151 
9.30213 

9.30846 
9.30911 
9.30975 
9.31040 
9.31104 

0.69154 
0.69089 
0.69025 
0.68960 
0.68896 

9.99119 
9.99117 
9.99114 
9.99112 
9.99109 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

40 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

9.30275 
9.30336 
9.30398 
9.30459 
9.30521 

9.31168 
9.31233 
9.31297 
9.31361 
9.31425 

0.68832 
0.68767 
0.68703 
0.68639 
0.68575 

9.99106 
9.99104 
9.99101 
9.99099 
9.99096 

25 
24 
23 
22 
21 
20 
19 
18 
17 
16 

9.30582 
9.30643 
9.30704 
9.30765 
9.30826 

9.31489 
9.31552 
9.3161C 
9.31679 
9.31743 

0.68511 
0.68448 
0.68384 
0.68321 
0.68257 

9.99093 
9.99091 
9.99088 
9.99086 
9.99083 

9.30887 
9.30947 
9.31008 
9.31068 
9.31129 

9.31806 
9.31870 
9.31933 
9.31996 
9.32059 

0.68194 
0.68130 
0.68067 
0.68004 
0.67941 

9.99080 
9.99078 
9.99075 
9.99072 
9.99070 

15 
14 
13 
12 
11 

9.31189 
9.31250 
9.31310 
9.31370 
9.31430 

9.32122 
9.32185 
9.32248 
9.32311 
9.32373 

0.67878 
0.67815 
0.67752 
0.67689 
0.67627 

9.99067 
9.99064 
9.99062 
9.99059 
9.99056 

10 

9 
8 
7 
6 

9.31490 
9.31549 
9.31609 
9.31669 
9.31728 

9.32436 
9.32498 
9.32561 
9.32623 
9.32685 
9.32747 

0.67564 
0.67502 
0.67439 
0.67377 
0.67315 

9.99054 
9.99051 
9.99048 
9.99046 
9.99043 

5 
4 
3 
2 
1 

T 

9.31788 

0.67253 

9.99040 

L.  Cos. 

d. 

L.  Cotg. 

d.  c.  L.Tang. 

L.  Sin. 

/ 

P.P. 

76C 


1040 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
12° 


1 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

P.P. 

0 

1 

2 
3 
4 

9.31788 
9.31847 
9.31907 
9.31966 
9.32025 

59 
60 
59 
59 
59 
59 
59 
59 
58 
59 
59 
58 
58 
59 
58 
58 
58 
58 
58 
58 
58 
57 
58 
57 
58 
57 
57 
58 
57 
57 
57 
56 
57 
57 
57 
56 
57 
56 
56 
57 
56 
56 
56 
56 
56 
56 
55 
56 
55 
56 
55 
56 
55 
55 
55 
55 
55 
55 
55 
55 

9.32747 
9.32810 
9.32872 
9.32933 
9.32995 

63 
62 
61 
62 
62 
62 
61 
62 
61 
62 
61 
61 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
60 
61 
60 
60 
60 
60 
60 
59 
60 
60 
59 
60 
59 
59 
59 
60 
59 
59 
59 
59 
58 
59 
59 
58 
59 
58 
59 
58 
58 
58 
58 
58 
58 
58 
58 
58 
57 

0.67253 
0.67190 
0.67128 
0.67067 
0.67005 

9.99040 
9.99038 
9.99035 
9.99032 
9.99030 

60 

59 

58 
57 
56 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 

7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
'  50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

63 

6.3 
7.4 
8.4 
9.5 
10.5 
21.0 
31.5 
42.0 
52.5 

61 

6.1 
7.1 
8.1 
9.2 
10.2 
20.3 
30.5 
40.7 
50.8 

5 
6  f 
7  ( 
8   \ 
9   I 
10   < 
20  IS 
30  2< 
40  '  3< 
50  4< 

58 

5.8 
6.8 
7.7 
8.7 
9.7 
19.3 
29.0 
38.7 
48.3 

56 

5.6 
6.5 
7.5 
8.4 
9.3 
18.7 
28.0 
37.3 
46.7 

3 

1  0.3 
0.4 
0.4 
0.5 
0.5 
1.0 
1.5 
2.0 
2.5 

62 

6.2 
7.2 
8.3 
9.3 
10.3 
20.7 
31.0 
41.3 
51.7 

60 

6.0 
7.0 
8.0 
9.0 
10.0 
20.0 
30.0 
40.0 
50.0 

9 
>.9 
>.9 
.9 
!.9 
1.8 
).7 
>.5 
1.3 
>.2 

57 
5.7 

6.7 
7.6 
8.6 
9.5 
19.0 
28.5 
38.0 
47.5 

55 

5.5 

6.4 
7.3 

8.3 
9.2 

18.3 
27.5 
36.7 
45.8 

2 

0.2 
0.2 
0.3 
0.3 
0.3 
0.7 
1.0 
1.3 
1.7 

5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

9.32084 
9.32143 
9.32202 
9.32261 
9.32319 

9.33057 
9.33119 
9.33180 
9.33242 
9.33303 

0.66943 
0.66881 
0.66820 
0.66758 
0.66697 

9.99027 
9.99024 
9.99022 
9.99019 
9.99016 

55 
54 
53 
52 
51 

9.32378 
9.32437 
9.32495 
9.32553 
9.32612 

9.33365 
9.33426 
9.33487 
9.33548 
9.33609 

0.66635 
0.66574 
0.66513 
0.66452 
0.66391 

9.99013 
9.99011 
9.99008 
9.99005 
9.99002 

50 

49 
48 
47 
46 

15 
16 
17 
18 
19 

9.32670 
9.32728 
9.32786 
9.32844 
9.32902 

9.33670 
9.33731 
9.33792 
9.33853 
9.33913 

0.66330 
0.66269 
0.66208 
0.66147 
0.66087 

9.99000 
9.98997 
9.98994 
9.98991 
9.98989 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 
~25~ 
26 
27 
28 
29 

9.32960 
9.33018 
9.33075 
9.33133 
9.33190 

9.33974 
9.34034 
9.34095 
9.34155 
9.34215 

0.66026 
0.65966 
0.65905 
0.65845 
0.65785 

9.98986 
9.98983 
9.98980 
9.98978 
9.98975 

40 

39 
38 
37 
36 
35 
34 
33 
32 
31 

9.33248 
9.33305 
9.33362 
9.33420 
9.33477 

9.34276 
9.34336 
9.343% 
9.34456 
9.34516 

0.65724 
0.65664 
0.65604 
0.65544 
0.65484 

9.98972 
9.98969 
9.98967 
9.98964 
9.98961 

30 

31 
32 
33 
34 

9.33534 
9.33591 
9.33647 
9.33704 
9.33761 

9.34576 
9.34635 
9.34695 
9.34755 
9.34814 

0.65424 
0.65365 
0.65305 
0.65245 
0.65186 

9.98958 
9.98955 
9.98953 
9.98950 
9.98947 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

9.33818 
9.33874 
9.33931 
9.33987 
9.34043 

9.34874 
9.34933 
9.34992 
9.35051 
9.35111 

0.65126 

0.65067 
0.65008 
0.64949 
0.64889 

9.98944 
9.98941 
9.98938 
9.98936 
9.98933 

25 
24 
23 
22 
21 

9.34100 
9.34156 
9.34212 
9.34268 
9.34324 

9.35170 
9.35229 
9.35288 
9.35347 
9.35405 

0.64830 
0.64771 
0.64712 
0.64653 
0.64595 

9.98930 
9.98927 
9.98924 
9.98921 
9.98919 

20 

19 
18 
17 
16 

9.34380 
9.34436 
9.34491 
9.34547 
9.34602 

9.35464 
9.35523 
9.35581 
9.35640 
9.35698 

0.64536 
0.64477 
C.64419 
0.64360 
0.64302 

9.98916 
9.98913 
9.98910 
9.98907 
9.98904 

15 
14 
13 
12 
11 

50 
51 

52 
53 
54 

9.34658 
9.34713 
9.34769 
9.34824 
9.34879 

9.35757 
9.35815 
9.35873 
9.35931 
9.35989 

0.64243 
0.64185 
0.64127 
0.64069 
0.64011 

9.98901 
9.98898 
9.98896 
9.98893 
9.98890 

10 

9 

8 
7 
6 

55 
56 
57 
58 
59 

9.34934 
9.34989 
9.35044 
9.35099 
9.35154 

9.36047 
9.36105 
9.36163 
9.36221 
9.36279 

0.63953 
0.63895 
0.63837 
0.63779 
0.63721 

9.98887 
9.98884 
9.98881 
9.98878 
9.98875 

5 
4 
3 
2 
1 

60 

9.35209 

9.36336 

0.63664 

9.98872 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.  c. 

L.Tang. 

L.  Sin. 

' 

P.P. 

77° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 
13° 


1041 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

P.P. 

0 

1 

2 
3 

4 

9.35209 
9.35263 
9.35318 
9.35373 
9.35427 

54 
55 
55 
54 
£4 

9.36336 
9.36394 
9.36452 
9.36509 
9.36566 

58 
58 
57 
57 

CO 

0.63664 
0.63606 
0.63548 
0.63491 
0.63434 

9.98872 
9.98869 
9.98867 
9.98864 
9.98861 

60 

59 
58 
57 
56 

6 

7 
8 
g 

58 

5.8 
6.8 
7.7 
87 

57 

5.7 
6.7 
7.6 
8  6 

5 

6 
7 
8 
9 

9.35481 
9.35536 
9.35590 
9.35644 
9.35698 

55 
54 
54 
54 
54 

9.36624 
9.36681 
9.36738 
9.36795 
9.36852 

57 
57 
57 
57 
*S7 

0.63376 
0.63319 
0.63262 
0.63205 
0.63148 

9.98858 
9.98855 
9.98852 
9.98849 
9.98846 

55 
54 
53 
52 
51 

10 
20 
30 
40 
50, 

9.7 
19.3 
29.0 

38.7 
48.3 

9.5 
19.0 
28.5 
38.0 
47.5 

10 

11 
12 
13 
14 

9.35752 
9.35806 
9.35860 
9.35914 
9.35968 

54 
54 
54 
54 

fiA       ' 

9.36909 
9.36966 
9.37023 
9.37080 
9.37137 

57 

57 
57 
57 

CC 

0.63091 
0.63034 
0.62977 
0.62920 
0.62863 

9.98843 
9.98840 
9.98837 
9.98834 
9.98831 

50 

49 
48 
47 
46 

6 

7 
8 

g 

56 

5.6 
6.5 
7.5 

Q    A, 

55 

5.5 
6.4 
7.3 

0  0 

15 
16 
17 

18 
19 

9.36022 
9.36075 
9.36129 
9.36182 
9.36236 

53 
54 
53 
54 

RQ 

9.37193 
9.37250 
9.37306 
9.37363 
9.37419 

57 
56 
57 
56 

PS] 

0.62807 
0.62750 
0.62694 
0.62637 
0.62581 

9.98828 
9.98825 
9.98822 
9.98819 
9.98816 

45 
44 
43 
42 
41 

10 

20 
30 
40 
50 

9.3 
18.7 
28.0 
37.3 
46.7 

9.2 
18.3 

27.5 
36.7 
45.8 

20 

21 
22 
23 
24 

9.36289 
9.36342 
9.36395 
9.36449 
9.36502 

53 
53 
54 
53 

9.37476 
9.37532 
9.37588 
9.37644 
9.37700 

56 
56 
56 
56 

0.62524 
0.62468 
0.62412 
0.62356 
0.62300 

9.98813 
9.98810 
9.98807 
9.98804 
9.98801 

40 

39 
38 
37 
36 

5 

6     G 
7      C 
8     7 

4 
.4 
.3 
.2 

25 
26 
27 
28 
29 

9.36555 
9.36608 
9.36660 
9.36713 
9.36766 

53 
52 
53 
53 

9.37756 
9.37812 
9.37868 
9.37924 
9.37980 

56 
56 

56 
56 

0.62244 
0.62188 
0.62132 
0.62076 
0.62020 

9.98798 
9.98795 
9.98792 
9.98789 
9.98786 

35 
34 
33 
32 
31 

1C     £ 
20    1£ 
30    2" 
40    3( 
50    4f 

.0 

.0 
.0 
.0 

>.o 

30 

31 
32 
33 

34 

9.36819 
9.36871 
9.36924 
9.36976 
9.37028 

52 
53 
52 
52 

9.38035 
9.38091 
9.38147 
9.38202 
9.38257 

56 
56 
55 
55 

fSft 

0.61965 
0.61909 
0.61853 
0.61798 
0.61743 

9.98783 
9.98780 
9.98777 
9.98774 
9.98771 

30 

29 
28 
27 
26 

6 

7 
8 

53 

5.3 
6.2 
7.1 

52 

5.2 
6.1 
6.9 

35 
36 
37 
38 
39 

9.37081 
9.37133 
9.37185 
9.37237 
9.37289 

52 
52 
52 
52 

eo 

9.38313 
9.38368 
9.38423 
9.38479 
9.38534 

55 
55 
56 
55 
FA 

0.61687 
0.61632 
0.61577 
0.61521 
0.61466 

9.98768 
9.98765 
9.98762 
9.98759 
9.98756 

25 
24 
23 
22 
21 

9 
10 
20 
30 
40 
50 

8.0 
8.8 
17.7 
26.5 
35.3 
442 

7.8 
8.7 
17.3 
26.0 
34.7 
433 

40 

41 
42 
43 
44 

9.37341 
9.37393 
9.37445 
9.37497 
9.37549 

52 

52 
52 
52 

9.38589 
9.38644 
9.38699 
9.38754 
9.38808 

55 
55 
55 
54 

KK 

0.61411 
0.61356 
0.61301 
0.61246 
0.61192 

9.98753 
9.98750 
9.98746 
9.98743 
9.98740 

20 

19 
18 
17 
16 

6 

7 
8 

51 

5.1 
6.0 

6.8 

4 
0.4 
0.5 
0.5 

45 
46 
47 
48 
49 

9.37600 
9.37652 
9.37703 
9.37755 
9.37806 

52 
51 
52 
51 

9.38863 
9.38918 
9.38972 
9.39027 
9.39082 

55 
54 
55 
55 

0.61137 
0.61082 
0.61028 
0.60973 
0.60918 

9.98737 
9.98734 
9.98731 

9.98728 
9.98725 

15 
14 
13 
12 
11 

9 
10 
20 
30 
40 
F:A 

V.V 
8.5 
17.0 
25.5 
34.0 

49  S 

0.6 
0.7 
1.3 
2.0 
2.7 

0  0 

50 

51 
52 
53 
54 

9.37858 
9.37909 
9.37960 
9.38011 
9.38062 

51 
51 
51 
51 

M 

9.39136 
9.39190 
9.39245 
9.39299 
9.39353 

54 
55 

54 
54 
54 

0.60864 
0.60810 
0.60755 
0.60701 
0.60647 

9.98722 
9.98719 
9.98715 
9.98712 
9.98709 

10 

9 
8 
7 
6 

6 
7 
8 

3 

0.3 
0.4 
0.4 

2 

0.2 
0.2 
0.3 

55 

56 
57 
58 
59 

9.38113 
9.38164 
9.38215 

9.38266 
9.38317 

51 
51 
51 
51 

9.39407 
9.39461 
9.39515 
9.39569 
9.39623 

54 
54 
54 
54 
fv4 

0.60593 
0.60539 
0.60485 
0.60431 
0.60377 

9.98706 
9.98703 
9.98700 
9.98697 
9.98694 

5 
4 
3 
2 
1 

S 
1C 
2C 
3C 

.4C 

O.b 
0.5 
1.0 
1.5 
2.0 

0.3 
0.3 
0.7 
1.0 
1.3 

60 

9.38368 

9.39677 

0.60323 

9.98690 

0 

L.Cos 

d 

L.  Cotg 

do. 

L.Tang 

L.  Sin. 

/ 

P.  I 

i 

66 

76° 

1042 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
14° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P 

0 

1 

2 
3 

4 

9.38368 
9.38418 
9.38469 
9.38519 
9.38570 

50 
51 
50 
51 
50 

9.39677 
9.39731 
9.39785 
9.39838 
9.39892 

54 
54 
53 
54 
53 

0.60323 
0.60269 
0.60215 
0.60162 
0.60108 

9.98690 
9.98687 
9.98684 
9.98681 
9.98678 

3 

3 
3 
3 

60 

59 
58 
57 
56 

6 
7 

54 

5.4 
6  3 

53 

5.3 

6  2 

5 
6 

7 
8 
9 

9.38620 
9.38670 
9.38721 
9.38771 
9.38821 

50 
51 
50 
50 

en 

9.39945 
9.39999 
9.40052 
9.40106 
9.40159 

54 

53 
54 
53 

KO 

0.60055 
0.60001 
0.59948 
0.59894 
0.59841 

9.98675 
9.98671 
9.98668 
9.98665 
9.98662 

4 
3 
3 
3 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

7.2 
8.1 
9.0 
18.0 
27.0 

7!l 
8.0 
8.8 
17.7 
26.5 

10 

11 
12 
13 
14 

9.38871 
9.38921 
9.38971 
9.39021 
9.39071 

50 
50 
50 
50 
*so 

9.40212 
9.40266 
9.40319 
9.40372 
9.40425 

54 
53 
53 
53 

to 

0.59788 
0.59734 
0.59681 
0.59628 
0.59575 

9.98659 
9.98656 
9.98652 
9.98649 
9.98646 

3 
4 
3 
3 

50 

49 
48 
47 
46 

40 
50 

36.0 
45.0 

ft? 

35.3 
44.2 

51 

15 
16 
17 
18 
19 

9.39121 
9.39170 
9.39220 
9.39270 
9.39319 

49 
50 
50 
49 

9.40478 
9.40531 
9.40584 
9.40636 
9.40689 

53 

53 
52 
53 

0.59522 
0.59469 
0.59416 
0.59364 
0.59311 

9.98643 
9.98640 
9.98636 
9.98633 
9.98630 

3 
4 
3 
3 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

5.2 
6.1 
6.9 

7.8 
8.7 

5.1 
6.0 
6.8 
7.7 
8.5 

ZO 

21 
22 
23 
24 

9.39369 
9.39418 
9.39467 
9.39517 
9.39566 

49 
49 
50 
49 

9.40742 
9.40795 
9.40847 
9.40900 
9.40952 

53 
52 
53 
52 

KQ 

0.59258 
0.59205 
0.59153 
0.59100 
0.59048 

9.98627 
9.98623 
9.98620 
9.98617 
9.98614 

4 
3 
3 
3 

40 

39 
38 
37 
36 

20 
30 
40 
50 

IV.  3 
26.0 
34.7 
43.3 

17.0 
25.5 
34.0 
42.5 

25 
26 
27 
28 
29 

9.39615 
9.39664 
9.39713 
9.39762 
9.39811 

49 
49 
49 
49 

AQ 

9.41005 
9.41057 
9.41109 
9.41161 
9.41214 

52 

52 
52 
53 

KO 

0.58995 
0.58943 
0.58891 
0.58839 
0.58786 

9.98610 
9.98607 
9.98604 
9.98601 
9.98597 

3 
3 
3 

4 

35 
34 
33 
32 
31 

6 

7 
8 

50 

5.0 

5.8 
6.7 

49 

4.9 
5.7 
6.5 

30 

31 
32 
33 
34 

9.39860 
9.39909 
9.39958 
9.40006 
9.40055 

49 
49 
48 
49 

48 

9.41266 
9.41318 
9.41370 
9.41422 
9.41474 

52 
52 
52 
52 
52 

0.58734 
0.58682 
0.58630 
0.58578 
0.58526 

9.98594 
9.98591 
9.98588 
9.98584 
9.98581 

3 
3 
4 
3 
3 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

7.5 
8.3 
16.7 
25.0 
33.3 
41  7 

7.4 
8.2 
16.3 
24.5 
32.7 
40  8 

35 
36 
37 
38 
39 

9.40103 
9.40152 
9.40200 
9.40249 
9.40297 

49 
48 
49 
48 

9.41526 
9.41578 
9.41629 
9.41681 
9.41733 

52 
51 

52 
52 

fVI 

0.58474 
0.58422 
0.58371 
0.58319 
0.58267 

9.98578 
9.98574 
9.98571 
9.98568 
9.98565 

4 

3 
3 
3 

25 
24 
23 
22 
21 

6 

48 

4.8 

47 

4.7 

c  k 

40 

41 
42 
43 
44 

9.40346 
9.40394 
9.40442 
9.40490 
9.40538 

48 
48 
48 
48 

9.41784 
9.41836 
9.41887 
9.41939 
9.41990 

52 
51 
52 
51 

ft1 

0.58216 
0.58164 
0.58113 
0.58061 
0.58010 

9.98561 
9.98558 
9.98555 
9.98551 
9.98548 

3 
3 

4 
3 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

6.4 
7.2 
8.0 
16.0 
MO 

6.3 
7.1 

7.8 
15.7 
23.5 

45 
46 
47 
48 
49 

9.40586 
9.40634 
9.40682 
9.40730 
9.40778 

48 
48 
48 
48 
47 

9.42041 
9.42093 
9.42144 
9.42195 
9.42246 

52 
51 
51 
51 
51 

0.57959 
0.57907 
0.57856 
0.57805 
0.57754 

9.98545 
9.98541 
9.98538 
9.98535 
9.98531 

4 
3 
3 
4 
3 

15 
14 
13 
12 
11 

40 
50 

32.0 
40.0 

4 

31.3 
39.2 

3 

50 
51 
52 
53 
54 

9.40825 
9.40873 
9.40921 
9.40968 
9.41016 

48 
48 
47 
48 
47 

9.42297 
9.42348 
9.42399 
9.42450 
9.42501 

51 
51 
51 
51 
61 

0.57703 
0.57652 
0.57601 
0.57550 
0.57499 

9.98528 
9.98525 
9.98521 
9.98518 
9.98515 

3 

4 
3 
3 
4 

10 

9 
8 
7 
6 

6 
7 
8 
9 
10 

0.4 
0.5 
0.5 
0.6 
0.7 

0.3 
0.4 
0.4 
0.5 
0.5 

55 
56 

57 
58 
59 

9.41063 
9.41111 
9.41158 
9.41205 
9.41252 

48 
47 
47 
47 

40 

9.42552 
9.42603 
9.42653 
9.42704 
9.42755 

51 
50 
51 
51 

*)Q 

0.57448 
0.57397 
0.57347 
0.57296 
0.57245 

9.98511 
9.98508 
9.98505 
9.98501 
9.98498 

3 

4 
3 

4 

5 

4 
3 
2 

1 

20 
30 
40 
50 

1.3 
2.0 
2.7 
3.3 

1.0 
1.5 
2.0 
2.5 

60 

9.41300 

9.42805 

0.57195 

9.98494 

0 

L.  Cos. 

d. 

L.  Cotg 

d.  c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P 

75° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
15° 


1043 


1 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P.  P 

0 

1 

2 
3 
4 

9.41300 
9.41347 
9.41394 
9.41441 
9.41488 

47 
47 
47 
47 
47 

9.42805 
9.42856 
9.42906 
9.42957 
9.43007 

51 
50 
51 
50 

V) 

0.57195 
0.57144 
0.57094 
0.57043 
0.56993 

9.98494 
9.98491 
9.98488 
9.98484 
9.98481 

3 
3 
4 
3 

60 

59 
58 
57 
56 

6 

7 

51 
5.1 

fi  0 

50 

5.0 

5 
6 

7 
8 
9 

9.41535 
9.41582 
9.41628 
9.41675 
9.41722 

47 
46 
47 
47 
46 

9.43057 
9.43108 
9.43158 
9.43208 
9.43258 

51 
50 
50 
50 
50 

0.56943 
0.56892 
0.56842 
0.56792 
0.56742 

9.98477 
9.98474 
9.98471 
9.98467 
9.98464 

3 
3 
4 
3 

55 
54 
53 
52 
51 

8 
9 

10 
20 
30 

6.8 
7.7 
8.5 
17.0 
25.5 

6.7 
7.5 
8.3 
16.7 
25.0 

10 

11 
12 
13 
14 

9.41768 
9.41815 
9.41861 
9.41908 
9.41954 

47 
46 
47 
46 
47 

9.43308 
9.43358 
9.43408 
9.43458 
9.43508 

50 
50 
50 
50 

PLf) 

0.56692 
0.56642 
0.56592 
0.56542 
0.56492 

9.98460 
9.98457 
9.98453 
9.98450 
9.98447 

3 
4 
3 
3 

50 

49 
48 
47 
46 

40 
50 

34.0 
42.5 

49 

33.3 
41.7 

48 

15 
16 
17 
18 
19 

9.42001 
9.42047 
9.42093 
9.42140 
9.42186 

46 
46 
47 
46 

4fi 

9.43558 
9.43607 
9.43657 
9.43707 
9.43756 

49 
50 
50 
49 

0.56442 
0.56393 
0.56343 
0.56293 
0.56244 

9.98443 
9.98440 
9.98436 
9.98433 
9.98429 

3 
4 
3 

4 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

4.9 
5.7 
6.5 
7.4 
8.2 

4.8 
5.6 
6.4 
7.2 
8.0 

20 

21 
22 
23 
24 

9.42232 
9.42278 
9.42324 
9.42370 
9.42416 

46 
46 
46 
46 
45 

9.43806 
9.43855 
9.43905 
9.43954 
9.44004 

49 
50 
49 
50 
4Q 

0.56194 
0.56145 
0.56095 
0.56046 
0.55996 

9.98426 
9.98422 
9.98419 
9.98415 
9.98412 

4 
3 
4 
3 

40 

39 
38 
37 
36 

20 
30 
40 
50 

16.3 
24.5 
32.7 
40.8 

16.0 
24.0 
32.0 
40.0 

25 
26 
27 
28 
29 

9.42461 
9.42507 
9.42553 
9.42599 
9.42644 

46 
46 
46 
45 
4fi 

9.44053 
9.44102 
9.44151 
9.44201 
9.44250 

49 
49 
50 
49 

0.55947 
0.55898 
0.55849 
0.55799 
0.55750 

9.98409 
9.98405 
9.98402 
9.98398 
9.98395 

4 
3 
4 
3 

35 
34 
33 
32 
31 

6 

7 
8 

47 

4.7 
5.5 
6.3 

46 

4.6 
5.4 
6.1 

30 

31 
32 
33 
34 

9.42690 
9.42735 
9.42781 
9.42826 
9.42872 

45 
46 
45 
46 

AK. 

9.44299 
9.44348 
9.44397 
9.44446 
9.44495 

49 
49 
49 
49 
4Q 

0.55701 
0.55652 
0.55603 
0.55554 
0.55505 

9.98391 
9.98388 
9.98384 
9.98381 
9.98377 

3 
4 
3 

4 

4 

30 

29 
28 
27 
26 

9 

10 
20 
30 
40 
50 

7.1 
7.8 
15.7 
23.5 
31.3 
392 

6.9 
7.7 
15.3 
23.0 
30.7 
38  3 

35 
36 
37 
38 
39 

9.42917 
9.42962 
9.43008 
9.43053 
9.43098 

45 
46 
45 
45 

9.44544 
9.44592 
9.44641 
9.44690 
9.44738 

48 
49 
49 
48 

0.55456 
0.55408 
0.55359 
0.55310 
0.55262 

9.98373 
9.98370 
9.98366 
9.98363 
9.98359 

3 
4 
3 

4 

25 
24 
23 
22 
21 

6 

45 

4.5 

44 
4.4 

40 

41 
42 
43 
44 

9.43143 
9.43188 
9.43233 
9.43278 
9.43323 

45 
45 
45 

45 
44 

9.44787 
9.44836 
9.44884 
9.44933 
9.44981 

49 
48 
49 

48 
40 

0.55213 
0.55164 
0.55116 
0.55067 
0.55019 

9.98356 
9.98352 
9.98349 
9.98345 
9.98342 

4 
3 
4 
3 

20 

19 
18 
17 
16 

8 

9 
10 
20 
30 

6.0 
6.8 
7.5 
15.0 
TO.fi 

5.9 
6.6 
7.3 
14.7 
22.0 

45 

46 

47 
48 
49 

9.43367 
9.43412 
9.43457 
9.43502 
9.43546 

45 
45 
45 
44 
4c 

9.45029 
9.45078 
9.45126 
9.45174 
9.45222 

49 
48 
48 
48 

0.54971 
0.54922 
0.54874 
0.54826 
0.54778 

9.98338 
9.98334 
9.98331 
9.98327 
9.98324 

4 
3 
4 
3 

4 

15 
14 
13 
12 
11 

40 
50 

30.0 
37.5 

4 

29.3 
36.7 

3 

50 

51 
52 
53 
54 

9.43591 
9.43635 
9.43680 
9.43724 
9.43769 

44 

45 
44 
45 
44 

9.45271 
9.45319 
9.45367 
9.45415 
9.45463 

48 
48 
48 
48 
48 

0.54729 
0.54681 
0.54633 
0.54585 
0.54537 

9.98320 
9.98317 
9.98313 
9.98309 
9.98306 

3 
4 
4 
3 
4 

10 

9 
8 
7 
6 

6 
7 
8 
9 
10 

0.4 
0.5 
0.5 
0.6 
0.7 

0.3 
0.4 
0.4 
0.5 
0.5 

55 
56 
57 
58 
59 

9.43813 
9.43857 
9.43901 
9.43946 
9.43990 

44 

44 
45 
44 
44 

9.45511 
9.45559 
9.45606 
9.45654 
9.45702 

48 
47 
48 
48 
48 

0.54489 
0.54441 
0.54394 
0.54346 
0.54298 

9.98302 
9.98299 
9.98295 
9.98291 
9.98288 

3 

4 
4 
3 
4 

5 
4 
3 
2 
1 

20 
30 
40 
50 

1.3 
2.0 
2.7 
3.3 

1.0 
1.5 
2.0 
2.5 

60 

9.44034 

9.45750 

0.54250 

9.98284 

0 

L.  Cos. 

d. 

j.  Cotg. 

d.c. 

..Tang. 

L.  Sin. 

d. 

' 

P.  P. 

74° 


1044 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
16° 


/ 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P.  P 

0 

1 

2 
3 
4 

9.44034 
9.44078 
9.44122 
9.44166 
9.44210 

44 
44 
44 
44 

9.45750 
9.45797 
9.45845 
9.45892 
9.45940 

47 

48 
47 

48 

0.54250 
0.54203 
0.54155 
0.54108 
0.54060 

9.98284 
9.98281 
9.98277 
9.98273 
9.98270 

3 
4 
4 
3 

60 

59 
58 
57 
56 

6 
7 

48 

4.8 
5  6 

47 

4.7 
5  5 

5 
6 

7 
8 
9 

9.44253 
9.44297 
9.44341 
9.44385 
9.44428 

44 

44 
44 
43 

AA 

9.45987 
9.46035 
9.46082 
9.46130 
9.46177 

48 
47 
48 
47 

0.54013 
0.53965 
0.53918 
0.53870 
0.53823 

9.98266 
9.98262 
9.98259 
9.98255 
9.98251 

4 
3 
4 
4 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

6.4 
7.2 
8.0 
16.0 
24.0 

6.3 
7.1 

7.8 
15.7 
23.5 

10 

11 
12 
13 
14 

9.44472 
9.44516 
9.44559 
9.44602 
9.44646 

44 
43 
43 
44 
43 

9.46224 
9.46271 
9.46319 
9.46366 
9.46413 

47 
48 
47 
47 

0.53776 
0.53729 
0.53681 
0.53634 
0.53587 

9.98248 
9.98244 
9.98240 
9.98237 
9.98233 

4 
4 
3 
4 
4 

50 

49 
48 
47 
46 

40 
50 

32.0 
40.0 

4R 

31.3 
39.2 

45 

15 
16 

17 
18 
19 

9.44689 
9.44733 
9.44776 
9.44819 
9.44862 

44 
43 
43 
43 

9.46460 
9.46507 
9.46554 
9.46601 
9.46648 

47 
47 
47 
47 

0.53540 
0.53493 
0.53446 
0.53399 
0.53352 

9.98229 
9.98226 
9.98222 
9.98218 
9.98215 

3 
4 
4 
3 

45 
44 
43 
42 
41 

6 
7 

8 
9 
10 

4.6 
5.4 
6.1 
6.9 
7.7 

4.5 
5.3 
6.0 
6.8 
7.5 

20 

21 
22 
23 
24 

9.44905 
9.44948 
9.44992 
9.45035 
9.45077 

43 
44 
43 
42 

9.46694 
9.46741 
9.46788 
9.46835 
9.46881 

47 
47 
47 
46 

0.53306 
0.53259 
0.53212 
0.53165 
0.53119 

9.98211 
9.98207 
9.98204 
9.98200 
9.98196 

4 
3 
4 
4 

40 

39 
38 
37 
36 

20 
30 
40 
50 

15.3 
23.0 
30.7 
38.3 

15.0 
22.5 
30.0 
37.5 

26 
27 
28 
29 

9.45120 
9.45163 
9.45206 
9.45249 
9.45292 

43 
43 
43 
43 

9.46928 
9.46975 
9.47021 
9.47068 
9.47114 

47 
46 
47 
46  N 

0.53072 
0.53025 
0.52979 
0.52932 
0.52886 

9.98192 
9.98189 
9.98185 
9.98181 
9.98177 

3 

4 
4 
4 

35 
34 
33 
32 
31 

6 
7 
8 

44 

4.4 
5.1 
5.9 

43 

4.3 

5.0 
5.7 

30 

31 
32 
33 
34 

9.45334 
9.45377 
9.45419 
9.45462 
9.45504 

43 
42 
43 

42 
40 

9.47160 
9.47207 
9.47253 
9.47299 
9.47346 

47 
46 
46 
47 

0.52840 
0.52793 
0.52747 
0.52701 
0.52654 

9.98174 
9.98170 
9.98166 
9.98162 
9.98159 

4 
4 
4 
3 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

6.6 
7.3 
14.7 
22.0 
29.3 
36  7 

6.5 
7.2 
14.3 
21.5 

28.7 
35  g 

35 
36 
37 
38 
39 

9.45547 
9.45589 
9.45632 
9.45674 
9.45716 

42 
43 
42 
42 
40 

9.47392 
9.47438 
9.47484 
9.47530 
9.47576 

46 
46 
46 
46 

0.52608 
0.52562 
0.52516 
0.52470 
0.52424 

9.98155 
9.98151 
9.98147 
9.98144 
9.98140 

4 
4 
3 
4 
4 

25 
24 
23 
22 
21 

6 

7 

42 

4.2 

4  Q 

41 

4.1 

4  Q 

40 

41 
42 
43 
44 

9.45758 
9.45801 
9.45843 
9.45885 
9.45927 

43 

42 
42 
42 

9.47622 
9.47668 
9.47714 
9.47760 
9.47806 

46 
46 
46 
46 

0.52378 
0.52332 
0.52286 
0.52240 
0.52194 

9.98136 
9.98132 
9.98129 
9.98125 
9.98121 

4 
3 
4 
4 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

5.6 
6.3 
7.0 
14.0 
?1  0 

5.5 
6.2 
6.8 
13.7' 
20.5 

45 
46 
47 
48 
49 

9.45969 
9.46011 
9.46053 
9.46095 
9.46136 

42 
42 
42 
41 

9.47852 
9.47897 
9.47943 
9.47989 
9.48035 

45 
46 
46 

46 

0.52148 
0.52103 
0.52057 
0.52011 
0.51965 

9.98117 
9.98113 
9.98110 
9.98106 
9.98102 

4 
3 
4 
4 

15 
14 
13 
12 
11 

40 
50 

2S.O 
35.0 

4 

27.3 
34.2 

3 

50 

51 
52 
53 
54 

9.46178 
9.46220 
9.46262 
9.46303 
9.46345 

42 
42 
41 
42 
41 

9.48080 
9.48126 
9.48171 
9.48217 
9.48262 

46 
45 
46 
45 
45 

0.51920 
0.51874 
0.51829 
0.51783 
0.51738 

9.98098 
9.98094 
9.98090 
9.98087 
9.98083 

4 
4 
3 

4 
4 

10 

9 

8 
7 
6 

6 
7 
8 
9 
10 

0.4 
0.5 
0.5 
0.6 
0.7 

0.3 
0.4 
0.4 
0.5 
0.5 

55 
56 
57 
58 
59 

9.46386 
9.46428 
9.46469 
9.46511 
9.46552 

42 
41 
42 
41 
40 

9.48307 
8.48353 
9.48398 
9.48443 
9.48489 

46 
45 
45 
46 

0.51693 
0.51647 
0.51602 
0.51557 
0.51511 

9.98079 
9.98075 
9.98071 
9.98067 
9.98063 

4 
4 
4 
4 

5 
4 
3 
2 
1 

20 
30 
40 
50 

1.3 
,2.0 
2.7 
3.3 

1.0 
1.5 
2.0 
2.5 

60 

9.46594 

9.48534 

0.51466 

9.98060 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P. 

73° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
17° 


1045 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

1 

P 

.P 

0 

1 

2 
3 
4 

9.46594 
9.46635 
9.46676 
9.46717 
9.46758 

41 
41 
41 
41 

42 

9.48534 
9.48579 
9.48624 
9.48669 
9.48714 

45 

45 
45 
45 

4c 

0.51466 
0.51421 
0.51376 
0.51331 
0.51286 

9.98060 
9.98056 
9.98052 
9.98048 
9.98044 

4 
4 

4 
4 

60 

59 

58 
57    K 

5<>  5 

A 

< 

5 

.5 

44 

4.4 

5 
6 

7 
8 
9 

IF 

11 

12 
13 
14 

9.46800 
9.46841 
9.46882 
9.46923 
9.46964 
9.47005 
9.47045 
9.47086 
9.47127 
9.47168 

41 
41 
41 
41 
41 
40 
41 
41 
41 
41 

9.48759 
9.48804 
9.48849 
9.48894 
9.48939 
9.48984 
9.49029 
9.49073 
9.49118 
9.49163 

45 
45 
45 
45 
45 
45 
44 
45 
45 
44 

0.51241 
0.51196 
0.51151 
0.51106 
0.51061 
0.51016 
0.50971 
0.50927 
0.50882 
0.50837 

9.98040 
9.98036 
9.98032 
9.98029 
9.98025 
9.98021 
9.98017 
9.98013 
9.98009 
9.98005 

4 
4 
3 
4 
4 
4 
4 
4 
4 

55    8 
54    9 
53   10 
52   20 
51   30 
50   40 
49   50 
48 
47 
46 

e 
e 

if 

21 

3( 

s: 

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4 

5.9 
6.6 
7.3 
14.7 
22.0 
29.3 
36.7 

3 

15 
16 

17 
18 
19 

9.47209 
9.47249 
9.47290 
9.47330 
9.47371 

40 
41 
40 
41 
4f> 

9.49207 
9.49252 
9.49296 
9.49341 
9.49385 

45 
44 
45 
44 
4c 

0.50793 
0.50748 
0.50704 
0.50659 
0.50615 

9.98001 
9.97997 
9.97993 
9.97989 
9.97986 

4 
4 
4 
3 

45 
44 
43 
42 
41    ] 

6 

7 

8 
9 
0 

4 

6 
5 
6 
7 

3 
0 

7 
5 
2 

20 

21 
22 
23 
24 

9.47411 
9.47452 
9.47492 
9.47533 
9.47573 

41 
40 
41 
40 
40  ' 

9.49430 
9.49474 
9.49519 
9.49563 
9.49607 

44 
45 
44 
44 
4c 

0.50570 
0.50526 
0.50481 
0.50437 
0.50393 

9.97982 
9.97978 
9.97974 
9.97970 
9.97966 

4 
4 
4 
4 

40     ; 

39   i 

38     4 
37     £ 
36 

0 

0 
0 
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14 

21 

28 
35 

3 
5 

7 
8 

25 
26 
27 
28 
29 

9.47613 
9.47654 
9.47694 
9.47734 
9.47774 

41 
40 
40 
40 
40 

9.49652 
9.49696 
9.49740 
9.49784 
9.49828 

44 
44 
44 
44 
44 

0.50348 
0.50304 
0.50260 
0.50216 
0.50172 

9.97962 
9.97958 
9.97954 
9.97950 
9.97946 

4 
4 
4 
4 

35 
34 
33    6 
32    7 

31    9 

4 
4 
4 
1 

2 

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41 
4.1 
4.8 
5.5 

30 

31 
32 
33 
34 

9.47814 
9.47854 
9.47894 
9.47934 
9.47974 

40 
40 
40 
40 

9.49872 
949916 
9.49960 
9.50004 
9.50048 

44 
44 
44 
44 

0.50128 
0.50084 
0.50040 
0.49996 
0.49952 

9.97942 
9.97938 
9.97934 
9.97930 
9.97926 

4 

4 
4 

4 

30   .« 
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28    on 
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6.8 
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35 
36 
37 
38 
39 

9.48014 
9.48054 
9.48094 
9.48133 
9.48173 

40 
40 
39 
40 

9.50092 
9.50136 
9.50180 
9.50223 
9.50267 

44 
44 
43 
44 

0.49908 
0.49864 
0.49820 
0.49777 
0.49733 

9.97922 
9.97918 
9.97914 
9.97910 
9.97906 

4 
4 
4 
4 

25  1 
24 
23 
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4 

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0 

.0 

7 

39 

3.9 
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40 

41 
42 
43 
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9.48213 
9.48252 
9.48292 
9.48332 
9.48371 

39 
40 
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39 

9.50311 
9.50355 
9.50398 
9.50442 
9.50485 

44 
43 

44 
43 

0.49689 
0.49645 
0.49602 
0.49558 
0.49515 

9.97902 
9.97898 
9.97894 
9.97890 
9.97886 

4 
4 
4 
4 
4 

20    g 

19    9 
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£ 
€ 
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5.2 
5.9 
6.5 
13.0 
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45 
46 
47 
48 
49 

9.48411 
9.48450 
9.48490 
9.48529 
9.48568 

39 
40 
39 
39 

9.50529 
9.50572 
9.50616 
9.50659 
9.50703 

43 
44 
43 
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0.49471 
0.49428 
0.49384 
0.49341 
0.49297 

9.97882 
9.97878 
9.97874 
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4 
4 
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15   40 
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9.48607 
9.48647 
9.48686 
9.48725 
9.48764 

40 
39 
39 
39 

9.50746 
9.50789 
9.50833 
9.50876 
9.50919 

43 
44 
43 
43 

0.49254 
0.49211 
0.49167 
0.49124 
0.49081 

9.97861 
9.97857 
9.97853 
9.97849 
9.97845 

4 
4 
4 
4 
4 

10   6  ( 
9   7  ( 
8   8  ( 
7   9  ( 
6  |10  ( 

).5 
).6 
).7 

).8 
).8 

0 
0. 
0. 
0. 
0. 

4  0.3 
5  0.4 
5  0.4 
6  0.5 
7  0.5 

55 
56 
57 
58 
59 

9.48803 
9.48842 
9.48881 
9.48920 
9.48959 

39 
39 

39 
39 

9.50962 
9.51005 
9.51048 
9.51092 
9.51135 

43 
43 
44 
43 
43 

0.49038 
0.48995 
0-.48952 
0.48908 
0.48865 

9.97841 
9.97837 
9.97833 
9.97829 
9.97825 

4 
4 
4 

4 
4 

5  2u  J 
4  30  '< 

0   40   £ 

2  50  4 
1 

./ 
5.5 
,.3 

L2 

1. 

2. 
2. 
3. 

3  1.0 
0  1.5 
7  2.0 
3  2.5 

60 

9.48998 

9.51178 

0.48822 

9.97821 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

'  1 

P 

1J. 

72° 

1046  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

18° 


t 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P 

0 

1 

2 
3 
4 

9.48998 
9.49037 
9.49076 
9.49115 
9.49153 

39 
39 
39 
38 
39 

9.51178 
9.51221 
9.51264 
9.51306 
9.51349 

43 
43 
42 
43 
43 

0.48822 
0.48779 
0.48736 
0.48694 
0.48651 

9.97821 
9.97817 
9.97812 
9.97808 
9.97804 

4 
5 
4 
4 

60 

59 
58 
57 
56 

6 

7 

43 

4.3 
5  0 

42 

4.2 
4  9 

5 
6 

7 
8 
9 

9.49192 
9.49231 
9.49269 
9.49308 
9.49347 

39 
38 
39 
39 

38 

9.51392 
9.51435 
9.51478 
9.51520 
9.51563 

43 
43 
42 
43 
40 

0.48608 
0.48565 
0.48522 
0.48480 
0.48437 

9.97800 
9.97796 
9.97792 
9.97788 
9.97784 

4 
4 
4 
4 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

5.7 
6.5 
7.2 
14.3 
21.5 

5.6 
6.3 
7.0 
14.0 
21.0 

10 

11 
12 
13 
14 

9.49385 
9.49424 
9.49462 
9.49500 
9.49539 

39 
38 
38 
39 
38 

9.51606 
9.51648 
9.51691 
9.51734 
9.51776 

42 
43 
43 
42 

XQ 

0.48394 
0.48352 
0.48309 
0.48266 
0.48224 

9.97779 
9.97775 
9.97771 
9.97767 
9.97763 

4 

4 
4 
4 

50 

49 
48 
47 
46 

40 
50 

28.7 
35.8 

4 

28.0 
35.0 

| 

15 
16 
17 
18 
19 

9.49577 
9.49615 
9.49654 
9.49692 
9.49730 

38 
39 
38 
38 
38 

9.51819 
9.51861 
9.51903 
9.51946 
9.51988 

42 
42 
43 
42 

0.48181 
0.48139 
0.48097 
0.48054 
0.48012 

9.97759 
9.97754 
9.97750 
9.97746 
9.97742 

5 

4 

4 
4 

45 
44 
43 

42 
41 

] 

6   4 
7   4 
8   5 
9   6 
0   6 

1 
8 
5 
2 
8 

20 

21 
22 
23 
24 

9.49768 
9.49806 
9.49844 
9.49882 
9.49920 

38 

38 
38 
38 
38 

9.52031 
9.52073 
9.52115 
9.52157 
9.52200 

42 
42 
42 
43 

49 

0.47969 
0.47927 
0.47885 
0.47843 
0.47800 

9.97738 
9.97734 
9.97729 
9.97725 
9.97721 

4 
5 
4 

t 

40 

39 
38 
37 
36 

il 
I 
-I 
1 

0  13 
0  20 
0  27 
0  34 

7 
5 
3 
2 

25 
26 
27 
28 
29 

9.49958 
9.49996 
9.50034 
9.50072 
9.50110 

38 
38 
38 
38 
38 

9.52242 
9.52284 
9.52326 
9.52368 
9.52410 

42 
42 
42 
42 
42 

0.47758 
0.47716 
0.47674 
0.47632 
0.47590 

9.97717 
9.97713 
9.97708 
9.97704 
9.97700 

4 
5 
4 
4 
4 

35 
34 
33 
32 
31 

6 

7 
8 

39 

3.9 
4.6 
5.2 

38 

3.8 
4.4 
5.1 

30 

31 
32 
33 
34 

9.50148 
9.50185 
9.50223 
9.50261 
9.50298 

37 
38 
38 
37 
38 

9.52452 
9.52494 
9.52536 
9.52578 
9.52620 

42 
42 
42 
42 
41 

0.47548 
0.47506 
0.47464 
0.47422 
0.47380 

9.97696 
9.97691 
9.97687 
9.97683 
9.97679 

5 

4 
4 
4 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

6.5 
13.0 
19.5 
26.0 
32  5 

6.3 
12.7 
19.0 
25.3 
31  7 

35 
36 
37 
38 
39 

9.50336 
9.50374 
9.50411 
9.50449 
9.50486 

38 
37 
38 
37 
37 

9.52661 
9.52703 
9.52745 
9.52787 
9.52829 

42 
42 
42 
42 

0.47339 
0.47297 
0.47255 
0.47213 
0.47171 

9.97674 
9.97670 
9.97666 
9.97662 
9.97657 

4 
4 
4 
5 

25 
24 
23 
22 
21 

6 

37 

3.7 

36 

3.6 

40 
41 

42 
43 
44 

9.50523 
9.50561 
9.50598 
9.50635 
9.50673 

38 
37 
37 
38 
37 

9.52870 
9.52912 
9.52953 
9.52995 
9.53037 

42 
41 
42 
42 

0.47130 
0.47088 
0.47047 
0.47005 
0.46963 

9.97653 
9.97649 
9.97645 
9.97640 
9.97636 

4 
4 
5 
4 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

4.9 
5.6 
6.2 
12.3 
18.5 

4.8 
5.4 
6.0 
12.0 
18.0 

45 
46 
47 
48 
49 

9.50710 
9.50747 
9.50784 
9.50821 
9.50858 

37 
37 
37 
37 

38 

9.53078 
9.53120 
9.53161 
9.53202 
9.53244 

42 
41 
41 
42 

0.46922 
0.46880 
0.46839 
0.46798 
0.46756 

9.97632 
9.97628 
9.97623 
9.97619 
9.97615 

4 
5 
4 
4 

15 
14 
13 
12 
11 

40 
50 

24.7 
30.8 

5 

24.0 
30.0 

4 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 
60 

9.50896 
9.50933 
9.50970 
9.51007 
9.51043 
9.51080 
9.51117 
9.51154 
9.51191 
9.51227 
9.51264 

37 
37 
37 
36 
37 
37 
37 
37 
36 
37 

9.53285 
9.53327 
9.53368 
9.53409 
9.53450 
9.53492~ 
9.53533 
9.53574 
9.53615 
9.53656 
9.53697 

42 
41 
41 
41 
42 
41 
41 
41 
41 
41 

0.46715 
0.46673 
0.46632 
0.46591 
0.46550 
0.46508 
0.46467 
0.46426 
0.46385 
0.46344 
0.46303 

9.97610 
9.97606 
9.97602 
9.97597 
9.97593 
9.97589 
9.97584 
9.97580 
9.97576 
9.97571 
9.97567 

4 
4 
5 
4 
4 
5 
4 
4 
5 
4 

10 

9 
8 
7 
6 
5 
4 
3 
2 
1 
0 

6 
7 
8 
9 
10 
20 
30 
40 
50 

0.5 
0.6 
0.7 
0.8 
0.8 
1.7 
2.5 
3.3 
4.2 

0.4 
0.5 
0.5 
0.6 
0.7 
1.3 
2.0 
2.7 
3.3 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P 

71° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
19° 


1047- 


1 

L.  Sin. 

d. 

.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P. 

0 

2 
3 

4 

9.51264 
9.51301 
9.51338 
9.51374 
9.51411 

37 
37 
36 
37 

Ofi 

9.53697 
9.53738 
9.53779 
9.53820 
9.53861 

41 
41 
41 
41 
41 

0.46303 
0.46262 
0.46221 
0.46180 
0.46139 

9.97567 
9.97563 
9.97558 
9.97554 
9.97550 

4 
5 

4 
4 

60 

59 
58 
57 
56 

6 

7 

41 

4.1 

4  8 

40 

4.0 

4  7 

5 

6 

1  7 
8 
9 

9.51447 
9.51484 
9.51520 
9.51557 
9.51593 

37 
36 
37 
36 

9.53902 
9.53943 
9.53984 
9.54025 
9.54065 

41 
41 
41 
40 
4.1 

0.46098 
0.46057 
0.46016 
0.45975 
0.45935 

9.97545 
9.97541 
9.97536 
9.97532 
9.97528 

4 
5 
4 
4 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

5.5 
6.2 
6.8 
13.7 
20.5 

5.3 
6.0 
6.7 
13.3 
20.0 

10 

11 
12 
13 
14 

9.51629 
9.51666 
9.51702 
9.51738 
9.51774 

37 
36 
36 
36 

9.54106 
9.54147 
9.54187 
9.54228 
9.54269 

41 
40 
41 
41 

0.45894 
0.45853- 
0.45813 
0.45772 
0.45731 

9.97523 
9.97519 
9.97515 
9  97510 
9.97506 

4 
4 
5 
4 

50 

49 
48 
47 
46 

40 
50 

27.3 
34.2 

3< 

26.7 
33.3 

i 

15 
16 
17 
18 
19 

9.51811 
9.51847 
9.51883 
9.51919 
9.51955 

36 
36 
36 
36 

9.54309 
9.54350 
9.54390 
9.54431 
9.51471 

41 

40 
41 
40 

0.45691 
0.45650 
0.45610 
0.45569 
0.45529 

9.97501 
9.97497 
9.97492 
9.97488 
9.97484 

4 
5 
4 
4 

45 
44 
43 
42 

41 

1 

6   3 
7   4 
8  5 
9  5 
0   6 

9 
6 
2 
9 
5 

20 

21 
22 
23 
24 

9.51991 
9.52027 
9.52063 
9.52099 
9.52135 

36 
36 
36 
36 

9.54512 
9.54552 
9.54593 
9.54633 
9.54673 

40 
41 

40 
40 

0.45488 
0.45448 
0.45407 
0.45367 
0.45327 

9.97479 
9.97475 
9.97470 
9.97466 
9.97461 

4 
5 

4 
5 
4 

40 

39 
38 
37 
36 

2 
2 
4 
i 

0  13 
0  19 
0  26 
.0  32 

0 
5 
0 
.5 

25 
26 

27 
28 
29 

9.52171 
9.52207 
9.52242 
9.52278 
9.52314 

36 
35 
36 
36 

9.54714 
9.54754 
9.54794 
9.54835 
9.54875 

40 
40 
41 
40 

0.45286 
0.45246 
0.45206 
0.45165 
0.45125 

9.97457 
9.97453 
9.97448 
9.97444 
9.97439 

4 
5 
4 
5 
4 

35 
34 
33 
32 
31 

6 
7 
8 

Q 

37 

3.7 
4.3 
4.9 

C  fi 

36 

3.6 
4.2 
4.8 
fi  4. 

30 
31 
32 
33 
34 

9.52350 
9.52385 
9.52421 
9.52456 
9.52492 

35 

36 
35 
36 

9.54915 
9.54955 
9.54995 
9.55035 
9.55075 

40 
40 
40 
40 
40 

0.45085 
0.45045 
0.45005 
0.44965 
0.44925 

9.97435 
9.97430 
9.97426 
9.97421 
9.97417 

5 
4 
5 
4 
5 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

6.2 
12.3 
18.5 
24.7 
30.8 

6.0 
12.0 
18.0 
24.0 
30.0 

35 
36 

37 
38 

Li. 

40 
41 
42 
43 
44 

9.52527 
9.52563 
9.52598 
9.52634 
9.52669 
9.52705 
9,52740 
9.52775 
9.52811 
9.52846 

36 
35 
36 
35 
36 
35 
35 
36 
35 

9.55115 
9.55155 
9.55195 
955235 
9.55275 
9.55315 
9.55355 
9.55395 
9.55434 
9.55474 

40 
40 
40 
40 
40 
40 
40 
39 
40 
4ft 

0.44885 
0.44845 
0.44805 
0.44765 
0.44725 
1)744685 
0.44645 
0.44605 
0.44566 
0.44526 

9.97412 
9.97408 
9.97403 
9.97399 
9.97394 
9.97390 
9.97385 
9.97381 
9.97376 
9.97372 

4 

5 
4 
5 
4 
5 
4 
5 
4 
5 

25 
24 
23 
22 
21 
20 
19 
18 
17 
16 

6 
7 

8 
9 
10 

20 
30 

35 
3.5 
4.1 
4.7 
5.3 
5.8 
11.7 
17.5 

34 

3.4 
4.0 
4.5 
5.1 
5.7 
11.3 
17.0 

46 

47 
48 
49 

9.52881 
9.52916 
9.52951 
9.52986 
9.53021 

35 
35 
35 
35 

9.55514 
9.55554 
9.55593 
9.55633 
9.55673 

40 
39 
40 
40 

on 

0.44486 
0.44446 
0.44407 
0.44367 
0.44327 

9.97367 
9.97363 
9.97358 
9.97353 
9.97349 

4 
5 
5 

4 
5 

15 
14 
13 
12 
11 

40 
50 

23.3 
29.2 

5 

22.7 
28.3 

4 

50 

51 
52 
53 
54 

9.53056 
9.53092 
9.53126 
9.53161 
9.53196 

36 
34 
35 
35 

9.55712 
9.55752 
9.55791 
9.55831 
9.55870 

40 
39 
40 
39 

0.44288 
0.44248 
0.44209 
0.44169 
0.44130 

9.97344 
9.97340 
9.97335 
9.97331 
9.97326 

4 
5 
4 
5 
4 

$0 

9 

8 
7 
6 

6 
7 
8 
9 
10 

0.5 
0.6 
0.7 
0.8 
0.8 

0.4 
0.5 
0.5 
0.6 
0.7 

55 
1  56 

I  57 
1  58 
1  59 

9.53231 
9.53266 
9.53301 
9.53336 
9.53370 

35 
35 
35 
35 
34 

9.55910 
9.S5&49 
9.55989 
9.56028 
9.56067 

39 
40 
39 
39 
4A 

0.44090 
0.44051 
0.44011 
0.43972 
0.43933 

9.97322 
9.97317 
9.97312 
9.97308 
9.97303 

5 

5 
4 
5 
4 

5 
4 
3 
2 

1 

20 
30 
40 
50 

1.7 
2.5 
3.3 
4.2 

1.3 
2.0 
2.7 
3.3 

60 

9.53405 

9.56107 

j  '  ' 

0.43893 

9.97299 
L  Sin 

d 

0 

/ 

P  V 

1 

1— 

70° 

1048  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

20° 


1 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P.P 

0 

1 

2 
3 
4 

9.53405 
9.53440 
9.53475 
9.53509 
9.53544 

35 
35 
34 
35 

9.56107 
9.56146 
9.56185 
9.56224 
9.56264 

39 
39 
39 
40 

0.43893 
0.43854 
0.43815 
0.43776 
0.43736 

9.97299 
9.97294 
9.97289 
9.97285 
9.97280 

5 
5 
4 
5 

60 

59 
58 
57 
56 

6 

40 

4.0 

39 

3.9 

5 
6 

7 
8 
9 

9.53578 
9.53613 
9.53647 
9.53682 
9.53716 

35 
34 
35 
34 

oe 

9.56303 
9.56342 
9.56381 
9.56420 
9.56459 

39 
39 
39 
39 
qq 

0.43697 
0.43658 
0.43619 
0.43580 
0.43541 

9.97276 
9.97271 
9.97266 
9.97262 
9.97257 

5 
5 
4 
5 

55 
54 
53 
52 
51 

8 
9 
10 
20 

m 

5.3 
€.0 
6.7 
13.3 
20,0 

5.2 
5.9 
6.5 
13.0 
195 

10 

11 
12 
13 
14 

9.53751 
9.53785 
9.53819 
9.53854 
9.53888 

34 
34 
35 
34 

04 

9.56498 
9.56537 
9.56576 
9.56615 
9.56654 

39 
39 
39 
39 

qq 

0.43502 
0.43463 
0.43424 
0.43385 
0.43346 

9.97252 
9.97248 
9.97243 
9.97238 
9.97234 

4 
5 
5 
4 

50 

49 
48 
47 
46 

40 
50 

26.7 
33.3 

38 

26.0 
32.5 

37 

15 
16 
17 
18 
19 

9.53922 
9.53957 
9.53991 
9.54025 
9.54059 

35 
34 
34 
34 

04. 

9.56693 
9.56732 
9.56771 
9.56810 
9.56849 

39 
39 
39 
89 

qo 

0.43307 
0.43268 
0.43229 
0.43190 
0.43151 

9.97229 
9.97224 
9.97220 
9.97215 
9.97210 

5 

4 
5 
5 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

3.8 
4.4 
5.1 
5.7 
6.3 

3.7 
4.3 
4.9 
5.6 
6.2 

20 

21 
22 
23 
24 

9.54093 
9,54127 
9.54161 
9.54195 
9.54229 

34 
34 
34 
34 
34 

9.56887 
9.56926 
9.56965 
9.57004 
9.57042 

89 

39 
39 
38 

qq 

0.43113 
0.43074 
0.43035 
0.42996 
0.42958 

9.97206 
9.97201 
9.97196 
9.97192 
9.97187 

5 

5 
4 
5 

40 

39 
38 
37 
36 

20 
30 
40 
50 

12.V 
19.0 
25.3 
31.7 

12.3 

18.5 
24.7 
30.8 

25 
26 
27 

28 
29 

9.54263 
9.54297 
9.54331 
9.54365 
9.54399 

34 

34 
34 
34 

9.57081 
9.57120 
9.57158 
9.57197 
9.57235 

39 
38 
89 
38 

0.42919 
0.42880 
0.42842 
0.42803 
0.42765 

9.97182 
9.97178 
9.97173 
9.97168 
9.97163 

4 
5 
5 
5 

35 
34 
33 
32 
31 

3 
6   3 
7   4 
8  4 

.5 
.1 

.7 

30 

31 
32 
33 
34 

9.54433 
9.54466 
9.54500 
9.54534 
9.54567 

33 

34 
34 
33 

9.57274 
9.57312 
9.57351 
9.57389 
9.57428 

38 
39 
38 
39 

0.42726 
0.42688 
0.42649 
0.42611 
0.42572 

9.97159 
9.97154 
9.97149 
9.97145 
9.97140 

5 
5 
4 
5 

30 

29 
28 
27 
26 

• 

I 

i! 
>  i 
{ 

9   5 
LO   5 
JO  11 
JO  17 
10  23 
)0  29 

.3 

.8 
.7 
.5 
.3 
2 

35 
36 
37 
38 
39 

9.54601 
9.54635 
9.54668 
9.54702 
9.54735 

34 

33 
34 
33 

9.57466 
9.57504 
9.57543 
9.57581 
9.57619 

38 
39 
38 
38 

0.42534 
0.42496 
0.42457 
0.42419 
0.42381 

9.97135 
9.97130 
9.97126 
9.97121 
9.97116 

5 
4 
5 
5 

25 
24 
23 
22 
21 

6 

34 

3.4 

33 

3.3 

40 

41 

42 
43 
44 

9.54769 
9.54802 
9.54836 
9.54869 
9.54903 

33 
34 
33 
34 

OQ 

9.57658 
9.57696 
9.57734 
9.57772 
9.57810 

38 

38 
38 
88 

OQ 

0.42342 
0.42304 
0.42266 
0.42228 
0.42190 

9.97111 
9.97107 
9.97102 
9.97097 
9.97092 

4 
5 
5 
5 

20 

19 
18 
17 
16 

8 
9 

10 
20 
30 

4.5 
5.1 
5.7 
11.3 
17,0 

4.4 
5.0 
5.5 
11.0 
165 

45 
46 

47 
48 
49 

9.54936 
9.54969 
9.55003 
9.55036 
9.55069 

33 
34 
33 
33 

OQ 

9.57849 
9.57887 
9.57925 
9.57963 
9.58001 

38 
38 
38 
38 

00 

0.42151 
0.42113 
0.42075 
0.42037 
0.41999 

9.97087 
9.97083 
9.97078 
9.97073 
9.97068 

4 
5 
5 
5 

15 
14 
13 
12 
11 

40 
50 

22.7 
28.3 

5 

22.0 
27.5 

4 

50 

51 
52 
53 
54 

9.55102 
9.55136 
9.55169 
9.55202 
9.55235 

34 
33 
33 
33 

9.58039 
9.58077 
9.58115 
9.58153 
9.58191 

38 
38 
38 
38 

0.41961 
0.41923 
0.41885 
0.41847 
0.41809 

9.97063 
9.97059 
9.97054 
9.97049 
9.97044 

4 
5 
5 
5 

10 

9 
8 
7 
6 

6 
7 
8 
9 
10 

0.5 
0.6 
0.7 
0.8 
0.8 

0.4 
0.5 
0.5 
0.6 
0.7 

55 
56 
57 
58 
59 

9.55268 
9.55301 
9.55334 
9.55367 
9.55400 

33 
33 
33 
33 

OQ 

9.58229 
9.58267 
9.58304 
9.58342 
9.58380 

38 
37 
38 
38 

qa 

0.41771 
0.41733 
0.41696 
0.41658 
0.41620 

9.97039 
9.97035 
9.97030 
9.97025 
9.97020 

4 
5 
5 
5 

5 
4 
3 
2 

1 

20 
30 
40 
50 

1.7 
2.5 
3.3 
4.2 

1.3 
2.0 
2.7 
3.3 

60 

9.55433 

9.58418 

0.41582 

9.97015 

0 

L.Cos. 

d. 

j.  Cotg. 

d.c. 

L.Tang. 

L.Sin^ 

d. 

/ 

P.P. 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
21° 


1049 


L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P 

0 

1 

2 
3 
4 

9.55433 
9.55466 
9.55499 
9.55532 
9.55564 

33 
33 
33 
32 
33 

9.58418 
9.58455 
9.58493 
9.58531 
9.58569 

37 
38 
38 
38 
37 

0.41582 
0.41545 
0.41507 
0.41469 
0.41431 

9.97015 
9.97010 
9.97005 
9.97001 
9.96996 

5 
5 
4 
5 

60 

59 
58 
57 
56 

6 

7 

38 

3.8 

37 

3.7 

5 
6 

7 
8 
9 

9.55597 
9.55630 
9.55663 
9.55695 
9.55728 

33 
33 
32 
33 
33 

9.58606 
9.58644 
9.58681 
9.58719 
9.58757 

38 
37 
38 
38 

07 

0.41394 
0.41356 
0.41319 
0.41281 
0.41243 

9.96991 
9.96986 
9.96981 
9.96976 
9.96971 

5 
5 
5 
5 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

5.1 
5.7 
6.3 
12.7 
190 

4.9 
5.6 
6.2 
12.3 
18.5 

10 
11 

12 
13 
14 

9.55761 
9.55793 
9.55826 
9.55858 
9.55891 

32 
33 
32 
33 
32 

9.58794 
9.58832 
9.58869 
9.58907 
9.58944 

38 
37 
38 
37 
37 

0.41206 
0.41168 
0.41131 
0.41093 
0.41056 

9.96966 
9.96962 
9.96957 
9.96952 
9.96947 

4 
5 
5 
5 

50 

49 
48 
47 
46 

40 
50 

25.3 
31.7 

36 

24.7 
30.8 

33 

15 
16 
17 
18 
19 

9.55923 
9.55956 
9.55988 
9.56021 
9.56053 

33 

32 
33 
32 
qo 

9.58981 
9.59019 
9.59056 
9.59094 
9.59131 

38 
37 
38 
37 

0.41019 
0.40981 
0.40944 
0.40906 
0.40869 

9.96942 
9.96937 
9.96932 
9.96927 
9.96922 

5 
5 
5 
5 

45 
44 

43 
42 
41 

6 

7 
8 
9 
10 

3.6 
4.2 
4.8 
5.4 
6.0 

3.3 
3.9 
4.4 
5.0 
5.5 

20 

21 
22 
23 
24 

9.56085 
9.56118 
9.56150 
9.56182 
9.56215 

33 
32 
32 
33 

qo 

9.59168 
9.59205 
9.59243 
9.59280 
9.59317 

37 
38 
37 
37 
07 

0.40832 
0.40795 
0.40757 
0.40720 
0.40683 

9.96917 
9.96912 
9.96907 
9.96903 
9.96898 

5 
5 
4 
5 

40 

39 
38 
37 
36 

20 
30 
40 
50 

12.0 
18.0 
24.0 
30.0 

11.0 
16.5 
22.0 
27.5 

25 
26 
27 
28 
29 

9.56247 
9.56279 
9.56311 
9.56343 
9.56375 

32 
32 
32 
32 
33 

9.59354 
9.59391 
9.59429 
9.59466 
9.59503 

37 
38 
37 
37 
37 

0.40646 
0.40609 
0.40571 
0.40534 
0.40497 

9.96893 
9.96888 
9.96883 
9.96878 
9.96873 

5 
5 
5 
5 
5 

35 
34 
33 
32 
31 

3 

6   3 

7   3 
8   4 

2 

.2 
.7 
.3 

30 

31 
32 
33 
34 

9.56408 
9.56440 
9.56472 
9.56504 
9.56536 

32 

32 
32 
32 

00 

9.59540 
9.59577 
9.59614 
9.59651 
9.59688 

37 
37 
37 
37 
07 

0.40460 
0.40423 
0.40386 
0.40349 
0.40312 

9.96868  < 
9.96863 
9.96858 
9.96853 
9.96848 

5 
5 
5 
5 

30 

29 
28 
27 
26 

] 

f 

A 

F 

9   4 
0   5 
!0  10 
0  16 
0  21 
»0  26 

.8 
.3 
.7' 
.0 
.3 
7 

35 
36 
37 

38 
39 

9.56568 
9.56599 
9.56631 
9.56663 
9.56695 

31 
32 
32 
32 
32 

9.59725 
9.59762 
9.59799 
9.59835 
9.59872 

37 
37 
36 
37 
37 

0.40275 
0.40238 
0.40201 
0.40165 
0.40128 

9.96843 
9.96838 
9.96833 
9.96828 
9.96823 

5 

5 
5 
5 
5 

25 
24 
23 
22 
21 

6 

31 
3.1 

q  c 

6 

0.6 

0  7 

40 
41 
42 
43 
44 

9.56727 
9.56759 
9.56790 
9.56822 
9.56854 

32 
31 
32 
32 

00 

9.59909 
9.59946 
9.59983 
9.60019 
9.60056 

37 
37 
36 
37 
07 

0.40091 
0.40054 
0.40017 
0.39981 
0.39944 

9.96818 
9.96813 
9.96808 
9.96803 
9.96798 

5 

5 
5 
5 

K 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

4.1 

4.7 
5.2 
10.3 
15,5 

0.8 
0.9 
1.0 
2.0 
3.0 

45 

46 
47 
48 
49 

9.56886 
9.56917 
9.56949 
9.56980 
9.57012 

31 
32 
31 
32 

9.60093 
9.60130 
9.60166 
9.60203 
9.60240 

37 
36 
37 
37 

0.39907 
0.39870 
0.39834 
0.39797 
0.39760 

9.96793 
9.96788 
9.96783 
9.96778 
9.96772 

5 
5 
5 
6 

15 
14 
13 
12 
11 

40 
50 

20.7 
25.8 

5 

4.0 
5.0 

4 

50 

51 
52 
53 
54 

9.57044 
9.57075 
9.57107 
9.57138 
9.57169 

31 
32 
31 
31 

00 

9.60276 
9.60313 
9.60349 
9.60386 
9.60422 

37 
36 
37 
36 
37 

0.39724 
0.39687 
0.89651 
0.39614 
0.39578 

9.96767 
9.96762 
9.96757 
9.96752 
9.96747 

5 
5 
5 
5 
5 

10 

9 
8 
7 
6 

6 
7 
8 
9 
10 

0.5 
0.6 
0.7 
0.8 
0.8 

0.4 
0.5 
0.5 
0.6 
0.7 

55 
56 
57 
58 
59 

9.57201 
9.57232 
9.57264 
9.57295 
9.57326 

31 
32 
31 
31 

9.60459 
9.60495 
9.60532 
9.60568 
9.60605 

36 

37 
36 
37 
36 

0.39541 
0.39505 
0.39468 
0.39432 
0.39395 

9.96742 
9.96737 
9.96732 
9.96727 
9.96722 

5 
5 
5 
5 
5 

5 
4 
3 
2 
1 

20 
30 
40 
50 

l.V 
2.5 
3.3 
4.2 

1.3 
2.0 
2.7 
3.3 

60 

9.57358 

9.60641 

0.39359 

9.96717 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P. 

68° 


1050 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
22° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P. 

0 

1 

2 
3 
4 
5 
6 
7 
8 
9 

10 

11 
12 
13 
14 
15 
16 
17 
18 
19 

9.57358 
9.57389 
9.57420 
9.57451 
9.57482 

31 
31 
31 
31 
32 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
30 
31 
31 
31 
30 
31 
31 
31 
30 
31 
30 
31 
30 
31 
30 
31 
30 
31 
30 
31 
30 
30 
30 
31 
30 
30 
30 
31 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
30 
29 
30 
30 
30 

9.60641 
9.60677 
9.60714 
9.60750 
9.60786 

36 
37 
36 
36 
37 
36 
36 
36 
36 
37 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
36 
35 
36 
36 
36 
35 
36 
36 
36 
35 
36 
35 
36 
36 
35 
36 
35 
36 
35 
36 
35 
36 
35 
35 
36 
35 
35 
36 
35 
35 
35 
36 

y> 

35 
35 
35 

0.39359 
0.39323 
0.39286 
0.39250 
0.39214 

9.96717 
9.96711 
9.96706 
9.96701 
9.96696 

6 
5 
5 
5 
5 
5 
5 
5 
6 
5 
5 
5 
5 
5 
5 
6 
5 
5 
5 
5 
6 
5 
5 
5 
5 
6 
5 
5 
5 
5 
6 
5 
5 
5 
6 
5 
5 
5 
6 
5 
5 
6 
5 
5 
5 
6 
5 
5 
6 
5 
5 
6 
5 
5 
6 
5 
5 
6 
5 
5 

60 

59 
58 
57 
56 

6 
7 
8 
9 
10 
20 
30 
40 
50 

1 
\ 

•  .< 
J 

6 

7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

37 

3.7 
4.3 
4.9 
5.6 
6.2 
12.3 
18.5 
24.7 
30.8 

3 

6   3 

7   4 
8   4 
9   5 
0   5 
•0  11 
K>  17 
10  23 
>0  29 

32 

3.2 
3.7 
4.3 

4.8 
5.3 
10.7 
16.0 
21.3 
26.7 

30 

3.0 
3.5 
4.0 
4.5 
5.0 
10.0 
15.0 
20.0 
25.0 

6 

0.6 
0.7 
0.8 
0.9 
1.0 
2.0 
3.0 
4.0 
5.0 

36 

3.6 
4.2 
4.8 
5.4 
6.0 
12.0 
18.0 
24.0 
30.0 

5 
.5 
.1 

.7 
.3 

.8- 

5 
.3 
.2 

31 

3.1 
3.6 

4.1 
4.7 
5.2 
10.3 
15.5 
20.7 
25.8 

29 

2.9 
3.4 
3.9 
4.4 
4.8 
9.7 
14.5 
19.3 
24.2 

5 
0.5 
0.6 
0.7 
0.8 
0.8 
1.7 
2.5 
3.3 
4.2 

9.57514 
9.57545 
9.57576 
9.57607 
9.57638 
9.57669 
9.57700 
9.57731 
9.57762 
9.57793 

9.60823 
9.60859 
9.60895 
9.60931 
9.60967 
9.61004" 
9.61040 
9.61076 
9.61112 
9.61148 

0.39177 
0.39141 
0.39105 
0.39069 
0.39033 
0.38996 
0.38960 
0.38924 
0.38888 
0.38852 

9.96691 
9.96686 
9.96681 
9.96676 
9.96670 
9.96665 
9.96660 
9.96655 
9.96650 
9.96645 

55 
54 
53 
52 
51 
^0~ 
49 
48 
47 
46 

9.57824 
9.57855 
9.57885 
9.57916 
9.57947 

9.61184 
9.61220 
9.61256 
9.61292 
9.61328 

0.38816 
0.38780 
0.38744 
0.38708 
0.38672 

9.96640 
9.96634 
9.96629 
9.96624 
9.96619 

45 
44 
43 
42 

41 

20 

21 
22 
23 
24 

9.57978 
9.58008 
9.58039 
9.58070 
9.58101 
9.58131 
9.58162 
9.58192 
9.58223 
9.58253 
9.58284 
9.58314 
9.58345 
9.58375 
9.58406 

9.61364 
9.61400 
9.61436 
9.61472 
9.61508 

0.38636 
0.38600 
0.38564 
0.38528 
0.38492 

9.96614 
9.96608 
9.96603 
9.96598 
9.96593 

40 

39 
38 
37 
36 
lJ5~ 
34 
33 
32 
31 

~w 

29 
28 
27 
26 

25 
26 
27 
28 
29 

9.61544 
9.61579 
9.61615 
9.61651 
9.61687 

0.38456 
0.38421 
0.38385 
0.38349 
0.38313 

9.96588 
9.96582 
9.96577 
9.96572 
9.96567 

30 

31 
32 
33 
34 

9.6172t 
9.61758 
9.61794 
9.61830 
9.61865 

0.38278 
0.38242 
0.38206 
0.38170 
0.38135 

9.96562 
9.96556 
9.96551 
9.96546 
9.96541 

35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

9.58436 
9.58467 
9.58497 
9.58527 
9.58557 

9.61901 
9.61936 
9.61972 
9.62008 
9.62043 

0.38099 
0.38064 
0.38028 
0.37992 
0.37957 

9.96535 
9.96530 
9.96525 
9.96520 
9.96514 

25 
24 
23 
22 
21 

9.58588 
9.58618 
9.58648 
9.58678 
9.58709 

9.62079 
9.62114 
9.62150 
9.62185 
9.62221 

0.37921 
0.37886 
0.37850 
0.37815 
0.37779 

9.96509 
9.96504 
9.96498 
9.96493 
9.96488 

20 

19 
18 
17 
16 
15 
14 
13 
12 
11 

9.58739 
9.58769 
9.58799 
9.58829 
9.58859 
9.58889 
9.58919 
9.58949 
9.58979 
9.59009 

9.62256 
9.62292 
9.62327 
9.62362 
9.62398 

0.37744 
0.37708 
0.37673 
0.37638 
0.37602 

9.96483 
9.96477 
9.96472 
9.96467 
9.96461 

50 

51 
52 
53 
54 
~55~ 
56 
57 
58 
59 

9.62433 
9.62468 
9.62504 
9.62539 
9.62574 

0.37567 
0.37532 
0.37496 
0.37461 
0.37426 

9.96456 
9.96451 
9.96445 
9.96440 
9.96435 

10 

9 

8 
7 
6 

9.59039 
9.59069 
9.59098 
9.59128 
9.59158 

9.62609 
9.62645 
9.62680 
9.62715 
9.62750 

0.37391 
0.37355 
0.37320 
0.37285 
0.37250 

9.96429 
9.96424 
9.96419 
9.96413 
9.96408 

5 
4 
3 
2 
1 

60 

9.59188 

9.62785 

0.37215 

9.96403 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.tf. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P. 

67° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
23° 


1051 


/ 

L.  Sin.; 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P. 

0 

1 

2 
3 
4 

6 

7 
8 
9 

9.59188 
9.59218 
9.59247 
9.59277 
9.59307 

30 
29 
30 
30 
29 
30 
30 
29 
30 
29 

9.62785 
9.62820 
9.62855 
9.62890 
9.62926 

35 
35 
35 
36 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
34 
35 
35 
34 
35 
34 
35 
35 
34 
35 
34 
35 
34 
35 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
34 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 

0.37215 
0.37180 
0.37145 
0.37110 
0.37074 

9.96403 
9.96397 
9.96392 
9.96387 
9.96381 

6 
5 
5 
6 
5 
6 
5 
5 
6 
5 
6 
5 
5 
6 
5 
6 
5 
6 
5 
6 
5 
5 
6 
5 
6 
5  . 
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5 
6 
5 
6 
5 
6 
5 
6 
5 
6 
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5 
6 
5 
6 
5 
6 
6 
5 
6 
5 
6 
6 
5 
6 
5 
6 

60 

59 
58 
57 
56 

6 

7 
8 
9 
10 
20 
30 
40 
50 

1 

2 
3 
4 

5 

6 
7 
8 
9 
10 
20 
30 
40 
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6 
7 
8 
9 
10 
20 
30 
40 
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36 

3.6 
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7   4 
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7   3 

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0.6 
0.7 
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17.5 
23.3 
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1 

4 
0 
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7 
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29 

2.9 
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0.5 
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9.59366 
9.59396 
9.59425 
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9.62961 
9.62996 
9.63031 
9.63066 
9.63101 

0.37039 
0.37004 
0.36969 
0.36934 
0.36899 

9.96376 
9.96370 
9.96365 
9.96360 
9.96354 

55 
54 
53 
52 
51 

10 

11 

12 
13 
14 

9.59484 
9.59514 
9.59543 
9.59573 
9.59602 

30 
29 
30 
29 
30 
29 
29 
30 
29 
29 
30 
29 
29 
29 
29 
30 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
28 
29 
29 
29 
28 
29 
29 
29 
28 
29 
28 
29 
29 
28 
29 
28 
29 
28 
29 
28 
28 

9.63135 
9.63170 
9.63205 
9.63240 
9.63275 

0.36865 
0.36830 
0.36795 
0.36760 
0.36725 

9.96349 
9.96343 
9.96338 
9.96333 
9.96327 

50 

49 
48 
47 
46 

15 
16 
17 

18 
19 

9.59632 
9.59661 
9.59690 
9.59720 
9.59749 

9.63310 
9.63345 
9.63379 
9.63414 
9.63449 

0.36690 
0.36655 
0.36621 
0.36586 
0.36551 

9.96322 
9.96316 
9.96311 
9.96305 
9.96300 

45 
44 
43 
42 
41 
40 
39 
38 
37 
36 

20 

21 
22 
23 
24 

9.59778 
9.59808 
9.59837 
9.59866 
9.59895 

9.63484 
9.63519 
9.63553 
9.63588 
9.63623 

0.36516 
0.36481 
0.36447 
0.36412 
0.36377 

9.96294 
9.96289 
9.96284 
9.96278 
9.96273 

25 
26 
27 
28 
29 

31 
32 
33 
34 
35 
36 
37 
38 
39 

9.59924 
9.59954 
9.59983 
9.60012 
9.60041 

9.63657 
9.63692 
9.63726 
9.63761 
9.63796 

0.36343 
0.36308 
0.36274 
0.36239 
0.36204 

9.96267 
9.96262 
9.96256 
9.96251 
9.96245 

35 
34 
33 
32 
31 

9.60070 
9.60099 
9.60128 
9.60157 
9.60186 

9.63830 
9.63865 
9.63899 
9.63934 
9.63968 

0.36170 
0.36135 
0.36101 
0.36066 
0.36032 

9.96240 
9.96234 
9.96229 
9.96223 
9.96218 

30 

29 
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27 
26 
25 
24 
23 
22 
21 

9.60215 
9.60244 
9.60273 
9.60302 
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9.60359 
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9.60446 
9.60474 

9.64003 
9.64037 
9.64072 
9.64106 
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0.35997 
0.35963 
0.35928 
0.35894 
0.35860 

9.96212 
9.96207 
9.96201 
9.96196 
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40 

41 
42 
43 
44 

46 
47 
48 
49 

9.64175 
9.64209 
9.64243 
9.64278 
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0.35825 
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0.35757 
0.35722 
0.35688 

9.96185 
9.96179 
9.96174 
9.96168 
9.96162 

20 

19 
18 
17 
16 

9.60503 
9.60532 
9.60561 
9.60589 
9.60618 

9.64346 
9.64381 
9.64415 
9.64449 
9.64483 
9.64517 
9.64552 
9.64586 
9.64620 
9.64654 
9.64688 
9.64722 
9.64756 
9.64790 
9.64824 

0.35654 
0.35619 
0.35585 
0.35551 
0.35517 

9.96157 
9.96151 
9.96146 
9.96140 
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15 
14 
13 
12 
11 

50 

51 
52 
53 

54 

9.60646 
9.60675 
9.60704 
9.60732 
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0.35483 
0.35448 
0.35414 
0.35380 
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0.35278 
0.35244 
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9.96129 
9.96123 
9.96118 
9.96112 
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10 

9 
8 
7 
6 

55 
56 
57 
58 
59 

9.60789 
9.60818 
9.60846 
9.60875 
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9.96101 
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5 
4 
3 
2 
1 

60 

9.60931 

9.64858 

0.35142 

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d. 

L.  Cotg. 

d.c. 

L.Tang 

L.  Sin. 

d. 

P.  F. 

1052  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

24° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

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9.60931 
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34 
34 
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0.35142 
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0.35040 
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9.96073 
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6 
6 

60 

59 
58 
57 
56 

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7  4 

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9.61073 
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28 
28 
29 
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9.65028 
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34 
34 
34 
34 

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0.34972 
0.34938 
0.34904 
0.34870 
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9.96045 
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9.61270 
9.61298 
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28 
28 
28 
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9.65197 
9.65231 
9.65265 
9.65299 
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34 
34 
34 
34 

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0.34803 
0.34769 
0.34735 
0.34701 
0.34667 

9.96017 
9.96011 
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49 
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28 
29 
27 
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9.65366 
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34 
34 
33 
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0.34634 
0.34600 
0.34566 
0.34533 
0.34499 

9.95988 
9.95982 
9.95977 
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5 
6 
6 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2 
8 

3 
4 
4 

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20 

21 
22 
23 
24 

9.61494 
9.61522 
9.61550 
9.61578 
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28 
28 
28 
28 

00 

9.65535 
9.65568 
9.65602 
9.65636 
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33 
34 
34 

33 
04 

0.34465 
0.34432 
0.34398 
0.34364 
0.34331 

9.95960 
9.95954 
9.95948 
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6 
6 
6 
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40 

39 
38 
37 
36 

20 
30 
40 
50 

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14 
11 
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26 

27 
28 
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9.61634 
9.61662 
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28 

27 
28 
28 

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9.65703 
9.65736 
9.65770 
9.65803 
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33 
34 
33 
34 

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0.34297 
0.34264 
0.34230 
0.34197 
0.34163 

9.95931 
9.95925 
9.95920 
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6 
5 
6 
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35 
34 
33 
32 
31 

6 

7 
8 

2 
2 
1 
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30 
31 
32 
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9.61800 
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9.61856 
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27 
28 
28 
27 
28 

9.65870 
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9.65937 
9.65971 
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34 
33 
34 
33 

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0.34130 
0.34096 
0.34063 
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9.95902 
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29 
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40 
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35 
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28 
27 
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33 
33 
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0.33896 
0.33862 
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9.95873 
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5 
6 
6 
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25 
24 
23 
22 
21 

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2 

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7 
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40 

41 
42 
43 
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28 
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9.66204 
9.66238 
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34 
33 
33 
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0.33796 
0.33762 
0.33729 
0.33696 
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9.95844 
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6 
6 
6 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

3 
4 
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45 
46 
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28 
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33 
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q-i 

0.33629 
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0.33463 
0.33430 
0.33397 
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55 
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9.62459 
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27 
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33 
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d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

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p. 

65° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
25C 


1053 


J_ 

L.  Sin 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

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0.32313 
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54 

9.63924 
9.63950 
9.63976 
9.64002 
9.64028 

26 
26 
26 
26 
9fi 

9.68497 
9.68529 
9.68561 
9.68593 
9.68626 

32 
32 
32 
33 

00 

0.31503 
0.31471 
0.31439 
0.31407 
0.31374 

9.95427 
9.95421 
9.95415 
9.95409 
9.95403 

6 
6 
6 
6 

10 

9 

8 
7 
6 

6  0 

7  0 
8  0 
9  0 
10  1 

6 

7 
8 
9 
0 

055 
0.6 
0.7 
0.8 
0.8 

55 
56 
57 
!58 
59 

9.64054 
9.64080 
9.64106 
9.64132 
9.64158 

26 
26 
26 
26 
26 

9.68658 
9.68690 
9.68722 
9.68754 
9.68786 

32 
32 
32 
32 
32 

0.31342 
0.31310 
0.31278 
0.31246 
0.31214 

9.95397 
9.95391 
9.95384 
9.95378 
9.95372 

6 
7 
6 
6 
g 

5 
4 
3 
2 
1 

20  2 
30  3 
40  4 
50  5 

0 
0 
0 
0 

1.7 

2.5 
3.3 
4.2 

SO 

9.64184 

9.68818 

0.31182 

9.95366 

0 

L.  Cos, 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P. 

P. 

64° 


1054  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

26° 


•_ 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P 

.  P 

0 

1 

2 
3 
4 

9.64184 
9.64210 
9.64236 
9.64262 
9.64288 

26 
26 
26 
26 
25 

9.68818 
9.68850 
9.68882 
9.68914 
9.68946 

32 
32 
32 
32 

00 

0.31182 
0.31150 
0.31118 
0.31086 
0.31054 

9.95366 
9.95360 
9.95354 
9.95348 
9.95341 

6 
6 
6 

7 

60 

59 
58 
57 
56 

6 

7 

: 

2 

5.2 

f  n 

31 

3.1 

5 
6 
7 
8 
9 

9.64313 
9.64339 
9.64365 
9.64391 
9.64417 

26 
26 
26 
26 

OK 

9.68978 
9.69010 
9.69042 
9.69074 
9.69106 

32 
32 
32 
32 

00 

0.31022 
0.30990 
0.30958 
0.30926 
0.30894 

9.95335 
9.95329 
9.95323 
9.95317 
9.95310 

6 
6 
6 
7 

55 
54 
53 

52 
51 

8 
9 
10 
20 
30 

t 
,"•  , 

i 
K 
it 

1.3 

U 

U) 

4.1 
4.7 
5.2 
10.3 
15.5 

10 

11 
12 
13 
14 

9.64442 
9.64468 
9.64494 
9.64519 
9.64545 

26 
26 
25 
26 

9.69138 
9.69170 
9.69202 
9.69234 
9.69266 

32 

32 
32 
32 

00 

0.30862 
0.30830 
0.30798 
0.30766 
0.30734 

9.95304 
9.95298 
9.95292 
9.95286 
9.95279 

6 
6 
6 
6 

7 

50 

49 
48 
47 
46 

40 
50 

2 

2( 

.3 

5.7 

2 

20.7 
25.8 

g 

15 
16 
17 
18 
19 

9.64571 
9.64596 
9.64622 
9.64647 
9.64673 

25 
26 
26 
26 
25 

9.69298 
9.69329 
9.69361 
9.69393 
9.69425 

31 
32 
32 
32 

00 

0.30702 
0.30671 
0.30639 
0.30607 
0.30575 

9.95273 
9.95267 
9.95261 
9.95254 
9.95248 

6 

6 
7 
6 

45 
44 
43 
42 
41 

; 

6 

7 
8 
9 
0 

2 
I 

3 
8 
4 

.6 
.0 
.5 
.9 
.3 

20 

21 
22 
23 
24 

964698 
9.64724 
9.64749 
9.64775 
9.64800 

26 
26 
26 
26 
2fi 

9.69457 

9.69488 
9.69520 
9.69552 
9.69584 

31 
32 
32 
32 

0.30543 
0.30512 
0.30480 
0.30448 
0.30416 

9.95242 
9.95236 
9.95229 
9.95223 
9.95217 

6 

7 
6 
6 

40 

39 
38 
37 
36 

|i 

H 
( 

'0 
0 
0 
•0 

8 
It! 
17 
21 

.7 
.0 
.3 
.7 

25 
26 
27 
28 
29 

9.64826 
9.64851 
9.64877 
9.64902 
9.64927 

25 
26 
25 
25 
2fi 

9.69615 
9.69647 
9.69679 
9.69710 
9.69742 

32 
32 
31 
32 

00 

0.30385 
0.30353 
0.30321 
0.30290 
0.30258 

9.95211 
9.95204 
9.95198 
9.95192 
9.95185 

7 

6 
6 

7 

35 
34 
33 
32 
31 

6 

7 
8 

2 

2 
2 
| 

5 
.5 
.9 
.3 

30 

31 
32 
33 
34 

9.64953 
9.64978 
9.65003 
9.65029 
9.65054 

25 
26 
26 
25 
25 

9.69774 
9.69805 
9.69837 
9.69868 
9.69900 

31 
32 
31 
32 

00 

0.30226 
0.30195 
0.30163 
0.30132 
0.30100 

9.95179 
9.95173 
9.95167 
9.95160 
9.95154 

6 
6 

7 
6 

30 

29 
28 
27 
26 

1 

! 

2 
4 
| 

y 

0 
0 
0 
0 

o 

S 

4 

8 
12 
16 
°0 

.8 
.2 
.3 
.5 
.7 
g 

35 
36 
37 
38 
39 

9.65079 
9.65104 
9.65130 
9.65155 
9.65180 

25 
26 
25 
25 
25 

9.69932 
9.69963 
9.69995 
9.70026 
9.70058 

31 
32 
31 
82 

01 

0.30068 
0.30037 
0.30005 
0.29974 
0.29942 

9.95148 
9.95141 
9.95135 
9.95129 
9.95122 

7 
6 
6 
7 

25 
24 
23 
22 
21 

6 

2 

2 

4 
.4 

40 
41 

42 
43 
44 

9.65205 
9.65230 
9.65255 
9.65281 
9.65306 

25 
25 
26 
25 
25 

9.70089 
9.70121 
9.70152 
9.70184 
9.70215 

32 
31 
32 
31 

00 

0.29911 
0.29879 
0.29848 
0.29816 
0.29785 

9.95116 
9.95110 
9.95103 
9.95097 
9.95090 

6 

7 
6 

7 

20 

19 
18 
17 
16 

h 

'2 
I 

8 
9 
0 
0 
0 

3 
3 

4 
8 
1? 

.2 
6 
.0 
0 
0 

45 
46 

47 
48 
49 

9.65331 
9.65356 
9.65381 
9.65406 
9.65431 

25 
25 
25 
25 
25 

9.70247 
9.70278 
9.70309 
9.70341 
9.70372 

31 

31 
32. 
31 
32 

0.29753 
0.29722 
0.29691 
0.29659 
0.29628 

9.95084 
&.95078 
9.95071 
9.95065 
9.95059 

6 
7 
6 
6 

15 
14 
13 
12 
11 

4 
5 

0 
0 

16 
20 

7 

0 
0 

6 

50 
51 
52 
53 
64 

9.65456 
9.65481 
9.65506 
9.65531 
9.65556 

25 
25 
25 
25 
24 

9.70404 
9.70435 
9.70466 
9.70498 
9.70529 

31 
31  . 
32 
31 

o-i 

0.29596 
0.29565 
0.29534 
0.29502 
0.29471 

9.95052 
9.95046 
9.95039 
9.95033 
9.95027 

6 
7 
6 
6 

10 

9 
8 
7 
6 

6 

7 
8 
9 
10 

0 
0 
0 
1 

1 

.7 
.8 
.9 
.1 
.2 

0.6 
0.7 
0.8 
0.9 
1.0 

55 
56 
57 
58 
59 

9.65580 
9.65605 
9.65630 
9.65655 
9.65680 

25 
25 
25 
25 
25 

9.70560 
9.70592 
9.70623 
9.70654 
9.70685 

32 
31 
31 
31 
32 

0.29440 
0.29408 
0.29377 
0.29346 
0.29315 

9.95020 
9.95014 
9.95007 
9.95001 
9.94995 

6 

7 
6 
6 

5 
4 
3 
2 

1 

20 
30 
40 
60 

2 
3 
4 
5 

.3 
.5 
.7 
.8 

2.0 
3.0 
4.0 
5.0 

60 

9.65705 

9.70717 

0.29283 

9.94988 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

i 

P. 

P. 

63? 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
27° 


1055 


L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos. 

d. 

P.P. 

1 

9.65705 
9.65729 
9.65754 
9.65779 
9.65804 

24 
25 
25 
25 
24 

9.70717 
9.70748 
9.70779 
9.70810 
9.70841 

31 
31 
31 
31 
32 

0.29283 
0.29252 
0.29221 
0.29190 
0.29159 

9.94988 
9.94982 
9.94975 
9.94969 
9.94962 

6 

7 
6 
7 
g 

60 

59 
58 
57 
56 

6 

32 

3.2 

3  7 

31 

3.1 
3  6 

) 

7 

8 
9 

9.65828 
9.65853 
9.65878 
9.65902 
9.65927 

25 
25 
24 
25 
25 

9.70873 
9.70904 
9.70935 
9.70966 
9.70997 

31 
31 
'31 
31 

O.1 

0.29127 
0.29096 
0.29065 
0.29034 
0.29003 

9.94956 
9.94949 
9.94943 
9.94936 
9.94930 

7 
6 
7 
6 

7 

55 
54 
53 
52 
51 

8 
9 
10 

20 
30 

4.3 

4.8 
5.3 
10.7 
16.0 

4.1 
4.7 
5.2 
10.3 
15.5 

0 

3 
14 

9.65952 
9.65976 
9.66001 
9.66025 
9.66050 

24 
25 
24 
25 

9.71028 
9.71059 
9.71090 
9.71121 
9.71153 

31 
31 
31 
32 

0.28972 
0.28941 
0.28910 
0.28879 
0.28847 

9.94923 
9.94917 
9.94911 
9.94904 
9.94898 

6 
6 
7 
6 

7 

50 

49 

48 
47 
46 

40 
50 

21.3 
26.7 

3 

20.7 
25.8 

j 

6 
17 
18 
19 

9.66075 
9.66099 
9.66124 
9.66148 
9.66173 

24 

25 
24 
25 

9.71184 
9.71215 
9.71246 
9.71277 
9.71308 

31 
31 
31 
31 

01 

0.28816 
0.28785 
0.28754 
0.28723 
0.28692 

9.94891 
9.94885 
9.94878 
9.94871 
9.94865 

6 

7 
7 
6 
7 

45 
44 
43 
42 
41 

1 

6   3 
7   3 
8  4 
9   4 
0   5 

0 
5 
0 
5 
0 

20 

21 
22 
23 
24 

9.66197 
9.66221 
9.66246 
9.66270 
9.66295 

24 
25 
24 
25 

9.71339 
9.71370 
9.71401 
9.71431 
9.71462 

31 
31 
30 
31 
31 

0.28661 
0.28630 
0.28599 
0.28569 
0.28538 

9.94858 
9.94852 
9.94845 
9.94839 
9.94832 

6 

7 
6 
7 
g 

40 

39 
38 
37 
36 

2 

S 
4 
E 

0  10 
0  15 
0  20 
>0  25 

0 
0 
0 
0 

25 
26 
27 
28 
29 

9.66319 
9.66343 
9.66368 
9.66392 
9.66416 

24 
25 
24 
24 
25 

9.71493 
9.71524 
9.71555 
9.71586 
9.71617 

31 
31 
31 
31 
31 

0.28507 
0.28476 
0.28445 
0.28414 
0.28383 

9.94826 
9.94819 
9.94813 
9.94806 
9.94799 

7 
6 
7 
7 
g 

35 
34 
33 
32 
31 

6 

7 
8 

25 

2.5 
2.9 
3.3 

24 

2.4 
2.8 
3.2 

30 

31 
32 
33 
34 

9.66441 
9.66465 
9.66489 
9.66513 
9.66537 

24 
24 
24 
24 

9.71648 
9.71679 
9.71709 
9.71740 
9.71771 

31 
30 
31 
31 

01 

0.28352 
0.28321 
0.28291 
0.28260 
0.28229 

9.94793 
9.94786 
9.94780 
9.94773 
9.94767 

7 
6 
7 
6 
7 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

4.2 
8.3 
12.5 
16.7 
20.8 

4.0 
8.0 
12.0 
16.0 
20.0 

35 
36 
37 
38 
39 

9.66562 
9.66586 
9.66610 
9.66634 
9.66658 

24 
24 
24 
24 
04 

9.71802 
9.71833 
9.71863 
9.71894 
9.71925 

31 
30 
31 
31 

30 

0.28198 
0.28167 
0.28137 
0.28106 
0.28075 

9.94760 
9.94753 
9.94747 
9.94740 
9.94734 

7 
6 
7 
6 

7 

25 
24 
23 
22 
21 

2 

6   2 

7   2 

3 

.3 

7 

40 
41 

42 
3 

9.66682 
9.66706 
9.66731 
9.66755 
9.66779 

24 
25 
24 
24 

9.71955 
9.71986 
9.72017 
9.72048 
9.72078 

31 
31 
31 
30 

01 

0.28045 
0.28014 
0.27983 
0.27952 
0.27922 

9.94727 
9.94720 
9.94714 
9.94707 
9.94700 

7 
6 
7 
7 
g 

20 

19 
18 
17 
16 

8   3 
9   3 
LO   3 
20   7 
K)  11 

.1 

.5 

.8 
.7 
.5 

5 

46 
47 
48 
49 

9.66803 
9.66827 
9.66851 
9.66875 
9.66899 

24 
24 
24 
24 

9.72109 
9.72140 
9.72170 
9.72201 
9.72231 

31 
30 
31 
30 

o-i 

0.27891 
0.27860 
0.27830 
0.27799 
0.27769 

9.94694 
9.94687 
9.94680 
9.94674 
9.94667 

7 
7 
6 

7 
7 

15 
14 
13 
12 
11 

i 

1 

W  15 
>0  19 

7 

.3 

.2 

6 

0 

53 
54 

9.66922 
9.66943 
9.66970 
9.66994 
9.67018 

24 

24 
24 
24 

9.72262 
9.72293 
9.72323 
9.72354 
9.72384 

31 
30 
31 
30 

0.27738 
0.27707 
0.27677 
0.27646 
0.27616 

9.94660 
9.94654 
9.94647 
9.94640 
9.94634 

6 

7 
7 
6 

7 

10 

9 

8 
7 
6 

6 
7 
8 
9 
10 

LI 
1.2 

0.6 
0.7 
0.8 
0.9 
1.0 

6 
37 
38 
39 

9.67042 
9.67066 
9.67090 
9.67113 
9.67137 

24 

24 
23 
24 

9.72415 
9.72445 
9.72476 
9.72506 
9.72537 

30 
31 
30 
31 
30 

0.27585 
0.27555 
0.27524 
0.27494 
0.27463 

9.94627 
9.94620 
9.94614 
9.94607 
9.94600 

7 
6 

7 
7 
7 

5 
4 
3 
2 
1 

20 
30 
40 
50 

2.3 
3.5 
4.7 

2.0 
3.0 
4.0 
5.0 

0 

9.67161 

9.72567 

0.27433 

9.94593 

0 

L.  Cos. 

d. 

L.  Cotg 

d.c. 

L.Tang 

L.  Sin. 

d. 

* 

P.P 

62° 


1056  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

28° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.  c. 

L.  Cotg. 

L.  Cos.  | 

d. 

F 

.P 

0 

1 

2 
3 
4 

9.67161 
9.67185 
9.67208 
9.67232 
9.67256 

24 
23 

24 
24 

9.72567 
9.72598 
9.72628 
9.72659 
9.72689 

31 
30 
31 
30 

0.27433 
0.27402 
0.27372 
0.27341 
0.27311 

9.94593 
9.94587 
9.94580 
9.94573 
9.94567 

6 

7 
7 
6 

60 

59 
58 
57 
56 

6 

7 

! 
J 
j 

II 

.1 

i; 

30 

3.0 
3  5 

5 
6 

7 
8 
9 

9.67280 
9.67303 
9.67327 
9.67350 
9.67374 

23 
24 
23 
24 
94 

9.72720 
9.72750 
9.72780 
9.72811 
9.72841 

30 
30 
31 
30 

01 

0.27280 
0.27250 
0.27220 
0.27189 
0.27159 

9.94560 
9.94553 
9.94546 
9.94540 
9.94533 

7 
7 
6 
7 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

4 
4 
";l 
11 
If 

.1 
.7 
2 
;3 
.5 

4.0 
4.5 
5.0 
10.0 
15.0 

10 

11 
12 
13 
14 

9.67398 
9.67421 
9.67445 
9.67468 
9.67492 

23 
24 
23 
24 
23 

9.72872 
9.72902 
9.72932 
9.72963 
9.72993 

30 
30 
31 
30 

on 

0.27128 
0.27098 
0.27068 
0.27037 
0.27007 

9.94526 
9.94519 
9.94513 
9.94506 
9.94499 

7 
6 
7 

7 

7 

50 

49 
48 
47 
46 

40 
50 

2L 
2£ 

&•• 
.8 

? 

20.0 
25.0 

9 

15 
16 

17 
18 
19 

9.67515 
9.67539 
9.67562 
9.67586 
9.67609 

24 
23 
24 
23 

9.73023 
9.73054 
9.73084 
9.73114 
9.73144 

31 
30 
30 
30 

0.26977 
0.26946 
0.26916 
0.26886 
0.26856 

9.94492 
9.94485 
9.94479 
9.94472 
9.94465 

7 
6 
7 
7 

45 
44 
43 
42 
41 

] 

6 

7 

cS 

9 

0 

2 
8 

8 

4 
4 

9 
4 
9 
4 

8 

20 

21 
22 
23 
24 

9.67633 
9.67656 
9.67680 
9.67703 
9.67726 

23 
24 
23 
23 
04 

9.73175 
9.73205 
9.73235 
9.73265 
9.73295 

30 

30 
30 

30 

0.26825 
0.26795 
0.26765 
0.26735 
0.26705 

9.94458 
9.94451 
9.94445 
9.94438 
9.94431 

7 
6 
7 
7 

40 

39 
38 
37 
36 

a 

\ 

:  4 

I 

1) 
0 
0 
4) 

i» 

14 
19 
21 

.7 
5 
.3 
2 

25 

26 
27 
28 
29 

9.67750 
9.67773 
9.67796 
9.67820 
9.67843 

23 
23 
24 
23 

00 

9.73326 
9.73356 
9.73386 
9.73416 
9.73446 

30 
30 
30 
30 

OA 

0.26674 
0.26644 
0.26614 
0.26584 
0.26554 

9.94424 
9.94417 
9.94410 
9.94404 
9.94397 

7 
7 
6 

7 

35 
34 
33 
32 
31 

6 

7 
8 

2 

s 
1 
1 

4 

.4 

.8 
:l 

23 

2.3 
2.7 
3.1 

30 
31 

32 
33 
34 

9.67866 
9.67890 
9.67913 
9.67936 
9.67959 

24 
23 
23 
23 
23 

9.73476 
9.73507 
9.73537 
9.73567 
9.73597 

31 
30 
30 
30 

on 

0.26524 
0.26493 
0.26463 
0.26433 
0.26403 

9.94390 
9.94383 
9.94376 
9.94369 
9.94362 

7 
7 
7 
7 
7 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

4 
* 
ll 
11 

•>f 

.(> 
.0 
.0 
.0 

.0 

D 

3.5 
3.8 
7.7 
11.5 
15.3 
19  2 

35 
36 
37 
38 
39 

9.67982 
9.68006 
9.68029 
9.68052 
9.68076 

24 
23 
23 
23 
23 

9.73627 
9.73657 
9.73687 
9.73717 
9.73747 

30 
30 
30 
30 

on 

0.26373 
0.26343 
0.26313 
0.26283 
0.26253 

9.94355 
9.94349 
9.94342 
9.94335 
9.94328 

6 

7 
7 
7 

7 

25 
24 

23 
22 
21 

6 

2 

2 

2 

.2 

c 

40 

41 
42 
43 
44 

9.68098 
9.68121 
9.68144 
9.68167 
9.68190 

23 
23 
23 
23 
23 

9.73777 
9.73807 
9.73837 
9.73867 
9.73897 

30 
30 
30 
30 
30 

0.26223 
0.26193 
0.26163 
0.26133 
0.26103 

9.94321 
9.94314 
9.94307 
9.94300 
9.94293 

7 

7 
7 
7 

7 

20 

19 
18 
17 
16 

•  1l 

1 

8 

9 
0 
!0 
$0 

2 
3 
3 

7 
11 

.9 
.3 
.7 
.3 
.0 

45 

46 

:47 
48 
49 

9.68213 
9.68237 
9.68260 
9.68283 
9.68305 

24 
23 
23 
22 
23 

9.73927 
9.73957 
9.73987 
9.74017 
9.74047 

30 
30 
30 
30 

on 

0.26073 
0.26043 
0.26013 
0.25983 
0.25953 

9.94286 
9.94279 
9.94273 
9.94266 
9.94259 

7 
6 

7 
7 
7 

15 
14 
13 
12 
11 

<: 
{ 

K) 
>0 

14 

18 

7 

.7 
.3 

g 

50 

51 
52 
53 
54 

9.68328 
9.68351 
9.68374 
9.68397 
9.68420 

23 
23 
23 
23 
23 

9.74077 
9.74107 
9.74137 
9.74166 
9.74196 

30 
30 
29 
30 

OA 

0.25923 
0.25893 
0.25863 
0.25834 
0.25804 

9.94252 
9.94245 
9.94238 
9.94231 
9.94224 

7 
7 
7 
7 
7 

10 
9 

8 
7 
6 

6 
7 
8 
9 
10 

( 

( 
( 

1 
] 

).7 

).8 
).9 

Li 

.2 

0.6 
0.7 
0.8 
0.9 
1.0 

55 
56 
57 
58 
59 

9.68443 
9.68466 
9.68489 
9.68512 
9.68534 

23 
23 

23 
22 
23 

9.74226 
9.74256 
9.74286 
9.74316 
9.74345 

30 
30 
30 
29 

on 

0.25774 
0.25744 
0.25714 
0.25684 
0.25655 

9.94217 
9.94210 
9.94203 
9.94196 
9.94189 

7 

7 
7 

7 

7 

5 
4 
3 
2 
1 

20 
30 
40 
50 

1 
^ 

1 

I:A 

5.5 
t.7 

).8 

2.0 
3.0 
4.0 
5.0 

60 

9.68557 

9.74375 

0.25625 

9.94182 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P 

.P 

61° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
29° 


1057 


' 

L.  Sin. 

d. 

L.Tang 

d.  c.  |L.  Cotg 

L.  Cos. 

d. 

P.P. 

0 

1 

3 
4 

9.68557 
9.68580 
9.68603 
9.68625 
9.68648 

23 

23 
22 
23 
23 
23 
22 
23 
23 
22 
23 
22 
23 
23 
22 
23 
22 
23 
22 
23 
22 
23 
22 
23 
22 
22 
23 
22 
23 
22 
22 
23 
22 
22 
22 
23 
22 
22 
22 
22 
23 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 

9.74375 
9.74405 
9.74435 
9.74465 
9.74494 

30 
30 
30 
29 
30 
30 
29 
30 
30 
30 
29 
30 
30 
29 
30 
30 
29 
30 
29 
30 
29 
30 
30 
29 
30 
29 
30 
29 
30 
29 
30 
29 
30 
29 
29 
30 
29 
30 
29 
29 
30 
29 
30 
29 
29 
30 
29 
29 
29 
30 
29 
29 
29 
30 
29 
29 
29 
30 
29 
29 

0.25625 
0.25595 
0.25565 
0.25535 
0.25506 

9.94182 
9.94175 
9.94168 
9.94161 
9.94154 

7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
8 
7 
7 
7 
8 
7 
7 
7 

60 

59 
58 
57 
56 
55 
54 
53 
52 
51 

6 

7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6 

7 
8 
9 
10 
20 
30 
40 
50 

6 
7 
8 
9 
10 
20 
30 
40 
50 

6  0 
7  0 
8  1 
9  1 
10  1 
20  2 
30  4 
40  5 
50  6 

30 

3.0 
3.5 
4.0 
4.5 
5.0 
10.0 
15.0 
20.0 
25.0 

29 

2.9 
3.4 
3.9 
4.4 
4.8  ' 
9.7 
14.5 
19.3 
24.2 

23 

2.3 

2.7 
3.1 
3.5 
3.8 
7.7 
11.5 
15.3 
19.2 

22 

2.2 
2.6 
2.9 
3.3 
3.7 
7.3 
11.0 
14.7 
18.3 

5   7 

.8  0.7 
9  0.8 
1  0.9 
2  1.1 
3  1.2 
7  2.3 
0  3.5 
3  4.7 
7  5.8 

5 
6 
7 
8 
9 

9.68671 
9.68694 
9.68716 
9.68739 
9.68762 

9.74524 
9.74554 
9.74583 
9.74613 
9.74643 

0.25476 
0.25446 
0.25417 
0.25387 
0.25357 

9.94147 
9.94140 
9.94133 
9.94126 
9.94119 

10 

11 
12 
13 
14 

9.68784 
9.68807 
9.68829 
9.68852 
9.68875 

9.74673 
9.74702 
9.74732 
9.74762 
9.74791 

0.25327 
0.25298 
0.25268 
0.25238 
0.25209 

9.94112 
9.94105 
9.94098 
9.94090 
9.94083 

50 

49 
48 
47 
46 

15 
16 
17 
18 
19 

9.68897 
9.68920 
9.68942 
9.68965 
9.68987 

9.74821 
9.74851 
9.74880 
9.74910 
9.74939 

0.25179 
0.25149 
0.25120 
0.25090 
0.25061 

9.94076 
9.94069 
9.94062 
9.94055 
9.94048 

45 
44 
43 
42 
41 
40 
39 
38 
37 
36 

20 

21 
22 
23 
24 

9.69010 
9.69032 
9.69055 
9.69077 
9.69100 

9.74969 
9.74998 
9.75028 
9.75058 
9.75087 

0.25031 
0.25002 
0.24972 
0.24942 
0.24913 

9.94041 
9.94034 
9.94027 
9.94020 
9.94012 

25 
26 
27 
28 
29 

9.69122 
9.69144 
9.69167 
9.69189 
9.69212 

9.75117 
9.75146 
9.75176 
9.75205 
9.75235 

0.24883 
0.24854 
0.24824 
0.24795 
0.24765 

9.94005 
9.93998 
9.93991 
9.93984 
9.93977 

35 
34 
33 
32 
31 

30 

31 
32 
33 
34 

9.69234 
9.69256 
9.69279 
9.69301 
9.69323 

9.75264 
9.75294 
9.75323 
9.75353 
9.75382 

0.24736 
0.24706 
0.24677 
0.24647 
0.24618 

9.93970 
9.93963 
9.93955 
9.93948 
9.93941 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.69345 
9.69368 
9.69390 
9.69412 
9.69434 

9.75411 
9.75441 
9.75470 
9.75500 
9.75529 

0.24589 
0.24559 
0.24530 
0.24500 
0.24471 

9.93934 
9.93927 
9.93920 
9.93912 
9.93905 

25 
24 
23 
22 
21 

40 

41 
42 
43 
44 

9.69456 
9.69479 
9.69501 
9.69523 
9.69545 

9.75558 
9.75588 
9.75617 
9.75647 
9.75676 

0.24442 
0.24412 
0.24383 
0.24353 
0.24324 

9.93898 
9.93891 
9.93884 
9.93876 
9.93869 

20 

19 
18 
17 
16 

45 
46 
47 
48 
49 

TF 

51 
52 
53 
54 

9.69567 
9.69-589 
9.69611 
9.69633 
9.69655 

9.75705 
9.75735 
9.75764 
9.75793 
9.75822 

0.24295 
0.24265 
0.24236 
0.24207 
0.24178 

9.93862 
9.93855 
9.93847 
993840 
9.93833 

15 
14 
13 
12 
11 

9.69677 
9.69699 
9.69721 
9.69743 
9.69765 

9.75852 
9.75881 
9.75910 
9.75939 
9.75969 

0.24148 
0.24119 
0.24090 
0.24061 
0.24031 

9.93826 
9.93819 
9.93811 
9.93804 
9.93797 

7 
8 
7 

7 

10 

9 
8 
7 
6 

55 

56 
57 
58 
59 

9.69787 
9.69809 
9.69831 
9.69853 
9.69875 

9.75998 
9.76027 
9.76056 
9.76086 
9.76115 

0.24002 
0.23973 
0.23944 
0.23914 
0.23885 

9.93789 
9.93782 
9.93775 
9.93768 
9.93760 

7 

7 
7 
8 

7 

5 
4 
3 
2 
1 

60 

9.69897 

9.76144 

0.23856 

9.93753 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P.P. 

67 


60° 


1058  LOGARITHMS  &F  TRIGONOMETRIC  FUNCTIONS 

30° 


' 

L.  Bin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

r 

0 

1 

2 
3 

4 

9.69897 
9.69919 
9.69941 
9.69963 
9.69984 

22 

22 
22 
21 
22 

9.76144 
9.76173 
9.76202 
9.76231 
9.76261 

29 
29 
29 
30 

9Q 

0.23856 
0.23827 
0.23798 
0.23769 
0.23739 

9.93753 
9.93746 
9.93738 
9.93731 
9.93724 

7 
8 
7 
7 

60 

59 
58 
57 
56 

3 

6   3 
7   3 

0 

.0 

•-, 

29 

2.9 
3  4 

5 
6 

7 
8 
9 

9.70006 
9.70028 
9.70050 
9.70072 
9.70093 

22 
22 
22 
21 
99 

9.76290 
9.76319 
9.76348 
9.76377 
9.76406 

29 
29 
29 
29 

0.23710 
0.23681 
0.23652 
0.23623 
0.23594 

9.93717 
9.93709 
9.93702 
9.93695 
9.93687 

8 

7 
7 
8 

55 
54 
53 
52 
51 

8   4 
9   4 
10   5 
20  10 
30  15 

.0 
.5 
.0 
.0 

.0 

3.9 
4.4 
4.8 
9.7 
14.5 

10 

11 
12 
13 
14 

9.70115 
9.70137 
9.70159 
9.70180 
9.70202 

22 
22 
21 

22 
22 

9.76435 
9.76464 
9.76493 
9.76522 
9.76551 

29 
29 
29 
29 

On 

0.23565 
0.23536 
0.23507 
0.23478 
0.23449 

9.93680 
9.93673 
9.93665 
9.93658 
9.93650 

7 
8 
7 
8 

50 

49 

48 
47 
46 

40  20 
50  25 

.0 
.0 

? 

19.3 
24.2 

8 

15 
16 
17 
18 
19' 

9.70224 
9.70245 
9.70267 
9.70288 
9.70310 

21 
22 
21 

22 
22 

9.76580 
9.76609 
9.76639 
9.76668 
9.76697 

29 
30 
29 
29 
28 

0.23420 
0.23391 
0.23361 
0.23332 
0.23303 

9.93643 
9.93636 
9.93628 
9.93621 
9.93614 

7 
8 
7 
7 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2 

3 
8 

4 
4 

.8 
.3 

.7 
.2 

.7 

20 

21 
22 
23 
24 

9.70332 
9.70353 
9.70375 
9.703% 
9.70418 

21 
22 
21 
22 
21 

9.76725 
9.76754 
9.76783 
9.76812 
9.76841 

29 
29 
29 
29 

on 

0.23275 
0.23246 
0.23217 
0.23188 
0.23159 

9.93606 
9.93599 
9.93591 
9.93584 
9.93577 

7 
8 

7 
7 

40 

39 
38 
37 
36 

20 
30 
40 
50 

y 

14 
18 
23 

.3 
.0 
.7 
.3 

25 
26 

27 
28 
29 

9.70439 
9.70461 
9.70482 
9.70504 
9.70525 

22 
21 
22 
21 
22 

9.76870 
9.76899 
9.76928 
9.76957 
9.76986 

29 
29 
29 
29 

OQ 

0.23130 
0.23101 
0.23072 
0.23043 
0.23014 

9.93569 
9.93562 
9.93554 
9.93547 
9.93539 

7 
8 
7 
8 

7 

35 
34 
33 
32 
31 

6 

7 
8 

2 

2 
2 
2 

2 

.2 
.6 
.9 

30 

31 
32 
33 
34 

9.70547 
9.70568 
9.70590 
9.70611 
9.70633 

21 
22 
21 
22 
21 

9.77015 
9.77044 
9.77073 
9.77101 
9.77130 

29 
29 
28 
29 
29 

0.22985 
0.22956 
0.22927 
0.22899 
0.22870 

9.93532 
9.93525 
9.93517 
9.93510 
9.93502 

7 
8 
7 
8 
7 

30 

29 
28 
27 
26 

9 
10 

20 
30 

40 
50 

3 
7 
11 
14 

!*• 

.3 
.7 
.3 
.0 
.7 
.3 

35 
36 
37 
38 
39 

9.70654 
9.70675 
9.70697 
9.70718 
9.70739 

21 
22 
21 
21 
22 

9.77159 

9.77188 
9.77217 
9.77246 
9.77274 

29 
29 
29 
28 

on 

0.22841 
0.22812 
0.22783 
0.22754 
0.22726 

9.93495 
9.93487 
9.93480 
9.93472 
9.93465 

8 

7 
8 

7 

25 
24 
23 
22 
21 

6 

2 

2 

1 

.1 

40 

41 
42 
43 
44 

9.70761 
9.70782 
9.70803 
9.70824 
9.70846 

21 
21 
21 
22 
21 

9.77303 
9.77332 
9.77361 
9.77390 
9.77418 

29 
29 
29 
28 
29 

0.22697 
0.22668 
0.22639 
0.22610 
0.22582 

9.93457 
9.93450 
9.93442 
9.93435 
9.93427 

7 
8 
7 
8 

7 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

J 

2 
3 
7 
1( 

.8 
.2 
.5 
.0 
.5 

45 
46 

47 
48 
49 

9.70867 
9.70888 
9.70909 
9.70931 
9.70952 

21 
21 
22 
21 
21 

9.77447 
9.77476 
9.77505 
9.77533 
9.77562 

29 
29 
28 
29 
29 

0.22553 
0.22524 
0.22495 
0.22467 
0.22438 

9.93420 
9.93412 
9.93405 
9.93397 
9.93390 

8 

7 
8 

7 
g 

15 
14 
13 
12 
11 

40 
50 

14 

17 

8 

.0 
.5 

7 

50 

51 
52 

53 
54 

9.70973 
9.70994 
9.71015 
9.71036 
9.71058 

21 

21 
21 
22 
21 

9.77591 
9.77619 
9.77648 
9.77677 
9.77706 

28 
29 
29 
29 

28 

0.22409 
0.22381 
0.22352 
0.22323 
0.22294 

9.93382 
9.93375 
9.93367 
9.93360 
9.93352 

7 
8 
7 
8 

10 

9 

8 

7 
6 

6  ( 

7  ( 
8  1 
9  ] 
10  ] 

).8 
).9 
.1 
.2 
.3 

0.7 
0.8 
0.9 
1.1 
1.2 

55 
56 
57 
58 
59 

9.71079 
9.71100 
9.71121 
9.71142 
9.71163 

21 
21 
21 
21 
21 

9.77734 
9.77763 
9.77791 
9.77820 
9.77849 

29 
28 
29 
29 

OQ 

0.22266 
0.22237 
0.22209 
0.22180 
0.22151 

9.93344 
9.93337 
9.93329 
9.93322 
9.93314 

7 
8 
7 
8 

5 
4 
3 
2 
1 

20  '< 
30  <• 
40  { 
50  ( 

>.7 
1.0 
>.3 
5.7 

2.3 
3.5 
4.7 
5.8 

60 

9.71184 

9.77877 

0.22123 

9.93307 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P 

.P 

59° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS. 
31° 


1059 


t 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P. 

P. 

0 

1 

2 
3 
4 

9.71184 
9.71205 
9.71226 
9.71247 
9.71268 

21 
21 
21 
21 
21 

9.77877 
9.77906 
9.77935 
9.77963 
9.77992 

29 
29 
28 
29 

OQ 

0.22123 
0.22094 
0.22065 
0.22037 
0.22008 

9.93307 
9.93299 
9.93291 
9.93284 
9.93276 

8 
8 
7 
8 

60 

59 
58 
57 
56 

6 

7 

29 

2.9 

5 
6 

7 
8 
9 

9.71289 
9.71310 
9.71331 
9.71352 
9.71373 

21 
21 
21 
21 
20 

9.78020 
9.78049 
9.78077 
9.78106 
9.78135 

29 

28 
29 
29 
28 

0.21980 
0.21951 
0.21923 
0.21894 
0.21865 

9.93269 
9.93261 
9.93253 
9.93246 
9.93238 

8 
8 

7 
8 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

3.9 
4.4 
4.8 
9.7 
14.5 

10 
11 

12 
13 
14 

9.71393 
9.71414 
9.71435 
9.71456 
9.71477 

21 
21 
21 
21 

01 

9.78163 
9.78192 
9.78220 
9.78249 
9.78277 

29 
28 
29 
28 

OQ 

0.21837 
0.21808 
0.21780 
0.21751 
0.21723 

9.93230 
9.93223 
9.93215 
9.93207 
9.93200 

7 
8 
8 

7 

SO 

49 
48 
47 
46 

40 
50 

19.3 
24.2 

28 

15 
16 
17 
18 
19 

9.71498 
9.71519 
9.71539 
9.71560 
9.71581 

21 
20 
21 
21 
21 

9.78306 
9.78334 
9.78363 
9.78391 
9.78419 

28 
29 
28 
28 
29 

0.21694 
0.21666 
0.21637 
0.21609 
0.21581 

9.93192 
9.93184 
9.93177 
9.93169 
9.93161 

8 

7 
8 
8 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2.8 
3.3 
3.7 
4.2 
4.7 

20 

21 

22 
23 
24 

9.71602 
9.71622 
9.71643 
9.71664 
9.71685 

20 
21 
21 
21 

9.78448 
9.78476 
9.78505 
9.78533 
9.78562 

28 
29 
28 
29 

OQ 

0.21552 
0.21524 
0.21495 
0.21467 
0.21438 

9.93154 
9.93146 
9.93138 
9.93131 
9.93123 

8 

8 
7 
8 

40 

39 
38 
37 
36 

20 
30 
40 
50 

9.3 
14.0 
18.7 
23.3 

25 
26 

27 
28 
29 

9.71705 
9.71726 
9.71747 
9.71767 
9.71788 

21 
21 

20 
21 

9.78590 
9.78618 
9.78647 
9.78675 
9.78704 

28 
29 
28 
29 

OQ 

0.21410 
0.21382 
0.21353 
0.21325 
0.21296 

9.93115 
9.93108 
9.93100 
9.93092 
9.93084 

7 
8 
8 
8 
7 

35 
34 
33 
32 
31 

6 

7 
8 

21 
2.1 
2.5 

2.8 

30 

31 
32 
33 
34 

9.71809 
9.71829 
9.71850 
9.71870 
9.71891 

20 
21 
20 
21 

9.78732 
9.78760 
9.78789 
9.78817 
9.78845 

28 
29 
28 
28 

0.21268 
0.21240 
0.21211 
0.21183 
0.21155 

9.93077 
9.93069 
9.93061 
9.93053 
9.93046 

8 
8 
8 

7 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

3.5 
7.0 

10.5 
14.0 
175 

35 
36 
37 
38 
39 

9.71911 
9.71932 
9.71952 
9.71973 
9.71994 

21 
20 
21 
21 

9.78874 
9.78902 
9.78930 
9.78959 
9.78987 

28 
28 
29 
28 

OQ 

0.21126 
0.21098 
0.21070 
0.21041 
0.21013 

9.93038 
9.93030 
9.93022 
9.93014 
9.93007 

8 
8 
8 

7 

25 
24 
23 
22 
21 

6 

7 

20 

2.0 
2  3 

40 

41 
42 
43 
44 

9.72014 
9.72034 
9.72055 
9.72075 
9.720% 

20 
21 
20 
21 
20 

9.79015 
9.79043 
9.79072 
9.79100 
9.79128 

28 
29 
28 
28 
28 

0.20985 
0.20957 
0.20928 
0.20900 
0.20872 

9.92999 
9.92991 
9.92983 
9.92976 
9.92968 

8 
8 

7 
8 

g 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

2.7 
3.0 
3.3 
6.7 
10.0 

45 
46 

47 
48 
49 

9.72116 
9.72137 
9.72157 
9.72177 
9.72198 

21 
20 
20 
21 

9.79156 
9.79185 
9.79213 
9.79241 
9.79269 

29 
28 
28 
28 

0.20844 
0.20815 
0.20787 
0.20759 
0.20731 

9.92960 
9.92952 
9.92944 
9.92936 
9.92929 

8 
8 
8 

7 

15 
14 
13 
12 
11 

40 
50 

13.3 
16.7 

8   7 

50 

51 
52 
53 
54 

9.72218 
9.72238 
9.72259 
9.72279 
9.72299 

20 
21 
20 
20 

9.79297 
9.79326 
9.79354 
9.79382 
9.79410 

29 
28 
28 
28 
28 

0.20703 
0.20674 
0.20646 
0.20618 
0.20590 

9.92921 
9.92913 
9.92905 
9.92897 
9.92889 

8 
8 
8 
8 
3 

10 

9 

8 
7 
6 

6  C 
7  0 
8  1 
9  1 
10  1 

.8  0.7 
.9  0.8 
.1  0.9 
.2  1.1 
.3  1.2 

55 
56 
57 
58 
59 

9.72320 
9.72340 
9.72360 
9.72381 
9.72401 

20 
20 
21 
20 
20 

9.79438 
9.79466 
9.79495 
9.79523 
9.79551 

28 
29 
28 
28 
28 

0.20562 
0.20534 
0.20505 
0.20477 
0.20449 

9.92881 
9.92874 
9.92866 
9.92858 
9.92850 

7 
8 
8 
8 
8 

5 
4 
3 
2 
1 

20  2 
30  4 
40  £ 
50  ( 

.7  2.3 
.0  3.5 
.3  4.7 
.7  5.8 

60 

9.72421 

9.79579 

0.20421 

9.92842 

0 

L.  Cos. 

d. 

L.  Cotg 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P 

.P. 

58° 

1060  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

32° 


/ 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P. 

P. 

0 

1 

2 
3 
4 

9.72421 
9.72441 
9.72461 
9.72482 
9.72502 

20 
20 
21 
20 
20 

9.79579 
9.79607 
9.79635 
9.79663 
9.79691 

28 
28 
28 
28 
oc 

0.20421 
0.20393 
0.20365 
0.20337 
0.20309 

9.92842 
9.92834 
9.92826 
9.92818 
9.92810 

8 
8 
8 
8 
7 

60 

59 
58 
57 
56 

6 

7 

2 

1-1 

9 

.9 
4 

28 

2.8 
33 

0 

6 
7 
8 
9 

9.72522 
9.72542 
9.72562 
9.72582 
9.72602 

20 
20 
20 
20 
20 

9.79719 
9.79747 
9.79776 
9.79804 
9.79832 

28 
29 
28 
28 

0.20281 
0.20253 
0.20224 
0.20196 
0.20168 

9.92803 
9.92795 
9.92787 
9.92779 
9.92771 

8 
8 
8 

8 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

a 

4 
4 

9 
14 

.9 
.4 

.8 
.7 
.8 

3.7 
4.2 
4.7 
9.3 
14.0 

10 

11 
12 
13 
14 

9.72622 
9.72643 
9.72663 
9.72683 
9.72703 

21 
20 
20 
20 
20 

9.79860 
9.79888 
9.79916 
9.79944 
9.79972 

28 
28 
28 
28 
oa 

0.20140 
0.20112 
0.20084 
0.20056 
0.20028 

9.92763 
9.92755 
9.92747 
9.92739 
9.92731 

8 
8 
8 
8 

50 

49 
48 
47 
46 

40 
50 

19 
24 

.8 

.2 

? 

18.7 
23.3 

7 

15 
16 
17 
18 
19 

9.72723 
9.72743 
9.72763 
9.72783 
9.72803 

20 
20 
20 
20 
20 

9.80000 
9.80028 
9.80056 
9.80084 
9.80112 

28 
28 
28 
28 
28 

0.20000 
0.19972 
0.19944 
0.19916 
0.19888 

9.92723 
9.92715 
9.92707 
9.92699 
9.92691 

8 
8 
8 
8 

45 
44 
43 
42 
41 

6 

7 
« 
9 
10 

2 
8 

8 
4 
4 

.7 
.2 
.6 
.1 
.5 

20 

21 
22 
23 
24 

9.72823 
9.72843 
9.72863 
9.72883 
9.72902 

20 
20 
20 
19 
90 

9.80140 
9.80168 
9.80195 
9.80223 
9.80251 

28 
27 
28 
28 

0.19860 
0.19832 
0.19805 
0.19777 
0.19749 

9.92683 
9.92675 
9.92667 
9.92659 
9.92651 

8 
8 
8 
8 

40 

39 
38 
37 
36 

20 
30 
40 
50 

G 
18 

18 
22 

.0 
.5 
.0 
.5 

25 
26 
27 
28 
29 

9.72922 
9.72942 
9.72962 
9.72982 
9.73002 

20 
20 
20 
20 
20 

9.80279 
9.80307 
9.80335 
9.80363 
9.80391 

28 
28 
28 
28 

OQ 

0.19721 
0.19693 
0.19665 
0.19637 
0.19609 

9.92643 
9.92635 
9.92627 
9.92619 
9.92611 

8 
8 
8 
8 

35 
34 
33 
32 
31 

6 

7 
8 

2 

2 
'2 
2 

a 

6 

8 

20 

2.0 

2.3 

2.7 

30 

31 
32 
33 
34 

9.73022 
9.73041 
9.73061 
9.73081 
9.73101 

19 
20 
20 
20 
20 

9.80419 
9.80447 
9.80474 
9.80502 
9.80530 

28 
27 
28 
28 
28 

0.19581 
0.19553 
0.19526 
0.19498 
0.19470 

9.92603 
9.92595 
9.92587 
9.92579 
9.92571 

8 
8 
8 
8 

30 

29 
28 
27 
26 

10 
20 
30 
40 

^ 

3 

7 

10 
14 
17 

5 
0 
5 
0 
5 

3.3 
6.7 
10.0 
13.3 
167 

35 
36 
37 
38 
39 

9.73121 
9.73140 
9.73160 
9.73180 
9.73200 

19 
20 
20 
20 
1Q 

9.80558 
9.80586 
9.80614 
9.80642 
9.80669 

28 
28 
28 
27 

0.19442 
0.19414 
0.19386 
0.19358 
0.19331 

9.92563 
9.92555 
9.92546 
9.92538 
9.92530 

8 
9 
8 
8 

25 
21 
23 
22 
21 

6 

19 

1. 
o 

9 

40 

41 
42 
43 
44 

9.73219 
9.73239 
9.73259 
9.73278 
9.73298 

20 
20 
19 
20 
90 

9.80697 
9.80725 
9.80753 
9.80781 
9.80808 

28 
28 
28 
27 

OQ 

0.19303 
0.19275 
0.19247 
0.19219 
0.19192 

9.92522 
9.92514 
9.92506 
9.92498 
9.92490 

8 
8 
8 
8 

20 

19 
18 
17 
16 

8 
9 
10 

20 
30 

2. 
2. 
K 
6 

9 

5 
9 
2 
3 

i 

45 
46 
47 

48 
49 

9.73318 
9.73337 
9.73357 
9.73377 
9.73396 

19 

20 
20 
19 
20 

9.80836 
9.80864 
9.80892 
9.80919 
9.80947 

28 
28 

27 
28 

OQ 

0.19164 
0.19136 
0.19108 
0.19081 
0.19053 

9.92482 
9.92473 
9.92465 
9.92457 
9.92449 

9 
8 
8 
8 

15 
14 
13 
12 
11 

40 
50 

q 

12. 
15. 

8 

7 
8 

7 

50 

51 
52 
53 
54 

9.73416 
9.73435 
9.73455 
9.73474 
9.73494 

19 

20  - 
19 
20 

-1Q 

9.80975 
9.81003 
9.81030 
9.81058 
9.81086 

28 
27 
28 

28 

0.19025 
0.18997 
0.18970 
0.18942 
0.18914 

9.92441 
9.92433 
9.92425 
9.92416 
9.92408 

8 
8 
9 
8 

10 

9 
8 
7 
6 

6 
7 
8 
9 
10 

0.9 
1.1 
1.2 
1.4 

1.5 

O.J 

OA 

1.1 

LS 
1J 

0.7 
0.8 
0.9 
.  1.1 
!  1.2 

55 
56 
57 
58 
59 

9.73513 
9.73533 
9.73552 
9.73572 
9.73591 

20 
19 
20 
19 
20 

9.81113 
9.81141 
9.81169 
9.81196 
9.81224 

28 
28 
27 
28 
28 

0.18887 
0.18859 
0.18831 
0.18804 
0.18776 

9.92400 
9.92392 
9.92384 
9.92376 
9.92367 

8 
8 
8 
9 

5 
4 
3 
2' 
1 

20 
30 
40 
50 

3.0 
4.5 
6.0 
7.5 

2.5 

4.( 
5.1 
6.' 

2.3 
>  3.5 
4.7 

5.8 

60 

9.73611 

9.81252 

0.18748 

9.92359 

0 

L.Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P. 

P. 

57° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
33° 


1061 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P 

0 

1 

2 
3 

4 

9.73611 
9.73630 
9.73650 
9.73669 
9.73689 

19 
20 
19 
20 

9.81252 
9.81279 
9.81307 
9.81335 
9.81362 

27 
28 
28 
27 

0.18748 
0.18721 
0.18693 
0.18665 
0.18638 

9.92359 
9.92351 
9.92343 
9.92335 
9.92326 

8 
8 
8 
9 

60 

59 
58 
57 
56 

2 
6   S 

7  9 

8 

.8 

^ 

27 

2.7 
3  2 

5 

6 

7 
8 
9 

9.73708 
9.73727 
9.73747 
9.73766 
9.73785 

19 
20 
19 
19 
on 

9.81390 
9.81418 
9.81445 
9.81473 
9.81500 

28 
27 
28 
27 

OQ 

0.18610 
0.18582 
0.18555 
0.18527 
0.18500 

9.92318 
9.92310 
9.92302 
9.92293 
9.92285 

8 
8 
9 
8 

55 
54 
53 
52 
51 

8  S 
9   4 
10   4 
20   £ 
30  14 

.7 
.2 
.7 
.8 
.0 

3.6 
4.1 
4.5 
9.0 
13.5 

10 

11 
12 
13 
14 

9.73805 
9.73824 
9.73843 
9.73863 
9.73882 

19 
19 
20 
19 

HI 

9.81528 
9.81556 
9.81583 
9.81611 
9.81638 

28 
27 
28 
27 
28 

0.18472 
0.18444 
0.18417 
0.18389 
0.18362 

9.92277 
9.92269 
9.92260 
9.92252 
9.92244 

8 
9 
8 
8 
9 

50 

49 
48 
47 
46 

40  18 
50  23 

.7 
.3 

? 

18.0 
22.5 

0 

15 
16 
17 
18 
19 

9.73901 
9.73921 
9.73940 
9.73959 
9.73978 

20 
19 

19 
19 

9.81666 
9.81693 
9.81721 
9.81748 
9.81776 

27 
28 
27 
28 

0.18334 
0.18307 
0.18279 
0.18252 
0.18224 

9.92235 
9.92227 
9.92219 
9.92211 
9.92202 

8 
8 
8 
9 

45 

44 
43 
42 
41 

6 
7 
8 
9 
10 

2 
2 
2 
3 
3 

.0 
.3 
.7 
.0 
.3 

20 

21 
22 
23 
24 

9.73997 
9.74017 
9.74036 
9.74055 
9.74074 

20 
19 
19 
19 
10 

9.81803 
9.81831 
9.81858 
9.81886 
9.81913 

28 
27 
28 

27 

OQ 

0.18197 
0.18169 
0.18142 
0.18114 
0.18087 

9.92194 
9.92186 
9.92177 
9.92169 
9.92161 

8 
9 
8 
8 
9 

40 

39 
38 
37 
36 

20 
30 
40 
50 

6 

10 
13 
1G 

.7 
.0 
.3 
.7 

25 

26 

27 
28 
29 

9.74093 
9.74113 
9.74132 
9.74151 
9.74170 

20 
19 
19 
19 

9.81941 
9.81968 
9.81996 
9.82023 
9.82051 

27 
28 
27 
28 

0.18059 
0.18032 
0.18004 
0.17977 
0.17949 

9.92152 
9.92144 
9.92136 
9.92127 
9.92119 

8 
8 
9 

8 
g 

35 
34 
33 
32 
31 

6 

7 
8 

1 

1 

2 
2 

9 
.9 

.2 
.5 

30 

31 
32 
33 
34 

9.74189 
9.74208 
9.74227 
9.74246 
9.74265 

19 
19 
19 
19 

9.82078 
9.82106 
9.82133 
9.82161 
9.82188 

28 
27 
28 
27 
97 

0.17922 
0.17894 
0.17867 
0.17839 
0.17812 

9.92111 
9.92102 
9.92094 
9.92086 
9.92077 

9 
8 
8 
9 
g 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

3 

e 
9 

12 
15 

.2 
.3 
.5 

.7 
.8 

35 
36 
37 
38 
39 

9.74284 
9.74303 
9.74322 
9.74341 
9.74360 

19 
19 
19 
19 

1Q 

9.82215 
9.82243 
9.82270 
9.82298 
9.82325 

28 
27 
28 
27 
27 

0.17785 
0.17757 
0.17730 
0.17702 
0.17675 

9.92069 
9.92060 
9.92052 
9.92044 
9.92035 

9 

8 
8 
9 
g 

25 
24 
23 

22 
21 

6 
7 

1 

1 

0 

8 
.8 
1 

40 
41 

42 
43 
44 

9.74379 
9.74398 
9.74417 
9.74436 
9.74455 

19 
19 
19 
19 

9.82352 
9.82380 
9.82407 
9.82435 
9.82462 

28 
27 
28 
27 
97 

0.17648 
0.17620 
0.17593 
0.17565 
0.17538 

9.92027 
9.92018 
9.92010 
9.92002 
9.91993 

9 
8 
8 
9 

g 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

2 
2 
3 
6 
9 

.4 
.7 
.0 
.0 
.0 

45 
46 
47 
48 
49 

9.74474 
9.74493 
9.74512 
9.74531 
9.74549 

19 
19 
19 
18 

9.82489 
9.82517 
9.82544 
9.82571 
9.82599 

28 
27 
27 
28 
97 

0.1751! 
0.17483 
0.17456 
0.17429 
0.17401 

9.91985 
9.91976 
9.91968 
9.91959 
9.91951 

9 
8 
9 
8 
9 

15 
14 
13 
12 
11 

40 
50 

12 
15 

9 

.0 
.0 

8 

To~ 

51 
52 
53 
54 

9.74568 
9.74587 
9.74606 
9.74625 
9.74644 

19 
19 
19 
19 

9.82626 
9.82653 
9.82681 
9.82708 
9.82735 

27 
28 
27 
27 

0.17374 
0.17347 
0.17319 
0.17292 
0.17265 

9.91942 
9.91934 
9.91925 
9.91917 
9.91908 

8 
9 
8 
9 

g 

10 

9 
8 
7. 
6 

6  C 
7  1 
8  1 
9  ] 
10  1 

.9 
.1 
.2 
.4 
.5 

0.8 
0.9 
1.1 
1.2 
1.3 

55 
56 
57 
58 
59 

9.74662 
9.74681 
9.74700 
9.74719 
9.74737 

19 
Id 
19 

18 

9.82762 
9.82790 
9.82817 
9.82844 
9.82871 

28 
27 
27 
27 
28 

0.17238 
0.17210 
0.17183 
0.17156 
0.17129 

9.91900 
9.91891 
9.91883 
9.91874 
9.91866 

9 
8 
9 
8 
9 

5 
4 
3 
2 
1 

20  £ 
30  4 
40  6 
50  "i 

.0 
.5 
.0 
.5 

2.7 
4.0 
5.3 
6.7 

60 

9.74756 

9.82899 

0.17101 

9.91857 

0 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P 

.P 

58° 

1062 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
34° 


' 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg 

L.  Cos. 

d. 

P.P. 

0 

1 

2 
3 
4 

9.74756 
9.74775 
9.74794 
9.74812 
9.74831 

19 
19 
18 
19 
19 
18 
19 
19 
18 
19 
18 
19 
19 
18 
19 
18 
19 
18 
19 
18 
19 
18 
19 
18 
19 
18 
19 
18 
18 
19 
18 
19 
18 
18 
19 
18 
18 
18 
19 
18 
18 
19 
18 
18 
18 
18 
19 
18 
18 
18 
18 
18 
19 
18 
18 
18 
18 
18 
18 
18 

9.82899 
9.82926 
9.82953 
9.82980 
9.83008 

27 
27 

27 
28 
27 
27 
27 
28 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
26 
27 
27 
27 
27 
27 
27 
27 
27 
27 

0.17101 
0.17074 
0.17047 
0.17020 
0.16992 

9.91857 
9.91849 
9.91840 
9.91832 
9.91823 

8 
9 
8 
9 

8 
9 
8 
9 
8 
9 
9 
8 
9 
8 
9 
9 
8 
9 
8 
9 
9 
8 
9 
9 
8 
9 
9 
8 
9 
9 
8 
9 
9 
8 
9 
9 
9 
8 
9 
9 
8 
9 
9 
9 
8 
9 
9 
9 
9 
8 
9 
9 
9 
9 
8 
9 
9 
9 
9 
9 

60 

59 
58 
57 
56 

6 

7 
8 
9 
10 
20 
30 
40 
50 

:i 

'5 
! 
4 

r 

M 

'  j 
i 

.'i 

:l 

':  \ 
1 
\ 

4 
5 

6 
7 
8 
9 
«10 
20 
30 
40 
50 

J 

*v 
"•ji 
'[  , 
i 
I 
If 

2; 
r> 

7 
X 
9 
0 
\) 
0 
0 
0 

0 

7 
8 
9 
0 
0 
0 
0 
0 

6 

7 
8 
9 
0 
0 
0 
0 
0 

0 

] 
1 
1 
1 

3 

4 
6 

7 

!8   27 

2.8   2.7 
J.3   3.2 
J.7   3.6 
1.2   4.1 
L7   4.5 
).3   9.0 
1.0  13.5 
5.7  18.0 
5.3  22.5 

26 

2.6 
3.0 
3.5 
3.9 
4.3 
8.7 
13.0 
17.3 
21.7 

19 

1.9 
2.2 
2.5 
2.9 
3.2 
6.3 
9.5 
12.7 
15.8 

18 

1.8 
2.1 
2.4 
2.7 
3.0 
6.0 
9.0 
12.0 
15.0 

9   8 

.9  0.8 
.1  0.9 
.2  1.1 
.4  1.2 
.5  1.3 
.0  2.7 
.5  4.0 
.0  5.3 
.5  6.7 

5 
6 

7 
8 
9 

9.74850 
9.74868 
9.74887 
9.74906 
9.74924 

9.83035 
9.83062 
9.83089 
9.83117 
9.83144 

0.16965 
0.16938 
0.16911 

o!l6856 

9.91815 
9.91806 
9.91798 
9.91789 
9.91781 

55 
54 
53 
52 
51 

10 
11 
12 
13 
14 

9.74943 
9.74961 
9.74980 
9.74999 
9.75017 

9.83171 
9.83198 
9.83225 
9.83252 
9.83280 

0.16829 
'  0.16802 
0.16775 
0.16748 
0.16720 

9.91772 
9.91763 
9.91755 
9.91746 
9.91738 

50 

49 
48 
47 
46 

15 
16 
17 
18 
19 

9.75036 
9.75054 
9.75073 
9.75091 
9.75110 

9.83307 
9.83334 
9.83361 
9.83388 
9.83415 

0.16693 
0.16666 
0.16639 
0.16612 
0.16585 

9.91729 
9.91720 
9.91712 
9.91703 
9.91695 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

9.75128 
9.75147 
9.75165 
9.75184 
9.75202 

9.83442 
9.83470 
9.83497 
9.83524 
9.83551 

0.16558 
0.16530 
0.16503 
0.16476 
0.16449 

9.91686 
9.91677 
9.91669 
9.91660 
9.91651 

40 

39 
38 
37 
36 

25 
26 
27 
28 
29 
"30" 
31 
32 
33 
34 

9.75221 
9.75239 
9.75258 
9.75276 
9.75294 

9.83578 
9.83605 
9.83632 
9.83659 
9.83686 

0.16422 
0.16395 
0.16368 
0.16341 
0.16314 

9.91643 
9.91634 
9.91625 
9.91617 
9.91608 

35 
34 
33 
32 
31 

9.75313 
9.75331 
9.75350 
9.75368 
9.75386 

9.83713 
9.83740 
9.83768 
9.83795 
9.83822 

0.16287 
0.16260 
0.16232 
0.16205 
0.16178 

9.91599 
9.91591 
9.91582 
9.91573 
9.91565 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.75405 
9.75423 
9.75441 
9.75459 
9.75478 

9.83849 
9.83876 
9.83903 
9.83930 
9.83957 

0.16151 
0.16124 
0.16097 
0.16070 
0.16043 

9.91556 
9.91547 
9.91538 
9.91530 
9.91521 

25 
24 
23 
22 
21 

20 

19 
18 
17 
16 

14 
13 
12 
11 

40 

41 
42 
43 
44 

9.75496 
9.75514 
9.75533 
9.75551 
9.75569 

9.83984 
9.84011 
9.84038 
9.84065 
9.84092 

0.16016 
0.15989 
0.15962 
0.15935 
0.15908 

9.91512 
9.91504 
9.91495 
9.91486 
9.91477 

45 
46 
47 
48 
49 

9.75587 
9.75605 
9.75624 
9.75642 
9.75660 

9.84119 
9.84146 
9.84173 
9.84200 
9.84227 

0.15881 
0.15854 
0.15827 
0.15800 
0.15773 

9.91469 
9.91460 
9.91451 
9.91442 
9.91433 

50 

51 

52 
53 
54 
55 
56 
57 
58 
59 

9.75678 
9.75696 
9.75714 
9.75733 
9.75751 

9.84254 
9.84280 
9.84307 
9.84334 
9.84361 

0.15746 
0.15720 
0.15693 
0.15666 
0.15639 

9.91425 
9.91416 
9.91407 
9.91398 
9.91389 

10 

9 
8 
7 
6 

9.75769 
9.75787 
9.75805 
9.75823 
9.75841 

9.84388 
9.84415 
9.84442 
9.84469 
9.84496 

0.15612 
0.15585 
0.15558 
0.15531 
0.15504 

9.91381 
9.91372 
9.91363 
9.91354 
9.91345 

5 
4 
3- 
2 
1 

60 

9.75859 

9.84523 

0.15477 

9.91336 

0 

L.  Cos. 

d. 

L.  Cotgr. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

P.P. 

55° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
35° 


1063 


1 

L.  Sin. 

d. 

L.Tang 

d.  c. 

L.  Cotg 

L.  Cos. 

d. 

I 

'.P 

0 

1 

2 
3 
4 

9.75859 
9.75877 
9.75895 
9.75913 
9.75931 

18 
18 
18 
18 
18 

9.84523 
9.84550 
9.84576 
9.84603 
9.84630 

27 
26 
27 
27 
27 

0.15477 
0.15450 
0.15424 
0.15397 
0.15370 

9.91336 
9.91328 
9.91319 
9.91310 
9.91301 

8 
9 
9 
9 

60 

59 

58 
57 
56 

2 

6   5 

7 

7 

>.7 
!  ° 

26 

2.6 

0  A 

5 

6 
7 
8 
9 

9.75949 
9.75967 
9.75985 
9.76003 
9.76021 

18 
18 
18 
18 
18 

9.84657 
9.84684 
9.84711 
9.84738 
9.84764 

27 
27 
27 
26 
97 

0.15343 
0.15316 
0.15289 
0.15262 
0.15236 

9.91292 
9.91283 
9.91274 
9.91266 
9.91257 

9 
9 
8 
9 

55 
54 
53 
52 
51 

8  J 
9   4 
10   4 

20   < 
30  1J 

.1 
.5 
.0 

5 

3.5 
3.9 
4.3 
8.7 
13.0 

10 

11 
12 
13 

14 

9.76039 
9.76057 
9.76075 
9.76093 
9.76111 

18 
18 
18 
18 
18 

9.84791 
9.84818 
9.84845 
9.84872 
9.84899 

27 
27 
27 
27 
26 

0.15209 
0.15182 
0.15155 
0.15128 
0.15101 

9.91248 
9.91239 
9.91230 
9.91221 
9.91212 

9 
9 
9 
9 

50 

49 
48 
47 
46 

40  18 
50  22 

.0 
.5 

| 

17.3 
21.7 

| 

15 
16 
17 

18 
19 

9.76129 
9.76146 
9.76164 
9.76182 
9.76200 

17 

18 
18 
18 
18 

9.84925 
9.84952 
9.84979 
9.85006 
9.85033 

27 
27 
27 
27 
9fi 

0.15075 
0.15048 
0.15021 
0.14994 
0.14967 

9.91203 
9.91194 
9.91185 
9.91176 
9.91167 

9 
9 
9 
9 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

1 
2 

2 
2 
3 

.8 
.1 
.4 
.7 
.0 

20 

21 
22 
23 
24 

9.76218 
9.76236 
9.76253 
9.76271 
9.76289 

18 
17 
18 
18 
18 

9.85059 
9.85086 
9.85113 
9.85140 
9.85166 

27 
27 
27 
26 
27 

0.14941 
0.14914 
0.14887 
0.14860 
0.14834 

9.91158 
9.91149 
9.91141 
9.91132 
9.91123 

9 
8 
9 
9 

40 

39 
38 
37 
36 

20 
30 
40 
50 

6 
9 
12 
15 

.0 
.0 
.0 
.0 

25 
26 

27 
28 
29 

9.76307 
9.76324 
9.76342 
9.76360 
9.76378 

17 
18 
18 
18 
17 

9.85193 
9.85220 
9.85247 
9.85273 
9.85300 

27 
27 
26 
27 

0.14807 
0.14780 
0.14753 
0.14727 
0.14700 

9.91114 
9.91105 
9.91096 
9.91087 
9.91078 

9 
9 
9 
9 

35 
34 
33 
32 
31 

6 

7 
8 

1 

1 

2 

2 

7 

.7 
.0 
.3 

30 

31 
32 
33 
34 

9.76395 
9.76413 
9.76431 
9.76448 
9.76466 

18 
18 
17 
18 

-IQ 

9.85327 
9.85354 
9.85380 
9.85407 
9.85434 

27 
26 
27 
27 
oc 

0.14673 
0.14646 
0.14620 
0.14593 
0.14566 

9.91069 
9.91060 
9.91051 
9.91042 
9.91033' 

9 
9 
9 
9 
10 

30 

29 

28 
27 
26 

9 
10 
20 
30 
40 
50 

2 
2 
5 
8 
11 
}<\ 

.6 
.8 
.7 
.5 
.3 
2 

35 
36 
37 
38 
39 

9.76484 
9.76501 
9.76519 
9.76537 
9.76554 

17 
18 
18 
17 

9.85460 
9.85487 
9.85514 
9.85540 
9.85567 

27 
27 
26 
27 

0.14540 
0.14513 
0.14486 
0.14460 
0.14433 

9.91023 
9.91014 
9.91005 
9.90996 
9.90987 

9 
9 
9 
9 

25 
24 
23 
22 
21 

6 

7 

1 

1 

3 

0 
n 

40 

41 
42 
43 
44 

9.76572 
9.76590 
9.76607 
9.76625 
9.76642 

18 
17 

18 
17 

18 

9.85594 
9.85620 
9.85647 
9.85674 
9.85700 

26 
27 
27 
26 
97 

0.14406 
0.14380 
0.14353 
0.14326 
0.14300 

9.90978 
9.90969 
9.90960 
9.90951 
9.90942 

9 
9 
9 
9 
9 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

1 
1 
1 
3 
5 

3 
5 
7 
3 
0 

45 
46 
47 
48 
49 

9.76660 
9.76677 
9.76695 
9.76712 
9.76730 

17 
18 
17 
18 
17 

9.85727 
9.85754 
9.85780 
9.85807 
9.85834 

27 
26 
27 
27 
9fi 

0.14273 
0.14246 
0.14220 
0.14193 
0.14166 

9.90933 
9.90924 
9.90915 
9.90906 
9.90896 

9 
9 
9 
10 
9 

15 
14 

13 
12 
11 

40 
50 

6 

8 

B 

7 
3 

8 

50 

51 
52 
53 
54 

9.76747 
9.76765 
976782 
9.76800 
9.76817 

18 
17 
18 
17 

-IQ 

9.85860 
9.85887 
9.85913 
9.85940 
9.85967 

27 
26 
27 
27 
9fi 

0.14140 
0.14113 
0.14087 
0.14060 
0.14033 

9.90887 
9.90878 
9.90869 
9.90860 
9.90851 

9 
9 
9 
9 
9 

10 

9 

8. 

6 

6  0 
7  1 
8  1 
9  1 
10  1 

.9 
.1 
.2 
.4 
.5 

0.8 
0.9 
1.1 
1.2 
1.3 

55 
56 
57 
58 
59 

9.76835 
9.76852 
9.76870 
9.76887 
9.76904 

17 
18 
17 
17 

9.85993 
9.86020 
9.86046 
9.86073 
9.86100 

27 
26 
27 
27 
9fi 

0.14007 
0.13980 
0.13954 
0.13927 
0.13900 

9.90842 
9.90832 
9.90823 
9.90814 
9.90805 

10 
9 
9 
9 
9 

5 
4 
3 
2 

1 

20  3 
30  4 
40  6 
50  7 

.U 

.5 
.0 
.5 

2.7 
4.0 
5.3 
6.7 

60 

9.76922 

9.86126 

0.13874 

9.90796 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.C. 

L.Tang. 

L.  Sin. 

d. 

' 

P 

P. 

54° 


1064            LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
_ 36° 


1 

L.Sin 

d. 

L.Tang 

d.  c 

L.  Cotg 

L.Cos 

d. 

! 

M 

t  '  ' 

0 

1 

2 
3 
4 

9.76922 
9.76939 
9.76957 
9.76974 
9.76991 

17 

18 
17 
17 
18 

9.86126 
9.86153 
9.86179 
9.86206 
9.86232 

27 
26 
27 
26 
27 

0.13874 
0.13847 
0.13821 
0.13794 
0.13768 

9.90796 
9.90787 
9.90777 
9.90768 
9.90759 

1C 
9 

9 

60 

59 

58 
57 
56 

6 

7 

>7 

2.7 
3  ° 

26 

2.6 
3  0 

5 
6 
7 
8 
9 

9.77009 
9.77026 
9.77043 
9.77061 
9.77078 

17 
17 
18 
17 
17 

9.86259 
9.86285 
9.86312 
9.86338 
9.86365 

26 

27 
26 
27 
97 

0.13741 
0.13715 
0.13688 
0.13662 
0.13635 

9.90750 
9.90741 
9.90731 
9.90722 
9.90713 

9 
10 
9 
9 

55 
54 
53 

52 
51 

8 
9 
10 
20 
30 

1 

3.6 
1.1 
1.5 

?  ") 

3.5 
3.9 
'4.3 

8.7 
13.0 

10 

11 
12 
13 
14 

9.77095 
9.77112 
9.77130 
9.77147 
9.77164 

17 
18 
17 
17 
17 

9.86392 
9.86418 
9.86445 
9.86471 
9.86498 

26 
27 
26 
27 

0.13608 
0.13582 
0.13555 
0.13529 
0.13502 

9.90704 
9.90694 
9.90685 
9.90676 
9.90667 

10 
9 
9 
9 
10 

50 

49 
48 
47 
46 

40 
50 

1, 

2 

v'0 
tf 

J 

17.3 
21.7 

8 

15 
16 
17 
18 
19 

9.77181 
9.77199 
9.77216 
9.77233 
9.77250 

18 
17 
17 
17 
18 

9.86524 
9.86551 
9.86577 
9.86603 
9.86630 

27 
26 
26 

27 

0.13476 
0.13449 
0.13423 
0.13397 
0.13370 

9.90657 
9.90648 
9.90639 
9.90630 
9.90620 

9 
9 
9 
10 

45 
44 
43 
42 
41 

6 

7 
8 
9 
0 

1 

4 
'   -1 

i 

L.8 

IA 
1.7 
5.0 

20 

21 
22 
23 
24 

9.77268 
9.77285 
9.77302 
9.77319 
9.77336 

17 
17 

17 
17 
17 

9.86656 
9.86683 
9.86709 
9.86736 
9.86762 

27 
26 
27 
26 
27 

0.13344 
0.13317 
0.13291 
0.13264 
0.13238 

9.90611 
9.90602 
9.90592 
9.90583 
9.90574 

9 
10 
9 
9 
9 

40 

39 
38 
37 
36 

' 

.JO 
50 
10 

)0 

( 

( 

ii 

M 

25 
26 
27 
28 
29 

9.77353 
9.77370 
9.77387 
9.77405 
9.77422 

17 
17 
18 
17 
17 

9.86789 
9.86815 
9.86842 
9.86868 
9.86894 

26 
27 
26 
26 

0.13211 
0.13185 
0.13158 
0.13132 
0.13106 

9.90565 
9.90555 
9.90546 
9.90537 
9.90527 

10 
9 
9 
10 

35 
34 
33 
32 
31 

f> 
7 
8 

I 

i 

! 

J'j 
.7 
.0 
.3 

30 

31 
32 
33 
34 

9.77439 
9.77456 
9.77473 
9.77490 
9.77507 

17 
17 
17 

17 
17 

9.86921 
9,86947 
9.86974 
9.87000- 
9.87027 

26 
27 
26 
27 
2fi 

0.13079 
0.13053 
0.13026 
0.13000 
0.12973 

9.90518 
9.90509 
9.90499 
9.90490 
9.90480 

9 
10 
9 
10 

30 

29 
28 
27 
26 

': 

f  * 
\  "\ 

9 

0 
JO 

0 
0 

o 

S 
5 
8 
11 
1  1 

.6 
.8- 
.7 
.5 
.3 
2 

35 
36 
37 
38 
39 

9.77524 
9.77541 
9.77558 
9.77575 
9.77592 

17 
17 
17 
17 
17 

9.87053 
9.87079 
9.87106 
9.87132 
9.87158 

26 
27 
26 

26 
27 

0.12947 
0.12921 
0.12894 
0.12868 
0.12842 

9.90471 
9.90462 
9.90452 
9.90443 
9.90434 

9 
10 
9 
9 

1ft 

25 
24 
23 
22 
21 

6 

r 
i 

6 
.6 

40 

41 
42 
43 
44 

9.77609 
9.77626 
9.77643 
9.77660 
9.77677 

17 
17 
17 
17 
17 

9.87185 
9.87211 
9.87238 
9.87264 
9.87290 

26 

27 
26 
26 

0.12815 
0.12789 
0.12762 
0.12736 
0.12710 

9.90424 
9.90415 
9.90405 
9.90396 
9.90386 

9 
10 
9 
10 

20 

19 
18 
17 
16 

j 
*  <« 

r'  j] 

8 
9 
0 
0 
0 

2 
2 
5 

8 

.1 
.4 
.7 
.3 

.0 

45 
46 
47 
48 
49 

9.77694 
9.77711 
9.77728 
9.77744 
9.77761 

17 
17 
16 
17 
17 

9.87317 
9.87343 
9.87369 
9.87396 

9.87422 

26 

26 
27 
26 

0.12683 
0.12657 
0.12631 
0.12604 
0.12578 

9.90377 
9.90368 
9.90358 
9.90349 
9.90339 

9 
10 
9 
10 

15 
14 
13 
12 
11 

4 

5 

0 
0 

1 

10 
13 

Q 

.7 
.3 

g 

50 

51 
52 
53 
54 

9.77778 
9.77795 
9.77812 
9.77829 
9.77846 

17 
17 
17 
17 
16 

9.87448 
9.87475 
9.87501 
9.87527 
9.87554 

27 
26 
26 
27 
26 

0.12552 
0.12525 
0.12499 
0.12473 
0.12446 

9.90330 
9.90320 
9.90311 
9.90301 
9.90292 

10 
9 
10 
9 
10 

10 

9 
8 
7 
6 

6 

7 
8 
9 
10 

1 

I 

1 
1 
1 

0 

0 

8 

5 

7 

0.9 
1.1 
1.2 
1.4 
1.5 

55 
56 
57 
58 
59 

9.77862 
9.77879 
9.77896 
9.77913 
9.77930 

17 
17 
17 
17 
16 

9.87580 
9.87606 
9.87633 
9.87659 
9.87685 

26 
27 
26 
26 
26 

0.12420 
0.12394 
0.12367 
0.12341 
0.12315 

9.90282 
9.90273 
9.90263 
9.90254 
9.90244 

9 
10 
9 
10 
9 

5 
4 
3 
2 
1 

20 
30 
40 
50 

3 

5 
6 

8 

3 

0 
7 
3 

3.0 
4.5 
6.0 
7.5 

60 

9.77946 

9.87711 

0.12289 

9.90235 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin 

d. 

/" 

P. 

P. 

53° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
37° 


1065 


> 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P. 

0 

1 

2 
3 
4 

9.77946 
9.77963 
9.77980 
9.77997 
9.78013 

17 
17 
17 
16 
17 

9.87711 
9.87738 
9.87764 
9.87790 
9.87817 

27 
26 
26 
27 
26 

0.12289 
0.12262 
0.12236 
0.12210 
0.12183 

9.90235 
9.90225 
9.90216 
9.90206 
9.90197 

10 
9 
10 
9 

60 

59 
58 
57 
56 

6 

7 

27 

2.7 
q  o 

5 
6 

7 
8 
9 

9.78030 
9.78047 
9.78063 
9.78080 
9.78097 

17 

16 
17 
17 

9.87843 
9.87869 
9.87895 
9.87922 
9.87948 

26 
26 
27 
26 
2fi 

0.12157 
0.12131 
0.12105 
0.12078 
0.12052 

9.90187 
9.90178 
9.90168 
9.90159 
9.90149 

9 
10 
9 
10 

55 
54 
53 
52 
51 

8 
9 
10 
20 
•30 

3.6 
4.1 
4.5 
9.0 
13.5 

10 

11 
12 
13 
14 

9.78113 
9.78130 
9.78147 
9.78163 
9.78180 

17 
17 
16 
17 

9.87974 
9.88000 
9.88027 
9.88053 
9.88079 

26 
27 
26 
26 
26 

0.12026 
0.12000 
0.11973 
0.11947 
0.11921 

9.90139 
9.90130 
9.90120 
9.90111 
9.90101 

9 
10 
9 
10 

SO 

49 

48 
47 
46 

40 
50 

18.0 
22.5 

26 

15 
16 
17 

18 
19 

9.78197 
9.78213 
9.78230 
9.78246 
9.78263 

16 
17 
16 
17 
17 

9.88105 
9.88131 
9.88158 
9.88184 
9.88210 

26 
27 
26 
26 
26 

0.11895 
0.11869 
0.11842 
0.11816 
0.11790 

9.90091 
9.90082 
9.90072 
9.90063 
9.90053 

9 
10 
9 
10 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2.6 
3.0 
3.5 
3.9 
4.3 

20 

21 
22 
23 
24 

9.78280 
9.78296 
9.78313 
9.78329 
9.78346 

16 
17 
16 
17 

9.88236 

9.88262 
9.88289 
9.88315 
9.88341 

26 
27 
26 
26 
26 

0.11764 
0.11738 
0.11711 
0.11685 
0.11659 

9.90043 
9.90034 
9.90024 
9.90014 
9.90005 

9 
10 
10 
9 

40 

39 
38 
37 
36 

20 
30 
40 
50 

8.7 
13.0 
17.3 
21.7 

25 
26 
27 
28 
29 

9.78362 
9.78379 
9.78395 
9.78412 
9.78428 

17 
16 
17 
16 

9.88367 
9.88393 
9.88420 
9.88446 
9.88472 

26 
27 
26 
26 
26 

0.11633 
0.11607 
0.11580 
0.11554 
0.11528 

9.89995 
9.89985 
9.89976 
9.89966 
9.89956 

10 
9 
10 
10 

35 
34 
33 
32 
31 

6 

7 
8 

17 

1.7 
2.0 
2.3 

30 

31 
32 
33 
34 

9.78445 
9.78461 
9.78478 
9.78494 
9.78510 

16 
17 
16 
16 

9.88498 
9.88524 
9.88550 
9.88577 
9.88603 

26 
26 
27 
26 
26 

0.11502 
0.11476 
0.11450 
0.11423 
0.11397 

9.89947 
9.89937 
9.89927 
9.89918 
9.89908 

10 
10 
9 
10 

30 

29 

28 
27 
26 

9 
10 
20 
30 
40 
50 

2.6 
2.8 
5.7 
8.5 
11.3 
142 

35 
36 
37 
38 
39 

9.78527 
9.78543 
9.78560 
9.78576 
9.78592 

16 

17 
16 
16 
17 

9.88629 
9.88655 
9.88681 
9.88707 
9.88733 

26 
26 
26 
26 
26 

0.11371 
0.11345 
0.11319 
0.11293 
0.11267 

9.89898 
9.89888 
9.89879 
9.89869 
9.89859 

10 
9 
10 
10 
10 

25 
24 
23 
22 
21 

6 

7 

16 

1.6 
1  9 

40 

41 

42 
43 
44 

9.78609 
9.78625 
9.78642 
9.78658 
9.78674 

16 
17 
16 
16 

9.88759 
9.88786 
9.88812 
9.88838 
9.88864 

27 
26 
26 
26 
26 

0.11241 
0.11214 
0.11188 
0.11162 
0.11136 

9.89849 
9.89840 
9.89830 
9.89820 
9.89810 

9 
10 
10 
10 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

2.1 
2.4 
2.7 
5.3 
8.0 

45 

46 
47 

48 
49 

9.78691 
9.78707 
9.78723 
9.78739 
9.78756 

16 
16 
16 
17 

9.88890 
9.88916 
9.88942 
9.88968 
9.88994 

26 
26 
26 
26 
26 

0.11110 
0.11084 
0.11058 
0.11032 
0.11006 

9.89801 
9.89791 
9.89781 
9.89771 
9.89761 

10 
10 
10 
10 

15 
14 
13 
12 
11 

40 

50 

| 

10.7 
13.3 

0   9 

50 

51 
52 
53 
54 

9.78772 
9.78788 
9.78805 
9.78821 
9.78837 

16 
17 
16 
16 
16 

9.89020 
9.89046 
9.89073 
9.89099 
9.89125 

26 
27 
26 
26 

9g 

0.10980 
0.10954 
0.10927 
0.10901 
0.10875 

9.89752 
9.89742 
9.89732 
9.89722 
9.89712 

10 
10 
10 
10 
10 

10 

9 

8 
7 
6 

6  1 

7  1 
8  1 
9  1 
10  1 

.0  0.9 
.2  1.1 
.3  1.2 
.5  1.4 
.7  1.5 

55 
56 
57 
58 
59 

9.78853 
9.78869 
9.78886 
9.78902 
9.78918 

16 
17 
16 
16 
16 

9.89151 
9.89177 
9.89203 
9.89229 
9.89255 

26 
26 
26 
26 
26 

0.10849 
0.10823 
0.10797 
0.10771 
0.10745 

9.89702 
9.89693 
9.89683 
9.89673 
9.89663 

9 

10 
10 
10 
10 

5 
4 
3 
2 

1 

20  3 
30  5 
40  6 
50  8 

.3  3.0 
.0  4.5 
.7  6.0 
.3  7.5 

60 

9.78934 

9.89281 

0.10719 

9.89653 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P 

.P. 

52° 


1066  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

38° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

P 

0 

1 

2 
3 
4 

9.78934 
9.78950 
9.78967 
9.78983 
9.78999 

16 
17 
16 
16 
Ifi 

9.89281 
9.89307 
9.89333 
9.89359 
9.89385 

26 
26 
26 
26 
2fi 

0.10719 
0.10693 
0.10667 
0.10641 
0.10615 

9.89653 
9.89643 
9.89633 
9.89624 
9.89614 

10 
10 
9 
10 
10 

60 

59 
58 
57 
56 

6 

*j 

2 

2 

3 

6 
.6 

Q 

25 

2.5 
2  9 

5 
6 

7 
8 
9 

9.79015 
9.79031 
9.79047 
9.79063 
9.79079- 

16 
16 
16 
16 

16 

9.89411 
9.89437 
9.89463 
9.89489 
9.89515 

26 
26 
26 
26 
26 

0.10589 
0.10563 
0.10537 
0.10511 
0.10485 

9.89604 
9.89594 
9.89584 
9.89574 
9.89564 

10 
10 
10 
10 
10 

55 

54 
53 
52 
51 

8 
9 
10 
20 
30 

3 
3 
4 

8 
1?, 

5 
9 
8 
7 
0 

3.3 
3.8 
4.2 
8.3 
12.6 

10 

11 
12 
13 
14 

9.79095 
9.79111 
9.79128 
9.79144 
9.79160 

16 
17 
16 
16 
Ifi 

9.89541 
9.89567 
9.89593 
9.89619 
9.89645 

26 
26 
26 
26 
9fi 

0.10459 
0.10433 
0.10407 
0.10381 
0.10355 

9.89554 
9.89544 
9.89534 
9.89524 
9.89514 

10 
10 
10 
10 

10 

50 

49 
48 
47 
46 

40 
50 

17 
21 

3 

7 

1 

16.7 
20.8 

7 

15 
16 
17 
18 
19 

9.79176 
9.79192 
9.79208 
9.79224 
9.79240 

16 
16 
16 
16 
Ifi 

9.89671 
9.89697 
9.89723 
9.89749 
9.89775 

26 
26 
26 
26 
9fi 

0.10329 
0.10303 
0.10277 
0.10251 
0.10225 

9.89504 
9.89495 
9.89485 
9.89475 
9.89465 

9 

10 
10 
10 
10 

45 
44 
43 
42 
41 

[: 

6 

7 
8 
9 
0 

1 
'3 
-3 
5 
5 

.7 
.0 
.3 
.6 

.8 

20 

21 
22 
23 
24 

9.79256 
9.79272 
9.79288 
9.79304 
9.79319 

16 
16 
16 
15 
Ifi 

9.89801 
9.89827 
9.89853 
9.89879 
9.89905 

26 
26 
26 
26 
9fi 

0.10199 
0.10173 
0.10147 
0.10121 
0.10095 

9.89455 
9.89445 
9.89435 
9.89425 
9.89415 

10 
10 
10 
10 
10 

40 

39 
38 
37 
36 

j  ! 
•  < 

'.  i 

^U 

io 

10 
>U 

'.i 

11 

U 

.7 
.5 
.3 
.2 

25 
26 

27 
28 
29 

9.79335 
9.79351 
9.79367 
9.79383 
9.79399 

16 
16 
16 
16 

9.89931 
9.89957 
9.89983 
9.90009 
9.90035 

26 
26 
26 
26 

0.10069 
0.10043 
0.10017 
0.09991 
0.09965 

9.89405 
9.89395 
9.89385 
9.89375 
9.89364 

10 
10 
10 

11 

35 
34 
33 
32 
31 

6 

7 
8 

1 

1 
1 

2 

3 

6 
9 

1 

15 
1.5 
1.8 
2.0 

30 

31 
32 
33 
34 

9.79415 
9.79431 
9.79447 
9.79463 
9.79478 

16 
16 
16 
15 
Ifi 

9.90061 
9.90086 
9.90112 
9.90138 
9.90164 

25 
26 
26 
26 
2fi 

0.09939 
0.09914 
0.09888 
0.09862 
0.09836 

9.89354 
9.89344 
9.89334 
9.89324 
9.89314 

10 
10 
10 
10 
10 

30 

29 

28 
27 
26 

9 
10 
20 
30 
40 
50 

2 
2 
5 
8 
10 
IS 

4 
7 
3 

.0 
7 
8 

2.3 
2.5 
5.0 
7.5 
10.0 
125 

35 
36 
37 
38 
39 

9.79494 
9.79510 
9.79526 
9.79542 
9.79558 

16 
16 
16 
16 
TS 

9.90190 
9.90216 
9.90242 
9.90268 
9.90294 

26 
26 
26 
26 
2fi 

0.09810 
0.09784 
0.09758 
0.09732 
0.09706 

9.89304 
9.89294 
9.89284 
9.89274 
9.89264 

10 
10 
10 
10 
10 

25 
24 
23 
22 
21 

6 

7 

1 

1 
] 

1'  ' 

1 
3 

40 

41 
42 
43 
44 

9.79573 
9.79589 
9.79605 
9.79621 
9.79636 

16 
16 
16 
15 

9.90320 
9.90346 
9.90371 
9.90397 
9.90423 

26 
25  . 
26 
26 

0.09680 
0.09654 
0.09629 
0.09603 
0.09577 

9.89254 
9.89244 
9.89233 
9.89223 
9.89213 

10 

11 

10 
10 
10 

20 

19 
18 
17 
16 

8 
9 
10 
20 
-to 

1 
1 
1 

3 
6 

5 
7 
8 
7 
5 

45 
46 
47 
48 
49 

9.79652 
9.79668 
9.79684 
9.79699 
9.79715 

16 
16 
15 
16 
Ifi 

9.90449 
9.90475 
9.90501 
9.90527 
9.90553 

26 
26 
26 
26 

nr. 

0.09551 
0.09525 
0.09499 
0.09473 
0.09447 

9.89203 
9.89193 
9.89183 
9.89173 
9.89162 

10 
10 
10 

11 

10 

15 
14 
13 
12 
11 

40 
50 

| 

7 
9 

n 

3 
2 

9 

50 

51 
52 
53 
54 

9.79731 
9.79746 
9.79762 
9.79778 
9.79793 

15 
16 
16 
15 

9.90578 
9.90604 
9.90630 
9.90656 
9.90682 

26 
26 
26 
26 

0.09422 
0.09396 
0.09370 
0.09344 
0.09318 

9.89152 
9.89142 
9.89132 
9.89122 
9.89112 

10 
10 
10 
10 

10 

9 

8 
7 
6 

6 

7 
8 
9 
10 

1 
1 

1 
1 

1 

.0 
.2 

.3 
.5 

.7 

0.9 
1.1 
1.2 
1.4 
1.5 

55 
56 
57 
58 
59 

9.79809 
9.79825 
9.79840 
9.79856 
9.79872 

16 
15 
16 
16 

•IK 

9.90708 
9.90734 
9.90759 
9.90785 
9.90811 

26 
25 
26 
26 
Qfi 

0.09292 
0.09266 
0.09241 
0.09215 
0.09189 

9.89101 
9.89091 
9.89081 
9.89071 
9.89060 

10 
10 
10 

11 

10 

5 
4 
3 
2 
1 

20 
30 
40 
50 

3 
5 
6 

8 

.3 
.0 
.7 
.3 

3.0 
4.5 
6.0 

7.5 

60 

9.79887 

9.90837 

0.09163 

9.89050 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

r 

P 

P 

LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
39° 


1067 


' 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg.l  L.  Cos. 

d. 

P 

.P. 

0 

1 

2 
3 
4 

9.79887 
9.79903 
9.79918 
9.79934 
9.79950 

16 
15 
16 
16 

1C 

9.90837 
9.90863 
9.90889 
9.90914 
9.90940 

26 
26 
25 
26 

0.09163  9.89050 
0.09137  9.89040 
0.09111  9.89030 
0.09086  9.89020 
0.09060  9.89009 

10 
10 
10 
11 

60 

59 
58 
57 
56 

6 

26 

2.6 

5 
6 

7 
8 
9 

9.79965 
9.79981 
9.79996 
9.80012 
9.80027 

16 
15 
16 
15 
16 

9.90966 
9.90992 
9.91018 
9.91043 
9.91069 

26 
26 
25 
26 

0.09034  9.88999 
0.09008  9.88989 
0.08982  9.88978 
0.08957  9.88968 
0.08931  9.88958 

10 
11 
10 
10 

55 
54 
53 
52 
51 

"8 
9 
10 
20 
30 

3.5 
3.9 
4.3 
8.7 
13.0 

10 

11 
12 
13 
14 

9.80043 
9.80058 
9.80074 
9.80089 
9.80105 

15 
16 
15 
16 

1C 

9.91095 
9.91121 
9.91147 
9.91172 
9.91198 

26 
26 
25 
26 

0.08905  9.88948 
0.08879  9.88937 
0.08853  9.88927 
0.08828  9.88917 
0.08802  9.88906 

11 
10 
10 

11 

50 

49 
48 
47 
46 

40 
50 

17.3 
21.7 

25 

15 
16 
17 
18 
19 

9.80120 
9.80136 
9.80151 
9,80166 
9.80182 

16 
15 
15 
16 

lit 

9.91224 
9.91250 
9.91276 
9.91301 
9.91327 

26 
26 
25 
26 

0.08776  9.88896 
0.08750  9.88886 
0.08724  9.88875 
0.08699  9.88865 
0.08673  9.88855 

10 

11 

10 
10 

45 
44 
43 
42 
41 

6 

7 
8 
9 
10 

2.5 
2.9 
3.3 
3.8 
4.2 

20 

21 
22 
23 
24 

9.80197 
9.80213 
9.80228 
9.80244 
9.80259 

16 
15 
16 
15 
15 

9.91353 
9.91379 
9.91404 
9.91430 
9.91456 

26 
25 
26 
26 
2fi 

0.08647  9.88844 
0.08621  9.88834 
0.08596  9.88824 
0.08570  9.88813 
0.08544  9.88803 

10 
10 

11 

10 
10 

40 

39 
38 
37 
36 

20 
30 
40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 
27 
28 
29 

9.80274 
9.80290 
9.8C305 
9.80320 
9.80336 

16 
15 
15 
16 

9.91482 
9.91507 
9.91533 
9.91559 
9.91585 

25 
26 
26 
26 

0.08518  9.88793 
0.08493  9.88782 
0.08467  9.88772 
0.08441  9.88761 
0.08415  9.88751 

11 

10 

11 

10 

35 
34 
33 
32 
31 

6 

7 
8 

16 
1.6 
1.9 
2.1 

30 

31 
32 
33 
34 

9.80351 
9.80366 
9.80382 
9.80397 
9.80412 

15 
16 
15 
15 
16 

9.91610 
9.91636 
9.91662 
9.916S8 
9.91713 

26 
26 
26 
25 
9fi 

0.08390  9.88741 
0.08364  9.88730 
0.08338  9.88720 
0.08312  9.88709 
0.08287  9.88699 

11 

10 

11 

10 
11 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

2.4 

2.7 
5.3 
8.0 
10.7 
133 

35 
36 
37 
38 
39 

9.80428 
9.80443 
9.80458 
9.80473 
9.80489 

15 
15 
15 
16 

1C 

9.91739 
9.91765 
9.91791 
9.91816 
9.91842 

26 
26 
25 
26 

0.08261  9.88688 
0.08235  9.88678 
0.08209  9.88668 
0.08184  9.88657 
0.08158  9.88647 

10 
10 

11 

10 

25 
24 
23 
22 
21 

6 

15 

1.5 

40 

41 
42 
43 
44 

9.80504 
9.80519 
9.80534 
9.80550 
9.80565 

15 
15 
16 
15 

9.91868 
9.91893 
9.91919 
9.91945 
9.91971 

25 
26 
26 
26 

0.08132  9.88636 
0.08107  9.88626 
0.08081  9.88615 
0.08055  9.88605 
0.08029  9.88594 

10 

11 

10 

11 

20 

19 

18 
17 
16 

8 
9 
10 
20 
30 

2.0 
2.3 
2.5 
5.0 

7.5 

45 
46 
47 
48 
49 

9.80580 
9.80595* 
9.80610 
9.80625 
9.80641 

15 
15 
15 
16 
15 

9.91996 
9.92022 
9.92048 
9.92073 
9.92099 

26 
26 
25 
26 
9fi 

0.08004  9.88584 
0.07978  9.88573 
0.07952  9.88563 
0.07927  9.88552 
0.07901  9.88542 

11 

10 

11 

10 
11 

15 
14 
13 
12 
11 

40 
50 

| 

10.0 
12.5 

1   10 

50 

51 
52 
53 
54 

9.80656 
9.80671 
9.80686 
9.80701 
9.80716 

15 
15 
15 
15 
15 

9.92125 
9.92150 
9.92176 
9.92202 
9.92227 

25 
26 
26 
25 
2fi 

0.07875  9.88531 
0.07850  9.88521 
0.07824  9.88510 
0.07798  9.88499 
0.07773  9.88489 

10 

11 
11 

10 
11 

10 

9 

8 
7 
6 

6  1 

7  1 
8  1 
9  1 
10  1 

1  1.0 
3  1.2 
5  1.3 
7  1.5 
8  1.7 

55 
56 
57 
58 
59 

9.80731 
9.80746 
9.80762 
9.80777 
9.80792 

15 
16 
15 
15 

-1C 

9.92253 
9.92279 
9.92304 
9.92330 
9.92356 

26 
25 
26 
26 

OK 

0.07747  9.88478 
0.07721  9.88468 
0.07696  9.88457 
0.07670  9.88447 
0.07644  9.88436 

10 

11 

10 

11 

11 

5 
4 
3 
2 
1 

20  3 
30  5 
40  7 
50  9 

7  3.3 
5  5.0 
3  6.7 
2  8.3 

60 

9.80807 

9.92381 

0.07619  9.88425 

0 

L.  Cos. 

d. 

L.  Cotg. 

rt.c. 

L.Tang.  |  L.  Sin. 

d. 

/ 

P 

P. 

50° 


1068 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
40° 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P. 

0 

1 

2 
3 
4 

9.80807 
9.80822 
9.80837 
9.80852 
9.80867 

15 
15 
15 
15 
-ic 

9.92381 
9.92407 
9.92433 
9.92458 
9.92484 

26 
26 
25 
26 
26 

0.07619 
0.07593 
0.07567 
0.07542 
0.07516 

9.88425 
9.88415 
9.88404 
9.88394 
9.88383 

10 
11 
10 

11 

60 

59 
58 
57 
56 

6 

7 

26 

2.6 
3  0 

5 

6 
7 
8 
9 

9.80882 
9.80897 
9.80912 
9.80927 
9.80942 

15 
15 
15 
15 

9.92510 
9.92535 
9.92561 
9.92587 
9.92612 

25 
26 
26 
25 
9fi 

0.07490 
0.07465 
0.07439 
0.07413 
0.07388 

9.88372 
9.88362 
9.88351 
9.88340 
9.88330 

10 

11 
11 

10 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

3.5 
3.9 
4.3 

8.7 
13.0 

10 

11 
12 
13 
14 

9.80957 
9.80972 
9.80987 
9.81002 
9.81017 

15 
15 
15 
15 

9.92638 
9.92663 
9.92689 
9.92715 
9.92740 

25 
26 
26 
25 
2fi 

0.07362 
0.07337 
0.07311 
0.07285 
0.07260 

9.88319 
9.88308 
9.88298 
9.88287 
9.88276 

11 

10 

11 
11 
in 

50 

49 
48 
47 
46 

40 
50 

17.3 

21.7 

25 

15 
16 
17 
18 
19 

9.81032 
9.81047 
9.81061 
9.81076 
9.81091 

15 
14 
15 
15 
IS 

9.92766 
9.92792 
9.92817 
9.92843 
9.92868 

26 
25 
26 
25 
26 

0.07234 
0.07208 
0.07183 
0.07157 
0.07132 

9.88266 
9.88255 
9.88244 
9.88234 
9.88223 

11 
11 

10 

11 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2.5 
2.9 
3.3 
3.8 
4.2 

20 

21 
22 
23 
24 

9.81106 
9.81121 
9.81136 
9.81151 
9.81166 

15 
15 
15 
15 
14 

9.92894 
9.92920 
9.92945 
9.92971 
9.92996 

26 
25 
26 
25 
26 

0.07106 
0.07080 
0.07055 
0.07029 
0.07004 

9.88212 
9.88201 
9.88191 
9.88180 
9.88169 

11 

10 

11 
11 

n 

40 

39 

38 
37 
36 

20 
30 
40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 
27 

28 
29 

9.81180 
9.81195 
9.81210 
9.81225 
9.81240 

15 
15 
15 
15 

9.93022 
9.93048 
9.93073 
9.93099 
9.93124 

26 
25 
26 
25 

0.06978 
0.06952 
0.06927 
0.06901 
0.06876 

9.88158 
9.88148 
9.88137 
9.88126 
9.88115 

10 

11 
11 
11 

35 
34 
33 
32 
31 

6 

7 
8 

15 
1.5 
1.8 
2.0 

SO 

81 
32 
33 
34 

9.81254 
9.81269 
9.81284 
9.81299 
9.81314 

15 
15 
15 
15 

9.93150 
9.93175 
9.93201 
9.93227 
9.93252 

25 
26 
26 
25 

9fi 

0.06850 
0.06825 
0.06799 
0.06773 
0.06748 

9.88105 
9.88094 
9.88083 
9.88072 
9.88061 

11 
11 
11 
11 

1ft 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

2.3 
2.5 

5.0 
7.5 
10.0 
12  5 

35 
36 
37 
38 
39 

9.81328 
9.81343 
9.81358 
9.81372 
9.81387 

15 
15 
14 

15 

1C 

9.93278 
9.93303 
9.93329 
9.93354 
9.93380 

25 
26 
25 
26 

9fi 

0.06722 
0.06697 
0.06671 
0.06646 
0.06620 

9.88051 
9.88040 
9.88029 
9.88018 
9.88007 

11 
11 
11 
11 

25 
24 
23 
22 
21 

6 

14 

1.4 

40 

41 
42 
43 
44 

9.81402 
9.81417 
9.81431 
9.81446 
9.81461 

15 
14 
15 
15 
14 

9.93406 
9.93431 
9.93457 
9.93482 
9.93508 

25 
26 
25 
26 
25 

0.06594 
0.06569 
0.06543 
0.06518 
0.06492 

9.87996 
9.87985 
9.87975 
9.87964 
9.87953 

11 

10 

11 
11 

J]_ 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

1.9 
2.1 
2.3 

4.7 
7.0 

45 
46 
47 
48 
49 

9.81475 
9.81490 
9.81505 
9.81519 
9.81534 

15 
15 
14 
15 

1C 

9.93533 
9.93559 
9.93584 
9.93610 
9.93636 

26 
25 
26 
26 

0.06467 
0.06441 
0.06416 
0.06390 
0.06364 

9.87942 
9.87931 
9.87920 
9.87909 
9.87898 

11 
11 
11 
11 

15 
14 
13 
12 
11 

40 
50 

9.3 
11.7 

1   10 

50 

51 
52 
53 
54 

9.81549 
9.81563 
9.81578 
9.81592 
9.81607 

14 
15 
14 
15 
15 

9.93661 
9.93687 
9.93712 
9.93738 
9.93763 

26 
25 
26 
25 
Ofi 

0.06339 
0.06313 
0.06288 
0.06262 
0.06237 

9.87887 
9.87877 
9.87866 
9.87855 
9.87844 

10 

11 
11 
11 

10 

9 
8 
7 
6 

6  1 
7  1 
8  1 
9  1 
10  1 

.1  1.0 
.3  1.2 
.5  1.3 
.7  1.5 

.8  1.7 

55 
56 
57 
58 
59 

9.81622 
9.81636 
9.81651 
9.81665 
9.81680 

14 
15 
14 
15 

9.93789 
9.93814 
9.93840 
9.93865 
9.93891 

25 
26 
25 
26 

0.06211 
0.06186 
0.06160 
0.06135 
0.06109 

9.87833 
9.87822 
9.87811 
9.87800 
9.87789 

11 
11 
11 
11 

5 
4 
3 
2 
1 

20  3 
30  5 
40  7 
50  9 

.7  3.3 
.5  5.0 
3  6.7 
.2  8.3 

60 

9.81694 

9.93916 

0.06084 

9.87778 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.G. 

L.Tang. 

L.  Sin. 

d. 

i 

P 

P. 

49° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
41° 


1069 


'_ 

L.  Sin. 

d. 

L.Tang 

d.c. 

L.  Cotg 

L.  Cos 

d. 

P 

.P. 

0 

1 

2 
3 
4 

9.81694 
9.81709 
9.81723 
9.81738 
9.81752 

15 
14 
15 
14 
15 

9.93916 
9.93942 
9.93967 
9.93993 
9.94018 

26 
25 
26 
25 
9fi 

0.06084 
0.06058 
0.06033 
0.06007 
0.05982 

9.87778 
9.87767 
9.87756 
9.87745 
9.87734 

11 
11 
11 
11 

60 

59 
58 
57 
56 

6 

26 

2.6 

5 

6 

7 
8 
9 

9.81767 
9.81781 
9.81796 
9.81810 
9.81825 

14 
15 
14 
15 
14 

9.94044 
9.94069 
9.94095 
9.94120 
9.94146 

25 
26 
25 
26 
25 

0.05956 
0.05931 
0.05905 
0.05880 
0.05854 

9.87723 
9.87712 
9.87701 
9.87690 
9.87679 

11 
11 
11 
11 
11 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

3.5 
3.9 
4.3 
8.7 
13.0 

10 

11 
12 
13 
14 

9.81839 
9.81854 
9.81868 
9.81882 
9.81897 

15 

14 
14 
15 
14 

9.94171 
9.94197 
9.94222 
9.94248 
9.94273 

26 
25 
26 
25 

26 

0.05829 
0.05803 
0.05778 
0.05752 
0.05727 

9.87668 
9.87657 
9.87646 
9.87635 
9.87624 

11 
11 
11 
11 

50 

49 
48 
47 
46 

40 
50 

17.3 
21.7 

25 

15 

16 
17 
18 
19 

9.81911 
9.81926 
9.81940 
9.81955 
9.81969 

15 
14 
15 
14 
14 

9.94299 
9.94324 
9.94350 
9.94375 
9.94401 

25 
26 
25 
26 
25 

0.05701 
0.05676 
0.05650 
0.05625 
0.65599 

9.87613 
9.87601 
9.87590 
9.87579 
9.87568 

12 
11 
11 
11 

45 
44 
43 
42 
41 

6 

7 
8 
9 

•  10 

2.5 
2.9 
3.3 
3.8 
4.2 

20 

21 
22 
23 
24 

9.81983 
9.81998 
9.82012 
9.82026 
9.82041 

15 
14 
14 
15 

9.94426 
9.94452 
9.94477 
9.94503 
9.94528 

26 
25 
26 
25 

0.05574 
0.05548 
0.05523 
0.05497 
0.05472 

9.87557 
9.87546 
9.87535 
9.87524 
9.87513 

11 
11 
11 
11 

40 

39 
38 
37 
36 

20 
30 
40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 

27 
28 
29 

9.82055 
9.82069 
9.82084 
9.82098 
9.82112 

14 
15 
14 
14 
14 

9.94554 
9.94579 
9.94604 
9.94630 
9.94655 

25 
25 
26 
25 
9fi 

0.05446 
0.05421 
0.05396 
0.05370 
0.05345 

9.87501 
9.87490 
9.87479 
9.87468 
9.87457 

11 

11 
11 
11 

35 
34 
33 
32 
31 

6 

7 
8 

15 
1.5 
18 
2.0 

30 

31 
32 
33 
34 

9.82126 
9.82141 
9.82155 
9.82169 
9.82184 

15 
14 
14 
15 
14 

9.94681 
9.94706 
9.94732 
5.94757 
9.94783 

25 
26 
25 
26 
25 

0.05319 
0.05294 
0.05268 
0.05243 
0.05217 

9.87446 
9.87434 
9.87423 
9.87412 
9.87401 

12 
11 
11 
11 

30 

29 

28 
27 
26 

9 
10 
20 
30 
40 
50 

2.3 

2.5 
5.0 
7.5 
10.0 
12  5 

35 
36 
37 
38 
39 

9.82198 
9.82212 
9.82226 
9.82240 
9.82255 

14 
14 
14 
15 
14. 

9.94808 
9.94834 
9.94859 
9.94884 
9.94910 

26 
25 
25 
26 

oc 

0.05192 
0.05166 
0.05141 
0.05116 
0.05090 

9.87390 
9.87378 
9.87367 
9.87356 
9.87345 

12 
11 
11 
11 

25 
24 
23 
22 
21 

6 

14 

1.4 

40 

41 
42 
43 
44 

9.82269 
9.82283 
9.82297 
9.82311 
9.82326 

14 
14 
14 
15 
14 

9.94935 
9.94961 
9.94986 
9.95012 
9.95037 

26 
25 
26 
25 
25 

0.05065 
0.05039 
0.05014 
0.04988 
0.04963 

9.87334 
9.87322 
9.87311 
9.87300 
9.87288 

12 
11 
11 
12 
11 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

1.9 
2.1 
2.3 

4.7 
7.0 

45 
46 
47 
48 
49 

9.82340 
9.82354 
9.82368 
9.82382 
9.82396 

14 
14 
14 
14 
•  14 

9.95062 
9.95088 
9.95113 
9.95139 
9.95164 

26 
25 
26 
25 
26 

0.04938 
0.04912 
0.04887 
0.04861 
0.04836 

9.87277 
9.87266 
9.87255 
9.87243 
9.87232 

11 
11 
12 
11 
11 

15 
14 
13 
12 
11 

40 
50 

| 

9.3 
11.7 

2   II 

SO 

51 
52 
53 
54 

9.82410 
9.82424 
9.82439 
9.82453 
9.82467 

14 

15 
14 
14 
14 

9.95190 
9.95215 
9.95240 
9.95266 
9.95291 

25 
25 
26 
25 
26 

0.04810 
0.04785 
0.04760 
0.04734 
0.04709 

9.87221 
9.87209 
9.87198 
9.87187 
9.87175 

12 
11 
11 
12 
11 

10 

9 

8 
7 
6 

6   1 
7   1 
8   1 
9   1 
10   2 

.2  1.1 
.4  1.3 
.6  1.5 
.8  1.7 

0  1.8 

55 
56 
57 
58 
59 

9.82481 
9.82495 
9.82509 
9.82523 
9.82537 

14 
14 
14 
14 
14 

9.95317 
9.95342 
9.95368 
9.95393 
9.95418 

25 
26 
25 
25 
26 

0.04683 
0.04658 
0.04632 
0.04607 
0.04582 

9.87164 
9.87153 
9.87141 
9.87130 
9.87119 

11 

12 
11 
11 
12 

5 
4 
3 
2 
1 

20   4 
30   6 
40   8 
50  10 

.0  3.7 
.0  5.5 
.0  7.3 
.0  9.2 

60 

9.82551 

9.95444 

0.04556 

9.87107 

0 

L.  Cos. 

d. 

L.CotgJ 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P. 

P. 

48° 


1070  LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

42° 


t 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P. 

0 

1 

2 
3 

4 

9.82551 
9.82565 
9.82579 
9.82593 
9.82607 

14 
14 
14 
14 

9.95444 
9.95469 
9.95495 
9.95520 
9.95545 

25 
26 
25 
25 

9fi 

0.04556 
0.04531 
0.04505 
0.04480 
0.04455 

9.87107 
9.87096 
9.87085 
9.87073 
9.87062 

11 

11 
12 
11 

60 

59 
58 
57 
56 

6 

7 

26 

2.6 
3  0 

5 

6 
7 
8 
9 

9.82621 
9.82635 
9.82649 
9.82663 
9.82677 

14 
14 
14 
14 
14 

9.95571 
9.95596 
9.95622 
9.95647 
9.95672 

25 
26 
25 
25 
26 

0.04429 
0.04404 
0.04378 
0.04353 
0.04328 

9.87050 
9.87039 
9.87028 
9.87016 
9.87005 

11 
11 
12 
11 

19 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

3.5 
3.9 
4.3 

8.7 
13.0 

10 

11 
12 
13 
14 

9.82691 
9.82705 
9.82719 
9.82733 
9.82747 

14 
14 

14 
14 
14 

9.95698 
9.95723 
9.95748 
9.95774 
9.95799 

25 
25 
26 
25 

26 

0.04302 
0.04277 
0.04252 
0.04226 
0.04201 

9.86993 
9.86982 
9.86970 
9.86959 
9.86947 

11 

12 
11 
12 
jl 

50 

49 
48 
47 
46 

40 

50 

17.3 
21.7 

25 

15 
16 
17 
18 
19 

9.82761 
9.82775 
9.82788 
9.82802 
9.82816 

14 
13 
14 
J4 

14 

9.95825 
9.95850 
9.95875 
9.95901 
9.95926 

25 
25 
26 
25 
2fi 

0.04175 
0.04150 
0.04125 
0.04099 
0.04074 

9.86936 
9.86924 
9.86913 
9.86902 
9.86890 

12 
11 
11 
12 

45 
44 
43 
42 
41 

6 
7 
8 
9 
10 

2.5 
2.9 
3.3 
3.8 
4.2 

20 

21 
22 
23 
24 

9.82830 
9.82844 
9.82858 
9.82872 
9.82885 

14 
14 
14 
13 
14 

9.95952 
9.95977 
9.96002 
9.96028 
9.96053 

25 
25 
26 
25 
25 

0.04048 
0.04023 
0.03998 
0.03972 
0.03947 

9.86879 
9.86867 
9.86855 
9.86844 
9.86832 

12 
12 
11 
12 

40 

39 
38 
37 
36 

20 
30 

40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 

27 
28 
29 

9.82899 
9.82913 
9.82927 
9.82941 
9.82955 

14 
14 
14 
14 
13 

9.96078 
9.96104 
9.96129 
9.96155 
9.96180 

26 
25 
26 
25 

OX 

0.03922 
0.03896 
0.03871 
0.03845 
0.03820 

9.86821 
9.86809 
9.86798 
9.86786 
9.86775 

12 
11 
12 
11 

35 
34 
33 
32 
31 

6 

7 
8 

14 

1.4 
1.6 
1.9 

30 

31 
32 
33 
34 

9.82968 
9.82982 
9.82996 
9.83010 
9.83023 

14 
14 
14 
13 
14 

9.96205 
9.96231 
9.96256 
9.96281 
9.96307 

26 
25 
25 
26 
25 

0.03795 
0.03769 
0.03744 
0.03719 
0.03693 

9.86763 
9.86752 
9.86740 
9.86728 
9.86717 

11 
12 
12 
11 

30 

29 
28 
27 
26 

9 
10 
20 
30 
40 
50 

2.1 
2.3 
4.7 
7.0 
9.3 
11  7 

35 
36 
37 
38 
39 

9.83037 
9.83051 
9.83065 
9.83078 
9.83092 

14 
14 
13 
14 
14 

9.96332 
9.96357 
9.96383 
9.96408 
9.96433 

25 

26 
25 
25 
26 

0.03668 
0.03643 
0.03617 
0.03592 
0.03567 

9.86705 
9.86694 
9.86682 
9.86670 
9.86659 

11 

12 
12 
11 
19 

25 

24 
23 
22 
21 

6 

7 

13 

1.3 
1  ^ 

40 

41 
42 
43 
44 

9.83106 
9.83120 
9.83133 
9.83147 
9.83161 

14 

13 
14 
14 
13 

9.96459 
9.96484 
9.96510 
9.96535 
9.96560 

25 

26 
25 
25 
26 

0.03541 
0.03516 
0.03490 
0.03465 
0.03440 

9.86647 
9.86635 
9.86624 
9.86612 
9.86600 

12 
11 
12 
12 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

1.7 
2.0 
2.2 
4.3 
6.5 

45 
46 
47 
48 
49 

9.83174 
9.83188 
9.83202 
9.83215 
9.83229 

14 
14 
13 
14 
13 

9.96586 
9.96611 
9.96636 
9.96662 
9.96687 

25 
25 
26 
25 
25 

0.03414 
0.03389 
0.03364 
0.03338 
0.03313 

9.86589 
9.86577 
9.86565 
9.86554 
9.86542 

12 
12 
11 
12 
19 

15 
14 
13 
12 
11 

40 
60 

8.7 
10.8 

2   II 

50 

51 
52 
53 

54 

9.83242 
9.83256 
9.83270 
9.83283 
9.83297 

14 
14 
13 
14 
13 

9.96712 
9.96738 
9.96763 
9.96788 
9.96814 

26 
25 
25 
26 
25 

0.03288 
0.03262 
0.03237 
0.03212 
0.03186 

9.86530 
9.86518 
9.86507 
9.86495 
9.86483 

12 
11 
12 
12 

10 
9 
8 

7 
6 

6   1 
7  ] 
8   ] 
9   ] 

10  ; 

L.2  1.1 
.4  1.3 
..6  1.5 
..8  1.7 
5.0  1.8 

55 

56 
57 
58 
59 

9.83310 
9.83324 
9.83338 
9.83351 
9.83365 

14 
14 
13 
14 
13 

9.96839 
9.96864 
9.96890 
9.96915 
9.96940 

26 
25 
25 
26 

0.03161 
0.03136 
0.03110 
0.03085 
0.03060 

9.86472 
9.86460 
9.86448 
9.86436 
9.86425 

12 
12 
12 
11 
12 

5 
4 
3 
2 
1 

20   4 
30   ( 
40   * 
50  1( 

1.0  3.7 
>.0  5.5 
5.0  7.3 
>.0  9.2 

60 

9.83378 

9.96966 

0.03034 

9.86413 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

/ 

P 

P. 

47° 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 
43° 


1071 


/ 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

P. 

0 

1 

2 
3 

4 

9.83378 
9.83392 
9.83405 
9.83419 
9.83432 

14 
13 
14 
13 
14 

9.96966 
9.96991 
9.97016 
9.97042 
9.97067 

25 
25 
26 
25 
25 

0.03034 
0.03009 
0.02984 
0.02958 
0.02933 

9.86413 
9.86401 
9.86389 
9.86377 
9.86366 

12 
12 
12 
11 

60 

59 
58 
57 
56 

6 

7 

26 

2.6 
3  0 

5 
6 

7 
8 
9 

9.83446 
9.83459 
9.83473 
9.83486 
9.83500 

13 
14 
13 
14 

-iq 

9.97092 
9.97118 
9.97143 
9.97168 
9.97193 

26 
25 

25 
25 

0.02908 
0.02882 
0.02857 
0.02832 
0.02807 

9.86354 
9.86342 
9.86330 
9.86318 
9.86306 

12 
12 
12 
12 

55 
54 
53 
52 
51 

8 
•9 
10 
20 
30 

3.5 
3.9 

4.3 
8.7 
18.0 

10 
11 

12 
13 
14 

9.83513 
9.83527 
9.83540 
9.83554 
9.83567 

14 
13 
14 
13 
14 

9.97219 
9.97244 
9.97269 
9.97295 
9.97320 

25 

25 
26 
25 
25 

0.02781 
0.02756 
0.02731 
0.02705 
0.02680 

9.86295 
9.86283 
9.86271 
9.86259 
9.86247 

12 
12 
12 
12 
12 

50 

49 

48 
47 
46 

40 
50 

17.3 
21.7 

25 

15 
16 
17 
18 
19 

9.83581 
9.83594 
9.83608 
9.83621 
9.83634 

13 
14 
13 
13 

9.97345 
9.97371 
9.97396 
9.97421 
9.97447 

26 
25 
25 
26 

0.02655 
0.02629 
0.02604 
0.02579 
0.02553 

9.86235 
9.86223 
9.86211 
9.86200 
9.86188 

12 
12 
11 
12 
12 

45 
44 
43 

42 
41 

6 

7 
8 
9 
10 

2.5 
2.9 
3.3 
3.8 
4.2 

20 

21 
22 
23 
24 

9.83648 
9.83661 
9.83674 
9.83688 
9.83701 

13 
13 
14 
13 

9.97472 
9.97497 
9.97523 
9.97548 
9.97573 

25 
26 
25 
25 

0.02528 
0.02503 
0.02477 
0.02452 
0.02427 

9.86176 
9.86164 
9.86152 
9.86140 
9.86128 

12 
12 
12 
12 

40 

39 
38 
37 
36 

20 
30 
40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 
27 
28 
29 

9.83715 
9.83728 
9.83741 
9.83755 
9.83768 

13 
13 
14 
13 

9.97598 
9.97624 
9.97649 
9.97674 
9.97700 

26 
25 
25 
26 

oc 

0.02402 
0.02376 
0.02351 
0.02326 
0.02300 

9.86116 
9.86104 
9.86092 
9.86080 
9.86068 

12 
12 
12 
12 
12 

35 
34 
33 
32 
31 

6 

7 
8 

14 

1.4 
1.6 
1.9 

30 
31 
32 
33 
34 

9.83781 
9.83795 
9.83808 
9.83821 
9.83834 

14 
13 
13 
13 
14 

9.97725 
9.97750 
9.97776 
9.97801 
9.97826 

25 
26 
25 
25 
25 

0.02275 
0.02250 
0.02224 
0.02199 
0.02174 

9.86056 
9.86044 
9.86032 
9.86020 
9.86008 

12 
12 
12 
12 
12 

30 

29 

28 
27 
26 

10 
20 
30 
40 
50 

2.3 

4.7 
7.0 
9.3 
11.7 

35 
36 
37 
38 
39 

9.83848 
9.83861 
9.83874 
9.83887 
9.83901 

13 
13 
13 
14 

9.97851 
9.97877 
9.97902 
9.97927 
9.97953 

26 
25 
25 
26 

OE 

0.02149 
0.02123 
0.02098 
0.02073 
0.02047 

9.85996 
9.85984 
9.85972 
9.85960 
9.85948 

12 
12 
12 
12 
12 

25 
24 
23 
22 
21 

6 

7 

13 
1.3 

1  5 

40 

41 
42 
43 
44 

9.83914 
9.83927 
9.83940 
9.83954 
9.83967 

13 
13 
14 
13 

10 

9.97978 
9.98003 
9.98029 
9.98054 
9.98079 

25 
26 
25 
25 
25 

0.02022 
0.01997 
0.01971 
0.01946 
0.01921 

9.85936 
9.85924 
9.85912 
9.85900 
9.85888 

12 
12 
12 
12 
12 

20 

19 

18 
17 
16 

8 
9 
10 
20 
30 

1.7 
2.0 
2.2 
4.3 
6.5 

45 

46 

47 
48 
49 

9.83980 
9.83993 
9.84006 
9.84020 
9.84033 

13 
13 
14 
13 

9.98104 
9.98130 
9.98155 
9.98180 
9.98206 

26 
25 
25 
26 

0.01896 
0.01870 
0.01845 
0.01820 
0.01794 

9.85876 
9.85864 
9.85851 
9.85839 
9.85827 

12 
13 
12 
12 
12 

15 
14 
13 
12 
11 

40 
50 

8.7 
10.8 

2   II 

50 

51 
52 
53 
54 

9.84046 
9.84059 
9.84072 
9.84085 
9.84098 

13 
13 
13 
13 

9.98231 
9.98256 
9.98281 
9.98307 
9.98332 

25 
25 
26 
25 
9^ 

0.01769 
0.01744 
0.01719 
0.01693 
0.01668 

9.85815 
9.85803 
9.85791 
9.85779 
9.85766 

12 
12 
12 
13 
12 

10 
9 
8 
7 
6 

6 

7 
8 
9 
10 

1.2  1.1 
1.4  1.3 
1.6  1.5 

1.8  1.7 
2.0  1.8 

55 
56 
57 
58 
59 

9.84112 
9.84125 
9.84138 
9.84151 
9.84164 

13 
13 
13 
13 

9.98357 
9.98383 
9.98408 
9.98433 
9.98458 

26 
25 
25 
25 
2fi 

0.01643 
0.01617 
0.01592 
0.01567 
0.01542 

9.85754 
9.85742 
9.85730 
9.85718 
9.85706 

12 
12 
12 
12 
13 

5 
4 
3 
2 
1 

20 
30 
40 
50  1 

4.0  3.7 
6.0  5.5 
8.0  7.3 
0.0  9.2 

60 

9.84177 

9.98484 

0.01516 

9.85693 

0 

L.  Cos. 

d 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

P 

.P. 

46° 


1072 


LOGARITHMS  OF  TRIGONOMETRIC  FUNCTIONS 

A.AO 


1 

L.  Sin. 

d. 

L.Tang. 

d.c. 

L.  Cotg. 

L.  Cos. 

d. 

P 

.P. 

0 

1 

2 
3 
4 

9.84177 
9.84190 
9.84203 
9.84216 
9.84229 

13 
13 
13 
13 

•10 

9.98484 
9.98509 
9.98534 
9.98560 
9.98585 

25 
25 
26 
25 

OK 

0.01516 
0.01491 
0.01466 
0.01440 
0.01415 

9.85693 
9.85681 
9.85669 
9.85657 
9.85645 

12 
12 
12 
12 

iq 

60 

59 

58 
57 
56 

6 

7 

26 
2.6 
30 

5 
6 

7 
8 
9 

9.84242 
9.84255 
9.84269 
9.84282 
9.84295 

13 
14 
13 
13 

9.98610 
9.98635 
9.98661 
9.98686 
9.98711 

25 
26 
25 
25 

0.01390 
0.01365 
0.01339 
0.01314 
0.01289 

9.85632 
9.85620 
9.85608 
9.85596 
9.85583 

12 
12 
12 
13 

55 
54 
53 
52 
51 

8 
9 
10 
20 
30 

3.5 
3.9 
4.3 

8.7 
13.0 

10 

11 
12 
13 
14 

9.84308 
9.84321 
9.84334 
9.84347 
9.84360 

13 
13 
13 
13 

•to 

9.98737 
9.98762 
9.98787 
9.98812 
9.98838 

25 
25 
25 
26 

oc 

0.01263 
0.01238 
0.01213 
0.01188 
0.01162 

9.85571 
9.85559 
9.85547 
9.85534 
9.85522 

12 
12 
13 
12 
19 

SO 

49 
48 
47 
46 

40 
50 

17.3 
21.7 

25 

15 
16 
17 
18 
19 

9.84373 
9.84385 
9.84398 
9.84411 
9.84424 

12 
13 
13 

13 

TO 

9.98863 
9.98888 
9.98913 
9.98939 
9.98964 

25 
25 
26 
25 

oc 

0.01137 
0.01112 
0.01087 
0.01061 
0.01036 

9.85510 
9.85497 
9.85485 
9.85473 
9.85460 

13 
12 
12 
13 
12 

45 
44 
43 
42 
41 

6 

7 
8 
9 
10 

2.5  ' 
2.9 
3.3 
8.8 
4.2 

20 

21 
22 
23 
24 

9.84437 
9.84450 
9.84463 
9.84476 
9.84489 

13 
13 
13 
13 

9.98989 
9.99015 
9.99040 
9.99065 
9.99090 

26 
25 
25 
25 

0.01011 
0.00985 
0.00960 
0.00935 
0.00910 

9.85448 
9.85436 
9.85423 
9.85411 
9.85399 

12 
13 
12 
12 

iq 

40 

39 
38 
37 
36 

20 
30 
40 
50 

8.3 
12.5 
16.7 
20.8 

25 
26 

27 
28 
29 

9.84502 
9.84515 
9.84528 
9.84540 
9.84553 

13 
13 
12 
13 

9.99116 
9.99141 
9.99166 
9.99191 
9.99217 

25 
25 
25 
26 

nr. 

0.00884 
0.00859 
0.00834 
0.00809 
0.00783 

9.85386 
9.85374 
9.85361 
9.85349 
9.85337 

12 
13 
12 
12 
13 

35 
34 
33 
32 
31 

6 

7 
8 

14 

1.4 
1.6 
1.9 

SO 

31 
32 
33 
34 

9.84566 
9.84579 
9.84592 
9.84605 
9.84618 

13 
13 
13 

13 
19 

9.99242 
9.99267 
9.99293 
9.99318 
9.99343 

25 
26 
25 
25 

OK 

0.00758 
0.00733 
0.00707 
0.00682 
0.00657 

9.85324 
9.85312 
9.85299 
9.85287 
9.85274 

12 
13 
12 
13 
12 

30 

29 
28 
27 
26 

10 
20 
30 
40 
50 

2.3 

4.7 
7.0 
9.3 
11.7 

35 
36 
37 
38 

9.84630 
9.84643 
9.84656 
9.84669 
9.84682 

13 
13 
13 
13 

9.99368 
9.99394 
9.99419 
9.99444 
9.99469 

26 
25 
25 
25 

0.00632 
0.00606 
0.00581 
0.00556 
0.00531 

9.85262 
9.85250 
9.85237 
9.85225 
9.85212 

12 
13 
12 
13 
12 

25 
24 
23 
22 
21 

6 

<j 

13 
1.3 

1  c 

40 

41 
42 
43 
44 

9.84694 
9.84707 
9.84720 
9.84733 
9.84745 

13 
13 
13 
12 

9.99495 
9.99520 
9.99545 
9.99570 
9.99596 

25 
25 
25 
26 

Oft 

0.00505 
0.00480 
0.00455 
0.00430 
0.00404 

9.85200 
9.85187 
9.85175 
9.85162 
9.85150 

13 
12 
13 
12 
13 

20 

19 
18 
17 
16 

8 
9 
10 
20 
30 

1.7 
2.0 
2.2 
4.3 
6.5 

45 
46 
47 
48 
49 

9.84758 
9.84771 
9.84784 
9.84796 
9.84809 

13 
13 
12 
13 

9.99621 
9.99646 
9.99672 
9.99697 
9.99722 

25 
26 
25 
25 

0.00379 
0.00354 
0.00328 
0.00303 
0.00278 

9.85137 
9.85125 
9.85112 
9.85100 
9.85087 

12 
13 
12 
13 

iq 

15 
14 
13 
12 
11 

40 
50 

8.7 
10.8 

12 

50 

51 
52 
53 

54 

9.84822 
9.84835 
9.84847 
9.84860 
9.84873 

13 
12 
13 
13 

•to 

9.99747 
9.99773 
9.99798 
9.99823 
9.99848 

26 
25 
25 
25 
9,fi 

0.00253 
0.00227 
0.00202 
0.00177 
0.00152 

9.85074 
9.85062 
9.85049 
9.85037 
9.85024 

12 
13 
12 
13 
12 

10 

9 
8 

7 
6 

6 

7 
8 
9 
10 

1.2 
1.4 
1.6 
1.8 
2.0 

55 
56 
57 
58 
59 

9.84885 
9.84898 
9.84911 
9.84923 
9.84936 

13 
13 
12 
13 

9.99874 
9.99899 
9.99924 
9.99949 
9.99975 

25 
25 
25 
26 

oc 

0.00126 
0.00101 
0.00076 
0.00051 
0.00025 

9.85012 
9.84999 
9.84986 
9.84974 
9.84961 

13 
13 
12 
13 
12 

5 
4 
3 
2 
1 

20 
30 
40 
50 

4.0 
6.0 
8.0 
10.0 

60 

9.84949 

0.00000 

0.00000 

9.84949 

0 

L.  Cos. 

d. 

L.  Cotg. 

d.c. 

L.Tang. 

L.  Sin. 

d. 

' 

P 

P. 

45C 


TRAVERSE  TABLES  1073 

TRAVERSE  TABLES 

To  use  the  tables,  find  the  number  of  degrees  in  the  left-hand  column  if 
the  angle  is  less  than  45°,  and  in  the  right-hand  column  if  greater  than  45°. 
The  numbers  on  the  same  line  running  across  the  page  are  the  latitudes  and 
departures  for  that  angle  and  for  the  respective  distances,  1,  2,  3,  4,  5,  6,  7,  8,  9, 
which  appear  at  the  top  and  bottom  of  the  pages.  Thus,  if  the  bearing  of  a 
line  is  10°  and  the  distance  4,  the  latitude  will  be  3.939  and  the  departure 
.695;  with  the  same  bearing,  and  the  distance  8,  the  latitude  will  be  7.878  and 
the  departure  1.389.  The  latitude  and  departure  for  80  is  10  times  the  lati- 
tude and  departure  for  8,  and  is  found  by  moving  the  decimal  point  one  place 
to  the  right;  that  for  500  is  100  times  the  latitude  and  departure  for '5,  and  is 
found  by  moving  the  decimal  point  two  places  to  the  right  and  so  on._  By 
moving  the  decimal  point  one,  two,  or  more  places  to  the  right,  the  latitude 
and  departure  may  be  found  for  any  multiple  of  any  number  given  in  the 
table.  In  finding  the  latitude  and  departure  for  any  number  such  as  453,  the 
number  is  resolved  into  three  numbers  viz.:  400,  50,  3,  and  the  latitude  and 
departure  for  each  taken  from  the  table  and  then  added  together. 

Rule. — Write  down  the  latitude  and  departure,  neglecting  the  decimal  points, 
for  the  first  figure  of  the  given  distance;  write  under  them  the  latitude  and  depar- 
ture for  the  second  figure,  setting  them  one  place  farther  to  the  right;  under  these, 
place  the,  latitude  and  departure  for  the  third  figure,  setting  them  one  place  still 
farther  to  the  right,  and  so  continue  until  all  the  figures  of  the  given  distance  have 
been  used;  add  these  latitudes  and  departures,  and  point  off  on  the  right  of  their 
sums  a  number  of  decimal  places  equal  to  the  number  of  decimal  places  to  which 
the  tables  being  used  are  carried;  the  resulting  numbers  will  be  the  latitude  and 
departure  of  the  given  distance  in  feet,  links,  chains,  or  whatever  unit  of  measure- 
ment is  adopted. 

EXAMPLE. — A  bearing  is  16°  and  the  distance  725  ft.;  what  is  the  latitude 
and  departure? 

SOLUTION. — Applying  the  rule  just  given: 

Distances  Latitudes  Departures 

700  6729  1929 

20  1923  0551 

5  4806  1378 

725  696.936  199.788 

Taking  the  nearest  whole  numbers  and  rejecting  the  decimals  the  latitude 
and  departure  are  found  to  be  697  and  200  respectively. 

When  a  0  occurs  in  the  given  number,  the  next  figure  must  be  set  two 
places  tc  the  right  as  in  the  following  example: 

EXAMPLES.— The  bearing  is  22°  and  the  distance  907  ft.;  required,  the  lati- 
tude and  departure. 

SOLUTION. — Applying  the  rule  just  given. 

Distances  Latitudes  Departures 

900  8345  3371 

~7  6490  2622 


907  840.990  339.722 

Here  the  place  of  0  both  in  the  distance  column  and  in  the  latitude  and 
departure  columns  is  occupied  by  a  dash  — .  Rejecting  the  decimals,  the 
latitude  is  841  ft.  and  the  departure  340  ft. 

When  the  bearing  is  more  than  45°,  the  names  of  the-  columns  must  be 
read  from  the  bottom  of  the  page.  The  latitude  of  any  bearing  as 
the  departure  of  its  complement,  30°;  and  the  departure  of  any  bearing,  as 
30°,  is  the  latitude  of  its  complement,  60°  Where  the  bearings  are  given 
in  smaller  fractions  of  degrees  than  is.  found  in  the  table,  the  latitudes  and 
departures  can  be  found  by  interpolation. 


68 


1074 


LATITUDES  AND  DEPARTURES 


1 

1 

2 

3 

4 

5 

.E 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

0° 

1.000 

0.000 

2.000 

0.000 

3.000 

0.000 

4.000 

0.000 

5.000 

90° 

0* 

1.000 

0.004 

2.000 

0.009 

3.000 

0.013 

4.000. 

0.017 

5.000 

89* 

0* 

1.000 

0.009 

2.000 

0.017 

3.000 

0.026 

4.000 

0.035 

5.000 

0* 

1.000 

0.013 

2.000 

0.026 

3.000 

0.039 

4.000 

0.052 

5.000 

89* 

1° 

1.000 

0.017 

2.000 

0.035 

3.000 

0.052 

3.999 

0.070 

4.999 

89° 

1* 

1.000 

0.022 

2.000 

0.044 

2.999 

0.065 

3.999 

0.087 

4.999 

88* 

It 

1.000 

0.026 

1.999 

0.052 

2.999 

0.079 

3.999 

0.105 

4.998 

1* 

1.000 

0.031 

1.999 

0.061 

2.999 

0.092 

3.998 

0.122 

4.998 

88* 

2° 

0.999 

0.035 

1.999 

0.070 

2.998 

0.105 

3.998 

0.140 

4.997 

88° 

2* 

0.999 

0.039 

1.998 

0.079 

2.998 

0.118 

3.997 

0.157 

4.996 

87* 

2* 

0.999 

0.044 

1.998 

0.087 

2.997 

0.131 

3.996 

0.174 

4.995 

2* 

0.999 

0.048 

1.998 

0.096 

2.997 

0.144 

3.995 

0.192 

4.994 

87* 

3° 

0.999 

0.052 

1.997 

0.105 

2.996 

0.157 

3.995 

0.209 

4.993 

87° 

3* 

0.998 

0.057 

1.997 

0.113 

2.995 

0.170 

3.994 

0.227 

4.992 

86* 

3* 

0.998 

0.061 

1.996 

0.122 

2.994 

0.183 

3.993 

0.244 

4.991 

3* 

0.998 

0.065 

1.996 

0.131 

2.994 

0.196 

3.991 

0.262 

4.989 

86- 

4° 

0.998 

0.070 

1.995 

0.140 

2.993 

0.209 

3.990 

0.279 

4.988 

86° 

4* 

0.997 

0.074 

1.995 

0.148 

2.992 

0.222 

3.989 

0.296 

4.986 

85* 

4* 

0.997 

0.078 

1.994 

0.157 

2.991 

0.235 

3.988 

0.314 

4.985 

4* 

0.997 

0.083 

1.993 

0.166 

2.990 

0.248 

3.986 

0.331 

4.983 

85* 

5° 

0.996 

0.087 

1.992 

0.174 

2.989 

0.261 

3.985 

0.349 

4.981 

85° 

5* 

0.996 

0.092 

1.992 

0.183 

2.987 

0.275 

3.983 

0.366 

4.979 

84* 

6* 

0.995 

0.096 

1.991 

0.192 

2.986 

0.288 

3.982 

0.383 

4.977 

84i 

5* 

0.995 

0.100 

.1.990 

0.200 

2.985 

0.301 

3.980 

0.401 

4.975 

84* 

6° 

0.995 

0.105 

1.989 

0.209 

2.984 

0.314 

3.978 

0.418 

4.973 

84° 

6* 

0.994 

0.109 

1.988 

0.218 

2.982 

0.327 

3.976 

0.435 

4.970 

83* 

65 

0.994 

0.113 

1.987 

0.226 

2.981 

0.340 

3.974 

0.453 

4.968 

83* 

6* 

0.993 

0.118 

1.986 

0.235 

2.979 

0.353 

3.972 

0.470 

4.965 

83* 

7° 

0.993 

0.122 

1.985 

0.244 

2.978 

0.366 

3.970 

0.487 

4.963 

83° 

7* 

0.992 

0.126 

1.984 

0.252 

2.976 

0.379 

3.968 

0.505 

4.960 

82* 

7i 

0.991 

0.131 

1.983 

0.261 

2.974 

0.392 

3.966 

0.522 

4.957 

7* 

0.991 

0.135 

1.982 

0.270 

2.973 

0.405 

3.963 

0.539 

4.954 

82* 

8° 

0.990 

0.139 

1.981 

0.278 

2.971 

0.418 

3.961 

0.557 

4.951 

82° 

8* 

0.990 

0.143 

1.979 

0.287 

2.969 

0.430 

3.959 

0.574 

4.948 

81* 

8* 

0.989 

0.148 

1.978 

0.296 

2.967 

0.443 

a  956 

0.591 

4.945 

81* 

8* 

0.988 

0.152 

1.977 

0.304 

2.965 

0.456 

3.953 

0.608 

4.942 

81* 

9° 

0.988 

0.156 

1.975 

0.313 

2.963 

0.469 

3.951 

0.626 

4.938 

81° 

9* 

0.987 

0.161 

1.974 

0.321 

2.961 

0.482 

3.948 

0.643 

4.935 

80* 

9* 

0.986 

0.165 

1.973 

0.330 

2.959 

0.495 

3.945 

0.660 

4.931 

9* 

0.986 

0.169 

1.971 

0.339 

2.957 

0.508 

3.942 

0.677 

4.928 

80* 

10° 

0.985 

0.174 

1.970 

0.347 

2.954 

0.521 

3.939 

0.695 

4.924 

80° 

10* 

0.984 

0.178 

1.968 

0.356 

2.952 

0.534 

3.936 

0.712 

4.920 

79* 

0.983 

0.182 

1.967 

0.364 

2.950 

0.547 

3.933 

0.729 

4.916 

79* 

10* 

0.982 

0.187 

1.965 

0.373 

2.947 

0.560 

3.930 

0.746 

4.912 

79* 

1  1° 

0.982 

0.191 

1.963 

0.382 

2.945 

0.572 

3.927 

0.763 

4.908 

79° 

11* 

0.981 

0.195 

1.962 

0.390 

2.942 

0.585 

3.923 

0.780 

4.904 

78* 

11* 

0.980 

0.199 

1.960 

0.399 

2.940 

0.598 

3.920 

0.797 

4.900 

0.979 

0.204 

1.958 

0.407 

2.937 

0.611 

3.916 

0.815 

4.895 

78-*- 

*2° 

0.978 

0.208 

1.956 

0.416 

2.934 

0.624 

3.913 

0.832 

4.891 

78° 

12* 

0.977 

0.212 

1.954 

0.424 

2.932 

0.637 

3.909 

0.849 

4.886 

77* 

m 

0.976 

0.216 

1.953 

0.433 

2.929 

0.649 

3.905 

0.866 

4.881 

77* 

0.975 

0.221 

1.951 

0.441 

2.926 

0.662 

3.901 

0.883 

4.877 

77* 

*3° 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897 

0.900 

4.872 

77° 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

bo 

1 

1 

2 

3 

4 

5 

1 

LATITUDES  AND  DEPARTURES 


1075 


- 

5 

6 

7 

8 

9 

oo 

c 

1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0° 

0.000 

6.000 

0.000 

7.000 

0.000 

8.000 

0.000 

9.000 

0.000 

90° 

0* 

0.022 

6.000 

0.026 

7.000 

0.031 

8.000 

0.035 

9.000 

0.039 

89* 

0* 

0.044 

6.000 

0.052 

7.000 

0.061 

8.000 

0.070 

9.000 

0.079 

89* 

0* 

0.065 

5.999 

0.079 

6.999 

0.092 

7.999 

0.105 

8.999 

0.118 

89* 

1° 

0.087 

5.999 

0.105 

6.999 

0.122 

7.999 

0.140 

8.999 

0.157 

89° 

1* 

0.109 

5.999 

0.131 

6.998 

0.153 

7.998 

0.175 

8.998 

0.196 

88* 

1* 

0.131 

5.998 

0.157 

6.998 

0.183 

7.997 

0.209 

8.997 

0.236 

88* 

1* 

0.153 

5.997 

0.183 

6.997 

0.214 

7.996 

0.244 

8.996 

0.275 

88* 

2° 

0.174 

5.996 

0.209 

6.996 

0.244 

7.995 

0.279 

8.995 

0.314 

88° 

2* 

0.196 

5.995 

0.236 

6.995 

0.275 

7.994 

0.314 

8.993 

0.353 

87* 

2* 

0.218 

5.994 

0.262 

6.993 

0.305 

7.992 

0.349 

8.991 

0.393 

87* 

2* 

0.240 

5.993 

0.288 

6.992 

0.336 

7.991 

0.384 

8.990 

0.432 

87* 

3° 

0.262 

5.992 

0.314 

6.990 

0.366 

7.989 

0.419 

8.988 

0.471 

87° 

0.283 

5.990 

0.340 

6.989 

0.397 

7.987 

0.454 

8.986 

0.510 

86* 

3* 

0.305 

5.989 

0.366 

6.987 

0.427 

7.985 

0.488 

8.983 

0.549 

86* 

3* 

0.327 

5.987 

0.392 

6.985 

0.458 

7.983 

0.523 

8.981 

0.589 

86* 

4° 

0.349 

5.985 

0.419 

6.983 

0.488 

7.981 

0.558 

8.978 

0.628 

0.371 

5.984 

0.445 

6.981 

0.519 

7.978 

0.593 

8.975 

0.667 

85* 

4* 

0.392 

5.982 

0.471 

6.978 

0.549 

7.975 

0.628 

8.972 

0.706 

85* 

4* 

0.414 

5.979 

0.497 

6.976 

0.580 

7.973 

0.662 

8.969 

0.745 

85* 

5° 

0.436 

5.977 

0.523 

6.973 

0.610 

7.970 

0.697 

8.966 

0.784 

85° 

0.458 

5.975 

0.549 

6.971 

0.641 

7.966 

0.732 

8.962 

0.824 

84* 

5* 

0.479 

5.972 

0.575 

6.968 

0.671 

7.963 

0.767 

8.959 

0.863 

84* 

5* 

0.501 

5.970 

0.601 

6.965 

0.701 

7.960 

0.802 

8.955 

0.902 

84* 

6° 

0.523 

5.967 

0.627 

6.962 

0.732 

7.956 

0.836 

8.951 

0.941 

84° 

0.544 

5.964 

0.653 

6.958 

0.762 

7.952 

0.871 

8.947 

0.980 

83* 

6* 

0.566 

5.961 

0.679 

6.955 

0.792 

7.949 

0.906 

8.942 

1.019 

6* 

0.588 

5.958 

0.705 

6.951 

0.823 

7.945 

0.940 

8.938 

1.058 

7° 

0.609 

5.955 

0.731 

6.948 

0.853 

7.940 

0.975 

8.933 

1.097 

„„ 

7* 

0.631 

5.952 

0.757 

6.944 

0.883 

7.936 

1.010 

8.928 

1.136 

82* 

7* 

0.653 

5.949 

0.783 

6.940 

0.914 

7.932 

1.044 

8.923 

1.175 

82* 

7* 

0.674 

5.945 

0.809 

6.936 

0.944 

7.927 

1.079 

8.918 

1.214 

82* 

8° 

0.696 

5.942 

0.835 

6.932 

0.974 

7.922 

1.113 

8.912 

1.253 

82° 

0.717 

5.938 

0.861 

6.928 

1.004 

7.917 

1.148 

8.907 

1.291 

81* 

8* 

0.739 

5.934 

0.887 

6.923 

1.035 

7.912 

1.182 

8.901 

1.330 

81* 

8* 

0.761 

5.930 

0.913 

6.919 

1.065 

7.907 

1.217 

8.895 

1.369 

81* 

9° 

0.782 

5.926 

0.939 

6.914 

1.095 

7.902 

1.251 

8.889 

1.408 

81° 

0.804 

5.922 

0.964 

6.909 

1.125 

7.896 

1.286 

8.883 

1.447 

80* 

9* 

0.825 

5.918 

0.990 

6.904 

1.155 

7.890 

1.320 

8.877 

1.485 

80* 

9* 

0.847 

5.913 

1.016 

6.899 

1.185 

7.884 

1.355 

8.870 

1.524 

80* 

10° 

0.868 

5.909 

1.042 

6.894 

1.216 

7.878 

1.389 

8.863 

1.563 

80° 

III 

10* 

0.890 
0.911 
0.933 

5.904 
5.900 
5.895 

1.068 
1.093 
1.119 

6.888 
6.883 
6.877 

1.246 
1.276 
1.306 

7.872 
7.866 
7.860 

1.424 
1.458 
1.492 

8.856 
8.849 
8.842 

1.601 
1.640 
1.679 

79* 

III 

11° 

0.954 

5.890 

1.145 

6.871 

1.336 

7.853 

1.526 

8.835 

1.717 

79° 

11* 

0.975 

5.885 

1.171 

6.866 

1.366 

7.846 

1.561 

8.827 

1.756 

78* 

11* 

0.997 

5.880 

1.196 

6.859 

1.396 

7.839 

1.595 

8.819 

1.794 

78* 

11* 

1.018 

5.874 

1.222 

6.853 

1.425 

7.832 

1.629 

8.811 

1.833 

78* 

12° 

1.040 

5.869 

1.247 

6.847 

1.455 

7.825 

1.663 

8.803 

1.871 

78° 

1.061 

5.863 

1.273 

6.841 

1.485 

7.818 

1.697 

8.795 

1.910 

77* 

12* 
1 

1.082 
1.103 
1.125 

5.858 
5.852 
5.846 

1.299 
1.324 
1.350 

6.834 
6.827 
6.821 

1.515 
1.545 
1.575 

7.810 
7.803 
7.795 

1.732 
1.766 
1.800 

8.787 
8.778 
8.769 

1.948 
1.986 
2.025 

77* 
77* 
77° 

f 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

bo 
c 

« 

5 

6 

7 

8 

9 

: 

CD 

1076 


LATITUDES  AND  DEPARTURES 


00 

i 

2 

3 

4 

5 

bo 
e 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a 

13° 

0.974 

0.225 

1.949 

0.450 

2.923 

0.675 

3.897 

0.900 

4.872 

77° 

13* 

0.973 

0.229 

1.947 

0.458 

2.920 

0.688 

3.894 

0.917 

4.867 

76* 

ill 

0.972 
0.971 

0.233 
0.238 

1.945 
1.943 

0.467 
0.475 

2.917 
2.914 

0.700 
0.713 

3.889 
3.885 

0.934 
0.951 

4.862 
4.857 

?8 

14° 

0.970 

0.242 

1.941 

0.484 

2.911 

0.726 

3.881 

C.968 

4.851 

76° 

14* 

0.969 

0.246 

1.938 

0.492 

2.908 

0.738 

3.877 

0.985 

4.846 

75* 

14* 

0.968 

0.250 

1.936 

0.501 

2.904 

0.751 

3.873 

1.002 

4.841 

75* 

14* 

0.967 

0.255 

1.934 

0.509 

2.901 

0.764 

3.868 

1.018 

4.835 

75* 

15° 

0.966 

0.259 

1.932 

0.518 

2.898 

0.776 

3.864 

1.035 

4.830 

75° 

15- 

0.965 

0.263 

1.930 

0.526 

2.894 

0.789 

3.859 

1.052 

4.824 

74* 

15* 

0.964 

0.267 

1.927 

0.534 

2.891 

0.802 

3.855 

1.069 

4.818 

74* 

15* 

0.962 

0.271 

1.925 

0.543 

2.887 

0.814 

3.850 

1.086 

4.812 

74* 

16° 

0.961 

0.276 

1.923 

0.551 

2.884 

0.827 

3.845 

1.103 

4.806 

74° 

16* 

0.960 

0.280 

1.920 

0.560 

2.880 

0.839 

3.840 

1.119 

4.800 

73* 

0.959 

0.284 

1.918 

0.568 

2.876 

0.852 

3.835 

1.136 

4.794 

73* 

0.958 

0.288 

1.915 

0.576 

2.873 

0.865 

3.830 

1.153 

4.788 

73* 

0.956 

0.292 

1.913 

0.585 

2.869 

0.877 

3.825 

1.169 

4.782 

73° 

17*- 

0.955 

0.297 

1.910 

0.593 

2.865 

0.890 

3.820 

1.186 

4.775 

72* 

17* 

0.954 

0.301 

1.907 

0.601 

2.861 

0.902 

3.815 

1.203 

4.769 

72* 

17* 

0.952 

0.305 

1.905 

0.610 

2.857 

0.915 

3.810 

1.220 

4.762 

72* 

18° 

0.951 

0.309 

1.902 

0.618 

2.853 

0.927 

3.804 

1.236 

4.755 

72° 

18* 

0.950 

0.313 

1.899 

0.626 

2.849 

0.939 

3.799 

1.253 

4.748 

71* 

18* 

0.948 

0.317 

1.897 

0.635 

2.845 

0.952 

3.793 

1.269 

4.742 

71* 

18* 

0.947 

0.321 

1.894 

0.643 

2.841 

0.964 

3.788 

1.286 

4.735 

71* 

19° 

0.946 

0.326 

1.891 

0.651 

2.837 

0.977 

3.782 

1.302 

4.728 

71° 

19* 

0.944 

0.330 

1.888 

0.659 

2.832 

0.989 

3.776 

1.319 

4.720 

70* 

19* 

0.943 

0.334 

1.885 

0.668 

2.828 

1.001 

3.771 

1.335 

4.713 

70* 

19* 

0.941 

0.338 

1.882 

0.676 

2.824 

1.014 

3.765 

1.352 

4.706 

70* 

20° 

0.940 

0.342 

1.879 

0.684 

2.819 

1.026 

3.759 

1.368 

4.698 

70° 

20i 

0.938 

0.346 

1.876 

0.692 

2.815 

1.038 

3.753 

1.384 

4.691 

69* 

20* 

0.937 

0.350 

1.873 

0.700 

2.810 

1.051 

3.747 

1.401 

4.683 

69* 

20* 

0.935 

0.354 

1.870 

0.709 

2.805 

1.063 

3.741 

1.417 

4.676 

69* 

21° 

0.934 

0.358 

1.867 

0.717 

2.801 

1.075 

3.734 

1.433 

4.668 

69° 

2H 

0.932 

0.362 

1.864 

0.725 

2.796 

1.087 

3.728 

1.450 

4.660 

68* 

21* 

0.930 

0.367 

1.861 

0.733 

2.791 

1.100 

3.722 

1.466 

4.652 

68* 

0.929 

0.371 

1.858 

0.741 

2.786 

1.112 

3.715 

1.482 

4.644 

68* 

22° 

0.927 

0.375 

1.854 

0.749 

2.782 

1.124 

3.709 

1.498 

4.636 

68° 

22* 

0.926 

0.379 

1.851 

0.757 

2.777 

1.136 

3.702 

1.515 

4.628 

67* 

22* 

0.924 

0.383 

1.848 

0.765 

2.772 

1.148 

3.696 

1.531 

4.619 

67* 

22* 

0.922 

0.387 

1.844 

0.773 

2.767 

1.160 

3.689 

1.547 

4.611 

67* 

23° 

0.921 

0.391 

1.841 

0.781 

2.762 

1.172 

3.682 

1.563 

4.603 

67° 

23* 

0.919 

0.395 

1.838 

0.789 

2.756 

1.184 

3.675 

1.579 

4.594 

66* 

23* 

0.917 

0.399 

1.834 

0.797 

2.751 

1.196 

3.668 

1.595 

4.585 

66* 

23* 

0.915 

0.403 

1.831 

0.805 

2.746 

1.208 

3.661 

1.611 

4.577 

66* 

24° 

0.914 

0.407 

1.827 

0.813 

2.741 

1.220 

3.654 

1.627 

4.568 

68° 

24* 

0.912 

0.411 

1.824 

0.821 

2.735 

1.232 

3.647 

1.643 

4.559 

65* 

24* 

0.910 

0.415 

1.820 

0.829 

2.730 

1.244 

3.640 

1.659 

4.550 

65* 

24* 

0.908 

0.419 

1.816 

0.837 

2.724 

1.256 

3.633 

1.675 

4.541 

65* 

25° 

0.906 

0.423 

1.813 

0.845 

2.719 

1.268 

3.625 

1.690 

4.532 

65° 

25* 

0.904 

0.427 

1.809 

0.853 

2.713 

1.280 

3.618 

1.706 

4.522 

64* 

25* 

0.903 

0.431 

1.805 

0.861 

2.708 

1.292 

3.610 

1.722 

4.513 

64* 

25* 

0.901 

0.434 

1.801 

0.869 

2.702 

1.303 

3.603 

1.738 

4.503 

64* 

26° 

0.899 

0.438 

1.798 

0.877 

2.696 

1.315 

3.595 

1.753 

4.494 

64° 

? 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

? 

~ 

•c 

i 

1 

2 

3 

4 

5 

a 

LATITUDES  AND  DEPARTURES 


1077 


? 

5 

( 

1 

r 

( 

1 

! 

| 

be 

JE 

1 
oa 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i 

13° 

1.125 

5.846 

1.350 

6.821 

1.575 

7.795 

1.800 

8.769 

2.025 

77° 

13i 

1.146 

5.840 

1.375 

6.814 

1.604 

7.787 

1.834 

8.760 

2.063 

76? 

13i 

1.167 

5.834 

1.401 

6.807 

1.634 

7.779 

1.868 

8.751 

2.101 

76i 

13? 

1.188 

5.828 

1.426 

6.799 

1.664 

7.771 

1.902 

8.742 

2.139 

76i 

14° 

1.210 

5.822 

1.452 

6.792 

1.693 

7.762 

1.935 

8.733 

2.177 

76° 

14i 

1.231 

5.815 

1.477 

6.785 

1.723 

7.754 

1.969 

8.723 

2.215 

75? 

1« 

1.252 

5.809 

1.502 

6.777 

1.753 

7.745 

2.003 

8.713 

2.253 

75i 

14* 

1.273 

5.802 

1.528 

6.769 

1.782 

7.736 

2.037 

8.703 

2.291 

75^ 

15° 

1.294 

5.796 

1.553 

6.761 

1.812 

7.727 

2.071 

8.693 

2.329 

76° 

1*1 

1.315 

5.789 

1.578 

6.754 

1.841 

7.718 

2.104 

8.683 

2.367 

74? 

15i 

1.336 

5.782 

1.603 

6.745 

1.871 

7.709 

2.138 

8.673 

2.405 

74* 

15? 

1.357 

5.775 

1.629 

6.737 

1.900 

7.700 

2.172 

8.662 

2.443 

74f 

16° 

1.378 

5.768 

1.654 

6.729 

1.929 

7.690 

2.205 

8.651 

2.481 

74° 

wi 

1.399 

5.760 

1.679 

6.720 

1.959 

7.680 

2.239 

8.640 

2.518 

73? 

161 

1.420 

5.753 

1.704 

6.712 

1.988 

7.671 

2.272 

8.629 

2.556 

73i 

16? 

1.441 

5.745 

1.729 

6-703 

2.017 

7.661 

2.306 

8.618 

2.594 

73i 

17° 

1.462 

5.738 

1.754 

6.694 

2.047 

7.650 

2.339 

8.607 

2.631 

73° 

17i 

1.483 

5.730 

1.779 

6.685 

2.076 

7.640 

2.372 

8.595 

2.669 

72? 

17$ 

1.504 

5.722 

1.804 

6.676 

2.105 

7.630 

2.406 

8.583 

2.706 

72i 

17? 

1.524 

5.714 

1.829 

6.667 

2.134 

7.619 

2.439 

8.572 

2.744 

72i 

18° 

1.545 

5.706 

1.854 

6.657 

2.163 

7.608 

2.472 

8.560 

2.781 

72° 

I8i 

1.566 

5.698 

1.879 

6.648 

2.192 

7.598 

2.505 

8.547 

2.818 

71? 

18| 

1.587 

5.690 

1.904 

6.638 

2.221 

7.587 

2.538 

8.535 

2.856 

TO 

18| 

1.607 

5.682 

1.929 

6.629 

2.250 

7.575 

2.572 

8.522 

2.893 

7H 

19° 

1.628 

5.673 

1.953 

6.619 

2.279 

7.564 

2.605 

8.510 

2.930 

71° 

19i 

1.648 

5.665 

1.978 

6.609 

2.308 

7.553 

2.638 

8.497 

2.967 

70? 

19* 

1.669 

5.656 

2.003 

6.598 

2.337 

7.541 

2.670 

8.484 

3.004 

70£ 

19? 

1.690 

5.647 

2.028 

6.588 

2.365 

7.529 

2.703 

8.471 

3.041 

70i 

20° 

1.710 

5.638 

2.052 

6.578 

2.394 

7.518 

2.736 

8.457 

3.078 

70° 

20i 

1.731 

5.629 

2.077 

6.567 

2.423 

7.506 

2.769 

8.444 

3.115 

69? 

20£ 

1.751 

5.620 

2.101 

6.557 

2.451 

7.493 

2.802 

8.430 

3.152 

69* 

20? 

1.771 

5.611 

2.126 

6.546 

2.480 

7.481 

2.834 

8.'416 

3.189 

69i 

21° 

1.792 

5.601 

2.150 

6.535 

2.509 

7.469 

2.867 

8.402 

3.225 

69° 

211 

1.812 

5.592 

2.175 

6.524 

2.537 

7.456 

2.900 

8.388 

3.262 

68? 

2H 

1.833 

5.582 

2.199 

6.513 

2.566 

7.443 

2.932 

8.374 

3.299 

68i 

2l| 

1.853 

5.573 

2.223 

6.502 

2.594 

7.430 

2.964 

8.359 

3.335 

68i 

22° 

1.873 

5.563 

2.248 

6.490 

2.622 

7.417 

2.997 

8.345 

3.371 

68° 

22i 

1.893 

5.553 

2.272 

6.479 

2.651 

7.404 

3.029 

8.330 

3.408 

67? 

22| 

1.913 

5.543 

2.296 

6.467 

2.679 

7.391 

3.061 

8.315 

3.444 

67i 

22? 

1.934 

5.533 

2.320 

6.4,55 

2.707 

7.378 

3.094 

8.300 

3.480 

67i 

23° 

1.954 

5.523 

2.344 

6.444 

2.735 

7.364 

3.126 

8.285 

3.517 

67° 

23i 

1.974 

5.513 

2.368 

6.432 

2.763 

7.350 

3.158 

8.269 

3.553 

66? 

23i 

1.994 

5.502 

2.392 

6.419 

2.791 

7.336 

3.190 

8.254 

3.589 

66^ 

23? 

2.014 

5.492 

2.416 

6.407 

2.819 

7.322 

3.222 

8.238 

3.625 

66| 

24° 

2.034 

5.481 

2.440 

6.395 

2.847 

7.308 

3.254 

8.222 

3.661 

66° 

24| 

2.054 

5.471 

2.464 

6.382 

2.875 

7.294 

3.286 

8.206 

3.696 

65? 

24£ 

2.073 

5.460 

2.488 

6.370 

2.903 

7.280 

3.318 

8.190 

3.732 

65* 

24? 

2.093 

5.449 

2.512 

6.357 

2.931 

7.265 

3.349 

8.173 

3.768 

65i 

25° 

2.113 

5.438 

2.536 

6.344 

2.958 

7.250 

3.381 

8.157 

3.804 

65° 

25i 

2.133 

5.427 

2.559 

6.331 

2.986 

7.236 

3.413 

8.140 

3.839 

64? 

25£ 

2.153 

5.416 

2.583 

6.318 

3.014 

7.221 

3.444 

8.123 

3.875 

64i 

25? 

2.172 

5.404 

2.607 

6.305 

3.041 

7.206 

3.476 

8.106 

3.910 

64| 

26° 

2.192 

5.393 

2.630 

6.292 

3.069 

7.190 

3.507 

8.089 

3.945 

64° 

c 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.. 

Dep. 

Lat. 

Dep. 

Lat. 

/ 

I 

a 
00 

5 

i 

1 

I 

I 

1 

1 

• 

1078 


LATITUDES  AND  DEPARTURES 


* 

1 

2 

3 

4 

5 

M 
C 

1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a 
00 

28° 

0.899 

0.438 

1.798 

0.877 

2.696 

1.315 

3.595 

1.753 

4.494 

64° 

26* 

0.897 

0.442 

1.794 

0.885 

2.691 

1.327 

3.587 

1.769 

4.484 

63* 

26i 

0.895 

0.446 

1.790 

0.892 

2.685 

1.339 

3.580 

1.785 

4.475 

63i 

26* 

0.893 

0.450 

1.786 

0.900 

2.679 

1.350 

3.572 

1.800 

4.465 

63* 

27° 

0.891 

0.454 

1.782 

0.908 

2.673 

1.362 

3.564 

1.816 

4.455 

63° 

27* 

0.889 

0.458 

1.778 

0.916 

2.667 

1.374 

3.556 

1.831 

4.445 

62* 

0.887 

0.462 

1.774 

0.923 

2.661 

1.385 

3.548 

1.847 

4.435 

27* 

0.885 

0.466 

1.770 

0.931 

2.655 

1.397 

3.540 

1.862 

4.425 

62* 

28° 

0.883 

0.469 

1.766 

0.939 

2.649 

1.408 

3.532 

1.878 

4.415 

62° 

28* 

0.881 

0.473 

1.762 

0.947 

2.643 

1.420 

3.524 

1.893 

4.404 

61* 

0.879 

0.477 

1.758 

0.954 

2.636 

1.431 

3.515 

1.909 

4.394 

28! 

0.877 

0.481 

1.753 

0.962 

2.630 

1.443 

3.507 

1.924 

4.384 

61* 

29° 

0.875 

0.485 

1.749 

0.970 

2.624 

1.454 

3.498 

1.939 

4.373 

81° 

29* 

0.872 

0.'489 

1.745 

0.977 

2.617 

1.466 

3.490 

1.954 

4.362 

60* 

291 

0.870 

0.492 

1.741 

0.985 

2.611 

1.477 

3.481 

1.970 

4.352 

60s 

29* 

0.868 

0.496 

1.736 

0.992 

2.605 

1.489 

3.473 

1.985 

4.341 

60* 

30° 

0.866 

0.500 

1.732 

1.000 

2.598 

1.500 

3.464 

2.000 

4.330 

60° 

30* 

0.864 

0.504 

1.728 

1.008 

2.592 

1.511 

3.455 

2.015 

4.319 

59* 

30i 

0.862 

0.508 

1.723 

1.015 

2.585 

1.523 

3.447 

2.030 

4.308 

59* 

30* 

0.859 

0.511 

1.719 

1.023 

2.578 

1.534 

3.438 

2.045 

4.297 

59* 

31° 

0.857 

0.515 

1.714 

1.030 

2.572 

1.545 

3.429 

2.060 

4.286 

59° 

31* 

0.855 

0.519 

1.710 

1.038 

2.565 

1.556 

3.420 

2.075 

4.275 

58* 

3H 

0.853 

0.522 

1.705 

1.045 

2.558 

1.567 

3.411 

2.090 

4.263 

31* 

0.850 

0.526 

1.701 

1.052 

2.551 

1.579 

3.401 

2.105 

4.252 

58- 

32° 

0.848 

0.530 

1.696 

1.060 

2.544 

1.590 

3.392 

2.120 

4.240 

58° 

32* 

0.846 

0.534 

1.691 

1.067 

2.537 

1.601 

3.383 

2.134 

4.229 

57* 

0.843 

0.537 

1.687 

1.075 

2.530 

1.612 

3.374 

2.149 

4.217 

32* 

0.841 

0.541 

1.682 

1.082 

2.523 

1.623 

3.364 

2.164 

4.205 

57* 

33° 

0.839 

0.545 

1.677 

1.089 

2.516 

1.634 

3.355 

2.179 

4.193 

57° 

33* 

0.836 

0.548 

1.673 

1.097 

2.509 

1.645 

3.345 

2.193 

4.181 

56* 

33* 

0.834 

0.552 

1.668 

1.104 

2.502 

1.656 

3.336 

2.208 

4.169 

56i 

33* 

0.831 

0.556 

1.663 

1.111 

2.494 

1.667 

3.326 

2.222 

4.157 

56* 

34° 

0.829 

0.559 

1.658 

1.118 

2.487 

1.678 

3.316 

2.237 

4.145 

56° 

34* 

0.827 

0.563 

1.653 

1.126 

2.480 

1.688 

3.306 

2.251 

4.133 

55* 

0.824 

0.566 

1.648 

1.133 

2.472 

1.699 

3.297 

2.266 

4.121 

55i 

34* 

0.822 

0.570 

1.643 

1.140 

2.465 

1.710 

3.287 

2.280 

4.108 

55* 

35° 

0.819 

0.574 

1.638 

1.147 

2.457 

1.721 

3.277 

2.294 

4.096 

55° 

35* 

0.817 

0.577 

1.633 

1.154 

2.450 

1.731 

3.267 

2.309 

4.083 

54* 

35i 

0.814 

0.581 

1.628 

1.161 

2.442 

1.742 

3.257 

2.323 

4.071 

54* 

35* 

0.812 

0.584 

1.623 

1.168 

2.435 

1.753 

3.246 

2.337 

4.058 

54* 

36° 

0.809 

0.588 

1.618 

1.176 

2.427 

1.763 

3.236 

2.351 

4.045 

54° 

36* 

0.806 

0.591 

1.613 

1.183 

2.419 

1.774 

3.226 

2.365 

4.032 

53* 

36  * 

0.804 

0.595 

1.608 

1.190 

2.412 

1.784 

3.215 

2.379 

4.019 

36* 

0.801 

0.598 

1.603 

1.197 

2.404 

1.795 

3.205 

2.393 

4.006 

53* 

37° 

0.799 

0.602 

1.597 

1.204 

2.396 

1.805 

3.195 

2.407 

3.993 

53° 

37* 

0.796 

0.605 

1.592 

1.211 

2.388 

1.816 

3.184 

2.421 

3.980 

52* 

0.793 

0.609 

1.587 

1.218 

2.380 

1.826 

3.173 

2.435 

3.967 

37* 

0.791 

0.612 

1.581 

1.224 

2.372 

1.837 

3.163 

2.449 

3.953 

52* 

38° 

0.788 

0.616 

1.576 

1.231 

2.364 

1.847 

3.152 

2.463 

3.940 

52° 

0.785 

0.619 

1.571 

1.238 

2.356 

1.857 

3.141 

2.476 

3.927 

51* 

38| 

0.783 

0.623 

1.565 

1.245 

2.348 

1.868 

3.130 

2.490 

3.913 

51* 

38* 

0.780 

0.626 

1.560 

1.252 

2.340 

1.878 

3.120 

2.504 

3.899 

51* 

39° 

0.777 

0.629 

1.554 

1.259 

2.331 

1.888 

3.109 

2.517 

3.886 

51° 

00 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

c 

1 

I 

2 

3 

4 

5 

a 
t> 
00 

LATITUDES  AND  DEPARTURES 


1079 


1 

5 

6 

7 

8 

9 

| 

B 

m 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

c 

26° 

2.192 

5.393 

2.630 

6.292 

3.069 

7.190 

3.507 

8.089 

3.945 

64° 

26} 

2.211 

5.381 

2.654 

6.278 

3.096 

7.175 

3.538 

8.072 

3.981 

63* 

i 

2.231 
2.250 

5.370 
5.358 

2.677 
2.701 

6.265 
6.251 

3.123 
3.151 

7.160 
7.144 

3.570 
3.601 

8.054 
8.037 

4.016 
4.051 

1! 

27° 

2.270 

5.346 

2.724 

6.237 

3.178 

7.128 

3.632 

8.019 

4.086 

63° 

27} 

2.289 

5.334 

2.747 

6.223 

3.205 

7.112 

3.663 

8.001 

4.121 

62* 

274 

2.309 

5.322 

2.770 

6.209 

3.232 

7.096 

3.694 

7.983 

4.156 

62* 

27* 

2.328 

5.310 

2.794 

6.195 

3.259 

7.080 

3.725 

7.965 

4.190 

62} 

28° 

2.347 

5.298 

2.817 

6.181 

3.286 

7.064 

3.756 

7.947 

4.225 

62° 

28} 

2.367 

5.285 

2.840 

6.166 

3.313 

7.047 

3.787 

7.928 

4.260 

61* 

28* 

2.386 

5.273 

2.863 

6.152 

3.340 

7.031 

3.817 

7.909 

4.294 

61* 

28* 

2.405 

5.260 

2.886 

6.137 

3.367 

7.014 

3.848 

7.891 

4.329 

6H 

29° 

2.424 

5.248 

2.909 

6.122 

3.394 

6.997 

3.878 

7.872 

4.363 

61° 

29} 

2.443 

5.235 

2.932 

6.107 

3.420 

6.980 

3.909 

7.852 

4.398 

60* 

29* 

2.462 

5.222 

2.955 

6.093 

3.447 

6.963 

3.939 

7.833 

4.432 

60* 

I    29-3- 

2.481 

5.209 

2.977 

6.077 

3.474 

6.946 

3.970 

7.814 

4.466 

60| 

I    3o° 

2.500 

5.196 

3.000 

6.062 

3.500 

6.928 

4.000 

7.794 

4.500 

60° 

30} 

2.519 

5.183 

3.023 

6.047 

3.526 

6.911 

4.030 

7.775 

4.534 

59* 

30* 

2.538 

5.170 

3.045 

6.031 

3.553 

6.893 

4.060 

7.755 

4.568 

59* 

30* 

2.556 

5.156 

3.068 

6.016 

3.579 

6.875 

4.090 

7.735 

4.602 

59} 

31° 

2.575 

5.143 

3.090 

6.000 

3.605 

6.857 

4.120 

7.715 

4.635 

59° 

31i 

2.594 

5.129 

3.113 

5.984 

3.631 

6.839 

4.150 

7.694 

4.669 

58* 

3H 

2.612 

5.116 

3.135 

5.968 

3.657 

6.821 

4.180 

7.674 

4.702 

58* 

31* 

2.631 

5.102 

3.157 

5.952 

3.683 

6.803 

4.210 

7.653 

4.736 

58} 

32° 

2.650 

5.088 

3.180 

5.936 

3.709 

6.784 

4.239 

7.632 

4.769 

58° 

32} 

2.668 

5.074 

3.202 

5.920 

3.735 

6.766 

4.269 

7.612 

4.802 

57* 

32* 

2.686 

5.060 

3.224 

5.904 

3.761 

6.747 

4.298 

7.591 

4.836 

57* 

32* 

2.705 

5.046 

3.246 

5.887 

3.787 

6.728 

4.328 

7.569 

4.869 

57} 

33° 

2.723 

5.032 

3.268 

5.871 

3.812 

6.709 

4.357 

7.548 

4.902 

57° 

33} 

2.741 

5.018 

3.290 

5.854 

3.838 

6.690 

4.386 

7.527 

4.935 

56* 

33* 

2.760 

5.003 

3.312 

5.837 

3.864 

6.671 

4.416 

7.505 

4.967 

56* 

33* 

2.778 

4.989 

3.333 

5.820 

3.889 

6.652 

4.445 

7.483 

5.000 

56} 

34° 

2.796 

4.974 

3.355 

5.803 

3.914 

6.632 

4.474 

7.461 

5.033 

56° 

34} 

2.814 

4.960 

3.377 

5.786 

3.940 

6.613 

4.502 

7.439 

5.065 

55* 

m 

2.832 

4.945 

3.398 

5.769 

3.965 

6.593 

4.531 

7.417 

5.098 

55* 

34* 

2.850 

4.930 

3.420 

5.752 

3.990 

6.573 

4.560 

7.395 

5.130 

55} 

35° 

2.868 

4.915 

3.441 

5.734 

4.015 

6.553 

4.589 

7.372 

5.162 

55° 

35} 

2.886 

4.900 

3.463 

5.716 

4.040 

6.533 

4.617 

7.350 

5.194 

54* 

35* 

2.904 

4.885 

3.484 

5.699 

4.065 

6.513 

4.646 

7.327 

5.226 

54* 

35* 

2.921 

4.869 

3.505 

5.681 

4.090 

6.493 

4.674 

7.304 

5.258 

54} 

36° 

2.939 

4.854 

3.527 

5.663 

4.115 

6.472 

4.702 

7.281 

5.290 

54° 

36} 

2.957 

4.839 

3.548 

5.645 

4.139 

6.452 

4.730 

7.258 

5.322 

53* 

36* 

2.974 

4.823 

3.569 

5.627 

4.164 

6.431 

4.759 

7.235 

5.353 

53* 

36* 

2.992 

4.808 

3.590 

5.609 

4.188 

6.410 

4.787 

7.211 

5.385 

53} 

37° 

3.009 

4.792 

3.611 

5.590 

4.213 

6.389 

4.815 

7.188 

5.416 

53° 

37} 

3.026 

4.776 

3.632 

5.572 

4.237 

6.368 

4.842 

7.164 

5.448 

52* 

37* 

3.044 

4.760 

3.653 

5.554 

4.261 

6.347 

4.870 

7.140 

5.479 

52* 

37* 

3.061 

4.744 

3.673 

5.535 

4.286 

6.326 

4.898 

7.116 

5.510 

52} 

38° 

3.078 

4.728 

3.694 

5.516 

4.310 

6.304 

4.925 

7.092 

5.541 

52° 

38} 

3.095 

4.712 

3.715 

5.497 

4.334 

6.283 

4.953 

7.068 

5.572 

51* 

38* 

3.113 

4.696 

3.735 

5.478 

4.358 

6.261 

4.980 

7.043 

5.603 

51* 

38* 

3.130 

4.679 

3.756 

5.459 

4.381 

6.239 

5.007 

7.019 

5.633 

51} 

39° 

3.147 

4.663 

3.776 

5.440 

4.405 

6.217 

5.035 

6.994 

5.664 

51° 

s 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

.5 

m 

n 

• 
m 

5 

6 

7 

8 

9 

£ 

1080 


LATITUDES  AND  DEPARTURES 


t» 

c 

1 

2 

3 

4 

5 

S* 

— 

s 

00 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

39° 

0.777 

0.629 

1.554 

1.259 

2.331 

1.888 

3.109 

2.517 

3.886 

51° 

39} 

0.774 

0.633 

1.549 

1.265 

2.323 

1.898 

3.098 

2.531 

3.872 

50* 

39* 

0.772 

0.636 

1.543 

1.272 

2.315 

1.908 

3.086 

2.544 

3.858 

50* 

39* 

0.769 

0.639 

1.538 

1.279 

2.307 

1.918 

3.075 

2.558 

3.844 

50} 

40° 

0.766 

0.643 

1.532 

1.286 

2.298 

1.928 

3.064 

2.571 

3.830 

50° 

40} 

0.763 

0.646 

1.526 

1.292 

2.290 

1.938 

3.053 

2.584 

3.816 

49* 

40* 

0.760 

0.649 

1.521 

1.299 

2.281 

1.948 

3.042 

2.598 

3.802 

49* 

40$ 

0.758 

0.653 

1.515 

1.306 

2.273 

1.958 

3.030 

2.611 

3.788 

49} 

4,0 

0.755 

0.656 

1.509 

1.312 

2.264 

1.968 

3.019 

2.624 

3.774 

49° 

41} 

0.752 

0.659 

1.504 

1.319 

2.256 

1.978 

3.007 

2.637 

3.759 

48* 

41* 

0.749 

0.663 

1.498 

1.325 

2.247 

1.988 

2.996 

2.650 

3.745 

48* 

41* 

0.746 

0.666 

1.492 

1.332 

2.238 

1.998 

2.984 

2.664 

3.730 

48} 

42° 

0.743 

0.669 

1.486 

1.338 

2.229 

2.007 

2.973 

2.677 

3.716 

48° 

42} 

0.740 

0.672 

1.480 

1.345 

2.221 

2.017 

2.961 

2.689 

3.701 

47* 

42* 

0.737 

0.676 

1.475 

1.351 

2.212 

2.027 

2.949 

2.702 

3.686 

47* 

42| 

0.734 

0.679 

1.469 

1.358 

2.203 

2.036 

2.937 

2.715 

3.672 

47} 

43° 

0.731 

0.682 

1.463 

1.364 

2.194 

2.046 

2.925 

2.728 

3.657 

47° 

43} 

0.728 

0.685 

1.457 

1.370 

2.185 

2.056 

2.913 

2.741 

3.642 

46* 

43* 

0.725 

0.688 

1.451 

1.377 

2.176 

2.065 

2.901 

2.753 

3.627 

46* 

43* 

0.722 

0.692 

1.445 

1.383 

2.167 

2.075 

2.889 

2.766 

3.612 

46} 

44° 

0.719 

0.695 

1.439 

1.389 

2.158 

2.084 

2.877 

2.779 

3.597 

46° 

44} 

0.716 

0.698 

1.433 

1.396 

2.149 

2.093 

2.865 

2.791 

3.582 

45* 

44* 

0.713 

0.701 

1.427 

1.402 

2.140 

2.103 

2.853 

2.804 

3.566 

45* 

44*. 

0.710 

0.704 

1.420 

1.408 

2.131 

2.112 

2.841 

2.816 

3.551 

45} 

45° 

0.707 

0.707 

1.414 

1.414 

2.121 

2.121 

2.828 

2.828 

3.536 

45° 

Bear- 
ing. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Bear- 
ing. 

no 

B 

5 

6 

7 

8 

9 

bo 

c 

CD 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S 

00 

39° 

3.147 

4.663 

3.776 

5.440 

4.405 

6.217 

5.035 

6.994 

5.664 

51° 

39} 

3.164 

4.646 

3.796 

5.421 

4.429 

6.195 

5.062 

6.970 

5.694 

50* 

39* 

3.180 

4.630 

3.816 

5.401 

4.453 

6.173 

5.089 

6.945 

5.725 

50* 

39* 

3.197 

4.613 

3.837 

5.382 

4.476 

6.151 

5.116 

6.920 

5.755 

50} 

40° 

3.214 

4.596 

3.857 

5.362 

4.500 

6.128 

5.142 

6.894 

5.785 

50° 

40} 

3.231 

4.579 

3.877 

5.343 

4.523 

6.106 

5.169 

6.869 

5.815 

49* 

40* 

3.247 

4.562 

3.897 

5.323 

4.546 

6.083 

5.196 

6.844 

5.845 

49* 

40* 

3.264 

4.545 

3.917 

5.303 

4.569 

6.061 

5.222 

6.818 

5.875 

49} 

4,0 

3.280 

4.528 

3.936 

5.283 

4.592 

6.038 

5.248 

6.792 

5.905 

49° 

41} 

3.297 

4.511 

3.956 

5.263 

4.615 

6.015 

5.275 

6.767 

5.934 

48* 

41* 

3.313 

4.494 

3.976 

5.243 

4.638 

5.992 

5.301 

6.741 

5.964 

48* 

41* 

3.329 

4.476 

3.995 

5.222 

4.661 

5.968 

5.327 

6.715 

5.993 

48} 

42° 

3.346 

4.459 

4.015 

5.202 

4.684 

5.945 

5.353 

6.688 

6.022 

48° 

42} 

3.362 

4.441 

4.034 

5.182 

4.707 

5.922 

5.379 

6.662 

6.051 

47* 

42* 

3.378 

4.424 

4.054 

5.161 

4.729 

5.898 

5.405 

6.635 

6.080 

47* 

42* 

3.394 

4.406 

4.073 

5.140 

4.752 

5.875 

5.430 

6.609 

6.109 

47} 

43° 

3.410 

4.388 

4.092 

5.119 

4.774 

5.851 

5.456 

6.582 

6.138 

47° 

43} 

3.426 

4.370 

4.111 

5.099 

4.796 

5.827 

5.481 

6.555 

6.167 

46* 

43* 

3.442 

4.352 

4.130 

5.078 

4.818 

5.803 

5.507 

6.528 

6.195 

46* 

43* 

3.458 

4.334 

4.149 

5.057 

4.841 

5.779 

5.532 

6.501 

6.224 

46} 

44° 

3.473 

4.316 

4.168 

5.035 

4.863 

5.755 

5.557 

6.474 

6.252 

46° 

44} 

3.489 

4.298 

4.187 

5.014 

4.885 

5.730 

5.582 

6.447 

6.280 

45* 

44* 

3.505 

4.280 

4.206 

4.993 

4.906 

5.706 

5.607 

6.419 

6.308 

45* 

44* 

3.520 

4.261 

4.224 

4.971 

4.928 

5.681 

5.632 

6.392 

6.336 

45} 

45° 

3.536 

4.243 

4.243 

4.950 

4.950 

5.657 

5.657 

6.364 

6.364 

45° 

Bear- 
ing 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Bear- 

ing 

CIRCUMFERENCES  AND  AREAS 


1081 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS, 
CIRCUMFERENCES,  AND  AREAS 


No. 

Square 

Cube 

Sq.  Boot 

Cu.  Root 

Reciprocal 

Circum. 

Area 

1 

1 

1 

1.0000 

l.'OOOO 

1.000000000 

3.1416 

0.7854 

2 

4 

8 

1.4142 

1.2599 

.500000000 

6.2832 

3.1416 

3 

9 

27 

1.7321 

1.4422 

.333333333 

9.4248 

7.0686 

4 

16 

64 

2.0000 

1.5874 

.250000000 

12.5664 

12.5664 

5 

25 

125 

2.2361 

1.7100 

.200000000 

15.7080 

19.635 

6 

36 

216 

2.4495 

1.8171 

.166666667 

18.850 

28.274 

7 

49 

343 

2.6458 

1.9129 

.142857143 

21.991 

38.485 

8 

64 

512 

2.8284 

2.0000 

.125000000 

25.133 

50.266 

9 

81 

729 

3.0000 

2.0801 

.111111111 

28.274 

63.617 

10 

100 

1,000 

3.1623 

2.1544 

.100000000 

31.416 

78.540 

11 

121 

1,331 

3.3166 

2.2240 

.090909091 

34.558 

95.033 

12 

144 

1,728 

3.4641 

2.2894 

.083333333 

37.699 

113.10 

13 

169 

2,197 

3.6056 

2.3513 

.076923077 

40.841 

132.73 

14 

196 

2,744 

3.7417 

2.4101 

.071428571 

43.982 

153.94 

15 

225 

3,375 

3.8730 

2.4662 

.066666667 

47.124 

176.71 

16 

256 

4,096 

4.0000 

2.5198 

.062500000 

50.265 

201.06 

17 

289 

4,913 

4.1231 

2.5713 

.058823529 

53.407 

226.98 

18 

324 

5,832 

4.2426 

2.6207 

.055555556 

56.549 

254.47 

19 

361 

6,859 

4.3589 

2.6684 

.052631579 

59.690 

283.53 

20 

400 

8,000 

4.4721 

2.7144 

.050000000 

62.832 

314.16 

21 

441 

9,261 

4.5826 

2.7589 

.047619048 

65.973 

346.36 

22 

484 

10,648 

4.6904 

2.8020 

.045454545 

69.115 

380.13 

23 

529 

12,167 

4.7958 

2.8439 

.043478261 

72.257 

415.48 

24 

576 

13,824 

4.8990 

2.8845 

.041666667 

75.398 

452.39 

25 

625 

15,625 

5.0000 

2.9240 

.040000000 

78.540 

490.87 

26 

676 

17,576 

5.0990 

2.9625 

.038461538 

81.681 

530.93 

27 

729 

19,683 

5.1962 

3.0000 

.037037037 

84.823 

572.56 

28 

784 

21,952 

5.2915 

3.0366 

.035714286 

87.965 

615.75 

29 

841 

24,389 

5.3852 

3.0723 

.034482759 

91.106 

660.52 

30 

900 

27,000 

5.4772 

3.1072 

.033333333 

94.248 

706.86 

31 

961 

29,791 

5.5678 

3.1414 

.0322580G5 

97.389 

754.77 

32 

1,024 

32,768  - 

5.6569 

3.1748 

.031250000 

100.53 

804.25 

33 

1,089 

35,937 

5.7446 

3.2075 

.030303030 

103.67 

855.30 

34 

1,156 

39,304 

5.8310 

3.2396 

.029411765 

106.81 

907.92 

35 

1,225 

42,875 

5.9161 

3.2717 

.028571429 

109.96 

962.11 

36 

1,296 

46,656 

6.0000 

3.3019 

.027777778 

113.10 

1,017.88 

37 

1,369 

50,653 

6.0828 

3.3322 

.027027027 

116.24 

1,075.21 

38 

1,444 

54,872 

6.1644 

3.3620 

.026315789 

119.38 

1,134.11 

39 

1,521 

59,319 

6.2450 

3.3912 

.025641026 

122.52 

1,194.59 

40 

1,600 

64,000 

6.3246 

3.4200 

.025000000 

125.66 

1,256.64 

41 

1,681 

68,921 

6.4031 

3.4482 

.024390244 

128.81 

1,320.25 

42 

1,764 

74,088 

6.4807 

3.4760 

.023809524 

131.95 

1,385.44 

43 

1,849 

79,507 

6.5574 

3  5034 

.023255814 

135.09 

1,452.20 

44 

1,936 

85,184 

6.6332 

3  5303 

.022727273 

138.23 

1,520.53 

45 

2,025 

91,125 

6.7082 

3.5569 

.022222222 

141.37 

1,590.43 

46 

2,116 

97,336 

67823 

35830 

.021739130 

144.51 

1.661.90 

47 

2,209 

103,823 

68557 

36088 

.021276600 

147.65 

1,734.94 

48 

2,304 

110,592 

6.9282 

3.6342 

.020833333 

150.80 

1,809.56 

49 

2,401 

117,649 

7.0000 

36593 

.020408163 

153.94 

1,885.74 

50 

2,500 

125,000 

7.0711 

3.6840 

.020000000 

157.08 

1,963.50 

51 

2,601 

132,651 

7.1414 

3.7084 

.019607843 

160.22 

2,042.82 

52 

2,704 

140,608 

7.2111 

3.7325 

.019230769 

163.36 

2,123.72 

53 

2,809 

148,877 

7.2801 

3.7563 

.018867925 

66.50 

2,206.18 

54 

2,916 

157,464 

7.3485 

3.7798 

.018518519 

69.65 

2,290.22 

55 

3,025 

166,375 

7.4162 

3.8030 

.018181818 

72.79 

2,375.83 

1082 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum 

Area 

56 

3,136 

175,616 

7.4833 

3.8259 

.017857143 

175.93 

2,463.01 

57 

3,249 

185,193 

7.5498 

3.8485 

.017543860 

179.07 

2,551.76 

58 

3,364 

195,112 

7.6158 

3.8709 

.017241379 

182.21 

2,642.08 

59 

3,481 

205,379 

7.6811 

3.8930 

.016949153 

185.35 

2,733.97 

60 

3,600 

216,000 

7.7460 

3.9149 

.016666667 

188.50 

2,827.43 

61 

3,721 

226,981 

7.8102 

3.9365 

.016393443 

191.64 

2,922.47 

62 

3,844 

238,328 

7.8740 

3.9579 

.016129032 

194.78 

3,019.07 

63 

3,969 

250,047 

7.9373 

3.9791 

.015873016 

197.92 

3,117.25 

64 

4,096 

262,144 

8.0000 

4.0000 

.015625000 

201.06 

3,216.99 

65 

4,225 

274,625 

8.0623 

4.0207 

.015384615 

204.20 

3,318.31 

66 

4,356 

287,496 

8.1240 

4.0412 

.015151515 

207.34 

3,421.19 

67 

4,489 

300,763 

8.1854 

4.0615 

.014925373 

210.49 

3,525.65 

68 

4,624 

314,432 

8.2462 

4.0817 

.014705882 

213.63 

3,631.68 

69 

4,761 

328,509 

8.3066 

4.1016 

.014492754 

216.77 

3,739.28 

70 

4,900 

343,000 

8.3666 

4.1213 

.014285714 

219.91 

3,848.45 

71 

5,041 

357,911 

8.4261 

4.1408 

.014084517 

223.05 

3,959.19 

72 

5,184 

373,248 

8.4853 

4.1602 

.013888889 

226.19 

4,071.50 

73 

5,329 

389,017 

8.5440 

4.1793 

.013698630 

229.34 

4,185.39 

74 

5,476 

405,224 

8.6023 

4.1983 

.013513514 

232.48 

4,300.84 

75 

5,625 

421,875 

8.6603 

4.2172 

.013333333 

235.62 

4,417.86 

76 

5,776 

438,976 

8.7178 

4.2358 

.013157895 

238.76 

4,536.46 

77 

5,929 

456,533 

8.7750 

4.2543 

.012987013 

241.90 

4,656.63 

78 

6,084 

474,552 

8.8318 

4.2727 

.012820513 

245.04 

4,778.36 

79 

6,241 

493,039 

8.8882 

4.2908 

.012658228 

248.19 

4,901.67 

80 

6,400 

512,000 

8.9443 

4.3089 

.012500000 

251.33 

5,026.55 

81 

6,561 

531,441 

9.0000 

4.3267 

.012345679 

254.47 

5,153.00 

82 

6,724 

551,368 

9.0554 

4.3445 

.012195122 

257.61 

5,281.02 

83 

6,889 

571,787 

9.1104 

4.3621 

.012048193 

260.75 

5,410.61 

84 

7,056 

592,704 

9.1652 

4.3795 

.011904762 

263.89 

5,541.77 

85 

7,225 

614,125 

9.2195 

4.3968 

.011764706 

267.04 

5,674.50 

86 

7,396 

636,056 

9.2736 

4.4140 

.011627907 

270.18 

5,808.80 

87 

7,569 

658,503 

9.3274 

4.4310 

.011494253 

273.32 

5,944.68 

88 

7,744 

681,472 

9.3808 

4.4480 

.011363636 

276.46 

6,082.12 

89 

7,921 

704,969 

9.4340 

4.4647 

.011235955 

279.60 

6,221.14 

90 

8,100 

729,000 

9.4868 

4.4814 

.011111111 

282.74 

6,361.73 

91 

8,281 

753,571 

9.5394 

4.4979 

.010989011 

285.88 

6,503.88 

92 

8,464 

778,688 

9.5917 

4.5144 

.010869565 

289.03 

6,647.61 

93 

8,649 

804,357 

9.6437 

4.5307 

.010752688 

292.17 

6,792.91 

94 

8,836 

830,584 

9.6954 

4.5468 

.010638298 

295.31 

6,939.78 

95 

9,025 

857,375 

9.7468 

4.5629 

.030526316 

298.45 

7,088.22 

96 

9,216 

884,736 

9.7980 

4.5789 

.010416667 

301.59 

7,238.23 

97 

9,409 

912,673 

9.8489 

4.5947 

.010309278 

304.73 

7,389.81 

98 

9,604 

941,192 

9.8995 

4.6104 

.010204082 

307.88 

7,542.96 

99 

9,801 

970,299 

9.9499 

4.6261 

.010101010 

311.02 

7,697.69 

100 

10,000 

1,000,000 

10.0000 

4.6416 

.010000000 

314.16 

7,853.98 

101 

10,201 

1,030,301 

10.0499 

4.6570 

.009900990 

317.30 

8,011.85 

102 

10,404 

1,061,208 

10.0995 

4.6723 

.009803922 

320.44 

8,171.28 

103 

10,609 

1,092,727 

10.1489 

4.6875 

.009708738 

323.58 

8,332.29 

104 

10,816 

1,124,864 

10.1980 

4.7027 

.009615385 

326.73 

8,494.87 

105 

11,025 

1,157,625 

10.2470 

4.7177 

.009523810 

329.87 

8,659.01 

106 

11,236 

1,191,016 

10.2956 

4.7326 

.009433962 

333.01 

8,824.73 

107 

11,449 

1,225,043 

10.3441 

4.7475 

.009345794 

336.15 

8,992.02 

108 

11,664 

1,259,712 

10.3923 

4.7622 

.009259259 

339.29 

9,160.88 

109 

11,881 

1,295,029 

10.4403 

4.7769 

.009174312 

342.43 

9,331.32 

110 

12,100 

1,331,000 

10.4881 

4.7914 

.009090909 

345.58 

9,503.32 

111 

12,321 

1,367,631 

10.5357 

4.8059 

.009009009 

348.72 

9,676.89 

112 

12,544 

1,404,928 

10.5830 

4.8203 

.008928571 

351.86 

9,852.03 

113 

12,769 

1,442,897 

10.6301 

4.8346 

.008849558 

355.00 

10,028.75 

114 

12,996 

1,481,544 

10.6771 

4.8488 

.008771930 

358.14 

10,207.03 

115 

13,225 

1,520,875 

10.7238 

4.8629 

.008695652 

361.28 

10,386.89 

116 

13,456 

1,560,896 

10.7703 

4.8770 

.008020690 

364.42 

10,568.32 

117 

13,689 

1,601,613 

10.8167 

4.8910 

.008547009 

367.57 

10,751.32 

118 

13,924 

1,643,032 

10.8628 

4.9049 

.008474576 

370.71 

10,935.88 

CIRCUMFERENCES,  AND  AREAS 


1083 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

119 

14,161 

1,685,159 

10.9087 

4.9187 

.008403361 

373.85 

11,122.02 

120 

14,400 

1,728,000 

10.9545 

4.9324 

.008333333 

376.99 

11,309.73 

121 

14,641 

1,771,561 

11.0000 

4.9461 

.008264463 

380.13 

11,499.01 

122 

14,834 

1,815,848 

11.0454 

4.9597 

.008196721 

383.27 

11,689.87 

123 

15,129 

1,860,867 

11.0905 

4.9732 

.008130081 

386.42 

11,882.29 

124 

15,376 

1,906,624 

11.1355 

4.9866 

.008064516 

389.56 

12,076.28 

125 

15,625 

1,953,125 

11.1803 

5.0000 

.008000000 

392.70 

12,271.85 

126 

15,876 

2,000,376 

11.2250 

5.0133 

.007936508 

395.84 

12,468.98 

127 

16,129 

2,048,383 

11.2694 

5.0265 

.007874016 

398.98 

12,667.69 

128 

16,384 

2,097,152 

11.3137 

5.0397 

.007812500 

402.12 

12,867.96 

129 

16,641 

2,146,689 

11.3578 

5.0528 

.007751938 

405.27 

13,069.81 

130 

16,900 

2,197,000 

11.4018 

5.0658 

.007692308 

408.41 

13,273.23 

131 

17,161 

2,248,091 

11.4455 

5.0788 

.007633588 

411.55 

13,478.22 

132 

17,424 

2,299,968 

11.4891 

5.0916 

.007575758 

414.69 

13,684.78 

133 

17,689 

2,352,637 

11.5326 

5.1045 

.007518797 

417.83 

13,892.91 

134 

17,956 

2,406,104 

11.5758 

5.1172 

.007462687 

420.97 

14,102.61 

135 

18,225 

2,460,375 

11.6190 

5.1299 

.007407407 

424.12 

14,313.88 

136 

18,496 

2,515,456 

11.6619 

5.1426 

.007352941 

427.26 

14,526.72 

137 

18,769 

2,571,353 

11.7047 

5.1551 

.007299270 

430.40 

14,741.14 

138 

19,044 

2,628,072 

11.7473 

5.1676 

.007246377 

433.54 

14,957.12 

139 

19,321 

2,685,619 

11.7898 

5.1801 

.007194245 

436.68 

15,174.68 

140 

19,600 

2,744,000 

11.8322 

5.1925 

.007142857 

439.82 

15,393.80 

141 

19,881 

2,803,221 

11.8743 

5.2048 

.007092199 

442.96 

15,614.50 

142 

20,164 

2,863,288 

11.9164 

5.2171 

.007042254 

446.11 

15,836.77 

143 

20,449 

2,924,207 

11.9583 

5.2293 

.006993007 

449.25 

16,060.61 

144 

20,736 

2,985,984 

12.0000 

5.2415 

.006944444 

452.39 

16,286.02 

145 

21,025 

3,048,625 

12.0416 

5.2536 

.006896552 

455.53 

16,513.00 

146 

21,316 

3,112,136 

12.0830 

5.2656 

.006849315 

458.67 

16,741.55 

147 

21,609 

3,176,523 

12.1244 

5.2776 

.006802721 

461.81 

16,971.67 

148 

21,904 

3,241,792 

12.1655 

5.2896 

.006756757 

464.96 

17,203.36 

149 

22,201 

3,307,949 

12.2066 

5.3015 

.006711409 

468.10 

17,436.62 

150 

22,500 

3,375,000 

12.2474 

5.3133 

.006666667 

471.24 

17,671.46 

151 

22,801 

3,442,951 

12.2882 

5.3251 

.006622517 

474.38 

17,907.86 

152 

23,104 

3,511,008 

12.3288 

5.3368 

.006578947 

477.52 

18,145.84 

153 

23,409 

3,581,577 

12.3693 

5.3485 

.006535948 

480.66 

18,385.39 

154 

23,716 

3,652,264 

12.4097 

5.3601 

.006493506 

483.81 

18,626.50 

155 

24,025 

3,723,875 

12.4499 

5.3717 

.006451613 

486.95 

18,869.19 

156 

24,336 

3,796,416 

12.4900 

5.3832 

.006410256 

490.09 

19,113.45 

157 

24,649 

3,869,893 

12.5300 

5.3947 

.006369427 

493.23 

19,359.28 

158 

24,964 

3,944,312 

12.5698 

5.4061 

.006329114 

496.37 

19,606.68 

159 

25,281 

4,019,679 

12.6095 

5.4175 

.006289308 

499.51 

19,855.65 

160 

25,600 

4,096,000 

12.6491 

5.4288 

.006250000 

502.65 

20,106.19 

161 

25,921 

4,173,281 

12.6886 

5.4401 

.006211180 

505.80 

20,358.31 

162 

26,244 

4,251,528 

12.7279 

5.4514 

.006172840 

508.94 

20,611.99 

163 

26,569 

4,330,747 

12.7671 

5.4626 

.006134969 

512.08 

20,867.24 

164 

26,896 

4,410,944 

12.8062 

5.4737 

.006097561 

515.22 

21,124.07 

165 

27,225 

4,492,125 

12.8452 

5.4848 

.006060606 

518.36 

21,382.46 

166 

27,556 

4,574,296 

12.8841 

5.4959 

.006024096 

521.50 

21,642.43 

167 

27,889 

4,657,463 

12.9228 

5.5069 

.005988024 

524.65 

21,903.97 

168 

28,224 

4,741,632 

12.9615 

5.5178 

.005952381 

527.79 

22,167.08 

169 

28,561 

4,826,809 

13.0000 

5.5288 

.005917160 

530.93 

22,431.76 

170 

28,900 

4,913,000 

13.9384 

5.5397 

.005882353 

534.07 

22,698.01 

171 

29,241 

5,000,211 

13.0767 

5.5505 

.005847953 

537.21 

22,965.83 

172 

29,584 

5,088,448 

13.1149 

5.5613 

.005813953 

540.35 

23,235.22 

173 

29,929 

5,177,717 

13.1529 

5.5721 

.005780347 

543.50 

23,506.18 

174 

30,276 

5,268,024 

13.1909 

5.5828 

.005747126 

546.64 

23,778.71 

175 

30,625 

5,359,375 

13.2288 

5.5934 

.005714286 

549.78 

24,052.82 

176 

30,976 

5,451,776 

13.2665 

5.6041 

.005681818 

552.92 

24,328.49 

177 

31,329 

5,545,233 

13.3041 

5.6147 

.005649718 

556.06 

24,605.74 

178 

31,684 

5,639,752 

13.3417 

5.6252 

.005617978 

559.20 

24,884.56 

179 

32,041 

5,735,339 

13.3791 

5.6357 

.005586592 

562.35 

25,164.94 

180 

32,400 

5,832,000 

13.4164 

5.6462 

.005555556 

565.49 

25,446.90 

181 

32,761 

5,929,741 

13.4536 

5.6567 

.005524862 

568.63 

25,730.48 

1084 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

182 

33,124 

6,028,568 

13.4907 

5.6671 

.005494505 

571.77 

26,015.53 

183 

33,489 

6,128,487 

13.5277 

5.6774 

.005464481 

574.91 

26,302.20 

184 

83,856 

6,229,504 

13.5647 

5.6877 

.005434783 

578.05 

26,590.44 

185 

34,225 

6,331,625 

13.6015 

5.6980 

.005405405 

581.19 

26,880.25 

186 

34,596 

6,434,856 

13.6382 

5.7083 

.005376344 

584.34 

27,171.63 

187 

34,969 

6,539,203 

13.6748 

5.7185 

.005347594 

587.48 

27,464.59 

188 

35,344 

6,644,672 

13.7113 

5.7287 

.005319149 

590.62 

27,759.11 

189 

35,721 

6,751,269 

13.7477 

5.7388 

.005291005 

593.76 

28,055.21 

190 

36,100 

6,859,000 

13.7840 

5.7489 

.005263158 

596.90 

28,352.87 

191 

36,481 

6,967,871 

13.8203 

5.7590 

.005235602 

600.04 

28,652.11 

192 

36,864 

7,077,888 

13.8564 

5.7690 

.005208333 

603.19 

28,952.92 

193 

37,249 

7,189,017 

13.8924 

5.7790 

.005181347 

606.33 

29,255.30 

194 

37,636 

7,301,384 

13.9284 

5.7890 

.005154639 

609.47 

29,559.25 

195 

38,025 

7,414,875 

13.9642 

5.7989 

.005128205 

612.61 

29,864.77 

196 

38,416 

7,529,536 

14.0000 

5.8088 

.005102041 

615.75 

30,171.86 

197 

38,809 

7,645,373 

14.0357 

5.8186 

.005076142 

618.89 

30,480.52 

198 

39,204 

7,762,392 

14.0712 

5.8285 

.005050505 

622.04 

30,790.75 

199 

39,601 

7,880,599 

14.1067 

5.8383 

.005025126 

625.18 

31,102.55 

200 

40,000 

8,000,000 

14.1421 

5.8480 

.005000000 

628.32 

31,415.93 

201 

40,401 

8,120,601 

14.1774 

5.8578 

.004975124 

631.46 

31,730.87 

202 

40,804 

8,242,408 

14.2127 

5.8675 

.004950495 

634.60 

32,047.39 

203 

41,209 

8,365,427 

14.2478 

5.8771 

.004926108 

637.74 

32,365.47 

204 

41,616 

8,489,664 

14.2829 

5.8868 

.004901961 

640.88 

32,685.13 

205 

42,025 

8,615,125 

14.3178 

5.8964 

.004878049 

644.03 

33,006.36 

206 

42,436 

8,741,816 

14.3527 

5.9059 

.004854369 

647.17 

33,329.16 

207 

42,849 

8,869,743 

14.3875 

5.9155 

.004830918 

650.31 

33,653.53 

208 

43,264 

8,998,912 

14.4222 

5.9250 

.004807692 

653.45 

33,979.47 

209 

43,681 

9,129,329 

14.4568 

5.9345 

.004784689 

656.59 

34.306.98 

210 

44,100 

9,261,000 

14.4914 

5.9439 

.004761905 

659.73 

34,636.06 

211 

44,521 

9,393,931 

14.5258 

5.9533 

.004739336 

662.88 

34,966.71 

212 

44,944 

9,528.128 

14.5608 

5.9627 

.004716981 

666.02 

35,298.94 

213 

45,369 

9,663,597 

14.5945 

5.9721 

.004694836 

669.16 

35,632.73 

214 

45,796 

9,800,344 

14.6287 

5.9814 

.004672897 

672.30 

35,968.09 

215 

46,225 

9,938,375 

14.6629 

5.9907 

.004651163 

675.44 

36,305.03 

216 

46,656 

10,077,696 

14.6969 

6.0000 

.004629630 

678.58 

36,643.54 

217 

47,089 

10,218,313 

14.7309 

6.0092 

.004608295 

681.73 

36,983.61 

218 

47,524 

10,360,232 

14.7648 

6.0185 

.004587156 

684.87 

37,325.26 

219 

47,961 

10,503,459 

14.7986 

6.0277 

.004566210 

688.01 

37,668.48 

220 

48,400 

10,648,000 

14.8324 

6.0368 

.004545455 

691.15 

38,013.27 

221 

48,841 

10,793,861 

14.8661 

6.0459 

.004524887 

694.29 

38,359.63 

222 

49,284 

10,941,048 

14.8997 

6.0550 

.004504505 

697.43 

38,707.56 

223 

49,729 

11,089,567 

14.9332 

6.0641 

.004484305 

700.58 

39,057.07 

224 

50,176 

11,239,424 

14.9666 

6.0732 

.004464286 

703.72 

39,408.14 

225 

50,625 

11,390,625 

15.0000 

6.0822 

.004444444 

706.86 

39,760.78 

226 

51,076 

11,543,176 

15.0333 

6.0912 

.004424779 

710.00 

40,115.00 

227 

51,529 

11,697,083 

15.0665 

6.1002 

.004405286 

713.14 

40,470.78 

228 

51,984 

11,852,352 

15.0997 

6.1091 

.004385965 

716.28 

40,828.14 

229 

52,441 

12,008,989 

15.1327 

6.1180 

.004366812 

719.42 

41,187.07 

230 

52,900 

12,167,000 

15.1658 

6.1269 

.004347826 

722.57 

41,547.56 

231 

53,361 

12,326,391 

15.1987 

6.1358 

.004329004 

725.71 

41,909.63 

232 

53,824 

12,487,168 

15.2315 

6.1446 

.004310345 

728.85 

42,273.27 

233 

54,289 

12,649,337 

15.2643 

6.1534 

.004291845 

731.99 

42,638.48 

234 

54,756 

12,812,904 

15.2971 

6.1622 

.004273504 

735.13 

43,005.26 

235 

55,225 

12,977,875 

15.3297 

6.1710 

.004255319 

738.27 

43,373.61 

236 

55,696 

13,144,256 

15.3623 

6.1797 

.004237288 

741.42 

43,743.54 

237 

56,169 

13,312,053 

15.3948 

6.1885 

.004219409 

744.56 

44,115.03 

238 

56,644 

13,481,272 

15.4272 

6.1672 

.004201681 

747.70 

44,488.09 

239 

57,121 

13,651,919 

15.4596 

6.2058 

.004184100 

750.84 

44,862.73 

240 

57,600 

13,824,000 

15.4919 

6.2145 

.004166667 

753.98 

45,238.93 

241 

58,081 

13,997,521 

15.5242 

6.2231 

.004149378 

757.12 

45,616.71 

242 

58,564 

14,172,488 

15.5563 

6.2317 

.004132231 

760.27 

45,996.06 

243 

59,049 

14,348,907 

15.5885 

6.2403 

.004115226 

763.41 

46,376.98 

244 

59,536 

14,526,784 

15.6205 

6.2488 

.004098361 

766.55 

46,759.47 

CIRCUMFERENCES,  AND  AREAS 


1085 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

245 

60,025 

14,706,125 

15.6525 

6.2573 

.004081633 

769.69 

47,143.52 

246 

60,516 

14,886,936 

15.6844 

6.2658 

.004065041 

772.83 

47,529.16 

247 

61,009 

15,069,223 

15.7162 

6.2743 

.004048583 

775.97 

47,916.36 

248 

61,504 

15,252,992 

15.7480 

6.2828 

.004032258 

779.11 

48,305.13 

249 

62,001 

15,438,249 

15.7797 

6.2912 

.004016064 

782.26 

48,695.47 

250 

62,500 

15,625,000 

15.8114 

6.2996 

.004000000 

785.40 

49,087.39 

251 

63,001 

15,813,251 

15.8430 

6.3080 

.003984064 

788.54 

49,480.87 

252 

63,504 

16,003,008 

15.8745 

6.3164 

.003968254 

791.68 

49,875.92 

253 

64,009 

16,194,277 

15.9060 

6.3247 

.003952569 

794.82 

50,272.55 

254 

64,516 

16,387,064 

15.9374 

6.3330 

.003937008 

797.96 

50,670.75 

255 

65,025 

16,581,375 

15.9687 

6.3413 

.003921569 

801.11 

51,070.52 

256 

65,536 

16,777,216 

16.0000 

6.3496 

.003906250 

804.25 

51,471.85 

257 

66,049 

16,974,593 

16.0312 

6.3579 

.003891051 

807.39 

51,874.76 

258 

66,564 

17,173,512 

16.0624 

6.3661 

.003875969 

810.53 

52,279.24 

259 

67,081 

17,373,979 

16.0935 

6.3743 

.003861004 

813.67 

52,685.29 

260 

67,600 

17,576,000 

16.1245 

6.3825 

.003846154 

816.81 

53,092.92 

261 

68,121 

17,779,581 

16.1555 

6.3907 

.003831418 

819.96 

53,502.11 

262 

68,644 

17,984,728 

16.1864 

6.3988 

.003816794 

823.10 

53,912.87 

263 

69,169 

18,191,447 

16.2173 

6.4070 

.003802281 

826.24 

54,325.21 

264 

69,696 

18,399,744 

16.2481 

6.4151 

.003787879 

829.38 

54,739.11 

265 

70,225 

18,609,625 

16.2788 

6.4232 

.003773585 

832.52 

55,154.59 

266 

70,756 

18,821,096 

16.3095 

6.4312 

.003759398 

835.66 

55,571.63 

267 

71,289 

19,034,163 

16.3401 

6.4393 

.003745318 

838.81 

55,990.25 

268 

71,824 

19,248,832 

16.3707 

6.4473 

.003731343 

841.95 

56,410.44 

269 

72,361 

19,465,109 

16.4012 

6.4553 

.003717472 

845.09 

56,832.20 

.270 

72,900 

19,683,000 

16.4317 

6.4633 

.003703704 

848.23 

57,255.53 

271 

73,441 

19,902,511 

16.4621 

6.4713 

.003690037 

851.37 

57,680.43 

272 

73,984 

20,123,643 

16.4924 

6.4792 

.003676471 

854.51 

58,106.90 

273 

74,529 

20,346,417 

16.5227 

6.4872 

.003663004 

857.65 

58,534.94 

274 

75,076 

20,570,824 

16.5529 

6.4951 

.003649635 

860.80 

58,964.55 

275 

75,625 

20,796,875 

16.5831 

6.5030 

.003636364 

863.94 

59,395.74 

276 

76,176 

21,024,576 

16.6132 

6.5108 

.003623188 

867.08 

59,828.49 

277 

76,729 

21,253,933 

16.6433 

6.5187 

.003610108 

870.22 

60,262.82 

278 

77,284 

21,484,952 

16.6783 

6.5265 

.003597122 

873.36 

60,698.71 

279 

77,841 

21,717,639 

16.7033 

6.5343 

.003584229 

876.50 

61,136.18 

280 

78,400 

21,952,000 

16.7332 

6.5421 

.003571429 

879.65 

61,575.22 

281 

78,961 

22,188,041 

16.7631 

6.5499 

.003558719 

882.79 

62,015.82 

282 

79,524 

22,425,768 

16.7929 

6.5577 

.003546099 

885.93 

62,458.00 

283 

80,089 

22,665,187 

16.8226 

6.5654 

.003533569 

889.07 

62,901.75 

284 

80,656 

22,906,304 

16.8523 

6.5731 

.003522127 

892.21 

63,347.07 

285 

81,225 

23,149,125 

16.8819 

6.5808 

.003508772 

895.35 

63,793.97 

286 

81,796 

23,393,656 

16.9115 

6.5885 

.003496503 

898.50 

64,242.43 

287 

82,369 

23,639,903 

16.9411 

6.5962 

.003484321 

901.64 

64,692.46 

288 

82,944 

23,887,872 

16.9706 

6.6039 

.003472222 

904.78 

65,144.07 

289 

83,521 

24,137,569 

17.0000 

6.6115 

.003460208 

907.92 

65,597.24 

290 

84,100 

24,389,000 

17.0294 

6.6191 

.003448276 

911.06 

66,051.99 

291 

84,681 

24,642,171 

17.0587 

6.6267 

.003436426 

914.20 

66,508.30 

292 

85,264 

24,897,088 

17.0880 

6.6343 

.003424658 

917.35 

66,966.19 

293 

85,849 

25,153,757 

17.1172 

6.6119 

.003412969 

920.49 

67,425.65 

294 

86,436 

25,412,184 

17.1464 

6.6494 

.003401361 

923.63 

67,886.68 

295 

87,025 

25,672,375 

17.1756 

6.6569 

.003389831 

926.77 

68,349.28 

296 

87,616 

25,934,836 

17.2047 

6.6644 

.003378378 

929:91 

68,813.45 

297 

88,209 

26,198,073 

17.2337 

6.6719 

.003367003 

933.05 

69,279.19 

298 

88,804 

26,463,592 

17.2627 

6.6794 

.003355705 

936.19 

69,746.50 

299 

89,401 

26,730,899 

17.2916 

6.6869 

.003344482 

939.34 

70,215.38 

300 

90,000 

27,000,000 

17.3205 

6.6943 

.003333333 

942.48 

70,685.83 

301 

90,601 

27,270,901 

17.3494 

6.7018 

.003322259 

945.62 

71,157.86 

302 

91,204 

27,543,608 

17.3781 

6.7092 

.003311258 

948.76 

71,631.45 

303 

91,809 

27,818,127 

17.4069 

6.7166 

.003301330 

951.90 

72,106.62 

304 

92,416 

28,094,464 

17.4356 

6.7240 

.003289474 

955.04 

72,583.36 

305 

93.025 

28,372,625 

17.4642 

6.7313 

.003278689 

958.19 

73,061.66 

306 

93,636 

28,652,616 

17.4929 

6.7387 

.003267974 

961.33 

73,541.54 

307 

94,249 

28,934,443 

17.5214 

6.7460 

.003257329 

964.47 

74,022.99 

1086 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

308 

94,864 

29,218,112 

17.5499 

6.7533 

.003246753 

967.61 

74,506.01 

309 

95,481 

29,503,629 

17.5784 

6.7606 

.003236246 

970.75 

74,990.60 

310 

96,100 

29,791,000 

17.6068 

6.7679 

.003225806 

973.89 

75,476.76 

311 

96,721 

30,080,231 

17.6352 

6.7752 

.003215434 

977.04 

75,964.50 

312 

97,344 

30,371,328 

17.6635 

6.7824 

.003205128 

980.18 

76,453.80 

313 

97,969 

30,664,297 

17.6918 

6.7897 

.003194888 

983.32 

76,944.67 

314 

98,596 

30,959,144 

17.7200 

6.7969 

.003184713 

986.46 

77,437.12 

315 

99,225 

31,255,875 

17.7482 

6.8041 

.003174603 

989.60 

77,931.13 

316 

99,856 

31,554,496 

17.7764 

6.8113 

.003164557 

992.74 

78,426.72 

317 

100,489 

31,855,013 

17.8045 

6.8185 

.003154574 

995.88 

78,923.88 

318 

101,124 

32,157,432 

17.8326 

6.8256 

.003144654 

999.03 

79,422.60 

319 

101,761 

32,461,759 

17.8606 

6.8328 

.003134796 

1,002.17 

79,922.90 

320 

102,400 

32,768,000 

17.8885 

6.8399 

.003125000 

1,005.31 

80,424.77 

321 

103,041 

33,076,161 

17.9165 

6.8470 

.003115265 

1,008.45 

80,928.21 

322 

103,684 

33,386,248 

17.9444 

6.8541 

.003105690 

1,011.59 

81,433.22 

323 

104,329 

33,698,267 

17.9722 

6.8612 

.003095975 

1,014.73  81,939.80 

324 

104,976 

34,012,224 

18.0000 

6.8683 

.003086420 

1,017.88  82,447.96 

325 

105,625 

34,328,125 

18.0278 

6.8753 

.003076923 

1,021.02 

82,957.68 

326 

106,276 

34,645,976 

18.0555 

6.8824 

.003067485 

1,024.16 

83,468.98 

327 

106,929 

34,965,783 

18.0831 

6.8894 

.003058104 

1,027.30 

83,981.84 

328 

107,584 

35,287,552 

18.1108 

6.8964 

.003048780 

1,030.44 

84,496.28 

329 

108,241 

35,611,289 

18.1384 

6.9034 

.003039514 

1,033.58 

85,012.28 

330 

108,900 

35,937,000 

18.1659 

6.9104 

.003030303 

1,036.73 

85,529.86 

331 

109,561 

36,264,691 

18.1934 

6.9174 

.003021148 

1,039.87 

86,049.01 

332 

110,224 

36,594,368 

18.2209 

6.9244 

.003012048 

1,043.01 

86,569.73 

333 

110,889 

36,926,037 

18.2483 

6.9313 

.003003003 

1,046.15 

87,092.02 

334 

111,556 

37,259,704 

18.2757 

6.9382 

.002994012 

1,049.29 

87,615.88 

335 

112,225 

37,595,375 

18.3030 

6.9451 

.002985075 

1,052.43 

88,141.31 

336 

112,896 

37,933,056 

18.3303 

6.9521 

.002976190 

1,055.58 

88,668.31 

337 

113,569 

38,272,753 

18.3576 

6.9589 

.002967359 

1,058.72 

89,196.88 

338 

114,244 

38,614,472 

18.3848 

6.9658 

.002958580 

1,061.86 

89,727.03 

339 

114,921 

38,958,219 

18.4120 

6.9727 

.002949853 

1,065.00 

90,258.74 

340 

115,600 

39,304,000 

18.4391 

6.9795 

.002941176 

1,068.14 

90,792.03 

341 

116,281 

39,651,821 

18.4662 

6.9864 

.002932551 

1,071.28 

91,326.88 

342 

116,964 

40,001,688 

18.4932 

6.9932 

.002923977 

1,074.42 

91  ,863.31 

343 

117,649 

40,353,607 

18.5203 

7.0000 

.002915452 

1,077.57 

92,401.31 

344 

118,336 

40,707,584 

18.5472 

7.0068 

.002906977 

1,080.71 

92,940.88 

345 

119,025 

41,063,625 

18.5742 

7.0136 

.002898551 

1,083.85 

93,482.02 

346 

119,716 

41,421,736 

18.6011 

7.0203 

.002890173 

1,086.99 

94,024.73 

347 

120,409 

41,781,923 

18.6279 

7.0271 

.002881844 

1,090.13 

94,569.01 

348 

121,104 

42,144,192 

18.6548 

7.0338 

.002873563 

1,093.27 

95,114.86 

349 

121,801 

42,508,549 

18.6815 

7.0406 

.002865330 

1,096.42 

95,662.28 

350 

122,500 

42,875,000 

18.7083 

7.0473 

.002857143 

1,099.56 

96,211.28 

351 

123,201 

43,243,551 

18.7350 

7.0540 

.002849003 

1,102.70 

96,761.84 

352 

123,904 

43,614,208 

18.7617 

7.0607 

.002840909 

1,105.84 

97,313.97 

353 

124,609 

43,986,977 

18.7883 

7.0674 

.002832861 

1,108.98 

97,867.68 

354 

125,316 

44,361,864 

18.8149 

7.0740 

.002824859 

1,112.12 

98,422.96 

355 

126,025 

44,738,875 

18.8414 

7.0807 

.002816901 

1,115.27 

98,979.80 

356 

126,736 

45,118,016 

18.8680 

7.0873 

.002808989 

1,118.41 

99,538.22 

357 

127,449 

45,499,293 

18.8944 

7.0940 

.002801120 

1,121.55 

100,098.21 

358 

128,164 

45,882,712 

18.9209 

7.1006 

.002793296 

1,124.69 

100,659.77 

359 

128,881 

46,268,279 

18.9473 

7.1072 

.002785515 

1,127.83 

101,222.90 

360 

129,600 

46,656,000 

18.9737 

7.1138 

.002777778 

1,130.97 

101,787.60 

361 

130,321 

47,045,881 

19.0000 

7.1204 

.002770083 

1,134.11 

102,353.87 

362 

131,044 

47,437,928 

19.0263 

7.1269 

.002762431 

1,137.26 

102,921.72 

363 

131,769 

47,832,147 

19.0526 

7.1335 

.002754821 

1,140.40 

103,491.13 

364 

132,496 

48,228,544 

19.0788 

7.1400 

.002747253 

1,143.54 

104,062.12 

365 

133,225 

48,627,125 

19.1050 

7.1466 

.002739726 

1,146.68 

104,634.67 

366 

133,956 

49,027,896 

19.1311 

7.1531 

.002732240 

1,149.82 

105,208.80 

367 

134,689 

49,430,863 

19.1572 

7.1596 

.002724796 

1,152.96 

105,784.49 

368 

135,424 

49,836,032 

19.1833 

7.1661 

.002717391 

1,156.11 

106,361.76 

369 

136,161 

50,243,409 

19.2094 

7.1726 

.002710027 

1,159.25 

106,940.60 

370 

136,900 

50,653,000 

19.2354 

7.1791 

.002702703 

1,162.39 

107,521.01 

CIRCUMFERENCES,  AND  AREAS 


1087 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

371 

137,641 

51,064,811 

19.2614 

7.1855 

.002695418 

1,165.53 

108,102.99 

372 

138,384 

51,478,848 

19.2873 

7.1920 

.002688172 

1,168.67 

108,686.54 

373 

139,129 

51,895,117 

19.3132 

7.1984 

.002680965 

1,171.81 

109,271.66 

374 

139,876 

52,313,624 

19.3391 

7.2048 

.002673797 

1,174.96 

109,858.35 

375 

140,625 

52,734,375 

19.3649 

7.2112 

.002666667 

1,178.10 

110,446.62 

376 

141,376 

53,157,376 

19.3907 

7.2177 

.002659574 

1,181.24 

111,036.45 

377 

142,129 

53,582,633 

19.4165 

7.2240 

.002652520 

1,184.38 

111,627.86 

378 

142,884 

54,010,152 

19.4422 

7.2304 

.002645503 

1,187.52 

112,220.83 

379 

143;  641 

54,439,939 

19.4679 

7.2368 

.002638521 

1,190.66 

112,815.38 

380 

144,400 

54,872,000 

19.4936 

7.2432 

.002631579 

1,193.81 

113,411.49 

381 

145,161 

55,306,341 

19.5192 

7.2495 

.002624672 

1,196.95 

114,009.18 

382 

145,924 

55,742,968 

19.5448 

7.2558 

.002617801 

1,200.09 

114,608.44 

383 

146,689 

56,181,887 

19.5704 

7.2622 

.002610966 

1,203.23 

115,209.27 

384 

147,456 

56,623,104 

19.5959 

7.2685 

.002604167 

1,206.37 

115,811.67 

385 

148,225 

57,066,625 

19.6214 

7.2748 

.002597403 

1,209.51 

116,415.64 

386 

148,996 

57,512,456 

19.6469 

7.2811 

.002590674 

1,212.65 

117,021.18 

387 

149,769 

57,960,603 

19.6723 

7.2874 

.002583979 

1,215.80 

117,628.30 

388 

150,544 

58,411,072 

19.6977 

7.2936 

.002577320 

1,218.94 

118,236.98 

389 

151,321 

68,863,869 

19.7231 

7.2999 

.002570694 

1,222.08 

118,847.24 

390 

152,100 

59,319,000 

19.7484 

7.3061 

.002564103 

1,225.22 

119,459.06 

391 

152,881 

59,776,471 

19.7737 

7.3124 

.002557545 

1,228.36 

120,072.46 

392 

153,664 

60,236,288 

19.7990 

7.3186 

.002551020 

1,231.50 

120,687.42 

393 

154,449 

60,698,457 

19.8242 

7.3248 

.002544529 

1,234.65 

121,303.96 

394 

155,236 

61,162,984 

19.8494 

7.3310 

.002538071 

1,237.79 

121,922.07 

395 

156,025 

61,629,875 

19.8746 

7.3372 

.002531646 

1,240.93 

122,541.75 

396 

156,816 

62,099,136 

19.8997 

7.3434 

.002525253 

1,244.07 

123,163.00 

397 

157,609 

62,570,773 

19.9249 

7.3496 

.002518892 

1,247.21 

123,785.82 

398 

158,404 

63,044,792 

19.9499 

7.3558 

.002512563 

1,250.35 

124,410.21 

399 

159,201 

63,521,199 

19.9750 

7.3619 

.002506266 

1,253.50 

125,036.17 

400 

160,000 

64,000,000 

20.0000 

7.3681 

.002500000 

1,256.64 

125,663.71 

401 

160,801 

64,481,201 

20.0250 

7.3742 

.002493766 

1,259.78 

126,292.81 

402 

161,604 

64,964,808 

20.0499 

7.3803 

.002487562 

1,262.92 

126,923.48 

403 

162,409 

65,450,827 

20.0749 

7.3864 

.002481390 

1,266.06 

127,555.73 

404 

163,216 

65,939,264 

20.0998 

7.3925 

.002475248 

1,269.20 

128.189.55 

405 

164,025 

66,430,125 

20.1246 

7.3986 

.002469136 

1.272.35 

128,824.93 

406 

164,836 

66,923,416 

20.1494 

7.4047 

.002463054 

1,275.49 

129,461.89 

407 

165,649 

67,419,143 

20.1742 

7.4108 

.002457002 

1,278.63 

130,100.42 

408 

166,464 

67,917,312 

20.1990 

7.4169 

.002450980 

1,281.77 

130,740.52 

409 

167,281 

68,417,929 

20.2237 

7.4229 

.002444988 

1,284.91 

131,382.19 

410 

168,100 

68,921,000 

20.2485 

7.4290 

.002439024 

1,288.05 

132,025.43 

411 

168,921 

69,426,531 

20.2731 

7.4350 

.002433090 

1,291.19 

132,670.24 

412 

169,744 

69,934,528 

20.2978 

7.4410 

.002427184 

1,294.34 

133,316.63 

413 

170,569 

70,444,997 

20.3224 

7.4470 

.002421308 

1,297.48 

133,964.58 

414 

171,396 

70,957,944 

20.3470 

7.4530 

.002415459 

1,300.62 

134,614.10 

415 

172,225 

71,473,375 

20.3715 

7.4590 

.002409639 

1,303.76 

135,265.20 

416 

173,056 

71,991,296 

20.3961 

7.4650 

.002406846 

1,306.90 

135,917.86 

417 

173,889 

72,511,713 

20.4206 

7.4710 

.002398082 

1,310.04 

136,572.10 

418 

174,724 

73,034,632 

20.4450 

7.4770 

.002392344 

1,313.19 

137,227.91 

419 

175,561 

73,560,059 

20.4695 

7.4829 

.002386635 

1,316.33 

137,885.29 

420 

176,400 

74,088,000 

20.4939 

7.4889 

.002380952 

1,319.47 

138,544.24 

421 

177,241 

74,618,461 

20.5183 

7.4948 

.002375297 

1,322.61 

139,204.76 

422 

178,084 

75,151,448 

20.5426 

7.5007 

.002369668 

1,325.75 

139,866.85 

423 

178,929 

75,686,967 

20.5670 

7.5067 

.002364066 

1,328.89 

140,530.51 

424 

179,776 

76,225,024 

20.5913 

7.5126 

.002358491 

1,332.04 

141,195.74 

425 

180,625 

76,765,625 

20.6155 

7.5185 

.002352941 

1,335.18 

141,862.54 

426 

181,476 

77,308,776 

20.6398 

7.5244 

.002347418 

1,338.32 

142,530.92 

427 

182J329 

77,854,483 

20.6640 

7.5302 

.002341920 

1,341.46 

143,200.86 

428 

183,184 

78,402,752 

20.6882 

7.5361 

.002336449 

1,344.60 

143,872.38 

429 

184,041 

78,953,589 

20.7123 

7.5420 

.002331002 

1,347.74 

144,545.46 

430 

184[900 

79,507,000 

20.7364 

7.5478 

.002325581 

1,350.88 

145,220.12 

431 

185,761 

80,062,991 

20.7605 

7.5537 

.002320186 

1,354.03 

145.896.35 

432 

186'  624 

80,621,568 

20.7846 

7.5595 

.002314815 

1,357.17 

146,574.15 

433 

187,489 

81,182,737 

20.8087 

7.5654 

.002309469 

1,360.31 

147,253.52 

1088 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

434 

188,356 

81,746,504 

20.8327 

7.5712 

.002304147 

1,363.45 

147,934.46 

435 

189,225 

82,312,875 

20.8567 

7.5770 

.002298851 

1,366.59 

148,616.97 

436 

190,096 

82,881,856 

20.8806 

7.5828 

.002293578 

1,369.73 

149,301.05 

437 

190,969 

83,453,453 

20.9045 

7.5886 

.002288330 

1,372.88 

149,986.70 

438 

191,844 

84,027,672 

20.9284 

7.5944 

.002283105 

1,376.02 

150,673.93 

439 

192,721 

84,604,519 

20.9523 

7.6001 

.002277904 

1,379.16 

151,362.72 

440 

193,600 

85,184,000 

20.9762 

7.6059 

.002272727 

1,382.30 

152,053.08 

441 

194,481 

85,766,121 

21.0000 

7.6117 

.002267574 

1,385.44 

152,745.02 

442 

195,364 

86,350,888 

21.0238 

7.6174 

.002262443 

1,388.58 

153,438.53 

443 

196,249 

86,938,307 

21.0476 

7.6232 

.002257336 

1,391.73 

154,133.60 

444 

197,136 

87,528,384 

21.0713 

7.6289 

.002252252 

1,394.87 

154,830.25 

445 

198,025 

88,121,125 

21.0950 

7.6346 

.002247191 

1,398.01 

155,528.47 

446 

198,916 

88,716,536 

21.1187 

7.6403 

.002242152 

1,401.15 

156,228.26 

447 

199,809 

89,314,623 

21.1424 

7.6460 

.002237136 

1,404.29 

156,929.62 

448 

200,704 

89,915,392 

21.1660 

7.6517 

.002232143 

1,407.43 

157,632.55 

449 

201,601 

90,518,849 

21.1896 

7.6574 

.002227171 

1,410.58 

158,337.06 

450 

202,500 

91,125,000 

21.2132 

7.6631 

.002222222 

1,413.72 

159,043.13 

451 

203,401 

91,733,851 

21.2368 

7.6688 

.002217295 

1,416.86 

159,750.77 

452 

204,304 

92,345,408 

21.2603 

7.6744 

.002212389 

1,420.00 

160,459.99 

453 

205,209 

92,959,677 

21.2838 

7.6801 

.002207506 

1,423.14 

161,170.77 

454 

206,116 

93,576,664 

21.3073 

7.6857 

.002202643 

1,426.28 

161,883.13 

455 

207,025 

94,196,375 

21.3307 

7.6914 

.002197802 

1,429.42 

162,597.05 

456 

207,936 

94,818,816 

21.3542 

7.6970 

.002192982 

1,432.57 

163,312.55 

457 

208,849 

95,443,993 

21.3776 

7.7026 

.002188184 

1,435.71 

164,029.62 

458 

209,764 

96,071,912 

21.4009 

7.7082 

.002183406 

1,438.85 

164,748.26 

459 

210,681 

96,702,579 

21.4243 

7.7188 

.002178649 

1,441.99 

165,468.47 

460  ' 

211,600 

97,336,000 

21.4476 

7.7194 

.002173913 

1,445.13 

166,190.25 

461 

212,521 

97,972,181 

21.4709 

7.7250 

.002169197 

1,448.27 

166,913.60 

462 

213,444 

98,611,128 

21.4942 

7.7306 

.002164502 

1,451.42 

167,638.53 

463 

214,369 

99,252,847 

21.5174 

7.7362 

.002159827 

1,454.56 

168,365.02 

464 

215,296 

99,897,344 

21.5407 

7.7418 

.002155172 

1,457.70 

169,093.08 

465 

216,225 

100,544,625 

21.5639 

7.7473 

.002150538 

1,460.84 

169,822.72 

466 

217,156 

101,194,696 

21.5870 

7.7529 

.002145923 

1,463.98 

170,553.92 

467 

218,089 

101,847,563 

21.6102 

7.7584 

.002141328 

1,467.12 

171,286.70 

468 

219,024 

102,503,232 

21.6333 

7.7639 

.002136752 

1,470.27 

172,021.05 

469 

219,961 

103,161,709 

21.6564 

7.7695 

.002132196 

1,473.41 

172,756.97 

470 

220,900 

103,823,000 

21.6795 

7.7750 

.002127660 

1,476.55 

173,494.45 

471 

221,841 

104,487,111 

21.7025 

7.7805 

.002123142 

1,479.69 

174,233.51 

472 

222,784 

105,154,048 

21.7256 

7.7860 

.002118644 

1,482.83 

174,974.14 

473 

223,729 

105,823,817 

21.7486 

7.7915 

.002114165 

1,485.97 

175,716.35 

474 

224,676 

106,496,424 

21.7715 

7.7970 

.002109705 

1,489.11 

176,460.12 

475 

225,625 

107,171,875 

21.7945 

7.8025 

.002105263 

1,492.26 

177,205.46 

476 

226,576 

107,850,176 

21.8174 

7.8079 

.002100840 

1,495.40 

177,952.37 

477 

227,529 

108,531,333 

21.8403 

7.8134 

.002096486 

1,498.54 

178,700.86 

478 

228,484 

109,215,352 

21.8632 

7.8188 

.002092050 

1,501.68 

179,450.91 

479 

229,441 

109,902,239 

21.8861 

7.8243 

.002087683 

1,504.82 

180,202.54 

480 

230,400 

110,592,000 

21.9089 

7.8297 

.002083333 

1,507.96 

180,955.74 

481 

231,361 

111,284,641 

21.9317 

7.8352 

.002079002 

1,511.11 

181,710.50 

482 

232,324 

111,980,168 

21.9545 

7.8406 

.002074689 

1,514.25 

182,466.84 

483 

233,289 

112,678,587 

21.9775 

7.8460 

.002070393 

1.517.39 

183,224.75 

484 

234,256 

113,379,904 

22.0000 

7.8514 

.002066116 

1,520.53 

183,984.23 

485 

235,225 

114,084,125 

22.0227 

7.8568 

.002061856 

1,523.67 

184,745.28 

486 

236,196 

114,791,256 

22.0454 

7.8622 

.002057613 

1,526.81 

185,507.90 

487 

237,169 

115,501,303 

22.0681 

7.8676 

.002053388 

1,529.96 

186,272.10 

488 

238,144 

116,214,272 

22.0907 

7.8730 

.002049180 

1,533.10 

187,037.86 

489 

239,121 

116,930,169 

22.1133 

7.8784 

.002044990 

1,536.24 

87,805.19 

490 

240,100 

117,649,000 

22.1359 

7.8837 

.002040816 

1,539.38 

188,574.10 

491 

241,081 

118,370,771 

22.1585 

7.8891 

.002036660 

1,542.52 

89,344.57 

492 

242,064 

119,095,488 

22.1811 

7.8944 

.002032520 

1,545.66 

190,116.62 

493 

243,049 

119,823,157 

22.2036 

7.8998 

.002028398 

1,548.81 

190,890.24 

494 

244,036 

120,553,784 

22.2261 

7.9051 

.002024291 

1,551.95 

91,665.43 

495 

245,025 

121,287,375 

22.2486 

7.9105 

.002020292 

1,555.09 

92,442.18 

496 

246,016 

122,023,936 

22.2711 

7.9158 

.002016129 

1,558.23 

193,220.51 

CIRCUMFERENCES,  AND  AREAS            1089 

No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

497 

247,009 

122,763,473 

22.2935 

7.9211 

.002012072 

1,561.37 

194,000.41 

498 

248,004 

123,505,992 

22.3159 

7.9264 

.002008032 

1,564.51 

194,781.89 

499 

249,001 

124,251,499 

22.3383 

7.9317 

.002004008 

1,567.65 

195,564.93 

500 

250,000 

125,000,000 

22.3607 

7.9370 

.002000000 

1,570.80 

196,349.54 

501 

251,001 

125,751,501 

22.3830 

7.9423 

.001996008 

1,573.94 

197,135.72 

502 

252,004 

126,506,008 

22.4054 

7.9476 

.001992032 

1,577.08 

197,923.48 

503 

253,009 

127,263,527 

22.4277 

7.9528 

.001988072 

1,580.22 

198,712.80 

504 

254,016 

128,024,064 

22.4499 

7.9581 

.001984127 

1,583.36 

199,503.70 

505 

255,025 

128,787,625 

22.4722 

7.9634 

.001980198 

1,586.50 

200,296.17 

506 

256,036 

129,554,216 

22.4944 

7.9686 

.001976285 

1,589.65 

201,090.20 

507 

257,049 

130,323,843 

22.5167 

7.9739 

.001972387 

1,592.79 

201,885.81 

508 

258,064 

131,096,512 

22.5389 

7.9791 

.001968504 

1,595.93 

202,682.99 

509 

259,081 

131,872,229 

22.5610 

7.9843 

.001964637 

1,599.07 

203,481.74 

510 

260,100 

132,651,000  . 

22.5832 

7.9895 

.001960785 

1,602.21 

204,282.06 

511 

261,121 

133,432,831 

22.6053 

7.9948 

.001956947 

1,605.35 

205,083.95 

512 

262,144 

134,217,728 

22.6274 

8.0000 

.001953125 

1,608.50 

205;  887.42 

513 

263,169 

135,005,697 

22.6495 

8.0052 

.001949318 

1,611.64 

206,692.45 

514 

264,196 

135,796,744 

22.6716 

8.0104 

.001945525 

1,614.78 

207,499.05 

515 

265,225 

136,590,875 

22.6936 

8.0156 

.001941748 

1,617.92 

208,307.23 

516 

266,256 

137,388,096 

22.7156 

8.0208 

.001937984 

1,621.06 

209,116.97 

517 

267,289 

138,188,413 

22.7376 

8.0260 

.001934236 

1,624.20 

209,928.29 

518 

268,324 

138,991,832 

22.7596 

8.0311 

.001930502 

1,627.34 

210,741.18 

519 

269,361 

139,798,359 

22.7816 

8.0363 

.001926782 

1,630.49 

211,555.63 

520 

270,400 

140,608,000 

22.8035 

8.0415 

.001923077 

1,633.63 

212,371.66 

521 

271,411 

141,420,761 

22.8254 

8.0466 

.001919386 

1,636.77 

213,189.26 

522 

272,484 

142,236,648 

22.8473 

8.0517 

.001915709 

1,639.91 

214,008.43 

523 

273,529 

143,055,667 

22.8692 

8.0569 

.001912046 

1,643.05 

214,829.17 

524 

274,576 

143,877,824 

22.8910 

8.0620 

.001908397 

1,646.19 

215,651.49 

525 

275,625 

144,703,125 

22.9129 

8.0671 

.001904762 

1,649.34 

216,475.37 

526 

276,676 

145,531,576 

22.9347 

8.0723 

.001901141 

1,652.48 

217,300.82 

527 

277,729 

146,363,183 

22.9565 

8.0774 

.001897533 

1,655.62 

218,127.85 

528 

278,784 

147,197,952 

22.9783 

8.0825 

.001893939 

1,658.76 

218,956.44 

529 

279,841 

148,035,889 

23.0000 

8.0876 

.001890359 

1,661.90 

219,786.61 

530 

280,900 

148,877,001 

23.0217 

8.0927 

.001886792 

1,665.04 

220,618.34 

531 

281,961 

149,721,291 

23.0434 

8.0978 

.001883239 

1,668.19 

221,451.65 

532 

283,024 

150,568,768 

23.0651 

8.1028 

.001879699 

1,671.33 

222,286.53 

533 

284,089 

151,419,437 

23.0868 

8.1079 

.001876173 

1,674.47 

223,122.98 

534 

285,156 

152,273,304 

23.1084 

8.1130 

.001872659 

1,677.61 

223,961.00 

535 

286,225 

153,130,375 

23.1301 

8.1180 

.001869159 

1,686.75 

224,800.59 

536 

287,296 

153,990,656 

23.1517 

8.1231 

.001865672 

1,683.89 

225,641.75 

537 

288,369 

154,854,153 

23.1733 

8.1281 

.001862197 

1,687.04 

226,484.48 

538 

289,444 

155,720,872 

23.1948 

8.1332 

.001858736 

1,690.18 

227,328.79 

539 

290,521 

156,590,819 

23.2164 

8.1382 

.001855288 

1,693.32 

228,174.66 

540 

291,600 

157,464,000 

23.2379 

8.1433 

.001851852 

1,696.46 

229,022.10 

541 

292,681 

158,340,421 

23.2594 

8.1483 

.001848429 

1,699.60 

229,871.12 

512 

293,764 

159,220,088 

23.2809 

8.1533 

.001845018 

1,702.74 

230,721.71 

543 

294,849 

160,103,007 

23.3024 

8.1583 

.001841621 

1,705.88 

231,573.86 

544 

295,936 

160,989,184 

23.3238 

8.1633 

.001838235 

1,709.03 

232,427.59 

545 

297,025 

161,878,625 

23.3452 

8.1683 

.001834862 

1,712.17 

233,282.89 

546 

298,116 

162,771,336 

23.3666 

8.1733 

.001831502 

1,715.31 

234,139.76 

547° 

299,209 

163,667,323 

23.3880 

8.17&3 

.001828154 

1,718.45 

234,998.20 

548 

300,304 

164,566,592 

23.4094 

8.1833 

.001824818 

1,721.59 

235,858.21 

549 

301,401 

165,469,149 

23.4307 

8.1882 

.001821494 

1,724.73 

236,719.79 

550 

302500 

166,375,000 

23.4521 

8.1932 

.001818182 

1,727.88 

237,582.94 

551 

303,601 

167,284,151 

23.4734 

8.1982 

.001814882 

1,731.02 

238,447.67 

552 

304,704 

168,196,608 

23.4947 

8.2031 

.001811594 

1,734.16 

239,313.96 

553 

305,809 

169,112,377 

23.5160 

8.2081 

.001808318 

1,737.30 

240,181.83 

554 

306,916 

170,031,464 

23.5372 

8.2130 

.001805054 

1,740.44 

241,051.26 

555 

308,025 

170,953,875 

23.5584 

8.2180 

.001801802 

1,743.58 

241,922.27 

556 

309,136 

171,879,616 

23.5797 

8.2229 

.001798561 

1,746.73 

242,794.85 

557 

310,249 

172,808,693 

23.6008 

8.2278 

.001795332 

1,749.87 

243,668.99 

558 
569 

311,364 
312,481 

173,741,112 
174,676,879 

23.6220 
23.6432 

8.2327 
8.2377 

.001792115 
.001788909 

1,753.01 
1,756.15 

244,544.71 
245,422.00 

69 

1090 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No 

Square 

Cube 

Sq.Roo 

Cu.Roo 

Reciprocal 

Circum. 

Area 

660 

313,600 

175,616,000 

23.664 

8.2426 

.001785714 

1,759.29 

246,300.86 

561 

314,721 

176,558,481 

23.6854 

8.2475 

.001782531 

1,762.43 

247,181.30 

562 

315,844 

177,504,328 

23.7065 

8.2524 

.001779359 

1,765.58 

248,063.30 

563 

316,969 

178,453,547 

23.7276 

8.2573 

.001776199 

1,768.72 

248,946.87 

564 

318,096 

179,406,144 

23.7487 

8.2621 

.001773050 

1,771.86 

249,832.01 

565 

319,225 

180,362,125 

23.7697 

8.2670 

.001769912 

1,775.00 

250,718.73 

566 

320,356 

181,321,496 

23.7908 

8.2719 

.001766784 

1,778.14 

251,607.01 

567 

321,489 

182,284,263 

23.8118 

8.2768 

.001763668 

1,781.28 

252,496.87 

568 

322,624 

183,250,432 

23.8328 

8.2816 

.001760563 

1,784.42 

253,388.30 

569 

323,761 

184,220,009 

23.8537 

8.2865 

.001757469 

1,787.57 

254,281.29 

570 

324,900 

185,193,000 

23.8747 

8.2913 

.001754386 

1,790.71 

255,175.86 

571 

326,041 

186,169,411 

23.8956 

8.2962 

.001751313 

1,793.85 

256,072.00 

572 

327,184 

187,149,248 

23.9165 

8.3010 

.001748252 

1,796.99 

256,969.71 

573 

328,329 

188,132,517 

23.9374 

8.3059 

.001745201 

1,800.13 

257,868.99 

674 

329,476 

189,119,224 

23.9583 

8.3107 

.001742164 

1,803.27 

258,769.85 

575 

330,625 

190,109,375 

23.9792 

8.3155 

.001739130 

1,806.42 

259,672.27 

576 

331,776 

191,102,976 

24.0000 

8.3203 

.001736111 

1,809.56 

260,576.26 

577 

332,929 

192,100,033 

24.0208 

8.3251 

.001733102 

1,812.70 

261,481.83 

578 

334,084 

193,100,552 

24.0416 

8.3300 

.001730104 

1,815.84 

262,388.96 

579 

335,241 

194,104,539 

24.0624 

8.3348 

.001727116 

1,818.98 

263,297.67 

580 

336,400 

195,112,000 

24.0832 

8.3396 

.001724138 

,822.12 

264,207.94 

581 

337,561 

196,122,941 

24.1039 

8.3443 

.001721170 

,825.27 

65,119.79 

582 

338,724 

197,137,368 

24.1247 

8.3491 

.001718213 

,828.41 

66,033.21 

583 

339,889 

198,155,287 

24.1454 

8.3539 

.001715266 

,831.55 

66,948.20 

584 

341,056 

199,176,704 

24.1661 

8.3587 

.001712329 

,834.69 

67,864.76 

585 

342,225 

200,201,625 

24.1868 

8.3634 

.001709402 

,837.83 

68,782.89 

586 

343,396 

201,230,056 

24.2074 

8.3682 

.001706485 

,840.97 

69,702.59 

587 

344,569 

202,262,003 

24.2281 

8.3730 

.001703578 

,844.11 

270,623.86 

588 

345,744 

203,297,472 

24.2487 

8.3777 

.001700680, 

,847.26 

271,546.70 

589 

346,921 

204,336,469 

24.2693 

8.3825 

.001697793 

,850.40 

272,471.12 

590 

348,100 

205,379,000 

24.2899 

8.3872 

.001694915 

,853.54 

273,397.10 

591 

349,281 

206,425,071 

24.3105 

8.3919 

.001692047 

856.68 

274,324.66 

592 

350,464 

207,474,688 

24.3311 

8.3967 

.001689189 

859.82 

275,253.78 

593 

351,649 

208,527,857 

24.3516 

8.4014 

.001686341 

862.96 

276,184.48 

594 

352,836 

209,584,584 

24.3721 

8.4061 

.001683502 

866.11 

277,116.75 

595 

354,025 

210,644,875 

24.3926 

8.4108 

.001680672 

869.25 

278,050.58 

596 

355,216 

211,708,736 

24.4131 

8.4155 

.001677852 

872.39 

278,985.99 

597 

356,409 

212,776,173 

24.4336 

8.4202 

.001675042 

875.53 

279.922.97 

598 

357,604 

213,847,192 

24.4540 

8.4249 

.001672241 

878.67 

280,861.52 

599 

358,801 

214,921,799 

24.4745 

8.4296 

001669449 

881.81 

281,801.65 

600 

360,000 

216,000,000 

24.4949 

8.4343 

001666667 

884.96 

282,743.34 

601 

361,201 

217,081,801 

24.5153 

8.4390 

001663894 

888.10 

283,686.60 

602 

362,404 

218,167,208 

24.5357 

8.4437 

001661130 

891.24 

284,631.44 

603 

363,609 

219,256,227 

24.5561 

8.4484 

001658375 

894.38 

285,577.84 

604 

364,816 

220,348,864 

24.5764 

8.4530 

001655629 

897.52 

286,525.82 

605 

366,025 

221,445,125 

24.5968 

8.4577 

001652893 

900.66 

287,475.36 

606 

367,236 

222,545,016 

24.6171 

8.4623 

001650165 

903.81 

288,426.48 

607 

368,449 

223,648,543 

24.6374 

8.4670 

001647446 

906.95 

289,379.17 

608 

369,664 

224,755,712 

24.6577 

8.4716 

001644737 

910.09 

290,333.43 

609 

370,881 

225,866,529 

4.6779 

8.4763 

001642036 

913.23 

291,289.26 

610 

372,100 

226,981,000 

24.6982 

8.4809 

001639344 

916.37  . 

292,246.66 

611 

373,321 

228,099,131 

24.7184 

8.4856 

001636661 

919.51 

293,205.63 

612 

374,544 

229,220,928 

4.7386 

8.4902 

001633987 

922.65 

294,166.17 

613 

375,769 

230,346,397 

4.7588 

8.4948 

001631321 

925.80 

295.128.28 

614 

376,996 

231,475,544 

4.7790 

8.4994 

001628664 

928.94  1296,091.97 

615 

378,225 

232,608,375 

4.7992 

8.5040 

001626016 

932.08  J 

J97.057.22 

616 

379,456 

233,744,896 

24.8193 

8.5086 

001623377 

935.22  I 

298,024.05 

617 

380,689 

234,885,113 

24.8395 

8.5132 

001620746 

938.36  I 

598,992.44 

618 

381,924 

236,029,032 

24.8596 

8.5178 

001618123 

941.50  J 

!99,962.41 

619 

383,161 

237,176,659 

24.8797 

8.5224 

001615509 

944.65  c 

00,933.95 

620 

384,400 

238,328,000 

4.8998 

8.5270 

001612903 

947.79  rc 

•01,907.05 

621 

385,641 

239,483,061 

24.9199 

8.5316 

001610306 

950.93  ? 

02,881.73 

622 

386,884 

240,641,848 

4.9399 

8.5362 

001607717 

954.07  2 

.03,857.98 

CIRCUMFERENCES,  AND  AREAS 


1091 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Boot 

Reciprocal 

Circum. 

Area 

623 

388,129 

241,804,367 

24.9600 

8.5408 

.001605136 

1,957.21 

304,835.80 

624 

389,376 

242,970,624 

24.9800 

8.5453 

.001602564 

1,960.35 

305,815.20 

625 

390,625 

244,140,625 

25.0000 

8.5499 

.001600000 

1,963.50 

306,796.16 

626 

391,876 

245,314,376 

25.0200 

8.5544 

.001597444 

1,966.64 

307,778.69 

627 

393,129 

246,491,883 

25.0400 

8.5589 

.001594896 

1,969.78 

308,762.79 

628 

394,384 

247,673,152 

25.0599 

8.5635 

.001592357 

1,972.92 

309,748.47 

629 

395,641 

248,858,189 

25.0799 

8.5681 

.001589825 

1,976.06 

310,735.71 

630 

396,900 

250,047,000 

25.0998 

8.5726 

.001587302 

1,979.20 

311,724.53 

631 

398,161 

251,239,591 

25.1197 

8.5772 

.001584786 

1,982.35 

312,714.92 

632 

399,424 

252,435,968 

25.1396 

8.5817 

.001582278 

1,985.49 

313,706.88 

633 

400,689 

253,636,137 

25.1595 

8.5862 

.001579779 

1,988.63 

314,700.40 

634 

401,956 

254,840,104 

25.1794 

8.5907 

.001577287 

1,991.77 

315,695.50 

635 

403,225 

256,047,875 

25.1992 

8.5952 

.001574803 

1,994.91 

316,692.17 

636 

404,496 

257,259,456 

25.2190 

8.5997 

.D01572327 

1,998.05 

317,690.42 

637 

405,769 

258,474,853 

25.2389 

8.6043 

.001569859 

2,001.19 

318,690.23 

638 

407,044 

259,694,072 

25.2587 

8.6088 

.001567398 

2,004.34 

319,691.61 

639 

408,321 

260,917,119 

25.2784 

8.6132 

.001564945 

2,007.48 

320,694.56 

;  640 

409,600 

262,144,000 

25.2982 

8.6177 

.001562500 

2,010.62 

321,699.09 

641 

410,881 

263,374,721 

25.3180 

8.6222 

.001560062 

2,013.76 

322.705.18 

642 

412,164 

264,609,288 

25.3377 

8.6267 

.001557632 

2,016.90 

323,712.85 

643 

413,449 

265,847,707 

25.3574 

8.6312 

.001555210 

2,020.04 

324,722.09 

644 

414,736 

267,089,984 

25.3772 

8.6357 

.001552795 

2,023.19 

325,732.89 

645 

416,125 

268,336,125 

25.3969 

8.6401 

.001550388 

2,026.33 

326,745.27 

646 

417,316 

269,585,136 

25.4165 

8.6446 

.001547988 

2,029.47 

327,759.22 

647 

418,609 

270,840,023 

25.4362 

8.6490 

.001545595 

2,032.61 

328,774.74 

648 

419,904 

272,097,792 

25.4558 

8.6535 

.001543210 

2,035.75 

329,791.83 

649 

421,201 

273,359,449 

25.4755 

8.6579 

.001540832 

2,038.89 

330,810.49 

650 

422,500 

274,625,000 

25.4951 

8.6624 

.001538462 

2,042.04 

331,830.72 

651 

423,801 

275,894,451 

25.5147 

8.6668 

.001536098 

2,045.18 

332,852.53 

652 

425,104 

277,167,808 

25.5343 

8.6713 

.001533742 

2,048.32 

333,875.90 

653 

426,409 

278,445,077 

25.5539 

8.6757 

.001531394 

2,051.46 

334,900.85 

654 

427,716 

279,726,264 

25.5734 

8.6801 

.001529052 

2,054.60 

335,927.36 

655 

429,025 

281,011,375 

25.5930 

8.6845 

.001526718 

2,057.74 

336,955.45 

656 

430,336 

282,300,416 

25.6125 

8.6890 

.001524390 

2,060.88 

337,985.10 

657 

431,639 

283,593,393 

25.6320 

8.6934 

.001522070 

2,064.03 

339,016.33 

658 

432,964 

284,890,312 

25.6515 

8.6978 

.001519751 

2,067.17 

340,049.13 

659 

434,281 

286,191,179 

25.6710 

8.7022 

.001517451 

2,070.31 

341,083.50 

660 

435,600 

287,496,000 

25.6905 

8.7066 

.001515152 

2,073.45 

342,119.44 

661 

436,921 

288,804,781 

25.7099 

8.7110 

.001512859 

2,076.59 

343,156.95 

1  662 

438,244 

290,117,528 

25.7294 

8.7154 

.001510574 

2,079.73 

344,196.03 

1  663 

439,569 

291,434,247 

25.7488 

8.7198 

.001508296 

2,082.88 

345,236.69 

1  664 

440,896 

292,754,944 

25.7682 

8.7241 

.001506024 

,086.02 

346,278.91 

I  665 

442,225 

294,079,625 

25.7876 

8.7285 

.001503759 

,089.16 

347,322.70 

1  666 

443,556 

295,408,296 

25.8070 

8.7329 

.001501502 

,092.30 

348,368.07 

II  667 

444,899 

296,740,963 

25.8263 

8.7373 

.001499250 

,095.44 

349,415.00 

II  668 

446,224 

298,077,632 

25.8457 

8.7416 

.001497006 

,098.58 

350,463.51 

1  669 

447,561 

299,418,309 

25.8650 

8.7460 

.001494768 

,101.73 

351,513.59 

1  670 

448,900 

300,763,000 

25.8844 

8.7593 

.001492537 

,104.87 

352,565.24 

I  671 

450,241 

302,111,711 

25.9037 

8.7547 

.001490313 

,108.01 

353,618.45 

II  672 

451,584 

303,464,448 

25.9230 

8.7590 

.001488095 

,111.15 

354,673.24 

1  673 

452,929 

304,821,217 

25.9422 

8.7634 

.001485884 

,114.29 

355,729.60 

1  C74 

454,276 

306,182,024 

25.9615 

8.7677 

.001483680 

,117.43 

356,787.54 

1  675 

455,625 

307,546,875 

25.9808 

8.7721 

.001481481 

,120.58 

357,847.04 

1  676 

456,976 

308,915,776 

26.0000 

8.7764 

.001479290 

,123.72 

358,908.11 

1  677 

458,329 

310,288,733 

26.0192 

8.7807 

.001477105 

,126.86 

359,970.75 

I1  678 

459,684 

311,665,752 

26.0384 

8.7850 

.001474926 

,130.00 

361,034.97 

I  679 

461,041 

313,046,839 

26.0576 

8.7893 

.001472754 

,133.14 

362,100.75 

1  680 

462,400 

314,432,000 

26.0768 

8.7937 

.001470588 

,136.28 

363,168.11 

1  681 

463,761 

315,821,241 

26.0960 

8.7980 

.001468429 

,139.42 

364,237.04 

1  682 

465,124 

317,214,568 

26.1151 

8.8023 

.001466276 

,142.57 

365,307.54 

1  683 

466,489 

318,611,987 

26.1343 

8.8066 

.001464129 

,145.71 

366,379.60 

1  684 

467,856 

320,013,504 

26.1534 

8.8109 

.001461988 

,148.85 

367,453.24 

1  685 

469,225 

321,419,125 

26.1725 

8.8152 

.001459854 

,151.99 

368,528.45 

1092 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

686 

470,596 

322,828,856 

26.1916 

8.8194 

.001457726 

2,155.13 

369,605.23 

687 

471,969 

324,242,703 

26.2107 

8.8237 

.001455604 

2,158.27 

370,683.59 

688 

473,344 

325,660,672 

26.2298 

8.8280 

.001453488 

2,161.42 

371,763.51 

689 

474,721 

327,082,769 

26.2488 

8.8323 

.001451379 

2,164.56 

372,845.00 

690 

476,100 

328,509,000 

26.2679 

8.8366 

.001449275 

2,167.70 

373,928.07 

691 

477,481 

329,939,371 

26.2869 

8.8408 

.001447178 

2,170.84 

375,012.70 

692 

478,864 

331,373,888 

26.3059 

8.8451 

.001445087 

2,173.98 

376,098.91 

693 

480,249 

332,812,557 

26.3249 

8.8493 

.001443001 

2,177.12 

377,186.68 

694 

481,636 

334,255,384 

26.3439 

8.8536 

.001440922 

2,180.27 

378,276.03 

695 

483,025 

335,702,375 

26.3629 

8.8578 

.001438849 

2,183.41 

379,366.95 

696 

484,416 

337,153,536 

26.3818 

8.8621 

.001436782 

2,186.55 

380,459.44 

697 

485,809 

338,608,873 

26.4008 

8.8663 

.001434720 

2,189.69 

381,553.50 

698 

487,204 

340,068,392 

26.4197 

8.8706 

.001432665 

2,192.83 

382,649.13 

699 

488,601 

341,532,099 

26.4386 

8.8748 

.001430615 

2,195.97 

383,746.33 

700 

490,000 

343,000,000 

26.4575 

8.8790 

.001428571 

2,199.11 

384,845.10 

701 

491,401 

344,472,101 

26.4764 

8.8833 

.001426534 

2,202.26 

385,945.44 

702 

492,804 

345,948,408 

26.4953 

8.8875 

.001424501 

2,205.40 

387,047.36 

703 

494,209 

347,428,927 

26.5141 

8.8917 

.001422475 

2,208.54 

388,150.84 

704 

495,616 

348,913,664 

26.5330 

8.8959 

.001420455 

2,211.68 

389,255.90 

705 

497,025 

350,402,625 

26.5518 

8.9001 

.001418440 

2,214.82 

390,362.52 

706 

498,436 

351,895,816 

26.5707 

8.9043 

.001416431 

2,217.96 

391,470.72 

707 

499,849 

353,393,243 

26.5895 

8.9085 

.001414427 

2,221.11 

392,580.49 

708 

501,264 

354,894,912 

26.6083 

8.9127 

.001412429 

2,224.25 

393,691.82 

709 

502,681 

356,400,829 

26.6271 

8.9169 

.001410437 

2,227.39 

394,804.73 

710 

504,100 

357,911,000 

26.6458 

8.9211 

.001408451 

2,230.53 

395,919.21 

711 

505,521 

359,425,431 

26.6646 

8.9253 

.001406470 

2,233.67 

397,035.26 

712 

506,944 

360,944,128 

26.6833 

8.9295 

.001404494 

2,236.81 

398,152.89 

713 

508,369 

362,467,097 

26.7021 

8.9337 

.001402525 

2,239.96 

399,272.08 

714 

509,796 

363,994,344 

26.7208 

8.9378 

.001400560 

2,243.10 

400,392.84 

715 

511,225 

365,525,875 

26.7395 

8.9420 

.001398601 

2,246.24 

401,515.18 

716 

512,656 

367,061,696 

26.7582 

8.9462 

.001396648 

2,249.38 

402,639.08 

717 

514,089 

368,601,813 

26.7769 

8.9503 

.001394700 

2,252.52 

403,764.56 

718 

515,524 

370,146,232 

26.7955 

8.9545 

.001392758 

2,255.66 

404,891.60 

719 

516,961 

371,694,959 

26.8142 

8.9587 

.001390821 

2,258.81 

406,020.22 

720 

518,400 

373,248,000 

26.8328 

8.9628 

.001388889 

2,261.95 

407,150.41 

721 

519,841 

374,805,361 

26.8514 

8.9670 

.001386963 

2,265.09 

408,282.17 

722 

521,284 

376,367,048 

26.8701 

8.9711 

.001385042 

2,268.23 

409,415.50 

723 

522,729 

377,933,067 

26.8887 

8.9752 

.001383126 

2,271.37 

410,550.40 

724 

524,176 

379,503,424 

26.9072 

8.9794 

.001381215 

2,274.51 

411,686.87 

725 

525,625 

381,078,125 

26.9258 

8.9835 

.001379310 

2,277.65 

412,824.91 

726 

527,076 

382,657,176 

26.9444 

8.9876 

.001377410 

2,280.80 

413,964.52 

727 

528,529 

384,240,583 

26.9629 

8.9918 

.001375516 

2,283.94 

415,105.71 

728 

529,984 

385,828,352 

26.9815 

8.9959 

.001373626 

2,287.08 

416,248.46 

729 

531,441 

387,420,489 

27.0000 

9.0000 

.001371742 

2,290.22 

417,392.79 

730 

532,900 

389,017,000 

27.0185 

9.0041 

.001369863 

2,293.36 

418,538.68 

731 

534,361 

390,617,891 

27.0370 

9.0082 

.001367989 

2,296.50 

419,686.15 

732 

535,824 

392,223,168 

27.0555 

9.0123 

.001366120 

2,299.65 

420,835.19 

733 

537,289 

393,832,837 

27.0740 

9.0164 

.001364256 

2,302.79 

421,985.79 

734 

538,756 

395,446,904 

27.0924 

9.0205 

.001362398 

2,305.93 

423,137.97 

735 

540,225 

397,065,375 

27.1109 

9.0246 

.001360544 

2,309.07 

424,291.72 

736 

54  J,  696 

398,688,256 

27.1293 

9.0287 

.001358696 

2,312.21 

425,447.04 

737 

543,169 

400,315,553 

27.1477 

9.0328 

.001356852 

2,315.35 

426,603.94 

738 

544,644 

401,947,272 

27.1662 

9.0369 

.001355014 

2,318.50 

427,762.40 

739 

546,121 

403,583,419 

27.1846 

9.0410 

.001353180 

2,321.64 

428,922.43 

740 

547,600 

405,224,000 

27.2029 

9.0450 

.001351351 

2,324.78 

430,084.03 

741 

549,801 

406,869,021 

27.2213 

9.0491 

.001349528 

2,327.92 

431,247.21 

742 

550,564 

408,518,488 

27.2397 

9.0532 

.001347709 

2,331.06 

432,411.95 

743 

552,049 

410,172,407 

27.2580 

9.0572 

.001345895 

2,334.20 

433,578.27 

744 

553,536 

411,830,784 

27.2764 

9.0613 

.001344086 

2,337.34 

434,746.16 

745 

555,025 

413,493,625 

27.2947 

9.0654 

.001342282 

2,340.49 

435,915.62 

746 

556,516 

415,160,936 

27.3130 

9.0694 

.001340483 

2,343.63 

437,086.64 

747 

558,009 

416,832,723 

27.3313 

9.0735 

.001338688 

2,346.77 

438,259.24 

748 

559,504 

418,508,992 

27.3496 

9.0775 

.001336898 

2,349.91 

439,433.41 

CIRCUMFERENCES,  AND  AREAS 


1093 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

749 

561,001 

420,189,749 

27.3679 

9.0816 

.001335113 

2,353.05 

440,609.16 

750 

562,500 

421,875,000 

27.3861 

9.0856 

.001333333 

2,356.19 

441,786.47 

751 

564,001 

423,564,751 

27.4044 

9.0896 

.001331558 

2,359.34 

442,965.35 

752 

565,504 

425,259,008 

27.4226 

9.0937 

.001329787 

2,362.48 

444,145.80 

753 

567.009 

426,957,777 

27.4408 

9.0977 

.001328021 

2,365.62 

445,327.83 

754 

568i516 

428,661,064 

27.4591 

9.1017 

.001326260 

2,368.76 

446,511.42 

755 

570,025 

430,368,875 

27.4773 

9.1057 

.001324503 

2,371.90 

447,696.59 

756 

571,536 

432,081,216 

27.4955 

9.1098 

.001322751 

2,375.04 

448,883.32 

757 

573,049 

433,798,093 

27.5136 

9.1138 

.001321004 

2,378.19 

450,071.63 

758 

574,564 

435,519,512 

27.5318 

9.1178 

.001319261 

2,381.33 

451,261.51 

759 

576,081 

437,245,479 

27.5500 

9.1218 

.001317523 

2,384.47 

452,452.96 

760 

577,600 

438,976,000 

27.5681 

9.1258 

.001315789 

2,387.61 

453,645.98 

761 

579,121 

440,711,081 

27.5862 

9.1298 

.001314060 

2,390.75 

454,840.57 

762 

580,644 

442,450,728 

27.6043 

9.1338 

.001312336 

2,393.89 

456,036.73 

763 

582,169 

444,194,947 

27.6225 

9.1378 

.001310616 

2,397.04 

457,234.46 

764 

583,696 

445,943,744 

27.6405 

9.1418 

.001308901 

2,400.18 

458,433.77 

765 

585,225 

447,697,125 

27.6586 

9.1458 

.001307190 

2,403.32 

459,634.64 

766 

586,756 

449,455,096 

27.6767 

9.1498 

.001305483 

2,406.46 

460,837.08 

767 

588,289 

451,217,663 

27.6948 

9.1537 

.001303781 

2,409.60 

462,041.10 

768 

589,824 

452,984,832 

27.7128 

9.1577 

.001302083 

2,412.74 

463,246.69 

769 

591,361 

454,756,609 

27.7308 

9.1617 

.001300390 

2,415.88 

464,453.84 

770 

592,900 

456,533,000 

27.7489 

9.1657 

.001298701 

2,419.03 

465,662.57 

771 

594,441 

458,314,011 

27.7669 

9.1696 

.001297017 

2,422.17 

466,872.87 

772 

595,984 

460,099,648 

27.7849 

9.1736 

.001295337 

2,425.31 

468,084.74 

773 

597,529 

461,889,917 

27.8029 

9.1775 

.001293661 

2,428.45 

469,298.18 

774 

599,076 

463,684.824 

27.8209 

9.1815 

.001291990 

2,431.59 

470,513.19 

775 

600,625 

465,484,375 

27.8388 

9.1855 

.001290323 

2,434.73 

471,729.77 

776 

602,176 

467,288,576 

27.8568 

9.1894 

.001288660 

2,437.88 

472,947.92 

777 

603,729 

469,097,433 

27.8747 

9.1933 

.001287001 

2,441.02 

474,167.65 

778 

605,284 

470,910,952 

27.8927 

9.1973 

.001285347 

2,444.16 

475,388.94 

779 

606,841 

472,729,139 

27.9106 

9.2012 

.001283697 

2,447.30 

476,611.81 

780 

608,400 

474,552,000 

27.9285 

9.2052 

.001282051 

2,450.44 

477,836.24 

781 

609,961 

476,379,541 

27.9464 

9.2091 

.001280410 

2,453.58 

479,062.25 

782 

611,524 

478,211,768 

27.9643 

9.2130 

.001278772 

2,456.73 

480,289.83 

783 

613,089 

480,048,687 

27  9821 

9.2170 

.001277139 

2,459.87 

481,518.97 

784 

614,656 

481,890,304 

28.0000 

9.2209 

.001275510 

2,463.01 

482,749.69 

785 

616,225 

483,736,625 

28.0179 

9.2248 

.001273885 

2,466.15 

483,981.98 

786 

617,796 

485,587,656 

28.0357 

9.2287 

.001272265 

2,469.29 

485,215.84 

787 

619,369 

487,443,403 

28.0535 

9.2326 

.001270648 

2,472.43 

486,451.28 

788 

620,944 

489,303,872 

28.0713 

9.2365 

.001269036 

2,475.58 

487,688.28 

789 

622,521 

491,169,069 

28.0891 

9.2404 

.001267427 

2,478.72 

488,926.85 

790 

624,100 

493,039,000 

28.1069 

9.2443 

.001265823 

2,481.86 

490,166.99 

791 

625,681 

494,913,671 

28.1247 

9.2482 

.001264223 

2,485.00 

491,408.71 

792 

627,264 

496,793,088 

28.1425 

9.2521 

.001262626 

2,488.14 

492,651.99 

793 

628,849 

498,677,257 

28.1603 

9.2560 

.001261034 

2,491.28 

493,896.85 

794 

630,436 

500,566,184 

28.1780 

9.2599 

.001259446 

2,494.42 

495,143.28 

795 

632,025 

502,459,875 

28.1957 

9.2638 

.001257862 

2,497.57 

496,391.27 

796 

633,616 

504,358,336 

28.2135 

9.2677 

.001256281 

2,500.71 

497,640.84 

797 

635,209 

506,261,573 

28.2312 

9.2716 

.001254705 

2,503.85 

498,891.98 

798 

636,804 

508,169,592 

28.2489 

9.2754 

.001253133 

2,506.99 

500,144.69 

799 

638,401 

510,082,399 

28.2666 

9.2793 

.001251364 

2,510.13 

501,398.97 

800 

640,000 

512,000,000 

28.2843 

9.2832 

..001250000 

2,513.27 

502,654.82 

801 

641,601 

513,922,401 

28.3019 

9.2870 

.001248439 

2,516.42 

503,912.25 

802 

643,204 

515,849,608 

28.3196 

9.2909 

.001246883 

2,519.56 

505,171.24 

803 

644,809 

517,781,627 

28.3373 

9.2948 

.001245330 

2,522.70 

506,431.80 

804 

646,416 

519,718,464 

28.3549 

9.2986 

.001243781 

2,525.84 

507,693.94 

805 

648,025 

521,660,125 

28.3725 

9.3025 

.001242236 

2,'528.98' 

508,957.64 

806 

649,636 

523,606,616 

28.3901 

9.3063 

.001240695 

2,532.12 

510,222.92 

807 

651,249 

525,557,943 

28.4077 

9.3102 

.001239157 

2,535.27 

511,489.77 

808 

652,864 

527,514,112 

28.4253 

9.3140 

.001237624 

2,538.41 

512,758.19 

809 

654,481 

529,475,129 

28.4429 

9.3179 

.001236094 

2,541.55 

514,028.18 

810 

656100 

531,441,000 

28.4605 

9.3217 

.001234568 

2,544.69 

515,299.74 

811 

657,721 

533,411,731 

28.4781 

9.3255 

.001233046 

2,547.83 

516,572.87 

1094 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cn.  Root 

Reciprocal 

Circum. 

Area 

812 

659,344 

535,387,328 

28.4956 

9.3294 

.001231527 

2,550.97 

517,847.57 

813 

660,969 

537,367,797 

28.5132 

9.3332 

.001230012 

2,554.11 

519,123.84 

814 

662,596 

539,353,144 

28.5307 

9.3370 

.001228501 

2,557.26 

520,401.68 

815 

664,225 

541,343,375 

28.5482 

9.3408 

.001226994 

2,560.40 

521,681.10 

816 

665,856 

543,338,496 

28.5657 

9.3447 

.001225490 

2,563.54 

522,962.08 

817 

667,489 

545,338,513 

28.5832 

9.3485 

.001223990 

2,566.68 

524,244.63 

818 

669,124 

547,343,432 

28.6007 

9.3523 

.001222494 

2,569.82 

525,528.76 

819 

670,761 

549,353,259 

28.6182 

9.3561 

.001221001 

2,572.96 

526,814.46 

820 

672,400 

551,368,000 

28.6356 

9.3599 

.001219512 

2,576.11 

528,101.73 

821 

674,041 

553,387,661 

28.6531 

9.3637 

.001218027 

2,579.25 

529,390.56 

822 

675,584 

555,412,248 

28.6705 

9.3675 

.001216545 

2,582.39 

530,680.97 

823 

677,329 

557,441,767 

28.6880 

9.3713 

.001215067 

2,585.53 

531,972.95 

824 

678,976 

559,476,224 

28.7054 

9.3751 

.001213592 

2,588.67 

533,266.50 

825 

680,625 

561,515,625 

28.7228 

9.3789 

.001212121 

2,591.81 

534,561.62 

826 

682,276 

563,559,976 

28.7402 

9.3827 

.001210654 

2,594.96 

535,858.32 

827 

683,929 

565,609,283 

28.7576 

9.3865 

.001209190 

2,598.10 

537,156.58 

828 

685,584 

567,663,552 

28.7750 

93902 

.001207729 

2,601.24 

538,456.41 

829 

687,241 

569,722,789 

28.7924 

9.3940 

.001206273 

2,604.38 

539,757.82 

830 

688,900 

571,787,000 

28.8097 

9.3978 

.001204819 

2,607.52 

541,060.79 

831 

690,561 

573,856,191 

28.8271 

9.4016 

.001203369 

2,610.66 

542,365.34 

832 

692,224 

575,930,368 

28.8444 

9.4053 

.001201923 

2,613.81 

543,671.46 

833 

693,889 

578,009,537 

28.8617 

9.4091 

.001200480 

2,616.95 

544,979.15 

834 

695,556 

580,093,704 

28.8791 

9.4129 

.001199041 

2,620.09 

546,288.40 

835 

697,225 

582,182,875 

28.8964 

9.4166 

.001197605 

2,623.23 

547,599.23 

836 

698,896 

584,277,056 

28.9137 

9.4204 

.001196172 

2,626.37 

548,911.63 

837 

700,569 

586,376,253 

28.9310 

9.4241 

.001194743 

2,629.51 

550,225.61 

838 

702,244 

588,480,472 

28.9482 

9.4279 

.001193317 

2,632.65 

551,541.15 

839 

703,921 

590,589,719 

2H.%f>5 

9.4316 

.001191895 

2,635.80 

552,858.26 

840 

705,600 

592,704,000 

28.9828 

9.4354 

.001190476 

2,638.94 

554,176.94 

841 

707,281 

594,823,321 

29.0000 

9.4391 

.001189061 

2,642.08 

555,497.20 

842 

708,964 

596,947,688 

29.0172 

9.4429 

.001187648 

2,645.22 

556,819.02 

843 

710,649 

599,077,107 

29.0345 

9.4466 

.001186240 

2,648.36 

558,142.42 

344 

712,336 

601,211,584 

29.0517 

9.4503 

.001184834 

2,651.50 

559,467.39 

845 

714,025 

603,351,125 

29.0689 

9.4541 

.001183432 

2,654.65 

560,793.92 

846 

715,716 

605,495,736 

29.0861 

9.4578 

.001182033 

2,657.79 

562,122.03 

847 

717,409 

607,645,423 

29.1033 

9.4615 

.001180638 

2,660.93 

563,451.71 

848 

719,104 

609,800,192 

29.1204 

9.4652 

.001179245 

2,664.07 

564,782.96 

849 

720,801 

611,960,049 

29.1376 

9.4690 

.001177856 

2,667.21 

566,115.78 

850 

722,500 

614,125,000 

29.1548 

9.4727 

.001176471 

2,670.35 

567,450.17 

851 

724,201 

616,295,051 

29.1719 

9.4764 

.001175088 

2,673.50 

568,786.14 

852 

725,904 

618,470,208 

29.1890 

9.4801 

.001173709 

2,676.64 

570,123.67 

853 

727,609 

620,650,477 

29.2062 

9.4838 

.001172333 

2,679.78 

571,462.77 

854 

729,316 

622,835,864 

29.2233 

9.4875 

.001170960 

2,682.92 

572,803.45 

855 

731,025 

625,026,375 

29.2404 

9.4912 

.001169591 

2,686.06 

574,145.69 

856 

732,736 

627,222,016 

29.2575 

9.4949 

.001168224 

2,689.20 

575,489.51 

857 

734,449 

629,422,793 

29.2746 

9.4986 

.001166861 

2,692.34 

576,834.90 

858 

736,164 

631,628,712 

29.2916 

9.5023 

.001165501 

2,695.49 

578,181.85 

859 

737,881 

633,839,779 

29.3087 

9.5060 

.001164144 

2,698.63 

579,530.38 

860 

739,600 

636,056,000 

29.3258 

9.5097 

.001162791 

2,701.77 

580,880.48 

861 

741,321 

638,277,381 

29.3428 

9.5135 

.001161440 

2,704.91 

582,232.15 

862 

743,044 

640,503,928 

29.3598 

9.5171 

.001160093 

2,708.05 

583,585.39 

863 

744,769 

642,735,647 

29.3769 

9.5207 

.001158749 

2,711.19 

584,940.20 

864 

746,496 

644,972,544 

29.3939 

9.5244 

.001157407 

2,714.34 

586,296.59 

865 

748,225 

647,214,625 

29.4109 

9.5281 

.001156069 

2,717.48 

587,654.54 

866 

749,956 

649,461,896 

29.4279 

9.5317 

.001154734 

2,720.62 

589,014.07 

867 

751,689 

651,714,363 

29.4449 

9.5354 

.001153403 

2,723.76 

590,375.16 

868 

753,424 

653,972,032 

29.4618 

9.5391 

.001152074 

2,726.90 

591,737.83 

869 

755,161 

656,234,909 

29.4788 

9.5427 

.001150748 

2,730.04 

593,102.06 

870 

756,900 

658,503,000 

29.4958 

9.5464 

.001149425 

2,733.19 

594,467.87 

871 

758,641 

660,776,311 

29.5127 

9.5501 

.001148106 

2,736.33 

595,835.25 

872 

760,384 

663,054,848 

29.5296 

9.5537 

.001146789 

2,739.47 

597,204.20 

873 

762,129 

665,338,617 

29.5466 

9.5574 

.001145475 

2,742.61 

598,574.72 

874 

763,876 

667,627,624 

29.5635 

9.5610 

.001144165 

2,745.75 

599,946.81 

CIRCUMFERENCES,  AND  AREAS 


1095 


NO. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Ciroum. 

Area 

875 

765,625 

669,921,875 

29.5804 

9.5647 

.001142857 

2,748.89 

601,320.47 

876 

767,376 

672,221,376 

29.5973 

9.5683 

.001141553 

2,752.04 

602,695.70 

877 

769,129 

674,526,133 

29.6142 

9.5719 

.001140251 

2,755.18 

604,072.50 

878 

770,884 

676,836,152 

29.6311 

9.5756 

.001138952 

2,758.32 

605,450.88 

879 

772,641 

679,151,439 

29.6479 

9.5792 

.001137656 

2,761.46 

606,830.82 

880 

774,400 

681,472,000 

29.6648 

9.5828 

.001136364 

2,764.60 

608,212.34 

881 

776,161 

683,797,841 

29.6816 

9.5865 

.001135074 

2,767.74 

609,595.42 

882 

777,924 

686,128,968 

29.6985 

9.5901 

.001133787 

2,770.88 

610,980.08 

883 

779,689 

688,465,387 

29.7153 

9.5937 

.001132503 

2,774.03 

612,366.31 

884 

781,456 

690,807,104 

29.7321 

9.5973 

.001131222 

2,777.17 

613,754.11 

885 

783,225 

693,154,125 

29.7489 

9.6010 

.001129944 

2,780.31 

615,143.48 

886 

784,996 

695,506,456 

29.7658 

9.6046 

.001128668 

2,783.45 

616,534.42 

887 

786,769 

697,864,103 

29.7825 

9.6082 

.001127396 

2,786.59 

617,926.93 

1  888 

788,544 

700,227,072 

29.7993 

9.6118 

.001126126 

2,789.73 

619,321.01 

I  889 

790,321 

702,595,369 

29.8161 

9.6154 

.001124859 

2,792.88 

620,716.66 

890 

792,100 

704,969,000 

29.8329 

9.6190 

.001123596 

2,796.02 

622,113.89 

891 

793,881 

707,347,971 

29.8496 

9.6226 

.001122334 

2,799.16 

623,512.68 

892 

795,664 

707,932,288 

29.8664 

9.6262 

.001121076 

2,802.30 

624,913.04 

893 

797,449 

712,121,957 

29.8831 

9.6298 

.001119821 

2,805.44 

626,314.98 

894 

799,236 

714,516,984 

29.8998 

9.6334 

.001118568 

2,808.58 

627,718.49 

895 

801,025 

716,917,375 

29.9166 

9.6370 

.001117818 

2,811.73 

629,123.56 

896 

802,816 

719,323,136 

29.9333 

9.6406 

.001116071 

2,814.87 

630,530.21 

1  897 

804,609 

721,734,273 

29.9500 

9.6442 

.001114827 

2,818.01 

631,938.43 

898 

806,404 

724,150,792 

29.9666 

9.6477 

.001113586 

2,821.15 

633,348.22 

899 

808,201 

726,572,699 

29.9833 

9.6513 

.001112347 

2,824.29 

634,759.58 

900 

810,000 

729,000,000 

30.0000 

9.6549 

.001111111 

2,827.43 

636,172.51 

901 

811,801 

731,432,701 

30.0167 

9.6585 

.001109878 

2,830.58 

637,587.01 

902 

813,604 

733,870,808 

30.0333 

9.6620 

.001108647 

2,833.72 

639,003.09 

903 

815,409 

736,314,327 

30.0500 

9.6656 

.001107420 

2,836.86 

640,420.73 

904 

817,216 

738,763,264 

30.0666 

9.6692 

.001106195 

2,840.00 

641,839.95 

905 

819,025 

741,217,625 

30.0832 

9.6727 

.001104972 

2,843.14 

643,260.73 

906 

820,836 

743,677,416 

30.0998 

9.6763 

.001103753 

2,846.28 

644,683.09 

907 

822,649 

746,142,643 

30.1164 

9.6799 

.001102536 

2,849.42 

646,107.01 

908 

824,464 

748,613,312 

30.1330 

9.6834 

.001101322 

2,852.57 

647,532.51 

909 

826,281 

751,089,429 

30.1496 

9.6870 

.001100110 

2,855.71 

648,959.58 

910 

828,100 

753,571,000 

30.1662 

9.6905 

.001098901 

2,858.85 

650,388.22 

911 

829,921 

756,058,031 

30.1828 

9.6941 

.001091695 

2,861.99 

651,818.43 

912 

831,744 

758,550,825 

30.1993 

9.6976 

.001096491 

2,865.13 

653,250.21 

913 

833,569 

761,048,497 

30.2159 

9.7012 

.001095290 

2,868.27 

654,683.56 

914 

835,396 

763,551,944 

30.2324 

9.7047 

.001094092 

2,871.42 

656,118.48 

915 

837,225 

766,060,875 

30.2490 

9.7082 

.001092896 

2,874.56 

657,554.98 

916 

839,056 

768,575,296 

30.2655 

9.7118 

.001091703 

2,877.70 

658,993.04 

917 

840,889 

771,095,213 

30.2820 

9.7153 

.001090513 

2,880.84 

660,432.68 

918 

842,724 

773,620,632 

30.2985 

9.7188 

.001089325 

2,883.98 

661,873.88 

1  919 

844,561 

776,151,559 

30.3150 

9.7224 

.001088139 

2.887.12 

663,316.66 

920 

846,400 

778.688,000 

30.3315 

9.7259 

.001086957 

2,890.27 

664,761.01 

921 

848,241 

78i;229,961 

30.3480 

9.7294 

.001085776 

2,893.41 

666,206.92 

922 

850,084 

783,777,448 

30.3645 

9.7329 

.001084599 

2,896.55 

667,654.41 

923 

851,929 

786,330,467 

30.3809 

9.7364 

.001083423 

2,899.69 

669,103.47 

924 

853,776 

788,889,024 

30.3974 

9.7400 

.001082251 

2,902.83 

670,554.10 

925 

855,625 

791,453,125" 

30.4138 

9.7435 

.001081081 

2,905.97 

672,006.30 

926 

857,476 

794,022,776 

30.4302 

9.7470 

.001079914 

2,909.11 

673,460.08 

927 

859,329 

796,597,983 

30.4467 

9.7505 

.001078749 

2,912.26 

674,915.42 

928 

861,184 

799,178,752 

30.4631 

9.7540 

.001077586 

2,915.40 

676,372.33 

929 

863,041 

801,765.089 

30.4795 

9.7575 

.001076426 

2,918.54 

677,830.82 

930 

864,900 

804,357,000 

30.4959 

9.7610 

.001075269 

2,921.68 

679,290.87 

931 

866,761 

806,954,491 

30.5123 

9.7645 

.001074114 

2,924.82 

680,752.50 

932 

868,624 

809,557,568 

30.5287 

9.7680 

.001072961 

2,927.96 

682,215.69 

933 

870,489 

812,166,237 

30.5450 

9.7715 

.001071811 

2,931.11 

683,680.46 

934 

872,356 

814,780,504 

30.5614 

9.7750 

.001070664 

2,934.25 

685,146.80 

1  935 

874,225 

817,400,375 

30.5778 

9.7785 

.001069519 

2,937.39 

686,614.71 

936 

876.096 

820,025,856 

30.5941 

9.7829 

.001068376 

2,940.53 

688,084.19 

937 

877,969 

822,656,953 

30.6105 

9.7854 

.001067236 

2,943.67 

689,555.24 

1096 


SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS 


No. 

Square 

Cube 

Sq.  Root 

Cu.  Root 

Reciprocal 

Circum. 

Area 

938 

879,844 

825,293,672 

30.6268 

9.7889 

.001066098 

2,946.81 

691,027.86 

939 

881,721 

827,936,019 

30.6431 

9.7924 

.001064963 

2,949.96 

692,502.05 

940 

883,600 

830,584,000 

30.6594 

9.7959 

.001063830 

2,953.10 

693,977.82 

941 

885,481 

833,237,621 

30.6757 

9.7993 

.001062699 

2,956.24 

695,455.15 

942 

887,364 

835,896,888 

30.6920 

9.8028 

.001061571 

2,959.38 

696,934.06 

943 

889,249 

838,561,807 

30.7083 

9.8063 

.001060445 

2,962.52 

698,414.53 

944 

891,136 

841,232,384 

30.7246 

9.8097 

.001059322 

2,965.66 

699,896.58 

945 

893,025 

843,908,625 

30.7409 

9.8132 

.001058201 

2,968.81 

701,380.19 

946 

894,916 

846,590,536 

30.7571 

9.8167 

.001057082 

2,971.95 

702,865.38 

947 

896,808 

849,278,123 

30.7734 

9.8201 

.001055966 

2,975.09 

704,352.14 

948 

898,704 

851,971,392 

30.7896 

9.8236 

.001054852 

2,978.23 

705,840.47 

949 

900,601 

854,670,349 

30.8058 

9.8270 

.001053741 

2,981.37 

707,330.37 

950 

902,500 

857,375,000 

30.8221 

9.8305 

.001052632 

2,984.51 

708,821.84 

951 

904,401 

860,085,351 

30.8383 

9.8339 

.001051525 

2,987.65 

710,314.88 

952 

906,304 

862,801,408 

30.8545 

9.8374 

.001050420 

2,990.80 

711,809.50 

953 

908,209 

865,523,177 

30.8707 

9.8408 

.001049318 

2,993.94 

713,305.68 

954 

910,116 

868,250,664 

30.8869 

9.8443 

.001048218 

2,997.08 

714,803.43 

955 

912,025 

870,983,875 

30.9031 

9.8477 

.001047120 

3,000.22 

716,302.76 

956 

913,936 

873,722,816 

30.9192 

9.8511 

.001046025 

3,003.36 

717,803.66 

957 

915,849 

876,467,493 

30.9354 

9.8546 

.001044932 

3,006.50 

719,306.12 

958 

917,764 

879,217,912 

30.9516 

9.8580 

.001043841 

3,009.65 

720,810.16 

959 

919,681 

881,974,079 

30.9677 

9.8614 

.001042753 

3,012.79 

722,315.77 

960 

921,600 

884,736,000 

30.9839 

9.8648 

.001041667 

3,015.93 

723,822.95 

961 

923,521 

887,503,681 

31.0000 

9.8683 

.001040583 

3,019.07 

725,331.70 

962 

925,444 

890,277,128 

31.0161 

9.8717 

.001039501 

3,022.21 

726,842.02 

963 

927,369 

893,056,347 

31.0322 

9.8751 

.001038422 

3,025.35 

728,353.91 

964 

929,296 

895,841,344 

31.0483 

9.8785 

.001037344 

3,028.50 

729,867.37 

965 

931,225 

898,632,125 

31.0644 

9.8819 

.001036269 

3,031.64 

731,382.40 

966 

933,156 

901,428,696 

31.0805 

9.8854 

.001035197 

3,034.78 

732,899.01 

967 

935,089 

904,231,063 

31.0966 

9.8888 

.001034126 

3,037.92 

734,417.18 

968 

937,024 

907,039,232 

31.1127 

9.8922 

.001033058 

3,041.06 

735,936.93 

969 

938,961 

909,853,209 

31.1288 

9.8956 

.001031992 

3,044.20 

737,458.24 

970 

940,900 

912,673,000 

31.1448 

9.8990 

.001030928 

3,047.34 

738,981.13 

971 

942,841 

915,498,611 

31.1609 

9.9024 

.001029866 

3,050.49 

740,505.59 

972 

944,784 

918,330,048 

31.1769 

9.9058 

.001028807 

3,053.63 

742,031.62 

973 

946,729 

921,167,317 

31.1929 

9.9092 

.001027749 

3,056.77 

743,559.22 

974 

948,676 

924,010,424 

31.2090 

9.9126 

.001026694 

3,059.91 

745,088.39 

975 

950,625 

926,859,375 

31.2250 

9.9160 

.001025641 

3,063.05 

746,619.13 

976 

952,576 

929,714,176 

31.2410 

9.9194 

.001024590 

3,066.19 

748,151.44 

977 

954,529 

932,574,833 

31.2570 

9.9228 

.001023541 

3,069.34 

749,685.32 

978 

956,484 

935,441,352 

31.2730 

9.9261 

.001022495 

3,072.48 

751,220.78 

979 

958,441 

938,313,739 

31.2890 

9.9295 

.001021450 

3,075.62 

752,757.80 

980 

960,400 

941,192,000 

31.3050 

9.9329 

.001020408 

3.078.76 

754,296.40 

981 

962,361 

944,076,141 

31.3209 

9.9363 

.001019168 

3,081.90 

755,836.56 

982 

964,324 

946,966,168 

31.3369 

9.9396 

.001018330 

3,085.04 

757,378.30 

983 

966,289 

949,862,087 

31.3528 

9.9430 

.001017294 

3,088.19 

758,921.61 

984 

968,256 

952,763,904 

31.3688 

9.9464 

.001016260 

3,091.33 

760,466.48 

985 

970,225 

955,671,625 

31.3847 

9.9497 

.001015228 

3,094.47 

762,012.93 

986 

972,196 

958,585,256 

31.4006 

9.9531 

.001014199 

3,097.61 

763,560.95 

987 

974,169 

961,504,803 

31.4166 

9.9565 

.001013171 

3,100.75 

765,110.54 

988 

976,144 

964,430,272 

31.4325 

9.9598 

.001012146 

3,103.89 

766,661.70 

989 

978,121 

967,361,669 

31.4484 

9.9632 

.001011122 

3,107.04 

768,214.44 

990 

980,100 

970,299,000 

31.4643 

9.9666 

.001010101 

3,110.18 

769,768.74 

991 

982,081 

973,242,271 

31.4802 

9.9699 

.001009082 

3,113.32 

771,324.61 

992 

984,064 

976,191,488 

31.4960 

9.9733 

.001008065 

3,116.46 

772,882.06 

993 

986,049 

979,146,657 

31.5119 

9.9766 

.001007049 

3,119.60 

774,441.07 

994 

988,036 

982,107,784 

31.5278 

9.9800 

.001006036 

3,122.74 

776,001.66 

995 

990,025 

985,074,875 

31.5436 

9.9833 

.001005025 

3,125.88 

777,563.82 

996 

992,016 

988,047,936 

31.5595 

9.9866 

.001004016 

3,129.03 

779,127.54 

997 

994,009 

991,026,973 

31.5753 

9.9900 

.001003009 

3,132.17 

780,692.84 

998 

996,004 

994,011,992 

31.5911 

9.9933 

.001002004 

3,135.31 

782,259.71 

999 

998,001 

997,002,999 

31.6070 

9.9967 

.001001001 

3,138.45 

783,828.15 

1000 

1,000,000 

1,000,000,000 

31.6228 

10.0000 

.001000000 

3,141.59 

-85,398.16 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES  1097 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES  FROM  1-64  to  100 


Diam. 

Circum.  Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

i 

.0491 

.0002 

6 

18.8496 

28.2744 

13 

41.2335 

135.297 

$s 

.0982 

.0008 

6- 

19.2423 

29.4648 

13 

41.6262 

137.887 

JL 

.1963 

.0031 

6 

19.6350 

30.6797 

42.0189 

140.501 

I 

.3927 

.0123 

6 

20.0277 

31.9191 

13* 

42.4116 

143.139 

TS6 

.5890 

.0276 

6 

20.4204 

33.1831 

13* 

42.8043 

145.802 

i 

.7854 

.0491 

6 

20.8131 

34.4717 

13? 

43.1970 

148.490 

A 

.9817 

.0767 

6* 

21.2058 

35.7848 

13* 

43.5897 

151.202 

i 

1.1781 

.1104 

61 

21.5985 

37.1224 

14  , 

43.9824 

153.938 

7 

1.3744 

.1503 

7 

21.9912 

38.4846 

44.3751 

156.700 

J 

1.5708 

.1963 

7* 

22.3839 

39.8713 

14* 

44.7678 

159.485 

A 

1.7671 

.2485 

7; 

- 

22.7766 

41.2826 

14  4 

45.1605 

162.296 

1 

1.9635 

.3068 

7 

23.1693 

42.7184 

14* 

45.5532 

165.130 

2.1598 

.3712 

7 

23.5620 

44.1787 

14 

45.9459 

167.990 

a 

2.3562 

.4418 

7 

• 

23.9547 

45.6636 

14 

46.3386 

170.874 

ri 

2.5525 

.5185 

7i 

24.3474 

47.1731 

46.7313 

173.782 

j 

2.7489 

.6013 

7- 

24.7401 

48.7071 

15* 

47.1240 

176.715 

ti 

2.9452 

.6903 

8 

25.1328 

50.265C 

15  - 

47.5167 

179.673 

1 

3.1416 

.7854 

8- 

. 

25.5255 

51.8487 

15i 

47.9094 

182.655 

H 

3.5343 

.9940 

8; 

. 

25.9182 

53.4563 

15* 

48.3021 

185.661 

l{ 

3.9270 

1.2272 

8 

• 

26.3109 

55.0884 

15* 

48.C948 

188.692 

If 

4.3197 

1.4849 

8* 

26.7036 

56.7451 

15* 

49.0875 

191.748 

l* 

4.7124 

1.7671 

8 

• 

27.0963 

58.4264 

15J 

49.4802 

194.828 

if 

5.1051 

2.0739 

27.4890 

60.1322 

15* 

49.8729 

197.933 

If 

5.4978 

2.4053 

8 

27.8817 

61.8625 

16 

50.2656 

201.062 

1* 

5.8905 

2.7612 

9 

28.2744 

63.6174 

16 

50.6583 

204.216 

2 

6.2832 

3.1416 

9- 

. 

28.6671 

65.3968 

16 

51.0510 

207.395 

2* 

6.6759 

3.5466 

9; 

29.0598 

67.2008 

16 

51.4437 

210.598 

3 

7.0686 

3.9761 

9 

29.4525 

69.0293 

16 

51.8364 

213.825 

2* 

7.4613 

4.4301 

9 

29.8452 

70.8823 

16 

52.2291 

217.077 

2* 

7.8540 

4.9087 

9 

• 

30.2379 

72.7599 

16J 

52.6218 

220.354 

8.2467 

5.4119 

9 

• 

30.6306 

74.6621 

16* 

53.0145 

223.655 

2* 

8.6394 

5.9396 

9i 

31.0233 

76.589 

17 

53.4072 

226.981 

2*  . 

9.0321 

6.4918 

10 

31.4160 

78.540 

17 

53.7999 

230.331 

3 

9.4248 

7.0686 

10- 

. 

31.8087 

80.516 

17 

54.1926 

233.706 

3* 

9.8175 

7.6699 

10 

32.2014 

82.516 

17 

54.5853 

237.105 

3 

10.2102 

8.2958 

10* 

32.5941 

84.541 

17 

54.9780 

240.529 

3* 

10.6029 

8.9462 

10 

• 

32.9868 

86.590 

17 

55.3707 

243.977 

3* 

10.9956 

9.6211 

10 

• 

33.3795 

88.664 

17 

55.7634 

247.450 

11.3883 

10.3206 

10J 

33.7722 

90.763 

56.1561 

250.948 

3} 

11.7810 

11.0447 

10 

34.1649 

92.886 

18* 

56.5488 

254.470 

3* 

12.1737 

11.7933 

11 

34.5576 

95.033 

18* 

56.9415 

258.016 

4 

12.5664 

12.5664 

11- 

. 

34.9503 

97.205 

18- 

57.3342 

261.587 

4* 

12.9591 

13.3641 

11 

35.3430 

99.402 

18* 

57.7269 

265.183 

3 

13.3518 

14.1863 

11* 

35.7357 

101.623 

18* 

58.1106 

268.803 

4* 

13.7445 

15.0330 

11 

i 

36.1284 

103.869 

18 

58.5123 

272.448 

4* 

14.1372 

15.9043 

11 

• 

36.5211 

106.139 

18 

58.9050 

276.117 

14.5299 

16.8002 

11 

• 

36.9138 

108.434 

18* 

59.2977 

279.811 

4 

14.9226 

17.7206 

111 

• 

37.3065 

110.754 

19 

59.6904 

283.529 

4* 

15.3153 

18.6555 

12 

37.6992 

113.098 

19 

60.0831 

287.272 

5 

15.7080 

19.6350 

12- 

38.0919 

115.466 

19, 

60.4758 

291.040 

16.1007 

20.6290 

12 

38.4846 

117.859 

19- 

60.8685 

294.832 

rjl 

16.4934 

21.6476 

12 

38.8773 

120.277 

19 

61.2612 

29S.&48 

5i 

16.8861 

22.6907 

12 

39.2700 

122.719 

19 

61.6539 

302.489 

c? 

17  2788 

23.7583 

12 

39.6627 

125.185 

19 

62.0466 

306.355 

5* 

17.6715 

24.8505 

12 

40.0554 

127.677 

19 

62.4393 

310.245 

5f 

18.0642 

25.9673 

• 

40.4481 

130.192 

20 

62.8320 

314.160 

5* 

18.4569 

27.1086 

13 

40.8408 

132.733 

20* 

63.2247 

318.099 

1098 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

20} 

63.6174 

322.063 

28 

\  ' 

88.3575 

621.264 

36 

113.098 

1,017.878 

20f 

64.0101 

326.051 

28 

I 

88.7502 

626.798 

361 

113.490 

1,024.960 

201 

64.4028 

330.064 

28 

( 

89.1429 

632.357 

36* 

113.883 

1,032.065 

64.7955 

334.102 

28 

1 

89.5356 

637.941 

36| 

114.276 

1,039.195 

20* 

65.1882 

338.164 

28 

t;-' 

89.9283 

643.549 

36| 

114.668 

1,046.349 

201 

65.5809 

342.250 

28* 

90.3210 

649.182 

115.061 

1,053.528 

21 

65.9736 

346.361 

28 

f, 

90.7137 

654.840 

36* 

115.454 

1,060.732 

21; 

66.3663 

350.497 

29 

91.1064 

660.521 

361 

115.846 

1,067.960 

21; 

66.7590 

354.657 

29 

91.4991 

666.228 

37 

116.239 

1,075.213 

21- 

67.1517 

358.842 

29 

91.8918 

671.959 

371 

116.632 

1,082.490 

2li 

67.5444 

363.051 

29 

92.2845 

677.714 

8?| 

117.025 

1,089.792 

21i 

67.9371 

367.285 

29 

92.6772 

683.494 

37* 

117.417 

1,097.118 

21; 

68.3298 

371.543 

29 

93.0699 

689.299 

371 

117.810 

1,104.469 

211 

68.7225 

375.826 

29 

93.4626 

695.128 

37* 

118.203 

1,111.844 

22 

69.1152 

380.134 

291 

93.8553 

700.982 

37* 

118.595 

1,119.244 

22} 

69.5079 

384.466 

30 

94.2480 

706.860 

371 

118.988 

1,126.669 

22- 

69.9006 

388.822 

30 

I 

94.6407 

712.763 

38 

119.381 

1,134.118 

22f 

70.2933 

393.203 

30* 

95.0334 

718.690 

38} 

119.773 

1,141.591 

22y 

70.6860 

397.609 

30 

\\~ 

95.4261 

724.642 

38} 

120.166 

1,149.089 

224 

71.0787 

402.038 

30 

95.8188 

730.618 

38| 

120.559 

1,156.612 

22* 

71.4714' 

406.494 

30 

96.2115 

736.619 

38} 

120.952 

1,164.159 

221 

71.8641 

410.973 

30 

} 

96.6042 

742.645 

121.344 

1,171.731 

23 

72.2568 

415.477 

30- 

>  _• 

96.9969 

748.695 

38* 

121.737 

1,179.327 

23  - 

72.6495 

420.004 

31 

97.3896 

754.769 

381 

122.130 

1,186.948 

23! 

73.0422 

424.558 

31- 

97.7823 

760.869 

39 

122.522 

1,194.593 

23f 

73.4349 

429.135 

31 

98.1750 

766.992 

391 

122.915 

1,202.263 

231 

73.8276 

433.737 

31 

98.5677 

773.140 

39| 

123.308 

1,209.958 

23| 

74.2203 

438.364 

31 

98.9604 

779.313 

123.700 

1,217.677 

23* 

74.6130 

443.015 

31; 

99.3531 

785.510 

39! 

124.093 

1,225.420 

231 

75.0057 

447.690 

31 

99.7458 

791.732 

39* 

124.486 

1,233.188 

24j 

75.3984 

452.390 

31j 

• 

100.1385 

797.979 

39* 

124.879 

1,240.981 

75.7911 

457.115 

32 

100.5312 

804.250 

391 

125.271 

1,248.798 

24- 

76.1838 

461.864 

32; 

100.9239 

810.545 

40 

125.664 

1,256.640 

24| 

76.5765 

466.638 

32 

101.3166 

816.865 

40} 

126.057 

1,264.510 

76.9692 

471.436 

32; 

101.7093 

823.210 

40| 

126.449 

1,272.400 

24| 

77.3619 

476.259 

32, 

102.1020 

829.579 

40* 

126.842 

1,280.310 

24* 

77.7546 

481.107 

32i 

102.4947 

835.972 

401 

127.235 

1,288.250 

241 

78.1473 

485.979 

323 

102.8874 

842.391 

40| 

127.627 

1,296.220 

25 

78.5400 

490.875 

321 

103.280 

848.833 

40* 

128.020 

1,304.210 

251 

78.9327 

495.796 

33 

103.673 

855.301 

401 

128.413 

1,312.220 

25} 

79.3254 

500.742 

33i 

104.065 

861.792 

41 

128.806 

1,320.260 

25f 

79.7181 

505.712 

33: 

104.458 

868.309 

41} 

129.198 

1,328.320 

25} 

80.1108 

510.706 

33; 

104.851 

874.850 

129.591 

1,336.410 

25| 

80.5035 

515.726 

33i 

105.244 

881.415 

41f 

129.984 

1,344.520 

25* 

80.8962 

520.769 

33i 

105.636 

888.005 

130.376 

1,352.660 

251 

81.2889 

525.838 

33; 

106.029 

894.620 

4l| 

130.769 

1,360.820 

26 

81.6816 

530.930 

106.422 

901.259 

41* 

131.162 

1,369.000 

26} 

82.0743 

536.048 

341 

106.814 

907.922 

411 

131.554 

1,377.210 

26|- 

82.4670 

541.190 

34! 

107.207 

914.611 

42 

131.947 

1,385.450 

26| 

82.8597 

546.356 

34* 

107.600 

921.323 

42} 

132.340 

1,393.700 

26} 

83.2524 

551.547 

34| 

107.992 

928.061 

42} 

132.733 

1,401.990 

26| 

83.6451 

556.763 

108.385 

934.822 

42* 

133.125 

1,410.300 

26* 

84.0378 

562.003 

34i 

108.778 

941.609 

421 

133.518 

1,418.630 

261 

84.4305 

567.267 

34; 

109.171 

948.420 

42| 

133.911 

1,426.990 

27 

84.8232 

572.557 

109.563 

955.255 

42* 

134.303 

1,435.370 

27} 

85.2159 

577.870 

35* 

109.956 

962.115 

421 

134.696 

1,443.770 

27} 

85.6086 

583.209 

351 

110.349 

969.000 

43 

135.089 

1,452.200 

27* 

86.0013 

588.571 

35^ 

110.741 

975.909 

43} 

135.481 

1,460.660 

271 

86.3940 

593.959 

358 

111.134 

982.842 

43} 

135.874 

1,469.140 

27* 

86.7867 

599.371 

35* 

111.527 

989.800 

43J 

136.267 

1,477.640 

27* 

87.1794 

604.807 

35| 

111.919 

996.783 

431 

136.660 

1,486.170 

271 

87.5721 

610.268 

351 

112.312 

1,003.790 

43| 

137.052 

1,494.730 

28 

87.9648 

615.754 

351 

112.705 

1,010.822 

43* 

137.445 

1,503.300 

CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 


1099 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

43} 

137.838 

1,511.910 

51$ 

162.578 

2,103.35 

59| 

187.318 

2,792.21 

44 

138.230 

1,520.530 

51} 

162.970 

2,113.52 

59$ 

187.711 

2,803.93 

44} 

138.623 

1,529.190 

52 

163.363 

2,123.72 

59} 

188.103 

2,815.67 

44} 

139.016 

1,537.860 

52} 

163.756 

2,133.94 

60 

188.496 

2,827.44 

44f 

139.408 

1,546.56 

52} 

164.149 

2,144.19 

60} 

188.889 

2,839.23 

44} 

139.801 

1,555.29 

52f 

164.541 

2,154.46 

60} 

189.281 

2,851.05 

44| 

140.194 

1,564.04 

52} 

164.934 

2,164.76 

60f 

189.674 

2,862.89 

44$ 

140.587 

1,572.81 

52| 

165.327 

2,175.08 

60} 

190.067 

2,874.76 

44} 

140.979 

1,581.61 

52$ 

165.719 

2,185.42 

60| 

190.459 

2,886.65 

45I 

141.372 

1,590.43 

52} 

166.112 

2,195.79 

60$ 

190.852 

2,898.57 

141.765 

1,599.28 

53 

166.505 

2,206.19 

60} 

191.245 

2,910.51 

45{ 

142.157 

1,608.16 

53} 

166.897 

2,216.61 

61 

191.638 

2,922.47 

45| 

142.550 

1,617.05 

53} 

167.290 

2,227.05 

61} 

192.030 

2,934.46 

142.943 

1,625.97 

53f 

167.683 

2,237.52 

61} 

192.423 

2,946.48 

45| 

143.335 

1,634.92 

53} 

168.076 

2,248.01 

61  a 

192.816 

2,958.52 

45$ 

143.728 

1,643.89 

53| 

168.468 

2,258.53 

61} 

193.208 

2,970.58 

45} 

144.121 

1,652.89 

53$ 

168.861 

2,269.07 

193.601 

2,982.67 

46 

144.514 

1,661.91 

53} 

169.254 

2,279.64 

61$ 

193.994 

2,994.78 

46} 

144.906 

1,670.95 

54 

169.646 

2,290.23 

61} 

194.386 

3,006.92 

46} 

145.299 

1,680.02 

54} 

170.039 

2,300.84 

62 

194.779 

3,019.08 

46| 

145.692 

1,689.11 

54} 

170.432 

2,311.48 

62} 

195.172 

3,031.26 

46} 

146.084 

1,698.23 

54f 

170.824 

2,322.15 

62} 

195.565 

3,043.47 

46| 

146.477 

1,707.37 

54} 

171.217 

2,332.83 

62| 

195.957 

3,055.71 

46$ 

146.870 

1,716.54 

54f 

171.610 

2,343.55 

62} 

196.350 

3,067.97 

46} 

147.262 

1,725.73 

172.003 

2,354.29 

62| 

196.743 

3,080.25 

47 

147.655 

1,734.95 

54} 

172.395 

2,365.05 

62$ 

197.135 

3,092.56 

47} 

148.048 

1,744.19 

55 

172.788 

2,375.83 

62} 

197.528 

3,104.89 

47| 
47| 

148.441 
148.833 

1,753.45 
1,762.74 

1! 

173.181 
173.573 

2,386.65 
2,397.48 

63 
63} 

197.921 
198.313 

3,117.25 
3,129.64 

47} 

149.226 

1,772.06 

55| 

173.966 

2,408.34 

63} 

198.706 

3,142.04 

47| 

149.619 

1,781.40 

55} 

174.359 

2,419.23 

63f 

199.099 

3,154.47 

47$ 

150.011 

1,790.76 

55| 

174.751 

2,430.14 

63} 

199.492 

3,166.93 

47} 

150.404 

1,800.15 

55$ 

175.144 

2,441.07 

63| 

199.884 

3,179.41 

48 

150.797 

1,809.56 

55} 

175.537 

2,452.03 

63$ 

200.277 

3,191.91 

48} 

151.189 

1,819.00 

56 

175.930 

2,463.01 

63} 

200.670 

3,204.44 

48} 

a 

151.582 
151.975 
152.368 

1,828.46 
1,837.95 
1,847.46 

1 

176.322 
176.715 
177.108 

2,474.02 
2,485.05 
2,496.11 

64 

64} 
64} 

201.062 
201.455 
201.848 

3,217.00 
3,229.58 
3,242.18 

48| 

152.760 

1,856.99 

561 

177.500 

2,507.19 

64| 

202.240 

3,254.81 

48$ 

153.153 

1,866.55 

56| 

177.893 

2,518.30 

64} 

202.633 

3,267.46 

48} 

153.546 

1,876.14 

178.286 

2,529.43 

64| 

203.026 

3,280.14 

49 

153.938 

1,885.75 

56} 

178.678 

2,540.58 

64$ 

203.419 

3,292.84 

1 

154.331 
154.724 

1,895.38 
1,905.04 

57 
57} 

179.071 
179.464 

2,551.76 
2,562.97 

64} 
65 

203.811 
204.204 

3,305.56 
3,318.31 

155.116 
155.509 

1,914.72 
1,924.43 

57; 

179.857 
180.249 

2,574.20 
2,585.45 

i? 

204.597 
204.989 

3,331.09 
3,343.89 

49| 

155.902 

1,934.16 

57i- 

180.642 

2,596.73 

65f 

205.382 

3,356.71 

49$ 

156.295 

1,943.91 

674 

181.035 

2,608.03 

65} 

205.775 

3,369.56 

491 

156.687 

1,953.69 

57; 

181.427 

2,619.36 

65* 

206.167 

3,382.44 

50 
1 

157.080 
157.473 
157.865 

1,963.50 
1,973.33 
1,983.18 

57} 
58 
58} 

181.820 
182.213 
182.605 

2,630.71 
2,642.09 
2,653.49 

65$ 
65} 
66 

206.560 
206.953 
207.346 

3,395.33 
3,408.26 
3,421.20 

158.258 

1,993.06 

58} 

182.998 

2,664.91 

m 

207.738 

3,434.17 

1 

158.651 
159.043 
159  436 

2,002.97 
2,012.89 
2,022.85 

58| 
58}. 

183.391 
183.784 
184.176 

2,676.36 
2,687.84 
2,699.33 

eel 

66| 
66} 

208.131 
208.524 
208.916 

8,447.17 
3,460.19 
3,473.24 

51 

51} 

51f 

159.829 
160.222 
160.614 
161.007 
161.400 
161.792 

2,032.82 
2,042.83 
2,052.85 
2,062.90 
2,072.98 
2  083.08 

58} 
59i 

59| 

184.569 
184.962 
185.354 
185.747 
186.140 
186.532 

2,710.86 
2,722.41 
2,733.98 
2,745.57 
2,757.20 
2,768.84 

66| 
66$ 
66} 
67 
67} 
67} 

209.309 
209.702 
210.094 
210.487 
210.880 
211.273 

3,486.30 
3,499.40 
3,512.52 
3,525.66 
3,538.83 
3,552.02 

51| 

162.185 

2,093.20 

59} 

186.925 

2,780.51 

67| 

211.665 

3,565.24 

1100 


CIRCUMFERENCES  AND  AREAS  OF  CIRCLES 


Diarn. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

67} 

212.058 

3,578.48 

75| 

236.798 

4,462.16 

83} 

261.538 

5,443.26 

67| 

212.451 

3,591.74 

75} 

237.191 

4,476.98 

83* 

261.931 

5,459.62 

67* 

212.843 

3,605.04 

75| 

237.583 

4,491.81 

83} 

262.324 

5,476.01 

67* 

213.236 

3,618.35 

75* 

237.976 

4,506.67 

83! 

262.716 

5,492.41 

68 

213.629 

3,631.69 

75* 

238.369 

4,521.56 

83* 

263.109 

5,508.84 

68} 

214.021 

3,645.05 

76 

238.762 

4,536.47 

83} 

263.502 

5,525.30 

68} 

214.414 

3,658.44 

76} 

239.154 

4,551.41 

84 

263,894 

5,541.78 

68f 

214.807 

3,671.86 

76} 

239.547 

4,566.36 

84} 

264.287 

5,558.29 

68} 

215.200 

3,685.29 

76| 

239.940 

4,581.35 

84} 

264.680 

5,574.82 

68| 

215.592 

3,698.76 

76} 

240.332 

4,596.36 

84| 

265.072 

5,591.37 

68* 

215.985 

3,712.24 

76| 

240.725 

4,611.39 

84} 

265.465 

5,607.95 

68} 

216.378 

3,725.75 

76* 

241.118 

4,626.45 

84! 

265.858 

5,624.56 

69 

216.770 

3,739.29 

76} 

241.510 

4,641.53 

84* 

266.251 

5,641.18 

69} 

217.163 

3,752.85 

77 

241.903 

4,656.64 

84} 

266.643 

5,657.84 

69} 

217.556 

3,766.43 

77} 

242.296 

4,671.77 

85 

267.036 

5,674.51 

69J 

217.948 

3,780.04 

77| 

242.689 

4,686.92 

85} 

267.429 

5,691.22 

69} 

218.341 

3,793.68 

77J 

243.081 

4,702.10 

85- 

267.821 

5,707.94 

69! 

218.734 

3,807.34 

77} 

243.474 

4,717.31 

851 

268.214 

5,724.69 

69* 

219.127 

3,821.02 

77! 

243.867 

4,732.54 

85} 

268.607 

5,741.47 

69* 

219.519 

3,834.73 

77$ 

244.259 

4,747.79 

85| 

268.999 

5,758.27 

70 

219.912 

3,848.46 

77* 

244.652 

4,763.07 

85* 

269.392 

5,775.10 

70} 

220.305 

3,862.22 

78 

245.045 

4,778.37 

85} 

269.785 

5,791.94 

7(4 

220.697 

3,876.00 

78} 

245.437 

4,793.70 

86 

270.178 

5,808.82 

70| 

221.090 

3,889.80 

78} 

245.830 

4,809.05 

86J 

270.570 

5,825.72 

70} 

221.483 

3,903.63 

78| 

246.223 

4,824.43 

86} 

270.963 

5,842.64 

70| 

221.875 

3,917.49 

78} 

246.616 

4,839.83 

86| 

271.356 

5.859.59 

70* 

222.268 

3,931.37 

78| 

247.008 

4,855.26 

86} 

271.748 

5,876.56 

70} 

222.661 

3,945.27 

78* 

247.401 

4,870.71 

86| 

272.141 

5,893.55 

71 

223.054 

3,959.20 

78} 

247.794 

4,886.18 

86* 

272.534 

5,910.58 

71} 

223.446 

3,973.15 

79 

248.186 

4,901.68 

86} 

272.926 

5,927.62 

71} 

223.839 

3,987.13 

79} 

248.579 

4,917.21 

87 

273.319 

5,944.69 

71! 
7U 

224.232 
224.624 

4,001.13 
4,015.16 

79} 
79| 

248.972 
249.364 

4,932.75 
4,948.33 

87} 

87} 

273.712 
274.105 

5,961.79 
5,978.91 

71| 

225.017 

4,029.21 

79} 

249.757 

4,963.92 

87| 

274.497 

5,996.05 

71* 

225.410 

4,043.29 

79| 

250.150 

4,979.55 

87} 

274.890 

6,013.22 

71} 

225.802 

4,057.39 

79* 

250.543 

4,995.19 

87! 

275.283 

6,030.41 

72 

226.195 

4,071.51 

79} 

250.935 

5,010.86 

87* 

275.675 

6,047.63 

72} 

226.588 

4,085.66 

80 

251.328 

5,026.56 

87} 

276.068 

6,064.87 

72| 

226.981 

4,099.84 

80} 

251.721 

5,042.28 

88 

276.461 

6,082.14 

72| 

227.373 

4,114.04 

80} 

252.113 

5,058.03 

88} 

276.853 

6,099.43 

72* 

227.766 

4,128.26 

252.506 

5,073.79 

88} 

277.246 

6,116.74 

72| 

228.159 

4,142.51 

80} 

252.899 

5,089.59 

88} 

277.629 

6,134.08 

72* 

228.551 

4,156.78 

80| 

253.291 

5,105.41 

88} 

278.032 

6,151.45 

72* 

228.944 

4,171.08 

80* 

253.684 

5,121.25 

88! 

278.424 

6,168.84 

73 

229.337 

4,185.40 

80} 

254.077 

5,137.12 

88* 

278.817 

6,186.25 

73} 

229.729 

4,199.74 

81 

254.470 

5,153.01 

88} 

279.210 

6,203.69 

73} 

230.122 

4,214.11 

81} 

254.862 

5,168.93 

8» 

279.602 

6,221.15 

78t 

230.515 

4,228.51 

81} 

255.255 

5,184.87 

279.995 

6,238.64 

73} 

230.908 

4,242.93 

81J 

255.648 

5,200.83 

ggi 

280.388 

6,256.15 

73| 

231.300 

4,257.37 

81} 

256.040 

5,216.82 

89| 

280.780 

6,273.69 

73* 

231.693 

4,271.84 

81| 

256.433 

5,232.84 

89} 

281.173 

6,291.25 

73} 

232.086 

4,286.33 

81* 

256.826 

5,248.88 

89! 

281.566 

6,308.84 

74 

232.478 

4,300.85 

81} 

257.218 

5,264.94 

89* 

281.959 

6,326.45 

74} 

232.871 

4,315.39 

82 

257.611 

5,281.03 

89} 

282.351 

6,344.08 

74 
74| 

233.264 
233.656 

4,329.96 
4,344.55 

82} 
82} 

258.004 
258.397 

5,297.14 
5,313.28 

90 
90} 

282.744 
283.137 

6,361.74 
6,379.42 

74} 

234.049 

4,359.17 

82f 

258.789 

5,329.44 

90} 

283.529 

6,397.13 

74| 

234.442 

4,373.81 

82} 

259.182 

5,345.63 

90f 

283.922 

6,414.86 

74* 

234.835 

4,388.47 

82! 

259.575 

5,361.84 

90} 

284.315 

6,432.62 

74} 

235.227 

4,403.16 

82* 

259.967 

5,378.08 

90! 

284.707 

6,450.40 

75 

235.620 

4,417.87 

82} 

260.360 

5,394.34 

90* 

285.100 

6,468.21 

75} 

236.013 

4,432.61 

83 

250.753 

5,410.62 

90} 

285.493 

6,486.04 

75* 

236.405 

4,447.38 

83} 

261.145 

5,426.93 

91 

285.886 

6,503.90 

A  GLOSSARY  OF  MINING  TERMS 


1101 


Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

Diam. 

Circum. 

Area 

9U 

286.278 

6,521.78 

CM  * 
*^*T 

295.703 

6,958.26 

97j 

305.128 

7,408.89 

9l| 

286.671 

6,539.68 

94^ 

296.096 

6,976.76 

97- 

305.521 

7,427.97 

91$ 

287.064 

6,557.61 

94| 

296.488 

6,995.28 

97, 

305.913 

7,447.08 

9H 

287.456 

6,575.56 

296.881 

7,013.82 

97, 

306.306 

7,466.21 

91| 

287.849 

6,593.54 

94f 

297.274 

7,032.39 

97j 

306.699 

7,485.37 

91f 

288.242 

6,611.55 

94* 

297.667 

7,050.98 

97; 

307.091 

7,504.55 

288.634 

6,629.57 

94J 

298.059 

7,069.59 

97* 

307.484 

7,523.75 

92! 

289.027 

6,647.63 

95 

298.452 

7,088.24 

98 

307.877 

7,542.98 

289.420 

6,665.70 

95i 

298.845 

7,106.90 

98; 

308.270 

7,562.24 

92^- 

289.813 

6,683.80 

9-4 

299.237 

7,125.59 

98- 

308.662 

7,581.52 

92| 

290.205 

6,701.93 

96| 

299.630 

7,144.31 

9s; 

309.055 

7,600.82 

92* 

290.598 

6,720.08 

300.023 

7,163.04 

98- 

309.448 

7,620.15 

92| 

290.991 

6,738.25 

95f 

300.415 

7,181.81 

98 

309.840 

7,639.50 

92* 

291.383 

6,756.45 

95* 

300.808 

7,200.60 

98: 

310.233 

7,658.88 

291.776 

6,774.68 

95* 

301.201 

7,219.41 

98* 

310.626 

7,678.28 

93¥ 

292.169 

6,792.92 

96 

301.594 

7,238.25 

99 

311.018 

7,697.71 

292.562 

6,811.20 

96£ 

301.986 

7,257.11 

99J 

311.411 

7,717.16 

93- 

292.954 

6,829.49 

96i 

302.379 

7,275.99 

99i 

311.804 

7,736.63 

93| 

293.347 

6,847.82 

96f 

302.772 

7,294.91 

99| 

312.196 

7,756.13 

93i 

293.740 

6,866.16 

96} 

303.164 

7,313.84 

99* 

312.589 

7,775.66 

93| 

294.132 

6,884.53 

96| 

303.557 

7,332.80 

99| 

312.982 

7,795.21 

93* 

294.525 

6,902.93 

96* 

303.950 

7,351.79 

99* 

313.375 

7,814.78 

93J 

294.918 

6,921.35 

96* 

304.342 

7,370.79 

99* 

313.767 

7,834.38 

94 

295.310 

6,939.79 

97 

304.735 

7,389.83 

100 

314.160 

7,854.00 

The  preceding  table  may  be  used  to  determine  the  diameter  when 
the  circumference  or  area  is  known.  Thus,  the  diameter  of  a  circle  having 
an  area  of  7,200  sq.  in.  is  approximately  95*  in. 


A  GLOSSARY  OF  MINING  TERMS 


The  glossary  of  mining  terms  here  presented  is  taken  largely  from  that 
given  in  the  10th  Edition  of  the  Coal  and  Metal  Miners'  Pocketbook.  This 
was  a  combination  of  glossaries  including:  Raymond's  Glossary  of  Mining 
and  Metallurgical  Terms,  Powers'  Pocketbook  for  Miners  and  Metallurgists, 
Locke's  Miners'  Pocketbook,  Vol.  AC,  Second  Pennsylvania  Geological 
Survey,  Ilhseng's  Manual  of  Mining,  Chism's  Encyclopedia  of  Mexican 
Mining  Law,  a  Glossary  of  Terms  as  Used  in  Coal  Mining,  by  W.  S.  Gresley, 
llth  Annual  Report  of  the  State  Mine  Inspector  of  Missouri,  Bullman's 
Colliery  Working  and  Management,  Reynolds'  Handbook  of  Mining  Laws, 
Report  of  the  Mine  Inspector  of  Tennessee  for  1897,  Smithsonian  Report 
for  1886,  and  words  from  other  stray  sources.  In  the  present  glossary 
words  which  may  be  applied  only  to  metal  mining  have  been  omitted. 
Many  words  also  not  found  in  the  original  list  have  been  added.  Other 
terms  also  have  been  included  which  are  by  no  means  peculiar  to  the  coal- 
mining industry.  It  has  been  the  aim,  however,  to  include  such  terms  as  are 
in  common  use  by  those  engaged  in  coal  production  regardless  of  whether 
they  apply  only  to  that  industry  or  to  others  as  well.  Various  foreign 
words  have  been  selected  as  being  those  which  an  American  is  most  likely  to 
encounter.  This  list  is,  however,  by  no  means  exhaustive.  For  a  large  num- 
ber of  purely  local  terms  used  in  the  various  coal  fields  of  Great  Britain  the 
reader  is  referred  to  Mr.  Gresley's  glossary. 


1102  A  GLOSSARY  OF  MINING  TERMS 

GLOSSARY 

Abattis  (Leicester). — Cross-packing  of  branches  or  rough  wood,  used  to  keep 
roads  open  for  ventilation. 

Absolute  Pressure. — The  pressure  reckoned  from  a  vacuum. 

Absolute  Temperature. — The  temperature  reckoned  from  the  absolute  zero, 
- 459.2°  F.  or  -273°  C. 

Accompt  (Cornish). — Settling  day  or  place. 

Achicar  (Mexican). — To  diminish  the  quantity  of  water^in  any  gallery  or 
working,  generally  by  carrying  it  out  in  buckets  or  in  leather  bags. 
Achicadores. — Laborers  employed  for  said  purpose.  Achichinques. — 
Same  as  Achicadores.  Also  applied  to  hangers^n  about  police  courts, 
etc.  Such  people  as  are  generally  called  strikers  in  the  United  States. 

Acreage  Rent  (English). — Royalty  or  rent  for  working  minerals. 

Addlings  (North  of  England). — Earnings. 

Ademador  (Spanish). —  Mine  carpenter,  or  timberman. 

Ademar  (Spanish). — To  timber. 

Adit. — A  nearly  horizontal  passage  from  the  surface,  by  which  a  mine  is 
entered  and  unwatered  with  just  sufficient  slope  to  insure  drainage. 
In  the  United  States,  an  adit  driven  across  the  measures  is  usually  called 
a  tunnel,  though  the  latter,  strictly  speaking,  passes  entirely  through  a 
hill,  and  is  open  at  both  ends. 

Aodobe. — Sun-dried  brick. 

A  dventurers. — Original  prospectors. 

Adverse. — To  oppose  the  granting  of  a  patent  to  a  mining  claim. 

Adze. — A  curved  cutting  instrument  for  dressing  timber.  * 

Aerage  (French). — Ventilation. 

Aerometers. — The  air  pistons  of  a  Struve  ventilator. 

Aerophore. — The  name  given  to  an  apparatus  that  wilt  enable  a  man  to  enter 
places  in  mines  filled  with  explosive  or  other  deadly  gases,  with  safety. 

Afterdamp. — The  gaseous  mixture  resulting  from  an  explosion  of  firedamp. 

Agent. — The  manager  of  a  mining  property. 

Ahondar  (Spanish). — To  sink. 

Air. — The  current  of  atmospheric  air  circulating  through  and  ventilating  the 
workings  of  a  mine. 

Air  Box. — Wooden  tubes  used  to  convey  air  for  ventilating  headings  or 
sinkings  or  other  local  ventilation. 

Air  Compartment. — An  air-tight  portion  of  any  shaft,  winze,  rise,  or  level, 
used  for  improving  ventilation. 

Air-Course. — See  Airway. 

Air  Crossing. — A  bridge  that  carries  one  air-course  over  another,  an  overcast 

Air  Cushion. — A  cushion  or  spring  caused  by  confined  air. 

Air  Door. — A  door  for  the  regulation  of  currents  of  air  through  the  workings 
of  a  mine. 

Air-End  Way  (Locke). — Ventilation  levels  run  parallel  with  main  level. 

Air  Furnace. — A  ventilation  furnace. 

Air  Gates  (Locke). — (1)  Underground  roadways,  used  principally  for  ventilat- 
ing purposes.  (2)  An  air  regulator. 

Air  Head  (Staff). — Ventilation  ways. 

Air  Heading. — -An  airway,  or  air  course. 

Air  Hole  (Powers). — A  hole  drilled  in  advance  to  improve  ventilation  by 
communication  with  other  workings  or  the  surface. 

Airless  End. — The  extremity  of  a  stall  in  longwall  workings  in  which  there'is 
no  current  of  air,  or  circulation  of  ventilation,  but  which  is  kept  pure  by 
diffusion  and  by  the  ingress  and  egress  of  cars,  men,  etc. 

Air  Level. — A  level  or  airway  of  former  workings  made  use  of  in  subsequent 
deeper  mining  operations  for  ventilating  purposes. 

Air  Oven. — A  heated  chamber  for  drying  samples  of  ore,  coal,  etc. 

Air  Pipe. — A  pipe  made  of  canvas  or  metal,  or  a  wooden  box  used  in  con- 
veying air  to  the  workmen,  or  for  rock  drills  or  air  locomotives. 

Air-Shaft. — A  shaft  or  pit  used  expressly  for  ventilation. 

Air  Slit  (Yorks). — A  short  head  between  other  air  heads. 

Air  Sollar. — A  brattice  carried  beneath  the  tram  rails  or  road  bed  in  a  head- 
ing or  gangway. 

Air  Stack. — A  stack  or  chimney  built  over  a  shaft  for  ventilation. 

Airway. — Any  passage  through  which  air  is  carried. 

Ailch  Piece. — Parts  of  a  pump  in  which  the  valves  are  fixed. 

Albanil  (Spanish). — Mason. 


A  GLOSSARY  OF  MINING  TERMS  1103 

Alive  (Cornish). — Productive. 

Alluvium. — Gravel,  sand,  and  mud  deposited  by  streams. 

Almagre  (Spanish). — Red  ocher. 

Alternating  Motion. — Up  and  down,  or  backward  and  forward  motion. 

Alto  (Mexican). — The  hanging  wall  of  a  vein.     See  Respaldos. 

Amygdaloidal. — Almond-shaped. 

Analysis. — The  determination  of  the  original  elements  and  the  proportions 

of  each  in  a  substance. 
Anemometer. — An  instrument  used  for  measuring  the  velocity  of  a  ventilating 

current  by  means  of  a  revolving  vane  wheel. 

Angle  Beam. — A  two-limbed  beam  used  for  turning  angles  in  shafts,  etc. 
Anhydrous. — Without  water  in  its  composition. 
Anneal.— To  toughen  or  soften  metals,  glass,  etc.,  by  first  heating  and  then 

cooling  very  slowly  or  quickly  depending  on  the  metal. 
Anthracite. — Coal  containing  a  small  percentage  of  volatile  matter. 
Anticline. — A  flexure  or  fold  in  which  the  rocks  on  the  opposite  sides  of  the 

fold  dip  away  from  each  other,  like  the  two  legs  of  the  letter  A.     The 

inclination  on  one  side  may  be  much  greater  than  on  the  opposite  side. 

An  anticlinal  is  said  to  be  overturned  when  the  rocks  on  both  sides  dip 

in  the  same  direction. 
Anticlinal  Axis. — The  ridge  of  a  saddle  in  a  mineral  vein,  or  the  line  along 

the  summit  of  a  vein,  from  which  the  vein  dips  in  opposite  directions. 
Anticlinal  Flexure;  Anticlinal  Fold. — An  anticline. 
Antiguos,    Los    (Mexican). — The    Spanish    or    Indian    miners    of    colonial 

times. 
Aparejo  (Mexican). — A  rigid  pair  of  large  stuffed  pads  connected  over  the 

back  of  a  pack  mule  by  an  unpadded  portion  to  protect  body  of  mule 

when  heavy  or  irregularly  shaped  loads  are  carried. 
Aperos  (Mexican). — All  kinds  of  mining  supplies  in  general.     Aperador. — A 

storekeeper. 
Apex. — The  landing  point  at  the  top  of  a  slope  or  inclined  plane,  the  knuckle; 

also,  the  top  of  an  anticlinal.     In  the  U.  S.  Revised  Statutes,  the  end  or 

edge  of  a  vein  nearest  the  surface. 
A  pique  (Mexican). — Perpendicular. 

Apron  (English). — (1)  A  covering  of  timber,  stone,  or  metal,  to  protect  a  sur- 
face against  the  action  of  water  flowing  over  it.      (2)  A  hinged  extension 

to  a  loading  chute. 
Aqua  Fortis. — Nitric  acid. 

Aquo  Regia. — A  mixture  of  hydrochloric  acid  and  nitric  acid. 
Aqueduct. — An  artificial  channel  for  carrying  water. 
Arajo  (Mexican). —  See  Hatajo. 
Arch  (Cornish). — Portion  of  lode  left  standing  to  support  hanging  wall,  or 

because  too  poor. 

Archean. — An  early  period  of  geological  time. 
Arching. — Brickwork  or  stonework  forming  the  roof  of   any  underground 

roadway. 
Arenaceous. — Sandy;  rocks  are  arenaceous  when  they  contain  a  considerable 

percentage  of  sand. 
Arenillas  (Spanish). — Refuse  earth. 

Argillaceous. — Clayey;  rocks  are  argillaceous  when  they  contain  a  consider- 
able percentage  of  clay,  or  have  some  of  the  characteristics  of  clay. 
Argol. — Crude  tartar  deposited  from  wine. 
Arm. — The  inclined  leg  of  a  set  of  timber. 
Arrastrar  (Mexican).— To  drag  along  the  ground.     Arrastrar  el  Agua.—To 

almost  completely  exhaust  the  water  in  a  sump  or  working. 
Arroba  (Mexican). — 25  Ib. 
Artesian  Well.— An  artificial  channel  of  escape,  made  by  a  bore  hole,  for  a 

subterranean  stream,  subject  to  hydrostatic  pressure. 
Ascensional   Ventilation. — The  arrangement  of   the  ventilating  currents  in 

such  a  manner  that  the  air  shall  continuously  rise  until  reaching  the 

bottom  of  the  upcast  shaft.     Particularly  applicable  to  steep  seams. 
Ashlar. — A  facing  of  cut  stone  applied  to  a  backing  of  rubble  or  rough 

masonry  or  brickwork. 

Aspirail  (French). — Opening  for  ventilation. 
Assay. — The  determination  of  the  quality  and  quantity  of  any  particular 

substance  in  a  mineral.     Assayer. — One  who  performs  assays. 
Assessment  Work. — The  annual  work  necessary  to  hold  a  mining  claim. 
Astel. — Overhead  boarding  in  a  gallery. 


1104  A  GLOSSARY  OF  MINING  TERMS 

Astyllen  (Cornish). — Small  dam  in  an  adit;  partition  between  ore  and  deads 
on  grass. 

Atacador  (Mexican). — A  tamping  bar  or  tamping  stick. 

Atecas  (Mexican). — Same  as  Achicadores,  etc. 

Atierres  (Spanish). — Refuse  rock  or  dirt  inside  a  mine,  gob. 

Attle  (Cornish). — Refuse  rock. 

Attle  (Addle). — The  waste  of  a  mine. 

Attrition. — The  act  of  wearing  away  by  friction. 

Auger  Stem. — The  iron  rod  or  bar  to  which  the  bit  is  attached. 

Auget. — Priming  tube. 

Ausscharen  (German). — Junction  of  lodes. 

Auszimmern  (German). — Timbering. 

Aviador  (Spanish). — One  who  provides  the  capital  to  work  a  mine.  Avio. — 
Money  furnished  to  the  proprietors  of  a  mine  to  work  the  mine  by 
another  peison,  the  Aviador.  Avio  Contract. — A  contract  between  two 
parties  for  working  a  mine  by  which  one  of  the  parties,  the  aviador, 
furnishes  the  money  to  the  proprietors  for  working  the  mine. 

Axis. — An  imaginary  line  passing  through  a  body  that  may  be  supposed  to 
revolve  around  it. 

Azimuth. — The  azimuth  of  a  body  is  that  arc  of  the  horizon  that  is  included 
between  the  meridian  circle  at  the  given  place  and  a  vertical  plane 
passing  through  the  body.  It  is  always  measured  from  due  north 
around  to  the  right. 

Atoic. — The  age  of  rocks  that  were  formed  before  animal  life  existed. 

Back. — (1)  A  plane  or  cleavage  in  coal,  etc.,  having  frequently  a  smooth 
parting  and  some  sooty  coal  included  in  it.  (2)  The  inner  end  of  a  head- 
ing or  gangway.  (3)  To  throw  back  into  the  gob  or  waste  the  small 
slack,  dirt,  etc.  (4)  To  roll  large  coals  out  of  a  waste  for  loading  into  cars. 

Back  Balance.— (I)  A  self-acting  incline  in  the  mine,  where  a  balance  car  and 
a  carriage  in  which  the  mine  car  is  placed  are  used.  The  loaded  car  upon 
the  carriage  will  hoist  the  balance  car,  and  the  balance  car  will  hoist  the 
carriage  and  empty  car.  (2)  A  weight  moving  vertically  or  on  an  in- 
cline which  places  tension  upon  a  tension  carriage. 

Backbye  Work. — Work  done  between  the  shaft  and  the  working  face,  in 
contradistinction  to  face  work,  or  work  done  at  the  face. 

Back  Casing. — A  wall  or  lining  of  dry  bricks  used  in  sinking  through  drift 
deposits,  the  permanent  walling  being  built  up  within  it.  The  use  of 
timber  cribs  and  planking  serves  the  same  purpose. 

Back  End  (England). — The  last  portion  of  a  jud. 

Backing. — (1)  The  rough  masonry  of  a  wall  faced  with  finer  work.  (2) 
Earth  deposited  behind  a  retaining  wall,  etc.  (3)  Timbers  let  into 
notches  in  the  rock  across  the  top  of  a  level. 

Backing  Deals. — Deal  boards  or  planking  placed  at  the  back  of  curbs  for 
supporting  the  sides  of  a  shaft  that  is  liable  to  run. 

Back  Joint. — Joint  plane  more  or  less  parallel  to  the  strike  of  the  cleavage, 
and  frequently  vertical. 

Backlash. — (1)  Backward  suction  of  air-currents  produced  after  an  explosion 
of  firedamp.  (2)  Reentry  of  air  into  a  fan.  (3)  Lost  motion  or  play 
between  the  teeth  of  gears. 

Back  Pressure. — The  loss,  expressed  in  pounds  per  square  inch,  due  to  getting 
the  steam  out  of  the  cylinder  of  an  engine  after  it  has  done  its  work. 

Back  Shift.— Afternoon  shift. 

Back  Skin  (North  of  England). — A  leather  jacket  for  wet  workings. 

Backstay. — A  wrought-iron  forked  bar  attached  to  the  back  of  cars  when 
ascending  an  inclined  plane,  which  throws  them  off  the  rails  if  the  rope  or 
coupling  breaks. 

Baff  Ends. — Long  wooden  edges  for  adjusting  linings  in  sinking  shafts  dur- 
ing the  operation  of  fixing  the  lining. 

Baffle. — (1)  To  brush  out  firedamp.  (2)  A  firebrick  partition  to  guide  the 
flue  gases  through  a  boiler. 

Bait. — Provisions. 

Bajo  (Mexican)  — The  footwall  of  a  vein.     See  Respaldo. 

Bal  (Cornish). — A  mine. 

Balance. — (1)  The  counterpoise  or  weights  attached  to  the  drum  of  a  winding 
engine,  to  assist  the  engine  in  lifting  the  load  out  of  a  shaft  bottom  and 
in  helping  it  to  slacken  speed  when  the  cage  reaches  the  surface.  It 
consists  often  of  a  bunch  of  heavy  chains  suspended  in  a  shallow  shaft, 


A  GLOSSARY  OF  MINING  TERMS  1105 

the  chains  resting  on  the  shaft  bottom  as  unwound  off  the  balance  drum 
attached  to  the  main  shaft  of  the  engine.  (2)  Scales  used  in  chemical 
analysis  and  assaying. 

Balance  Bob. — A  large  beam  or  lever  attached  to  the  main  rods  of  a  Cornish 
pumping  engine,  carrying  on  its  outer  end  a  counterpoise. 

Balance  Box. — A  large  box  placed  on  one  end  of  a  balance  bob  and  filled 
with  old  iron,  rock,  etc.,  to  counterbalance  the  weight  of  the  pump  rods. 

Balance  Brow. — An  inclined  plane  in  steep  seams  on  which  a  platform  on 
wheels  travels  and  carries  the  cars  of  coal. 

Balance  Car. — A  small  weighted  truck  mounted  upon  a  short  inclined  track, 
and  carrying  a  sheave  around  which  the  rope  of  an  endless  haulage 
system  passes  as  it  winds  off  the  drum. 

Balance  Pit. — A  pit  or  shaft  in  which  a  balance  rises  or  falls. 

Balanzon  (Mexican). — The  balance  bob  of  a  Cornish  pump. 

Balk. — (1)  A  more  or  less  sudden  thinning  put  of  a  seam  of  coal.  (2)  Irregu- 
lar-shaped masses  of  stone  intruding  into  a  coal  seam,  or  bulgings  out 
of  the  stone  roof  into  the  seam.  (3)  A  bar  of  timber  supporting  the  roof 
of  a  mine,  or  for  carrying  any  heavy  load. 

Ballast. — Broken  stone,  gravel,  sand,  etc.,  used  for  keeping  railroad  ties 
steady. 

Bancos  (Spanish). — Horses  in  a  vein  or  cross-courses. 

Band. — A  seam  or  thin  stratum  of  stone  or  other  refuse  in  a  seam  of  coal, 
a  parting. 

Bank. — (1)  The  top  of  the  shaft,  or  out  of  the  shaft.  (2)  The  surface  around 
the  mouth  of  a  shaft.  (3)  To  manipulate  coals,  etc.,  on  the  bank. 
(4)  The  whole  or  sometimes  only  one  side  or  one  end  of  a  working  place 
underground.  (5)  A  large  heap  of  mineral  on  the  surface. 

Bank  Chain. — A  chain  that  includes  the  bank  of  a  river  or  creek. 

Bank  Claim  (Australian). — Mining  right  on  bank  of  stream. 

Bank  Head. — The  upper  end  of  an  inclined  plane,  next  to  the  engine  or  drum, 
made  nearly  level. 

Bank  Right  (Australian). — Right  to  divert  water  to  bank  claim. 

Banksman. — The  man  in  attendance  at  the  top  of  the  shaft,  superintending 
the  work  of  banking. 

Bankwork. — A  system  of  working  coal  in  South  Yorkshire. 

Bank  to  Bank. — A  shift. 

Bannocking. — See  Kirving. 

Bar. — A  length  of  timber  placed  horizontally  for  supporting  the  root.  In 
some  cases,  bars  of  wrought  iron,  about  3  in.  X  1  in.  X  5  ft.  are  used. 

Bargain. — Portion  of  mine  worked  by  a  gang  on  contract. 

Baring. — See  Stripping. 

Barmaster  (Derbyshire). — Mine  manager,  agent,  and  engineer. 

Barney. — A  small  car,  used  on  inclined  planes  and  slopes  to  push  the  mine 
car  up  the  slope.  Barney  Pit. — A  pit  at  the  bottom  of  a  slope  or  plane 
into  which  the  barney  runs  to  allow  the  mine  car  to  pass  over  it. 

Barra  (Mexican). — (1)  A  bar,  as  of  gold,  silver,  iron,  steel,  etc.  (2)  A  cer- 
tain share  in  a  mine.  The  ancient  Spanish  laws,  from  time  immemorial, 
considered  a  mine  as  divided  into  24  parts,  and  each  part  was  called  a 

Barra  Viuda,  or  Aviada  (Mexican). — These  are  "barras"  or  shares  that  par- 
ticipate in  the  profits,  but  not  in  the  expenses,  of  mining  concerns. 
Their  share  of  the  expenses  is  paid  by  the  other  shares.  Non-assessable 

Barranca  (Mexican). — A  ravine,  a  gulch.     What  is  improperly  called  in  the 

United  States  a  canyon  or  canon. 
Barrena   (Mexican).— A  hand  drill  for  opening  holes  in  rocks  for  blasting 

Barrenarse   (Mexican). — When  two  mines  or  two  workings  (as  a  shaft  or 

winze,  or  a  gallery),  communicate  with  each  other. 
Barren  Ground. — Strata  unproductive  of  seams  of  coal,  etc.,  of  a  workable 

thickness. 
Barreno  (Mexican). — (1)  A  drill  hole  for  blasting  purposes.    In  mechanics,  any 

bored  hole      (2)  A  communication  between  two  mines  or  two  workings. 
Barretero   (Mexican).— A  miner  of  the  first  class;  one  that  knows  how  to 

point  his  holes,  drill,  and  blast,  or  work  with  a  gad. 
Barrier  Pillar.— A  solid  block  or  rib  of  coal,  etc.,  left  un worked  between  two 

collieries  or  mines  for  security  against  accidents  arising  from  influx  ot 

water. 

70 


1106  A  GLOSSARY  OF  MINING  TERMS 

Barrier  System. — The  method  of  working  a  colliery  by  pillar  and  stall,  where 

solid  ribs  or  barriers  of  coal  are  left  in  between  a  set  or  series  of  working 

places. 
Barrow. — (1)  A  box  with  two  handles  at  one  end  and  a  wheel  at  the  other. 

(2)  Heap  of  waste  stuff  raised  from  a  mine:  a  dump. 
Bar  Timbering. — A  system  of  supporting  a  tunnel  roof  by  long  top  bars,  while 

the  whole  lower  tunnel  core  is  taken  out,  leaving  an  open  space  for  the 

masons  to  run  up  the  arching.     Under  certain  conditions,  the  bars  are 

withdrawn  after  the  masonry  is  completed,  otherwise  they  are  bricked  in 

and  not  drawn. 
Basin. — (1)  A  coal  field  having  some  resemblance  in  form  to  a  basin.     (2) 

The  synclinal  axis  of  a  seam  of  coal  or  stratum  of  rock. 
Basket. — A  measure  of  weight  =  2  cwt. 
Basque. — Crucible  or  furnace  lining. 
Bass  (Derbyshire). — Indurated  clay. 
Basset. — Outcrop  of  a  lode  or  stratum. 
Bastard. — A  particularly  hard  massive  rock  or  boulder. 
Batch. — An  amount  of  concrete  material. 
Ball  (English). — (1)  A  highly  bituminous  shale  found  in  the  coal  measures. 

(2)  Hardened  clay,  but  not  fireclay.     Same  as  Bend  and  Bind. 
Batten. — A  piece  of.thin  board  less  than  12  in.  in  width. 
Batter. — The  inclination  of  a  face  of  masonry  or  of  any  inclined  portion  of 

a  frame  or  metal  structure. 
Battery. — (1)  A  structure  built  to  keep  coal  from  sliding  down  a  chute  or 

breast.     (2)  An  embankment  or  platform  on  which  miners  work.     (3) 

A  set  of  stamps.     (4)  Two  or  more  boilers  with  a  common  setting. 
Bay. — An  open  space  for  waste  between  two  packs  in  a  longwall  working. 

See  Board. 

Bay  of  Biscay  Country. — (Geological). — See  Crab  Holes. 

Beans  (North  of  England). — All  coal  that  will  pass  through  about  J-S-in.  screen. 
Bear. — A  deposit  of  iron  at  the  bottom  of  a  furnace. 
Bear;  to  Bear  In. — Underholing  or  undermining;  driving  in  at  the  top  or  at 

the  side  of  a  working. 
Bearers. — Pieces  of  timber  3  or  4  ft.  longer  than  the  breadth  of  a  shaft,  which 

are  fixed  into  the  solid  rock  at  the  sides  at  certain  intervals  apart;  used 

as  foundations  for  sets  of  timber. 
Bearing. — (1)  The  course  by  a  compass.     (2)  The  span  or  length  in  the  clear 

between  the  points  of  support  of  a  beam,  etc.     (3)  The  points  of  support 

of  a  beam,  shaft,  axle,  etc. 
Bearing  Door. — A  door  placed  for  the  purpose  of  directing  and  regulating  the 

amount  of  ventilation  passing  through  an  entire  district  of  a  mine. 
Bearing  In. — The  depth  or  distance  under  of  the  undercut  or  holing. 
Bearing-up  Pulley. — A  pulley  wheel  fixed  in  a  frame  and  arranged  to  tighten 

up  or  take  up  the  slack  rope  in  endless-rope  haulage. 
Bearing-up  Stop. — A  partition  of  brattice  or  plank  that  serves  to  conduct  air 

to  a  face. 

Beat  (Cornish). — To  cut  away  a  lode. 

Beataway. — Working  hard  ground  by  means  of  wedges  and  sledge  hammers. 
Bed. — (1)  The  level  surface  of  a  rock  upon  which  a  curb  or  crib  is  laid.     (2) 

A  stratum  of  coal,  ironstone,  clay,  etc. 

Bed  Claim  (Australian). — A  claim  that  includes  the  bed  of  a  river  or  creek. 
Bede. — Miners'  pickax. 
Bedplate, — A  large  plate  of  iron  used  as  a  foundation  for  an  engine  or  other 

machine. 

Bed  Rock. — The  solid  rock  underlying  the  soil,  drift,  or  alluvial  deposits. 
Beehive  Oven.— -The  ordinary  circular  or  rectangular  arched  oven  in  which 

coke  is  made  without  the  recovery  of  any  byproducts  other  than  in  some 

instances  the  heat. 

Bef ore-Breast. — Rock  or  vein,  which  still  lies  ahead. 
Bell. — Overhanging  rock  or  slate,  of  a  bell-like  form,  disconnected  from  the 

main  roof. 

Belly. — A  swelling  mass  of  mineral  in  a  lode. 
Bench. — (1)  A  natural  terrace  marking  the  outcrop  of  any  stratum.     (2)  A 

stratum  of  coal  forming  a  portion  of  the  vein. 
Benching. — To  break  up  with  wedges  the  bottom  coals  when  the  holing  is 

done  in  the  middle  of  the  seam. 

Benching  Up  (North  of  England). — Working  on  top  of  coal. 
Bench  Mark. — A  mark  cut  in  a  tree,  rock  or  on  some  solid  structure  whose 


A  GLOSSARY  OF  MINING  TERMS  1107 

elevation  is  known.  Used  by  surveyors  for  reference  in  determining 
elevations. 

Bench  Working. — The  system  of  working  one  or  more  seams  or  beds  of  min- 
eral by  open  working  or  stripping,  in  stages  or  steps. 

Bend  (Derbyshire). — Indurated  clay. 

Bessemer  Steel. — Steel  made  by  the  Bessemer  process. 

Beton  (English). — Concrete  of  hydraulic  cement  with  broken  stone,  bricks, 
gravel,  etc. 

Bevel. — The  slope  formed  by  trimming  away  on  edge. 

Bevel  Gear. — A  gear-wheel  whose  teeth  are  inclined  to  the  axis  of  the  wheel. 

Biche. — A  hollow-ended  tool  for  recovering  boring  rods. 

Billy  Boy. — A  boy  who  attends  a  Billy  Playfair. 

Billy  Playfair. — A  mechanical  contrivance  for  weighing  coal,  consisting  of  an 
iron  trough  with  a  sort  of  hopper  bottom,  into  which  all  the  small  coal 
passing  through  the  screen  is  conducted  and  weighed  off  and  emptied 
from  time  to  time. 

Bin. — A  box  or  receptacle  used  for  tools,  stones,  ore,  coal,  etc. 

Bind,  or  Binder. — Indurated  argillaceous  shales  or  clay,  very  commonly 
forming  the  roof  of  a  coal  seam  and  frequently  containing  clay  iron- 
stone. See  Bait. 

Binding. — Hiring  men. 

Bit. — (1)  A  piece  of  steel  placed  in  the  cutting  edge  of  a  drill  or  point  of  a 
pick.  (2)  The  cutting  tool  of  a  mining  machine. 

Blackband. — Carbonaceous  ironstone  in  beds,  mingled  with  coaly  matter 
sufficient  for  its  own  calcination. 

Black  Bait,  or  Black  Stone. — Black  carbonaceous  shale. 

Black  Butts.— See  Black  Ends. 

Blackdamp. — Carbonic-acid  gas. 

Black  Dimaonds. — Coal. 

Black  Ends. — Beehive  coke  of  inferior  quality  due  to  mismanipulation  or  dis- 
coloration. 

Black  Jack. — (1)  Properly  speaking,  dark  varieties  of  zinc  blend,  but  many 
miners  apply  it  to  any  black  mineral.  (2)  Crude  black  oil  used  to  oil 
mine  cars.  Often  called  Black  Strap. 

Black  Lead. — Graphite. 

Black  Stone. — A  carbonaceous  shale. 

Blast. — (1)  The  sudden  rush  of  fire,  gas,  and  dust  of  an  explosion  through  the 
workings  and  roadways  of  a  mine.  (2)  To  cut  or  bring  down  coal,  rocks, 
etc.,  by  the  explosion  9f  gunpowder,  dynamite,  etc. 

Blasting  Barrel. — A  small  pipe  used  for  blasting  in  wet  or  gaseous  places. 

Blast  Pipe. — A  pipe  for  supplying  air  to  furnaces^ 

Blind  Coal. — Coal  altered  by  the  heat  of  a  trap  dike. 

Blind  Creek. — (1)  A  creek  in  which  water  flows  only  in  very  wet  weather. 
(2)  (Australasian)  Dry  watercourse. 

Blind  Drift. — (1)  A  horizontal  passage  in  the  mine  not  yet  connected  with  the 
other  workings.  (2)  A  drift  not  opening  to  daylight. 

Blind  Joint. — Obscure  bedding  plane. 

Blind  Lead,  or  Blind  Lode. — A  vein  having  no  visible  outcrop. 

Blind  Level. — (1)  An  incomplete  level.     (2)  A  drainage  level. 

Blind  Shaft,  or  Blind  Pit. — A  shaft  not  coming  to  the  surface. 

Bloat. — A  hammer  swelled  at  the  eye.      • 

Block  Claim  (Australian). — A  square  mining  claim. 

Block  Coal. — Coal  that  breaks  in  large  rectangular  lumps. 

Block  Reefs. — Reefs  showing  frequent  contractions  longitudinally. 

Block  Tin. — Cast  tin. 

Bloomary. — A  forge  for  making  wrought  iron. 

Blossom. — The  decomposed  outcrop,  float,  surface  stain,  or  any  indicating 
traces  of  a  coal  bed  or  mineral  deposit.  Blossom  Rock. — (1)  Colored 
veinstone  detached  from  an  outcrop.  (2)  The  rock  detached  from  a 
vein,  but  which  has  not  been  transported. 

Blow. — (1)  To  blast  with  gunpowder,  etc.  (2)  A  dam  or  stopping  is  said  to 
blow  when  gas  escapes  through  it. 

Blower. — (1)  A  sudden  emission  or  outburst  of  gas  in  a  mine.  (2)  Any 
emission  of  gas  from  a  coal  seam  similar  to  that  from  an  ordinary  gas 
burner.  (3)  A  type  of  centrifugal  fan  used  largely  to  force  air  into 
furnaces.  (4)  A  blowdown  ventilating  fan. 

Blow  Fan.— A  small  centrifugal  fan  used  to  force  air  through  canvas  pipes  or 
wooden  boxes  to  the  workmen. 


1108  A  GLOSSARY  OF  MINING  TERMS 

Slowdown  Fan. — A  force  fan. 

Blown-out  Shot. — A  shot  that  has  blown  out  the  tamping,  but  not  broken 
the  coal  or  rock. 

Blow  Off. — To  let  off  excess  of  steam  from  a  boiler. 

Blow  Out. — (1)   To  finish  a  smelting  campaign.     (2)  A  blown-out  shot. 
(3)  The  decomposed  mineral  exposure  of  a  vein. 

Blowpipe. — An  instrument  for  creating  a  blast  whereby  the  heat  of  a  flame  or 
lamp  can  be  better  utilized. 

Blue  Cap. — The  blue  halo  of  ignited  gas  (firedamp  and  air)  on  the  top  of  the 
flame  in  a  safety  lamp. 

Blue  Elvan  (Cornish). — Greenstone. 

Blue  John. — Fluorspar. 

Blue  Metal. — A  local  term  for  shale  possessing  a  bluish  color. 

Blue  Peach  (Cornish). — A  slate-blue  fine-grained  schorl. 

Bluestone. — (1)  Sulphate  of  copper.  (2)  Lapis  lazuli.  (3)  Basalt.  (4) 
Maryland,  a  gray  gneiss^  in  Ohio,  a  gray  sandstone;  in  the  District  of 
Columbia,  a  mica  schist;  in  New  York,  a  blue-gray  sandstone;  in  Penu- 
sylvania,  a  blue-gray  sandstone.  (5)  A  popular  term  among  stone  men 
not  sufficiently  definite  to  be  of  value. 

Bluff. — Blunt. 

Board. — A  wide  heading  usually  from  3  to  5  yd.  wide. 

Boar d-and- Pillar. — A  system  of  working  coal  where  the  first  stage  of  exca- 
vation is  accomplished  with  the  roof  sustained  by  pillars  of  coal  left 
between  the  breasts;  often  called  Breast-and-Pillar. 

Bob. — An  oscillating  bell-crank,  or  lever,  through  which  the  motion  of  an 
engine  is  transmitted  to  the  pump  rods  in  an  engine  or  pumping  pit. 
There  are  J.  bobs,  L  bobs,  and  V  bobs. 

Boca  or  Boca  Mina  (Mexican). — Mouth  or  mine  mouth.  This  is  the  name 
applied  to  the  principal  or  first  opening  of  a  mine,  or  to  the  one  where 
the  miners  are  accustomed  to  descend. 

Bochorno  (Mexican). — Excessive  heat,  with  want  of  ventilation,  so  that  the 
lights  go  out.  See  Vapores. 

Body.—~(l)  An  ore  body,  or  pocket  of  mineral  deposit.  (2)  The  thickness  of 
a  lubricating  oil  or  other  liquid;  also  the  measure  of  that  thickness 
expressed  in  the  number  of  seconds  in  which  a  given  quantity  of  the 
oil  at  a  given  temperature  flows  through  a  given  aperture. 

Boleo  (Mexican). — A  dump  pile  for  waste  rock. 

Bond. — (1)  The  arrangement  of  blocks  of  stone  or  brickwork  to  form  a  firm 
structure  by  a  judicious  overlapping  of  each  other  so  as  to  break  J9int. 
(2)  An  agreement  for  hiring  men.  (3)  Apparatus  for  electrically  join- 
ing the  ends  of  adjacent  rails.  A  cross  bond  joins  both  rails  of  a  track. 

Bone. — Slaty  coal  or  carbonaceous  shale  found  in  coal  seams. 

Bone  Ash. — Burnt  bones  pulverized  and  sifted. 

Bonnet. — (1)  The  overhead  cover  of  a  cage.  (2)  A  cover  for  the  gauze  of  a 
safety  lamp.  (3)  A  cap  piece  for  an  upright  timber.  (4)  The  upper 
part  of  a  valve  containing  the  stuffing  box. 

Booming. — Ground  sluicing  on  a  large  scale  by  emptying  the  contents  of  a 
reservoir  at  once  on  material  collected  below,  thus  removing  boulders. 

Bord  (English). — A  narrow  breast. 

Bord-and-Pillar  (English). — See  Pillar-and-Breast. 

Bord  Room. — The  space  excavated  in  driving  a  bord.  The  term  is  used  in 
connection  with  the  "ridding"  of  the  fallen  stone  in  old  bords  when 
driving  roads  across  them  in  pillar  working;  thus,  "ridding  across  the 
old  bord  room." 

Bord  Ways  Course. — The  direction  at  right  angles  to  the  main  cleavage 
planes.  In  some  mining  districts  it  is  termed  "on  face." 

Bore. — To  drill. 

Bore  Hole. — A  hole  made  with  a  drill,  auger,  or  other  tools,  in  coal,  rock,  or 
other  material. 

Bort. — Amorphous  dark  diamond. 

Bosh. — The  plane  in  a  blast  furnace  where  the  greatest  diameter  is  reached. 

Boss  (English). — (1)  An  increase  of  the  diameter  at  any  part  of  the  shaft. 
(2)  A  person  in  charge  of  a  piece  of  work. 

Botas  (Mexican). — Buckets  made  of  an  entire  ox  skin,  to  take  out  water. 

Botryoidal. — Grape-like  in  appearance. 

Bottle  Chock. — A  pulley  with  a  wide  grooved  face  for  guiding  a  cable  around 
a  turn  in  the  track,  an  angle  sheave. 

Bottle  Jack  (English), — An  appliance  for  lifting  heavy  weights. 


A  GLOSSARY  OF  MINING  TERMS  1109 

Bottom. — (1)  The  landing  at  the  bottom  of  the  shaft  or  slope.     (2)  The  lowest 
point   of  mining   operations.      (3)    The  floor,   bottom  rock,  or  stratum 
underlying  a  coal  bed.      (4)  In  alluvial,  the  bed  rock  or  reef. 
Bottomer,  Bottomman. — The  person  that  loads  the  cages  at  the  pit  bottom 

and  gives  the  signal  to  bank.     The  onsetter  or  bottom  eager. 
Bottom  Joint. — Joint  or  bedding  plane,  horizontal  or  nearly  so. 
Bottom  Lift. — (1)  The  deepest  column  of  a  pump.     (2)  The  lowest  or  deepest 

lift  or  level  of  a  mine. 

Bottom  Pillars. — Large  pillars  left  around  the  bottom  of  a  shaft. 
Boulders. — Loose  rounded  masses  of  stone  detached  from  the  parent  rock. 
Bounce. — A  sudden  spalling  off  of  the  sides  of  ribs  and  pillars  due  to  excessive 

pressure;  a  bump. 
Bow.— The  handle  of  a  kibble. 
Bowk. — An  iron  barrel  or  tub  used  for  hoisting  rock  and  other  d6bris  when 

sinking  a  shaft. 

Bowke  (Staffordshire). — A  small  wooden  box  for  hauling  ironstone  under- 
ground. 

Box. — (1)  A  12'  to  14'  section  of  a  sluice.      (2)  A  mine  car. 
Box  Bill. — Tool  for  recovering  boring  rods. 

Boxing. — A  method  of  securing  shafts  solely  by  slabs  and  wooden  pegs. 
Brace. — ^1)  An  inclined  beam,  bar,  or  strut  for  sustaining  compression  or 

tension.     See  Tie-Brace,  Sway-Brace.     (2)  A  platform  at  the  top  of  a 

shaft  on  which  miners  stand  to  work  the  tackle.     (3)  (Cornish)  Building 

at  pit  mouth. 
Brace  Heads. — Wooden  handles  or  bars  for  raising  and  rotating  the  rods 

when  boring  a  deep  hole. 

Braize. — (1)  Charcoal  dust.     (2)  Pine  coke  refuse  or  breeze. 
Brake  Sieve. — Hand  jigger. 
Brances. — Iron  pyrites  in  coal. 
Branch. — Small  vein  shooting  off  from  main  lode. 
Brashy. — Short  and  tender. 

Brasque. — A  mixture  of  clay  and  coke  or  charcoal  used  for  furnace  bottoms. 
Brass. — (1)  Iron  pyrites  in  coal.     (2)  An  alloy  of  copper  and  zinc. 
Brasses  (English). — Pitting  of  brass  in  plummer  blocks,  etc.,  for  diminishing 

the  friction  of  revolving  journals  that  rest  upon  them. 
Brat. — A  thin  bed  of  coal  mixed  with  pyrites  or  limestone. 
Brattice. — A  lining  or  partition. 

Brattice  Cloth. — Ducking  or  canvas  used  for  making  a  brattice. 
Brazzil  (North  of  England). — Iron  pyrites  in  coal. 
Breaker. — In  anthracite  mining,  the  structure  in  which  the  coal  is  broken, 

sized,  and  cleaned  for  market.     Known  also  as  Coal  Breaker. 
Breaker  Boy. — A  boy  who  works  in  a  coal  breaker. 
Breakstaff. — The  lever  for  blowing  a  blacksmiths'  bellows,  or  for  working  bore 

rods  up  and  down. 

Breakthrough. — A  narrow  passage  cut  through  a  pillar  connecting  rooms. 
Breast. — (1)  A  stall,  board,  or  room  in  which  coal  is  mined.     (2)  The  face  or 

wall  of  a  quarry  is  sometimes  called  by  this  name. 
Breast-and-PiUar. —  A  system  of  working  coal  by  boards  or  rooms   with  pillars 

of  coal  between  them. 
Breast  Wall  (English). — A  wall  built  to  prevent  the  falling  of  a  vertical  face 

cut  into  the  natural  soil. 

Breccia. — A  rock  composed  of  angular  fragments  cemented  together. 
Breeding  Fire. — See  Gob  Fire. 
Breese. — Fine  slack. 

Breeze. — Small  coke,  probably  same  as  braize  or  braise. 
Brettis  (Derbyshire). — A  timber  crib  filled  with  slack. 
Bridge. — (1)  A  platform  on  wheels  running  on  rails  for  covering  the  mouth 

of  a  shaft  or  slope.     (2)  A  track  or  platform  passing  over  an  inclined 

haulageway  and  which  can  be  raised  out  of  the  way  of  ascending  and 

descending  cars.     (3)  An  air  crossing. 

Bridle  Bar. — The  transverse  bar  connecting  the  points  of  a  switch. 
Bridle  Chains. — Short  chains  by  which  a  cage,  car,  or  gunboat  is  attached  to 

a  winding  rope;  of  use  in  case  the  rope  pulls  out  of  its  socket. 
Briquets. — Fuel  made  of  slack  or  culm  and  pressed  into  brick  form. 
Broaching  Bit. — A  tool  for  reopening  a  bore  hole  that  has  been  partially 

closed  by  swelling  of  the  walls. 
Brob. — A  spike  to  prevent  timber  slipping. 
Broil  (Cornish).— Traces  of  a  vein  in  loose  matter. 


1110  A  GLOSSARY  OF  MINING  TERMS 

Broken.— A.  district  of  coal  pillars  in  process  of  removal,  so  called  in  contra- 
distinction to  the  first  working  of  a  seam  by  bord-and-wall,  or  working  in 

the  "whole."    See  Whole  Working. 
Broken  Coal. — Anthracite  coal  that  will  pass  through  a  mesh  or  bars  about 

3i  to  4J  in.,  and  over  a  mesh  2f  in.  square. 
Bronce  (Mexican). — In  mining,  copper  or  iron  pyrites. 
Brooching. — Smoothing. 
Brow. — An  underground  roadway  leading  to  a  working  place  driven  either  to 

the  rise  or  to  the  dip. 

Brown  Coal. — Lignite.     A  fuel  classed  between  peat  and  bituminous  coal. 
Brown  Spar. — Dolomite  containing  carbonate  of  iron. 
Brownstone. — (1)  Decomposed  iron  pyrites.     (2)  Brown  sandstone. 
Brujula  (Mexican). — A  surveyors'  (or  marine)  magnetic  compass. 
Brush. — (1)  To  mix  air  with  the  gas  in  a  mine  working  by  swinging  a  jacket, 

etc.,  which  creates  a  current.     (2)  To  "brush"  the  roof  is  to  take  down 

some  of  the  roof  slate  to  increase  the  height  or  headroom. 
Bryle  (Cornish). — Traces  of  a  vein  in  loose  matter. 
Bucket. — (1)  An  iron  or  wooden  receptacle  for  hoisting  ore,  or  for  raising  rock 

in  shaft  sinking.     (2)  The  top  valve  or  clack  of  a  pump. 
Bucket  Pump. — A  lifting  pump,  consisting  of  buckets  fastened  to  an  endless 

belt  or  chain. 

Bucket  Sword. — A  wrought-iron  rod  to  which  the  pump  bucket  is  attached. 
Bucket  Tree. — The  pipe  between  the  working  barrel  and  the  wind  bore. 
Bucking  Hammer. — An  iron  disk,  provided  with  a  handle,  used  for  breaking 

up  minerals  by  hand. 
Buckstay. — An  iron  or  steel  brace  resting  upon  or  built  into  a  boiler  setting  or 

furnace  wall  to  support  the  brickwork. 
Buckwheat. — Anthracite  coal  that  will  pass  through  a  mesh  of  about  $  in. 

and  over  a  mesh  \  in. 
Buddling. — Washing. 

Bug  Dust. — Fine  coal;  the  cutting  produced  by  a  chain  machine  or  puncher. 
Buggy. — A  small  mine  car. 

Bug  Hole. — A  small  cavity  usually  lined  with  crystals. 
Building. — A  built-up  block  or  pillar  of  stone  or  coal  to  support  the  roof. 
Bulkhead. — (1)  A  tight  partition  or  stopping.     (2)  The  end  of  a  flume  carry- 
ing water  for  hydraulicking. 

Bull. — An  iron  rod  used  in  ramming  clay  to  line  a  shot  hole. 
Bulldog. — A  barney. 
Bull  Engine. — A  single,  direct-acting  pumping  engine,  the  pump  rods  forming 

a  continuation  of  the  piston  rod. 
Butter  Shot. — A  second  shot  put  in  close  to,  and  to  do  the  work  not  done  by, 

a  blown-out  shot,  loose  powder  being  used. 
Bulling. — Lining  a  shot  hole  with  clay. 
Bull  Pump. — A  single-acting  pumping  engine  in  which  the  steam  cylinder  is 

placed  over  the  shaft  or  slope  and  the  pump  rods  are  attached  directly  to 

the  piston  rod.     The  steam  enters  below  the  piston  and  raises  the  pump 

rods;  the  water  is  pumped  on  the  down  stroke  by  the  weight  of  the 

rods. 

Bull  Pup. — A  worthless  claim. 
Bull  Wheel. — (1)  A  wheel  on  which  the  rope  carrying  the  boring  rod  is  coiled 

when  boring  by  steam  machinery.     (2)   The  principal  wheel  of  any 

machine,  usually  a  driving  wheel. 
Bully. — A  miners'  hammer. 
Bump. — See  Bounce. 

Bunding. — A  staging  in  a  level  for  carrying  debris. 
Bunkers. — (1)  Steam  coal  consumed  on  board  ship.     (2)  Receptacles  placed 

near  a  boiler  for  holding  a  supply  of  fuel. 
Bunions. — Timbers  placed  horizontally  across  a  shaft  or  slope  to  carry  the 

cage  guides,  pump  rods,  column  pipe,  etc.;  also,  to  strengthen  the  shaft 

timbering. 
Burden. — (1)  Earth  overlying  a  bed  of  useful  mineral.     (2)  The  proportion  of 

ore  and  flux  to  fuel  in  the  charge  of  a  blast  furnace. 
Burr.— Solid  rock. 
Burrow. — Refuse  heap. 

Buscones  (Spanish). — Prospectors,  fossickers,  tribute  workers. 
Bush. — To  line  a  circular  hole  with  a  ring  of  metal,  to  prevent  the  hole  from 

wearing  out. 
Butt.— (1)  Coal  surface  exposed  at  right  angles  to  the  face;  the  "ends"  of 


A  GLOSSARY  OF  MINING  TERMS  1111 

the  coal.  (2)  The  butt  of  a  slate  quarry  is  where  the  overlying  rock 
comes  in  contact  with  an  inclined  stratum  of  slate  rock. 

Butt  Entry. — A  gallery  driven  at  right  angles  with  the  butt  joint. 

Butterfly  Valve. — A  circular  valve  that  revolves  on  an  axis  passing  through  its 
center. 

Butt  Heading. — See  Butt  Entry. 

Butty. — A  partner  in  a  contract  for  driving  or  mining;  a  comrade,  crony. 
Sometimes  called  "Buddy." 

By  Level. — A  side  level  driven  for  some  unusual  but  necessary  purpose. 

Byproduct  Oven. — A  coke  oven  arranged  to  conserve  and  recover  the  various 
byproducts  of  the  coking  process. 

Byproducts. — Products  of  coking  other  than  coke.  The  more  common  by- 
products are  gas,  tar,  benzol  and  ammonium  sulphate. 

Caballo  (Mexican). — A  "horse"  or  mass  of  barren  rock  in  a  vein. 

Cabin. — (1)  A  miner's  house.     (2)  A  small  room  in  the  mine  for  the  use  of  the 

officials. 

Cable  Drilling. — Rope  drilling. 

Cage. — A  platform  on  which  mine  cars  are  raised  to  the  surface. 
Cage  Guides. — Vertical  rods  of  pine,  iron,  or  steel,  or  wire  rope,  fixed  in  a 

shaft,  between  which  cages  run,  and  whereby  they  are  prevented  from 

striking  one  another  or  against  any  portion  of  the  shaft. 
Cager. — The  person  that  puts  the  cars  on  the  cage  at  the  bottpm  or  top  of  the 

shaft. 
Cage  Seat. — Scaffolding,  sometimes  fitted  with  strorrg  springs,  to  receive  the 

shock,  and  on  which  the  cage  drops  when  reaching  the  pit  bottom. 
Cage  Sheets. — Short  props  or  catches  on  which  cages  stand  during  caging  or 

changing  cars. 

Caking  Coal. — Coal  that  agglomerates  on  the  grate. 
Cola  (Spanish). — Prospecting  pit. 
Calcareous. — Containing  lime. 
Calcine. — To  heat  a  substance,  not  sufficiently  to  melt  it,  but  enough  to  drive 

off  the  volatile  contents. 
California  Pump. — A  rude  pump  made  of  a  wooden  box  through  which  an 

endless  belt  with  floats  circulates;  used  for  pumping  water  from  shallow 

ground. 

Catty s  (Cornish). — Stratified  rocks  traversed  by  lodes. 
Cam. — (1)  A  curved  arm  attached  to  a  revolving  shaft  for  raising  stamps. 

(2)   Carbonate  of  lime  and  fluorspar,  found  on  the  joints  of  lodes. 
Camino   (Mexican). — Any  gallery,  winze,  or  shaft  inside  of  a  mine  used  for 

general  transit. 

Campaign. — The  length  of  time  a  furnace  remains  in  blast. 
Cafiada  (Mexican). — See  Barranca. 
Canch,  or  Caunche. — (1)  A  thickness  of  stone  required  to  be  removed  to  make 

height  or  to  improve  the  gradient  of  a  road  at  a  fault.     If  above  a  seam, 

it  is  termed  a  "top  canch;"  if  below,  a  "bottom  canch."     (2)  A  trench 

with  sloping  sides  and  very  narrow  bottom. 
Cand  (Cornish). — Fluorspar. 
Cank  (Derbyshire). — Whinstone. 
Canker. — The  ocherous  sediment  in  coal-pit  waters. 
Cannel  Coal.— See  Classification  of  Coals  (page  378). 

Canon  (Mexican).— (1)  A  level,  drift,  or  gallery  within  a  mine.     (2)  A  steep- 
sided  ravine.    Canon  de  Guia.—A.  drift  along  the  vein. 
Cants  (English).— The  pieces  forming  the  ends  of  buckets  of  a  waterwheel 
Cap.— (1)  A  piece  of  plank  placed  on  top  of  a  prop.     See,  also,  Collar.     ( 

The  pale  bluish  elongation  of  the  flame  of  a  lamp  caused  by  the  pre: 

of  RclS. 

Cap  Rock. — The  upper  rock  that  covers  the  bed  rock. 

Capstan.— A.  vertical  axle  used  for  heavy  hoisting,  and  worked  by  horizontal 
arms  or  bars. 

Captain.— Cornish  name  for  manager  or  boss  of  a  mine. 

Cor  __Any  car  used  for  the  conveyance  of  coal  along  the  gangways  or  haul- 
age roads  of  a  mine. 

Carat. — A  weight  nearly  equal  to  4  grams.  , 

Carbon.— A  combustible  elementary  substance  forming  the  largest  compo- 
nent part  of  coal. 

Carbonaceous. — Coaly,  C9ntainmg  carbon  or  coal. 

Carbonate, — Carbonic  acid  combined  with  a  base. 


1112  A  GLOSSARY  OF  MINING  TERMS 

Carboniferous. — Containing  or  carrying  coal. 

Cargo, (Mexican). — A  charge.  A  mule  load,  generally  of  300  lb.,  but  variable 
in  different  parts  of  Mexico. 

Carriage. — See  Cage  and  Slope  Cage. 

Cartridge. — Paper  or  waterproof  cylindrical  case  filled  with  explosive  forming 
the  charge  for  blasting. 

Cascajo  (Mexican). — Gravel. 

Case. — A  fissure  admitting  water  into  a  mine. 

Case-harden. — To  convert  the  outer  surface  of  wrought  iron  into  hard  steel 
by  heating  it  while  in  contact  with  charcoal,  cyanide,  etc.,  and  quenching. 

Casing. — Tubing  inserted  in  a  bore  hole  to  keep  out  water  or  to  protect  the 
sides  from  collapsing. 

Cast  Iron. — Pig  iron  that  contains  carbon  (up  to  5%),  silicon,  sulphur,  phos- 
phorus, etc. 

Cata  (Spanish). — A  mine  denounced  but  not  worked. 

Catches. — (1)  Iron  levers  or  props  at  the  top  and  bottom  of  a  shaft.  (2) 
Stops  fitted  on  a  cage  to  prevent  cars  from  running  off. 

Cauf  (North  of  England). — A  coal  bucket  or  basket. 

Cauldron  Bottoms. — The  fossil  remains  or  the  "casts"  of  the  trunks  of  sigil- 
laria  that  have  remained  vertical  above  or  below  the  seam. 

Caulk. — To  fill  seams  or  joints  with  something  to  prevent  leaking. 

Counter,  or  Counter  Lode  (Cornish). — A  vein  running  obliquely  across  the 
regular  veins  of  the  district. 

Cave,  or  Cave  In. — A  caving-in  of  the  roof  strata  of  a  mine,  sometimes  ex- 
tending to  the  surface. 

Cavils. — Lots  drawn  by  the  hewers  each  quarter  year  to  determine  their 
working  places. 

Cement. — A  binding  material. 

Center. — A  temporary  support,  serving  at  the  same  time  as  a  guide  to  the 
masons,  placed  under  an  arch  during  the  progress  of  its  construction. 

Centrifugal  Force. — A  force  drawing  away  from  the  center. 

Centripetal  Force. — A  force  drawing  toward  the  center. 

CH 4. — Marsh  gas  (see  page  859) . 

Chain.— A  measure  66  or  100  ft.  long,  divided  into  100  links. 

Chain-Brow  Way. — An  underground  inclined  plane  worked  on  the  endless- 
chain  system  of  haulage. 

Chain  Pillar. — A  pillar  left  to  protect  the  gangway  and  air-course,  and  run- 
ning parallel  to  these  passages. 

Chain  Road. — An  underground  wagonway  worked  on  the  endless-chain  sys- 
tem of  haulage. 

Chair. — Sometimes  applied  to  keeps. 

Chamber. — See  Breast. 

Char co  (Mexican). — A  pool  of  water. 

Charge. — (1)  The  amount  of  powder  or  other  explosive  used  in  one  blast  or 
shot.  (2)  The  material  fed  into  a  furnace  at  one  time. 

Charquear( Mexican). — To  dip  out  water  from  pools  within  the  mine,  throw- 
it  into  gutters  or  pipes  that  will  conduct  it  to  the  shaft. 

Check. — A  metal  token  used  to  identify  the  cars  loaded  by  each  particular 
miner. 

Check-Battery. — A  battery  to  close  the  lower  part  of  a  chute,  acting  as  a 
check  to  the  flow  of  coal  and  as  an  air  stopping. 

Checker  Coal. — Anthracite  coal  that  seems  to  be  made  up  of  rectangular 
grains. 

Check-Weighman. — A  man  appointed  and  paid  by  the  miners  to  check  the 
weighing  of  the  coal  at  the  surface. 

Cheek. — Wall. 

Chestnut  Coal. — Anthracite  coal  that  will  pass  through  a  mesh  If  in.  square 
and  over  a  mesh  f  in.  square  (see  page  952). 

Chiflon  (Mexican). — A  narrow  drift  directed  obliquely  downwards,  any 
pipe  from  which  issues  water  or  air  under  pressure,  or  at  high  velocity. 

Chilian  Mill. — A  roller  mill  for  crushing  ore  or  other  material. 

Chill  Hardening. — Giving  a  greater  hardness  to  the  outside  of  cast  iron  by 
pouring  it  into  iron  molds,  which  causes  the  skin  of  the  casting  to  cool 
rapidly. 

Chimney. — A  furnace  or  air  stack. 

Chinese  Pump. — Like  a  California  pump,  but  made  entirely  of  wood. 

Chock. — (1)  A  square  pillar  for  supporting  the  roof,  constructed  of  prop 
timber  laid  up  in  alternate  cross-layers,  in  log-cabin  style,  the  center 


A  GLOSSARY  OF  MINING  TERMS  1113 

being  filled  with  waste.  (2)  A  wooden  or  other  block  used  to  prevent 
the  movement  of  a  car  or  other  body.  (3)  To  secure  with  chocks. 

Chokedamp. — See  Blackdamp. 

Churn  Drill. — A  long  iron  bar  -with  a  cutting  end  of  steel,  worked  by  raising 
and  letting  it  fall.  When  worked  by  blows  of  a  hammer  or  sledge,  it 
is  called  a  "jumper." 

Chute  (also  spelled  Shute). — (1)  A  narrow  inclined  passage  in  a  mine,  down 
which  coal  or  ore  is  either  pushed  or  slides  by  gravity.  (2)  The  load- 
ing chute  of  a  tipple. 

Cielo. —  (Mexican). — A  ceiling.      Trabajar  de  Cielo. — Overhead   stoping. 

Clack. — A  valve  that  is  opened  and  closed  by  the  force  of  the  water;  a  check 
valve. 

Clack  Door. — The  opening  into  the  valve  chamber  to  facilitate  repairs  and 
renewals  without  unseating  the  pump  or  breaking  the  connections. 

Clack  Piece. — The  casting  forming  the  valve  chamber. 

Clack  Seal. — The  receptacle  for  the  valve  to  rest  on. 

Cloggy  (North  of  England). — When  coal  is  tightly  joined  to  the  roof. 

Claim. — A  portion  of  ground  staked  out  and  held  by  virtue  of  a  miner's  right. 

Clanny. — A  type  of.safety  lamp  invented  by  Dr.  Clanny. 

Claslic. — Constituted  of  rocks  or  minerals  that  are  fragments  derived  from 
other  rocks. 

Clay  Band. — Argillaceous  iron  ore;  common  in  many  coal  measures. 

Clay  Course. — A  clay  seam  or  gouge  found  at  the  sides  of  some  veins. 

Claying  Bar. — A  bar  for  molding  clay  in  a  wet  bore  hole. 

Clearance. — (1)  The  distance  between  the  piston  at  the  end  of  its  stroke  and 
the  end  of  the  cylinder^  (2)  The  volume  or  entire  space  filled  with 
steam  at  end  of  a  stroke,  including  the  space  between  piston  and  cylinder 
head,  and  the  steam  ducts  to  the  valve  seat. 

Cleat. — (1)  Vertical  cleavage  of  coal  seams,  irrespective  of  dip  or  strike.  (2) 
A  small  piece  of  wood  nailed  to  two  planks  to  keep  them  together,  or 
nailed  to  any  structure  to  make  a  support  for  something  else. 

Cleavage. — The  property  of  splitting  more  readily  in  some  directions  than  in 
others. 

Clinometer. — An  instrument  used  to  measure  the  angle  of  dip. 

Clod. — Soft  and  tough  shale  or  slate  forming  the  roof  or  floor  of  a  coal  seam. 

Clunch  (English). — Under  clay,  fireclay. 

Clutch. — A  device  for  transmitting  motion  at  will  from  one  shaft  to  another 
or  to  some  other  machine  part  such  as  a  pulley,  or  vice  versa. 

Coal  Breaker. — See  Breaker. 

Coal  Cutter. — A  machine  for  holing  or  undercutting  coal. 

Coal  Dust. — Very  finely  powdered  coal  suspended  in  the  airways  or  deposited 
along  the  passages  of  a  mine. 

Coal  Measures. — Strata  of  coal  with  the  attendant  rocks. 

Coal  Pipes  (North  of  England). — Very  thin  irregular  coal  beds. 

Coal  Road. — An  underground  roadway  or  heading  in  coal. 

Coal  Smut. — See  Blossom. 

Coaly  Rashings. — Soft  dark  shale,  in  small  pieces,  containing  much  carbona- 
ceous matter. 

Cobbing  Hammer. — A  short  two-faced  hammer  for  breaking  minerals  to  sizes. 

Cockermeg,  or  Cockers. — Timber  used  to  hold  coal  face  while  it  is  being 
undercut. 

Cod  (North  of  England). — The  bearing  of  an  axle. 

Cojer  (Derbyshire). — To  calk  a  shaft  by  ramming  clay  behind  the  lining. 

Coffer. — Mortar  box  of  a  battery. 

Coffer  Dam. — An  enclosure  built  in  the  water,  and  then  pumped  dry  so  as  to 
permit  masonry  or  other  work  to  be  carried  on  inside  of  it. 

Coffin  (Cornish). — An  old  pit. 

Cog. — (1)  A  chock.  (2)  A  wooden  gear  tooth.  (3)  Loosely,  any  gear  tooth 
or  even  gear  wheel 

Cohete  (Mexican). — A  rocket;  applied  to  a  blast  within  a  mine  or  outside. 

Coil  Drag. — A  tool  for  picking  pebbles,  etc.,  from  drill  holes. 

Coke. — The  fixed  carbon  and  ash  of  coal  sintered  together. 

Collar. — (1)  A  flat  ring  surrounding  anything  closely.  (2)  Collar  of  a  mine 
shaft  is  the  first  wood  frame  of  the  shaft.  (3)  The  bar  or  crosspiece  of  a 
framing  in  entry  timbering.  (4)  The  mouth  or  portal  of  a  slope  or  the 
first  set  of  timber  therein. 

Colliery. — The  whole  coal  mine  plant,  including  the  mine  and  all  adjuncts. 

Colliery  Warnings  (English).— Telegraphic  messages  sent  from  signal-service 


1114  A  GLOSSARY  OF  MINING  TERMS 

stations  to  the  principal  colliery  centers  to  warn  managers  of  mines 

when  sudden  falls  of  the  barometer  occur. 
Column,  or  Column  Pipe. — The  pipe  conveying  the  drainage  water  from  the 

mine  to  the  surface. 
Comer   (Mexican). — To  eat.     Comer 'se  los  Pilares. — To  take  out  the  last 

vestiges  of  mineral  from  the  sides  and  rock  pillars  of  a  mine. 
Conchoidal. — Shell-like,  such  as  the  curved  fracture  of  flint. 
Concrete. — Artificial  stone,  formed  by  mixing  broken  stone,  gravel,  etc.,  with 

lime,  cement,  tar,  or  other  binder.     When  hydraulic  cement  is  used 

instead  of  lime,  the  mixture  is  called  belon  (English). 
Concretion. — A  cemented   aggregation  of  one  or  more   kinds  of  minerals 

around  a  nucleus. 
Conduit. — (1)  A  covered  waterway.     (2)  An  airway.     (3)  A  pipe  or  box  for 

enclosing  and  protecting  an  electrical  conductor. 
Conduit  Hole. — A  flat  hole  drilled  for  blasting  up  a  thin  piece  in  the  bottom 

of  a  level. 

Conductors  (English). — See  Guides. 
Conformable. — Strata  are  conformable  when  they  lie  one  over  the  other  with 

the  same  dip. 
Conglomerate. — The  rock  formation  underlying  the  Coal  Measures;  a  rock 

containing  or  consisting  of  pebbles,   or  of  fragments  of  other  rocks 

cemented  together;  English  Pudding  Rock  or  millstone  grit. 
Conical  Drum. — The  rope  roll  or  drum  of  a  winding  engine,  constructed  in 

the  form  of  two  truncated  cones  placed  back  to  back,  the  outer  ends 

being  usually  the  smaller  in  diameter. 
Contact. — Union  of  different  f9rmations. 
Contact  Lode  or   Vein. — A  vein  lying  between  two  differently  constituted 

rocks. 

Contour. — (I)  The  line  that  bounds  the  figure  of  an  object.     (2)  In  survey- 
ing, a  contour  line  is  a  line  every  point  of  which  is  at  an  equal  elevation. 
Contramina  (Mexican). — Countermine.     Any  communication  between  two 

or  more  mines.  Also,  a  tunnel  communicating  with  a  shaft. 
Cope,  or  Coup.— An  exchange  of  working  places  between  hewers. 
Corbond. — An  irregular  mass  from  a  lode. 

Cord. — (1)  A  cord  weighs  about  8  tons.     (2)  '128  cu.  ft.  of  firewood. 
Core  Drill. — A  diamond  or  other  hollow  drill  for  securing  cores. 
Cores. — Cylinder-shaped  pieces  of  rock  produced  by  the  diamond-drill  sys- 
tem of  boring. 

Corf. — A  mine  wagon  or  tub. 
Cornish  Pumps. — A  single-acting  pump,  in  which  the  motion  is  transmitted 

through  a  walking  beam;  in  other  respects  similar  to  a  Bull  Pump. 
Cor  tar  Pillar  (Mexican). — To  form  a  rock  support  or  pillar  within  a  mine, 

at  the  opening  of  a  cross-cut  or  elsewhere. 
Cortar  Sogas  (Mexican). — Literally,  to  cut  the  ropes.     To  abandon  the  mine, 

taking  away  everything  useful  or  movable. 
Corve. — A  mining  wagon  or  tub. 

Costean  (Cornish). — To  prospect  a  lode  by  sinking  pits  on  its  supposed  course. 
Costeaning. — Trenching  for  a  lode. 
Cost  Book  (Cornish). — Mining  accounts. 

Cotton  Rock. — (1)   Decomposed  chert.     (2)  A  variety  of  earthy  limestone. 
Coulee. — (1)  A  solidified  stream  or  sheet  of  lava  extending  down  a  volcano, 

often  forming  a  ridge  or  spur.     (2)  A  deep  gulch  or  water  channel, 

usually  dry. 
Counter. — (1)  A  cross-vein.     (2)   (English)   An  apparatus  for  recording  the 

number  of  strokes  made  by  a  Cornish  pumping  engine  or  other  machine, 

or  the  revolutions  of  a  shaft  or  pully.     (3)   A  secondary  haulageway  in 

a  coal  mine. 
Counter  chute. — A  chute  down  which  coal  is  dumped  to  a  lower  level  or 

gangway. 
Counter  gangway. — A  level  or  gangway  driven  at  a  higher  level  than  the 

main  one. 

Country. — The  formation  traversed  by  a  lode. 
Country  Rock. — The  main  rock  of  the  region  through  which  the  veins  cut,  or 

that  surrounding  the  veins. 

Course. — The  direction  of  a  line  in  regard  to  the  points  of  compass. 
Coursing  or  Coursing  the  Air. — Conducting  it  through  the  different  portions 

of  a  mine  by  means  of  doors,  stoppings,  and  brattices. 
Cow. — A  self-acting  brake. 


A  GLOSSARY  OF  MINING  TERMS  1115 

Coyoting.  —  Irregular  mining  by  small  pits. 

Crab.  —  A  variety  of  windlass  or  capstan  consisting  of  a  short  shaft  or  axle, 
either  horizontal  or  vertical,  which  serves  as  a  rope  drum  for  raising' 
weights;  it  may  be  worked  by  a  winch  or  handspikes. 

Crab  Holes.  —  Holes  often  met  with  in  the  bed  rock  of  alluvial.  Also  depres- 
sions on  the  surface  owing  to  unequal  disintegration  of  the  underlying 
rock;  a  sink  hole  or  pot  hole. 

Cradle  Dump.  —  A  rocking  tipple  for  dumping  cars.     See  Dump. 

Cramp  (English).  —  (1)  A  short  bar  of  metal  having  its  two  ends  bent  down- 
wards at  right  angles  for  insertion  into  two  adjoining  pieces  of  stone, 
wood,  etc,,  to  hold  them  together.  (2)  A  pillar  left  for  support  in  a 
mine. 

Cranch.  —  Part  of  a  vein  left  by  previous  workers. 

Crane  (English).  —  A  hoisting  machine  consisting  of  a  revolving  vertical 
post  or  stalk,  a  projecting  jib,  and  a  stay  for  sustaining  the  outer  end  of 
the  jib;  these  do  not  change  their  relative  positions  as  they  do  in  a  der- 
rick. There  is  also  a  rope  drum  with  winding  rope,  etc.  (2) 


movable  or  traveling  lifting  d 
heaval  of 


(2)  Any 


Creep.  —  The  gradual  upheaval  of  the  floor  or  sagging  of  the  roof  of  mine 

workings  due  to  the  weighting  action  of  the  roof  and  a  tender  floor. 
Creston  (Mexican).  —  The  outcrop  or  apex  of  a  vein  or  mineral  deposit. 
Crevice.  —  A  fissure. 
Criadero  (Mexican).  —  (1)  A  mineral  deposit  of  irregular  form,  not  vein-like. 

(2)  Any  mineral  deposit.     This  latter  is  the  more  modern  sense,  and 

the  word  is  so  used  in  the  mining  laws  at  present  in  force  in  Mexico. 
Crib.  —  (1)  A  structure  composed  of  horizontal  timbers  laid  on  one  another, 

or  a  framework  built  like  a  log  cabin.     See  Chock.     (2)  A  miner's  lunch- 

eon.    (3)  See  Curb. 
Crib  Kettle.  —  A  dinner  pail. 
Cribbing.  —  Close  timbering,  as  the  lining  of  a  shaft,  or  the  construction  of 

cribs  of  timber,  or  timber  and  earth  or  rock  to  support  a  roof. 
Cribble.  —  A  sieve. 

Crisol  (Mexican).  —  A  crucible  of  any  kind. 
Crop.  —  See  Outcrop. 

Crop  Fall.  —  A  caving  in  of  the  surface  at  or  near  the  outcrop  of  a  bed  of  coal. 
Cropping  Coal.  —  The  leaving  of  a  small  thickness  of  coal  at  the  bottom  of  the 

seam  in  a  working  place,  usually  in  order  to  keep  back  water.     The  coal 

so  left  is  termed  "Cropper  Coal." 

Cropping  Out.  —  Appearing  at  the  surface;  outcropping. 
Croppings.  —  Portions  of  a  vein  as  seen  exposed  at  the  surface. 
Cross-Course.  —  A  vein  lying  more  or  less  at  right  angles  to  the  regular  vein  of 

the  district. 
Crosscut.  —  (1)  A  tunnel  driven  through  or  across  the  measures  from  one 

seam  to  another.     (2)  A  small  passageway  driven  at  right  angles  to  the 

main  gangway  to  connect  it  with  a  parallel  gangway  or  air-course. 
Crosses  and  Holes  (Derbyshire).  —  Made  in  the  ground  by  the  discoverer  of  a 

lode  to  temporarily  secure  possession. 
Cross-Heading.  —  A  passage  driven  for  ventilation  from  the  airway  to  the 

gangway,    or   from    one    breast    through    the    pillar   to  the  adjoining 

working. 
Cross-Heading,  or  Cross-Gateway.  —  A  road  kept  through  goaf  and  cutting  off 

the  gateways  at  right  angles  or  diagonally. 
Cross-Hole.  —  See  Crosscut  (2). 
Cross-Latches.  —  See  Latches. 
Cross-Vein.  —  An  intersecting  vein. 
Crouan  (Cornish).  —  Granite. 

Crowbar.  —  A  strong  iron  bar  with  a  slightly  curved  or  flattened  end. 
Crowfoot.  —  A  tool  for  drawing  broken  boring  rods. 
Crown  Tree.  —  A  piece  of  timber  set  on  props  to  support  the  roof. 
Crucero  (Mexican).  —  A  crosscut  for  ventilation  to  get  around  a  horse,  or  to 

prospect  for  the  vein. 
Crucible.  —  (1)   The  bottom  of  a  cupola  furnace  in  which  the  molten  materials 

collect.     (2)   Pots  for  smelting  assays  in  or  used  in  making  coal  analyses. 
Crush.  —  See  Squeeze,  Thrust. 

Crusher.  —  A  machine  used  for  crushing  ores,  rock  or  coal. 
Crushing.  —  Reduction  of  mineral  in  size  by  machinery. 
Crystal.  —  A  solid  of  definite  geometrical  form  which  mineral  (or  sometimes 

organic)  matter  has  assumed. 


1116  A  GLOSSARY  OF  MINING  TERMS 

Culm. — Anthracite-coal  dirt. 

Culm  Bank,  or  Culm  Dump. — Heaps  of  culm  now  generally  kept  separate 

from  the  rock  and  slate  dumps. 
Cuna   (Mexican). — Literally,  a  wedge.     A  short  drill  or  picker  generally 

known  in  the  United  States  as  a  "gad." 
Cundy. — -The  open  space  in  the  gob  of  long-wall  work. 
Cupel. — A  cup  made  of  bone  ash  for  absorbing  litharge. 
Curb. — (1)  A  timber  frame  intended  as  a  support  or  foundation  for  the  lining 

of  a  shaft.     (2)  The  heavy  frame  or  sill  at  the  top  of  a  shaft. 
Curbing.— The  wooden  lining  of  a  shaft. 
Curtain. — A  sheet  of  canvas  or  other  material  used  to  control  or  deflect  an 

air  current. 

Cut. — (1)  To  strike  or  reach  a  vein.     (2)  To  excavate  in  the  side  of   a  hill. 
Cutter. — A  term  employed  in  speaking  of  any  coal-cutting  or   rock-cutting 

machines;  the  men  operating  them,  or  the  men  engaged  in  underholing 

by  pick  or  drill. 
Cutting  Down. — To  cut  down  a  shaft  is  to  increase  its  sectional  area. 

Dam. — A  timber  bulkhead,  or  a  masonry  or  brick  stopping  built  to  prevent 
the  water  in  old  workings  from  flooding  other  workings,  or  to  confine 
the  water  in  a  mine  flooded  to  drown  out  a  mine  fire. 

Damp. — Mine  gases  and  gaseous  mixtures  are  called  damps.  See  also  After- 
damp, Blackdamp,  Firedamp,  Stinkdamp. 

Dan  (North  of  England). — A  truck  without  wheels. 

Danger  Board. — See  Fireboard. 

Dant  (North  of  England). — Soft  inferior  coal. 

Dap. — A  notch  cut  in  a  timber  to  receive  another  timber. 

Datum  Water  Level. — The  level  at  which  water  is  first  struck  in  a  shaft  sunk 
on  a  reef  or  gutter.. 

Davy. — A  safety  lamp  invented  by  Sir  Humphrey  Davy. 

Day. — Light  seen  at  the  top  of  a  shaft. 

Day  Fall. — See  Crop  Fall. 

Day  Shift. — The  relay  of  men  working  in  the  daytime. 

Dead. — The  air  of  a  mine  is  said  to  be  dead  or  heavy  when  it  contains  car- 
bonic-acid gas,  or  when  the  ventilation  is  sluggish. 

Dead. — (1)  Unproductive.     (2)  Unventilated. 

Dead  Roast. — To  completely  drive  off  all  volatile  substances. 

Deads. — Waste  or  rubbish  from  a  mine. 

Dead  Work. — 'Exploratory  or  prospecting  work  that  is  not  directly  productive; 
brushing  roof,  lifting  bottom,  cleaning  up  falls,  blowing  rock,  etc. 

Dean  (Cornish). — The  end  of  a  level. 

Debris. — Fragments  from  any  kind  of  disintegration. 

Deep  (English). —  (1)  "To  the  deep,"  toward  the  lower  portion  of  a  mine; 
hence,  the  lower  workings.  (2)  A  pasasge  driven  downward  in  the 
measure  being  worked.  The  main  deep  is  the  principal  or  hoisting  slope. 

Delta. — A  triangularly  shaped  piece  of  alluvial  land  at  the  mouth  of  a  river. 

Demasia  (Mexican). — A  piece  of  unoccupied  ground  between  two  mining 
concessions. 

Denudation. — The  laying  bare  by  water  or  other  agency. 

Denuncio  (Mexican). — Denouncement.  The  act  of  applying  for  a  mining 
concession  under  the  old  mining  laws. 

Deposit. — (1)  Irregular  mineral  bodies  not  veins.  (2)  A  bed  or  any  sedi- 
mentary formation. 

Deputy  (English). —  (1)  A  man  who  fixes  and  withdraws  the  timber  supporting 
the  roof  of  a  mine,  and  attends  to  the  safety  of  the  roof  and  sides,  builds 
stoppings,  puts  up  bratticing,  and  looks  after  the  safety  of  the  hewers, 
etc.  (2)  An  underground  official  -who  sees  to  the  general  safety  of  a 
certain  number  of  stalls  or  of  a  district,  but  does  not  set  the  timber  him- 
self, although  he  has  to  see  that  it  is  properly  and  sufficiently  done.  (3) 
(American)  A  deputy  sheriff. 

Derrick. — (!•)  A  crane  in  which  the  rope  or  chain  forming  the  stay  can  be  let 
out  or  hauled  in  at  pleasure,  thus  altering  the  inclination  of  a  jib. 
(2)  The  structure  erected  to  sink  a  drill  hole  and  the  framework  above 
shafts  are  sometimes  called  by  this  name. 

Derrumbe,  or  Derrumbamineto  (Mexican). — The  caving  in  of  the  whole  or  a 
portion  of  a  mine. 

Desaguador  (Spanish). — A  water  pipe  or  drain. 

Desague  (Mexican). — Drainage  of  a  mine  by  any  means. 


A  GLOSSARY  OF  MINING  TERMS  1117 

Descargar  (Mexican). — Literally,  "to  unload."  Descargar  un  Homo. — To 
tear  down  a  furnace. 

Descubridora  (Mexican). — The  first  mine  opened  in  a  new  district  or  on  a 
new  mineral  deposit. 

Desmontar  (Mexican). — Literally,  to  clear  away  underbrush.  In  mining,  to 
take  away  useless  and  barren  rocks;  to  remove  rubbish. 

Despensa  (Mexican). — (1)  A  pantry  or  storeroom.  (2)  A  secure  room  to  lock 
up  rich  ore. 

Dfspoblar  (Mexican). — To  suspend  work  in  a  mine. 

Dessue  (Cornish). — To  cut  away  the  ground  beside  a  thin  vein  so  as  to 
remove  the  latter  entire. 

Destajo  (Mexican). — (1)  A  contract  to  do  any  kind  of  work  in  9r  about  a  mine 
or  elsewhere  for  a  fixed  price.  (2)  Piece  work,  as  distinguished  from 
time  work.  Destajero. — A  contractor  for  piece  work. 

Detaching  Hook. — A  self-acting  mechanical  contrivance  for  setting  free  a 
winding  rope  from  a  cage  when  the  latter  is  raised  beyond  a  certain  point 
in  the  head-gear;  the  rope  being  released,  the  cage  remains  suspended  in 
the  frame. 

Diagonal  Joints. — Joints  diagonal  to  the  strike  of  the  cleavage. 

Dial  (English). — An  instrument  similar  to  a  surveyor's  compass,  with  vernier 
attached. 

Dialing. — Surveying. 

Die. — The  bottom  iron  block  of  a  battery,  or  grinding  pan  on  which  the  shoe 
acts. 

Digger  or  Dredge. — A  machine  for  removing  coal  from  the  bed  of  streams,  the 
coal  having -washed  down  from  collieries  or  culm  banks  above. 

Digging. — Mining  operations  in  coal  or  other  minerals. 

Dike. — See  also  Dyke. 

Ditties,  or  Ginneys. — Short  self-acting  inclines  where  one  or  two  tubs  at  a  time 
are  run. 

Dip. — (1)  To  slope  downwards.  (2)  The  inclination  of  strata  with  a  horizon- 
tal plane.  (3)  The  lower  workings  of  a  mine. 

Dip  Joint. — Vertical  joints  about  parallel  to  the  direction  of  the  cleavage  dip. 

Dippa  (Cornish). — A  small  catch- water  pit. 

Dirt  Fault. — A  confusion  in  a  seam  of  coal,  the  top  and  bottom  of  the  seam 
being  well  defined,  but  the  body  of  the  vein  being  soft  and  dirty. 

Disintegration. — Separation  by  mechanical  means,  not  by  decomposition. 

Ditch. — (1)  The  drainage  gutter  in  a  mine.  (2)  A  drainage  gutter  on  the  sur- 
face. (3)  An  open  conveyor  of  water  for  hydraulic  or  irrigation  purposes. 

Divide. — The  top  of  a  ridge,  hill,  or  mountain. 

Dividing  Slate. — A  stratum  of  slate  separating  two  benches  of  coal.  See 
Parting. 

Divining,  or  Dowsing  Rod. — A  small  forked  hazel  twig  that,  when  held  loosely 
in  the  hands,  is  supposed  to  dip  downwards  when  passing  over  water  or 
metallic  minerals. 

Dizzue  (Cornish). — See  Dessue. 

Dog. — (1)  An  iron  bar,  spiked  at  the  ends,  with  which  timbers  are  held 
together  or  steadied.  (2)  A  short  heavy  iron  bar,  used  as  a  drag  behind 
a  car  or  trip  of  cars  when  ascending  a  slope  to  prevent  their  running  back 
back  down  the  slope  in  case  of  accident.  See  Drag.  (3)  A  pawl. 

Dog  Hole. — A  little  opening  from  one  place  in  a  mine  to  another,  smaller  than 
a  breakthrough. 

Dog  Iron. — A  short  bar  of  iron  with  both  ends  pointed  and  bent  down  so  as  to 
hold  together  two  pieces  of  wood  into  which  the  points  are  driven.  Or 
one  end  may  be  bent  down  and  pointed,  while  the  other  is  formed  into 
an  eye,  so  that  if  the  point  be  driven  into  a  log,  the  other  end  may  be 
used  to  haul  on. 

Dolly. — (1)  A  machine  for  breaking  up  minerals,  being  a  rough  pestle  and 
mortar,  the  former  being  attached  to  a  spring  pole  by  a  rope.  (2)  A 
tool  used  to  sharpen  drills.  (3)  A  bar  against  which  rivets  are  driven. 

Donk  (North  of  England). — Soft  mineral  found  in  cross- veins. 

Donkey  Engine  (English). — (1)  A  small  steam  engine  attached  to  a  large  one, 
and  fed  from  the  same  boiler;  used  for  pumping  water  into  the  boiler. 
(2)  A  small  steam  engine. 

Door  Piece  (English). — The  portion  of  a  lift  of  pumps  in  which  the  clack  or 
valve  is  situated. 

Doors. — Wooden  doors  in  underground  roads  or  airways  to  deflect  the  air 
current. 


1118  A  GLOSSARY  OF  MINING  TERMS 

Door  Tender. — A  boy  whose  duty  it  is  to  open  and  close  a  mine  door  before 
and  after  the  passage  of  a  train  of  mine  cars;  a  trapper. 

Dope. — (1)  An  absorbent  for  holding  a  thick  liquid.  The  material  that 
absorbs  the  nitroglycerine  in  explosives.  (2)  Powder  cartridges. 

Double  Shift. — When  there  are  two  sets  of  men  at  work,  one  set  relieving  the 
other. 

Double  Tape  Fuse. — Fuse  of  superior  quality,  or  having  a  heavier  and  stronger 
covering. 

Double  Timber. — Two  props  with  a  bar  placed  across  the  tops  of  them  to  sup- 
port the  roof  and  sides. 

Downcast. — The  opening  through  which  the  fresh  air  is  drawn  or  forced  into 
the  mine;  the  intake. 

Draftage. — A  deduction  made  from  the  gross  weight  of  mineral  when  trans- 
ported, to  allow  for  loss. 

Drag. — (1)  The  frictional  resistance  offered  to  a  current  of  air  in  a  mine. 
(2)  See  Dog. 

Draw. — (1)  To  "draw"  the  pillars;  robbing  the  pillars  after  the  breasts  are 
exhausted.  (2)  An  effect  of  creep  upon  the  pillars  of  a  mine. 

Draw  a  Charge. — (1)  To  take  a  charge  from  a  furnace.  (2)  Remove  explo- 
sives (3)  Removing  the  coke  from  an  oven. 

Drawlift. — A  pump  that  receives  its  water  by  suction  and  will  not  force 
it  above  its  head. 

Draw-Hole. — An  aperture  in  a  battery  through  which  the  coal  is  drawn. 

Draw  Slate. — Fragile  slate  above  a  coal  measure,  which  must  be  removed  to 
prevent  caving. 

Drawing  an  Entry. — Removing  the  last  of  the  coal  from  an  entry. 

Drawn. — The  condition  in  which  an  entry  or  room  is  left  after  all  the  coal 
has  been  removed.  See  Robbed. 

Dresser  (Staffordshire). — A  large  coal  pick. 

Drift. — (1)  A  horizontal  passage  underground.  A  drift  follows  the  vein,  as 
distinguished  from  a  crosscut,  which  intersects  it,  or  a  level  or  gallery, 
which  may  do  either.  (2)  In  coal  mining,  a  gangway  above  water, 
level,  driven  from  the  surface  in  the  seam.  (3)  Unstratificd  diluvium. 

Drifting. — (1)  Driving  a  drift.  (2)  Cars,  locomotives,  etc.,  "drift "  when  they 
will  run  by  gravity  but  not  attain  a  dangerous  speed. 

Drill. — An  instrument  used  in  boring  holes. 

Drive  (Drift). — A  horizontal  passage  in  a  lode. 

Drive. — To  cut  an  opening  through  strata. 

Driving. — Excavating  horizontal  passages,  in  contradistinction  to  sinking  or 
raising. 

Driving  on  Line. — Keeping  a  heading  or  breast  accurately  on  a  given  course 
by  means  of  a  compass  or  transit. 

Dropper.— (1)  A  spur  dropping  into  the  lode.  (2)  A  feeder.  (3)  A  branch 
leaving  the  vein  on  the  footwall  side.  (4)  Water  dropping  from  the  roof. 

Drop  Shaft. — A  monkey  shaft  down  which  earth  and  other  matter  are  lowered 
by  means  of  a  drop  (i.e.,  a  kind  of  pulley  with  break  attached);  the 
empty  bucket  is  brought  up  as  the  full  one  is  lowered. 

Druggon  (Staffordshire). — A  vessel  for  carrying  fresh  water  into  a  mine. 

Drum. — The  cylinder  or  pulley  on  which  the  winding  ropes  are  coiled  or 
wound. 

Drum  Rings. — Cast-iron  rings  with  projections  to  which  are  bolted  the 
lagging  forming  the  surface  for  the  ropes  to  lap  upon. 

Drummy. — Sounding  loose,  open,  shaky,  or  dangerous  when  tested. 

Druse. — A  cavity  lined  with  small  crystals. 

Duck  Machine. — An  arrangement  of  two  boxes,  one  working  within  the 
other,  for  forcing  air  into  mines. 

Duelas  (Mexican). — Staves  of  a  barrel  or  cask,  etc. 

Dumb'd. — Choked,  said  of  a  sieve  or  grating. 

Dumb  Drift. — A  short  tunnel  or  passage  connecting  the  main  return  airways 
of  a  mine  with  the  upcast  shaft  some  distance  above  the  furnace,  in 
order  to  prevent  the  return  air  laden  with  mine  gases  from  passing 
through  or  over  the  ventilating  furnace. 

Dump. — (1)  A  pile  or  heap  of  ore,  coal,  culm,  slate,  or  rock.  (2)  The  tipple 
by  which  the  cars  are  dumped.  (3)  To  unload  a  car  by  tipping  it  up. 
(4)  The  pile  of  mullock  as  discharged  from  a  mine. 

Dumper. — A  car  so  constructed  that  the  body  may  be  revolved  to  dump  the 
material  in  front  or  on  either  side  of  the  track. 

Durn  (Cornish). — A  timber  frame. 


A  GLOSSARY  OF  MINING  TERMS  1119 

Durr  (German). — Barren  ground. 

Dust.— See  Coal  Dust. 

Duty. — The  unit  of  measure  of  the  work  of  a  pumping  engine  expressed  in 

foot-pounds  of  work  obtained  from  a  bushel,  or  100  lb.,  or  other  unit  of 

fuel. 
Dyke,  or  Dike. — (1)  A  wall  of  ignepus  rock  passing  through  strata.gtvith  or 

without  accompanying  dislocation  of  the  strata.     (2)  A  fissure  filled  with 

igneous  matter.     (3)  Barren  rock. 
Dzhu  (Cornish). — See  dessue. 

Ear. — The  inlet  or  intake  of  a  fan. 

Echado  (Mexican). — The  dip  of  the  vein. 

Edge  Coals  (English). — Highly  inclined  seams  of  coal,  or  those  having  a  dip 

greater  than  30°. 
Efflorescence. — An  incrustation  by  a  secondary  mineral,  due  to  loss  of  water  of 

crystallization. 
Egg  Coal. — Anthracite  coal  that  will  pass  through  a  2J-in.  square  mesh  and 

over  a  2-in.  square  mesh  (see  page  952). 

Elbow. — A  sharp  bend,  as  in  a  lode  or  pipe,  a  pipe-bend  fitting. 
Electric  Blast. — Instantaneous  blasting  of  material  by  means  of  electricity. 
Elevator  Pump. — An  endless  band  with  buckets  attached,  running  over  two 

drums  for  draining  shallow  ground. 

Elvan. — A  Cornish  name  applied  to  most  dike  rocks  of  that  county,  irre- 
spective of  the  mineral  constitution,  but  in  the  present  day  restricted 

to  quartz  porphyries. 
Emborrascarse  (Mexican). — To  go  barren  by  the  vein  terminating  or  pinching 

out,  etc. 

Empties. — Empty  mine  or  railroad  cars. 
Encino  (Mexican). — Live  oak. 
End  Joint  (End  Cleat). — A  joint  or  cleat  in  a  seam  about  at  right  angles  to 

the  principal  or  face  cleats. 
Endless  Chain. — A  system  of  haulage  or  pumping  by  the  moving  of  an  endless 

chain. 
Endless  Rope. — A  system  of  haulage  same  as  endless  chain,  except  that  a 

wire  rope  is  used  instead  of  chain. 
End,  or  End-On. — Working  a  seam  of  coal  at  right  angles  to  the  principal 

or  face  cleats. 
Engine  Plane. — An  incline    up   which  loaded  cars  are  drawn    by  a  rope 

operated  by  an  engine  located  at  the  top  or  bottom  of  the  incline.     The 

empty  cars  descend  by  gravity,  pulling  the  rope  after  them. 
Engineer. — (1)  One  who  has  charge  of  the  surveying  or  machinery  about  a 

mine.     (2)  One  who  runs  an  engine. 

Entibar  (Mexican). — To  timber  a  mine  or  any  part  thereof. 
Entry. — A  main  haulage  road,  gangway,  or  airway.     An  underground  passage 

used  for  haulage  or  ventilation,  or  as  a  manway. 
Entry  Stumps. — Pillars  of  coal  left  in  the  mouths  of  abandoned  rooms  to 

support  the  road,  entry,  or  gangway  till  the  entry  pillars  are  drawn. 
Erosion. — The  wearing  away  of  rocks  bv  the  elements. 
Escaleras  (Mexican). — Ladders,  generally  made  of  notched  sticks. 
Escarpment. — A  nearly  vertical  natural  face  of  rock  or  soil. 
Escoria  (Mexican). — Slag  of  cinders. 
Escorial. — Slag  pile. 

Exploder. — A  chemical  employed  for  the  instantaneous  explosion  of  powder. 
Exploitation. — The  working  of  a  mine,  and  similar  undertakings;  the  exami- 
nation instituted  for  that  purpose. 
Exploration. — Development. 

Explosion. — Sudden  ignition  of  a  body  of  firedamp,  dust,  etc. 
Eye  (English). — (1)   A  circular  hole  in  a  bar  for  receiving  a  pin  and  for 

other  purposes.     (2)  The  eye  of  a  shaft  is  the  very  beginning  of  a  pit. 

(3)  The  eye  of  a  fan  is  the  central  or  intake  opening. 

Face> — (i)  The  place  at  which  the  material  is  actually  being  worked,  either 
in  a   breast   or  heading  or  in  longwall.     (2)   The   end   of   a   drift  or 

Face-On.— When  the  face  of  the  breast  or  entry  is  parallel  to  the  face  cleats 

of  the  seam  (see  page  614). 
Face  Wall— A.  wall  built  to  sustain  a  face  cut  into  the  natural  earth,  m 

distinction  to  a  retaining  wall,  which  supports  earth  deposited  behind  it. 


1120  A  GLOSSARY  OF  MINING  TERMS 

Faenas  (Mexican). — Dead  work,  in  the  way  of  development. 

Fahlband  (German). — A  course  impregnated  with  metallic  sulphides. 

Fall. — (1)  A"masss  of  roof  or  side  which  has  fallen  in  any  part  of  a  mine. 
(2)  To  blast  or  wedge  down  coal. 

False  Bedding. — Irregular  lamination,  wherein  the  laminae,  though  for 
shoflfc  distances  parallel  to  each  other,  are  oblique  to  the  general  strati- 
fication, of  the  mass  at  varying  angles  and  directions. 

False  Bottom. — A  movable  bottom  in  some  apparatus. 

False  Cleavage. — A  secondary  slip  cleavage  superinduced  on  slaty  cleavage. 

False  Set. — A  temporary  set  of  timber  used  until  work  is  far  enough  advanced 
to  put  in  a  permanent  set. 

Famp  (North  of  England). — Thin  beds  of  soft  tough  shale. 

Fan. — A  machine  for  creating  a  circulation  of  air  in  a  mine. 

Fan  Drift. — A  short  tunnel  or  conduit  leading  from  the  top  of  the  air-shaft  to 
the  fan. 

Fanega  (Mexican). — A  Spanish  measure  of  about  2\  bushels. 

Fang  (Derbyshire). — An  air-course. 

Fascines  (English). — Bunches  of  twigs  and  small  branches  for  forming 
foundations  or  retaining  walls  in  soft  ground. 

Fast. — (1)  A  road  driven  in  a  seam  with  the  solid  coal  at  each  side.  "Fast 
at  an  end,"  or  "fast  at  one  side,"  implies  that  one  side  is  solid  coal  and 
the  other  open  to  the  goaf  or  some  previous  excavation.  (2)  Bed  rock. 

Fast  End. — An  end  of  a  breast  of  coal  that  requires  cutting. 

Fat  Coals. — Those  containing  volatile  oily  matters. 

Fathom  (English). — 6  ft. 

Fault. — A  fracture  or  disturbance  of  the  strata  breaking  the  continuity  of 
the  formation. 

Feather. — A  slightly  projecting  narrow  rib  lengthwise  on  a  shaft,  arranged 
to  catch  into  a  corresponding  groove  in  anything  that  surrounds  and 
slides  along  the  shaft. 

Feather  Edge. — (1)  A  passage  from  false  to  true  bottom.  (2)  The  thin  end 
of  a  wedge-shaped  piece  of  rock  or  coal. 

Feed. — Forward  motion  imparted  to  the  cutters  or  drills  of -rock-drilling  or 
coal-cutting  machinery,  either  hand  or  automatic. 

Feeder. — (1)  A  runner  of  water.  (2)  A  small  blower  of  gas.  (3)  A  device 
for  feeding  at  a  uniform  rate  to  any  machine  process. 

Fend-Off  (English). — A  sort  of  bell-crank  for  turning  a  pump  rod  past  the 
angle  of  a  crooked  shaft. 

Fiery. — Containing  explosive  gas. 

Fines. — Very  small  material  produced  in  breaking  up  large  lumps. 

Fire. — (1)  A  miners'  term  for  firedamp.  (2)  To  blast  with  gunpowder  or 
other  explosive.  (3)  A  word  shouted  by  miners  to  warn  one  another 
when  a  shot  is  to  be  fired. 

Fire-Bars  (English). — The  iron  bars  of  a  grate  on  which  the  fuel  rests. 

Fireboard. — A  piece  of  board  with  the  word  fire  painted  upon  it  and  sus- 
pended to  a  prop,  etc.,  in  the  workings,  to  caution  men  not  to  take  a 
naked  light  beyond  it,  or  to  pass  it  without  the  consent  of  the  foreman 
or  his  assistants. 

Fire  Boss. — An  underground  official  who  examines  the  mine  for  gas  and 
inspects  safety  lamps  taken  into  the  mine. 

Fireclay. — Any  clay  that  will  withstand  a  great  heat  without  vitrifying. 

Firedamp. — (1)  A  mixture  of  light  carburetted  hydrogen  (CHi)  and  air  in 
explosive  proportions;  often  applied  to  CHt  alone  or  to  any  explosive 
mixture  of  mine  gases. 

Fireman. — See  Fire  Boss. 

Fire-Setting. — The  process  of  exposing  very  hard  rock  to  intense  heat,  ren- 
dering it  thereby  easier  for  breaking  down. 

First  Aid. — The  assistance  or  treatment  which  should  be  given  an  injured 
person  immediately  upon  injury  or  as  soon  thereafter  as  possible. 

First  Working. — See  Whole  Working. 

Firsts. — The  best  mineral  picked  from  a  mine. 

Fish. — To  join  two  beams,  rails,  etc.,  together  by  long  pieces  at  their 
sides. 

Fish  Plates. — The  bars  used  to  join  the  ends  of  adjacent  rails  in  a  track 

Fissure. — An  extensive  crack. 

Fissure  Vein. — Any  mineralized  crevice  in  the  rock  of  very  great  depth. 

Flag. — A  track  signal  or  target. 

Flags. — Broad  flat  stones  for  paving. 


A  GLOSSARY  OF  MINING  TERMS  1121 

Flagstone. — Any  kind  of  a  stone  that  separates  naturally  into  thin  tabular 
plates  suitable  for  pavements  and  curbing.  Especially  applicable  to 
sandstone  and  schists. 

Flang  (Cornish). — A  double-pointed  pick. 

Flange  (English). — A  projecting  ledge  or  rim. 

Flat. — (1)  A  district  or  set  of  workings  separated  by  faults,  old  workings,  or 
barriers  of  solid  coal.  (2)  The  siding  or  station  laid  with  two  or  more 
lines  of  railway,  to  which  the  putters  bring  the  full  cars  from  the  work- 
ing face,  and  where  they  get  the  empty  cars  to  take  back.  (3)  The  area 
of  working  places,  from  which  coal  is  brought  to  the  same  station,  is  also 
called  "flat." 

Flat  Rod. — A  horizontal  rod  for  conveying  power  to  a  distance. 

Flats. — (1)   Narrow  decomposed  parts  of  limestones  that  are   mineralized. 

(2)  Flatcars. 

Flat  Sheet. — Sheet-iron  flooring  at  landings  and  in  the  plats,  chambers,  and 

junctions  of  drives,  to  facilitate  the  turning  and  management  of  trucks. 
Flat  Wall  (Cornish).— Foot-wall. 

Float. — Broken  and  transported  particles  or  boulders  of  vein  matter. 
Float  Stones. — Loose  boulders  from  lodes  lying  on  or  near  the  surface. 
Flood  Gate  (English). — A  gate  to  let  off  excess  of  water  in  flood  or  other 

times. 
Floor. — (1)   The  stratum  of  rock  upon  which  a  seam  of  coal  immediately 

lies.     (2)   That  part  of  a  mine  upon  which  you  walk  or  upon  which 

the  road  bed  is  laid. 

Flucan. — A  soft,  greasy,  clayey  substance  found  in  the  joints  of  veins. 
Fluke. — A  rod  for  cleaning  out  drill  holes. 
Flume. — An  artificial  watercourse. 
Flush. — (1)  To  clean  out  a  line  of  pipes,  gutters,  etc.,  by  letting  in  a  sudden 

rush  of  water.     (2)  The  splitting  of  the  edges  of  stone  under  pressure. 

(3)  Forming  an  even  continuous  line  or  surface.     (4)   To  fill  a  mine 
with  fine  material.     Sometimes  called  slush. 

Following  Stone. — Roof  stone  that  falls  on  the  removal  of  the  seam. 
Foot-Hole. — Holes  cut  in  the  sides  of  shafts  or  winzes  to  enable  miners  to 

ascend  and  descend. 
Foot-Piece. — (1)  A  wedge  of  wood  or  part-  of  a  slab  placed  on  the  foot- wall 

against  which  a  stull  piece  is  jammed.     (2)  A  piece  of  wood  placed  on 

the  floor  of  a  drive  to  support  a  leg  or  prop  of  timber. 
Foot-Wall. — The  lower  boundary  of  a  lode. 
Footway. — Ladders  in  mines. 
Force  Fan. — See  Blowdown  Fan. 

Force  Piece. — Diagonal  timbering  to  secure  the  ground. 
Force  Pump. — A  pump  that  forces  water  above  its  valves. 
Forebay. — Penstock.     The  reservoir  from  which  water  passes  directly  to  a 

waterwheel. 

Forepoling. — Driving  the  poles  over  the  timbers  so  that  their  ends  project 
•     beyond  the  last  set  of  timber,  so  as  to  protect  the  miner  from  roof  falls; 

used  also  in  quicksand  or  other  loose  material. 

Forewinning. — The  first  working  of  a  seam  in  distinction  from  pillar  drawing. 
Fork. — (1)  A  deep  receptacle  in  the  rock,  to  enable  a  pump  to  extract  the 

bottom  water.     A  pump  is  said  to  be  "going  in  fork"  when  the  water  is 

so  low  that  air  is  sucked  through  the  windbore.      (2)  (Cornish)  Bottom 

of  sump.     (3)  (Derbyshire)  Prop  for  soft  ground. 
Formation. — A  series  of  strata  that  belong  to  a  single  geological  age. 
Fossil. — Organic  remains  or  impressions  of  them  found  in  mineral  matter. 
Pother  (North  of  England).— i  chaldron. 
Frame  Set  — The  legs  and  cap  or  collar  arranged  so  as  to  support  a  passage 

mined  out  of  the  rock  or  lode;  also  called  Framing. 
Free,— Coal  is  said  to  be  "free"  when  it  is  loose  and  easily  mined,  or  whe: 

will  "run"  without  mining. 
Free  Miner. — Licensed  miner. 
Fresno  (Mexican). — An  ash  tree. 
Fronton  (Mexican). — Any  working  face. 

Furnace.— A^large  coal  fire  at 'or  near  the  bottom  9f  an  upcast  shaft,  for  pro- 
ducing a  current  of  air  for  ventilating  the  mine. 

Furnace  Shaft.— The  upcast  shaft  in  furnace  ventilation. 

Fuse, (i)  A  hollow  tube  filled  with  an  explosive  mixture  for  igniting  car- 
tridges.    (2)  To  melt. 
71 


1122  A  GLOSSARY  OF  MINING  TERMS 

Gad. — (1)  A  small  steel  wedge  used  for  loosening  jointy   ground,     (2)  A 

pointed  chisel. 

Gale. — A  grant  of  mining  ground. 

Galera  (Mexican). — A  shed;  any  long  or  large  room;  a  storehouse. 
Callage. — Royalty. 
Gallery. — A  horizontal  passage. 
Gallows  Frame. — The  frame  supporting  a  pulley  over  which  the  hoisting  rope 

passes  to  the  engine. 
Gang. — A  set  of  miners,  a  "shift." 
Gangway. — The  main  haulage  road  or  level. 
Canister. — A  hard,  compact,  extremely  silicious  fireclay. 
Gas. — See  Firedamp.     Any  firedamp  mixture  in  a  mine  is  called  gas. 
Gas    Coal. — Bituminous    coal    containing    a   large    percentage    of    volatile 

matter. 

Gash  Vein. — A  wedge-shaped  vein. 
Gasket. — A  band  or  ring  of  any  material  put  between  the  flanges  of  pipes, 

etc.,  before  bolting,  to  make  them  water-tight  or  steam-tight. 
Gale. — An  underground  road  connecting  a  stall  or  breast  with  a  main  road. 
Gateway. — (1)  A  road  kept  through  goaf  in  longwall  working.     (2)  A  gang- 
way having  ventilating  doors. 
Gauge  Door. — A  wooden  door  fixed  in  an  airway  for  regulating  the  supply 

of  ventilation  necessary  for  a  certain  district  or  number  of  men. 
Gauge  Pressure. — The  pressure  shown  by  an  ordinary  steam  gauge.     It  is 

the  pressure  above  that  of  the  atmosphere. 

Gears,  or  Pair  of  Gears. — (1)  Two  props  and  a  plank,  the  plank  being  sup- 
ported by  the  props  at  either  end.     (2)  Toothed  wheels  for  transmitting 

motion. 

Geodes. — Large  nodules  of  stone  with  a  hollow  in  the  center. 
Geordie. — A  safety  lamp  invented  by  George  Stephenson. 
Geyser. — Natural  fountain  of  hot  water  and  steam. 
Gib. — (1)   A  short  prop  of  timber  by  which  coal  is  supported  while  being 

holed  or  undercut.     (2)  A  piece  of  metal  often  used  in  the  same  hole 

with  a  wedge-shaped  key  for  holding  pieces  together. 
Ginneys. — See  Dillies. 
Gin,  or  Horse  Gin. — A  vertical  drum  and  framework  by  which  the  minerals 

and  dirt  are  raised  from  a  shallow  pit. 
Giraffe. — A  mechanical  appliance  for  receiving  and  tipping  a  car  full  of  mineral 

or  waste  rock  when  it  arrives  at  the  surface. 
Girdle. — A  thin  bed  or  band  of  stone.     A  roof  is  described  as  a  post  roof 

with  metal  girdles,  or  a  metal  roof  with  post  girdles,  according  as  the 

post  or  the  metal  predominates. 
Goaf,  or  Goave. — That  part  of  a  mine  from  which  the  coal  has  been  worked 

away,  and  the  space  more  or  less  filled  up  with  waste. 
Gob. — (1)   Another  word  for  Goaf.     (2)   To  leave  coal  and  other  minerals- 

that  are  not  marketable  in  the  mine.     (3)  To  stow  or  pack  any  useless 

underground  roadway  with  rubbish. 
Gob  Fire. — Spontaneous  combustion  underground  of  fine  coal  and  slack  in 

the  gob. 

Gobbing  Up. — Filling  with  waste. 

Gob  Road. — A  roadway  in  a  mine  carried  through  the  goaf. 
Going  Headways,  or  Going  Bord. — A  headway  or  bord  laid  with  rails,  and 

used  for  conveying  the  coal  tubs  to  and  from  the  face. 
Golpeador  (Mexican). — A  striker,  in  hand  drilling. 
Goths   (Staffordshire). — Sudden  burstings  of  coal   from  the  face,  owing  to 

tension  caused  by  unequal  pressure. 
Gouge. — The  layer  of  clay,  or  decomposed  rock,  that  lies  along  the  wall  or 

walls  of  a  vein.     It  is  not  always  valueless. 

Grade. — The  amount  of  fall  or  inclination  in  ditches,  flumes,  roads,  etc. 
Grain. — An  obscure  vertical  cleavage  usually  more  or  less  parallel  to  the  end 

or  dip  joints. 
Granza  (Mexican). — Metallic  minerals  from  the  size  of  rice  to  that  of  hens' 

eggs. 

Grass. — The  surface  of  the  ground. 
Grate  Coal. — See  Broken  Coal. 
Grating.— A.  perforated  iron  sheet  or  wire  gauze  placed  in  front  of  reducing 

machinery. 

Gravel. — Water-worn  stones  about  the  size  of  marbles. 
Gray  Metal, — Shale  of  a  grayish  color. 


A  GLOSSARY  OF  MINING  TERMS  1123 

Graywacke. — A    compact    gray    sandstone    frequently    found    in    Paleozoic 

formations. 
Greenstone. — A  general  term  employed  to  designate  green-colored  igneous 

rocks,  as  dionte,  dolerite,  diabase,  gabbro,  etc. 
Grid. — (1)  A  grated  opening.     (2)  A  section  of  electrical  resistance,  usually 

made  of  cast  iron. 

Griddle. — A  coarse  sieve  used  for  sifting  ores,  clay,  etc. 
Grizzly. — A  bar  screen. 

Ground  Rent. — Rent  paid  for  surface  occupied  by  the  plant,  etc.,  of  a  colliery 
Groundsill. — A  log  laid  on  the  floor  of  a  drive  on  which  the  legs  of  a  set  of 

timber  rest. 
Grout  (English). — Thin  mortar  poured  into  the  interstices  between  stones 

and  bricks. 

Grove  (Derbyshire). — A  mine. 

Grub  Stake. — The  mining  outfit  or  supplies  furnished  to  a  prospector  on  con- 
dition of  sharing  in  his  finds. 
Guag  (Cornish). — Worked-out  ground. 
Gualdria  (Mexican). — A  long  and  stout  beam,  generally  sustaining  other 

beams  or  some  heavy  weight. 

Guarda  Raya  (Mexican). — A  landmark;  a  monument.    ' 
Guides. — See  Cage  Guides. 
Guijo  (Mexican). — A  pointed  pivot,  upon  which  turns  the  upright  center 

piece  of  an  arrastre,  of  a  door,  etc. 
Gunboat. — A  self-dumping  car,  holding  from  5  to  8  tons  of  coal,  used  upon 

inclined  planes  or  slopes.     They  are  filled  by  emptying  the  mine  cars 

into  them  at  the  foot  of  the  slope. 
Gunnies  (Cornish). — 3  ft. 
Gutter. — (1)  A  small  water-draining  channel. 

Hade. — The  inclination  of  a  vein  or  fault,  taking  the  vertical  as  zero. 
Half  Course. — (1)  At  an  angle  of  45°  from  general  or  previous  course.      (2) 

Half  on  the  level  and  half  on  the  dip. 
Half  Set. — One  leg  piece  and  a  cap. 
Hammer-and-Plate. — A  signaling  apparatus. 

Hand  Barrow. — A  long  box  or  platform  with  handles  at  each  end. 
Hand  Dog. — A  kind  of  spanner  or  wrench  for  screwing  up  and  disconnecting 

the  joints  of  boring  rods  at  the  surface. 

Handspike. — A  wooden  lever  for  working  a  capstan  or  windlass. 
Hanger-On. — The  man  that  runs  the  loaded  cars  on  to  the  cages  and  gives 

the  signal  to  hoist.     See  Cager. 
Hanging  Spear  Rod. — Wooden  pump  rods  adjustable  by  screws,  etc.,  by  which 

a  sinking  set  of  pumps  is  suspended  in  a  shaft. 
Hanging    Wall. — In   metalliferous  mining,   the   stratum   lying  geologically 

directly  above  a  bed  or  vein. 
Hatajo  (Mexican). — A  drove  of  pack  mules. 
Hat  Rollers. — Cast-iron  or   steel  rollers  shaped   like  a  hat,  revolving  on  a 

vertical  pin,  for  guiding  inclined  haulage  ropes  around  curves. 
Hatter. — A  miner  working  by  himself  on  his  own  account. 
Haulage  Clip. — Levers,  jaws,  wedges,  etc.,  by  which  cars,  singly  or  in  trains, 

are  connected  to  the  hauling  ropes. 
Hauling. — The  drawing  of  conveying  of  the  product  of  the  mine  from  the 

working  places  to  the  bottom  of  the  hoisting  shaft,  or  slope. 
Haunches. — The  parts  of  an  arch  from  the  keystone  to  the  skew  back. 
Hazle  (North  of  England). — Sandstone  mixed  with  shale. 
Head. — (1)  Pressure  of   water  in  pounds  per  square  inch.      (2)  Any  subter- 
ranean passage  driven  in  solid  coal.     (3)  That  part  of  a  face  nearest 

Head,  or  Sluice  Head  (Australia  and  New  Zealand).— A  supply  of  1  cu.  ft.  of 
water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 

Head-Block. — (1)  A  stop  at  the  head  of  a  slope  or  shaft  to  stop  cars  from 
going  down  the  shaft  or  slope.  (2)  A  cap  piece. 

Headboard. — A  wedge  of  wood  placed  against  the  hanging  wall,  and  against 
which  one  end  of  the  stull  piece  is  jammed. 

Header.— (I)  A  rock  that  heads  off  or  delays  progress.  (2)  A  blast  hole  at  or 
above  the  head.  (3)  A  stone  or  brick  laid  lengthwise  at  right  angles  to 
the  face  of  the  masonry.  (4)  The  Stanley  Header  is  an  entry  boring 
machine  that  bores  the  entire  section  of  the  entry  in  one  operation. 

Head-Gear, — The  pulley  frame  erected  over  a  shaft. 


1124  A  GLOSSARY  OF  MINING  TERMS 

Head-House. — When  the  head-frame  is  housed  in,  the  structure  is  known  by 

this  name. 

Heading. — (1)  A  continuous  passage  for  air  or  for  use  as  a  manway;  a  gang- 
way or  entry.     (2)  A  connecting  passage  between  two  rooms,  breasts, 

or  other  working  places. 
Head-Piece. — A  cap;  a  collar. 

Headrace. — An  aqueduct  for  bringing  a  supply  of  water  on  to  the  ground. 
Headstocks. — Gallows  frame;  head-frame. 
Headways. — (1)   A  road;  usually  9  ft.  wide,  in  a  direction  parallel  to  the 

main-cleavage   planes  of    the   coal   seams,    which   direction   is    called 

"headways  course,"  and  is  generally 'about  north  and  south  in  the 

Newcastle  coal  field.     It  is  termed  "on  end"  in  other  districts.     (2) 

Cross- headings. 
Heave. — The  shifting  of  rocks,  seams,  or  lodes  on  the  face  of  a  cross-course, 

etc. 
Heaving. — The  rising  of  the  thill  (or  floor)  of  a  seam  where  the  coal  has  been 

removed. 

Hechado  (Spanish). — Dip. 

Heel  of  Coal. — A  small  body  of  coal  left  under  a  larger  body  as  a  support. 
Heel  of  a  Shot. — In  blasting,  the  front  of  a  shot,  or  the  face  of  the  shot 

farthest  from  the  charge. 

Heep  Stead  (English). — The  entire  surface  plant  of  a  colliery. 
Helper. — A  miner's  assistant,  who  works  under  the  direction  of  the  miner. 
Helve— A.  handle. 

Hewer. — A  collier  that  cuts  coal;  a  digger. 
High  Reef. — The  bed  rock  or  reef  is  frequently  found  to  rise  more  abruptly 

on  one  side  of  a  gutter  than  on  the  other,  and  this  abrupt  reef  is  termed 

a  high  reef. 
Hitch. — (1)  A  fault  or  dislocation  of  less  throw  than  the  thickness  of  the 

seam  in  which  it  occurs.     (2)  Step  cut  in  the  rock  or  lode  for  holding 

stay-beams,  or  timber,  etc.,  for  various  purposes. 
Hoarding. — A  temporary  close  fence  of  boards  placed  around  a  work  in 

progress. 
Hogback. — A  roll  occurring  in  the  floor  and  not  in  the  roof,  the  coal  being 

cut  out  or  nearly  so,  for  a  distance. 
Hoister. — A  machine  used  in  hoisting  the  product.     It  may  be  operated  by 

steampower  or  horsepower. 
Hole. — (1)  To  undercut  a  seam  of  coal  by  hand  or  machine.     (2)  A  bore 

hole.     (3)    To  make  a  communication  from  one  part  of    a  mine  to 

another. 
Holing. — (1)  The  portion  of  the  seam  or  underclay  removed  from  beneath 

the  coal  before  it  is  broken  down.     (2)  A  short  passage  connecting  two 

roads.     (3)  See  Kirving. 
Holing    Through. — Driving    a    passage    through  to  make    connection  with 

another  part  of  the  same  workings,  or  with  those  in  an  adjacent  mine. 
Hood. — See  Bonnet. 

Hopper. — A  coal  pocket;  a  funnel-shaped  feeding  trough. 
Horn  Coal. — Coal  worked  partly  end-on  and  partly  face-on. 
Horse  Gin. — A  gearing  for  winding  by  horsepower. 

Horsepower. — The  power  that  will  raise  33,000  Ib.  1  ft.  high  per  minute. 
Horse,  or  Horsebacks. — (1)  Natural  channels  cut  or  washed  away  by  water  in 

a  coal  seam  and  filled  up  with  shale  and  sandstone.     Sometimes  a  bank 

or  ridge  of  foreign  matter  in  a  coal  seam.     (2)  A  mass  of  country  rock 

lying  within  a  vein  or  bed.     (3)  Any  irregularity  cutting  out  a  portion 

of  the  vein.     See  Dirt  Fault  and  Rock  Fault. 
Horse  Whim. — A  vertical  drum  worked  by  a  horse,  for  hauling  or  hoisting. 

Called  also  Horse  Gin. 
Hose. — A  strong  flexible  pipe  made  of  leather,  canvas,  rubber,  etc.,  and  used 

for  the  conveyance  of  water,  steam,  or  air  under  pressure  to  any  particu- 
lar point. 
H     Piece. — The  portion  of  a  column  pipe  containing  the  valves  of  the 

pump. 

Hueco  (Mexican). — See  Demasia.. 

Hulk  (Cornish). — To  pick  out  the  soft  portions  of  a  lode. 
Hundido  (Mexican). — See  Derrumbe. 
Hungry. — Worthless  looking. 

Hurdy  Gurdy. — A  waterwheel  that  receives  motion  from  the  force  of  travel- 
ing water. 


A  GLOSSARY  OF  MINING  TERMS  1126 

Hung  Shot. — A  shot  which  does  not  explode  immediately  upon  detonation 

or  ignition. 

Hutch. — (English)  A  mine  car. 
Hydraulic  Cement. — A  mixture  of  lime,  magnesia,  alumina,  and  silica  that 

solidifies  beneath  water. 
Hydraulicking. — Working  or  removing  auriferous  or  other  gravel  b'eds  by 

hydraulic  power. 
Hydrocarbons. — Compounds  of  hydrogen  and  carbon. 

Igneous  Rocks. — Those  that  have  been  in  a  more  or  less  fused  state. 

Inbye. — In  a  direction  inward  toward  the  face  of  the  workings,  or  away  from 
the  entrance. 

Incline. — Short  for  inclined  plane.  Any  inclined  heading  or  slope  road  or 
track  having  a  general  inclination  or  grade  in  one  direction. 

Indicator. — (1)  A  mechanical  contrivance  attached  to  winding,  hauling,  or 
other  machinery,  which  shows  the  position  of  the  cages  in  the  shaft  or 
the  cars  on  an  incline  during  their  journey  or  run.  (2)  An  apparatus  for 
showing  the  presence  of  firedamp  in  mines,  the  temperature  of  goaves, 
the  speed  of  a  ventilator,  pressure  of  steam,  air,  or  water,  etc. 

Indicator  Card,  or  Diagram. — A  diagram  showing  the  variation  of  steam 
pressure  in  the  cylinder  of  an  engine  during  an  entire  stroke  or  revo- 
lution. 

Indoor  Catches. — Strong  beams  in  Cornish  pumping-engine  houses  to  catch 
the  beam  in  case  of  a  smash,  thus  preventing  damage  to  the  engine 
itself. 

In-Fork. — When  a  pump  continues  working  after  water  has  receded  below 
the  holes  of  the  wind  bore. 

Ingot. — A  lump  of  cast  metal. 

In  Place. — A  vein  or  deposit  in  its  original  position. 

Inset. — The  entrance  to  a  mine  at  the  bottom,  or  part  way  down  a  shaft 
where  the  cages  are  loaded. 

Inside  Slope. — A  slope  on  which  coal  is  raised  from  a  lower  to  a  higher 
gangway. 

Inspector. — A  government  official  whose  duties  are  to  enforce  the  laws  regu- 
lating the  working  of  mines. 

Instroke. — The  right  to  take  coal  from  a  royalty  to  the  surface  by  a  shaft  in 
an  adjoining  royalty.  A  rent  is  usually  charged  for  this  privilege. 

Intake. — (1)  The  passage  through  which  the  fresh  air  is  drawn  or  forced  in 
a  mine,  commencing  at  the  bottom  of  a  downcast  shaft,  or  the  mouth 
of  a  slope.  (2)  The  fresh  air  passing  int9  a  colliery. 

Inversion. — Such  a  change  in  the  dip  of  a  vein  or  seam  as  makes  the  foot- 
wall  or  floor  the  upper  and  the  hanging  wall  or  roof  the  lower  of  the  two. 

Irestone  (Cornish). — Any  hard  tough  stone. 

Iron  Man. — A  coal-cutting  machine. 

Jacal  (Mexican).— See  Xacal. 

Jack. — (1)  A  lantern-shaped  case  made  of  tin,  in  which  safety  lamps  are 
carried  in  strong  currents  of  air..  (?,)  A  device  for  lifting  heavy  weights. 

Jacket. — (1)  An  extra  surface  covering,  as  a  steam  jacket.  (2)  A  water- 
jacket  is  a  furnace  having  double  iron  walls,  between  which  water 
circulates. 

Jack-Lamp. — A  Davy  lamp,  with  the  addition  of  a  glass  cylinder  outside 
the  gauze. 

Jars. — In  rope  drilling,  two  long  links  which  take  up  the  shock  of  impact 
when  the  falling  tools  strike  the  bottom  of  the  hole. 

Jenkin. — A  road  cut  in  a  pillar  of  coal  in  a  bordways  direction,  that  is,  at 
right  angles  to  the  main  cleavage  planes. 

Jig. — (1)  A  self-acting  incline.  (2)  A  machine  for  separating  ores  or  minerals 
from  worthless  rock  by  means  of  their  difference  in  specific  gravity ; 
also  called  Jigger  or  Washer. 

Jigger. — (1)  A  kind  of  coupling  hook  for  connecting  cars  on  an  incline. 
(2)  An  allowance  of  liquor  sometimes  issued  to  workmen  (almost 
obsolete).  (3)  See  Jig. 

Jigging. — Separating  heavy  from  light  particles  by  agitation  in  water. 

Jockey. — A  self-acting  apparatus  carried  on  the  front  truck  of  a  set  for  re- 
leasing it  from  the  hauling  rope. 

Joggle. — A  joint  of  trusses  or  sets  of  timber  for  receiving  pressure  at  right 
angles,  or  nearly  so. 


1126  A  GLOSSARY  OF  MINING  TERMS 

Joints. — (1).  Divisional  planes  that  divide  the  rock  in  a  quarry  into  natural 
blocks.  There  are  usually  two  or  three  nearly  parallel  series,  called  by 
quarrymen  end  joints,  back  joints,  and  bottom  joints,  according  to  their 
position.  (2)  In  coal  seams,  the  less  pronounced  cleats  or  vertical 
cleavages  in  the  coal.  The  shorter  cleats,  about  at  right  angles  to  the 
face  cleats  and  the  bedding  plane  of  the  coal. 

Jud. — (1)  A  portion  of  the  working  face  loosened  by  "kirying"  underneath, 
and  "nicking"  up  one  side.  The  operation  of  kirying  and  nicking  is 
spoken  of  as  "making  a  jud."  (2)  The  term  jud  is  also  applied  to  a 
working  place,  usually  6  to  8  yd.  wide,  driven  in  a  pillar  of  coal.  When 
a  jud  has  been  driven  the  distance  required,  the  timber  and  rails  are 
removed,  and  this  is  termed  "drawing  a  jud." 

Judge  (Derbyshire  and  North  of  England). — A  measuring  staff. 

Jugglers,  or  Jugulars. — Timbers  set  obliquely  against  the  rib  in  a  breast,  to 
form  a  triangular  passage  to  be  used  as  a  manway,  airway,  or  chute. 

Jump. — An  upthrow  or  a  downthrow  fault. 

Jumper. — A  hand  drill  used  in  boring  holes  in  rock  for  blasting. 

Kann  (Cornish). — Fluorspar. 

Kazen  (Cornish). — A  sieve. 

Keeker. — An  official  that  superintends  the  screening  and  cleaning  of  the  coal. 

Keel  Wedge. — A  long  iron  wedge  for  driving  over  the  top  of  a  pick  hilt. 

Keeps,  or  Keps. — Wings,  catches,  or  rests  to  hold  the  cage  at  rest  when  it 

reaches  any  landing. 
Kenner. — Time  for  quitting  work. 

Kerf. — The  undercut  made  to  assist  the  breaking  of  the  coal. 
Kerve  (North  of  England). — In  coal  mining,  to  cut  under. 
Kettle  or  Kettle  Bottom. — The  petrified  stump  of  a  tree  or  other  fossil  in  the 

roof  of  a  mine. 
Key. — (1)  An  iron  bar  of  suitable  size  and  taper  for  filling  the  keyways  of 

shaft  and  pulley  so  as  to  keep  both  together.     (2)  A  kind  of  spanner 

used  in  deep  boring  by  hand. 
Kibble. — See  Bowk.     Often  made  with  a  bow  or  handle,  and  carrying  over  a 

ton  of  d6bris. 
Kick  Back. — A  track  arrangement  for  reversing  the  direction  of  travel  of 

cars  moving  by  gravity. 

Kickup. — An  apparatus  for  emptying  trucks. 
Kieve. — Tossing  tub. 
Killas  (Cornish).— Clay  slate. 
Kiln. — A  chamber  built  of  stone  or  brick,  or  sunk  in  the  ground,  for  burning 

minerals  in. 

Kind. — (1)  Tender,  soft,  easy.     (2)  Likely  looking  stone. 
Kind-Chaudron. — A  system  of  sinking  shafts  through  water-bearing  strata. 
Kirving  (North  of  England). — The  cutting  made  beneath  the  coal  seam. 
Kist. — The  wooden  box  or  chest  in  which  the  deputy  keeps  his  tools.     The 

chest  is  always  placed  at  the  flat  or  lamp  station,  and  this  spot  is  often 

referred  to  by  the  expression  "at  the  kist." 
Kit. — Any  workman's  necessary  outfit,  as  tools,  etc. 
Kitty. — A  squib  made  of  a  straw  tube  filled  with  powder. 
Knee  Piece. — A  bent  piece  of  piping. 
Knocker. — A  lever  that  strikes  on  a  plate  of  iron  at  the  mouth  of  a  shaft,  by 

means  of  which  miners  below  can  signal  to  those  on  the  top. 
Knocker  Line. — The  signal  line  extending  down  the  shaft  from  the  knocker. 
Koepe  System. — A  system  of  hoisting  without  using  drums,  the  rope  being 

endless  and  passing  over  pulleys  instead  of  around  a  drum. 

Labor  (Mexican). — Mine  workings  in  general.  Specifically,  a  stope  or  any 
other  place  where  mineral  is  being  taken  out. 

Ladder-way,  Ladder  Road. — The  particular  shaft,  or  compartment  of  a  shaft, 
used  for  ladders. 

Lagging. — (1)  Small  round  timbers,  slabs,  or  plank,  driven  in  behind  the 
1  egs  and  over  the  collar,  to  prevent  pieces  of  the  sides  or  roof  from  falling 
through.  ("2)  Long  pieces  of  timber  closely  fitted  together  and  fastened 
to  the  drum  rings  to  form  a  surface  for  the  rope  to  wind  onto. 

Lamina. — Sheets  not  naturally  separated,  but  which  may  be  forced  apart. 

Lamp  Men. — Cleaners,  repairers,  and  those  having  charge  of  the  safety 
lamps  at  a  colliery. 

Lamp  Stations, — Certain  fixed  stations  in  a  mine  at  which  safety  lamps 


A  GLOSSARY  OF  MINING  TERMS  1127 

are  allowed  to  be  opened  and  relighted  by  men  appointed  for  that 
purpose,  or  beyond  which,  on  no  pretense,  is  a  naked  light  allowed 
to  be  taken. 

Lander. — The  man  that  receives  a  load  of  mineral  at  the  mouth  of  a  shaft. 

Lander's  Crook. — A  hook  or  tongs  for  upsetting  the  bucket  of  hoisted  rock. 

Landing. — (1)  A  level  stage  for  loading  or  unloading  a  cage  or  skip.  (2) 
The  top  or  bottom  of  a  slope,  shaft,  or  inclined  plane. 

Land  Sale. — The  sale  of  coal  loaded  into  carts  or  wagons  for  local  consump- 
tion. 

Land-Sale  Collieries. — Those  selling  the  entire  product  for  local  consump- 
tion, and  shipping  none  by  rail  or  water. 

Lap. — One  coil  of  rope  on  a  drum  or  pulley. 

Large. — The  largest  lumps  of  coal  sent  to  the  surface,  or  all  coal  that  is  hand 
picked  or  does  not  pass  over  screens;  also,  the  large  coal  that  passes 
over  screens. 

Larry. — (1)  A  car  to  which  an  endless  rope  is  attached,  fixed  at  the  inside 
end  of  the  road,  forming  part  of  the  appliance  for  taking  up  slack  rope. 
See  Balance  Car.  (2)  See  Barney.  (3)  A  car  with  a  hopper  bottom  and 
adjustable  chutes  for  feeding  coke  ovens. 

Latches. — (1)  A  synonym  of  switch.  Applied  to  the  split  rail  and  hinged 
switches.  (2)  Hinged  switch  points,  or  short  pieces  of  rail  that  form 
rail  crossings. 

Lateral. — From  the  side. 

Lath. — A  plank  laid  over  a  framed  center  or  used  in  poling. 

Launder. — Water  trough. 

Laundry  Box. — The  box  at  the  surface  receiving  the  water  pumped  up 
from  below. 

Lava. — A  common  term  for  all  rock  matter  that  has  flowed  from  a  volcano  or 
fissure. 

Lazadores  (Mexican). — Men  formerly  employed  in  recruiting  Indians  for 
work  in  the  mines  by  the  gentle  persuasion  of  a  lasso. 

Lazy  Back  (Staffordshire). — A  coal  stack,  or  pile  of  coal. 

Leader. — A  seam  of  coal  too  small  to  be  worked  profitably,  but  often  being  a 
guide  to  larger  seams  lying  in  known  proximity  to  it. 

Leat. — A  small  water  ditch. 

Leg. — A  wooden  prop  supporting  one  end  of  a  collar. 

Leg  Piece. — An  upright  log  placed  against  the  side  of  a  drive  to  support  the 
cap  piece. 

Lefiador  (Mexican). — One  that  cuts,  carries,  or  furnishes  wood  for  com- 
bustible. 

Level. — A  road  or  gangway  running  parallel  or  nearly  so  with  the  strike 
of  the  seam. 

Lid. — A  cap  piece  used  in  timbering. 

Lift. — (1)  The  vertical  height  traveled  by  a  cage  in  a  shaft.  (2)  The  lift  of  a 
pump  is  the  theoretical  height  from  the  level  of  the  water  in  the  sump 
to  the  point  of  discharge.  (3)  The  distance  between  the  first  level  and 
the  surface,  or  between  two  levels.  (4)  The  levels  of  a  shaft  or  slope. 

Lifting  Guards. — Fencing  placed  around  the  mouth  of  a  shaft,  which  is 
lifted  out  of  the  way  by  the  ascending  cage. 

Lignite. — A  coal  of  a  woody  character  containing  about  66%  carbon  and 
having  a  brown  streak. 

Lime  Cartridge. — A  charge  or  measured  quantity  of  compressed  dry  caustic 
lime  made  up  into  a  cartridge  and  used  instead  of  gunpowder  for 
breaking  down  coal.  Water  is  applied  to  the  cartridge,  and  the  expan- 
sion breaks  down  the  coal  without  producing  a  flame. 

Lime  Coal. — Small  coal  suitable  for  lime  burning. 

Lines. — Plumb-lines,  not  less  than  two  in  number,  hung  from  hooks  or 
spads  driven  in  wooden  plugs.  A  line  drawn  through  the  centers  of 
the  two  strings  or  wires,  as  the  case  may  be,  represents  the  bearing  or 
course  to  be  driven  on. 

Lining. — The  planks  arranged  against  frame  sets. 

Linternilla  (Mexican). — The  drum  of  a  Horse  Whim. 

Lip  Screen.— (I)  A  small  screen  or  screen  bars,  placed  at  the  draw  hole  of  a 
coal  pocket  to  take  out  the  fine  coal.  (2)  A  stepped  coal  screen. 

Little  Giant.— The  name  given  to  a  special  sort  of  hydraulic  nozzle  used  & 
sluicing  purposes. 

Llaves  (Mexican). — Horizontal  cross-beams  in  a  shaft,  or  the  upright  pieces 
that  sustain  the  roof  beams  in  a  drift  or  tunnel. 


1128  A  GLOSSARY  OF  MINING  TERMS 

Loaded  Track. — Track  used  for  loaded  cars. 

Loader. — One  that  fills  the  mine  cars  at  the  working  places. 

Loam. — Any  natural  mixture  of  sand  and  clay  that  is  neither  distinctly  sandy 
nor  clayey. 

Location. — The  first  approximate  staking  out  or  survey  of  a  mining  claim,  in 
distinction  from  a  Patent  Survey,  or  a  Patented  Claim. 

Location  Survey. — See  Location. 

Lode  (Cornish). — Strictly  a  fissure  in  the  country  rock  filled  with  mineral; 
usually  applied  to  metalliferous  lodes.  In  general  miners'  usage,  a  lode, 
vein,  or  ledge  is  a  tabular  deposit  of  valuable  minerals  between  definite 
boundaries.  Whether  it  be  a  fissure  formation  or  not  is  not  always 
known,  and  does  not  affect  the  legal  title  under  the  United  States  federal 
and  local  statutes  and  customs  relative  to  lodes.  But  it  must  not  be  a 
placer,  i.e.,  it  must  consist  of  quartz  or  other  rock  in  place,  and  bearing 
valuable  mineral. 

Logs. — Portions  of  trunks  of  trees  cut  to  length  and  built  up  so  as  to  raise 
the  mouth  or  collar  of  a  shaft  from  the  surface,  in  order  to  give  the 
requisite  space  for  the  dumping  of  mullock  and  mineral. 

Long-Pillar  Work. — A  system  of  working  coal  seams  in  three  separate  opera- 
tions: (a)  Large  pillars  are  left;  (b)  a  number  of  parallel  headings  are 
driven  through  the  block;  and  (c)  the  ribs  or  narrow  pillars  are  worked 
away  in  both  directions. 

Long  Ton.— 2,240  Ib. 

Longwall. — A  system  of  working  a  seam  of  coal  in  which  the  whole  seam  is 
taken  out  and  no  pillars  left,  excepting  the  shaft  pillars,  and  sometimes 
the  main-road  pillars. 

Loose  End. — (1)  A  portion  of  a  seam  worked  on  two  sides.  (2)  A  portion 
that  projects  in  the  shape  of  a  wedge  between  previous  workings. 

Low  Grade. — Not  rich  in  mineral. 

Lumber. — Timber  cut  to  the  various  sizes  and  shapes  for  carpenters'  purposes. 

Lumbreras  (Mexican). — Ventilating  shafts  in  a  mine  or  other  underground 
work. 

Lump  Coal. — (1)  All  coal  (anthracite  only)  larger  than  broken  coal,  or,  when 
steamboat  coal  is  made,  lumps  larger  than  this  size.  (2)  In  soft  coal,  all 
coal  passing  over  the  screen. 

Lute. — An  adhesive  clay  used  either  to  protect  any  iron  vessel  from  too 
strong  a  heat  or  for  securing  air-  and  gas-tight  joints. 

Lye  (English). — A  siding  or  turnout. 

Machote  (Mexican). — A  stake  or  permanent  bench  mark  fixed  in  an  under- 
ground working,  from  which  the  length  and  progress  thereof  is  measured. 
Magnetic  Needle. — Needle  used  in  surveying. 
Magnetic  North. — The  direction  indicated  by  the  north  end  of  the  magnetic 

needle. 
Magnetic  Meridian. — The  line  or  great  circle  in  which  the  magnetic  needle 

sets  at  any  given  place. 
Main  Road. — The  principal  haulage  road  of  a  mine  from  which  the  several 

crossroads  lead  to  the  working  face. 
Main  Rod  (English).— See  Pump  Rod. 
Main   Rope. — In  tail-rope  haulage,  the  rope  that  draws  the  loaded  cars 

out. 

Makings  (North  of  England). — Small  coal  produced  in  kirving;  fines. 
Malacate  (Mexican). — A  Horse  Whim;  now  extended  to  any  hoisting  machine 

used  in  mines. 

Mamposteria  (Mexican). — Mason  work. 
Manager. — An  official  who  has  the  control  and  supervision  of  a  mine,  both 

under  and  above  ground. 
Man  Engine. — An  apparatus  consisting  of  one  or  two  reciprocating  rods,  to 

which  suitable  stages  are  attached,  used  for  lowering  and  raising  men 

in  shafts. 
Manhole. — (1)  A  refuge  hole  constructed  in  the  side  of  a  gangway,  tunnel, 

or  slope.      (2)  A  hole  in  boilers  through  which  a  man  can  get  into  the 

boiler  to  examine  and  repair  it. 
Manway. — A  small  passage  used  as  a  traveling  way  for  the  miner,  and  also 

often  used  as  an  airway  or  chute,  or  both. 
Marco  (Mexican). — A  weight  of  8  oz. 
Marcus. — A  patented  shaker  screen  with  a  non-harmonic  or  quick-return 

motion. 


A  GLOSSARY  OF  MINING  TERMS  1129 

MarL — Clay  containing  calcareous  matter. 

Marlinespike. — A  sharp-pointed  and  gradually  tapered  round  iron,  used  in 
splicing  ropes. 

Marrow. — A  partner. 

Marsaut  Lamp. — A  type  of  safety  lamp  whose  chief  characteristic  is  the 
multiple-gauze  chimneys. 

Marsh  Gas. — CH4,  often  used  synonymously  with  Firedamp  (see  page  859). 

Match. — (1)  A  charge  of  gunpowder  put  into  a  paper  several  inches  long,  and 
used  for  igniting  explosives.  (2)  The  touch  end  of  a  squib. 

Mattock. — A  kind  of  pick  with  broad  ends  for  digging. 

Maul. — A  driver's  hammer. 

Maundril. — A  pick  with  two  shanks  and  points,  used  for  getting  coal,  etc. 

Mear  (Derbyshire). — 32  yd.  along  the  vein. 

Measures. — Strata. 

Mecha  (Mexican). — A  wick  for  a  lamp  or  candle;  a  torch. 

Merced  (Mexican). — A  gift,  grant,  or  concession. 

Meridian. — A  north  and  south  line,  either  true  or  approximate. 

Metal. — (1)  In  coal  mining,  indurated  clay  or  slate.  (2)  An  element  that 
forms  a  base  by  combining  with  oxygen  and  which  is  solid  at  ordinary 
temperature  (with  exception  of  quicksilver),  opaque  (except  in  the  thin- 
nest possible  films),  has  a  metallic  luster,  and  is  a  good  conductor  of 
heat  and  electricity,  and,  as  a  rule,  of  a  higher  specific  gravity  than  the 
non-metals.  (3)  (Mexican)  All  kinds  of  metalliferous  minerals  are  called 
"metal"  in  Mexico. 

Mill  Cinder. — The  slag  from  the  puddling  furnace  of  a  rolling  mill. 

Mill  Hole. — An  auxiliary  shaft  connecting  a  stope  or  other  excavation  with 
the  level  below. 

Mine. — Any  excavation  made  for  the  extraction  of  minerals. 

Miner. — One  who  mines. 

Mineral. — Any  constituent  of  the  earth's  crust  that  has  a  definite  com- 
position. 

Mineral  Oil. — Petroleum  obtained  from  the  earth,  and  its  distillates. 

Miner o  (Mexican). — A  mine  owner;  a  mining  captain;  an  underground  boss. 

Mine  Road. — Any  mine  track  used  for  general  haulage. 

Mine  Run. — The  entire  unscreened  output  of  a  mine. 

Miner  o  Mayor  (Mexican). — The  head  mining  captain.  A  mining  workman 
is  called  Operario. 

Miners'  Dial. — An  instrument  used  in  surveying  underground  workings. 

Miners'  Inch. — A  measure  of  water  varying  in  different  districts,  being  the 
quantity  of  water  that  passes  through  a  slit  1  in.  high,  of  a  certain  width 
under  a  given  head  (see  page  309). 

Miner's  Right. — An  annual  permit  from  the  Government  to  occupy  and  work 
mineral  land. 

Mining. — In  its  broad  sense,  it  embraces  all  that  is  concerned  with  the 
extraction  of  minerals  and  their  complete  utilization. 

Mining  Engineer. — A  man  having  knowledge  and  experience  in  the  many 
departments  of  mining. 

Mining  Retreating. — A  process  of  min-ng  by  which  the  vein  is  untouched 
until  after  all  the  gangways,  etc.,  are  driven,  when  the  mineral  extraction 
begins  at  the  boundary  and  progresses  toward  the  shaft. 

Mistress  (North  of  England). — A  miner's  lamp. 

Moil. — (1)  A  short  length  of  steel  rod  tapered  to  a  point,  used  for  cutting 
hitches,  etc.  (2)  To  cut  with  a  moil. 

Monitor. — See  Gunboat. 

Monkey. — The  hammer  or  ram  of  a  pile  driver. 

Monkey  Drift. — A  small  drift  driven  in  for  prospecting  purposes,  or  a  crosscut 
driven  to  an  airway  above  the  gangway. 

Monkey  Gangway.— A  small  gangway  parallel  with  the  mam  gangway. 

Monkey  Rolls. — The  smaller  rolls  in  an  anthracite  breaker. 

Monkey  Shaft.— A  shaft  rising  from  a  lower  to  a  higher  level. 

Monoclinal. — Applied  to  an  area  in  which  the  rocks  all  dip  in  the  same 
direction. 

Mop. — Some  material  surrounding  a  drill  in  the  form  of  a  disk,  to  prevent 
water  from  splashing  up. 

Morgan.— (Cape  of  Good  Hope).     A  surface  measure  =  2.11  acres. 

Mortise.— A  hole  cut  in  one  piece  of  timber,  etc.,  to  receive  the  tenon  that 
projects  from  another  piece. 

Mote  (Moat). — A  straw  filled  with  gunpowder,  for  igniting  a  snot. 


1130  A  GLOSSARY  OF  MINING  TERMS 

Mother  Gate. — The  main  road  of  a  district  in  longwall  working. 

Mother  Lode  (Main  Lode). — The  principal  vein  of  any  district. 

Motive  Column. — The  length  of  a  column  of  air  whose  weight  is  equal  to  the 
difference  in  weight  of  like  columns  of  air  in  downcast  and  upcast  shafts. 
The  ventilating  pressure  in  furnace  ventilation  is  measured  by  the  differ- 
ence of  the  weights  of  the  air  columns  in  the  two  shafts. 

Mouth. — The  top  of  a  shaft  or  slope,  or  the  entrance  to  a  drift  or  tunnel. 

Moyle. — An  iron  with  a  sharp  steel  point,  for  driving  into  clefts  when 
levering  off  rock. 

Muck. — (1)  Any  material,  particularly  refuse,  removed  from  a  mine,  shaft 
or  slope.  (2)  To  remove  refuse. 

Mucker. — One  who  mucks  or  removes  refuse;  a  shoveler. 

Muckle. — Soft  clay  overlying  or  underlying  coal. 

Mucks  (Staffordshire). — Bad  earthy  coal. 

Muescas  (Mexican). — Notches  in  a  stick;  mortises;  notches  cut  in  a  round 
or  square  beam,  for  the  purpose  of  using  it  as  a  ladder. 

Mueseler  Lamp. — A  type  of  safety  lamp  invented  and  used  in  the  collieries 
of  Belgium.  Its  chief  characteristic  is  the  inner  sheet-iron  chimney  for 
increasing  the  draft  of  the  lamp. 

Muffle. — A  thin  clay  oven  heated  from  the  outside. 

Mullock. — Country  rock  and  worthless  minerals  taken  from  a  mine. 

Mundic. — Iron  pyrites. 

Naked  Light. — A  candle  or  any  form  of  lamp  that  is  not  a  safety  lamp. 
Narrow  Work. — (1)  All  work  for  which  a  price  per  yard  of  length  driven  is 

paid,  and  which,  therefore,  must  be  measured.     (2)  Headings,  chutes, 

crosscuts,  gangways,  etc. 

Natas  (Mexican). — Same  as  Escoria  or  Grasa. 
Natural  Ventilation. — Ventilation  of  a  mine  without  either  furnace  or  other 

artificial  means;  the  heat  imparted  to  the  air  by  the  strata,  men,  animals, 

and  lights  in  the  mine,  causing  it  to  flow  in  one  direction,  or  to  ascend. 
Neck. — A  cylindrical  body  of  rock  differing  from  the  country  around  it. 
Needle'. — (1)  A  sharp-pointed  metal  rod  with  which  a  small  hole  is  made 

through  the  stemming  to  the  cartridge  in  blasting  operations.     (2)  A 

hitch  cut  in  the  side  rock  to  receive  the  end  of  a  timber. 
Nick. — To  cut  or  shear  coal  after  holing. 
Nicking. — (1)  A  vertical  cutting  or   shearing  up  one  side  of   a  face  of  coal. 

(2)  The  chipping  of  the  coal  along  the  rib  of  an  entry  or  room  which  is 

usually  the  first  indications  of  a  squeeze. 
Night  Shift. — The  set  of  men  that  work  during  the  night. 
Nip. — When  the  roof  and  floor  of  a  coal  seam  come  close  together,  pinching 

the  coal  between  them. 
Nipper. — An  errand  boy,  particularly  one  who  carries  steel,  bits,  etc.,  to  be 

sharpened. 

Nip  Out. — The  disappearance  of  a  coal  seam  by  the  thickening  of  the  adjoin- 
ing strata,  which  takes  its  place. 

Nitro. — A  corrupted  abbreviation  for  nitroglycerine  or  dynamite. 
Nodules. — Concretions   that   are  frequently   found   to   enclose   organic  re- 

•  mains. 

Nogs. — Logs  of  wood  piled  one  on  another  to  support  the  roof.     See  Chock. 
Nook. — The  corner  of  a  working  place  made  by  the  face  with  one  sfde. 
Noria  (Spanish). — An  endless  chain  of  buckets. 
Nozzle. — The  front  nose  piece  of  bellows  or  blast  pipe  for  a  furnace,  or  of  a 

water  pipe. 

Nut  Coal. — A  contraction  of  the  term  chestnut  coal. 
Nuts. — Small  lumps  of  coal  that  will  pass  through  a  screen  or  bars,  the  spaces 

between  which  vary  in  width  from  £  to  2^  in. 

Ocote  (Mexican). — Pitch  pine. 

Odd  Work. — Work  other  than  that  done  by  contract,  such  as  repairing 
roads,  constructing  stoppings,  dams,  etc. 

Offtake. — The  raised  portion  of  an  upcast  shaft  above  the  surface,  for  carrying 
off  smoke  and  steam,  etc.,  produced  by  the  furnaces  and  engines  under- 
ground. 

Oil  Shale. — Shale  containing  such  a  proportion  of  hydrocarbons  as  to  be 
capable  of  yielding  mineral  oil  on  slow  distillation. 

Oil  Smellers. — Men  that  profess  to  be  able  to  indicate  where  petroleum  oil  is 
to  be  found. 


A  GLOSSARY  OF  MINING  TERMS  1131 

Old  Man. — (1)  Old  workings  in  a  mine.     (2)  An  appliance  for  holding  a  drill 

ratchet. 

Oolitic. — A  structure  peculiar  to  certain  rocks,  resembling  the  roe  of  a  fish. 
Open  Cast. — Workings  having  no  roof. 
Open  Cutting. — (1)   An  excavation  made   on  the  surface  for  the  purpose 

of  getting   a   face  wherein  a  tunnel  can   be  driven.     (2)  Any  surface 

excavation. 
Openings,  an  Opening. — Any  excavation  on  a  coal  or  ore  bed,  or  to  reach  the 

same;  a  mine. 
Openwork. — An  open  cut. 
Operario  (Mexican). — A  working  miner. 

Operator. — The  individual  or  company  actually  working  a  colliery. 
Ores.— Minerals  or  mineral  masses  from  which  metals  or  metallic  combina- 
tions can  be  extracted  on  a  large  scale  in  an  economic  manner. 
Outburst. — A  blower.     A  sudden  emission  of  large  quantities  of  occluded  gas. 
Outbye. — In  the  direction  of  the  shaft  or  slope  bottom,  or  toward  the  outside. 
Outcrop. — The  portion  of  a  vein  or  bed,  or  any  stratum  appearing  at  the 

surface,  or  occurring  immediately  below  the  soil  or  diluvial  drift. 
Outcropping. — See  Cropping  Out. 
Outlet. — A  passage  furnishing  an  outlet  for  air,  for  the  miners,  for  water,  or 

for  the  mineral  mined. 
Output. — The  product  of  a  mine  sent  to  market,  or  the  total  product  of  a 

mine. 

Outset. — The  walling  of  shafts  built  up  above  the  original  level  of  the  ground. 
Outstroke  Rent. — The  rent  that  the  owner  of  a  royalty  receives  on  coal  brought 

into  his  royalty  from  adjacent  properties. 
Outtake. — The  passage  by  which  the  ventilating  current  is  taken  out  of  the 

mine;  the  upcast. 
Overburden. — The  covering  of  rock,  earth,  etc.,  overlying  a  mineral  deposit 

that  must  be  removed  before  effective  work  can  be  performed. 
Overcast. — A  passage  through  which  the  ventilating  current  is  conveyed  over 

a  gangway  or  airway. 

Overhand  Sloping. — The  ordinary  method  of  stoping  upwards. 
Overlap 'Fault. — A  fault  in  which  the  shifted  strata  double  back  over  them- 
selves. 
Overman. — One  who  has  charge  of  the  workings  while  the  men  are  in  the 

mine.     He  takes  his  orders  from  the  Underviewer. 
Overwind. — To  hoist  the  cage  into  or  over  the  top  of  the  head-frame. 
Oyamel  (Mexican). — White  pine. 

Pack. — A  rough  wall  or  block  of  coal  or  stone  built  up  to  support  the  roof. 
Packing. — The  material  placed  in  stuffingboxes,  etc.,  to  prevent  leaks. 
Pack  Wall. — A  wall  of  stone  or  rubbish  built  on  either  side  of  a  mine  road,  to 

carry  the  roof  and  keep  the  sides  up. 

Paleozoic. — The  oldest  series  of  rocks  in  which  fossils  of  animals  occur. 
Paler o  (Mexican). — A  mine  carpenter. 
Palm. — A  piece  of  stout  leather  fitting  the  palm  of  the  hand,  and  secured  by 

a  loop  to  the  thumb;  this  has  a  flat  indented  plate  for  forcing  the  needle. 
Palm  Needle. — A  straight  triangular-sectioned  needle,  used  for  sewing  canvas. 
Palo  (Mexican). — A  stick;  a  piece  of  timber. 
Panel. — (1)    A   large  rectangular  block  or  pillar  of  coal   measuring,   say, 

130  by  100  yd.      (2)  A  group  of  breasts  or  rooms  separated  from  the 

other  workings  by  large  pillars. 
Panel  Working. — A  system  of  working  coal  seams  in  which  the  colliery  is 

divided  up  into  large  squares  or  panels,  isolated  or  surrounded  by  solid 

ribs  of  coal,  in  each  of  which  a  separate  set  of  breasts  and  pillars  is 

worked,  and  the  ventilation  is  kept  distinct,  that  is,  every  panel  has  its 

own  circulation,  the  air  of  one  not  passing  into  the  adjoining  one,  but 

being  carried  direct  to  the  main  return  airway. 
Parcionero  (Mexican). — A  partner  in  a  mining  contract. 
Parrot  Coal. — A  kind  of  coal  that  splits  or  cracks  with  a  chattering  noise 

when  on  the  fire. 
Parting.— (I)  Any  thin  interstratified  bed  of  earthy  material.     (2)  A  side 

track  or  turnout  in  a  haulage  road. 
Pass. — (1)  A  convenient  hole  for  throwing  down  ore  to  a  lower  level.     (2)  A 

passage  left  in  old  workings  for  men  to  travel  in  from  one  level  to 

another. 
Pass-By. — A  siding  in  which  cars  pass  one  another  underground;  a  turnout. 


1132  A  GLOSSARY  OF  MINING  TERMS 

Pass-Into. — When  one  mineral  gradually  passes  into  another  without  any 

sudden  change. 

Patch  or  Patcher. — A  driver's  assistant  or  helper;  a  brakeman  or  triprider. 
Patented  Claim. — A  claim  to  which  a  patent  right  has  been  secured  from  the 

government,  by  compliance  with  the  laws  relating  to  such  claims. 
Patent  Fuel. — Small  coal  mixed  with  small  amounts  of  pitch,  tar  or  other 

binder  and  compressed  by  machinery  into  bricks. 
Patent  Survey. — An  accurate  survey  of  a  claim  by  a  deputized  surveyor  as 

required  by  law  in  order  to  secure  a  patent  right  to  the  claim. 
Pavement. — The  floor. 
Pay  Out. — To  slacken  or  let  out  rope. 
Pay  Rock. — Mineralized  rock. 
Pay  Streak. — Mineralized  part  of  rock. 
Peach  Stone  (Cornish). — Chlorite  schist. 
Pea  Coal. — A  small  size  of  anthracite  coal  (see  page  952). 
Peas. — Small  coal  about  J  to  }  in.  cube. 
Peat. — The  decomposed  partly  carbonized  organic  matter  of  bogs,  swamps, 

etc. 

Penstock. — See  Forebay. 
Pent  House. — A  wooden  covering  for  the  protection  of  sinkers  working  in  a 

pit  bottom. 
P entice. — A  few  pieces  of  timber  laid  as  a  roof  over  men's  heads,  to  screen 

them  when  working  in  dangerous  places,  e.g.,  at  the  bottom  of  shafts. 
Pestle. — A  hard  rod  for  pounding  minerals,  etc. 

Peter  Out. — To  "peter.out"  is  to  thin  out,  or  gradually  decrease  in  thickness. 
Petrifaction. — Organic  remains  converted  into  stone. 
Petrol. — Variant  for  petroleum  or  its  derivatives,  particularly  gasoline  or 

motor  spirit. 
Pick. — (1)  A  tool  for  cutting   and   holing  coal.     (2)  To  dress   the  sides  or 

face  of  an  excavation  with  a  pick. 
Picker. — (1)  A  small  tool  used  to  pull  up  the  wick  of  a  miner's  lamp.     (2) 

A  person  who  picks  the  slate  from  the  coal  in  a  coal  breaker  or  tipple. 
Picking  Chute. — A  chute  in  an  anthracite  breaker  along  which   boys  are 

stationed  to  pick  the  slate  from  coal. 
Picking  Table. — (1)  A  flat  or  slightly  inclined  platform  on  which  anthracite 

coal  is  run  to  be  picked  free  from  slate.     (2)  A  sorting  table.     (3)  A 

moving  belt  or  steel  apron  on  which  coal  is  picked. 
Pico  (Mexican). — A  striking  or  sledge  hammer. 
Picture. — A  screen  to  keep  off  falling  water  from  men  at  work. 
Pig. — A  piece  of  lead  or  iron  cast  into  a  long  rough  mold. 
Pigsty  Timbering. — Hollow  pillars  built  up  of  logs  of  wood  laid  crosswise 

for  supporting  heavy  weights. 
Pike. — A  pick. 
Pileta  (Mexican). — A  sump. 
Piling. — Long  pieces  of  timber  driven  into  soft  ground  for  the  purpose    of 

securing  a  solid  base   on   which  to  build   any    superstructure     Sheet 

piling  consists  of  planks  or  steel  shapes  driven  into  the  ground  to  pre- 
vent an  influx  of  water,  quicksand  and  the  like. 
Pillar. — (1)  A  solid  block  of  coal,  etc.,  varying  in  area  from  a  few  square 

yards  to  several  acres.     (2)  Sometimes  applied  to  a  timber  support. 
Pillar-and-Room. — A  system  of  working  coal  by  which  solid  blocks  of  coal 

are  left  on  either  side  of  the  rooms,  entries,  etc.,  to  support  the  roof  until 

the  rooms  are  driven  up,  after  which  they  are  drawn  out. 
Pillar-and-Stall. — See  Breast-and-Pillar. 

Pillar  Roads. — Working  roads  or  inclines  in  pillars  having  a  range  of  long- 
wall  faces  on  either  side. 
Pinch. — A  contraction  in  the  vein. 

Pinch  Out. — When  a  lode  or  stratum  runs  out  to  nothing. 
Pipe. — An  elongated  body  of  mineral.     Also  the  name  given  to  the  fossil 

trunks  of  trees  found  in  coal  veins. 
Pipe  Clay.— A.  soft  white  clay. 

Piped  Air. — Air  carried  into  the  working  place  by  pipes  or  brattices. 
Pit. — (1)  A  shaft.     (2)  The  underground  portion  of  a  colliery,  including  all 

workings.     (3)  A  gravel  pit. 
Pit  Bank. — The  raised   ground  or  platform   where  the  coal  is  sorted  and 

screened  at  the  surface. 
Pit  Bottom. — The  portion  of  a  mine  immediately  around  the  bottom  of  a  shaft 

or  slope.     See  Shaft  Bottom. 


A  GLOSSARY  OF  MINING  TERMS  1133 

Pitch, — (1)  Rise  of  a  seam.      (2)  Grade  of  an  incline.      (3)  Inclination.      (4) 
(Cornish)  A  part  of  a  lode  let  out  to  be  worked  on  shares  or  by  the 

piece. 

Pit  Coal. — Generally  signifies  the  bituminous  varieties  of  coal. 
Pit  Frame. — See  Head-Frame. 

Pit  Headman.— The  man  who  has  charge  at  the  top  of  the  shaft  or  slope. 
Pitman. — A  miner;  also,  one  who  looks  after  the  pumps,  etc. 
Pit  Prop. — A  piece  9f  timber  used  as  a  temporary  support  for  the  roof. 
Pit  Rails. — Mine  rails  for  underground  roads. 

Pit^Room. — The  extent  of  underground  workings  in  use  or  available  for  use. 
Pit's  Eye. — Pit  bottom  or  entrance  into  a  shaft. 
Pit  Top. — The  mouth  of  a  shaft  or  slope. 
Place. — The  portion  of  coal  face  allotted  to  a  hewer  is  spoken  of  as  his 

"working  place,"  or  simply  "place." 
Plan. — (1)   The  system  on  which  a  colliery  is  worked  as  Long-wall,  Pillar- 

and-Breast,  etc.     (2)   A  map  or  plan  of  the  colliery  showing  outside 

improvements  and  underground  workings.     (3)    (Mexican)    The  very 

lowest    working    in    a    mine.      Trabajar   de  Plan. — To   work  to   gain 

depth. 
Plane. — A  main  road,  either  level  or  inclined,  along  which  coal  is  conveyed 

by  engine  power  or  gravity. 
Plane  Table. — A  simple  surveying  instrument  by  means  of  which  one  can 

plot  in  the  field. 
Plank   Dam. — A   water-tight   stopping   fixed  in  a   heading  constructed   of 

timber  placed  across  the  passage,  one  upon  another,  sidewise,  and  tightly 

wedged. 
Plank    Tubbing. — Shaft    lining    of    planks    driven    down    vertically   behind 

wooden  cribs  all  around  the  shaft,  all  joints  being  tightly  wedged,  to 

keep  back  the  water. 
Plant. — The  shafts  or  slope,  tunnels,  engine  houses,  railways,  machinery, 

workshops,  etc.,  of  a  colliery  or  other  mine. 
Plat,  or  Map. — A  map  of  the  surface  and  underground  workings,  or  of  either; 

to  draw  such  a  map  from  survey. 

Plate  (North  of  England). — Scaly  shale  in  limestone  beds. 
Plates. — Metal  rails  4  ft.  long. 
Plenum. — A  mode  of  ventilating  a  mine  or  a  heading  by  forcing  fresh  air 

into  it. 

Plomada  (Mexican). — A  plumb-line  or  plumb-bob. 
Plugging. — When  drift  water  forces  its  way  through  the  puddle  clay  into 

the  shaft,  holes  are  bored  through  the  slabs  near  the  leakage  point,  and 

plugs  of  c'ay  forced  into  them  until  the  leakage  is  stopped. 
Plumb.— Vertical. 
Plummet. — (1)  A  heavy  weight  attached  to  a  string  or  fine  copper  wire  used 

for  determining  the  verticality  of  shaft  timbering.     (2)  A  plumb-bob 

setting  a  surveying  instrument  over  a  point. 

Plunger. — The  solid  ram  of  a  force  pump  working  in  the  plunger  case. 
Plunger  Case. — The  pump  cylinder  or  barrel  in  which  the  plunger  works. 
Poblar  (Mexican). — To  set  men  at  work  in  a  mine. 
Pocket. — (1)  A  thickening  out  of  a  seam  of  coal  or  other  mineral  over  a  small 

area.     (2)  A  hopper-shaped  receptacle  from  which  coal  or  ore  is  loaded 

into  cars  or  boats. 
Pole  Tools. — Drilling  tools  used  in  drilling  in  the  old  fashion,  with  rods,  now 

superseded  by  the  rope-drilling  method. 

Poll  Pick. — A  pick  having  the  longer  end  pointed  and  the  shorter  end  ham- 
mer-shaped. 

Polrot  (Cornish).— Waterwheel  pit. 

Poppet  Heads. — The  pulley  frame  or  hoisting  gear  over  a  shaft. 
Poppet  (Puppet). — (1)  A  pulley  frame  or  the  head-gear  over  a  shaft.     (2)   A 

valve  that  lifts  bodily  from  its  seat  instead  of  being  hinged. 
posl. — (i)  Any  upright  timber;  applied  particularly  to  the  timbers  used  for 

propping.     See  Prop.     (2)  Local  term  for  sandstone.     Post  stone  may 

be  "strong,"  "framey,"  "short,"  or  "broken." 

Post-and-Stall. — A  system  of  working  coal  much  the  same  as  Pillar-and-Stall. 
Post-Tertiary. — Strata  younger  than  the  Tertiary  formation. 
Pot  Bottom. — A  large  boulder  in  the  roof  slate,  having  the  appearance  of  the 

rounded  bottom  of  a  pot,  and  which  easily  becomes  detached. 
Pot  Growan  (Cornish). — Decomposed  granite. 
Pot  Hole. — A  circular  hole  in  the  rock  caused  by  the  action  of  stones  whirled 


1134  A  GLOSSARY  OF  MINING  TERMS 

around  by  the  water  when  the  strata  was  covered  by  water.  They  are 
generally  filled  with  sand  and  drift. 

Power  Drill. — A  rock  drill  employing  steam,  air,  or  electricity  as  a  motor. 

Prian  (Cornish). — Soft  white  clay. 

Pricker. — (1)  A  thin  brass  rod  for  making  a  hole  in  the  stemming  when 
blasting,  for  the  insertion  of  a  fuse.  (2)  A  piece  of  bent  wire  by  which 
the  size  of  the  flame  in  a  safety  lamp  is  regulated  without  removing  the 
top  of  the  lamp. 

Prong  (English). — The  forked  end  of  the  bucket-pump  rods  for  attachment 
to  the  traveling  valve  and  seat. 

Prop. — A  wooden  or  metal  temporary  support  for  the  roof. 

Propping. — The  timbering  of  a  mine. 

Prospect. — The  name  given  to  underground  workings  whose  value  has  not 
yet  been  made  manifest.  A  prospect  is  to  a  mine  what  mineral  is  to  ore. 

Prospect  Hole. — Any  shaft  or  drift  hole  put  down  for  the  purpose  of  prospect- 
ing the  ground. 

Prospecting. — Examining  a  tract  of  country  in  search  of  minerals. 

Prospector. — One  engaged  in  searching  for  minerals. 

Prospect  Tunnel  or  Entry. — A  tunnel  or  entry  driven  through  barren  measures 
or  a  fault  to  ascertain  the  character  of  strata  beyond. 

Protector  Lamp. — A  safety  lamp  whose  flame  cannot  be  exposed  to  the  out- 
side atmosphere,  as  the  action  of  opening  the  lamp  extinguishes  the 
light. 

Prove. — (1)  To  ascertain,  by  boring,  driving,  etc.,  the  position  and  character 
of  a  coal  seam,  a  fault,  etc.  (2)  To  examine  a  mine  in  search  of  fire- 
damp, etc.,  known  as  "proving  the  pit." 

Proving  Hole. — (1)  A  bore  hole  driven  for  prospecting  purposes'.  (2)  A 
small  heading  driven  in  to  find  a  bed  or  vein  lost  by  a  dislocation  of 
the  strata,  or  to  prove  the  quality  of  the  mineral  in  advance  of  the  other 
workings. 

Pudding  Rock. — Conglomerate. 

Puddle. — (1)  Earth  well  rammed  into  a  trench,  etc.,  to  prevent  leaking.  (2) 
A  process  for  converting  cast  iron  into  wrought  iron. 

Pueble  (Mexican). — The  actual  working  of  a  mine;  the  aggregation  of  persons 
employed  therein. 

Puertas  (Mexican). — Massive  barren  rocks,  or  "horses,"  occurring  in  a  vein. 

Pug  Mill. — A  mill  for  preparing  clay  for  making  bricks,  pottery,  etc. 

Pulley. — (1)  The  wheel  over  which  a  winding  rope  passes  at  the  top  of  the 
head-gear.  (2)  Small  wooden  cylinders  over  which  a  winding  rope  is 
carried  on  the  floor  or  sides  of  a  plane. 

Pulleying. — Overwinding  or  drawing  up  a  cage  into  the  pulley  frame. 

Pump. — Any  mechanism  for  raising  water. 

Pump  Bob. — See  Bob. 

Pump  Ring. — A  flat  iron  ring  that,  when  lapped  with  tarred  baize  or  engine 
shag,  secures  the  jpints  of  water  columns. 

Pump  Rods. — Heavy  timbers  by  which  the  motion  of  the  engine  is  trans- 
mitted to  the  pump.  In  Cornish  and  bull  pumps,  the  weight  of  the 
rods  makes  the  effective  (pumping)  stroke,  the  engine  merely  lifting 
the  rods  on  the  up  stroke. 

Pump  Slope. — A  slope  used  for  pumping  machinery. 

Pump  Station. — An  enlargement  made  in  the  shaft,  slope,  or  gangway,  to 
receive  the  pump. 

Pump  Tree. — Cast-iron  pipes,  generally  9  ft.  long,  of  which  the  column  or  set 
is  formed. 

Punch-and-Thirl. — A  kind  of  pillar-and-stall  system  of  working. 

Punch  Prop. — A  short  timber  prop  set  on  the  top  of  a  crown  tree,  or  used  in 
holding,  as  a  sprag. 

Pyran  (Cornish). — See  Prian. 

Pyrites. — Sulphide  of  iron,  copper,  etc. 

Pyrometer. — An  instrument  for  measuring  high  degrees  of  heat. 

Quarry. — (1)  An  open  surface  excavation  for  working  valuable  rocks  or 
minerals.  (2)  An  underground  excavation  for  obtaining  stone  for 
stowage  or  pack  walls. 

Quaternary. — Post-tertiary  period. 

Quemados  (Mexican). — Burnt  stuff.  Any  dark  cinder-like  mineral  encoun- 
tered in  a  vein  or  mineral  deposit,  generally  manganiferous. 

Quick  (Adjective). — Soft,  running  ground.     Quick  (Noun). — Productive. 


A  GLOSSARY  OF  MINING  TERMS  1135 

Quicksand. — Soft  watery  strata  easily  moved,  or  readily  yielding  to  pressure. 
Quicksilver. — Mercury. 

Quitdpepena   (Mexican). — A  watchman  that  searches  the  miners  as  they 
come  out  at  the  mouth  of  a  mine. 

Race. — A  channel  for  conducting  water  to  or  from  the  place  where  it  per- 
forms work.     The  former  is  termed  the  headrace,  and  the  latter  the 

tailrace. 
Rack  (Cornish). — A  toothed  gear  of  infinite  radius,  i.e.  a  straight  gear  or  one 

whose  pitch  line  has  no  curvature. 

Rafter  Timbering. — That  in  which  the  timbers  appear  like  roof  rafters. 
Rag  Wheel. — Sprocket  wheel.     A  wheel  with  teeth  or  pins  that  catch  into  the 

links  of  chains. 
Rails. — The  iron  or  steel  portion  of  the  tramway  or  railroad  or  their  wooden 

counterparts. 

Rake  (Cornish). — (1)  A  vein.      (2)  (Derbyshire)  Fissure  vein  crossing  strata. 
Ram. — (1)  The  plunger  of  a  pump.     (2)  A  device  for  raising  water.     (3)  A 

machine  for  drawing  a  coke  charge  from  an  oven. 
Ramal  (Mexican). — A  branch  vein. 

Ramalear  (Mexican). — To  branch  off  into  various  divisions. 
Ramble. — Stone  of  little  coherence  above  a  seam  that  falls  readily  on  the 

removal  of  the  coal.     See  Following  Stone. 
Ranee. — A  pillar  of  coal. 
Rapper. — A  lever  with  a  hammer  attached  at  one  end,  which  signals  by 

striking  a  plate  of  metal,  when  the  signaling  wire  to  which  it  is  attached 

is  pulled. 
Rash. — A  term  used  to  designate  the  bottom  of  a  mine  when  soft  and  slaty; 

also  the  top* 

Reacher. — A  slim  prop  reaching  from  one  wall  to  the  other. 
Reamer. — An  enlarging  tool. 

Reaming. — Enlarging  the  diameter  of  a  bore  hole. 
Receiving  Pit. — A  shallow  pit  for  containing  material  run  into  it. 
Red- Ash  Coal. — Coal  that  produces  a  reddish  ash  when  burnt. 
Red  Rab  (Cornish).— Red  slaty  rock. 
Refuge  Chamber. — A  chamber  shut  off  from  the  rest  of  the  mine,  stored  with 

food,  etc.,  and  to  be  used  by  the  survivors  in  case  of  a  mine  disaster. 
Refuge  Hole. — A  place  formed  in  the  side  of  an  underground  passage  in  which 

a  man  can  take  refuge  during  the  passing  of  a  train,  or  when  shots  are 

fired. 
Regulator. — A  door  in  a  mine,  the  opening  or  shutting  of  which  regulates  the 

supply  of  ventilation  to  a  district  of  the  mine. 
Reliz  (Spanish).— Wall  of  lode. 
Rendrock. — A  variety  of  dynamite. 
Repairman. — A  workman  whose  duty  it  is  to  repair  tracks,  doors,  brattices, 

or  to  reset  timbers,  etc.,  under  the  direction  of  the  foreman. 
Rescue  and  Recovery. — The  work  of  removing  live  men  or  dead  bodies  after 

a  mine  disaster;  also  putting  the  mine  in  shape  for  operation  again. 
Reserve. — Mineral  already  opened  up  by  shafts,  winzes,  levels,  etc.,  which 

may  be  secured  at  short  notice  for  any  emergency.' 
Reservoir. — An  artificially  built,  dammed,  or  excavated  place  for  holding  a 

reserve  of  water. 
Respaldos   (Mexican). — The  walls  enclosing  a  vein.     Respaldo  Alto. — The 

hanging  wall.     Respaldo  Bajo. — 'The  foot-wall. 
Rests,  Keeps,  Wings. — Supports  on  which  a  cage  rests  when  the  loaded  car 

is  being  taken  off  and  the  empty  one  put  on. 
Resue. — See  Stripping. 

Retort  Oven. — A  coke  oven  which  conserves  the  gas  evolved. 
Return. — The  air-course  along  which  the  vitiated  air  of  a  mine  is  returned 

or  conducted  back  to  the  upcast  shaft. 

Return  Air. — The  air  that  has  been  passed  through  the  workings. 
Reverberator y. — A  class  of  furnaces  in  which  the  flame  from  the  fire-grate  is 

made  to  beat  down  on  the  charge  in  the  body  of  the  furnace. 
Reversed  Fault. — See  Overlap  Fault. 
Rib. — The  side  of  a  pillar. 

Rib-and-Pillar.—A.  system  of  working, similar  to  Pillar-and-Stall. 
Ribbon— A.  line  of  bedding  or  a  thin  bed  appearing  on  the  cleavage  surface 

and  sometimes  of  a  different  color. 
Rick. — Open  heap  in  which  coal  is  coked. 


1136  A  GLOSSARY  OF  MINING  TERMS 

Ridding. — Clearing  away  fallen  stone  and  debris. 

Riddle. — (1)  An  oblong  frame  holding  iron  bars  parallel  to  each  other,  used 

for  sifting  material  that  is  thrown  against  it.     (2)  A  hand  operated  sieve. 
Ride,  Riding. — To  be  conveyed  on  a  cage  or  mine  car. 
Rider. — (1)  A  guide  frame  for  steadying  a  sinking  bucket.      (2)   Boys  that 

ride  on  trips  on  mechanical  haulage  roads.     (3)  A  thin  seam  of  coal 

overlying  a  thicker  one. 

Right  Shore. — The  right  shore  of  a  river  is  on  the  right  hand  when  descend- 
ing the  river. 

Rim  Rock. — Bed  rock  forming  a  boundary  to  gravel  deposit. 
Ring. — (1)  A  complete  circle  of  tubbing  plates  placed  round  a  circular  shaft. 

(2)  Troughs  placed  in  shafts  to  catch  the  falling  water,  and  so  arranged 

as  to  convey  it  to  a  certain  point. 

Ripping. — Removing  stone  from  its  natural  position  above  the  seam. 
Rise. — The  inclination  of  the  strata,  when  looking  up  the  pitch. 
Rise  Workings. — Underground  workings  carried  on  to  the  rise  or  high  side 

of  the  shaft. 
Road. — (1)   Any  underground  passageway  or  gallery.     (2)   The  iron  rails, 

etc.,  of  underground  roads. 

Rob. — To  cut  away  or  reduce  the  size  of  pillars  of  coal. 
Robbing. — The  taking  of  mineral  from  pillars. 
Robbing  an  Entry. — See  Drawing  an  Entry. 

Rock. — A  mixture  of  different  minerals  in  varying  proportions. 
Rock  Chute.— See  Slate  Chute. 
Rock  Drill. — A  rock-boring  machine  worked  by  hand,  compressed  air,  steam, 

or  electrical  power. 
Rock  Fault. — A  replacement  of  a  coal  seam  over  greater  or  less  area,  by  some 

other  rock,  usually  sandstone.  * 

Rodding. — The  operation  of  fixing  or  repairing  wooden  eye  guides  in  shafts. 
Roll. — An  inequality  in  the  roof  or  floor  of  a  mine. 
Roller. — A  small  steel,  iron,  or  wooden  wheel  or  cylinder  upon  which  the 

hauling  rope  is  carried  just  above  the  floor. 
Rolleyway. — A  main  haulage  road. 
Rolling  Ground. — When  the  surface  is  much  varied  by  many  small  hills  and 

valleys. 
Rolls. — Cast-iron  cylinders,  either   plain  or  fitted  with  steel  teeth,  used  to 

break  coal  and  other  materials  into  various  sizes. 
Roof. — The  top  of  any  subterranean  passage. 
Room. — Synonymous  with  Breast. 

Room-and-Rance. — A  system  of  working  coal  similar  to  Pillar-and-Stall. 
Rope  Roll. — The  drum  of  a  winding  engine. 
Round  Coal. — Coal  in  large  lumps,  either  hand-picked,  or,  after  passing  over 

screens,  to  take  out  the  small. 

Royalty. — The  price  paid  per  ton  to  the  owner  of  mineral  land  by  the  lessee. 
Rubbing  Surface. — The  total  area  of  a  given  length  of  airway;  that  is,  the 

area  of  top,  bottom,  and  sides  added  together,  or  the  perimeter  multi- 
plied by  the  length. 
Rubble. — Coarse  pieces  of  rock. 

Rumbo  (Mexican). — -'The  course  or  direction  of  a  vein. 
Run. — (1)  The  sliding  and  crushing  of  pillars  of  coal.     (2)  The  length  of  a 

lease  or  tract  on  the  strike  of  the  seam. 
Run  Coal. — Soft  bituminous  coal. 

Rung,  Rundle,  or  Round. — A  step  or  cross-bar  of  a  ladder. 
Runner. — A  man  or  boy  whose  duty  it  is  to  run  mine  cars  by  gravity  from 

working  places  to  the  gangway. 
Running  Lift. — A  sinking  set  q    pumps  constructed  to  lengthen  or  shorten 

at  will,  by  means  of  a  sliding  or  telescoping  wind  bore. 
Rush. — An  old-fashioned  way  of  exploding  blasts  by  filling  a  hollow  stalk 

with  slow  powder  and  then  igniting  it. 
Rush  Together. — See  Caved  In. 
Rusty. — Stained  by  iron  oxide. 

Saddle. — An  anticlinal,  a  hogback. 

Saddleback. — A  depression  in  the  strata.     See  Roll. 

Safety  Cage. — A  cage  fitted  with  an  apparatus  for  arresting  its  motion  in  the 

shaft  in  case  the  rope  breaks. 
Safely  Car. — See  Barney. 
Safety  Catches. — Appliances  fitted  to  cages,  to  make  them  safety  cages. 


A  GLOSSARY  OF  MINING  TERMS  1137 

Safety  Door. — A  strongly  constructed  door,  hinged  to  the  roof,  and  always 
kept  open  and  hung  near  to  the  main  door,  for  immediate  use  when 
main  door  is  damaged  by  an  explosion  or  otherwise. 

Safety  First. — A  term  often  applied  to  accident  prevention  and  first  aid 
and  to  rescue  and  recovery  training  in  general. 

Safety  Fuse. — A  cord  with  slow-burning  powder  in  the  center  for  exploding 
charged  blast  holes. 

Safely  Lamp. — (1)  A  miner's  lamp  in  which  the  flame  is  protected  in  such  a 
manner  that  an  explosive  mixture  of  air  and  firedamp  can  be  detected 
by  the  mixture  burning  inside  the  gauze.  (2)  An  electric  cap  or  hand 
lamp  which  will  not  ignite  gas  even  when  broken. 

Sag. — A  depression,  e.g.,  m  ropes,  ranges  of  mountains,  etc.,  also  in  mine 
floors. 

Sagre,  or  Seggar. — A  local  term  for  fireclay,  often  forming  the  floor  (or  thill) 
of  coal  seams. 

Salting. — (1)  Changing  the  value  of  the  ore  in  a  mine  or  of  ore  samples 
before  they  have  been  assayed,  so  that  the  assay  will  show  much  higher 
values  than  it  should.  (2)  Sprinkling  salt  on  the  floors  of  underground 
passages  in  very  dry  mines,  in  order  to  lay.  the  dust. 

Sample. — A  representative  specimen  of  coal  from  a  much  larger  amount  as 
a  carload,  shipload,  or  from  the  face  of  a  room. 

Sampler. — (1)  An  instrument  or  apparatus  for  taking  samples.  (2)  One 
whose  duty  it  is  to  select  the  samples  for  an  assay  or  analysis,  or  to 
prepare  the  mineral  to  be  tested,  by  grinding  and  sampling. 

Samson  Post. — An  upright  supporting  the  working  beam  that  communicates 
oscillatory  motion  to  pump  or  drill  rod. 

Sand  Bag. — A  bag  filled  with  sand  for  preventing  a  washout  by  obstructing 
the  flow. 

Sand  Pump. — A  sludger;  a  cylinder  provided  with  a  stem  (or  other)  valve, 
lowered  into  a  drill  hole  to  remove  the  pulverized  rock. 

Scaffolding. — (1)  Incrustations  on  the  inside  of  a  blast  furnace.  (2)  False- 
work employed  in  building. 

Scale. — (1)  A  small  portion  of  the  ventilating  current  m  a  mine  passing 
through  a  certain  size  of  aperture.  (2)  The  rate  of  wages  to  be  paid, 
which  varies  under  certain  contingencies.  (3)  A  weighing  apparatus 
(4)  Incrustation  on  the  inside  of  a  boiler. 

Scnle  Door. — See  Regulator. 

Scallop. — To  hew  coal  without  kirying  or  nicking  or  shot  firing. 

Schist. — Crystalline  or  metamorphic  rocks  having  a  slaty  structure. 

Schute. — See  Chute. 

Scissors  Fault. — A  fault  of  dislocation,  in  which  two  beds  are  thrown  so  as  to 
cross  each  other. 

Scoop. — A  large-sized  shovel  with  a  scoop-shaped  blade. 

Scoria. — Ashes.  _ 

Scrap. — (1)    Worthless   or   obsolete    iron,    copper,    machinery,    etc.      (2)  To 

Scraper.— (1)  A  tool  for  cleaning  the  dust  out  of  the  bore  hole.  (2)  A 
mechanical  contrivance  used  at  colleries  to  scrape  the  culm  or  slack 
along  a  trough  to  the  place  of  deposit. 

Screen. — (1)  A  mechanical  apparatus  for  sizing,  materials.  (2)  A  cloth  brat- 
tice or  curtain  hung  across  a  road  in  a  mine,  to  direct  the  ventilation. 

Serin  (Derbyshire).— A  small  vein. 

Sculping. — Fracturing  the  state  along  the  gram,  i.e.,  across  the  cleavage. 

Scupper  Nails.— Nails  with  broad  heads,  for  nailing  down  canvas,  etc. 

Sea  Coal. — That  which  is  transported  by  sea. 

Sealing.— Shutting  off  all  air  from  a  mine  or  a  part  of  a  mine  by  stoppings. 

Seam. — Synonymous  with  Bed,  Vein,  etc. 

Seam-Out—  A  term  applied  to  a  shot  or  blast  that  has  simply  blown  out  ; 
softer  stratum  of  the  deposit  in  which  it  was  placed,  without  dislodging 
the  other  strata  or  layers  of  the  seam.  .  . 

Second  Outlet  (Second  Opening).— A  passageway  out  of  a  mine,  for  use  in  case 
of  accident  to  the  main  outlet. 

Seconds. — Second-class  coal,  not  best.  , 

Second  Working.— The  operation  of  getting  or  working  out  the  pillars  formed 
by  the  first  working.  .  .  , 

Section.— (I)  A  vertical  or  horizontal  exposure  of  strata.     (2)  A  drawing  or 
sketch  representing  the  rock  strata  as  cut  by  a  vertical  or  a  horizontal 
plane. 
72 


1138  A  GLOSSARY  OF  MINING  TERMS 

Sedimentary  Rocks. — Rocks  formed  from  deposits  of  sediment  by  wind  or 
water. 

Seedbag. — A  water-tight  packing  of  flaxseed  around  the  tube  in  a  drill  hole, 
to  prevent  the  influx  into  the  hole  of  water  from  above. 

Segregations. — Detached  portions  of  veins  in  place. 

Self- Acting  Plane. — An  inclined  plane  upon  which  the  weight  or  force  of 
gravity  acting  on  the  full  cars  is  sufficient  to  overcome  the  resistance  of 
the  empties;  in  other  words,  the  full  car,  running  down,  pulls  the  other 
car  up. 

Self-Detaching  Hook.— A  self-acting  hook  for  setting  free  a  hoisting  rope  in 
case  of  overwinding. 

Selvage. — The  clay  seam  on  the  walls  of  veins;  gouge. 

Separation  Doors. — The  main  doors  at  or  near  the  shaft  or  slope  bottom, 
which  separate  the  intake  from  the  return  airways. 

Separation  Valve. — A  massive  cast-iron  plate  suspended  from  the  roof  of  a 
return  airway  through  which  all  the  return  air  of  a  separate  district 
flows,  allowing  the  air  to  always  flow  past  or  underneath  it;  but  in 
the  event  of  an  explosion  of  gas,  the  force  of  the  blast  closes  it  against 
its  frame  or  seating,  and  prevents  a  communication  with  other  districts. 
The  blast  being  over,  the  weight  of  the  valve  allows  it  to  return  to  its 
normal  position. 

Set. — To  fix  in  place  a  prop  or  sprag. 

Set  Hammer. —  The  flat-faced  hammer  held  on  hot  iron  by  a  blacksmith  when 
shaping  or  smoothing  a  surface  by  aid  of  his  striker's  sledge. 

Set  of  Timber. — The  timbers  which  compose  any  framing,  whether  used  in 
a  shaft,  slope,  level,  or  gangway.  Thus,  the  four  pieces  forming  a  single 
course  in  the  curbing  of  a  shaft,  or  the  three  or  four  pieces  forming 
the  legs  and  collar,  and  sometimes  the  sill  of  an  entry  framing  are 
together  called  a  set  of  timber,  or  timber  set. 

Shackle. — A  U-shaped  link  in  a  chain  closed  by  a  pin;  when  the  latter  is  with- 
drawn the  chain  is  severed  at  that  point. 

Shaft. — A  vertical  or  highly  inclined  pit  or  hole  made  through  strata,  through 
which  the  product  of  the  mine  is  hoisted,  and  through  which  the  ventila- 
tion is  passed  either  into  or  out  of  the  mine.  A  shaft  sunk  from  one 
seam  to  another  is  called  a  "blind  shaft." 

Shaft  Pillar. — Solid  material  left  unworked  beneath  buildings  and  around 
the  shaft,  to  support  them  against  subsidence. 

Shaking  Screen  or  Shaker. — A  flat  screen,  often  inclined,  which  is  given  an 
oscillatory  motion  and  is  used  for  sizing  coal. 

Shale. — (1)  Strictly  speaking,  all  argillaceous  strata  that  split  up  or  peel  off 
in  thin  laminae.  (2)  A  laminated  and  stratified  sedimentary  deposit  of 
clay,  often  impregnated  with  bituminous  matter. 

Shank. — The  body  portion  of  any  tool,  up  from  its  cutting  edge  or  bit. 

Shearing. — Cutting  a  vertical  groove  in  a  coal  face  or  breast.  The  cutting  of 
a  "fast  end"  of  coal. 

Shear  Legs. — A  high  wooden  frame  placed  over  an  engine  or  pumping  shaft 
fitted  with  small  pulleys  and  rope  for  lifting  heavy  weights. 

Shears,  or  Sheers  (English). — Two  tall  poles,  with  their  feet  some  distance 
apart  and  their  tops  fastened  together,  for  supporting  hoisting  tackle. 

Shear  Zone. — Hogback. 

Sheave. — A  wheel  with  a  grooved  circumference  over  which  a  rope  is  passed 
either  for  the  transmission  of  power  or  for  winding 'or  hauling. 

Sheet  Pump. — See  Sludger. 

Sheets. — Coarse  cloth  curtains  or  screens  for  directing  the  ventilating  current 
underground. 

Shelly. — A  name  applied  to  coal  that  has  been  so  crushed  and  fractured  that 
it  easily  breaks  up  into  small  pieces.  The  term  is  also  applied  to  a  lami- 
nated roof  that  sounds  hollow  and  breaks  into  thin  layers  of  slate  or 
shale. 

Shet  (Staffordshire)  .-•— Fallen  roof  of  coal  mine. 

Sheth. — An  old  term  denoting  a  district  of  about  eight  or  nine  adjacent 
bords.  Thus,  a  "sheth  of  bords,"  or  a  "sheth  of  pillars." 

Shift. — (1)  The  number  of  hours  worked  without  change.  (2)  A  gang  or 
force  of  workmen  employed  at  one  time  upon  any  work,  as  the  day  shift, 
or  the  night  shift. 

Sheading  (Cornish) . — Prospecting. 

Shoe. — (1)  A  steel  or  iron  guide  piece  fixed  to  the  ends  or  sides  of  cages,  to 
fit  or  run  on  the  conductors.  (2)  The  lower  capping  of  any  post  or  pile, 


A  GLOSSARY  OF  MINING  TERMS  1139 

to  protect  its  end  while  driving.  (3)  A  wooden  or  sheet-iron  frame  or 
muff  arranged  at  the  bottom  of  a  shaft  while  sinking  through  quicksand, 
to  prevent  the  inflow  of  sand  while  inserting  the  shaft  lining. 

Shoot,  Chute,  Shute. — An  inclined  or  vertical  trough  or  pipe  for  conveying 
materials  from  a  higher  to  a  lower  level. 

Shoot. — To  break  rock  or  coal  by  means  of  explosives. 

Shooting. — Blasting  in  a  mine. 

Shore  (English). — A  studdle  or  thrusting  stay. 

Shore  Up. — To  stay,  prop  up,  or  support  by  braces. 

Shot. — (1)  A  charge  or  blast.  (2)  The  firing  of  a  blast.  (3)  Injured  by  a 
blast. 

Shot  Firer. — See  Shot  Lighter. 

Shot  Hole. — The  bore  hole  in  which  an  explosive  substance  is  placed  for 
blasting. 

Shot  Lighter,  or  Shot  Firer. — A  man  specially  appointed  by  the  manager  of 
the  mine  to  fire  off  every  shot  in  a  certain  district,  if,  after  he  has 
examined  the  immediate  neighborhood'of  the  shot,  he  finds  it  free  from 
gas,  and  otherwise  safe. 

Show. — When  the  flame  of  a  safety  lamp  becomes  elongated  or  unsteady, 
owing  to  the  presence  of  firedamp  in  the  air,  it  is  said  to  show. 

Showing. — The  first  appearance  of  float,  indicating  the  approach  to  an  out- 
cropping vein  or  seam.  Blossom. 

Shroud. — A  housing  or  jacket. 

Shute. — See  Chute,  Shoot,  and  Schute. 

Shutter. — (1)  A  movable  sliding  door,  fitted  within  the  outer  casing  of  a 
Guibal  or  other  closed  fan,  for  regulating  the  size  of  the  opening  from 
the  fan,  to  suit  the  ventilation  and  secure  economical  working  of  the 
machine.  (2)  A  slide  covering  the  opening  in  a  door  or  brattice,  and 
forming  a  regulator  for  the  proportionate  division  of  the  air  current 
between  two  or  more  districts  of  a  mine. 

Siddle. — Inclination. 

Side. — (1)  The  more  or  less  vertical  face  or  wall  of  coal  or  goaf  forming  one 
side  of  an  underground  working  place.  (2)  Rib.  (3)  A  district. 

Side  Chain. — A  chain  hooked  on  to  the  sides  of  cars  running  on  an  incline  or 
along  a  gangway,  to  keep  the  cars  together  in  case  the  coupling  breaks. 

Siding. — A  short  piece  of  track  parallel  to  the  main  track,  to  serve  as  a  pass- 
ing place. 

Siding  Over. — A  short  road  driven  in  a  pillar  in  a  headwise  direction. 

Sight. —  (1)  A  bearing  or  angle  taken  with  a  compass  or  transit  when  making 
a  survey.  (2)  Any  established  point  of  a  survey. 

Sights. — Bobs  or  weighted  strings  hung  from  two  or  more  established  points 
in  the  roof  of  a  room  or  entry,  to  give  direction  to  the  men  driving  the 
entry  or  room. 

Sill. — (1)  The  floor  piece  of  a  timber  set,  or  that  on  which  the  track  rests; 
the  base  of  any  framing  or  structure.  (2)  The  floor  of  a  seam. 

Sing. — The  noise  made  by  a  feeder  of  gas  issuing  from  the  coal. 

Singing  Coal. — Coal  from  which  gas  is  issuing  with  a  hissing  sound. 

Singing  Lamp. — A  safety  lamp,  which,  when  placed  in  an  atmosphere  of 
explosive  gas,  gives  out  a  peculiar  sound  or  note,  the  strength  of  the 
note  varying  in  proportion  to  the  percentage  of  firedamp  present. 

Single-Entry  System. — A  system  of  opening  a  mine  by  driving  a  single  entry 
only,  in  place  of  a  pjair  of  entries.  The  air  current  returns  along  the 
face  of  the  rooms,  which  must  be  kept  open. 

Single-Intake  Fan. — A  ventilating  fan  that  takes  or  receives  its  air  upon  one 
side  only. 

Single-Rope  Haulage. — A  system  of  underground  haulage  in  which  a  single 
'rope  is  used,  the  empty  trip  running  in  by  gravity.  This  is  engine-plane 
haulage. 

Sink. — To  excavate  a  shaft  or  slope;  to  bore  or  put  down  a  bore  hole. 

Sinker. — A  man  who  works  at  the  bottom  of  a  shaft  or  face  of  a  slope  during 
the  course  of  sinking. 

Sinker  Bar. — In  rope  drilling,  a  heavy  bar  attached  above  the  jars,  to  give 
force  to  the  up  stroke,  so  as  to  dislodge  the  bit  in  the  hole. 

Sinking. — The  process  of  excavating  a  shaft  or  slope  or  boring  a  hole. 

Siphon. — A  simple,  effective,  and  economical  mode  of  conveying  water  over 
a  hill  whose  height  is  not  greater  than  what  the  atmospheric  pressure 
will  raise  the  water.  Its  form  is  that  of  an  iron  pipe,  bent  like  an  in- 


J140  A  GLOSSARY  OF  MINING  TERMS 

verted  U ;  the  vertical  height  between  the  surface  of  the  water  in  the 

upper  basin  and  the  top  of  the  hill  is  called  the  lift  of  the  siphon:  while 

the  vertical  height  between  the  surfaces  of  the  water  in  the  upper  and 

lower  basins  is  called  the  fall  of  the  siphon. 
Sirdar. — A  foreman. 
Sizing. — To  sort  minerals  into  sizes. 
Skew  Back. — The  beveled  member  from  which  an  arch  springs,  and  upon  which 

it  rests. 

Skids. — Slides  upon  which  heavy  bodies  are  slid  from  place  to  place. 
Skip. — (1)  A  mine  car.     (2)  A  car  for  hoisting  out  of  a  slope.     (3)  A  thin 

slice  taken  off  from  a  breast  or  pillar  or  rib  along  its  entire  length  or 

part  of  its  length. 
Skit  (Cornish). — A  pump. 
Slab. — Split  pieces  of  timber  from  2  in.  to  3  in.  thick,  4  ft.  to  6  ft.  long,  and 

7  in.  to  14  in.  wide,  placed  behind  sets  or  frames  of  timber  in  shafts  or 

levels. 
Slack. — (1)   Fine  coal  that  will  pass  through  the  smallest  sized  screen.     The 

fine  coal  and  dust  resulting  from  the  handling  of  coal,  and  the  disinte- 
gration of  soft  coal.     (2)  The  process  by  which  lignite  disintegrates 

when  exposed  to  the  air  and  weather. 
Slant. — (1)  An  underground  roadway  driven  at  an  angle  between  the  full 

rise  or  dip  of  the  seam  and  the  strike  or  level.     (2)   Any  inclined  road 

in  a  seam. 
Slant  Chutes. — Chutes  driven  diagonally  across  a  pillar,  to  connect  a  breast 

manway  with  a  manway  chute. 
Slate. — (1)  A  hardened  clay  having  a  peculiar  cleavage.     (2)  About  coal 

mines,  slate  is  any  shale  accompanying  the  coal,  also  sometimes  applied 

to  bony  coal. 
Slate  Chute. — (1)  A  chute  for  conveying  slate  or  bony  coal  to  a  pocket  from 

which  it  is  loaded  into  "dumpers."     (2)  A  chute  driven  through  slate. 
Slate  Picker. — (1)  A  man  or  boy  that  picks  the  slate  or  bone  from  coal.     (2) 

A  mechanical  contrivance  for  separating  slate  and  coal. 
Sleek  (Derbyshire). — Mud  in  a  mine. 
Sled. — A  drag  used  to  convey  coal  along  the  face  to  the  road  head  where  it  is 

loaded,  or  to  the  chute. 
Sledge. — A  heavy  double-handed  hammer. 

Sleeper  (English). — The  foundation  pieces  or  cross- ties  on  which  rails  rest. 
Sleeve. — A  hollow  cylinder  usually  fitting  over  two  pieces,  to  hold  them  to- 
gether. 

Slickensides. — Polished  surfaces  of  vein  walls. 
Slide. — Loose  deposit  covering  the  outcrop  of  a  seam. 
Slides. — See  Guides. 
Sliding  Scale. — A  mode  of  regulating  the  wages  paid  workingmen  by  taking 

as  a  basis  for  calculation  the  market  price  of  coal,  the  wages  rising  and 

falling  with  the  state  of  trade. 
Sliding  Wind  Bore  (English). — The  bottom  pipe  9r  suction  piece  of  a  sinking 

set  of  pumps  having  a  lining  made  to  slide  like  a  telescope  within  it,  to 

give  length  without  altering  the  adjustment  of  the  whole  column  of  pipes. 
Slime,  Sludge. — The  pulp  or  fine  mud  from  a  drill  hole. 
Slings. — Pieces  of  ropes  or  cnains  to  be  put  around  stones,  etc.,  for  raising 

them. 
Slip. — (1)  A  fault.     (2)  A  smooth  joint  or  crack  where  the  strata  have 

moved  upon  each  other. 
Slip  Cleavage. — Microscopic  folding  and  fracture  accompanied  by  slippage; 

quarrymen's  "false  cleavage." 

Slit. — A  short  heading  put  through  to  connect  two  other  headings. 
Slitter. — See  Pick. 
Slope. — A  plane  or  inclined  roadway,  usually  driven  in  the  seam  from  the 

surface.     A  rock  slope  is  a  slope  driven  across  the  strata,  to  connect  two 

seams;  or  a  slope  opening  driven  from  the  surface,  to  reach  a  seam  below 

that  does  not  outcrop  at  an  accessible  point. 
Sludge. — See  Slime. 
Sludger,  Sludge  Pump. — A  cylinder  having  an  upward  opening  valve  at  the 

bottom,  which  is  lowered  into  a  bore  hole,  to  pump  out  the  sludge  or 

fine  rock  resulting  from  drillings. 
Sluice. — Any  overflow  channel. 
Sluice  Head,  or  Head  (Australia  and  New  Zealand). — A  supply  of  1  cu.  ft.  of 

water  per  second,  regardless  of  the  head,  pressure,  or  size  of  orifice. 


A  GLOSSARY  OF  MINING  TERMS  1141 

Small— Bee  Slack. 

Smift,  Snift. — A  bit  of  touch  paper,  touch  wood,  etc.,  attached  by  a  bit  of  clay 
or  grease  to  the  outside  end  of  the  train  of  gunpowder  when  blasting 

Smut  (Staffordshire).— Soft,  bad  coal. 

Snore,  Snore  Piece. — The  hole  in  the  lower  part  of  a  sinking  or  Cornish  pump 
through  which  water  enters. 

Snub  or  Snubbing. — (1)  To  undercut  by  means  of  explosives  or  otherwise. 
(2)  To  lower,  as  a  car,  by  a  turn  of  a  rope  around  a  post. 

Soapstone. — A  term  incorrectly  applied  by  the  miner  to  any  soft,  unctuous 
rock. 

Socavon  (Mexican). — A  mining  tunnel;  an  adit.  Socavon  d  kilo  de  veto. — A 
drift  tunnel.  Socavon  crucero. — A  crosscut  tunnel  or  adit. 

Socket. — (1)  The  innermost  end  of  a  shot  hole,  not  blown  away  after  firing. 
(2)  A  wrought-iron  contrivance  by  means  of  which  a  wire  rope  is  se- 
curely attached  to  a  chain  or  block. 

Sole,  Sole  Plate. — A  piece  of  timber  set  underneath  a  prop. 

Sollar. — (1)  A  wooden  platform  fixed  in  a  shaft,  for  the  ladders  to  rest  on.  (2) 
A  division  of  the  air  compartment  in  a  drift  or  slope. 

Sondear  (Mexican). — To  bore  for  prospecting  purposes. 

Sondeo  (Mexican). — A  boring  for  prospecting  purposes. 

Soplete  (Mexican). — A  blowpipe. 

Sorting. — Separating  valuable  from  worthless  material. 

Sounding. — (1)  Knocking  on  a  roof  to  see  whether  it  is  sound  or  safe  to 
work  under.  (2)  Rapping  on  a  pillar  so  that  a  person  on  the  other  side 
of  it  may  be  signaled  to,  or  to  enable  him  to  estimate  its  width. 

Sow. — (1)  A  tool  used  for  sharpening  drills.  (2)  Iron  deposits  at  the  bottom 
of  furnaces. 

Spad. — A  horseshoe  nail  with  a  hole  in  the  head,  or  a  similar  device  for 
driving  into  the  mine  timbers,  or  into  a  wooden  plug  fitted  into  the  roof, 
to  mark  a  survey  station. 

Spall. — To  break  up  rocks  with  a  large  hammer,  for  hand  sorting. 

Spalls. — The  chips  and  other  waste  material  cut  from  a  block  of  stone  in 
process  of  dressing. 

Spar. — A  name  given  to  certain  white  quartz-like  minerals,  e.g.,  calcspar, 
feldspar,  fluorspar. 

Spears. — Pump-rods. 

Specimen. — A  picked  piece  of  mineral.. 

Spelter. — The  commercial  name  for  zinc. 

Spent  Shot. — A  blast  hole  that  has  been  fired,  but  has  not  done  its  work. 

Spiders. — See  Drum  Rings. 

Spiegeleisen. — Manganiferous  white  cast  iron. 

Spiking  Curbs. — A  light  ring  of  wood  to  which  planks  are  spiked  when  plank 
tubbing  is  used. 

Spiles  (Cornish). — A  temporary  lagging*  driven  ahead  on  levels  in  loose 
ground.  Short  pieces  of  planking  sharpened  flatways,  and  used  for 
driving  into  watery  strata  as  sheath  piling,  to  assist  in  checking  the 
flow;  used  much  in  sinking  through  quicksands. 

Spiling. — A  process  of  timbering  through  soft  ground. 

Spiral. — A  spiral  coal  chute  which  mechanically  separates  the  slate  from  the 
coal. 

Spiral  Drum. — See  Conical  Drum. 

Splint,  or  Splent. — A  hard,  high  volatile  coal,  producing  a  white  ash,  inter- 
mediate between  cannel  and  bituminous  coal. 

Split. — (1)  To  divide  an  air  current  into  two  or  more  separate  currents.  (2) 
Any  division  or  branch  of  the  ventilating  current.  (3)  The  workings 
ventilated  by  that  branch.  (4)  Any  member  of  a  coal  bed  split  by 
thick  partings  into  two  or  more  seams.  (5)  A  bench  separated  by  a  con- 
siderable interval  from  the  other  benches  of  a  coal  bed. 

Spoil. — Debris  from  a  coal  mine. 

Spoon. — A  slender  iron  rod  with  a  cup-shaped  projection  at  right  angles  to 
the  rod,  used  for  scraping  drillings  out  of  a  bore  hole. 

Spout. — A  short  underground  passage  connecting  a  main  road  with  an  air- 
course. 

Sprag. — (1)  A  short  wooden  prop  set  in  a  slanting  position  for  keeping  up 
the  coal  during  the  operation  of  holing.  (2)  A  short  round  piece  of  hard 
wood,  pointed  at  both  ends,  to  act  as  a  brake  when  placed  between  the 
spokes  of  mine-car  wheels.  (3)  The  horizontal  member  of  a  square  set 
of  timber  running  longitudinally  with  the  deposit. 


1142  A  GLOSSARY  OF  MINING  TERMS 

Spragger. — One  who  attends  to  the  spragging  of  cars. 

Sprag  Road.— A  mine  road  having  such  a  sharp  grade  that  sprags  are  needed 

to  control  the  speed  of  the  cars. 

Spreader. — A  timber  stretched  across  a  shaft  or  stope. 

Spring  Beams. — Two  short  parallel  timber  beams,  built  with  a  Cornish  pump- 
ing engine  house,  nearly  on  a  level  with  the  engine  beam,  for  catching 

the  beam,  etc.,  and  preventing  a  smash  in  case  of  a  breakdown. 
Spring  Latch. — The  latch  or  tongue  of  an  automatic  switch,  operated  by  a 

spring  pole  at  the  side  of  the  track. 
Spring  Pole. — An  elastic  wooden  pole  from  which  boring  rods  are  suspended. 

Used  also  to  operate  a  spring  latch. 
Sprocket  Wheel  (English). — Rag  wheel.     A  wheel  with  teeth  or  pins  which 

engage  the  links  of  a  chain. 
Spur. — (1)  A  short  ridge  or  offsetting  pointed  branch  from  a  main  ridge  or 

mountain.     (2)  A  short  branch  or  feeder  from  the  main  lode  of  a  vein. 

(3)  A  branch  road. 

Square  Set. — A  variety  of  timbering  for  large  excavations. 
Squealer. — A  shot  which  breaks  the  coal  only  enough  to  allow  the  gases  of 

detonition  to  escape  with  a  whistling  or  squealing  sound;  also  called  a 

whistler. 

Squeeze. — See  Creep. 

Squib. — A  straw,  rush,  paper,  or  quill  tube  filled  with  a  priming  of  gun- 
powder, with  a  slow  match  on  one  end. 
Stage. — A  platform  on  which  mine  cars  stand. 
Stage  Pumping. — Draining  a  mine  by  means  of  two  or  more  pumps  placed  at 

different  levels,  each  of  which  raises  the  water  to  the  next  pump  above, 

or  to  the  surface. 
Stage  Working. — A  system  of  working  minerals  by  removing  the  strata  above 

the  beds,  after  which  the  various  beds  are  removed  in  steps  or  stages. 
Staging. — A  temporary  flooring  or  scaffold,  or  platform. 
Stalactites. — Icicle-shaped  formations  of  mineral  matter  depending  from  roof 

strata. 
Stalagmites. — Accumulations  of  mineral  matter  that  form  on  the  floor,  caused 

by  the  continual  dripping  of  water  impregnated  with  mineral  matter. 
Stall. — A  narrow  breast,  or  chamber. 
Stall  Gate. — A  road  along  which  the  mineral  worked  in  a  stall  is  conveyed  to 

the  main  road. 

Stanchion. — A  vertical  prop  or  strut. 
Standage. — Pump  reservoir. 

Standing. — Not  at  work,  not  going  forwards,  idle. 

Standing  Gas. — A  body  of  firedamp  known  to  exist  in  a  mine,  but  not  in  cir- 
culation; sometimes  fenced  off. 

Standing  Sett  (English). — A  fixed  lift  of  pumps  in  a  sinking  set. 
Staple. — (1)  A  shallow  pit  within  a  mine.     (2)  An  underground  shaft. 
Starter. — A  man  who  ascends  a  chute  to  the  battery  and  starts  the  coal  to 

running. 

Starved  (English). — When  a  pump  is  choked  at  the  brass  holes. 
Station. — A  flat  or  convenient  resting  place  in  a  shaft  or  level. 
Stave. — A  ladder  step. 

Stay  (English). — Props,  struts,  or  ties  for  keeping  anything  in  its  place. 
Steamboat  Coal. — In  anthracite  only,  coal  small  enough  to  pass  through  bars 

set  6  to  8  in.  apart,  but  too  large  to  pass  through  bars  from  85  to  5  in. 

Comparatively  few  collieries  make  steamboat  coal  except  to  fill  special 

contracts  or  orders. 

Steam  Coal. — A  hard,  free-burning,  non-caking  coal. 
Steam  Jet. — A  system  of  ventilating  a  mine  by  means  of  a  number  of  jets  of 

steam,  at  high  pressure,  kept  constantly  blowing  off  from  a  series  of  pipes 

in  the  bottom  of  the  upcast  shaft. 
Steel  Mill. — An  apparatus  for  obtaining  light  in  a  fiery  mine.     It  consisted 

of  a  revolving  steel  wheel,  to  which  a  piece  of  flint  was  held,  to  produce 

Steel  Needle. — An  instrument  used  in  preparing  blasting  holes,  before  the 

safety  fuse  was  invented. 

Steening,  or  Steining. — The  brick  or  stone  lining  of  a  shaft. 
Stemmer. — A  copper  or  wooden  bar  used  for  stemming. 
Stemming. — (1)  Fine  shale  or  dirt  put  into  a  shot  hole  after  the  powder,  and 

rammed  hard.      (2)   Tamping  a  shot. 
Step   (English). — (1)   The  cavity  in  a  piece  for  receiving  the  pivot  of  an 


A  GLOSSARY  OF  MINING  TERMS  1143 

upright  shaft,  or  the  end  of  an  upright  piece.  (2)  The  shearing  in  a 
coal  face. 

Stint. — The  amount  of  work  to  be  done  by  a  man  in  a  specified  time. 

Stitch. — To  fasten  a  timber  by  toe  nailing. 

Stobb. — A  long  steel  wedge  used  in  bringing  down  coal  after  it  has  been  holed. 

Stomp. — A  short  wooden  plug  fixed  in  the  roof  of  a  level,  to  serve  as  a  bench 
mark  for  surveys. 

Stone  Coal. — Anthracite;  also  other  hard  varieties  of  coal. 

Stone  Head. — A  heading  or  gangway  driven  in  stone.     A  tunnel. 

Stone  Tubbing. — Water-tight  stone  walling  of  a  shaft  cemented  at  the  back. 

Stook. — A  pillar  of  coal  about  4  yd.  square,  being  the  last  portion  of  a  full- 
sized  pillar  to  be  worked  away  in  bord-and-pillar  workings. 

Stook-and-Feather. — A  wedge  for  breaking  down  coal,  worked  by  hydraulic 
power,  the  pressure  being  applied  at  the  extreme  inner  end  of  the  drilled 

Stoop. — A  pillar  of  coal. 

Stoop-and-Room. — A  system  of  working  coal  very  similar  to  pillar-and-stall. 

Slop. — Any  cleat  or  beam  to  check  the  descent  of  a  cage,  car,  pump  rods,  etc. 

Slope.  — (1)  To  excavate  mineral  in  a  series  of  steps.  (2)  A  place  in  a  mine 
that  is  worked  by  stoping. 

Sloping. — Working  out  mineral  between  two  levels  or  on  the  surface,  by 
stopes  or  steps.  Stoping  Overhand. — Mining  a  stope  upwards,  the  flight 
of  steps  being  inverted.  Stoping  Underhand. — Mining  a  stppe  downwards 
in  such  a  series  that  it  presents  the  appearance  of  a  flight  of  steps. 

Stopping. — An  air-tight  wall  built  across  any  passageway  in  a  mine. 

Stove  Coal. — In  anthracite  only;  two  sizes  of  stove  coal  are  made,  large  and 
small:  large  stove,  known  as  No.  3,  passes  through  a  2i-in.  to  2-in.  mesh 
and  over  a  IJ-in.  to  1^-in.  mesh;  small  stove,  known  as  No.  4,  passes 
through  a  l|-in.  to  If-in.  mesh  and  over  a  U-in.  to  1-in.  mesh.  Only 
one  size  of  stove  coal  is  now  usually  made.  It  passes  through  a  2-in. 
square  mesh  and  over  If -in.  square  mesh. 

Stove  Up,  or  Slaved. — Upset.  When  a  rod  of  iron  heated  at  one  end  is  ham- 
mered endwise  the  diameter  of  that  end  is  enlarged,  and  it  is  said  to  be 
upset  or  stove  up.  " 

Stow~ — To  pack  away  rubbish  into  goaves  or  old  workings. 

Stowce. — (1)    Windlass.     (2)  Landmarks. 

Stowing. — The  debris  of  a  vein  thrown  back  of  a  miner  and  which  supports 
the  roof  or  hanging  wall  of  the  excavation. 

Straight  Ends  and  Walls. — A  system  of  working  coal  somewhat  similar  to 
bord-and-pillar.  Straight  ends  are  headings  from  4  ft.  6  in.  to  6  ft.  in 
width.  Walls  are  pillars  30  ft.  wide. 

Straight  Work. — A  system  of  getting  coal  by  headings  or  narrow  work. 

Stroke. — A  slightly  inclined  table  for  separating  heavier  minerals  from 
lighter  ones. 

Stratification. — Arrangement  in  layers. 

Stratum  (plural,  strata). — A  layer  or  bed  of  rocks,  or  other  deposit. 

Streak. — The  color  of  the  mark  made  when  a  mineral  is  scratched  against  a 
white  surface. 

Strett. — The  system  of  getting  coal  by  headings  or  narrow  work.  See  Bord- 
and-Pillar. 

Strike  (of  a  seam  or  vein). — The  intersection  of  an  inclined  seam  or  a  vein 
with  a  horizontal  plane.  A  level  course  in  the  seam.  The  direction  of 
strike  is  always  at  right  angles  to  the  direction  of  the  dip  of  the  seam. 

Strike  Joints. — Joints  or  cleavages  that  are  parallel  to  the  strike  of  the  seam. 

Striking  Deal. — Planks  fixed  in  a  sloping  direction  just  within  the  mouth  ot 
a  shaft,  to  guide  the  tub  to  the  surface. 

Stringer  (English). — Any  longitudinal  timber  or  beam. 

Stringpump—A.  system  of  pumping  whereby  the  motion  of  the  engine  is 
transmitted  to  the  pump  by  timbers  or  stringers  bolted  together.  . 

String  Rods.— A  line  of  surface  rods  connected  rigidly  for  the  transmission 
of  power;  used  for  operating  small  pumps  in  adjoining  shatts  tn 
central  station.  .         ...    ...   . 

Strip.— (i)  To  remove  the  overlying  strata  of  a  bed  or  vein.  (2)  Mining  a 
deposit  by  first  takirTf  off  the  overlying  material. 

Strut  (English)  — A  prop  to  sustain  compression,  whether  vertical  or  inclined. 

Struve  Ventilator.— A  pneumatic  ventilating  apparatus  consisting  of  two 
vessel-like  gas  holders,  which  are  moved  up  and  down  m  a  tank  01 
water.  By  this  means,  the  air  is  sucked  out  of  the  mine  as  required. 


1144  A  GLOSSARY  OF  MINING  TERMS 

Studdle. — A  piece  of  squared  timber  placed  vertically  between  two  sets  of 

timber  in  a  shaft. 

Stull. — A  post  for  supporting  the  wall  or  roof  in  a  mine;  a  prop  timber. 
Stump. — The  pillar  between  the  gangway  and  each  room  turned  off  the  gang- 
way.    Sometimes  the  entry  pillars  are  called  stumps. 
Stumping. — A  kind  of  pillar-and-stall  plan  of  getting  coal. 
Stup. — Powdered  coke  9r  coal  mixed  with  clay. 
Sturt. — A  tribute  bargain  profitable  to  the  miner. 
Stuttle,  or  Sprag. — The  horizontal  member  of  a  square  set  of  timber  running 

longitudinally  with  the  deposit. 
Stythe. — Carbonic-acid  gas  (blackdamp). 
Sucker  Rod. — The  pump  rod  of  an  oil  or  artesian  well. 
Suction  Pump  (English). — A  pump  wherein,  by  the  movement  of  the  piston, 

water  is  drawn  up  into  the  vacuum  caused. 
Sulphur. —  (1)  One  of  the  elements.     (2)   Iron  pyrites?. 
Sulphur et. — See  Sulphide. 

Sulphide. — A  combination  of  sulphur  and  a  base. 
Sump,  or  Sumpt.—A.  catch  basin  into  which  the  drainage  of  a  mine  flows  and 

from  which  it  is  pumped  to  the  surface. 
Sumping,  or  Sumping  Cut. — Forcing  the  cutter  bar  of  a  coal  cutter  into  or 

under  the  coal. 

Surface  Deposits. — Those  that  are  exposed  and  can  be  mined  from  the  surface. 
Swab  Stick. — A  short  wooden  rod,  bruised  into  a  kind  of  stumpy  brush  at  one. 

end,  for  cleaning  out  a  drill  hole. 

Swally,  or  Swelly. — A  trough,  or  syncline,  in  a  coal  seam. 
Swamp. — A  depression  or  natural  hollow  in  a  seam,  a  basin. 
Sweeping  Table. — A  stationary  buddle. 
Sweet. — Free  from  deleterious  gases. 
Swing. — The  arc  or  curve  described  by  the  point  of  an  instrument,  such  as  a 

pick  or  hammer,  when  being  used. 
Switch. — (1)  The  movable  tongue  or  rail  by  which  a  train  is  diverted  from 

one  track  to  another.     (2)  The  junction  of  two  tracks.     (3)  An  pa- 

paratus  for  changing  the  course  of  or  interrupting  an  electrical  current. 
Switchboard. — A  board  where  several  electrical  wires  terminate,  and  where, 

by  means  of  switches,  connection  may  be  established  between  any  of 

these  wires  and  the  main  wire. 
Synclinal  Axis. — The  line  or  course  of  a   syncline. 
Syncline.— The  point  or  axis  of  a  basin  toward  which  the  strata  upon  either 

side  dip.     An  inverted  anticline.     A  basin. 
Systematic  Timbering. — Placing  mine  timbers  according  to  a  predetermined 

plan,  regardless  of  roof  conditions. 

Tackle  (English). — (1)  Ropes,  chain,  detaching  hooks,  cages,  and  all  other 
apparatus  for  raising  coal  or  ore  in  shafts.  (2)  Any  rope  for  hoisting, 
as  a  tackle  rope,  block  and  tackle,  etc. 

Tail-Back. — When  the  firedamp  ignites  and  the  flame  is  elongated  or  creeps 
backwards  against  the  current  of  air,  it  is  said  to  tail-back. 

Tailing. — The  blossom;  the  outcrop  or  smut. 

Tailngs. — The  refuse  from  a  jig. 

Tail-Pipe. — The  suction  pipe  of  a  pump. 

Tailrace. — The  channel  along  which  water  flows  after  it  has  done  its  work. 

Tail-Rope. — (1)  In  a  tail-rope  system  of  haulage,  the  rope  that  is  used  to 
draw  the  empties  back  into  the  mine.  (2)  A  wire  rope  attached  beneath 
cages,  as  a  balance. 

Tail-Rope  System  of  Haulage. — A  haulage  system  in  which  the  full  trip  is 
drawn  out  by  the  main  rope  and  the  empty  trip  is  drawn  in  by  the  tail- 
rope,  these  ropes  being  attached  to  the  opposite  ends  of  the  trip. 

Tail-Sheave. — The  sheave  at  the  inbye  end  of  any  haulage  system.  See  Turn 
Pulley. 

Take  the  Air. — (1)  To  measure  the  ventilating  current.  (2)  Applied  to  a 
ventilating  fan  as  working  well,  or  working  poorly. 

Taladro  (Mexican). — A  drill  for  mechanical  or  mining  purposes.  Taladrar. — 
To  bore  or  drill. 

Tally. — (1)  A  mark  or  number  placed  by  the  mine?  on  every  car  of  coal  sent 
out  of  his  place,  usually  a  tin  ticket.  By  counting  these,  a  tally  is  made 
of  all  the  cars  of  coal  he  sends  out.  (2)  Any  numbering,  or  counting, 
or  memorandum,  as  a  tally  sheet. 

Tamp. — To  fill  a  bore  hole,  after  inserting  the  charge,  with  some  substance 


A  GLOSSARY  OF  MINING  TERMS  1145 

which  is  rammed  hard  as  it  is  put  into  the  hole.     Vertical  holes  are  often 

tamped  with  water,  when  blasting  with  dynamite. 
Tamping. — The  process  of  stemming  or  filling  a  bore  hole. 
Tamping  Bar.— A.  copper-tipped  bar,  for  ramming  the  tamping  or  stemming. 
Tanates  (Mexican). — Leather,  hide,  or  jute  bags,  to  carry  ore  or  waste  rock 

within  or  out  of  a  mine.     Tanatero. — A  laborer  or  bag  carrier. 
Tap. — (1)  To  cut  or  bore  into  old  workings,  for  the  purpose  of  liberating  ac- 
cumulations of  gas  or  water.     (2)  To  pierce  or  open  any  gas  or  water 

feeder.     (3)  To  win  coal  in  a  new  district. 
Tapextle  (Mexican). — A  working  platform  or  stage  built  up  in  a  stope  or  any- 
where m  a  mine;  a  landing  place  between  two  flights  of  ladders. 
Teem. — To  pour  or  tip. 

Teeming  Trough. — A  trough  into  which  the  water  from  a  mine  is  pumped. 
Telegraph.- — A  sheet-iron  trough-shaped  chute,  for  conveying  coal  or  slate 

from  the  screens  to  the  pockets,  or  boilers. 
Temper. — (1)   To  change  the  hardness  of  metals  by  first  heating  and  then 

plunging  them  into  water,  oil,  etc.      (2)   To  mix  mortar,  or  to  prepare 

clay  for  bricks,  etc. 
Tempering. — The  act  of  reheating  and  properly  cooling  a  bar  of  metal  to  any 

desired  degree  of  hardness. 
Temper  Screw. — In  rope  drilling,  a  screw  for  gradually  lowering  the  clamped 

(upper)  end  of  the  rope  as  the  hole  is  deepened. 
Tenon. — A  projecting  tongue  fitting  into  a  corresponding  cavity  called  a 

mortise. 
Tequio  (Mexican). — A  task  set  for  a  drillman  or  for  any  laborer  in  a  mine,  to 

be  regarded  as  a  day's  work. 
Terrace. — A  raised  level  bank,  such  as  river  terraces,  lake  terraces,  etc. 
Terrero  (Mexican). — The  dump  of  a  mine. 

Test. — A  trial  of  an  engine,  fan,  or  other  appliance  or  substance. 
Theodolite. — An  instrument  used  in  surveying,  for  taking  both  vertical  and 

horizontal   angular  measurements.     An -engineer's  large  transit,   with 

attachments. 
Thill.— See  Floor. 
Thimble. —  (1)  A  short  piece  of  tube  slid  over  another  piece,  to  strengthen  a 

joint,  etc.     (2)   An  iron  ring  with  a  groove  around  it  on  the  outside,  used 

as  an  eye  when  a  rope  is  doubled  about  it. 
Thirl. — See  Crosscut. 
Through-and-Through. — A  system  of  getting  bituminous  coal,  without  regard 

to  the  size  of  the  lump. 
Throw. — (1)  A  fault  of  dislocation.      (2)   The  vertical  distance  between  the 

two  ends  of  a  faulted  bed  of  coal. 
Thrown. — Faulted;  broken  by  a  fault. 
Thrust. — Creep  or  squeeze  due  to  excessive  weight,  hard  floor,  and  too  small 

pillars. 

Thurl  (Staffordshire). — To  cut  through  from  one  working  into  another. 
Tie- Back. — (1)  A  beam  serving  a  purpose  similar  to  a  fend-off  beam,  but 

fixed  at  the  opposite  side  of  the  shaft  or  inclined  road.     (2)  The  wire 

ropes  or  stayrods  which  are  sometimes  used  on  the  side  of  the  tower 

opposite  the  hoisting  engine,  in  place  of  or  to  reenforce  the  engine  braces. 
Tiff. — Calcite  or  carbonate  of  lime. 
Timber. — (1)  Props,  bars,  collars,  legs,  laggings,  etc.     (2)  To  set  or  place 

timber  in  a  mine  or  shaft. 

Timberer,  Timberman. — A  man  who  sets  timber. 
Time. — (1)  Hours    of    work    performed    by    workmen.     (2)   To    count    the 

strokes  of  a  pump  or  revolutions  of  an  engine  or  fan. 
Tin-Can  Safely  Lamp. — A  Dayy  lamp  placed  inside  a  tin  can  or  cylinder 

having  a  glass  in  front,  air  holes  near  the  bottom,  and  open-topped, 

making  the  lamp  safer  in  a  rapid  current  of  air. 
Tip. — A  dump.     See  Tipper,  or  Tipple. 
Tipper,  Tipple,  or  Tippler. — An  apparatus  for  emptying  cars  of  coal  or  ore, 

by  tipping  or  turning  them  upside  down,  and  then  bringing  them  back 

to  original  position,  with  a  minimum  of  manual  labor. 
Tipple.— The  dump  trestle  and  tracks  at  the  mouth  of  a  shaft  or  slope,  where 

the  output  of  a  mine  is  dumped,  screened,  and  loaded. 
Tiro  (Mexican).— A  mining  shaft.      Tiro  Vertical.— A.  vertical  shaft. 
Token.—  (1)  A  piece  of  leather  or  metal  stamped  with  the  hewer  s  or  putter  s 

number  or  distinctive  mark,  and  fastened  to  the  tub  he  is  filling  01 

putting. 


1146  A  GLOSSARY  OF  MINING  TERMS 

Ton. — A  measure  of  weight.  Long  ton  is  2,240  lb.;  short  ton  is  2,000  lb.; 
metric  ton  is  1,000  kilograms  =  2,204.6  lb. 

Top.— m  See  Roof.     (2)  Top  of  a  shaft;  surface  over  a  mine. 

Topit. — A  kind  of  brace  head  screwed  to  the  top  of  boring  rods,  when  with- 
drawing them  from  the  hole. 

Topping. — The  coal  on  a  car  above  the  t6p  of  the  car  box. 

Track. — Railways  or  tramways. 

Tracking. — Wooden  rails. 

Train  Boy. — A  boy  that  rides  on  a  trip,  to  attend  to  rope  attachments,  signal 
in  case  of  derailment  of  cars,  etc.  Trip  rider. 

Train,  or  Trip. — The  cars  taken  at  one  time  by  mules,  or  by  any  motor,  or 
run  at  one  time  on  a  slope,  plane,  or  sprag  road,  always  together. 

Tram. — A  mine  car,  or  the  track  on  which  it  rums. 

Trammer. — One  who  pushes  cars  along  the  track.  "    »•"' 

Tramroad. — A  mine  track  or  railroad. 

Tram  Rope. — A  hauling  rope,  to  which  the  cars  are  attached  by  a  clip  or 
chain,  either  singly  or  in  trips. 

Tramway. — A  small,  roughly  constructed  track  for  running  wagons  or  trucks 
on. 

Transfer  Carriage. — Movable  platform  or  truck  used  to  transfer  mine  cars 
from  one  track  to  another. 

Transome  (English). — A  heavy  wooden  bed  or  supporting  piece. 

Trap. — (1)  A  steep  heading  along  which  men  travel.  (2)  A  fault  of  dislo- 
cation. (3)  An  eruptive  rock.  (4)  A  dangerous  place.  (5)  To  tend 
door. 

Trjap  Dike. — A  fault  (not  necessarily  accompanied  by  displacement  of  strata) 
in  which  the  spaces  between  the  fractured  edges  of  the  beds  are  filled  up 
by  a  thick  wall  of  igneous  rock. 

Trap  Door. — A  small  door,  kept  locked,  fixed  in  a  stoping,  for  giving  access 
to  firemen  and  certain  others  to  the  return  airways,  dams,  or  other  un- 
used portions  of  the  mine'. 

Trapper. — A  boy  employed  underground  to  tend  doors. 

Traveling  Road. — An  underground  passage  or  way  used  expressly,  though 
not  always  exclusively,  for  men  to  travel  along  to  and  from  their  work- 
ing places. 

Treenail. — A  long  wooden  pin  for  securing  planks  or  beams  together. 

Trend. — The  course  of  a  vein,  fault,  or  other  feature. 

Tribute. — A  method  of  working  mines  by  contract,  whereby  the  miners 
receive  a  certain  share  of  the  products  won.  Tributers. — Miners  paid 
by  results. 

Trig. — A  sprag  used  to  block  or  stop  a  wheel  or  any  machinery. 

Trip. — The  mine  cars  in  one  train  or  set.     See  Train. 

Triple-Entry  System. — A  system  of  opening  a  mine  by  driving  three  parallel 
entries  for  the  main  entries. 

Triturate. — To  grind  or  pulverize. 

Trolley. — (1)  A  small  four-wheeled  truck,  used  for  carrying  the  ore  bucket 
underground.  (2)  An  electric  locomotive.  (3)  The  arm  of  a  loco- 
motive or  other  machine  that  conducts  the  electric  current  from  the  wire 
above  the  track  to  the  machine. 

Trompe. — An  apparatus  for  producing  ventilation  by  the  fall  of  water  down 
a  shaft. 

Trouble. — A  dislocation  or  fault;  any  irregularity  in  the  bed. 

Trough  Fault. — A  wedge-shaped  fault,  or,  more  correctly,  a  mass  of  rock, 
coal,  etc.;  let  down  in  between  two  faults,  which  faults,  however,  are 
not  necessarily  of  equal  throw. 

Troughs,  or  Thirling. — A  passage  cut  through  a  pillar  to  connect  two  rooms. 

Truck. — Used  synonymously  with  Barney. 

Truck  System. — Paying  miners  in  food  instead  of  money. 

Trunnions. — Cylindrical  projections  or  journals,  attached  to  the  sides  of  a 
vessel,  so  that  it  can  rotate  in  a  vertical  plane. 

Trying  the  Lamp. — The  examination  of  the  flame  of  a  safety  lamp  for  the 
purpose  of  forming  a  judgment  as  to  the  quantity  of  firedamp  mixed 
with  the  air. 

Tub. — (1)  A  mine  car.  (2)  An  iron  or  wooden  barrel  used  in  a  shaft,  for 
hoisting  material. 

Tubbing. — Cast  iron,  and  sometimes  timber,  lining  or  "walling  of  a  circular  shaft. 

Tubbing  Wedges. — Small  wooden  wedges  hammered  between  the  joints  of 
tubbing  plates. 


A  GLOSSARY  OF  MINING  TERMS  1147 

Tubing. — Iron  pipes  or  tubes  used  for  lining  bore  holes,  to  prevent  caving. 
Tunnel. — A  horizontal  passage  driven  across  the  measures  and  open  to  day  at 

both  ends;  applied  also  to  such  passages  open  to  day  at  only  one  end,  or 

not  open  to  day  at  either  end. 
furbary. — A  peat  bog. 
Turbine. — (1)  A  rapidly  revolving  waterwheel,  impelled  by  the  pressure  of 

water  upon  blades.     (2)  A  similar  type  of  power  generator  propelled  by 

steam  or  air. 
Turn. — (1)  The  hours  during  which  coal,  etc.,  is  being  raised  from  the  mine. 

(2)  See  Shift.     (3)  To  open  rooms,  headings,  or  chutes  off  from  an  entry 

or  gangway.     (4)  The  number  of  cars  allowed  each  miner. 
Turnout. — A  siding  or  passing  on  any  tram  or  haulage  road. 
Turn  Pulley. — A  sheave  fixed  at  the  inside  end  of  an  endless-  or  tail-rope 

haulage  plane,  around  which  the  rope  returns.     See  Tail-Sheave. 
Turntable. — A  revolving  platform  on  which  cars  or  locomotives  are  turned 

around. 

Tut  Work. — Breaking  ground  at  so  much  per  foot  or  fathom. 
Tuyere. — The  tubes  through  which  air  is  forced  into  a  furnace. 
Two-Throw.— When,  in  sinking,  a  depth  of  about  12  ft.  has  been  reached,  and 

the  d6bris  has  to  be  raised  to  the  surface  by  two  lifts  or  throws  with  the 

shovel,  one  man  working  on  staging  above  another. 
Unconformability. — When  one  layer  of  rock,  resting  on  another  layer,  does 

not  correspond  in  its  angle  of  bedding. 

Undercast, — An  air-course  carried  under  another  air-course  or  roadway. 
Underclay. — A  bed  of  fireclay  or  other  less  clayey  stratum,  lying  immediately 

beneath  a  seam  of  coal. 
Undercut. — To  remove  a  small  portion  of  the  bottom  of  the  bed  or  the  under- 

clay,  so  that  the  mass  of  coal  or  mineral  can  be  wedged  or  blasted  down. 
Underhand  Sloping. — See  Sloping  Underhand. 
Underhand  Work. — Picking  or  drilling  downwards. 
Underholing,  Undermining. — To  mine  out  a  portion  of  the  bottom  of  a  seam 

or  the  underclay,  by  pick  or  powder,  thus  leaving  the  top  unsupported 

and  ready  to  be  blown  down  by  shots,  broken  down  by  wedges,  or  mined 

with  a  pick  or  bar. 
Underlie,  or  Underlay. — The  inclination  of  a  stratum  at  right  angles  to  its 

course  or  strike;  the  true  dip. 
Underviewer,  or  Underlooker. — An  inside  foreman. 
Unwater. — To  drain  or  pump  the  water  from  a  mine  or  shaft. 
Upcast. — The  shaft  through  which  the  return  air  ascends. 
Upraise. — An  auxiliary  shaft,  a  mill  hole,  or  heading  carried  from  one  level  up 

toward  another. 

Upthrow. — A  fault  in  which  the  displacement  has  been  upward. 
Vapor    (Mexican). — Steam;  heated  and  stinking  gas  sometimes  found  in 

mines,  which  causes  candles  to  burn  dimly  and  go  out. 
Vein. — See  Lode.     Often  applied  incorrectly  to  a  seam  or  bed  of  coal  or  other 

mineral. 

Vena  (Mexican). — A  thin  vein,  not  over  3  in.  thick — a  knife-blade  vein. 
Vend  (North  of  England). — Total  sales  of  coal  from  a  mine. 
Vent,  or  Vent  Hole. — (1)  A  small  passage  made  with  a  needle  through  the 

tamping,  which  is  used  for  admitting  a  squib,  to  enable  the  charge  to  be 

lighted.     (2)  Any  opening  made  into  a  confined  space. 
Ventilating  Column. — See  Motive  Column. 
Ventilating  Pressure. — The  total  pressure  or  force  required  to  overcome  the 

friction  of  the  air  in  mines;  the  unit  of  ventilating  pressure  or  pressure 

per  sq.  ft.  of  area  multiplied  by  the  area  of  the  airway. 
Ventilation. — Circulation.     The  atmospheric  air  circulating  in  a  mine. 
Ventilator. — Any  means  or  apparatus  for  producing  a  current  of  air  in  a  mine 

or  other  airway. 

Vestry  (North  of  England). — A  refuse. 
Viewer. — The  general  manager  or  mining  engineer  of  one  or  more  collieries, 

who  has  control  of  the  whole  of  the  underground  works,  and  also  gen- 
erally of  those  on  the  surface. 
Vug,  or  Vugh  (Cornish). — A  cavity  in  the  rock. 
Wagon. — A  mine  car. 
Wagon  Breast. — A  breast  in  which  the  mine  cars  are  taken  up  to  the  working 

face. 
Wailing. — Picking  stones  and  dirt  from  among  coals. 


1148  A  GLOSSARY  OF  MINING  TERMS 

Wale  (North  of  England). — Hand-dressing  coal. 

Walking  Beam. — See  Working  Beam. 

Wall. — (1)  The  face  of  a  longwall  working  or  breast.  (2)  A  rib'of  solid  coal 
between  two  breasts.  (3)  A  crosscut  driven  between  bords. 

Walling. — See  Steening. 

Walling  Cribs. — Oak  cribs  or  curbs  upon  which  walling  is  built. 

Walling  Stage. — A  movable  wooden  scaffold  suspended  from  a  crab  on  the 
surface,  upon  which  the  workmen  stand  when  walling  or  lining  a  shaft. 

Wall  Plates. — The  two  longest  pieces  of  timber  in  a  set  used  in«a  rectangular 
shaft. 

Warners. — Apparatus  consisting  of  a  variety  of  delicately  constructed 
machines,  actuated  by  chemical,  physical,  electrical,  and  mechanical 
properties,  for  indicating  the  presence  of  small  quantities  of  firedamp  in 
the  mines.  At  present,  most  of  these  ingenious  contrivances  are  more 
suited  to  the  laboratory  than  for  practical  application  underground. 

Warning  Lamp. — A  safety  lamp  fitted  with  certain  delicate  apparatus,  for 
indicating  very  small  proportions  of  firedamp  in  the  atmosphere*  of  a 
mine.  As  small  a  quantity  as  3  %  can  be  determined  by  this  means. 

Wash. — Drift,  clay,  stones,  etc.,  overlying  the  strata. 

Washer. — A  jig. 

Wash  Fault. — A  portion  of  a  seam  of  coal  replaced  by  shale  or  sandstone. 

Washing  Apparatus,  or  Washery. — (1)  Machinery  and  appliances  erected  on 
the  surface  at  a  colliery,  often  in  connection  with  coke  ovens,  for  extract- 
ing, by  washing  with  water,  the  impurities  mixed  with  the  coal  dust  or 
small  slack.  (2)  Machinery  for  removing  impurities  from  small  sizes  of 
anthracite  coal. 

Washout. — The  erosion  of  an  appreciable  extent  of  a  coal  seam  by  aqueous 
agency. 

Waste. — (1)  See  Goaf.  (2)  Very  small  coal  or  slack.  (3)  The  portion  of  a 
mine  occupied  by  the  return  airways.  (4)  Also  used  to  denote  the 
spaces  between  the  pack  walls  in  the  gob  of  longwall  working.  (5) 
Refuse  material. 

Waste  Gate  (English). — A  door  for  regulating  discharge  of  surplus  water. 

Water  Blast. — The  sudden  escape  of  air  pent  up  in  rise  workings,  under  con- 
siderable pressure  from  a  head  of  water  that  has  accumulated  in  a 
connecting  shaft. 

Water  Cartridge. — A  waterproof  cartridge  surrounded  by  an  outer  case.  The 
space  between  being  filled  with  water,  which  is  employed  to  destroy  the 
name  produced  when  the  shot  is  fired,  thereby  lessening  the  chance  of  an 
explosion  should  gas  be  present  in  the  place. 

Water  Gauge.— An  instrument  for  measuring  the  pressure  per  square  foot 
producing  ventilation  in  a  mine. 

Water  Hammer. — The  hammering  noise  caused  by  the  intermittent  escape  of 
gas  through  water  in  pipes. 

Water-Jacket. — A  jacket  filled  with  water,  to  keep  cool  a  cylinder  or  furnace. 

Water  Level. — An  underground  passage  or  heading  driven  very  nearly  dead 
level  or  with  sufficient  grade  only  to  drain  off  the  water. 

Water  Right. — The  privilege  of  taking  a  certain  quantity  of  water  from  a 
watercourse. 

Watershed. — The  elevated  land  or  ridge  that  divides  drainage  areas. 

Waterwheel  (English). — Overshot,  undershot,  breast  wheels,  etc.  A  wheel 
provided  with  buckets,  which  is  set  in  motion  by  the  weight  or  impact 
of  a  stream  of  water. 

Weather. — To  crumble  by  exposure  to  the  atmosphere. 

Weather  Door. — See  Trap  Door. 

Web. — The  face  of  a  longwall  stall  in  course  of  being  holed  and  broken  down 
for  removal.  The  length  of  breast  or  face  brought  down  by  one  mining. 

Wedging. — The  material,  moss  or  wood,  used  to  render  the  shaft  lining  tight. 

Wedging  Crib. — A  curb  or  crib  of  wood  or  cast  iron  wedged  tightly  in  place 
and  packed,  in  order  to  form  a  water-tight  joint  and  upon  which  tubbing 
is  built. 

Wedging  Down. — Breaking  down  the  coal  at  the  face  with  hammers  and 
wedges  instead  of  by  blasting. 

Weigh  Bridge  (English). — A  platform  large  enough  to  carry  a  wagon,  resting 
on  a  series  of  levers,  by  means  of  which  heavy  bodies  are  weighed. 

Weize. — A  band  or  ring  of  spun  yarn,  rope,  rubber,  lead,  etc.,  put  in  between 
the  flanges  of  pipes  before  bolting  them  together,  in  order  to  make  a 
water-tight  joint;  a  gasket. 


.4  GLOSSARY  OF  MINING  TERMS  1149 

Well. — A  sump,  or  a  branch  from  the  sump. 
Whim. — A  winding  drum  worked  by  a  horse. 
Whim  Shaft. — A  shaft  through  which  coal,  ore,  water,  etc.,  are  raised  from  a 

mine  by  means  of  a  whim. 
Whin. — A  hard,  compact  rock. 
Whin  Dike. — A  fault  or  fissure  filled  with  whin  and  the  debris  of  other  rocks, 

sometimes  accompanied  by  a  dislocation  of  the  strata. 
Whip. — A  hoisting  appliance  consisting  of  a  pulley  supporting  the  hoisting 

rope  to  which  the  horse  is  directly  attached. 
Whitedamp. — Carbonic  oxide  (CO).     A  gas  found  in  coal  mines,  generally 

where  ventilation  is  slack.     A  product  of  slow  combustion  in  a  limited 

supply  of  air.     It  burns  and  will  support  combustion.     It  is  extremely 

poisonous. 

Whole  Working. — The  first  working  of  a  seam,  which  divi'des  it  into  pillars. 
Wild  Rock. — Any  rock  not  fit  tor  commercial  slate. 
Win. — To  sink  a  shaft  or  slope,  or  drive  a  drift  to  a  workable  seam  of  mineral 

in  such  a  manner  as  to  permit  its  being  successfully  worked. 
Winch,  or  Windlass. — A  hoisting  machine  consisting  of  a  horizontal  drum 

operated  by  crank-arm  and  manual  labor. 
Wind  Bore  (England). — The  bottom  or  suction  pipe  of  a  lift  of  pumps,  which 

has  suitable  brass  holes  or  perforations  for  suction  of  water  or  air. 
Wind  Gauge. — An  anemometer  for  testing  the  velocity  of  air  in  mines. 
Winding. — The  operation  of  raising  or  hauling  the  product  of  a  mine  by 

means  of  an  engine  and  ropes. 
Winding  Engines. — Hoisting  or  haulage  engines. 
Wind  Method. — A  system  of  separating  coal  into  various  sizes,  and  extracting 

the  dirt  from  it,  which  in  principle  depends  on  the  specific  gravity  or 

size  of  the  coal  and  the  strength  of  the  current  of  air. 
Wind  Sail. — The  top  part  of  canvas  piping,  which  is  used  for  conveying  air 

down  shallow  shafts. 
Wing  Bore. — A  side  or  flank  bore  hole. 
Wings. — See  Rests  and  Keeps. 
Winning. — A  sinking  shaft,  a  new  coal,  ironstone,  clay,  shale,  or  other  mine 

of  stratified  material.     A  working  place  in  a  mine. 

Winse. — 'Interior  shaft  connecting  levels,  sometimes  used  as  an  ore  chute. 
Won. — Proved,  sunk  to,  and  tested. 
Work. — (1)   To    mine.     (2)  Applied   to    mine    working    when    affected    by 

squeeze  or  creep. 

Workable. — Any  seam  that  can  be  profitably  mined. 
Worked  Out. — When  all  available  mineral  has  been  extracted  from  a  mine  it 

is  worked  out. 

Working. — Applied  to  mine  workings  when  squeezing. 
Working  Barrel. — The  water  cylinder  of  a  pump. 
Working  Beam  (English). — A  beam  having  a  vertical  motion  on  a  rock  shaft 

at  its  center,  one  end  being  connected  with  the  piston  rod  and  the  other 

with  a  crank  or  pump  rod,  etc. 

Working  Cost. — The  total  cost  of  producing  the  mineral. 
Working  Face. — See  Face. 
Working  Home — Getting  or  working  out  a  seam  of  coal,  etc.,  from  the 

boundary  or  far  end  of  the  mine  toward  the  shaft  bottom. 
Working  on  Air. — A  pump  works  on  air  when  air  is  sucked  up  with  the  water. 
Working  Out. — Working  outwards  or  in  the  direction  of  the  boundaries  of 

the  colliery. 

Working  Place. — The  actual  place  in  a  mine  at  which  the  coal  is  being  mined. 
Workings. — The  openings  of  a  colliery,  including  all  roads,  ways,  levels,  dips, 

airways,  etc. 

Wrought  Iron. — Iron  in  its  minimum  state  of  carbunzation. 
Wythern  (Wales).— Lode. 
Xacal  (Mexican). — A  miner's  cabin;  a  storehouse  for  mining  goods;  a  shaft 

house. 

Yardage,  Yard  Work. — Price  paid  per  yard  for  cutting  coal. 
Yard  Price. — Various  prices,  per  yard  driven  (in  addition  to  the  tonnage 

prices),  paid  for  roads  of  certain  widths  and  driven  in  certain  directions. 
Yield. — The  proportion  of  a  seam  sent  to  market. 
Zone. — In  coal-mining  phraseology  this  word  means  a  certain  series  of  coal 

seams  with  their  accompanying  shales,  etc.,  which  contain,  for  example, 

much  firedamp,  called  a  fiery  zone,  or,  if  much  water,  a  watery  zone. 


INDEX 


Abbreviations,  mathematical,  18 

surveyor's,  89 

weights  and  measures,  1-17 
Abel,  Prof.,  853,  948 
Absolute  zero,  353 
Abutments  of  dams,  328 
Accidents,  969,  975 
Acetylene,  871 

lamps,  900 

Acid  waters,  pumps  for,  346 
Afterdamp,  869 

Aggregates  in  concrete  work,  206 
Air,  atmospheric,  845 

compressed,  474-484 

diffusion  compared  to  gases,  843 

humidity,  843 

mine,  846 

psychrometers  or  hygrometers, 
844 

required     for     combustion     of 
gases,  447 

standard,  935 

weight  and  volume,   447,   841, 

842 

Air-lift  pumps,  349 
Aitkin's  gas  indicator,  894 
Alabama  methods  of  working  mines, 

632 

Alaskan  coals,  analyses,  390 
Alcohol  as  fuel,  536 
Alkalies,  effect  on  concrete,  210 
Allis-Chalmers  Co.,  251 
Almy  boilers,  416 

Altitude,   determination  of,   in  sur- 
veying, 105 

effect  on  boiling  point  of  water, 

363 

Aluminum  compared  to  copper,  490, 
491 

strength  of,  170 
American  Blower  Co.,  933 
American  Chemical  Society,  378 
American     Institute     of     Electrical 

Engineers,  755 
American  Medical  Association,  853, 

855 

American  Safety  Lamp  Co.,  878 
American  Society  of  Civil  Engineers: 

report  on  concrete,  207 

tests  of  cement,  198 
American     Society    of     Mechanical 

Engineers,  423,  431,  433 
American  Steel  and  Wire  Co.,  738 
American  Well  Works,  554 
American  wire  gauge,  490 
Ammonium  nitrate,  667 
Anaconda  Copper  Mining  Co.,  725, 


Analyses  of  coals,  378-391 
Andre's  rule  for  shaft  pillars,  697 
Angle  of  friction,  160 
Angles,  geometrical  construction  of, 
39 

latitudes  and  departure,  tables, 
1074 

logarithmic  tables,  1009 

logarithms      of      trigonometric 
functions,  1028 

method  of  laying  off,  9 

of  repose,  tables,  160,  161,  162 

sines  and  cosines  of,  989,  991 

tangents  and  cotangents,  1000 

traverse  tables,  1073 
Angular  measure,  9 
Annealed  copper  wire,  properties  of, 

489 

Ansell's  indicator,  893 
Anthracite  coal,  371 

change  to  wood,  368 

compressive  strength,  694 

crushing  strength,  694 

handling,  962 

preparation  of,  958 

pressure  against  vertical  walls, 

table.  966 

Apothecaries'  weight,  4 
Apparatus  for  mine  rescue,  986 
Arc,  geometrical  construction  of,  40 

time  equivalent,  10 
Areas,  tables,  1081,  1097    ' 
Arithmetic,  19-36 
Arithmetical  progression,  24 
Artificial  respiration,  970,  987 
Ashworth-Hepplewhite-Gray   lamp, 

876,  877,  888 

Asphyxiation,  recovery  from,  987 
Astronomical  time  in  surveying,  100 
Atkinson,  J.  J.,  909 
Atomic  weights  of  elements,  833 
Australian  woods,  weight,  281 
Avogadro's  law,  836 
A/pirdupois  weight,  5 
Axis  of  symmetry,  155 
Axle  and  wheel,  150 

oil,  168 
Axles,  coefficients  of  friction,  162 

Babcock  and  Wilcox,  366,  397,  416 
Baker,  863 

Baldwin  Locomotive  Works.  759 
Ball  bearing  on  mine-car  wheels,  166 
Bamford,  Roy,  310 
Barker,  870 
Barometers,  839 

Barometric  elevations,  table,  142 
leveling,  140 


1151 


1152 


INDEX 


Batteries,  electric,  514 
Baum6  hydrometer,  537 
Beams,  174 

deflection  formulas,  179 

designing  of,  176 

external     sheer     and     bending 
moment,  table,  175,  177 

iron  and  steel,  187 

modulus  of  rupture,  178 

problems  in  strength,  184 

stiffness,  178 

table  of  safe  loads,  186 
Beard,  T.  J.,  910,  920,  942,  943 
Beard-Mackie  sight  indicator,  894 
Bearing  values  of  rivets,  table,  173, 

174 

Beau  de  Rochas,  532 
Belting  in  power  transmission,  272 
Belt  pulleys,  271 
Bending  moment  of  a  beam,  table, 

175,  177 

Bethellizing  timber,  724 
Bickford's  fuse,  676 
Biram's  ventilator,  131 
Bitumen,  prospecting  for,  557 
Bituminous  coal,  372 

preparation  of,  959 

pressure       against       vertical 

walls,  965 

Black  Diamond  culm  plant,  702 
Blackdamp,  851,  869 
Blair,  855,  862 
Blasting,  638,  667-691 
Blossburg,  coal  region,  618 
Blow-offs,  boiler,  416,  417 
Board  measure,  302 
Boilers.  406-454 

air  required,  451 

blowing  down,  438 

blow-9ffs,  416,  417 

capacity  water  and  steam,  443 

care  of,  438 

chimneys,  446 

chimneys,  erection,  452 

cleaning,  438 

connecting,  434 

connection  of  steam  gauge,  416 

coverings  for  pipes,  419 

durability,  443         -     .3T,-*. 

efficiency,  433 

equalizing  feed,  435 

explosion,  liability  to,  442 

feeding  and  feedwater,  422 

feed  pumps,  335,  438 

feedwater,   factors  of  evapora- 
tion, 432 

feedwater,  heating,  430 

feedwater,  purification,  428 

feedwater,  testing,  428 

filling,  433 

fire,  cleaning  of,  435 

firing,  438 

firing  with  solid  fuel,  435 

fittings,  414 

fittings  inspection,  441 

foaming,  437,  439 

fuels,   temperature  of   ignition, 
448 

furnace  fittings,  417 


Boilers,  fusible  plugs,  415,  438 

gauges,  438 

grates,  417 

heating  surface,  ratio  of  horse- 
power, 444,  445 

horsepower,  standard  of,  431 

impurities  in  feedwater,  425 

incrustation  and  corrosion,  424 

injectors,  422 

inspection,  439 

loss  of  heat  from  pipes,  table, 
420 

management,  433 
of  fires,  434 

overheating  of  plates,  427 

oxygen    and    air    required    for 
combustion,  448 

piping,  412 

priming,  436 

production    and    measurement 
of  draft,  451,  453 

products  of  combustion,  446 

repairs,  443 

safety  valves,  414,  438 
valves,  inspection,  441 

scale,  425 . 

scale-forming    substances    and 
remedies,  427 

selection  of,  441 

shutting  down,  437 

size  of  chimneys  and  horsepower 
of  boilers,  454 

starting  up,  437 

steam,  406 

stokers,  418 

table  of  work,  445 

temperature  of  fire,  449 
of  ignition,  448 

trials,  430 

tubes,  weight,  297 

uniform  steam  pressure,  436 

water  circulation,  444 
level,  436,  438 
required,  table,  423 

weight  of  air,  water  vapor  and 

saturated  mixtures,  447 
Bolt  heads,  proportions,  300 

weight,  292 
Bolts,  weights,  299 
Bowron,  Chas.  E.f  776 
Box  regulators,  919,  920 
Boyle's  law,  475,  840 
Brackett,  F.  E.,  350 
Brass  sheets,  weights,  293 
Brass,  strength  of,  170 
Breathing  apparatus,  986 
Brick,  size  and  strength,  236 

masonry  piers,  235 
Brickwork,  measures  of,  6 
Bridge  wall  of  a  furnace,  417 
Bridges,  suspension,  ropes  for,  243, 

248 

Briggs,  882 
Briggs'  wire  loop,  894 
Briqueting  fuel,  967 
Briquets,  cement,  200 
British  thermal  unit,  353 
British  Westinghouse  Co.,  743 
Broockmann,  Dr.,  808 


INDEX 


1153 


Broderick  &  Bascom  Rope  Co.,  237 

Bronze,  strength  of,  170 

Brown,  Col.  D.  P.,  637 

Brown,   Thomas  J.,  402 

Brown  &  Sharpe  Gauge,  291,  293, 

490 

Brownhoist,  966 
Brunck,  Dr.,  862,  863,  870 
Buckets,  coal,  580,  963 
Building  materials,  weight,  283, 

284 

Bunsen  Coal  Co.,  738 
Burnettizing  timber,  724 
Burr,  W.  A.,  316 
Burrell,  G.  A.,  866,  868 
By-product  gas,  401 

Cables  for  suspension  bridges,  248 

strength  of,  183 
Cableways,  242,  258 
Cahall  boilers,  416 
Calorie,  354 

Calorific  value  of  fuel  oil,  396 
Calumet  &  Hecla  Mining  Co.,  475 
Calyx  drilling,  556 
Cambria  Steel  Co.,  .293 
Campbell,  Dr.  M.  R.,  372,  373 
Campbell,  J.  R.,  857 
Canadian  coals,  analyses,  388 
Canaries,  effect  of  afterdamp  on,  857 
Cantilever,  174 

Capacity,  metric  measures  of,  12 
Capell  ventilator,  933 
Carbon  as  fuel,  365 

dioxide,  848 

heat  and  products  of  combus- 
tion, 449 

in  coal,  369,  371 

monoxide,  852 
Carbureters,  541 
Carnegie  Steel  Co.,  Ltd.,  299,  730, 

764,  766 

Cartridges,  hydraulic,  686 
Cast-iron  pipe,  weight,  294 
Catlett,  Charles,  370 
Ceag  electric  lamp,  897 
Cement  testing.  195 

boiling  test,  197 

fineness,  203 

machines  for  testing,  200 

measurements  of  expansion,  196 

natural  and  slag  cements,  204 

normal  tests,  196 

primary  tests,  196 

results  of  tensile  strength  tests, 
201 

sampling,  195 

sand  for  mortar  tests,  199 

secondary  tests,  202 

soundness,  196 

specific  gravity,  203 

steam  test,  197 

tensile  strength,  198 

time  of  setting,  202 
Cementing  materials,  187 

injection  in  mine  shafts,  591 

mortars,  191,  193 

requirements  for,  205 

specifications,  204 

73 


Cements,  188 
Center  of  gravity,  155 
Centigrade  thermometers  and  Fahr- 
enheit compared,  355 
Central   Coal   Basin  rule  for  shaft 

pillars,  698 
Centrifugal  fans,  931 

pumps,  343 
Chain  machines,  645 
Chain,  surveyor's,  65 
Chains, -strength  of,  183 
Chamberlain,    Rollin    T.,  852,  859, 

864-871 

Chance,  E.  M.,  849 
Charcoal-iron  ropes,  237 
Charles'  law,  840 
Chemistry  of  gases,  831 
Chesneau  lamps,  875,  890 
Chester,  Thomas,  933 
Chimneys  of  boilers,  446 
combustion  rate,  453 
erection,  452 
production    and    measurement 

of  draft,  451,  453 
size  and  horsepower  of  boilers, 

454 

Christian,  L.  A.,  484 
Chutes,  coal,  962 
Circles,  48 

circumferences  and  areas,  tables, 

1097 

Circular  curves  in  railroad  survey- 
ing, 109 
measure,  9 
segments,  49 
Circumferences    and    areas,    tables, 

1081,  1097 

Circumferential  stress,  174 
Clanny,  Dr.  W.  R.,  874,  876 
Clanny  lamp,  880,  883,  886 
Clark,  D.  K.,  290 
Clearance  of  steam  engines,  454 
Clearfield  coal  region,  616 
Cleats,  614 
Clement,  J.  P.,  850 
Climax  boilers,  416 
Clinometer,  surveyor's,  67 
Clinton  wire  cloth,  218 
Closed  work  in  mines,  606 
Clowes,  847,  850,  855,  856,  862,  864, 

893 

Clowes'  hydrogen  lamp,  889,  983 
Coal,  Alaskan,  analyses,  390 

American,  analyses,  table,  382- 

385,  387 

analyses  of  typical,  381 
reports  of.  379 
proximate,  378 

anthracite,  see  Anthracite  Coal, 
as  fuel,  368-394 
ash,  379 
bituminous,      see     Bituminous 

Coal. 

blacksmith  coals,  374 
breakers  of  reinforced  concrete, 

227 

calorific  power,  392 
Canadian,  analyses,  388 
cannel,  378 


1154 


INDEX 


Coal  chutes,  962 

classification  and  localities,  370 
coke,  yield  of,  376 
coking,  374 
constituents,  368 
cost  of  unloading,  966 
crushing  and  compressive 

strength  of  anthracites,  694 
cubic  contents  of  2000  pounds, 

968 

cubic  feet  in  one  ton,  290 
domestic,  373 
Dulong's  formula,  394 
dust  explosions,  901 
fat  and  dry,  378 
firedamp  from  analyses  of,  864 
fixed  carbon,  379 
foreign,  analyses,  391 
formations,  550 
free-burning,  378 
gas,  analyses,  402,  403 
gas  coals,  373 
heating  value,  determination  of, 

392,  394 

heating  values,  table,  382-385 
Kent's  method,  392,  393,  394 
lands,    diagram    for    reporting, 

560 

lignite,  373 
Lord   and   Haas'   method,   392, 

393,  394 

mines,  see  Mines. 

moisture,  379 

non-coking,  378 

Pennsylvania  anthracite,  analy- 
ses, 386 

pillars  in  mines,  692 

Pish  el's  test  for  coking  qualities, 

377 

pockets  9f  concrete,  229 
preparation  of,  949-968 
products  of  combustion,  446 
proximate  analysis,  378 
sampling  for  analysis,  378 

in  prospecting,  559 
seams,  horizontal,  contents  of, 

289 

semianthracite,  372 
semibituminous,  372 
sizes  of  prepared  anthracite,  289 
smithing,  374 

specific  gravity,  tables,  286,  288 
splint,  378 

spontaneous  ignition,  948 
steam  coal,  374 
storage,  949 
sub-bituminous,  372 
sulphur  analysis,  379 
temperature  of  ignition,  448 
value    as    fuel    compared    with 

oil,  397 
volatile     combustible     matter, 

379 

washers,  953 

weight  equivalent  to  wood,  366 
weights      and      measurements, 
table,  287,  288 

of  English  and  French,  290 
Coefficient  of  elasticity,  171 


Coefficient  of  friction,  159 

Coefficients,  in  power  transmission, 
265 

Coins,  United  States  and  foreign,  16, 
18 

Coke-oven  gas,  402 

Coke  ovens,  566 

Coking  coals,  374 

Pishel's  test,  377 

Coleman  shaft,  350 

Colorado    Fuel   and   Iron    Co.,  903 

Columns,  strength,  table,  180,  181 
wooden,  formula,  182 

Combined  stresses,  182 

Combustion  of  fuels,  363 
of  gases,  447 

Compass,  surveyor's,  60-62 

Composition  of  forces,  153 

Compressed  air,  474-484 

classification     of     compressors, 

474 

compressors,  design  of,  483 
for  haulage  plants,  803 
installation,  483 
operation  of,  484 
construction     of     compressors, 

475 
efficiencies    of    compressors    at 

different  altitudes,  476 
explosions,  avoiding,  483 
friction  in  pipes,  482 
haulage  locomotives,  798 
hoisting  engines,  741 
horsepower  necessary  for  com- 
pressors, 807 

locomotive  storage  tanks,  803 
losses  in  transmission,  478-482 
pipe  for  haulage  plants,  805 
pipes  for  transmission,  476 
rating  of  compressors,  475 
theory  of,  475 
transmission  of  air  in  pipes,  476 

Compressibility  of  liquids,  307 

Compressive  stress,  169 

Compressors,  see  Compressed  Air. 

Concrete,  187-233 

aggregates  used,  206 

cementing  materials,  187 

crushing  strength,  212 

dams,  331 

destructive  agencies,  209 

expansion  and  contraction,  211 

fire,  effect  of,  210 

Fuller's  rule  for  quantities,  212 

joining  old  with  new,  213 

measuring  ingredients,  methods 

of,  211 

mine  shaft  lining,  737 
mine  water,  effect  of,  210 
mixing,  212 
plain,  206 
proportioning     of     ingredients, 

207,  208 

report  of  Joint  Committee,  207 
retempering,  213 
steel  reinforcement,  214 
strength  of,  table,  207,  208 
thermal  changes,  effect  of,  211 
vibration,  effect  of,  211 


INDEX 


1155 


Concrete,  water  used,  209 

weight  of  ingredients,   207 
working    at   freezing    and   high 

temperatures,  213 
working   stresses    and    strength 

values,  211 
Concrete,  reinforced,  214 

areas    and    weights    of    bars, 

table,  216 

braces  for  wall  forms,  223 
clamping   devices   and   plank 

holders,  223 
coal  breakers,  227 
coal  pockets,  229 
conduits,  226 
floor-systems,  218,  220 
form  work,  construction  and 

finish,  220,  221 
hooped  columns,  214 
materials  and  kinds  of  bars, 

217 
members    to    resist    lines    of 

failure,  215 
mixers,  223 
parts    of    steel    floor-system, 

214 
principles     of     construction, 

214 

retaining  walls,  226 
shaft  lining,  230 
tank  tower  construction,  223 
uses  in  engineering,  223 
wall  forms,  221,222  _ 
Condensers  for  steam  engines,   459 
Conducting  power  of  substances,  421 
Conduction  of  heat,  359 
Conductors  of  electricity,  488 
Conduits  of  reinforced  concrete,  226 
Cone,  53 

Conical  drums,  745 
Connecticut  River  rule,  302 
Connellsville,  Pa.,  method  of  mining, 

635 

Connor,  Eli  T.,  705 
Considere,  211 
Construction,  concrete,  214 
geometrical,  38 
masonry,  234 
Continental  Coke  Co.,  402 
Conversion  factors  of  liquids,  314 

of  metric  system,  13 
Copper,     compared    to    aluminum, 

490,  491 

sheets,  weights,  293 
strength  of,  170 
Coquillon's  gas  indicator,  892 
Cord,  dimensions  of,  6 
Corliss  engines,  333 

starting  and  stopping,  461 
Corliss-valve  hoisting  engine,  740 


Cornish  pumps,  333 
Corrosion  of  boil 


Corrosion  of  boilers,  424 

of  metal  reinforcement  in  con- 

crete, 209 

Cosines,  tables  of,  989,  991 
Cotangents,   tables  of,   989,   1000 
Coxe,  E.  B.,  950 
Coxe  Bros.  &  Co.,  287 
Cox's  formula,  323 


Crawford  and  McCrimmon,  941 

Crude  oil,  395 

Crushing  machinery,  949 

Cube  root,  27,  1081 

Cubes  of  numbers,  tables,  1081 

Cubic  measures,  6 

Culm,  flushing  of,  702 

Cuninghame-Cadbury     indicator, 

894 

Cunningham,  W.  H.,  734 
Currency,  United  States  and  foreign 

systems,  16,  17 
Current  motors,  332 
Curtis  turbine,  469,  470 
Curves  in  railroad  surveying,  109 
Cylinder  oil.  168 

Cylinder  ratios  of  steam  engines,  458 
Cylinders,  53 

contents,  295 
Cylindrical  rings,  52 

sheets,  strength  of,  174 

Dams,    abutments    and    discharge 
gates,  328 

earth,  329 

in  mines,  327 

masonry  and  concrete,  331 

outside  of  mines,  328 

pressure  against,  304 

refuse,  331 

spillways  or  waste  ways,  329 

stone,  329 

wing,  331 

wooden,  328 

D'Arcy's  formula,  320,  322,  477 
Davis,    investing    atoms    of    latent 

heat,  362 

Davis,  James  B.,  703,  705 
Davis,  W.  W.,   168 
Davy  lamp,  880,  883,  884 
Davy,  Sir  Humphrey,  874,  876 
Dawson,  Thomas  W.,  982 
Dead  plate  of  a  boiler,  418 
Decimal  fractions,  20 

gauge,  292 

Decimals,  tables,  2,  4,  5 
Deformation,  definition,  171 
Delabeche  &  Playfair,  290 
De  Laval  steam  turbine,  469,   471, 

472 

Demanet,  862 
Departures,  tables,  1074 
Designing  of  beams,  176 
Despritz  system  of  hoisting,  750 
Diamond  drill,  555 
Direct  stress,  171,  172 
Discounts,  definition,  23 
Displacement  of  a  ship,  7 
Ditches,  water,  315,  316 
Division  by  logarithms,  33 
Dodson  culm  plant,  702 
Dominion  Iron  and  Steel  Co.,  401 
Double  shear,  174 
Doyle's  rule,  302 
Drainage  of  shafts,  596 
Drilling  in  prospecting,  554 
Dron's  rule  for  shaft  pillars,  698 
Drouain,  856 
Dry  measure,  7 


1156 


INDEX 


Dudley,  C.  B.,  378 
Dulong's  formula,  394,  396 
Durability  of  stone,  236 
Dynamite,  charging  and  firing,  680 

composition  of,  668 

thawing,  673 
Dynamos,  497 

Earth,  coefficients  of  friction,  161 

specific  gravity,  table,  276 
Earthwork  in  railroad  surveying,  115 
Eavenson,  Howard  N.t  402 
Economic-type  boilers,  416 
Edison  electric  cell,  516 
Elastic  limit,  172 
Elasticity,  modulus  of,  171 
Electric  current  for  pumping  water, 

342 

hoisting  engines,  742 
safety  lamps,  896 
Electric-locomotive    haulage,     815- 

831 
advantages  and  disadvantages, 

815 
alter  nating-current  locomotives, 

830 

bonding,  818 

cable-reel  locomotives,  826 
capacity  of  locomotives,  824 
construction  of  motors,  822 
crab  locomotives,  827 
direct-current  locomotives,  822 
feeders,  819 

rack-rail   locomotives,    827 
resistance  of  steel  rails,  817 
sizes  of  locomotives,  rails  and 

bonds,  818 

sizes  of  wires,  table,  821 
storage-battery  locomotives, 

830 

tandem  locomotives,  826 
troubles,  828 
wiring,  816 
Electrical     shock,     protecting    men 

from,  980 
treatment  for,  972 
Electricity,  484-531 

alternating-current  dynamos, 

506 

alternating-current  motors,  508 
alternators,  506 
aluminum    and    copper    mines 

compared,  490,  491 
aluminum  cables,  breaking 

strength,  491 
annealed  copper  wire,  490 
annunciator  system,  517 
arc  lamps,  495 
armature  faults,  528 
armature,  heating  of,  524 
batteries,  514 
bearings,  heating  of,  524 
bell  wiring,  516 
brush  faults,  523 
calculation  of  wires  for  trans- 
mission, 492 
circuits,  486 
commutator  faults,  524 
compound-wound  dynamos,  501 


Electricity,  conductors,  488 

conductors  for  electric  haulage 

plants,  496 

connections  for  continuous-cur- 
rent motors,  504 
copper      cables,       breaking 

strength,  491 

copper  cables,  capacity,  490 
current  estimates,  494 
current  required  for  direct-cur- 
rent motors,  496 
direct-current  circuits,  calcula- 
tion of  wires,  492 
direct-current  dynamos,   497 
direct-current  motors,   501 
dynamo,  failure  to  generate,  527 
dynamos  and  motors,  497 
dynamos,    electromotive    force 

generated,  500 

dynamos,  field  excitation,  500 
electric  power,  485 
electrical  expressions  and  their 

equivalents,  486 
electromotive  force,  485 
electromotive    force    generated 

by  dynamos,  500 
field  coils,  heating  of,  524" 
field  excitation  of  dynamos,  500 
firing  explosives  by,  681 
heating  of  armature,  field  coil, 

and  bearings,  524 
incandescent  lamps,  494 
induction  motors,   508 
induction    motors,    installation 

and  care,  511 
insulated  wires,  494 
motors,  495 

multiphase  alternators,  507 
noise,  525 
Ohm's  law,  485 
regulation  of  speed  of  motors, 

526 

residual  magnetism,  527 
resistance,_485 
resistance  in  series  and  multiple, 

488 

resistance   of   conductors,    esti- 
mation of,  491 
rules  for  handling,  529 
series-wound  dynamos,  500 
shunt- wound  dynamos,  501 
signaling,  514 
sparking  at  brushes,  523 
speed  regulation  of  motors,  503 
strength  of  current,  484 
synchronous  motors,  508 
transformers,  513 
troubles      with      dynamo    and 

motor,  523 

weather-proof  line  wire,  494 
wire  gauze,  490 
wiring,  488 
Electrolysis  of  concrete  structures, 

209 

Elements,  atomic  weights  and  sym- 
bols, 833 

of  mechanics,  149 
Elevators,  water,  349 
Ellipse,  construction  of,  42 


INDEX 


1157 


Ellipse,  perimeter  of,  50 
Eloin  lamp,  876,  877 
Emery,  Charles  E.,  421 
Endless-rope  haulage  system,   785 
Engineers'  Club,  Scranton,  694 
Engineers,  stationary,  rules  for,  473 
Engine  management,  460 

oil,  168,  169 
Engines,  endless-rope  haulage,  787 

haulage  motor  gasoline,  540 

internal   combustion,   532-548 

stationary  gas,  540 

steam,  454 

English  coal,  weights  of,  290 
Entries  in  mines,   607 
Equations,   solution  by  logarithms, 

36 

Equilibrium  of  liquids,  303 
Equivalent  orifice,  910 
Eschka's  method  of  analyzing  coal, 

379 

Ethane,  870 
Ethylene,  871 
Euler's  formula,  180,  182 
Evan  Thomas  lamp,  886 
Evans,  .869 
Evolution  by  Ipgarithms,  34 

mathematical,  26 
Examples,  see  Problems. 
Excavations,  supporting,  692-738 
Expansion  by  heat,  354 
Explosives  and  blasting,  667-691 

amount  and  kind,  690 

analyses  of  mine  air  after  blast- 
ing, 670 

black   powder,    sizes   of   grains, 
667 

blasting  definitions,  687 

boiler,  442 

caps,  677 

care  of,  673 

charging  and  firing  black  pow- 
der, 678 

charging   and   firing   dynamite, 
680 

detonators,  677 

dynamites,  composition  of,  668 

effect   of  free  faces  in  mining, 
688 

electric  detonators,  677 

firing,  676,  679 

firing  by  electricity,  681 

for  coal  mines,   672 

for  rock  work,  668 

fuse,  676 

handling,  674 

high  explosives,  667,  669 

hydraulic  cartridge,   686 

in  mines,  900 

lime  cartridges,  687 

low  explosives,  667 

permissible,  672 

precautions  when  tamping,  680 

rjroduction     of     carbon     mon- 
oxide, 852 

products  of  combustion,  670 

reversing  air  current,  985 

rules   of   Bureau   of    Mines   for 
handling,  675 


Explosives  and  blasting,  squibs,  676 
storing,  673 

strength,  comparative,  670 
substitutes  for  blasting  in  dry 

•  mines,  685 

thawing  dynamite,  673 
water  cartridge,  687 
wedging  down  coal,  685 

External  shear  of  beams,  table,  175, 
177 

Eytelwein's  formula,  321 

Factor  of  safety,  172 

Fahrenheit  thermometers  and  Centi- 
grade compared,  355 
Fairbanks  Company,  200 
Fairmount  Coal  Co.,  776 
Falling  bodies,  velocity,  153 
Fanning,  J.  T.,  306 
Fanning's  tables,  322 
Fans,  929-944 

Biram's  ventilator,  931 

blades,  943 

capacities,  941 

Capell  ventilator,  933 

centrifugal,  930 

construction,  942 

diameter  and  speed,  934,  942 

disk  type,  929 

equivalent  orifice,  935 

evase  stack,  934 

exhaust,  930 

force  fans  and  blowers,  930 

Guibal  ventilator,  932 

inlet  velocity,  935 

manometrical  efficiency,  942 

mechanical  efficiency,  942 

motors,  934,  944 

Murgue's  formula,  936 

Murphy  ventilator,  933 

Nasmyth,  931 

position,  941 

ratings,  table,  938-940 

reversible,  936 

Schiele  ventilator,  932 

Sirocco  fan,  933 

size  of  orifice,  942 

spiral  casing,  944 

standard  air,  935 

Sullivan  fans,  936,  937 

tests,  944 

vacuum   and  plenum   systems, 
930 

Waddle  ventilator,  932 
Fathom,  1 

Feedwater  of  boilers,  422 
Fire,  effect  of,  on  concrete,  210 

temperature  of,  449 
Firedamp,  859,  864 

whistle,  895 
Fires  in  boilers,  434 

in  mines,  945-949 
First  aid,  969-975 
Flapping  of  belts,. 274 
Flue  dust,  briqueting,  968 
Flumes,  318 

Forbes'  gas  indicator,  895 
Forces,   composition  and  resolution 
of,  153 


1158 


INDEX 


Forces,  moments  of,  154 

Form  work  for  reinforced  concrete, 

220 

Formulas,  mathematical,  20 
Foster's  rule  for  shaft  pillars,  697 
Fractions,  arithmetical  and  decimal, 

19,  20 

Fraser  &  Chalmers,  251,  252 
French  coal,  weights  of,  290 
French  Coal  Commission,  448 
Frick,   H.    C.,    Coke   Co.,   230,   604, 

708,  738,  982 
Friction,  angle  of,  160 

coefficient  of,  159 

definition,  159 

in  haulage,  758 

mine  cars,  163 

reduction  by  lubrication,  166 

resistance  of  shafting,   162 

rolling,  table,  160,  162 

tables  of  coefficients  and  angles 
of  repose,  160-162 

tests  on  mine-car  wheels,  tables, 

164,  165 

Fuel  oils,  537;  see  also  Petroleum. 
Fuels,  365-406 

air  required  for  combustion,  451 

alcohol,  536 

briqueting,  967 

carbon,  365 

coal,  368 

coking  C9als,  374 

combustion  of,  363 

gas  engine,  536 

gaseous,  398 

gasoline,  536 

hydrogen,  365 

kerosene,  537 

liquid,  comparative  value,  537 

peat,  367 

petroleum,  395 

temperature  of  ignition,  448 

wood,  365 
Fuller,  W.  B.,  212 
Functions,  trigonometric,  of  angles, 

55 

Fundamental     relations     in     trigo- 
nometry, 55 
Furnace  fittings,  417 

mine,  927 
Fuse,  676 
Fusible  plugs,  415,  438 

Galloway,  G.,  736 

Garforth,  Sir  William,  877 
Garforth-Walker  gas  indicator,  893 
Gas,  coal,  analyses,  402,  403 

engine  fuels,  536 

indicators,  891 

natural,  400 

natural,  prospecting  for,  557 

producers,  404,  405 

water,  403 
Gases,  acetylene,  871 

afterdamp,  869 

analyses    and     heating    values 
398,  399 

as  fuels,  398" 

atmospheric  pressure,  838 


Gases,  atomic  weights,  833 

Avogadro's  law,  836 

barometers,  839 

blackdamp,  851 

blast-furnace,  398 

by-product,  401 

carbon  dioxide,  848 

carbon  monoxide,  852 

chemical  reactions,  weights  and 
volumes  of  gases,  834,  835 

chemistry  of,  831 

coke  oven,  402 

density,  836 

diffusion  of,  842 

ethylene,  871 

explosibility,  relative,  863 

fire  damp,  864 

heating  value  at" 32°  F.,  400 

hydrogen,  871 

hydrogen  sulphide,  871 

methane,  850,  859 

mine,  845 

molecular  weights,  834 

nitric  oxide,  872 

nitrogen,  848 

nitrogen  dioxide,  872 

occluded,  860 

occlusion  and  transpiration,  843 

olefin,  871 

oxygen,  846 

oxygen    and    air   required    for 
combustion,  447 

paraffin,  870 

percentage  composition,  834 

physics  of,  836 

rarer  mine  gases,  870 

specific  gravity,  277,  837 

specific  heats,  361 

sulphur  dioxide,  872 

symbols  of  elements,  833 

temperature  of  ignition,  448 

volume,  temperature,  pressure, 
etc.,  relations,  840 

volumes    when    burned  in   air, 
835 

weight  and  volume  of  air  and 

gases,  841 
Gasoline,  as  fuel,  536 

engines,  532 

hoisting  engines,  741 

locomotives  for  haulage  plants, 

807 

Gates,  dam,  328 
Gauges,  tables  of,  291,  292 
Gay-Lussac's  law,  475,  840 
Geological  chart  for.  United  States. 
551 

maps,  construction  of,  557 
Geometrical  construction,  38 

progression,  25 
Geometry,  36-43 

in  railroad  surveys,  109 
Geordie  lamps,  886 
George's  Creek  coal  district,  617 
Gilberton  water  shaft,  350 
Glossary  of  mining  terms,  1101 

of  wire-rope  terms,  262 
Gobert  system  of  freezing,  591 
Gordon  electric  cells,  516 


INDEX 


1159 


Gottlieb's  values  for  woods  as  fuel 

365,  366 

Gould,  E.  Sherman,  320 
Gow,  Alex  M.,  483 
Gradient,  hydraulic,  320 
Grady,  P.  A.,  811 
Graham,  854 
Graham's  law,  842 
Grates,  boiler,  417 
Gravity,  center  of,  155 
Great  Britain,  currency,  16 

weights  and  measures,  15 
Griffith,  William,  705 
Grouting,  194 
Guibal,  862 

ventilator,  932 
Gyration,  radius  of,  158 

Haas,  848,  853,  856,  861 
Haas'  formula,  392,  393,  394 
Haddock,  733 
Hailwood  lamp,  888 

locks  for  lamps,  879 
Halberstadt,  Dr.  G.  H.,  969 
Haldane,    Dr.,    846,    849-851,     854 

858,  869,  872-874 
Hall,  Clarence,  872 
Hamilt9n  Coal  Co.,  260 
Hardy  indicator,  895 
Harger,  870 

Hauger  gas-signaling  apparatus,  896 
Haulage,  758-831 

animal  haulage,  775 

calculations  for  jig  planes,  784 

calculations  for  low-  and  high- 
speed, endless-rope  engines, 
971 

calculations  for  self-acting  in- 
clines, 781 

comparison  of  endless-  and  tail- 
rope  systems,  794 

comparison  of  gasoline  and  other 
motors,  810 

compressed-air  haulage,  798 

cost  of  gasoline-locomotive 
haulage,  809 

cost  of  mule  haulage,  777 

curvature,  759,  763 

diamond  switch,  773 

electric-locomotive,  815 

endless-rope,  785 

engine  planes,  785 

engines  for  tail-rope  system,  793 

entry  switches,  770 

friction,  758 

frogs,  771 

gasoline-motor,  807 

gauge  of  track,  765 

grade  equivalents,  table,  761 

grade  resistance,  760 

grades  and  their  effects,  781 

grips  and  grip  cars,  788 

high  speed  endless-rope  haul- 
age, 790 

inertia,  762 

jig  planes,  783 

mules,  775 

overhead  endless-rope  haulage, 
790 


Haulage,  rail  elevation,  764 

rails,  weight  of,  766 

resistances,  758 

room  and  branch  switches,  771 

safe  grade  for  mules,  778 

self-acting  inclines,  778 

side-entry,  789 

slopes  and  engine  planes,  784 

spikes  for  rails,  769 

steam-locomotive  haulage,  795 

table   of   rails   and   accessories, 
764,  766,  768 

tail-rope  system,  792 

ties,  768,  770 

track  laying,  notes,  773 

tracks  on  inclines,  779 

trackwork,  762 

weight  of  rails  for  track,  768 
Hawksley's  formula,  321 
Hawsers,  243,  250 
Hazard  Manufacturing  Co.,  237 
Hazleton  boilers,  416 
Heading  machines,  647 
Heat,  352-364 

absolute  zero,  353 

boiling  point  of  water  at  vari- 
9113  altitudes,  363 

British  thermal  unit,  353 

calorie,  354 

coefficients  of  linear  expansion, 
359 

combustion  of  fuels,  363 

conducting  power  of  materials, 
421 

conduction  of,  359 

effect  of,  on  concrete,  211 

equivalence  of  units,  354 

expansion  by,  354 

mechanical  equivalent  of  heat, 
354 

melting  points  and  latent  heat 
of  fusion  of  metals,  362 

of  burning  carbon,  449 

radiation  of,  359 

sensible  and  latent,  361 

specific,  360 

thermometers,  352 
Heberle  gate,  955 
Heine  boilers,  416 
Hemp  rope  for  power  transmission, 

Hewitt,  William,  251,  253,  264 
Hillebrand,  W.  F.,  378 
Hoisting,  739-758 

balanced,  744 

calculations      for      first-motion 
engines,  751 

calculations   for  second-motion 
engines,  757 

compressed-air  engines,  741 

conical  drums,  745 

Despritz  system,  750 

electric  engines,  742 

engines,  739,  740 

first-motion  engines,  741 

flat  ropes  and  reels,  746 

forces  and  moments,  755 

gasoline  engines,  741 

hand- and  horsepower  hoists,  739 


1160 


INDEX 


Hoisting,  hydraulic  engines,  742 

Koepe  system,  748 

Monopol  system,  751 

reels,  746 

ropes,  239 

second-motion  engines,  740 

steam-power  engines,  740 

tail-rope  balancing,  745 

Whiting  system,  749 
Honeycombing     of     boiler     plates, 

426 

Hood,  O.  P.,  811,  813 
Horsepower,  compressed  air  require- 
ment, 807 

definition,  153 

of  a  stream,  331 

of  belts,  273 

of  hoisting  engines,  754 

of  Manila  ropes,  269 

of  steam  engines,  456 

required  to  raise  water,  table, 
339 

standard  of  boiler,  431 

transmission  by  shafting,  271 

transmission  by  wire  rope,  266, 

267 

Hughes,  H.  W.  775,  875,  881 
Hughes,  Thomas  E.,  254 
Hughes's  rule  for  shaft  pillars,  698 
Humidifying  air  current  in  mines, 

902 

Humphrey,  H.  A.,  398 
Hunt,  C.  W.,  486 
Hunt,  C.  W.,  Co.,  967 
Hutchinson,  869 
Hyatt  bar  for  reinforced  concrete, 

217 

Hydrated  lime,  188 
Hydraulic  coal  classifiers,  953 

gradient,  320 

hoisting  engines,  742 

limes,  188 
Hydraulics,  307-352 

conversion  factors,  314 

definitions,  307 

discharge  of  water,  table,  311 

flow  of  water  in  open  channels, 
315 

flow  through  pipes,  320 

flumes,  318 

formulas  for  velocity,  321 

gauging  by  weirs,  312-314 

gauging  water,  309 

horsepower    required    to    raise 
water,  table,  339 

irrigation  quantity,  tables,  330 

mine  dams,  327 

outside  dams,  328 

pump  machinery,  333 

reservoirs,  327 

tunnels,  319 

water  elevators,  349 

water  power,  331 

See  also  Water. 
Hydrogen,  871 

as  fuel,  365 

sulphide,  871 
Hydrostatics,  303 
Hygrometers,  844,  904 


Ignition,  temperature  of,  448 

Ilgner  system,  742 
Imperial  measure,  15 
Inclined    plane,    power   required   to 
hoist  on,  151 

stress    in    hoisting     ropes    on, 

254 

Incrustation  on  boilers,  424 
Indian  woods,  weight,  282 
Indiana  coal  mining,  618 
Indicators,  gas,  891 
Inertia,  moments  of,  157 
Injectors  for  boiler  feeding,  422 
Injuries,  treatment  of,  969 
Institution    of    Civil    Engineers    of 

Great  Britain,  398 
Instruments,  care  of  surveyor's,  92 
•  leveling,  73 

surveyor's,  60-67 
Interest  on  money,  computing,  23 
Internal-combustion    engines,    532- 
548 

at  mines,  538 

back  firing,  547 

carbureter  troubles,  548 

carbureters,  541 

compression  troubles,  548 

engine  starters,  545 

four-cycle  engines,  532,  533 

fuels,  536 

gasoline-engine  cycles,  532 

ignition,  542 

misfiring,  547 

operation,  545 

preignition,  548 

spark  plugs,  544 

starting  the  engine,  545 

stationary  gas  engines,  540 

stopping  the  engine,  545 

troubles  and  remedies,  547 

two-cycle  engines,  533,  534 
International     Bureau    of    Weights 

and  Measures,  11 
Interstitial  currents,  956 
Involution,  25 

by  logarithms,  34 
Iowa  coal  mining,  618 
Iron,  strength  of,  170 

plates,  weights,  293 

wrought,  weight,  293,  298,  301 
Irrigation  quantity,  tables,  330 

Jeffrey-Robinson  coal  washer,  953 

Jet  pump,  349 

Jig  planes,  783 

Johnson,  A.  L.,  217 

Johnson,  W.  R.,  288 

Joule's  investigations,  354 

Kahn    trussed    bar    for    reinforced 
concrete,  218,  226 

Kehley's  Run  Colliery,  327 

Kent's  method  of  determining  heat- 
ing value  of  coal,  392-394 

Kentucky  Mining  Institute,  731 

Kerosene  as  fuel,  537 

as  remover  of  scale  on  boilers, 
425 


INDEX 


1161 


Kind-Chaudron    system     of      shaft 

sinking,  592 
Kinetic  energy,  153 
King,  A.  J.,  811,  813,  866,  871 
Knight  bucket  impact  wheel,  475 
Koehler,  862 

Koepe  system  of  hoisting,  748 
Koppers'  regenerative  ovens,  401 
Kutter's  formula,  317,  321 

Lacing  of  power  belts,  274 

Laminations  of  boiler  plates,  426 
Lamps,  874-891 

acetylene,  900 

Ashworth-Hepplewhite-  Gray 
lamp,  888 

bonnets,  876 

bull's  eye,  887 

cap  electric  lamps,  898 

Chesneau  lamp,  875,  890 

circulation  of  air,  877 

Clanny  lamp,  880,  883,  886 

cleaning,  883 

Clowes'  hydrogen  lamp,  889, 983 

Davy  lamp,  880,  883,  884 

deflector,  887 

design,  875 

electric,  896 

Evan  Thomas  lamp,  886 

failure  of  lamps,  884 

gas    indicators    and    signaling 
devices,  891 

gauzes,  875 

Geordie  lamps,  886 

glasses,  876 

Hailwood  lamp,  888 

height  of  gas  cap,  882 

igniters,  878 

illuminating  power,  880 

locks,  878 

Marsaut    lamp,    874-876,    880, 
887 

Mauchline  lamp,  887 

Mueseler  lamp,  877,  887 

multiple  gauzes,  876 

oils,  879 

Pieler  lamp,  890 

principle  and  origin,  874 

protector  lamp,  888 

specifications,  875 

Stephenson  lamp,  880,  886 

Stokes'  alcohol  lamp,  889 

Stuchlick  acetylene  lamp,  891 

testing  fpr  gas,  882 

testing  for  methane,  881 

Tombelaine  acetylene  lamp,  891 

wicks,  877 

Wolf  lamp,  876,  878,  880,  888 
Lang  lay  ropes,  238,  242 
Latitude,  determination  of,  in  sur- 
veying, 105 

and  departures,  tables,  1074 
Law  of  mechanics,  149 
Lay  of  wire  ropes,  238 
Lead,  strength  of,  170 
League,  length  of,  1 
Le  Chatelier,  805 

flask,  204 

gas  indicator,  892 


Leclanche'  cell,  514 

Lehigh  and  Wilkes-Barre  Coal  Co., 

604,  734 

Lehigh  Valley  Coal  Co.,  735 
Lehmann,  872 

Leschen  &  Sons  Rope  Co.,  237 
Leveling,  73-76 

barometric,  140 
Lever  safety  valve,  414 
Levers,  149 
Lewes,  Prof.,  948 
Libin  gas  indicator,  893 
Lime  mortars,  191 
Limes,  188 
Line  shafting,  270 
Linear  measures,  1 
Link-Belt  Engineering  Co.,  237,  269, 

962,  968 
Lippman   system   of   shaft   sinking, 

593 

Liquid  measure,  7,  8 
Liquids,  comparative  value  as  fuel, 
537 

compressibility,  307 

equilibrium,  303 

pressure,  303-306 

specific  gravity,  277,  538 

specific  heats,  361 
Liveing  gas  indicator,  892 
Locomotive  boilers,  inspection,  441 
Locomotives,    electric,    for  haulage, 
815 

for  mine  haulage,  795 

gasoline,  807 
Logarithmic  tables,  1009 
Logarithms,  29-36 

of    trigo nometric    functions, 

table,  1028 

Longitude  and  time,  10 
Longwall  system  of  mining,  652-666 

advantages  and  disadvantages, 
654 

buildings,  pack  walls,  and  stow- 
ing, 666 

control  of  roof  pressure,  665 

in  contiguous  seams,  664 

in  flat  seams,  655 

in  inclined  thick  seams,  664 

in  panels,  661 

in  pitching  seams,  657 

in  thick  seams,  663 

labor  and  trade  conditions,  654 

rectangular  long  wall,  656 

roadways,  665 

roof  pressure,  653 

Scotch  or  Illinois  plan,  655 

starting  workings,  664 

surface  damage,  water,  gas,  etc., 
654 

timbering  the  face,  666 

waste,  653 
Lord  and  Haas'  method,  392,   393, 

394 

Lord,  N.  W.,  400 
Lovatt,  A.  L.,  788 
Low  gas-signaling  apparatus,  896 
Lubricant  tests,  168 
Lubricants,   best  for  different   pur- 
poses, 169 


1162  INDEX 


Lubrication,  166 

of  wire  ropes,  257 
Lucas,  F.  E.,  401 
Lungmotor,  987 

McCutcheon  gas  indicator,  893 
McDonald,  W.  Va.,  coal,  380 
McKibben,  Frank  P.,  705 
McMyler  dump,  967 
MacGeorge,  E.  F.,  555 
Machine  mining,  644 
Machinery,  crushing,  950 

elementary  forms,  149 
Manila  ropes,  horsepower  of,  269 
Mapping,  in  surveying,  95 
Maps,  geological,  557 
Mariotte's  law,  840 
Marks'  investigations,  362 
Marsaut  lamp,  874-876,  880,  887 
Marsh  gas,  859 
Marcus  screen,  960 
Martin,  R.  D.,  402 
Masonry,  234-236 

absorptive  power  of  stone,  230 

brick,  236 

crushing  strength  of  stones  and 
piers,  235 

dams,  331 

durability  of  stone,  236 

materials,    coefficients    of    fric- 
tion   and    angles    of    repose, 
160 

measures  of,  6 

safe-bearing  values  of  materials, 
234 

strength  of  stone,  234 

supports  for  excavations,  735 
Massachusetts  Institute  of  Technol- 
ogy, 421 
Materials,  properties  of,  275 

strength    of,    tables,    169,    170, 

171 

Mathematics,  18-59 
Mauchline  lamp,  887 
Measure,  angular,  8 

board,  302 

brickwork,  6 

circular,  9 

conversion  factors,   metric  and 
United  States,  13,  14 

displacement  of  ships,  7 

dry,  7 

Great  Britain,  15 

linear,  1 

liquid,  7 

masonry,  6 

metric  system,  10 

square,  3 

surface,  3 

surveyor's  linear,  1 

surveyor's  square,  3 

timber,  301 

time,  10 

tonnage  of  ships,  7 

volume,  6 

water,  volumes  and  weights,  8 

weight,  3 
Measurements  of  boiler  tubes,  297 

of  coal,  287,  288 


Mechanical  powers,  149 
Mechanics,  149-169 

center  of  gravity,  155 

composition   and   resolution   of 
forces,  153 

elements,  149 

falling  bodies,  153 

friction,  159 

moment  of  inertia,  157 

moments  of  forces,  154 

radius  of  gyration,  158 

section  modulus  and  moment  of 
resistance,  159 

work,  153 
Mensuration  of  solids,  50-54 

of  surfaces,  43-50 

Meridian,  determination  of,  in  sur- 
veying, 99 
Merivale's    rule    for    shaft    pillars, 

697 

Metals,   melting  points  and  latent 
heat  of  fusion,  362 

relative  heat  conductivities,  359 

specific  gravity,  table,  277 

strength,  170,  296 

weight,  table,  278 
Methane,  850,  859 
Methods  of  mining,  604-666 

Alabama  methods,  631 

battery  breasts,  626 

blasting  after  undercutting,  642 

Brown's  method,  637 

buggy  breasts,  622 

chutes,  623 

cleats,  614 

closed  work,  606 

Connellsville,  Pa.,  method,  635 

contiguous  seams,  629 

double-chute  rooms,  625 


drawing  pillars,  648 
entries,  607 


flat  seams,  616 
inclined  seams,  626 
longwall  w9rk,  644,  652-666 
machine  mining,  644 
mining  and  blasting  coal,  638 
New  Castle,  Col.,  method,  631 
open  work,  604 
panel  system,  637 
pillar-and-stall  systems,  634 
pillar  drawing,  648 
pitching  seams,  619 
roof  slip,  616 

room-and-pillar  systems,  607 
rooms,  611 

shooting  off  the  solid,  638 
single-chute  rooms,  624 
small  seams,  621 
steam-shovel  mines,  605 
Tesla,  Cal.,  method,  <632 
thick  and  gaseous  seams*  620 
thick  non-gaseous  seams,  621 
undercutting  and  solid  shooting, 

643 
Williams,  J.  L.,  method,  636 

Metric  system,  10 

conversion  factors,  13 

Mice,  effect  of  afterdamp  on,  857 

Midvalley  Coal  Co.,  810 


INDEX 


1163 


Vline  laws  of  Pennsylvania,  906,  918 
Mine-rescue  apparatus,  986 

work.  984 
Mine  safety,  975-989 

mismanipulation  of  controlling 
devices,  980 

premium  system  and  company 
rules,  976 

protecting  from  electricity,  980 

safeguarding  machinery,  978 

safety  practices  of  Prick  Coke 
Co.,  982 

supervision,  975 
Vline   surveying,  laying   out   sharp 

curves,  133 

shafts  and  slopes,  77-82 
underground,  83-92 
Vf  ine  timbering,  707-730 
longwalfface,  666 
Vline  water,  effect  of,  on  concrete, 

210 

Minerals,  specific  gravity,  table,  276 
Vliner's  inch,  309 
Vlines,  accidents,  969,  975 

air,  846 

air  affected  by  gasoline  locomo- 
tives, 811,  812 

air  after  blasting,  analyses,  670 

air,  humidity  of,  843 

batteries  for  signaling,  514 

blasting,  687 

blasting,  substitutes  for,  685 

cars,  friction,  163-166 

coal-bearing  formations,   550 

compressed-air  locomotives,  798 

dams,  327,  337 

drainage  of  shafts,  596 

effect  of  free  faces,  688 

electric-locomotive  haulage,  815 

entries,  607 

explosive  condition,  900 

explosives  and  blasting,  672 

fires,  945-949 

flushing  of  culm,  702 

furnace  construction,  927 

gases,  845 

gasoline-motor  haulage,  807 

haulage,  758-831 

heat    and    humidity,    effect    on 
miners,  873 

hoisting,  739-758 

induction  motors,  509 

internal     combustion     engines, 
538 

lamp  houses,  884,  899 

lamp  stations,  602 

machinery,  lubrication,   166 

methods  of  working,  604-666 

mules,  775 

opening  a  mine,  563-604 

plan  arrangement,  925 

prospecting,  549 

pump  machinery,   333 

pumps,  electrically  driven,  343 

pumps  for  acid  waters,  346 

refuse  dams,  331 

reporting    on    coal    lands,    dia- 
gram, 560 

rooms,  611 


Mines,  sampling  and  estimating 
amount  of  mineral  available, 
559 

sampling  coal  for  analysis,  378 

shaft  bottoms,  599 

shaft  lining  of  concrete,  230 

shafts,  578-596 

slope  bottoms,  596 

slopes,  575 

stables,  601 

steam  l9comotives,  795 

supporting     excavations,     692- 
738 

surf  ace  tracks,  603 

telephone  system,  521 

trackwork,  762 

tunnels,  509 

ventilation,  831-945 

water  buckets,  350 

water  elevators,  349 

wedging  down  coal,  685 

wire  ropes,  use  of,  237 
Mining   engineering   rule   for   shaft 
pillars,  697 

machines,  644 

methods,  604-666 

terms,  glossary,  1101 
Mixers  for  concrete,  223 
Modulus  of  elasticity,  171 

of  rupture,  178 

of  rupture  of  stone,  234 

section,  159 

Molecular  weights  of  elements,  834 
Moment  of  resistance,  159 

of  beams,  176 
Moments  of  forces,  154 

of  inertia,  157 
Monetary  systems,  16,  17 
Monopol  system  of  hoisting,  751 
Moore,  Edwin  A.,  401 
Mooring  lines,  250 
Morin's    experiments,    720 
Mortars,  191-205 

adhesion,  194 

cement,  191 

composition  in  brick  piers,  235 

compressive  strength,  193 

grouting,  194 

laying  in  freezing  weather,  194 

lime.  191 

materials  required,  192 

percentage   of   water  for  sand, 
199 

properties  of  cement,  193 

sand  for  tests,  199 

retempering,  194 

shrinkage,  194 

tensile  strength,  193 
Motors,  current,  332 

electric,  497 

Mueseler  lamp,  877,  887 
Mules  for  mine  haulage,  775,  809 
Multiplication  by  logarithms,  32 
Murgue,  M.  D.,  910,  936,  942 
Murphy  ventilator,  933 

Nails,  size  and  weight,  299 

Nasmith,  854 
Nasmyth  fan,  931 


1164 


INDEX 


Natural  cement,  188,  189 

sines  and  cosines,  tables,  991 
tangents  and  cotangents,  tables, 
1000 

Neville's  formula,  321 

New  Castle,  Col.,  method  of  work- 
ing mines,  631 

New  England   Gas  and   Coke   Co., 
Everett,  Mass.,  399,  401 

Nitric  oxide,  872 

Nitrogen,  848 
dioxide,  872 

Nitroglycerin,  667 

Nolten,  G.,  555 

Norris,  R.  Van  A.,  163,  944 

Nova  Scotia  Steel  and  Coal  Co.,  402 

Noyes,  W.  A.,  378 

Numbers,    squares    and    cubes    of, 
tables,  1081 

Nuts,  iron,  weights,  292 
proportion,  300 

Ohio  State  University,  392 

Ohm's  law,  485 

Oiling  of  mine  cars,  163 

of  mine  machinery,  166 
Oils,  for  safety  lamps,  879 

fuel  or  compound,  537 

tests,  168 
Opening  a  mine,  563-604 

coke  ovens,  566 

cost  of  opening  and  production, 
564 

drifts,  568 

engine  and  pump  room,  602 

grades,  565 

location  of  opening,  567 

locatio.n  of  surface  plant,  565 

mining  plant,  566 

mining  village,  566 

rock  tunnels,  571 

safety  appliances,  575 

shafts,  578-596 

sidings,  565 

slope  and  shaft  bottoms,  596 

slopes,  575 

stables,601 

surface    tracks    for    slopes    and 
shafts,  603 

tracks  on  bottom  of  slopes  and 
shafts,  596,  599 

tunnels,  569 
Open  work  in  mines,  604 
Ormsbee,  J.  J.,  954 
Orvitz,  870 

Otto  cycle  engines,  532 
Oxygen,  846 

required     for     combustion     of 
gases,  447 

Pamely's  rule  for  shaft  pillars,  697 

Panel  system  of  mining,  637 
Parallelogram  of  forces,  154 
Parallelograms,  44 
Parallelepipeds,  52 
Parr,  870 

Paul,  J.  W.,  875,  883 
Peat  as  fuel,  367 
Pdclet,  421 


Pelton  bucket  impact  wheel,  475 
Pelton  Water  Wheel  Co.,  322 
Pennsylvania    anthracite   coals,  an- 
alyses, 386 

Pennsylvania  Coal  Co.,  229 
Pennsylvania  Gas  Coal  Co.,  403 
Pennsylvania  R.  R.  Co.,  288 
Percentage,  22 
Perch,  dimensions  of,  1,  3,  6 
Percy,  Dr.,  948 
Pescheux    gas-signaling    apparatus, 

896 
Petroleum  as  fuel,  395 

advantages  and  disadvantages, 
397 

calorific  value,  396 

composition  of  crude,  395 

flash  point  and  firing  point,  395 

prospecting  for,  557 

ultimate  analysis,  396 

value  as  fuel  compared  to  coal, 

397 

Pfeiffer,  G.  W.,  900 
Philadelphia  &  Reading  Coal  &  Iron 

Co.,  350,  603,  725,  727,  969 
Philippine  woods,  weight,  281 
Phosphorus  in  coal,  370 
Physics  of  gases,  836 
Pick  machines,  644 
Picric  acid,  667 
Pieler  lamp,  890 
Piers,  stone  masonry,  235 
Piez,  967 
Pillar-and-stall  systems   of   mining, 

634 

Pillar  drawing,  648 
Pine  Hill  coal  breaker,  227 
Pins,  surveyor's,  66 
Pipes,  cast-iron,  weight,  294 

C9ntents,  295 

dimensions  of  iron  welded,  296 

thickness  for  heads   and   pres- 
sures, 306 

water,  friction  in,  323 

wood,  306,  307 
Piping  for  compressed  air,  476 

of  boilers,  412 

Pishel's  test  for  coking  coal,  377 
Piston  speed  for  steam  engines,  458 
Pittsburg  coal  region,  616 
Plane,  inclined,  power  required  on, 

151 

Plane  trigonometry,  54-59 
Plotain,  856 
Plow-steel  ropes,  238 
Plymouth  Coal  Co.,  733 
Poetsch  system  of  freezing,  591 
Polaris,  observation  of,  in  surveying, 

101-105 
Polygons,  45 
Polyhedrons,  50 
Porter,  870 

Porter,  H.  K.,  Company,  799,  801 
Portland  cement,  188,  189,  195,  204 
Power,  definition,  153 

pumps,  341 
Power  transmission,  264-275 

belt   pulleys.    271 

belting,  272 


INDEX 


1165 


Power  transmission,  constants  for 
ropes  on  different  materials, 
267 

diameters     of     sheaves,     table, 
266 

distance    between    bearings    of 
shafts,  270 

flapping  of  belts,  275 

formula    of    horsepower    trans- 
mitted, 266 

Jiemp  rope,  268 

horsepower       transmitted      by 
shafting,  table,  271 

horsepower  transmitted  uy  steel 
rope,  267 

line  shafting,  270 

manila  ropes,  269     • 

sheaves,  266 

value     of      coefficients,     table, 

265 

Powers  of  numbers,  26 
Preparation  of  coal,  949-968 

anthracite,  preparation  of,  958 

bituminous,  preparation  of,  959 

briqueting,  967 

buckets,  963 

chutes,  962 

corrugated  rolls,  950 

cost  of  unloading,  966 

cracking  rolls,  949 

crushing  machinery,  949 

disintegrating     rolls     and     pul- 
verizers, 950 

hammers,  950 

handling  of  material,  962 

hydraulic  classifiers,  953 

interstitial  currents,  956 

jigs,  954 

removal  of   sulphur  from  coal, 
957 

screens,  951 

sizing     and     classifying     appa- 
ratus, 951 

tipple  design,  962 
Pressure  of  liquids,  303-306 
Priestly,  849 
Prismoids,  50 

Problems:  air  compressors,  volume, 
476 

air  current,  division,  919 

air  current,  measurement,  908, 
912,  917 

air  current  regulators,  920,  921 

air  supply,  in  combustion,  451 

angle  of  repose,  160 

angles,  latitude  and  departure, 
1073 

area  of  wire,  490 

barometric  leveling,  141 

belting,  horsepower  of,  273 

bending  moment  of  a  beam,  176 

boiler  efficiency,  433 

boiler  feedwater,  factor  of  evap- 
oration, 433 

boiler    feedwater,    purification, 
429 

boiler  heating  surface,  445 

boiler  horsepower  and  evapora- 
tion, 431 


Problems:  cantilever  beam,  reaction. 

175 

center  of  gravity,  156 
chimney,  height  and  draft,  452, 

453 

coefficient  of  friction,  159 
combustion,  air  required  for,  448 
compressed   air   storage   tanks, 

804,  805 
compressors  for  haulage  plants, 

806 

cost  of  opening  a  mine,  564 
designing  of  beams,  178 
electric  current  estimates,  495 
electric  current,  etc.,  485 
electric  current  feeders,  497 
electric-locomotive  feeders,  820, 

821 

electric  resistance,  488 
electric  wire,  resistance,  491 
electricity,  transmission,  493 
gas    required   to  displace   coal, 

400 

gases,  chemical  reactions,  835 
gases,  ^percentage   composition, 

834 

gases,  volume,  weight,  tempera- 
ture, etc.,  840,  841 
gases,  volumes  when  burned,  836 
gases,  weight,  volume,  and  loss 

in  boilers,  446 
geometrical,  38-43 
haulage  on  inclines,  782,  784 
head  of  water,  322 
hoisting,  conical  drum  for,  745 
hoisting     engines,     calculations 

for,  754,  758 

hoisting,  rope  and  reel,  747 
horsepower  of  haulage  engines, 

791,  792 

horsepower  of  water,  153 
horsepower     required     on     in- 
clined plane,  151  _ 
humidity  of  mine  air,  844 
inertia,  moment  of,  158 
kinetic  energy  of  water,  153 
levers  and  power,  1.50 
logarithmic,  30-36 
mathematical,  22-29 
measuring    concrete    materials, 

212 

mensuration,  46-48 
mine  entries,  611 
mine  locomotive  power,  797,  798 
mine  pillars,  696 
mine  shaft  timbering,   715 
mine  shaft  tubbing,  737 
mine  shafts,  size,  579 
moment  of  resistance,   159 
mortar  materials,  192,  199 
power  transmission,  268,  269 
pressure  of  liquids,  304 
pulleys  in  power  transmission, 

272 
pump  and  horsepower  required 

to  raise  water,  338 
radius  of  gyration,  158 
resistance  to  haulage,  759,  760, 

761,  762 


1166 


INDEX 


Problems:  rope-size  for  hoisting,  245 
safety  valve,  weight  for,  414 
sand,    percentage   of    voids   in, 

190 

screw,  weight  raised  by,  151 
section  modulus,  159 
sines  of  angles,  990 
siphon  discharge,  352 
solar  observations  in  surveying, 

105 

specific  gravity,  275 
specific  heats,  361 
steam    engines,    cooling    water 

for  condenser,  460 
steam  engines,  cut  off  and  ex- 
pansions, 455 

steam  engines,  horsepower,  457 
steam  engines,  injection  water 

for  condensers,  460 
steam  engines,   mean    effective 

pressure,  456 

steam  engines,  piston  speed,  458 
steam  pipe,  elbows,  412 
steam  pressure,  408,  409 
steam,  quality  of,  410 
stiffness  of  beams,  178 
strength   of  beams  and  props, 

184 

strength  of  columns,  181 
strength  of  pipes,  174 
stress,  172 
surveying,  144-148 
surveying  shafts,  78-80 
temperature  of  fire,  450 
temperature  stress,  174 
ties  for  mine  tracks,  770 
timber  measures,  302 
time  and  longitude,  101 
track  curvature,  763 
trigonometric,  58,  59 
ventilating  pressure,  928 
water,    conversion   into   steam, 

362 

water  velocity,  307,  308 
wirfe  ropes,  bending  stress,  251 
Producer  gas,  404 
Progression,  arithmetical,  24 

geometrical,  25 
Prony's  formula,  321 
Properties  of  materials,  275     \ 
Proportion,  mathematical,  21 
Props,  strength  of,  184 
Prospecting,  549-563 

bore-hole  records,  558 
coal-bearing  formations,   550 
construction  of  geological  maps 

and  cross-sections,  557 
diagram  for  reporting  on  coal 

lands,  560 
dip  and  strike,  558 
drilling,  553 
earth  augers,  553 
exploration  by  drilling  or  bore 

holes,  553 
for  petroleum,  natural  gas,  and 

bitumen,  557 
outfit,  549 
percussion  drills,  554 
plan  of  operations,  549 


Prospecting,  sampling  and  estimat- 
ing amount  of  mineral,  559 
Protector  lamp,  888 
Psychrometers,  844 
Pulley,  belt,  for  power  transmission, 
271 

element  of  machinery,  152 
Pulmotor,  989 
Pulsometer,  349 
Pump  machinery,  333-352 

air-lift,  349 

amount    of     water    raised    by 
single-acting   lift   pump,    340 

boiler  feed-pumps,  335 

capacity,  table,  336,  340 

centrifugal,  343 

Cornish  pumps,  333 

depth  of  suction,  338 

discharge     at     various     piston 
speeds,  344 

electric    current   consumed   for 
pumping  water,  342 

electrically    driven,    in    mines, 
343 

for  acid  waters,  346 

foundations,  346 

horsepower  required,  336 

jet  pump,  349 

management,  346 

packing,  333 

piston  speed,  335 

power,  341,  342 

power,  electrically  driven,  342 

ratio  of  areas  to  diameters  of 
cylinders,  336,  337 

ratio     of     steam     and     water 
cylinders,  335 

simple  and  duplex  pumps,  333 

sinking  pumps,  346 

speed  of  water  through,  334 

stations,  346 

vacuum,  349 

valves,  341 
Puzzolan  cement,  188 
Pyramids,  53 

Quin,  Robert  A.,  289 

Radiation  of  heat,  359 

Radii  and  deflection,  table,  111 

Radius  of  gyration,  158 

Railroad  surveying,  109 

Rails,  table  9f,  764,  766,  768 

Ralph's  gas  indicator,  893 

Ramsay,  Sir  William,  845 

Ramsey,  Robert,  604 

Rankine's  formula,  180      \ 

Rjiteau  turbine,  409,  470 

Ratio,  21 

Reactions  of  beams,  175 

Reciprocals,  23 

Recovery  work,  985 

Refraction,  table,  107 

Refuse  dams,  331 

Regulators  of  air  current,  919,  920 

Reinforced  concrete,  214 

Repose,  angle  of,  160 

Rescue  work,  984 


INDEX 


1167 


Reservoirs,  327 
Resistance,  moment  of,  159 
Resolution  of  forces,  153,  154 
Resultant  of  forces,  153 
Resuscitation   apparatus,    987 
Reversing  air  current,  985 
Reynoldsville  coal  region,  617 
Richards,  Frank,  formula,  477 
Richards,  Prof.  R.  H.,  955,  956 
Right  angles,  9 
Rings,  49 

cylindrical,  52 
Risdon  Iron  Works,  309 
Rittinger,  955 
Rivets,  shearing  and  bearing  values, 

table,  173 
Roadway,    surface,    rolling    friction 

for,  162 

Roane  Iron  Co.,  809 
Robb-Mumford  boilers,  416 
Rock  tunnels,  571 
Roebling's  line  wire,  494 
Roebling's  Sons  Co.,  John  A.,  237, 

245,  264,  266,  291 
Roller  bearings  on  mine-car  wheels, 

166 

Rolling  friction,  table,  160,  162 
Root,  cube,  27,  1081 

fourth  and  fifth,  28 

method  of  extracting,  29 

square,  26,  1081 
Rope,  glossary  of  terms,  262 

hemp,  268 

manila,  269 

steel,  237 

strength  of,  183 

wire,  237 

Roper's  safety-valve  rules,  414 
Rupture,  modulus  of,  178 

Safety  devices,  575,  982 

factor  of,  172 

lamps,  874-891 

valves,  414 
Salt,  W.  G.,  788 
Sand  for  mortar  tests,  199 

used  in  cements,  189-191 
Scale  of  tenths  of  a  foot,  2 
Scale,  on  boilers,  425 
Schiele  ventilator,  932 
Schmidt,  E.  C.,  759 
Scholz,  873 
Schondorff,  805 
Scotch  boilers,  416 

longwall     system     of     mining, 

655 

Screens,  coal,  951 
Screw,  element  of  machinery,  151 

threads,  proportions,  300 
Screws,  wood,  298 
Scribner's  rule,  302 
Seale  ropes,  240,  242,  244 
Sea-water,  effect  on  concrete,  210 
Section  modulus,  159 
Sectors,  49 

Sederholm,  E.  T.,  251,  252 
Segments,  circular,  49 

spherical,  52 
Self  rescuer,  987 


Settling     factors     for     minerals     in 

water,  956 

Sewell  seam  coal,  380 
Shade  Coal  Mining  Co.,  810 
Shaf er  resuscitation  method,  970, 987 
Shafting,  frictional  resistance  of,  162 

line,  270 
Shafts,  bottoms,  599 

buckets,  580 

cementation  process,   591 

compartments,  578 

construction  of,  578-596 

covering,  582 

data,  table,  576,  577 

drainage  and  pumping,  596 

draining  the  ground,  586 

enlarging  and  deepening,  593 

freezing  processes,  591 

Kind-Chaudron  system,  592 

lining  of  concrete,  230 

Lippman  system,  593 

long-hole  method,  585 

pneumatic  process,  590 

shoes  for  shaft  sinking,  588 

sinking  head  frame,  581 

sinking    through    firm    ground, 
.  583 

sinking  through  running  ground, 
586 

sinking  tools,  580 

size,  578 

surveying,  77 

Triger  method,  590 

upraising,  594 

ventilation  and  lighting,  583 
Shaw  gas-testing  machines,  895 
Shearing  stress,  171 

values  of  rivets,  table,  173 
Sheaves  for  wire  rope  transmission, 

266 

Sheet-metal  gauges,  291 
Shipping,  measures  used  in,  7 
Shoes  for  shaft  sinking,  590 
Signs,  mathematical,  18 

trigonometric,  55 
Simon's  method,  856 
Simple  stress,  171,  172 
Sines,  tables  of,  989,  991 
Single  shear,  172 
Sinking  mine  shafts,  583 
Siphons,  351 
Sirocco  fan,  933 
Slope  bottoms,  596 
Slopes  in  mines,  575 

surveying,  82 
Sluice  head  of  water,  310 


Smith,  Joseph,  877 
Solar  observation, 


in  surveying,  105 
Solid  shooting,  638 
Solids,  center  of  gravity,  156 

mensuration  of,  50-54 

specific  heats,  360 
Southern  Coal  and  Coke  Co.,  809 
Spark  plugs  of  eng-ines,  544 
Specific  gravity,  275 

cement,  203 

coal,  tables,  286,  288 

dry  woods,  278 

gases  and  vapors,  table,  277 


1168 


'  INDEX 


Specific  gravity,  liquids,  277 

metals,  table,  277 

minerals  and  earth,  table,  276 

miscellaneous,  278 
Specific  heat,  360 
Specification  for  cement,  204 
Sphere,  51 
Spherical  segments,  52 

zcfties,  52 

Spikes,  size  and  weight,  299 
Spillways  of  dams,  329 
Splicing  wire  rope,  255,  256 
Splitting  of  air  current,  918,  922 
Spontaneous  combustion,  948 
Spring  Valley  Coal  Co.,  735 
Square  measure,  3 

root,  26,  1081 

Squares  of  numbers,  tables,  1081    ' 
Squibs,  676 
Stadia  surveying,  134 
Stag    Canon    Fuel    Company,    684, 

Stag  Canon  Mines,  402 

Stanley  header,  647 

Stassart,  880,  881 

Stationary  engineers,  rules  for,  473 

Steam,  flow  of,  410 

pipes,  covering  for,  419 
pipes  for  engines,  412 
quality,  410 
resistance  of  elbows  and  valves, 

411 

saturated,  properties,  406,  407 
superheated,  409 
weight  delivered,  table,  411 
Steam  engines,  454-474 

area  of  piston  rod,  allowance 

for,  458 
clearance,  454 
comparison     with     turbines, 

469 
compound  slide-valve  engine, 

462 

condensers,  459 
condensing     slide-valve     en- 
gine, 461 
Corliss     engine,     compound, 

461,  463 
cut-off,  455 
cylinder  ratios,  458 
•  engine  management,  460 
faulty  bearings,  463 
faulty  brasses,  466 
faulty  oiling,  467 
grit  in  bearings,  468 
hoisting  engines,  740 
horsepower,  456 
hot  bearings,  465 
improper  valve    setting,  464 
jet  condenser,  460 
mean  effective  pressure,  455 
mechanical  efficiency,  458 
non-condensing       slide-valve 

engine,  461 

oil  and  grease  cups,  461 
piston  speed,  458 
pounding  of  engines,  463 
priming,  464 
ratio  of  expansion,  455 


Steam  engines,  requirements,  454 
reversal  of  pressure,  464 
rules  for  stationary  engineers, 

starting  and  stopping,  460 

stating  sizes,  457 

surface  condensers,  459 
warming  up,  460 
Steam-shovel  mines,  605 
Steam  turbines,  469 

care    of    gears    in     DeLaval 
turbines,  472 

comparison  with  engines,  469 

consumption  of  steam,  469 

economy,  472 

finding  horsepower,   470 

operation,  471 

troubles,  470 

types,  469 

Stearns,  Irving  A.,  288 
Steavenson,  A.  L.,  895 
Steel  plates,  weights,  293 

reinforcement  of  concrete,  214 

rope,  see  Wire  Ropes. 

strength  of,  170 

supports  for  excavations,  730 

tape,  surveyor's,  66 
Stephenson,  George,  874,  876 
Stephenson  lamp,  880,  886 
Stirling  boilers,  416 
Stirling,  Paul,  958 
Stokers,  mechanical,  418 
Stokes'  alcohol  lamp,  889 
Stone,  absorptive  power,  236 

crushing  strength,  234,  235 

durability,  236 

in  masonry,  234 
Straight  line  formula,  180 
Strain,  171 
Strength  of  materials,  169-187 

beams,  table,  174,  186,  187 

brick  in  masonry,  236 

cement  briquets,  201 

cement  mortars,  193 

cement,  table,  208 

chains,  183 

columns,  180 

cylindrical     shells    and     pipes, 
174 

metals,  170,  296 

ropes,  183 

seasoned  timber,  184 

stone  in  masonry,  234 

tables,  170,  171,  181,  186 

wire  ropes,  246-249 

wood,  171 
Stress,  combined,  182 

definition,  169 

direct,  formulas,  172 

of  concrete,  211 

on  wire  rope,  251 

Stromberg-C  a  rlson  Tele  phone 
Manufacturing  Company, 
521 

Stuchlick  acetylene  safety  lamp,  891 
Suction  lift  of  pumps,  338 
Sullivan  fans,  936,  937 
Sullivan  pressed-steel  plank  holder, 
223 


INDEX 


1169 


Sulphur  dioxide,  872 

in  coal,  370 

Sun,  parallax  in  altitude,  table,  106 
Supporting  excavations,  692-738 

advantages  of  steel  timbering, 
735 

barrier  pillars,  table,  699,  700 

built-up  packs  and  cribs,  705 

chain  pillars,  699 

coal  pillars,  692 

cost  of  steel  and  wood  timber- 
ing, 733 

dry  filling,  strength,  706 

entry  pillars,  697 

flat  seams,  707 

flushing  of  culm,  702 

masonry  shaft  lining,  735 

packs  and  cribs,  705 

pillars  in  inclined  seams,  698 

pitching  seams,  712 

reserve  pillars,  699 

room  pillars,  695 

shaft  linings,  735 

shaft  pillars,  rules,  697 

slope  pillars,  696 

squeeze  and  creep,  701 

steel  and  masonry  supports,  730 

steel  gangway  timbers,  732 

timbering  with  wood,  707 

tubbing,  736 

weight  on  pillars,  696 
Surface  measures,  3 
Surfaces,  mensuration  of,  43-50 
Surveying,  60-148 

abbreviations,  89 

barometric  leveling,  140 

care  of  instruments,  92 

chain,  steel  tape,  and  pins,  65 

circular  curves,  109 

clinometer,  67 

compass,  60 

cost  of  railroad  work,  119 

curved  railroad  tracks,  124 

curves  in  a  mine,  laying  out,  133 

determination      by      observing 
Polaris,  101 

determination   of  latitude   and 
corrections  for  altitude,  105 

determination  of  meridian,  99 

errors  in  closure,  94 

field  notes  for  curves,  115 

instruments,  60-67 

leveling,  73,  90 

mine  corps,  92 

mine  surveys,  83 

note  taking,  88 

outside  surveys,  68 

pitching  work,  90 

Polaris,  observation  of,  101-105 

problems,  144 

radii  and  deflections,  table,  111 

railroad  location,  119 

railroad  surveys,  109 

shafts,  77 

slopes,  82 

solar  observation,  105 

stadia  surveys,  134 

time,  100 

transit,  62 


Surveying,  transit  surveying,  67 
traversing  and  mapping,  93 
underground  surveys,  83 
Surveyor's  linear  measure,  1 

square  measure,  3 
Suspension  bridges,   ropes  for,   243, 

^48 
Susquehanna    Coal    Co.,    163,    288, 

289,  735 

Swan  gas  indicator,  893 
Swedish  wire  rope,  237 
Swoboda,  H.  O.,  897 
Sykes,  Wilfred,  755 
Sylvester  resuscitation  method,  971, 

987 

Tangents,  tables  of,  989,  1000 

Tank  tower  of  reinforced  concrete, 
223 

Taylor  coal  breaker,  227,  229 

Taylor,  W.  Purves,  211 

Telephone  system  in  mines,  521 

Temperature  of  fire,  449 
stress,  174 

Temple  Iron  Co.,  737 

Tennessee    Coal,    Iron    &    Railroad 
Co.,  725,  738 

Tensile  stress,  169 

Tesla,     CaL,     method     of     working 
mines,  632 

Tests  of  cement,  195 
of  lubricants,  169 
of  mine-car  wheels,  163 

Thermometers,  352 

Fahrenheit      and      Centigrade 
compared,  355 

Thompson,  Prof,  G.  R.,  882 

Thurston,  169 

Tiller  rope,  244 

Timber  measure,  301 

table  of  constants  for,  184 
weight,  283 

Timbering  in  mines,  707-730 
bad  roofs,  709 
choice  of  timber,  707 
cost  compared  with  steel,  733 
cost  of  preservation,  methods, 

725,  726 

cutting  and  storing  timber,  722 
destructive  agencies,  723 
durabilityof  treated  timber,  727 
economy  in  use  of  treated  tim- 
ber, 728 

entry  timbering,  710,  713 
four-stick  sets,  711 
framing  timbers,  720 
in  flat  seams,  707,  710 
in  loose  dry  material,  716 
in  pitching  seams,  712,  713 
in  rock,  715 
in  swelling  ground,  717 
in  wet  ground  or  quicksand,  717 
joints,  721 

limiting  angle  of  resistance,  720 
longwall  face,  666 
open-tank  treatment,  724 
placing  sets,  720 
preservation,  723 
pressure  treatment,  724 


1170 


INDEX 


Timbering  in  mines,  props,  707 

room  timbering,  707,  712 

shaft  timbering,  715 

square  frame  at  foot  of  shaft, 
718 

square-set  timbering,  718 

supporting    face    while    under- 
cutting, 710 

systematic  timbering,  708 

three-stick  sets,  711,  714 

two-stick  sets,  710,  713 

undersetting  of  props,  712 
Time,  100 

measure  of,  10 
Tin,  strength  of,  170 
Tombelaine  acetylene  lamp,  891 
Ton,  cubic  measurement,  6 

long,  6 

shipping,  7 

short,  5 

Tonnage  of  ships,  7 
Torricelli  vacuum,  839 
Trackwork  in  mines,  762 
Tracks,  shaft  bottoms,  599,  601 

slope  bottoms,  596 

surface  tracks,  603 
Trade  discount  denned,  23 
Tramways,  260 

cables,  249 

ropes  for,  242 
Transformers,  electric,  513 
Transit,  surveyor's,  62-65,  67-73 
Transmission  of  power,  264-275 

of  pressure  through  water,  305 
Trapeziums,  45 
Trapezoids,  44 
Traverse  tables,  1073 
Traversing  in  surveying,  93 
Treatment  of  injured  persons,  969 
Trenton    Iron    Co.,    237,   251,   264, 

291 
Triangles,  43 

solution  of,  56 

Triger  method  of  sinking  shafts,  590 
Trigonometric  functions,    table   of 
logarithms  of,  1028 

leveling,  76 

tables,  989 

Trigonometry,  plane,  54-59 
Troy  weight,  4 
Tubes,  boiler,  297 
Tunnels  for  water,  319 

mine,  569 

Turbines,  steam,  469 
Turf  as  fuel,  367 
Turquand's  gas  indicator,  892 

Ultimate  strength  of  flexure,  178 

of  materials,  172 
Unit  stress,  169 
United-Otto  ovens,  401 
United  States,  currency,  16 

measures,  conversion  factors  to 

metric,  13-15 
United  States  Bureau  of  Mines,  286, 

386,  672,  675,  681,  847,  848 

851,  853,  857,  862,  868,  897, 

900,  902,  984 
United  States  Coal  &  Coke  Co.,  976 


United   States   Coast   and  Geodetic 

Survey,  11 

United  States  Forest  Service,  724 
United    States    Geological    Survey, 

382,  387,  390,  404 
United  States  Steamboat  Inspection 

Service,  414 
United    States    Testing    Board    on 

strength  of  cables,  183 
Upham,  C.  C.,  957 

Vacuum  pump,  349 
Vaporizer,  541 
Vapors,  specific  gravity,  277 
Velocity  of  falling  bodies,  153 
Ventilation  of  mines,  831-945 

acetylene,  871 

afterdamp,  869 

air  columns,  927 

air  current,  reversing,  985 

ascensional,  925 

atmospheric  and  mine  air,  845 

blackdamp,  851 

box  regulators,  919,  920 

carbon  dioxide,  848 

carbon  monoxide,  852 

centrifugal  fans,  931 

coal  dust  in  mine  workings,  901 

conducting  air  currents,  944 

current    produced    by  ventila- 
tors, 916 

derangement  of  ventilating  cur- 
rent, 901 

distribution  of  air,  917 

door  regulator,  920 

effect  of  heat  and  humidity  on 
miners,  873 

elements  in  ventilation,   907 

elements  in  ventilation,   varia- 
tion of,  915 

equivalent  orifice,  910,  935 

ethylene,  871 

explosive  conditions  in   mines, 
900 

fan  ratings,  table,  938-940 

fans,  929 

fire  damp,  864 

friction  of  air,  909 

furnace,  927 

gas    indicators    and    signaling 
devices,  891 

gases,  chemistry  of,  831 

gases,  volumes  when  burned  in 
air,  835 

humidifying    the    air    current, 
902 

hydrogen,  871 

hydrogen  sulphide,  871 

influence  of  seasons,  926 

measurement  of  currents,  907 

mechanical  ventilators,  929,  942 

methane,  850,  859 

mice    and    canaries    as   test    of 
aftermath,  857 

mine  gas,  845 

mine  plan,  925 

mine  resistance,  907,  909 

natural,  925 

nitric  oxide,  872 


INDEX 


1171 


Ventilation,  nitrogen,  848 

nitrogen  dioxide,  872 

olefin  gases,  871 

oxygen,  846 

paraffin  gases,  870 

physics  of  gases,  836 

plenum  system,  930 

potential  factor  of  a  mine,  910 

quantity  of  air  required,  906 

rarer  mine  gases,  870 

rise  and  dip  workings,  926 

safety  lamps,  874 

shafts,  583 

splitting  of  air  current,  918,  922 

sulphur  dioxide,  872 

vacuum  system,  930 

water  gauge,  908,  911 
Vernier,  -of  compass,  62 

of  transit,  63 

Vertical  curves  in  railway  survey- 
ing, 122 

Vicat  needle,  202 
Volume,  measure  of,  6 

metric  measures  of,  12 

Wabner,  854,  861,  862,  868 
Waddle  ventilator,  932 
Walker,  S.  F.,  893 
Walls,  retaining,  of  concrete,  226 
Ward,  169 

Wardle's  rule  for  shaft  pillars,  697 
Washers,  iron,  weight,  292 
Wasteways  of  dams,  329 
Water,    boiling    point    affected    by 
altitude,  363 

buckets,  in  mines,  350 

channels,  character  of,  317 

contraction    and    discharge   co- 
efficients, 308 

conversion  factors,  314 

dams,  327,  328 

delivering    to     boilers     by     in- 
jectors, 422 

discharge,  table,  311 

ditches,  315,  316 

electric    current    for    pumping, 
342 

elevators,  349 

flow  in  brooks  and  rivers,  317 

flow  in  open  channels,  315 

flow    in    pipes    by    diameters, 
table,  324 

flow  through  flumes,  319 

flumes,  318 

friction  in  pipes,  323 

gas,  403 

gauges,  908,  911 

gauging,  309 

irrigation  quantity,  tables,  330 

loss  of  head  by  friction,  322,  325 

measures  of,  8 

measuring  flow  in  channels,  317 

metric   equivalents   of   volume, 
weight  and  capacity,  12 

mine  dams,  327 

miner's  inch,  310 

outside  dams,  328 

pressure,  304,  305 

quantities  delivered,  table,  323 


Water,  resistance  of  soils  to  erosion 
by,  316 

safe  bottom'and  mean  velocities, 
315  ' 

sluice  head,  310 

specific  heat  at  various  tempera- 
tures, 360 

speed  through  pump  machinery, 
334 

thickness  of  pipes,  306 

tunnels,  319 

velocity,  307,  308 

weirs,  312-314 
Waterbury  Co.,  237 
Waterfall,  power  of,  332 
Water-power,  331 

current  motors,  332 

efficiency  of,  331 

utilizing  a  waterfall,  332 
Watertown  Arsenal  tests,  206 
Watteyne,   880,  881 
Webster  gas  indicator,  893 
Wedge,  element  of  machinery,   151 

form  of  a  trapezoid,  53 
Weight,  air,  841 
•     air  in  boilers,  447 

boiler  tubes,  297 

bolts,  299 

building  materials,  283,  284 

cast-iron  pipe,  294 

cements,   189 

coal,  American,  287,  288 

coal,  English  and    French,  290 

dry  woods,  279-282 

gases,  841 

iron  boltheads,  nuts  and  wash- 
ers, 292 

measures  of,  3 

metals,  278 

metric  measures  of,  12 

miscellaneous   materials,   284 

of  substances,  278    . 

rails  and  accessories,  764,  766, 
768 

sheets  and  plates  of  steel,  iron, 
etc.,  293 

spikes  and  nails,  299 

timbers,  American,  283 

water  vapor,  table,  447 

wood  as  to  fuel  values,  366 
Weights  and  measures,  1-17 
Weir,  gauging  by,  312-314 
Weisbach's  formula,  322 
Wellman-Seaver-M  organ     water 

hoist,  350 

West  Kentucky  Coal  Co.,  734 
West    Virginia    Coal    Mining   Insti- 
tute, 811 

West  Virginia  coal  region,  617 
Western  Electric  Company,  521 
Western  Society  of  Engineers,  401 
Westinghouse  Airbrake  Co.,  401 
Westinghouse-Parsons  turbine,  469, 

470 

Westinghouse  steam  engines,  457 
Westmoreland  Coal  Co.,  403 
Wheel  and  axle,  150 
Wheels  used  in  waterfalls,  332 
Whitedamp,  852 


1172 


INDEX 


Whiting  system  of  hoisting,  749 
Wilcox,  Babcock  and,  367,  397,  416 
Williams,  J.  L.,  method  of  mining, 

636 

Williams'   methanometer,  894 
Williams  steam  engine,  457 
Windlass,  150,  739 
Wing  dams,  331 

Wire,   annealed   copper,   properties^ 
489 

gauge,  291,  490 
Wire  ropes,  237-261 

bending  stress,  251 

cables  for  bridges,  248 

cableways,  242,  258 

calculations,  251 

care  of,  255 

cast-steel,   for   inclines,  life  of, 
254,  255 

construction,  238 

derrick  ropes,  243 

drums  and  fastenings,  244 

effect  of  sheaves  on  life,  254 

flat  ropes,  241 

flattened     strand    ropes,     240, 
242 

glossary  of  rope  terms,  262 

haulage  ropes,  241 

hawsers,  243,  250 

hoisting  ropes,  239 

horsepower      transmitted      by 
steel  rope,  268 

inspection  of,  257 

iron     hoisting     ropes,   life     of, 
255 

lay  of  ropes,  238 

life  pf,  for  hoisting,  254,  255 

lubrication  of,  257 

materials,  237 

mooring  lines,  250 

non-spinning,  240 

power   transmission   by,    264 

proper  working  load,  253 

round,  239 


Wire  ropes,  running  rope,  250 
scale  ropes,  240,  242,  244 
sizes  and  strength,  tables,  245 

-250 

sockets,  244 
splicing,  255,  256 
starting  stress,  253,  254 
stress  on  planes,  254 
suspension  bridges,  243,  248 
tables  of  sizes,  strengths,  etc. 

245-250 
taper  ropes,  241 
tiller  rope,  244 
tramway  cables,  249 
tramways,  260 
wear  of,  257 
working  load,  251 
See  also  Power  Transmission. 

Wolf  lamp,  876,  878,  880,  888 

Wood,  as  fuel,  365  , 

Australian,  weight,  281 
changed  to  anthracite,  368 
coal  equivalents  by  weight,  366 
composition  and  calorific  value, 

366 

crushing  loads,  185 
Indian,  weight,  282 
Philippine,  weight,  281 
screws,  diameters,  298 
specific  gravity,  278 
strength  of,  171,  184 
timbers,  American,  weight,  283 
weight  of  dry,  279 
weights  by  fuel  values,  366 

Wooden  pipe,  306,  307 

Woodworth,  R.  B.,  731 

Work,  definition,  153 

Working  a  mine,  methods,  604-666 
stress,  172 

Wrought  iron,  weight,  293,  298,  301 

Zero,  absolute,  353 

Zinc,  strength  of,  170 
Zones,  spherical,  52 


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LINK-BELT 

MACHINERY 

for  the  handling  and  preparation  of  coal  at  the  mine  includes: 


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Multi-Blade  Mine 
Ventilating  Fans 

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the  Products   of   Over  A 

Century's  Experience 

I^OR  COAL  MINING  in  gaseous  and  dusty 
mines,  our  "permissibles"  are  extensively 
used  to  the  entire  satisfaction  of  miners  and 
operators. 

MONOBEL  and  CARBONITE 

are  our  "permissibles"  and  are  subjected  to  the  severest 
tests  in  our  own  galleries  before  submission  to  the  Bureau 
of  Mines  for  approval.  We  make  twelve  kinds  —  a  wide 
range  which  assures  the  selection  of  a  "permissible"  ex- 
actly suited  to  local  mine  conditions.  FREE  booklet 
"PERMISSIBLE  EXPLOSIVES"  gives  a  complete  de- 
scription of  these  "safety-first"  blasting  agencies. 

BLASTING  POWDERS 

we  make  contain  the  best  of  materials  thoroughly  in- 
corporated, and  made  into  seven  standard  granulations 
to  meet  all  the  requirements  of  blasting  coal  and  ore. 

FOR  ORE  MINING 

in  the  open  or  in  mines,  we  have  an  assortment  of 
Gelatins,  Extra  and  Straight  Dynamites  scientifically  and 
expressly  made  for  blasting  ore  in  the  most  practical, 
expeditious  and  economical  manner. 

Descriptive  Booklets  iiving  detailed  information  about  DU  PONT  EXPLOSIVES 
and  practical  instruction  to  prospective  users  will  be  sent  free  to  applicants. 

E.  I.  DU  POINT  DE  NEMOURS  &  CO. 

POWDER  MAKERS  SINCE  1802 

WILMINGTON,  DELAWARE 


THE  BUYERS'  MANUAL 


B<SjfP|J)    C 
LASTING  SUPPLIEU 


Ensure  Maximum.  Efficiency 
of  Explosives 

THE    complete  detonation  of   explosives   is 
largely  dependent  on  the  efficiency  of  the 
detonators  employed. 

DU  PONT  DETONATORS 

Whether  the  charges  are  exploded  by  electric  blasting 
caps  or  with  blasting  caps  and  fuse,  use  a  detonator  of 
Du  Pont  manufacture. 

Years  of  field  experience  enable  us  to  produce  detonators 
capable  of  delivering  the  necessary  shock  to  ensure  com- 
plete detonation  and  consequent  efficiency  of  explosives. 

DU  PONT  BLASTING  MACHINES 

for  the  generation  of  electricity  for  firing  electric  blasting 
caps  are  practical  in  design,  compact  in  form  and  posi- 
tive in  action. 

GALVANOMETERS  and  RHEOSTATS 

are  blasting  machine  accessories  for  determining  the  con- 
dition of  the  blasting  circuit  and  the  assurance  that  the 
blasting  machine  is  up  to  its  capacity. 

OTHER  BLASTING  SUPPLIES 

consisting  of  connecting  and  leading  wire,  thawing  ket- 
tles, cap  crimpers,  blasting  mats,  tamping  bags  and  fuse 
can  be  used  with  the  same  assurance  of  entire  satisfaction. 

Get  the  maximum  efficiency  out  of  your  explosives  by  detonating  them  with  the 
requisite  Du  Pont  BLASTING  SUPPLIES. 

E.  I.  DU  PONT  DE  NEMOURS  &  CO. 

POWDER  MAKERS  SINCE  1802 

WILMINGTON,  DELAWARE 


THE  BUYERS'  MANUAL 


WHY  YOU  SHOULD  USE 

Williams  Crushers  is,  first  because  they  are 
of  proven  merit,  they  are  adaptable  to  all 
kinds  of  crushing,  coarse  or  fine,  for  stoker 
or  chain  grate  coal,  for  bee-hive  or  by-product 
oven  coal,  for  low-grade  ore,  or  for  grinding 
coal  for  burning  in  suspension.  They  are 
adjustable  for  any  size  crushing  desired,  and 
are  made  in  capacities  to  suit  any  and  all 
requirements. 

WILLIAMS 
COAL  CRUSHERS 

will  solve  your  crushing  problems ;  space  will 
not  permit  us  to  enumerate  here  their  nu- 
merous superior  features.  To  get  full  details 
write  for  catalog  No.  75. 


THE  WILLIAMS  PATENT 
CRUSHER  AND  PULVERIZER  CO. 

Works:  Gen.  Sales  Dept. 

ST.  LOUIS,  MO.        Old  Colony  Bldg.,  CHICAGO,  ILL. 


THE  BUYERS'  MANUAL 


PHILLIPS 

MINE  CAR  TRUCKS 

Excel  in  Efficiency 


Either  oil  or  semi-fluid  grease  can  be  used  as 
a  lubricant  in  the  Phillips  Open-Cap  Wheel. 
With  the  latter,  as  high  as  27  months' 
service  has  been  had  from  .one  lubrication. 
The  wheels  and  boxes  do  not  wear  large  in 
the  bore,  and  equipment  which  has  been  in 
service  for  over  8  years  shows  no  perceptible 
wear  internally.  Boxes  cannot  shift  or  axles 
get  out  of  alignment,  and  the  wheels  are  true 
to  gauge  at  all  times.  Many  concerns  use 
this  Truck  exclusively  on  account  of  its 
easy-running  qualities,  and  the  economies  it 
effects  in  repair  bills  and  lubricant. 

For  guarantee   and  further  information  write 

PHILLIPS  MINE  &  MILL  SUPPLY  CO. 

BUILDERS  OF  MINE  CARS  AND  TRUCKS- 
MINE  CAR  WHEELS— SCREENING  EQUIP- 
MENTS—PHILLIPS AUTOMATIC  CAR  DUMPS 

PITTSBURGH,  PA.  U.  S.  A. 


10 


THE  BUYERS'  MANUAL 


There  are  150  grades  and  kinds  of 
Atlas  Blasting  Explosives,  each  differ- 
ing in  some  important  property  from 
the  other.  Our  catalogue  describes 
them  in  a  general  way  but  if  you  want 
to  know  which  one  has  those  proper- 
ties that  make  it  the  most  efficient  and 
economical  for  your  work,  write  our 
blasting  department. 

ATLAS  POWDER  CO. 

WILMINGTON,  DEL. 


Catalog  on  Request 

WILLIAMSPORT  WIRE  ROPE  CO. 
Williamsport,  Pa. 


THE  BUYERS'  MANUAL 


11 


GOODMAN 

Coal  Mining 
Machines 


MANY 
TYPES 


Breast  Machines,       Straightface  Machines 

Shortwall  Machines,      Longwall  Machines 

Direct  or  Alternating   Current,    Compressed  Air 

Electric  Mine  Locomotives 


All   Sizes 

GATHERING  AND  MAIN  HAULAGE 

SINGLE-MOTOR  AND   TWO-MOTOR   TYPES 

TROLLEY  AND  STORAGE  BATTERY 

A   Locomotive  for  Every  Mine  Service 

Write  for  Descriptive  Bulletins 

GOODMAN  MANUFACTURING  CO. 


NEW  YORK 
PITTSBURGH 
CINCINNATI 
CHARLESTON,  W.  VA. 


CHICAGO 

ILLINOIS 


BIRMINGHAM 
ST.  LOUIS 
DENVER 
SEATTLE 


12  THE  BUYERS'  MANUAL 


Wyoming  Automatic  Eliminator 

To  keep  steam  dry  even  under 
the  most  unusual  conditions — 
that's  the  work  the  W  y  o  m  i  n  g 
Eliminator  does.  It  is 

"The  Watch  Dog  of  the  Steam" 

Four  baffle  plates  keep  the  steam 
dry.     No  chance  for  moisture  to  get 
back  into   steam;   vertical  corruga- 
tions prevent  moisture  from  being 
brushed  off  the  plates. 
This  is  one  reason  why  73  per  cent  of  the 
largest     coal    companies     use     Wyoming 
Eliminators. 

Ask  for  full  information 
Also  get  our  quotations  on 

Steam  Traps;  Boiler  Gauge  Cocks; 
Cylinder  Drip  Cocks;  Brake  Valves 
and  Gauge  Cocks  for  Mine  Locomo- 
tives; Shaft  Couplings  for  Breaker 
Shafts. 

W.  H.  Nicholson  &  Co. 

Wilkes-Barre,  Pa. 


SPECIAL 
MINING  MACHINERY 

We  have  the  very  latest  word  in 

Conveyor  and  Elevator  Chains,  Car  Hauls 
Par  risk  Flexible  Arm  Shaking  Screens 
Simplex  Jigs,  Vigilant  Jig  Plungers 
Lloyd  Compound  Gear  Driven  Rolls 
Hollow  Ground  Roll  Teeth 

Consult  us  before  closing  your  designs  and  specifications  for  ma- 
chinery to  be  used  in  the  mining  and  preparation  of  coal. 

WILMOT  ENGINEERING  CO. 

HAZLETON,  PA.  Works— WHITE  HAVEN,  PA. 


THE  BUYERS'  MANUAL  13 

"Hendrick" 

Perforated  Screens 

for  all  purposes — Special  Improved  Types 

FOR 

CLEANING 

COAL 
AND  COKE 


Our  Patent  Flanged 
Lip  Screen. 

This  screen  does  the  final 
cleaning  of  coal  and  coke 
at  the  loading  pockets  and 
on  shaking  screens.  It  does 
the  work. 

Write  for  Bulletin 
No.  27 


"HENDRICK" 
Manganese   Bronze   Screens 

have  been  resisting  the  action  of  sulphurous 
mine  waters  for  over  25  years 

ELEVATOR  BUCKETS,  FLIGHTS  AND  TROUGH 
GENERAL  SHEET  AND  PLATE  WORK 

Ask  for  Catalogue 

HENDRICK  MANUFACTURING  CO. 

CARBONDALE,  PA. 


14  THE  BUYERS'  MANUAL 


GENUINE 
ARMSTRONG  STOCKS  &  DIES 

FOR  THREADING  PIPE  OR  BOLTS 
MALLEABLE  IRON  HINGED  PIPE  VISES 

PIPE  CUTTERS 
PIPE  THREADING  MACHINES 

MANUFACTURED  BY 

THE  ARMSTRONG  M'FG.  CO. 

336  KNOWLTON  ST.,  BRIDGEPORT,  CONN. 

NEW  YORK— 248  Canal  Street 


WATER  SOFTENERS 
FILTERS,  PURIFIERS 

FOR 

Prevention  of  Scale  Deposits,  Mud  or 
Corrosion  in  Boilers,  Tubes  or  Pipes 
and  for  the  Purification  and  Filtration 
of  Water  Supplies  for  any  Purpose, 
Designed  and  Installed  Anywhere  by 

AMERICAN  WATER  SOFTENER  CO. 

1011  Chestnut  Street  PHILADELPHIA 


THE  BUYERS'  MANUAL  15 

HOCKENSMITH 
WHEEL  &  MINE  CAR  CO. 

(Pittsburg  District.)  Penns  Station,  Pa. 

MANUFACTURERS  OF 

Chilled  Annealed]  Self-Oiling 

Mine  Car   Wheels)    Roller  Bearing 

ANGLE  BAR  TRUCKS 

The  Truck  for  Severe  Service 

MINE  CARS 

Steel — Composite — Wood 

Awarded    Gold   Medal   Panama-Pacific  Exposition  for 
Mine  Cars,   Wheels  and  Oiling  System. 

Cast  Iron  Pipe — Frogs 

Turnouts — Mine  Car  Hitchings 
Motor  Wheels 

Our  Engineering  Department  is  prepared  to 
co-operate  with  you  in  the  design  of  any  equip- 
ment manufactured  by  us. 

Catalogue  upon  request 


16 


THE  BUYERS'  MANUAL 


The  Practical — 
the  Mechanical — 
Side  of  Coal  Mining 

The  Library  of  Coal  Mining  and  Engineering  is  gradually 
and  surely  establishing  itself  as  the  one  library  on  the  sub- 
ject which  fills  the  needs  of  that  great  body  of  men,  the  men 
who  are  perfecting  their  knowledge  of  the  practical  side  of 
coal  mining,  as  a  means  of  climbing  to  the  higher  positions 
in  the  industry. 

It  is  gradually  and  surely  establishing  a  precedent  in  self- 
help  mining  literature,  covering  as  it  does  the  entire  opera- 
tion, from  surveying,  shaft  and  drift  opening,  mechanical 
equipment  and  operation,  to  the  chemical  analysis  of  the 
output. 

Price  $16,  payable  $2  per  month.  Write  for  free 
examination. 

McGraw-Hill  Book  Co.,   Inc.,  239   West  39th   Street,   New  York 


THE  BUYERS'  MANUAL  17 

Copper  and  Iron 

Wire 

Exploders 

And 

Blasting   Supplies 


Star  Electric  Fuze  Works 

WILKES-BARRE  PENNA. 

New  Books  on  Coal  and  Coke 
Wagner — Coal  and  Coke 

By  FREDERICK  H.  WAGNER,  Member  American  Gas 
Institute;  Franklin  Institute.  431  pages,  6x9, 
137  illustrations,  $4.00  (173)  net,  postpaid. 

A  complete  treatise,  prepared  to  give  the  student  of  coal  gas  produc- 
tion data  in  concise  form  covering  the  various  systems  of  coal 
carbonization. 

Wagner — Coal  Gas  Residuals 

By   FREDERICK  H.  WAGNER.     176    pages,    6x9, 

illustrated,  $2.00  (8/4)  net,  postpaid. 

A  complete  treatise  giving  the  modern  methods  of  securing  the  resid- 
uals pertaining  to  the  carbonization  of  coal. 

Somermeier — Coal 

Its  Composition,  Analysis,  Utilization  and  Valuation. 
By  E.  E.  SOMERMEIER,  Professor  of  Metallurgy, 
Ohio  State  University.     175    pages,  6  x  9,  illus- 
trated, $2.00  (8/4)  net,  postpaid. 

Designed  to  increase  the  knowledge  of  the  properties  and  utilization 
of  coal. 

McGraw-Hill  Book  Company,  Inc. 
239  West  39th  Street  NEW  YORK 


18  THE  BUYERS'  MANUAL 

VULCAN    SAFETY 

QUALITY  FIRST 


FLEXIBILITY 
OF   CONTROL 

is  one  of  the  biggest  reasons  for  the  continued 
popularity  of  the  large  Vulcan  steam  hoisting 
engine.  The  thousands  of  mine  cars  that  are 
moved  at  high  speeds,  without  accident  each 
year,  are  proof  that  the  many  installations  of 

VULCAN 

HOISTING  ENGINES 

have  that  flexibility  of  control,  together  with 
the  proper  design  and  materials,  that  insure  a 
safe  and  economical  investment.  Write  now 
for  full  information  and  photos  of  big  and 
little  Vulcans  in  service. 


VULCAN  IRON  WORKS 

WILKES-BARRE      ::      PENNSYLVANIA 

NEW  YORK  CHICAGO 

30  Church  Street  913  McCormick  Building 


HIGH 
OUTPUT  EFFICIENCY 

is  one  of  the  strong  points  of  most  electrically- 
driven  machinery,  and  this  is  due  partly  to 
transmission  without  heavy  power  loss,  eco- 
nomical use  of  power,  and  concentrative 
designs  that  mean  low  maintenance. 

VULCAN 
ELECTRIC  HOISTS 

are  showing  high  output  efficiency  throughout 
the  mining  regions,  and  have  an  enviable 
record  for  continued  safe  and  efficient  opera- 
tion. Write  for  the  names  of  electric  hoist 
users  and  the  wide  range  of  types  and  sizes. 


VULCAN  IRON  WORKS 

WILKES-BARRE      ::      PENNSYLVANIA 

NEW  YORK  CHICAGO 

30  Church  Street  913  McCormick  Building 


20 


THE  BUYERS'  MANUAL 


PENNSYLVANIA  CRUSHER  CO. 

Stephen  Oirard  BW'g.,         PHILADELPHIA,  PA. 

NEW  YORK  PITTSBURGH 

50  Church  Street  Peoples  Bank  Bld'g. 

COAL  CRUSHING  &  CLEANING  MACHINERY  FOR  BY- 
PRODUCT COKE  PLANTS,  SWINGHAMMER  CRUSH- 
ERS, BRADFORD  COAL  CLEANERS,  SINGLE  ROLL 
CRUSHERS,  DELAMATER  "SINK  &  FLOAT"  TESTERS. 

"PENNSYLVANIA"  SWING-HAMMER  CRUSHERS 

Extensively  used  for  pulverizing  Bituminous  Coals  in  By- 
Product  and  Bee-Hive  Coking  Plants,  for  crushing  Cement 

Rock  and  Lime- 
stones in  Cement 
Mills,  for  Lime, 
Shales,  Bone  and  a 
multitude  of  other 
materials. 

Main  frame  fabri- 
cated Steel  practically 
immunefrom  breakage. 
Removable  Steel  Wear 
Liners,  Ball  &  Socket 
Bearings,  6,  8  and  10 
rows  of  Hammers,  large 
diameter  Steel  Discs, 
(Patented)  quick  adjustable  Grind- 

ing Cage.    Built  in  Capacities  3  tons  to  400  tons  hourly.     By  weight 
the  "Pennsylvania"  is  more  than  90  %  Steel. 

"PENNSYLVANIA"  BRADFORD  COAL  CLEANERS 
For  Power  Houses,  By-Product  Coke  Plants,  etc. 

In  addition  to  its  advantages  as  a  Crusher,  this  machine  has  the  re- 
markable ability  to  automatically  remove  impurities,  slate,  bone,  sul- 
phur balls  or  binder  from 
bituminous  steam  and  cok- 
ing coals,  thereby  reducing 
the  objectionable  ash  and 
sulphur. 

Used  extensively  in  pre- 


paring R.O.M.  coals  in  By- 
Prod 


uct  Coking  plants  and 
for  Bee-  Hive  Ovens. 

In  connection  with  its 
crushing  and  cleaning  func- 
tions for  R.O.M.  coal  for 
large  Power  Houses,  the 
"Pennsylvania"  Bradford 
is  most  efficient  in  remov- 
ing stray  iron,  coupling 
pins,  mine  props  and  all 
sorts  of  impedimenta  that 
damage  Conveyors,  Stokers  and  other  Power  House  machinery. 

For  Stoker  feed  it  Crushes  R.O.M.  with  I  ess  fines  than  Rolls. 

Absolutely  automatic  in  operation,  low  horse  power,  runs  12  to  15 
R.P.M.,  requires  no  labor  to  operate  other  than  occasional  oiling. 
Practically  "fool-proof." 

Several  "Pennsylvania"  Bradfords  are  successfully  operating  in 
Coal  Washers. 


(Patented) 


MINERAL  TESHNDLOGY  LIBRARY 

UNIVERSITY  OF  CALIFORNIA 
BERKELEY 

Return  to  desk  from  which  bor 
This  book  is  DUE  on  the  last  date  sta 


NOV  2  7 1950 


LD  21-100m-9,'48(B399sl6)476 


394012 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


